There is a posting on this blog titled "The Westbound Rule". This is an effort to make routine flight more efficient by parceling air corridors to take advantage of the earth's eastward rotation. I explained how it would be best if eastbound flights flew as low as is practical, because the earth's rotation is working with them, while westbound flights should fly as high as possible, to keep a distance from the rotation that is working against them.
Today, I would like to apply a similar concept to space flight between the earth and the moon.
The astronauts of the Apollo missions of around forty years ago obviously wanted to land on the moon where the sun was shining, not in the dark. The daylight on the moon made the mission much easier, particularly the taking of photographs, than it would been in the dark. But it is my observation that this may not be the best in the long run if lunar flight ever becomes routine.
Another factor in the lunar missions involved launches. The take-offs of the rockets during the afternoon was to accommodate the audiences and so that daylight would minimize the chances of errors and complications. But this meant that the spacecraft was launched eastward, along with the direction of the earth's rotation, and thus had to outpace the earth.
While this may have been good for public relations, it certainly was not the most efficient path.
Picture the moon orbiting the earth, as the earth orbits the sun. Of course, this is only an "apparent" orbit, as I described in the posting "The Earth, The Moon And, The Sun", simply because, at the moon, the gravity of the sun is more than twice as powerful as that of the earth. However, that is not very important for our purposes here.
Let's review the mechanics of the moon, as seen from our perspective on earth.
The moon orbits the earth every 29 days, in the same eastward direction that the earth rotates. This is why the moon rises 50 minutes later each day or night. 24 hours divided by 29 equals about 50 minutes. The same side of the moon always faces earth because the moon's rotation period, or day, is the same as it's orbital period.
The phases of the moon that we see are due to the changing angles between the earth, moon and, sun. Full moon is when the moon is on the opposite side of the sun from the earth, so that those on the night side of the earth see the moon fully illuminated by the sun. Unless, of course, there is a lunar eclipse. This happens when earth, moon and, sun are in the same lateral plane in a straight line so that the earth casts it's shadow on the moon.
New moon is when the moon is between the earth and the sun so that we cannot see the moon at all. A solar eclipse can happen at this point, if all three are in the same plane and in a straight line. Eclipses do not occur every month because there is a difference of about 5 degrees between the moon's path around the earth and the earth's orbit around the sun.
We see a half moon when the moon crosses the earth's path around the sun. A half moon when the moon's phase is waning, or getting less, between full and new moon, is when the moon crosses the earth's orbit in the direction from which the earth has already passed. A half moon when the phase is waxing, or increasing, is when the moon crosses the earth's path in the direction in which the earth is heading.
At sunrise, the direction overhead is the direction from which the earth has come in it's orbit around the sun. At sunset, the direction overhead is the direction in which the earth is heading. This means that a waxing half moon will be overhead at sunset, and a waning half moon will be overhead at sunrise, taking the observer's latitude into account.
Let's express the path of the moon around the earth, relative to the sun, in degrees and quadrants. Let 0 degrees be the new moon, 90 be waxing half moon, which is also called "first quarter". Let 180 be the full moon and 270 be the waning half moon, also known as "last quarter". This fits in with the posting on this blog, "New Trigonometric Functions", in which I proposed a function based on 180 degrees, "The Lunar Function", in addition to the standard 90 degree functions.
Here is a link to a diagram of the moon's phases: www.moonconnection.com/moon_phases.phtml
There are three gravitational zones that we will deal with in a trip between the earth and the moon. Simply that where the earth's gravity is the strongest influence on the spacecraft, that of the moon and, that of the sun. At the moon, the sun's gravity is more than twice as powerful as that of the earth so that the majority of the trip will be spent in the sun's gravitational zone.
The concept that I want to discuss today is my vision of optimum points of departure and return on opposite sides of the moon's path around the earth, about two weeks apart. The great advantage of this is that most of the flight will be simply letting gravity do the work for us. The spacecraft can be made to literally "fall" toward it's destination. First, to the moon, and then the return flight to the earth.
When a spacecraft is on the way to a destination toward the sun, such as Mercury or Venus, the sun's gravity can be put to work. At launch, the spacecraft is essentially a part of the earth orbiting the sun. If we point the engines of the spacecraft in the direction of the earth's orbital path, it will counteract the orbital momentum around the sun that the spacecraft has. This will cause it to lose orbital momentum and literally fall toward the sun, and it's destination.
My thought is that a launch early in the morning, some time after third quarter (waning half moon), would definitely bring about the best flight efficiency. Once the spacecraft left the earth's gravitational zone, the gravity of both the sun and the moon would be working for us, as well as the earth's rotational momentum. Assuming that the flight takes a few days, this would land the spacecraft on the moon with the new moon approaching, in which the side facing the earth is in the dark. Once we are more experienced at lunar landings, this should not be as much of a problem as it would have been in the days of the Apollo landings.
A first quadrant launch, between new moon and first quarter, is also a possibility. But this will make it necessary to speed up the spacecraft, to get ahead of earth in it's orbit around the sun. This would be less efficient than simply losing orbital momentum so that the spacecraft literally falls toward it's target.
I see the return flight back to earth as being best as we approach full moon, after first quarter. the gravity of both the earth and the sun would be working for us. Whereas if we went to the moon near full moon, this most powerful gravitational combination would be working against us. The return trip should be easier, simply because the gravity of the earth is much more powerful than that of the moon.
So, if we approach the moon between last quarter and new moon, and return between first quarter and full moon, all we need to do is to lose orbital momentum by pointing the rocket engines in the direction of the earth's orbit around the sun so that the rocket thrust counteracts this orbital momentum, and we will literally fall along either journey. Gravity will do most of the work for us. We must always consider the tremendous gravity of the sun so that we aim to hit the moon while it is toward the sun, and return to earth when it is toward the sun, relative to the moon.
There is another thing to consider for lunar flights. The Apollo lunar missions from Cape Canaveral in Florida first went into an equatorial orbit around the earth and then, upon arrival, and equatorial orbit around the moon. The landing sites were thus relatively close to the moon's equator.
Another possibility is using polar orbits. This would be more complex, in that we would have to calculate the trajectory in another dimension also, that of north-south. The moon would be approached so that the spacecraft would be to the north or south of the plane of the moon's path around the earth, and it would go into orbit over the moon's north and south poles rather than around it's equator. To accomplish this, we could make use of the 5 degree difference between the planes of the earth's orbit around the sun and the moon's path around the earth.
There are disadvantages to the polar orbit route. There is no rotational momentum to build on during launches, and the mission is simpler if all is kept in the same plane. But a polar approach would make it much easier to land on any specific site, both on the moon and the return to earth, instead of just in the zones around the equators.
One more thing to remember during spaceflights like these. The posting "The Effective Center Of Gravity" on my physics and astronomy blog, http://www.markmeekphysics.blogspot.com/ , explains why the commonly-held belief that the center of mass and the center of gravity for a moon or planet is the same thing, must be incorrect.
In that posting, I explained that while the center of mass will be constant, the effective center of gravity will vary with our distance from the moon or planet. The two will be the same only if we are an infinite distance from the moon or planet. This is because the near side of the planet is closer to us so that it must have a greater gravitational influence on us than the far side. The closer we are to the moon or planet, the closer is it's center of gravity to us and the more difference between the center of mass and the center of gravity.
Saturday, March 17, 2012
The Greatest Waste Of Fuel And Energy
It is well-known how inefficient car engines really are. What this means is that, no matter how well an engine is designed, most of the energy in the fuel that is released by combustion in the cylinders goes to produce heat, instead of useful mechanical energy. This is why an engine requires a cooling system. The engine would not take long to self-destruct if the excess heat could not be absorbed by liquid coolant and dissipated through the radiator.
What this means is that whenever you stop to put that expensive fuel into your tank, the majority of the energy in that fuel, which will be released in the engine, will not go into getting you to your destination. Rather, it will go toward heating up the coolant in your engine so that the heat can be dissipated by the radiator.
To be sure, this engine heat is not all wasted. Engine heat is useful in that it reduces the viscosity of the oil, enabling it to flow more readily to lubricate the engine parts. This is why the worst wear and tear on the engine occurs when it is started, before the oil has begun to flow. This also explains why an engine will wear faster in a cold climate.
Engine heat also warms the incoming air from the air filter, so that it can hold more vaporized (vapourised) fuel on it's way into the cylinders for combustion. Does anyone remember older cars, in which a choke would be closed upon starting to block incoming air so that the fuel-air mixture would not be too lean? The choke would then be opened after the engine had gained some warmth.
Finally, of course, the engine heat warms the passengers in cold weather when the antifreeze/coolant is circulated through small radiators in the passenger compartment. Readers in colder climates may have noticed that there are trucks in the winter with cardboard placed over the radiator grill to conserve heat in the engine.
Nevertheless, the fact is that most of the energy in the fuel that is released by combustion in your engine goes to produce heat, and most of that heat is wasted by dissipation through the radiator. What would it be like if we could only save or make use of this tremendous amount of wasted energy?
When combustion takes place in a cylinder of the engine, we want the combustion to be as rapid as possible. The quicker the combustion, the more mechanical energy is produce by the force of the rapidly expanding exhaust gases against the piston, as opposed to heat. The slower the combustion, the more energy is ends up as heat instead of useful mechanical energy.
Efforts have been made to speed combustion by using dual spark plugs in the cylinder, or by using small lasers to initiate combustion instead of spark plugs. But no matter how quickly combustion can be made to take place, or how efficient the engine can otherwise be made, most of the energy in fuel ends up as heat, and not as useful mechanical energy. The noise that is produced by an engine also requires energy, and is another route of waste.
This waste heat cannot be converted into mechanical energy, as it stands now. Saving heat wouldn't do any good either, if we insulated the engine to hold in heat it would only run hotter and not more efficiently.
But what if we could develop a small and efficient boiler, and replace the radiator with it? A boiler can generate electricity by using steam to move a piston. When boiling water under pressure is suddenly given the chance to expand, it will vaporize (vapourise) into steam which will exert great pressure on the piston, which would then move to create relative motion between a magnet and a coil of wire. We would logically use water, instead of the usual engine coolant, because the coolant raises the boiling point of water so that more energy would be required to make the steam. The energy which would otherwise be lost as heat from the engine could then be recouped as electricity.
The trouble is that small boilers are inefficient. The reason for this is that surface area is two-dimensional, while volume is three-dimensional. So as the size of something is reduced, the volume decreases faster than the surface area. It is from the surface area of a boiler that heat leaks away as waste. So, a smaller boiler will lose a greater proportion of heat, because it has a greater surface area relative to volume, and will thus be less efficient than a larger boiler. If you have ever seen a demonstration of a steam locomotive, it is easy to feel how much heat it throws off. This heat is, of course, waste.
However one crucial difference between a boiler and an internal combustion engine, with regard to efficiency, is that holding in heat by insulation will improve the efficiency of a boiler, while it would only make the engine run hotter.
Suppose that a car had a small, but efficient, insulated boiler which would use the waste heat from the engine to produce electricity. This boiler would not need to be any larger than the radiator is, which the boiler would replace. The electricity produced by this boiler would charge batteries, until there was enough electricity stored in these batteries to run the car on an electric motor, or four small electric motors, one at each wheel.
Think of pre-nuclear submarines. There used to be both a diesel and an electric motor on these boats. The sub would run on the diesel motor while on the surface. All the while, this motor would be re-charging the ship's batteries. Then, while the sub was submerged, it would run on the electric motor, drawing it's energy from the charged batteries. The electric motor, unlike the diesel motor, can operate underwater because it has no need of air.
Just think of the fantastic amount of energy that this would save. I think that this is a whole new avenue in the search for energy, and the effort to lessen global warming. In fact, I am sure that is is possible to design a dual engine which could operate either as an internal combustion engine or as an electric motor, so that the car would not require a separate electric motor. The car could automatically switch between electric and combustion modes according to the amount of electricity stored in the batteries.
Cars originated when fuel was cheap. Those days are long gone, but we are still using the same basic design of car. It's time for some new thinking.
What this means is that whenever you stop to put that expensive fuel into your tank, the majority of the energy in that fuel, which will be released in the engine, will not go into getting you to your destination. Rather, it will go toward heating up the coolant in your engine so that the heat can be dissipated by the radiator.
To be sure, this engine heat is not all wasted. Engine heat is useful in that it reduces the viscosity of the oil, enabling it to flow more readily to lubricate the engine parts. This is why the worst wear and tear on the engine occurs when it is started, before the oil has begun to flow. This also explains why an engine will wear faster in a cold climate.
Engine heat also warms the incoming air from the air filter, so that it can hold more vaporized (vapourised) fuel on it's way into the cylinders for combustion. Does anyone remember older cars, in which a choke would be closed upon starting to block incoming air so that the fuel-air mixture would not be too lean? The choke would then be opened after the engine had gained some warmth.
Finally, of course, the engine heat warms the passengers in cold weather when the antifreeze/coolant is circulated through small radiators in the passenger compartment. Readers in colder climates may have noticed that there are trucks in the winter with cardboard placed over the radiator grill to conserve heat in the engine.
Nevertheless, the fact is that most of the energy in the fuel that is released by combustion in your engine goes to produce heat, and most of that heat is wasted by dissipation through the radiator. What would it be like if we could only save or make use of this tremendous amount of wasted energy?
When combustion takes place in a cylinder of the engine, we want the combustion to be as rapid as possible. The quicker the combustion, the more mechanical energy is produce by the force of the rapidly expanding exhaust gases against the piston, as opposed to heat. The slower the combustion, the more energy is ends up as heat instead of useful mechanical energy.
Efforts have been made to speed combustion by using dual spark plugs in the cylinder, or by using small lasers to initiate combustion instead of spark plugs. But no matter how quickly combustion can be made to take place, or how efficient the engine can otherwise be made, most of the energy in fuel ends up as heat, and not as useful mechanical energy. The noise that is produced by an engine also requires energy, and is another route of waste.
This waste heat cannot be converted into mechanical energy, as it stands now. Saving heat wouldn't do any good either, if we insulated the engine to hold in heat it would only run hotter and not more efficiently.
But what if we could develop a small and efficient boiler, and replace the radiator with it? A boiler can generate electricity by using steam to move a piston. When boiling water under pressure is suddenly given the chance to expand, it will vaporize (vapourise) into steam which will exert great pressure on the piston, which would then move to create relative motion between a magnet and a coil of wire. We would logically use water, instead of the usual engine coolant, because the coolant raises the boiling point of water so that more energy would be required to make the steam. The energy which would otherwise be lost as heat from the engine could then be recouped as electricity.
The trouble is that small boilers are inefficient. The reason for this is that surface area is two-dimensional, while volume is three-dimensional. So as the size of something is reduced, the volume decreases faster than the surface area. It is from the surface area of a boiler that heat leaks away as waste. So, a smaller boiler will lose a greater proportion of heat, because it has a greater surface area relative to volume, and will thus be less efficient than a larger boiler. If you have ever seen a demonstration of a steam locomotive, it is easy to feel how much heat it throws off. This heat is, of course, waste.
However one crucial difference between a boiler and an internal combustion engine, with regard to efficiency, is that holding in heat by insulation will improve the efficiency of a boiler, while it would only make the engine run hotter.
Suppose that a car had a small, but efficient, insulated boiler which would use the waste heat from the engine to produce electricity. This boiler would not need to be any larger than the radiator is, which the boiler would replace. The electricity produced by this boiler would charge batteries, until there was enough electricity stored in these batteries to run the car on an electric motor, or four small electric motors, one at each wheel.
Think of pre-nuclear submarines. There used to be both a diesel and an electric motor on these boats. The sub would run on the diesel motor while on the surface. All the while, this motor would be re-charging the ship's batteries. Then, while the sub was submerged, it would run on the electric motor, drawing it's energy from the charged batteries. The electric motor, unlike the diesel motor, can operate underwater because it has no need of air.
Just think of the fantastic amount of energy that this would save. I think that this is a whole new avenue in the search for energy, and the effort to lessen global warming. In fact, I am sure that is is possible to design a dual engine which could operate either as an internal combustion engine or as an electric motor, so that the car would not require a separate electric motor. The car could automatically switch between electric and combustion modes according to the amount of electricity stored in the batteries.
Cars originated when fuel was cheap. Those days are long gone, but we are still using the same basic design of car. It's time for some new thinking.
Our Solar Future
Solar energy is already in widespread use across the world. Yet, we clearly have a very long way to go before it reaches anything like it's full potential. It seems to me that the state of solar energy today is very similar to that of electricity as a whole, back in the Nineteenth Century.
The first electric currents to be produced and controlled by people came from chemical reactions. A device made to produce electric current by chemistry is known as a battery. But batteries were only the beginning of electricity as we know and use it today. The vast majority of the electric current that we use is generated in some way. These generation methods can range from hydroelectric dams to use of steam produced by a boiler to turn a magnet relative to a coil of wire so that the magnetic lines of force will move electrons in the wire, resulting in an electric current.
Solar energy is used today to produce electricity primarily by solar cells. As the term implies, these cells are compact devices which take in energy from the sun and use it to produce an electric current.
Solar cells have proven to be extremely useful in a wide variety of applications, including spacecraft. But solar cells have a lot more in common with batteries than that they both give us electricity. Just as batteries were only the beginning of electricity as we use it today, solar cells are only the beginning of the "Solar Revolution".
As useful as batteries have always been, they are useful only for small-scale applications. They are wonderful for vehicles and portable devices of all kinds, but we cannot possibly power a city, or an entire country, with batteries. Batteries gave us the experience and understanding to handle electricity as required for the electrical grids across the world, but those grids were not possible until large-scale ways were developed to generate electricity.
I find that the same is true of solar cells. As useful as they are, they are necessarily only the beginning in the same way as batteries once were. A fortune in solar energy falls on the roof of any large building, even in the winter. Yet, solar cells are just too expensive to make to be a practical solution to harvesting this energy, except on a very limited scale. Just as the development of our modern electrical grids required methods of large-scale generation, the harvesting of solar energy will require large-scale methods which go far beyond solar cells.
Countries vary widely in their attitudes toward, and use of, nuclear power to generate electricity. But it is often said of nuclear power that no matter how much science there seems to be involved in it's use, all that nuclear power really comes down to is just another way to boil water. The steam from boiling water is used to provide mechanical energy which turns a magnet inside a coil of wire to generate electricity. It makes no difference whatsoever whether the heat to boil the water comes from a coal boiler or from a nuclear reaction.
So, if any method of making large quantities of water boil can be used to generate electricity, what about the sun? There are solar reflectors which concentrate the sun's energy to cook a meal, or to cut through a piece of steel, why can't we just concentrate the energy from the sun to boil water? We could then generate vast amounts of electric current.
Everyone has seen how the rays of the sun can be concentrated to a point by a magnifying glass. Why can't the roof of a generator building be constructed as a lens in the same way? The entire roof could be made of glass or plastic panels, assembled so that they focus the energy of the sun to a point inside the building. The roof would not necessarily have to be circular, it could be rectangular and focus the sun to a line, rather than a point.
The solar energy would be focused on a boiler, which would then produce electricity in the same way as a boiler heated in any other way. If any of the roof panels was knocked out of alignment by wind, for example, they could be recalibrated. There could be a reflector on the side of the roof opposite the sun, to bring in even more energy. Heat is of longer wavelength, and is less precise than light, so it would not be that important whether or not the energy was brought to a sharp focus. Of course, the solar roof would have to be kept clean and snow-free.
It is true that the larger such a generating plant was, the more efficient it would be. This is simply because large boilers are more efficient than small boilers. A boiler inevitably loses some waste heat through it's surface area, and the volume is three-dimensional while the surface area is only two-dimensional. This means that the volume changes faster than the surface area as the boiler changes in size, so that a larger boiler has less surface area per volume, through which to lose heat, than a smaller boiler.
There are certainly other possible variations on the plan of a solar generating station. Instead of a roof, acting as a lens, the boiler could be installed over a concave mirror which would focus the energy of the sun on it.
There could be smaller-scale generating facilities as "solar bubbles", with a boiler and generator inside.
Perhaps the easiest and most practical design of all for harvesting the abundant energy that comes from the sun is a long pipe, suspended above the ground, with a concave reflector underneath it's entire length. The sun would shine on the reflector, which would focus it on the pipe. The pipe would naturally be dark in color (colour) to absorb the maximum amount of solar energy. The pipe could be set up in either a straight line, or the more likely twists and turns. Cold water would go in one end of the pipe, and boiling water would emerge from the other end. The boiling water would then be used to generate electricity.
But whichever design is used, it seems very clear that while solar energy can provide us with all the energy we need, we are in the same place now with solar cells as we were with batteries in the early days of electricity. Some method of large-scale generation is the next step.
The first electric currents to be produced and controlled by people came from chemical reactions. A device made to produce electric current by chemistry is known as a battery. But batteries were only the beginning of electricity as we know and use it today. The vast majority of the electric current that we use is generated in some way. These generation methods can range from hydroelectric dams to use of steam produced by a boiler to turn a magnet relative to a coil of wire so that the magnetic lines of force will move electrons in the wire, resulting in an electric current.
Solar energy is used today to produce electricity primarily by solar cells. As the term implies, these cells are compact devices which take in energy from the sun and use it to produce an electric current.
Solar cells have proven to be extremely useful in a wide variety of applications, including spacecraft. But solar cells have a lot more in common with batteries than that they both give us electricity. Just as batteries were only the beginning of electricity as we use it today, solar cells are only the beginning of the "Solar Revolution".
As useful as batteries have always been, they are useful only for small-scale applications. They are wonderful for vehicles and portable devices of all kinds, but we cannot possibly power a city, or an entire country, with batteries. Batteries gave us the experience and understanding to handle electricity as required for the electrical grids across the world, but those grids were not possible until large-scale ways were developed to generate electricity.
I find that the same is true of solar cells. As useful as they are, they are necessarily only the beginning in the same way as batteries once were. A fortune in solar energy falls on the roof of any large building, even in the winter. Yet, solar cells are just too expensive to make to be a practical solution to harvesting this energy, except on a very limited scale. Just as the development of our modern electrical grids required methods of large-scale generation, the harvesting of solar energy will require large-scale methods which go far beyond solar cells.
Countries vary widely in their attitudes toward, and use of, nuclear power to generate electricity. But it is often said of nuclear power that no matter how much science there seems to be involved in it's use, all that nuclear power really comes down to is just another way to boil water. The steam from boiling water is used to provide mechanical energy which turns a magnet inside a coil of wire to generate electricity. It makes no difference whatsoever whether the heat to boil the water comes from a coal boiler or from a nuclear reaction.
So, if any method of making large quantities of water boil can be used to generate electricity, what about the sun? There are solar reflectors which concentrate the sun's energy to cook a meal, or to cut through a piece of steel, why can't we just concentrate the energy from the sun to boil water? We could then generate vast amounts of electric current.
Everyone has seen how the rays of the sun can be concentrated to a point by a magnifying glass. Why can't the roof of a generator building be constructed as a lens in the same way? The entire roof could be made of glass or plastic panels, assembled so that they focus the energy of the sun to a point inside the building. The roof would not necessarily have to be circular, it could be rectangular and focus the sun to a line, rather than a point.
The solar energy would be focused on a boiler, which would then produce electricity in the same way as a boiler heated in any other way. If any of the roof panels was knocked out of alignment by wind, for example, they could be recalibrated. There could be a reflector on the side of the roof opposite the sun, to bring in even more energy. Heat is of longer wavelength, and is less precise than light, so it would not be that important whether or not the energy was brought to a sharp focus. Of course, the solar roof would have to be kept clean and snow-free.
It is true that the larger such a generating plant was, the more efficient it would be. This is simply because large boilers are more efficient than small boilers. A boiler inevitably loses some waste heat through it's surface area, and the volume is three-dimensional while the surface area is only two-dimensional. This means that the volume changes faster than the surface area as the boiler changes in size, so that a larger boiler has less surface area per volume, through which to lose heat, than a smaller boiler.
There are certainly other possible variations on the plan of a solar generating station. Instead of a roof, acting as a lens, the boiler could be installed over a concave mirror which would focus the energy of the sun on it.
There could be smaller-scale generating facilities as "solar bubbles", with a boiler and generator inside.
Perhaps the easiest and most practical design of all for harvesting the abundant energy that comes from the sun is a long pipe, suspended above the ground, with a concave reflector underneath it's entire length. The sun would shine on the reflector, which would focus it on the pipe. The pipe would naturally be dark in color (colour) to absorb the maximum amount of solar energy. The pipe could be set up in either a straight line, or the more likely twists and turns. Cold water would go in one end of the pipe, and boiling water would emerge from the other end. The boiling water would then be used to generate electricity.
But whichever design is used, it seems very clear that while solar energy can provide us with all the energy we need, we are in the same place now with solar cells as we were with batteries in the early days of electricity. Some method of large-scale generation is the next step.
The Australia Sequence
There is a posting on this blog titled "The Other Side Of Global Warming". The posting discussed a side of global warming that does not get anywhere near as much attention as the increasing amount of carbon in the air. The removal of hundreds of millions of trees to make way for development has reduced the carbon sink that trees provide. Not only are we putting more carbon in the air, we are removing the trees that would have absorbed carbon from the air during their growth.
One of the perils of even a slight overall warming of the earth is extremely powerful and destructive hurricanes, and other wild weather. Today, I would like to discuss yet another side of global weather that does not get much attention.
In the posting on the meteorology blog, "The Atlas Barrier", we saw why there is a gap in the coastal barrier islands of the eastern and southern U.S. in the states of South Carolina and Georgia. It is because dust from North Africa is essential to provide condensation nuclei upon which water can condense to form the vast amount of dense cloud necessary for hurricanes. As the dust is swept out over the ocean by the east wind, it allows evaporated water from below to condense upon it. I identified the absence of significant barrier islands in those states as being due to the blocking of the wind-borne dust by the Atlas Mountains of Morocco.
This goes to show the vital role of dust in forming hurricanes. Air with the ordinary low level of dust cannot hold the tremendous volume of water necessary for hurricanes. That posting describes a hurricane as a self-sustaining circular storm. Hurricanes, which also go by other names such as "cyclone" and "typhoon", move generally westward because their spin, which they pick up from the spin of the earth, makes them semi-independent of the earth's gravity so that the earth rotates eastward under the storm.
It seems to me that dust is a forgotten side of extreme global weather. It is well-known that global warming creates wilder weather by causing more water to evaporate, but the air could not hold the water for long without abundant dust particles to serve as cloud condensation nuclei. The phenomenon of desertification, the increase of desert area, is pointed to as reducing arable land, but it also means more potential dust in the air to seed hurricanes if the prevailing winds are right to take the dust out to sea.
The way I see it, ground zero for global climate with regard to dust and extreme weather begins in Australia. Never mind the cricket rivalry between Australia and India, those two lands are linked not only by geology, they were once part of the same land mass, but by climate. It is dust from Australia, swept out to sea, that seeds the Monsoons and cyclones that afflict India and it's neighboring countries, in the same way that dust from North Africa is the foundation for the hurricanes that cross the Atlantic Ocean. The typhoons of the South China Sea are also seeded by dust from Australia. The prevailing winds over Australia carry it's loose dust northward, toward the equator.
Here is a map link: http://www.maps.google.com/
Australia is a dry continent, that is getting even dryer. There are areas which used to be farmed productively, which now cannot be farmed at all. The Government of Australia, along with that of China, is a leader in searching for ways to produce rain. This can only mean more dust becoming available to be swept out to sea by the wind.
When there is more dust in the air, it does not mean that more water will evaporate from the sea below. There is essentially no more water in the air, the dust just makes it more concentrated. This means that when the tremendous volumes of rain fall on the Indian Subcontinent, the air emerges dry as the prevailing wind at that latitude moves from the east. So that when the air gets downwind to the Arabian Peninsula, there is little or no water to provide rain.
If there was rain on the Arabian Peninsula, it would be lush and green with vegetation. Much of the water would reevaporate, or be transpired by the plants, and travel further west on the east wind to fall on the Sahara Desert of North Africa. Then if this area was lush and green, it would not be the source of dust that it is to seed the hurricanes that cross the Atlantic Ocean.
Can you now see how Australia is ground zero for so much of the global climate? it is the beginning of what I have termed "The Australia Sequence". If only we could make Australia lush and green, or even pave it over into a vast parking lot, so that it would not serve as a reservoir of dust, it would completely change the world.
(I am just using the parking lot as an illustration, the last thing that I would want to do would be to pave over Australia and upset Australian readers).
There would not be the dust to seed typhoons in the South China Sea. India, and neighboring countries, would not get the cyclones and extremely heavy rain. There would be water in the air to be carried along the east wind to fall as rain in Saudi Arabia. When that water reevaporated, it would carry further along the east wind to North Africa. The Sahara would become green, and would no longer be a source of dust to seed hurricanes heading for the western hemisphere.
What a better world that would be! This would most likely bring a potential increase in the world's food supply of between a quarter and a third, due to the vast increase in arable land.
If only we could make Australia into a lush and green place, it would cease to be a source of dust. India would get much milder rains, and the water that was left would fall on the Arabian Peninsula. Much of that would re-evaporate, or be transpired by plants, and would travel further downwind to fall on North Africa. This would, in turn, make what is now the Sahara Desert into a green place with thriving plants, meaning that North Africa would no longer act as a vast supplier of dust over the ocean to seed the hurricanes that afflict North America and the Caribbean.
It is easy to see why the east coast of South America is free of hurricanes, much unlike North America. Africa south of the Sahara is a land of expansive jungle and grassland. It is not dusty, and so does not supply the dust that would seed hurricanes that would move westward to strike South America. If only we could get Australia covered with plants, we would set a very beneficial sequence in motion.
By the way, this new plant life covering Australia, Arabia and, North Africa would absorb much of the world's carbon in the air that is the cause of global warming. We would definitely be "killing two birds with one stone", and really bettering the world in the process.
The main reason that Australia is so dry is that the winds, which might bring rain, are blocked by the Great Dividing Range of mountains, along the east coast of Australia. However, in east-central Australia lies the Great Artesian Basin. This is a vast area of low-lying land, which is Australia's main source of fresh water from wells. Much of the basin is below sea level, my world atlas has the surface of Lake Eyre North as 16 meters below sea level.
What if a canal could be dug, which would flood part of the Great Artesian Basin with sea water? This would form a vast, shallow salt-water reservoir west of the coastal mountains. This water would quickly re-evaporate to be carried westward by the prevailing winds.
Hopefully, it would fall as rain on the vast arid west of Australia. Plants would grow, and farming would thrive. The deserts would become grasslands and the continent would cease to be a source of a significant amount of dust to the region's large-scale weather patterns.
The area is sparsely populated anyway. This salt-water reservoir, covering hundreds of square kilometers would provide beaches and sites for resorts. Although it would not have the waves required for the Australian pastime of surfing. As fish-farming is becoming so popular across much of the world, the reservoir could be stocked with fish.
The reservoir would be shallow, and if Australians ever changed their minds about the project all that would be necessary is to close the canal and the water would not take long to evaporate.
The only drawback of the reservoir is that it would salinate the fresh water within it's shores. But this would be more than compensated for by the fresh water falling westward as rain.
This concerns the proposed project of digging a canal in Australia to flood part of the Great Artesian Basin with sea water. This is my idea to bring rain to Australia by bringing a large surface area of water west of the Great Dividing Range of mountains, since it is these mountains which block the east wind which would otherwise bring rain to this very dry land. This water would evaporate and fall as rain on the vast expanse of western Australia.
I believe that it is an accident of geology which prevented Australia from being the lush and green land that it could have been. This project could really change the world. China and Australia are already tied together economically. Australia is a source of raw materials for China, as well as a destination for Chinese tourists. Many signs in Australia are in Chinese.
Why not work together on this Project? There is a serious water shortage in parts of China. This project would result in milder rains that would carry much further inland in China, instead of the destructive typhoons along the coast. The governments of both countries have put a lot of effort into trying to induce rain artificially, why not try this idea?
It would be ideal if we could set up a parallel project to bring water to North Africa, the world's other great source of dust, as well. But there is no comparable area below sea level there which could be flooded. There is the Qattara Depression in Egypt's Western Desert, but I do not think that flooding it would have much effect on the rainfall.
One of the perils of even a slight overall warming of the earth is extremely powerful and destructive hurricanes, and other wild weather. Today, I would like to discuss yet another side of global weather that does not get much attention.
In the posting on the meteorology blog, "The Atlas Barrier", we saw why there is a gap in the coastal barrier islands of the eastern and southern U.S. in the states of South Carolina and Georgia. It is because dust from North Africa is essential to provide condensation nuclei upon which water can condense to form the vast amount of dense cloud necessary for hurricanes. As the dust is swept out over the ocean by the east wind, it allows evaporated water from below to condense upon it. I identified the absence of significant barrier islands in those states as being due to the blocking of the wind-borne dust by the Atlas Mountains of Morocco.
This goes to show the vital role of dust in forming hurricanes. Air with the ordinary low level of dust cannot hold the tremendous volume of water necessary for hurricanes. That posting describes a hurricane as a self-sustaining circular storm. Hurricanes, which also go by other names such as "cyclone" and "typhoon", move generally westward because their spin, which they pick up from the spin of the earth, makes them semi-independent of the earth's gravity so that the earth rotates eastward under the storm.
It seems to me that dust is a forgotten side of extreme global weather. It is well-known that global warming creates wilder weather by causing more water to evaporate, but the air could not hold the water for long without abundant dust particles to serve as cloud condensation nuclei. The phenomenon of desertification, the increase of desert area, is pointed to as reducing arable land, but it also means more potential dust in the air to seed hurricanes if the prevailing winds are right to take the dust out to sea.
The way I see it, ground zero for global climate with regard to dust and extreme weather begins in Australia. Never mind the cricket rivalry between Australia and India, those two lands are linked not only by geology, they were once part of the same land mass, but by climate. It is dust from Australia, swept out to sea, that seeds the Monsoons and cyclones that afflict India and it's neighboring countries, in the same way that dust from North Africa is the foundation for the hurricanes that cross the Atlantic Ocean. The typhoons of the South China Sea are also seeded by dust from Australia. The prevailing winds over Australia carry it's loose dust northward, toward the equator.
Here is a map link: http://www.maps.google.com/
Australia is a dry continent, that is getting even dryer. There are areas which used to be farmed productively, which now cannot be farmed at all. The Government of Australia, along with that of China, is a leader in searching for ways to produce rain. This can only mean more dust becoming available to be swept out to sea by the wind.
When there is more dust in the air, it does not mean that more water will evaporate from the sea below. There is essentially no more water in the air, the dust just makes it more concentrated. This means that when the tremendous volumes of rain fall on the Indian Subcontinent, the air emerges dry as the prevailing wind at that latitude moves from the east. So that when the air gets downwind to the Arabian Peninsula, there is little or no water to provide rain.
If there was rain on the Arabian Peninsula, it would be lush and green with vegetation. Much of the water would reevaporate, or be transpired by the plants, and travel further west on the east wind to fall on the Sahara Desert of North Africa. Then if this area was lush and green, it would not be the source of dust that it is to seed the hurricanes that cross the Atlantic Ocean.
Can you now see how Australia is ground zero for so much of the global climate? it is the beginning of what I have termed "The Australia Sequence". If only we could make Australia lush and green, or even pave it over into a vast parking lot, so that it would not serve as a reservoir of dust, it would completely change the world.
(I am just using the parking lot as an illustration, the last thing that I would want to do would be to pave over Australia and upset Australian readers).
There would not be the dust to seed typhoons in the South China Sea. India, and neighboring countries, would not get the cyclones and extremely heavy rain. There would be water in the air to be carried along the east wind to fall as rain in Saudi Arabia. When that water reevaporated, it would carry further along the east wind to North Africa. The Sahara would become green, and would no longer be a source of dust to seed hurricanes heading for the western hemisphere.
What a better world that would be! This would most likely bring a potential increase in the world's food supply of between a quarter and a third, due to the vast increase in arable land.
If only we could make Australia into a lush and green place, it would cease to be a source of dust. India would get much milder rains, and the water that was left would fall on the Arabian Peninsula. Much of that would re-evaporate, or be transpired by plants, and would travel further downwind to fall on North Africa. This would, in turn, make what is now the Sahara Desert into a green place with thriving plants, meaning that North Africa would no longer act as a vast supplier of dust over the ocean to seed the hurricanes that afflict North America and the Caribbean.
It is easy to see why the east coast of South America is free of hurricanes, much unlike North America. Africa south of the Sahara is a land of expansive jungle and grassland. It is not dusty, and so does not supply the dust that would seed hurricanes that would move westward to strike South America. If only we could get Australia covered with plants, we would set a very beneficial sequence in motion.
By the way, this new plant life covering Australia, Arabia and, North Africa would absorb much of the world's carbon in the air that is the cause of global warming. We would definitely be "killing two birds with one stone", and really bettering the world in the process.
The main reason that Australia is so dry is that the winds, which might bring rain, are blocked by the Great Dividing Range of mountains, along the east coast of Australia. However, in east-central Australia lies the Great Artesian Basin. This is a vast area of low-lying land, which is Australia's main source of fresh water from wells. Much of the basin is below sea level, my world atlas has the surface of Lake Eyre North as 16 meters below sea level.
What if a canal could be dug, which would flood part of the Great Artesian Basin with sea water? This would form a vast, shallow salt-water reservoir west of the coastal mountains. This water would quickly re-evaporate to be carried westward by the prevailing winds.
Hopefully, it would fall as rain on the vast arid west of Australia. Plants would grow, and farming would thrive. The deserts would become grasslands and the continent would cease to be a source of a significant amount of dust to the region's large-scale weather patterns.
The area is sparsely populated anyway. This salt-water reservoir, covering hundreds of square kilometers would provide beaches and sites for resorts. Although it would not have the waves required for the Australian pastime of surfing. As fish-farming is becoming so popular across much of the world, the reservoir could be stocked with fish.
The reservoir would be shallow, and if Australians ever changed their minds about the project all that would be necessary is to close the canal and the water would not take long to evaporate.
The only drawback of the reservoir is that it would salinate the fresh water within it's shores. But this would be more than compensated for by the fresh water falling westward as rain.
This concerns the proposed project of digging a canal in Australia to flood part of the Great Artesian Basin with sea water. This is my idea to bring rain to Australia by bringing a large surface area of water west of the Great Dividing Range of mountains, since it is these mountains which block the east wind which would otherwise bring rain to this very dry land. This water would evaporate and fall as rain on the vast expanse of western Australia.
I believe that it is an accident of geology which prevented Australia from being the lush and green land that it could have been. This project could really change the world. China and Australia are already tied together economically. Australia is a source of raw materials for China, as well as a destination for Chinese tourists. Many signs in Australia are in Chinese.
Why not work together on this Project? There is a serious water shortage in parts of China. This project would result in milder rains that would carry much further inland in China, instead of the destructive typhoons along the coast. The governments of both countries have put a lot of effort into trying to induce rain artificially, why not try this idea?
It would be ideal if we could set up a parallel project to bring water to North Africa, the world's other great source of dust, as well. But there is no comparable area below sea level there which could be flooded. There is the Qattara Depression in Egypt's Western Desert, but I do not think that flooding it would have much effect on the rainfall.
Do We Really Need Calculus?
I once took a class titled "Calculus-Based Physics". I was still learning calculus, and was more adept with spatial mathematics like geometry and trigonometry. I could not help noticing that just about anything that can be solved with calculus can also be solved without calculus. We live in a spatial universe, and the graphing used in calculus is just another way of solving spatial problems.
I find that an under-appreciated gem of basic physics is the Inverse Square Law. The Inverse Square Law states that an object that is twice as far away will appear as one-quarter the size or, if two radio antennae are broadcasting with equal strength, the signal from one twice as far away will have one-quarter the strength of the one that is closer.
If we look at a building some distance away, for example, the result is an isoceles triangle (one with two equal angles) with the observer at the point of the triangle and the width of the building forming the base of the triangle. This could also be expressed as a right triangle (one with a right angle) with the height of the building as the vertical axis of the triangle. The Inverse Square Law applies in that, if the building were twice as far away from the observer it would appear to the observer as having only a quarter it's former width, or height.
The reason for the Inverse Square Law is that the circumference of a circle is pi (3.1415927 is as many decimal places as I have it memorized) times the diameter of the circle, and the diameter is twice the radius. This means that if we double the radius, which represents the distance to the object, there are now four times the original radius in the diameter of the circle that the object lies on, with the observer at the center.
So, why can't we make use of the Inverse Square Law when dealing with anything that forms a triangle? It does not necessarily have to involve an actual spatial triangle, this law of physics can be applied to anything that forms a triangle in it's pattern of events. This opens up a whole world of possibilities.
Actually, anything which changes at a steady rate forms a triangle in pattern. Picture a right triangle, or a cone. If some entity begins at zero, and proceeds at a steady rate to some maximum, it can easily be expressed as a triangle. Let's replace the triangle formed by the observer looking at the building with the beginning at zero replacing the position at the point of the observer, and the maximum replacing the building.
Now, let's have a look at fractions. I find that fractions represent the way reality really operates. We count in tens, and so we prefer decimal expression. But that is an artificial numbering system and use of decimal tends to make patterns in numbers less apparent than if we used fractions.
Using a simple example of the Inverse Square Law, we can see that triangles have a very useful relationship with the squares of fractions.
Suppose that we have a right angle between two lines. The vertical line has a length of four units, and the horizontal line a length of six units. Let's draw a line from the end of the horizontal line to the top of the vertical line to form a right triangle. The triangle would have an area of twelve square units, since the triangle is half of what a square involving the two lines would be and such a square would have an area of 4 x 6 = 24 square units.
Next, let's consider the half of the horizontal line from the furthest point and moving toward the vertical line. This is the narrowest half of the triangle along the horizontal line. The vertical dimension of the triangle would be zero at the beginning point, and two units at the halfway point of the horizontal line of the triangle. This is because the vertical dimension reaches it's maximum of four units, and we have gone halfway there from the opposite point of the triangle.
The area of this narrow half of the triangle, along the horizontal axis line, would be half of six because 6 = 2 x 3. Thus, the area of the narrow horizontal half of the triangle would be three square units.
Do you see the Inverse Square Law at work? Starting at the narrow end of the triangle, we proceeded halfway toward the wide end of the triangle. In doing so, we passed one quarter of the area of the triangle because the total area of the triangle is twelve square units and the narrow half of the triangle, along the horizontal axis line, has a volume of three square units.
This means that we can do all manner of measurements of anything forming a triangle using the squares of fractions. If the narrow half of a triangle (or cone) contains one quarter of it's area or volume, it must mean that the widest half of the triangle contains 3/4 of it's area or volume. Likewise, the narrowest 1/3 of a triangle contains 1/9 of it's total area or volume. The widest 1/9 of the triangle contains 1/3 of it's total area or volume, and so on.
Now, let's move on. No one says that this very useful Inverse Square Law has to be limited to actual spatial applications. It must also apply to anything that forms a triangle in pattern, even if it does not involve an actual triangle in space. When you think about it, anything that proceeds between zero, or a minimum, and a maximum forms a triangle pattern if it were displayed on a graph.
An object in motion with a steady acceleration or deceleration forms a triangle, with the minimum at the point of the triangle and the maximum at it's widest part. Of course, if the minimum is other than zero, all we have to do is to add a rectangle beneath the triangle so that the width of the rectangle represents the value of the minimum. The most common use of calculus is to measure change, and change proceeds between a maximum and a minimum.
A falling object forms a definite triangle. The acceleration of falling due to gravity is the well-known 32 feet per second squared ( I won't convert this to metric because it is easier to express in feet). This means that if an object is dropped, it will go into the first second of fall with a velocity of zero feet per second and end the first second with a velocity of 32 feet per second, with the increase coming at a steady rate. This means that the average velocity of the object, in it's first second of fall, will be 16 feet per second. So, it will fall 16 feet in the first second.
The object enters it's second second of fall with a velocity of 32 feet per second, and ends the second with a velocity of 64 feet per second. This means that it's average velocity throughout the second second of fall was 48 feet per second. So, it fell 48 feet in the second second of fall.
In two seconds, the object has fallen 64 feet. The 16 feet that it fell in the first of the two seconds is 1/4 of 64. Can you see the triangle that is formed in this pattern, and the applicability of the Inverse Square Law?
(By the way, this 16 feet would be a very useful unit of vertical measurement because of how it relates to the velocity of falling objects. I named this unit a "grav", for gravity, and described it's use in the posting on this blog, "The Way Things Work", and in the book "The Patterns Of New Ideas").
A rising ballistic object forms a triangle in reverse to that of a falling object. Throw a ball into the air and it will form one triangle on the way up, by starting at a maximum vertical velocity and proceeding to zero as a result of the action of gravity, and then another triangle on the way down as it's velocity starts from zero, at the maximum altitude, and proceeds to a maximum.
Something like a ball rolling across the ground, with a steady deceleration, also forms a neat triangle that can readily be measured with this method.
What about a dam holding back a body of water? The pressure of the water against the dam also forms a triangle. The water pressure starts at zero at the surface of the water, and proceeds steadily to a maximum at the bottom of the water.
Anything spreading steadily along a circular front, such as an oil spill, forms the base of a cone in pattern that we can easily measure using this method. When half of the time from the beginning of the spill, if it was from an area of zero, to now had elapsed, the area covered by the spill was 1/4 of what it is now. We can also measure withdrawal at a steady rate in the same way.
Possibly the most useful application of the Inverse Square Law and the squares of fractions involves the total earnings of money which earns interest, with the interest rolled back in. This also forms a triangle, increasing at a steady rate between between minimum and maximum.
To find the sum total of any calculation, how much distance has been covered in the case of velocity, or how much money has been earned in the case of interest, just form a triangle and find the area under the triangle.
So far, we have seen how calculations can be done on anything involving change at a steady rate by using the Inverse Square Law of fundamental physics and basic fractions, with no need whatsoever to use calculus. But now, let's get a little bit more complicated.
It is easy enough to do measurements involving constant change, such as acceleration. But what if the rate of change is itself changing? For example, a graph of velocity will appear as a straight horizontal line for constant, unchanging velocity and a slanted line for constant change in velocity (acceleration or deceleration). But if the rate of acceleration was also changing, a graph of the velocity would show as a curve. The area under the curve would represent the total distance travelled. The trouble is that we do need calculus to find the area under a curve.
But a simple curve is the synthesis of two straight lines, with one of the lines changing in length, which forms the two axes of a triangle. There may be constant acceleration, or change of some kind, which would be expressed as a straight slanted line on a graph, which could be the hypotenuse of a right triangle. But there may be a change in the rate of acceleration, or a change in the change in the rate of acceleration. There may even be a change in the change of the change in the rate of change or acceleration.
To dispense with calculus, all we need to do is to arrive at triangles on our graph so that we can easily find the total distance travelled (or money earned, etc.) using ordinary geometry. No matter how complex the curve, we can find this by simply using multiple triangles and then adding their values to get a total. Of course, we would subtract the value that we get from the area under a triangle if it represented a negative value, such as deceleration, instead of positive acceleration.
Suppose that we wanted to find the total distance travelled by a moving object over a given period of time. But, the velocity of the object was contantly changing.
We would start with one triangle representing the acceleration of the object at the beginning. It would be graphed as a rectangle if it were a contant velocity, without acceleration.
If the object began to accelerate at a given point in time, we would start another triangle beginning at an axis representing the point in time at which the acceleration began.
If that acceleration rate was changing, rather than acting at a contant rate, we would set up another triangle representing that change, and continuing between the appropriate points in time represented by the common vertical axes of the triangles.
If there was a change in that rate, we would set up yet another triangle to represent it. If there was deceleration, we could set that up with the common time axis at the top, instead of the bottom of the graph, and subtract that from our final total rather than adding it.
Isn't this easier, and more enjoyable, than using calculus?
I find that an under-appreciated gem of basic physics is the Inverse Square Law. The Inverse Square Law states that an object that is twice as far away will appear as one-quarter the size or, if two radio antennae are broadcasting with equal strength, the signal from one twice as far away will have one-quarter the strength of the one that is closer.
If we look at a building some distance away, for example, the result is an isoceles triangle (one with two equal angles) with the observer at the point of the triangle and the width of the building forming the base of the triangle. This could also be expressed as a right triangle (one with a right angle) with the height of the building as the vertical axis of the triangle. The Inverse Square Law applies in that, if the building were twice as far away from the observer it would appear to the observer as having only a quarter it's former width, or height.
The reason for the Inverse Square Law is that the circumference of a circle is pi (3.1415927 is as many decimal places as I have it memorized) times the diameter of the circle, and the diameter is twice the radius. This means that if we double the radius, which represents the distance to the object, there are now four times the original radius in the diameter of the circle that the object lies on, with the observer at the center.
So, why can't we make use of the Inverse Square Law when dealing with anything that forms a triangle? It does not necessarily have to involve an actual spatial triangle, this law of physics can be applied to anything that forms a triangle in it's pattern of events. This opens up a whole world of possibilities.
Actually, anything which changes at a steady rate forms a triangle in pattern. Picture a right triangle, or a cone. If some entity begins at zero, and proceeds at a steady rate to some maximum, it can easily be expressed as a triangle. Let's replace the triangle formed by the observer looking at the building with the beginning at zero replacing the position at the point of the observer, and the maximum replacing the building.
Now, let's have a look at fractions. I find that fractions represent the way reality really operates. We count in tens, and so we prefer decimal expression. But that is an artificial numbering system and use of decimal tends to make patterns in numbers less apparent than if we used fractions.
Using a simple example of the Inverse Square Law, we can see that triangles have a very useful relationship with the squares of fractions.
Suppose that we have a right angle between two lines. The vertical line has a length of four units, and the horizontal line a length of six units. Let's draw a line from the end of the horizontal line to the top of the vertical line to form a right triangle. The triangle would have an area of twelve square units, since the triangle is half of what a square involving the two lines would be and such a square would have an area of 4 x 6 = 24 square units.
Next, let's consider the half of the horizontal line from the furthest point and moving toward the vertical line. This is the narrowest half of the triangle along the horizontal line. The vertical dimension of the triangle would be zero at the beginning point, and two units at the halfway point of the horizontal line of the triangle. This is because the vertical dimension reaches it's maximum of four units, and we have gone halfway there from the opposite point of the triangle.
The area of this narrow half of the triangle, along the horizontal axis line, would be half of six because 6 = 2 x 3. Thus, the area of the narrow horizontal half of the triangle would be three square units.
Do you see the Inverse Square Law at work? Starting at the narrow end of the triangle, we proceeded halfway toward the wide end of the triangle. In doing so, we passed one quarter of the area of the triangle because the total area of the triangle is twelve square units and the narrow half of the triangle, along the horizontal axis line, has a volume of three square units.
This means that we can do all manner of measurements of anything forming a triangle using the squares of fractions. If the narrow half of a triangle (or cone) contains one quarter of it's area or volume, it must mean that the widest half of the triangle contains 3/4 of it's area or volume. Likewise, the narrowest 1/3 of a triangle contains 1/9 of it's total area or volume. The widest 1/9 of the triangle contains 1/3 of it's total area or volume, and so on.
Now, let's move on. No one says that this very useful Inverse Square Law has to be limited to actual spatial applications. It must also apply to anything that forms a triangle in pattern, even if it does not involve an actual triangle in space. When you think about it, anything that proceeds between zero, or a minimum, and a maximum forms a triangle pattern if it were displayed on a graph.
An object in motion with a steady acceleration or deceleration forms a triangle, with the minimum at the point of the triangle and the maximum at it's widest part. Of course, if the minimum is other than zero, all we have to do is to add a rectangle beneath the triangle so that the width of the rectangle represents the value of the minimum. The most common use of calculus is to measure change, and change proceeds between a maximum and a minimum.
A falling object forms a definite triangle. The acceleration of falling due to gravity is the well-known 32 feet per second squared ( I won't convert this to metric because it is easier to express in feet). This means that if an object is dropped, it will go into the first second of fall with a velocity of zero feet per second and end the first second with a velocity of 32 feet per second, with the increase coming at a steady rate. This means that the average velocity of the object, in it's first second of fall, will be 16 feet per second. So, it will fall 16 feet in the first second.
The object enters it's second second of fall with a velocity of 32 feet per second, and ends the second with a velocity of 64 feet per second. This means that it's average velocity throughout the second second of fall was 48 feet per second. So, it fell 48 feet in the second second of fall.
In two seconds, the object has fallen 64 feet. The 16 feet that it fell in the first of the two seconds is 1/4 of 64. Can you see the triangle that is formed in this pattern, and the applicability of the Inverse Square Law?
(By the way, this 16 feet would be a very useful unit of vertical measurement because of how it relates to the velocity of falling objects. I named this unit a "grav", for gravity, and described it's use in the posting on this blog, "The Way Things Work", and in the book "The Patterns Of New Ideas").
A rising ballistic object forms a triangle in reverse to that of a falling object. Throw a ball into the air and it will form one triangle on the way up, by starting at a maximum vertical velocity and proceeding to zero as a result of the action of gravity, and then another triangle on the way down as it's velocity starts from zero, at the maximum altitude, and proceeds to a maximum.
Something like a ball rolling across the ground, with a steady deceleration, also forms a neat triangle that can readily be measured with this method.
What about a dam holding back a body of water? The pressure of the water against the dam also forms a triangle. The water pressure starts at zero at the surface of the water, and proceeds steadily to a maximum at the bottom of the water.
Anything spreading steadily along a circular front, such as an oil spill, forms the base of a cone in pattern that we can easily measure using this method. When half of the time from the beginning of the spill, if it was from an area of zero, to now had elapsed, the area covered by the spill was 1/4 of what it is now. We can also measure withdrawal at a steady rate in the same way.
Possibly the most useful application of the Inverse Square Law and the squares of fractions involves the total earnings of money which earns interest, with the interest rolled back in. This also forms a triangle, increasing at a steady rate between between minimum and maximum.
To find the sum total of any calculation, how much distance has been covered in the case of velocity, or how much money has been earned in the case of interest, just form a triangle and find the area under the triangle.
So far, we have seen how calculations can be done on anything involving change at a steady rate by using the Inverse Square Law of fundamental physics and basic fractions, with no need whatsoever to use calculus. But now, let's get a little bit more complicated.
It is easy enough to do measurements involving constant change, such as acceleration. But what if the rate of change is itself changing? For example, a graph of velocity will appear as a straight horizontal line for constant, unchanging velocity and a slanted line for constant change in velocity (acceleration or deceleration). But if the rate of acceleration was also changing, a graph of the velocity would show as a curve. The area under the curve would represent the total distance travelled. The trouble is that we do need calculus to find the area under a curve.
But a simple curve is the synthesis of two straight lines, with one of the lines changing in length, which forms the two axes of a triangle. There may be constant acceleration, or change of some kind, which would be expressed as a straight slanted line on a graph, which could be the hypotenuse of a right triangle. But there may be a change in the rate of acceleration, or a change in the change in the rate of acceleration. There may even be a change in the change of the change in the rate of change or acceleration.
To dispense with calculus, all we need to do is to arrive at triangles on our graph so that we can easily find the total distance travelled (or money earned, etc.) using ordinary geometry. No matter how complex the curve, we can find this by simply using multiple triangles and then adding their values to get a total. Of course, we would subtract the value that we get from the area under a triangle if it represented a negative value, such as deceleration, instead of positive acceleration.
Suppose that we wanted to find the total distance travelled by a moving object over a given period of time. But, the velocity of the object was contantly changing.
We would start with one triangle representing the acceleration of the object at the beginning. It would be graphed as a rectangle if it were a contant velocity, without acceleration.
If the object began to accelerate at a given point in time, we would start another triangle beginning at an axis representing the point in time at which the acceleration began.
If that acceleration rate was changing, rather than acting at a contant rate, we would set up another triangle representing that change, and continuing between the appropriate points in time represented by the common vertical axes of the triangles.
If there was a change in that rate, we would set up yet another triangle to represent it. If there was deceleration, we could set that up with the common time axis at the top, instead of the bottom of the graph, and subtract that from our final total rather than adding it.
Isn't this easier, and more enjoyable, than using calculus?
Monday, March 21, 2011
The Light Computer
The idea of computer systems based on pulses of light moving along fiber optic cables, rather than electrical pulses through conventional wiring, has been around for a number of years. I would like to add my input to it and also to describe my vision of a computer based on light moving beyond the usual binary encoding altogether. (Note-I will alternate the two global spellings of "fiber" and "fibre", and also "color" and "colour", to avoid continuous use of parenthesis).
Light has actually been gaining ground on traditional magnetic and electrical computation and communications for quite some time. The most obvious examples are fiber optic cables replacing copper wire in long distance telephone service and optical storage, first CDs then DVDs, being used to store data instead of magnetic media. In the newest generation of DVDs, blue lasers are being used because their shorter wavelength makes possible the storage of much more data in the same space, in comparision with that if a red laser were used.
The great advantage of fibre optic cable over electrical wires for communication is the lack of electrical interference. Metal telephone wires also act as antennae, picking up all kinds of electromagnetic waves, which results in random noise and static that degrades the quality of the signal. Fiber optic cable suffers no such interference. However, in the U.S. the "local loop" is still copper wire, fibre optic is used mainly in long distance service.
A great amount of effort goes into doing all that is possible to protect the flow of data from interference. Telephone wires are twisted together because it better protects against interference. Computer network cable like Unshielded Twisted Pair (UTP) is twisted for the same reason. Coaxial cable uses the outer shell as a shield against interference.
Communications cables often have grounded wires included that carry no data but help to absorb electrical interference. Parallel data cables, such as the printer cable, are limited in how long they can be because the signals on each wire will create electrical interference which may corrupt the signals on the other wires. Modems were designed to test the lines and adjust the baud rate accordingly.
Inside the computer, every electrical wire and circuit trace also acts as antennae picking up radiation given off by nearby wires. This degrades the quality of the signal and may make it unreliable. If we make the current carrying the signal stronger to better resist interference, then it will only produce more interference itself to corrupt the signals on other wires.
Designing a computer bus nowadays is a very delicate balancing act between making the signal in a given wire strong enough to resist interference, but not strong enough to interfere with the signals on other wires. The complexity of the computer bus only makes this dilemma worse.
As we know, computing is based on electrical pulses or magnetic bits which are either on or off, representing a 1 or a 0. This is called binary because it is a base-two number system. Each unit of magnetic storage because the possibility of being either a 1 or a 0 make it one bit of information.
Eight such bits are defined as a "byte". The two possibilities of a bit multiplied by itself eight times gives 256 different possibilities. This is used to encode the letters of the alphabet, numbers, punctuation and, unprinted control characters such as carriage return. Each of these is represented by one of the 256 possible numbers. This system is known as ASCII, you can read more about it on http://www.wikipedia.org/ if you like. The great thing about this binary system is that it is easily compatible with both boolean logic and the operation of transistors. This is what makes computers possible.
But, once again, so much of the design of computers and the use of signal bandwidth goes into making sure that the signal is reliable in that it has not been corrupted by electrical interference. The eighth bit in a byte is sometimes designated as a parity bit to guard against such interference. For example, if there is an even number of 1s in the other seven bits the parity bit would be set to 0. If there is an odd number of 1s in the seven bits, the parity bit would be set to 1. The parity bit technique takes up bandwidth that could otherwise be used for data transfer, but it provides some rudimentary error checking against electrical interference.
The TCP/IP packets that carry data across the internet can be requested to be resent if there is any possibility of data corruption along the way. A new development in computer buses is to create a negative copy of data, by inverting 1s and 0s, and send it along with the positive version in the theory that interference will affect the negative and positive copies equally.
The tremendous advantage of fiber optic is that we do not have to worry about any of this. With fibre optic cables carrying data as pulses of light, instead of electrical current, we can have hundreds of cables in close proximity to one another and there will not be the least interference between them. This is what makes the concept of computers based on light so promising.
If we could implement a data system using eleven fine lasers, each a different color, the computer could work with ordinary decimal numbers instead of binary. This would not only make computing far simpler, but would provide a five-fold increase in efficiency. We would use pulses of laser light representing 0 through 9 instead of electrical pulses representing 0s and 1s.
The eleventh colour would be a "filler" pulse to be used only when there were two or more consectutive pulses of the same color. This filler pulse would help to avoid confusion about how many pulses there are, in the event of attenuation or other distortion of the data. In addition, multiple filler pulses in a row could be used to indicate the end of one document and the beginning of another.
This new system need not change the existing ASCII coding, we could simply express a letter, number or, control code by it's number out of the 256 possibilities of a byte, rather than it's binary code of the eight bits in a byte. But this would make possible a new "extended ASCII" of 999 possibilities, instead of the current 256. It would also require only three bits, instead of the usual eight. The extra symbols could possibly be used to represent the most common words such as "the", "this", "that", "those", "we", etc.
There would be no 1s and 0s, as in binary. There would only be a stream of pulses of different colours with no modulation or encoding of information, such as the laser light carrying the sound of a voice in fibre optic non-digital telephone communication. All that would be necessary is to keep one color distinguishable from another and to keep them in the proper sequence. If we could do this, any attenuation in the length of the pulses would make no difference. As our technical capabilities increase, we could increase the data transfer rate by making the pulses shorter.
When you dial a telephone number, the sound pulses that you can hear have different frequencies to represent each number on the dialpad. This would be using exactly the same concept to handle the data in a computer using light.
It probably is not a good idea to try to use more than eleven colours at this point, because that would make it increasingly difficult to distinguish one pulse from another. This old binary and ASCII system is really antiquated and I think fiber optics gives us the opportunity to move beyond it. This is yet another example of how we make much technical progress while still using a system designed for past technology so that we end up technologically forward but system backward.
DATA STORAGE USING LIGHT
Computing is a very old idea, but it's progress is dependent on the technology available. Prehistoric people counted using piles of pebbles. Later, a skilled user of an abacus could quickly do arithmetical calculations. In the industrial era, Charles Babbage built the mechanical programmable computers that are considered as the beginning of computing as we know it. I have seen some of his work, and modern reconstructions of it, at the Science Museum in London.
The development of vacuum tubes opened the possibility of computing electronically. But since such tubes use a lot of power, generate a lot of heat, and have to be replaced on a regular basis, it was only when transistors and other semiconductors were developed that modern computers really became a possibility.
Thus, we can see that there has always been steady progress in the development, but this progress has been dependent on the materials and technology available at the time. This brings the question of what the next major step might be.
I think that there are some real possibilities for the future in the pairing of lasers and plastics. The structure of plastic is one of long polymers, based on carbon, which latch together to create a strong and flexible material that is highly resistant to erosion. Fuels are made of the same type of polymers, the main difference being that those in plastics are far longer so that they latch together to form a solid, rather than a liquid.
As we know, light consists of electromagnetic waves in space. Each color (colour) of light has it's specific wavelength. Red light has a long wavelength, and thus a low frequency, while blue light has a shorter wavelength and a higher frequency.
The difference between light from a laser and ordinary light is that the beam from a laser is of a sharply single wavelength and frequency (monochromatic) so that the peaks and troughs (high and low points) of the wave are "in step". This is not the case for non-laser light, which is invariably composed of a span of frequencies, which cannot be "in step" in the same way because their wavelengths vary.
This is why a laser can exert force on an object, the peaks and troughs of the light strike the object at the same instant. With ordinary light, this does not occur because the peaks and troughs are "out of step" due to the varying wavelengths of the light. Laser light can also cross vast distances of space without broadening, and dissipating, as does the ordinary light from a flashlight.
Now, back to plastics. Suppose that we could create a plastic of long, fine polymers aligned more in one direction than the perpendicular directions. You might be thinking that this would defeat the whole idea of plastics, since such a plastic could be more easily torn along the line of polymer alignment.
But what if the light from a laser could permanently imprint the wavelength of the light on the fine polymers of this plastic? If an ordinary beam of white light, which is a mix of all colours (colors), was then shone on the spot of plastic, it would have taken on the color (colour) of the laser and thus would relect this colour back.
We could refer to the plastic as a "photoplastic", because it's polymers would take on the color of whatever laser light was last applied to it. It would, of course, be required that the polymers of the plastic be considerably longer than the wavelengths of the laser light.
This photoplastic would not be useful for any type of photography, because the wide range of wavelengths of light falling on it would dissipate one another's influence on the polymers of the plastic. But it could be extremely useful for storing data.
In use of magnetic storage of data there are only two possibilities for each magnetic bit, either "off" and "on" or 1 and 0. Eight such bits are known as a "byte", and since 2 multiplied by itself eight times gives us 256 possible combinations, the ASCII coding which is the foundation of data storage is based on this.
But if we could use this photoplastic with lasers of eleven different colours, each bit would have eleven different possibilities rather than only two. Just as we can convey much more information with color images, rather than simple black and white, we can store far more data per density using this method instead of magnetic storage.
The processor of a computer processes data by using the so-called "opcodes" that are wired into it. A processor might have several hundred, or more, opcodes wired in. These opcodes are designated by using the base-sixteen hexadecimal number system, which uses the digits 0-9 and also the numbers A-F to make a total of sixteen characters.
These "hex" numbers as designators of the opcodes built into the processor are known as "machine code". Assembly Language is a step above machine code and uses simple instructions to combine these opcodes into still more operations. All of the other higher-level computer languages do the same thing, combine together the opcodes wired into the processor to accomplish the desired operations.
Until we can develop a "light processor" to work with the light storage and light transmission of data that I have described here, the actual processing will still have to be done with electrons. But it is clear to see that the use of light in computing would be the next step forward from what we have today.
Light has actually been gaining ground on traditional magnetic and electrical computation and communications for quite some time. The most obvious examples are fiber optic cables replacing copper wire in long distance telephone service and optical storage, first CDs then DVDs, being used to store data instead of magnetic media. In the newest generation of DVDs, blue lasers are being used because their shorter wavelength makes possible the storage of much more data in the same space, in comparision with that if a red laser were used.
The great advantage of fibre optic cable over electrical wires for communication is the lack of electrical interference. Metal telephone wires also act as antennae, picking up all kinds of electromagnetic waves, which results in random noise and static that degrades the quality of the signal. Fiber optic cable suffers no such interference. However, in the U.S. the "local loop" is still copper wire, fibre optic is used mainly in long distance service.
A great amount of effort goes into doing all that is possible to protect the flow of data from interference. Telephone wires are twisted together because it better protects against interference. Computer network cable like Unshielded Twisted Pair (UTP) is twisted for the same reason. Coaxial cable uses the outer shell as a shield against interference.
Communications cables often have grounded wires included that carry no data but help to absorb electrical interference. Parallel data cables, such as the printer cable, are limited in how long they can be because the signals on each wire will create electrical interference which may corrupt the signals on the other wires. Modems were designed to test the lines and adjust the baud rate accordingly.
Inside the computer, every electrical wire and circuit trace also acts as antennae picking up radiation given off by nearby wires. This degrades the quality of the signal and may make it unreliable. If we make the current carrying the signal stronger to better resist interference, then it will only produce more interference itself to corrupt the signals on other wires.
Designing a computer bus nowadays is a very delicate balancing act between making the signal in a given wire strong enough to resist interference, but not strong enough to interfere with the signals on other wires. The complexity of the computer bus only makes this dilemma worse.
As we know, computing is based on electrical pulses or magnetic bits which are either on or off, representing a 1 or a 0. This is called binary because it is a base-two number system. Each unit of magnetic storage because the possibility of being either a 1 or a 0 make it one bit of information.
Eight such bits are defined as a "byte". The two possibilities of a bit multiplied by itself eight times gives 256 different possibilities. This is used to encode the letters of the alphabet, numbers, punctuation and, unprinted control characters such as carriage return. Each of these is represented by one of the 256 possible numbers. This system is known as ASCII, you can read more about it on http://www.wikipedia.org/ if you like. The great thing about this binary system is that it is easily compatible with both boolean logic and the operation of transistors. This is what makes computers possible.
But, once again, so much of the design of computers and the use of signal bandwidth goes into making sure that the signal is reliable in that it has not been corrupted by electrical interference. The eighth bit in a byte is sometimes designated as a parity bit to guard against such interference. For example, if there is an even number of 1s in the other seven bits the parity bit would be set to 0. If there is an odd number of 1s in the seven bits, the parity bit would be set to 1. The parity bit technique takes up bandwidth that could otherwise be used for data transfer, but it provides some rudimentary error checking against electrical interference.
The TCP/IP packets that carry data across the internet can be requested to be resent if there is any possibility of data corruption along the way. A new development in computer buses is to create a negative copy of data, by inverting 1s and 0s, and send it along with the positive version in the theory that interference will affect the negative and positive copies equally.
The tremendous advantage of fiber optic is that we do not have to worry about any of this. With fibre optic cables carrying data as pulses of light, instead of electrical current, we can have hundreds of cables in close proximity to one another and there will not be the least interference between them. This is what makes the concept of computers based on light so promising.
If we could implement a data system using eleven fine lasers, each a different color, the computer could work with ordinary decimal numbers instead of binary. This would not only make computing far simpler, but would provide a five-fold increase in efficiency. We would use pulses of laser light representing 0 through 9 instead of electrical pulses representing 0s and 1s.
The eleventh colour would be a "filler" pulse to be used only when there were two or more consectutive pulses of the same color. This filler pulse would help to avoid confusion about how many pulses there are, in the event of attenuation or other distortion of the data. In addition, multiple filler pulses in a row could be used to indicate the end of one document and the beginning of another.
This new system need not change the existing ASCII coding, we could simply express a letter, number or, control code by it's number out of the 256 possibilities of a byte, rather than it's binary code of the eight bits in a byte. But this would make possible a new "extended ASCII" of 999 possibilities, instead of the current 256. It would also require only three bits, instead of the usual eight. The extra symbols could possibly be used to represent the most common words such as "the", "this", "that", "those", "we", etc.
There would be no 1s and 0s, as in binary. There would only be a stream of pulses of different colours with no modulation or encoding of information, such as the laser light carrying the sound of a voice in fibre optic non-digital telephone communication. All that would be necessary is to keep one color distinguishable from another and to keep them in the proper sequence. If we could do this, any attenuation in the length of the pulses would make no difference. As our technical capabilities increase, we could increase the data transfer rate by making the pulses shorter.
When you dial a telephone number, the sound pulses that you can hear have different frequencies to represent each number on the dialpad. This would be using exactly the same concept to handle the data in a computer using light.
It probably is not a good idea to try to use more than eleven colours at this point, because that would make it increasingly difficult to distinguish one pulse from another. This old binary and ASCII system is really antiquated and I think fiber optics gives us the opportunity to move beyond it. This is yet another example of how we make much technical progress while still using a system designed for past technology so that we end up technologically forward but system backward.
DATA STORAGE USING LIGHT
Computing is a very old idea, but it's progress is dependent on the technology available. Prehistoric people counted using piles of pebbles. Later, a skilled user of an abacus could quickly do arithmetical calculations. In the industrial era, Charles Babbage built the mechanical programmable computers that are considered as the beginning of computing as we know it. I have seen some of his work, and modern reconstructions of it, at the Science Museum in London.
The development of vacuum tubes opened the possibility of computing electronically. But since such tubes use a lot of power, generate a lot of heat, and have to be replaced on a regular basis, it was only when transistors and other semiconductors were developed that modern computers really became a possibility.
Thus, we can see that there has always been steady progress in the development, but this progress has been dependent on the materials and technology available at the time. This brings the question of what the next major step might be.
I think that there are some real possibilities for the future in the pairing of lasers and plastics. The structure of plastic is one of long polymers, based on carbon, which latch together to create a strong and flexible material that is highly resistant to erosion. Fuels are made of the same type of polymers, the main difference being that those in plastics are far longer so that they latch together to form a solid, rather than a liquid.
As we know, light consists of electromagnetic waves in space. Each color (colour) of light has it's specific wavelength. Red light has a long wavelength, and thus a low frequency, while blue light has a shorter wavelength and a higher frequency.
The difference between light from a laser and ordinary light is that the beam from a laser is of a sharply single wavelength and frequency (monochromatic) so that the peaks and troughs (high and low points) of the wave are "in step". This is not the case for non-laser light, which is invariably composed of a span of frequencies, which cannot be "in step" in the same way because their wavelengths vary.
This is why a laser can exert force on an object, the peaks and troughs of the light strike the object at the same instant. With ordinary light, this does not occur because the peaks and troughs are "out of step" due to the varying wavelengths of the light. Laser light can also cross vast distances of space without broadening, and dissipating, as does the ordinary light from a flashlight.
Now, back to plastics. Suppose that we could create a plastic of long, fine polymers aligned more in one direction than the perpendicular directions. You might be thinking that this would defeat the whole idea of plastics, since such a plastic could be more easily torn along the line of polymer alignment.
But what if the light from a laser could permanently imprint the wavelength of the light on the fine polymers of this plastic? If an ordinary beam of white light, which is a mix of all colours (colors), was then shone on the spot of plastic, it would have taken on the color (colour) of the laser and thus would relect this colour back.
We could refer to the plastic as a "photoplastic", because it's polymers would take on the color of whatever laser light was last applied to it. It would, of course, be required that the polymers of the plastic be considerably longer than the wavelengths of the laser light.
This photoplastic would not be useful for any type of photography, because the wide range of wavelengths of light falling on it would dissipate one another's influence on the polymers of the plastic. But it could be extremely useful for storing data.
In use of magnetic storage of data there are only two possibilities for each magnetic bit, either "off" and "on" or 1 and 0. Eight such bits are known as a "byte", and since 2 multiplied by itself eight times gives us 256 possible combinations, the ASCII coding which is the foundation of data storage is based on this.
But if we could use this photoplastic with lasers of eleven different colours, each bit would have eleven different possibilities rather than only two. Just as we can convey much more information with color images, rather than simple black and white, we can store far more data per density using this method instead of magnetic storage.
The processor of a computer processes data by using the so-called "opcodes" that are wired into it. A processor might have several hundred, or more, opcodes wired in. These opcodes are designated by using the base-sixteen hexadecimal number system, which uses the digits 0-9 and also the numbers A-F to make a total of sixteen characters.
These "hex" numbers as designators of the opcodes built into the processor are known as "machine code". Assembly Language is a step above machine code and uses simple instructions to combine these opcodes into still more operations. All of the other higher-level computer languages do the same thing, combine together the opcodes wired into the processor to accomplish the desired operations.
Until we can develop a "light processor" to work with the light storage and light transmission of data that I have described here, the actual processing will still have to be done with electrons. But it is clear to see that the use of light in computing would be the next step forward from what we have today.
Celestial Locator Grid
On thing that I have long been really interested in, and have not yet discussed on this blog system, is the possibility of extending the system of latitude and longitude, that we use to describe locations on the earth's surface, into outer space.
We have great difficulty in describing precise points in space. We make use of the background of constellations and distance from the sun, but it leaves a lot to be desired.
The standard system of degrees north and south of the celestial equator and declination are used to pinpoint astronomical objects. The expression of a remote location in terms of angular degrees has the advantage in that it is the way in which human beings look at things. The disadvantage is that it becomes less and less accurate the further away the remote location is.
Those who have read my book "The Patterns Of New Ideas" will recall that I presented a solution entitled "The Celestial Meridian", a straight line between the centers of the sun and the star Regulus, as the foundation of such a grid locator system in space. I chose Regulus because it is not only a bright star but is on the ecliptic, the line of the apparent movement of the sun across the background stars during the course of the year. The ecliptic is shaped like a sine wave due to the tilt of the earth's axis, which also produces the seasons.
Today, I would like to present another possible plan for a grid locator system in outer space which follows the same concept as the latitude/longitude system used on the earth's surface.
The trouble with trying to institute such a system is the lack of fixed reference points in space. In our Solar System, everything except the sun is in continuous relative motion. The planets are not even at fixed distances from the sun and do not orbit the sun in exactly the same lateral plane.
For example, there is a difference of about five degrees in the planes of the moon and the sun. If they were in the same plane, there would be both a lunar and a solar eclipse every month. Comets tend to orbit the sun far above and below the general plane of the planetary orbits.
Why not extend the earth's compass directions into space? North and south are already well-defined. The points in space directly above the north and south poles always remains the same. The earth's poles actually do shift, but only over the course of thousands of years.
The difficulty here is that the tilt of the earth's axis and the continuous variation in the overhead position of the sun on the earth's surface, from the Tropic of Cancer to the Tropic of Capricorn, producing the apparent sine wave in the ecliptic against the background stars, makes it impossible to define an obvious celestial east and west.
Compass directions on earth are fixed, making the latitude and longitude system possible. But these directions are tilted at 23 1/2 degrees relative to the earth's orbit around the sun. The tropics extend for 23 1/2 degrees either side of the equator. The tropics refers to the zone where the sun is directly overhead at some point during the year.
The axial tilt of 23 1/2 degrees is also reflected in the Arctic and Antarctic Circles, these define the zones on the earth's surface where the sun does not always rise and set once every 24 hours. Summer in either the northern or southern hemisphere is defined as the period where that hemisphere is pointing toward the sun due to the axial tilt and the opposite hemisphere is pointing away from the sun.
The angle between the earth's polar axis and the plane of the earth's orbit around the sun varies. It is at 23 1/2 degrees north of the equator on the first day of the northern hemisphere summer and 23 1/2 degrees south of the equator on the first day of the northern hemisphere winter. The first day of summer and winter are known as the solstices.
It is only on the first days of spring and autumn that the sun is directly overhead at the equator so that night and day are of equal length. For this reason, these two days are known as the equinoxes, meaning equal length of day and night. The equinoxes are also the only two days when the earth's polar axis is perpendicular to the plane of the earth's orbit around the sun.
Celestial north and south in our new space locator grid are very clearly defined by the points that are always overhead at the poles. Since the polar axis is perpendicular to the plane of the earth's orbit around the sun at the two equinoxes, let's define a line from the center of the sun to the center of the earth, and continuing on into space, at the vernal equinox (first day of northern hemisphere spring) as celestial east (for Easter), and an opposite line at the autumnal equinox as celestial west.
The earth's surface is two-dimensional, while space is three-dimensional. This means that we require another line to express a point in space. This can only be a line from the earth's center at summer solstice, through the center of the sun, to the earth's center at winter solstice from the point of view of either one of the hemispheres. Let's call this the solstice line, it is perpendicular to both the polar axis and the equinox line.
To avoid confusion and errors, let's refer to the two opposite directions on the solstice line simply as celestial june and celestial december, since this is when the solstices fall. Use of three coordinates in space can precisely define any point in neighborhood of the solar system. Maybe the Celestial Meridian can be used for deeper space.
The orbit of any body in the solar system can be easily described mathematically by use of such a grid system. we could easily plot relative positions of planets and other objects for any given time. The grid locator system can be centered on either the earth or the sun, or any point for that matter such as a spaceship, with a constantly varying conversion factor between the two. This system could also benefit from the 180 degree trigonometric function that I described in the posting "New Trigonometric Functions" on this blog.
We have great difficulty in describing precise points in space. We make use of the background of constellations and distance from the sun, but it leaves a lot to be desired.
The standard system of degrees north and south of the celestial equator and declination are used to pinpoint astronomical objects. The expression of a remote location in terms of angular degrees has the advantage in that it is the way in which human beings look at things. The disadvantage is that it becomes less and less accurate the further away the remote location is.
Those who have read my book "The Patterns Of New Ideas" will recall that I presented a solution entitled "The Celestial Meridian", a straight line between the centers of the sun and the star Regulus, as the foundation of such a grid locator system in space. I chose Regulus because it is not only a bright star but is on the ecliptic, the line of the apparent movement of the sun across the background stars during the course of the year. The ecliptic is shaped like a sine wave due to the tilt of the earth's axis, which also produces the seasons.
Today, I would like to present another possible plan for a grid locator system in outer space which follows the same concept as the latitude/longitude system used on the earth's surface.
The trouble with trying to institute such a system is the lack of fixed reference points in space. In our Solar System, everything except the sun is in continuous relative motion. The planets are not even at fixed distances from the sun and do not orbit the sun in exactly the same lateral plane.
For example, there is a difference of about five degrees in the planes of the moon and the sun. If they were in the same plane, there would be both a lunar and a solar eclipse every month. Comets tend to orbit the sun far above and below the general plane of the planetary orbits.
Why not extend the earth's compass directions into space? North and south are already well-defined. The points in space directly above the north and south poles always remains the same. The earth's poles actually do shift, but only over the course of thousands of years.
The difficulty here is that the tilt of the earth's axis and the continuous variation in the overhead position of the sun on the earth's surface, from the Tropic of Cancer to the Tropic of Capricorn, producing the apparent sine wave in the ecliptic against the background stars, makes it impossible to define an obvious celestial east and west.
Compass directions on earth are fixed, making the latitude and longitude system possible. But these directions are tilted at 23 1/2 degrees relative to the earth's orbit around the sun. The tropics extend for 23 1/2 degrees either side of the equator. The tropics refers to the zone where the sun is directly overhead at some point during the year.
The axial tilt of 23 1/2 degrees is also reflected in the Arctic and Antarctic Circles, these define the zones on the earth's surface where the sun does not always rise and set once every 24 hours. Summer in either the northern or southern hemisphere is defined as the period where that hemisphere is pointing toward the sun due to the axial tilt and the opposite hemisphere is pointing away from the sun.
The angle between the earth's polar axis and the plane of the earth's orbit around the sun varies. It is at 23 1/2 degrees north of the equator on the first day of the northern hemisphere summer and 23 1/2 degrees south of the equator on the first day of the northern hemisphere winter. The first day of summer and winter are known as the solstices.
It is only on the first days of spring and autumn that the sun is directly overhead at the equator so that night and day are of equal length. For this reason, these two days are known as the equinoxes, meaning equal length of day and night. The equinoxes are also the only two days when the earth's polar axis is perpendicular to the plane of the earth's orbit around the sun.
Celestial north and south in our new space locator grid are very clearly defined by the points that are always overhead at the poles. Since the polar axis is perpendicular to the plane of the earth's orbit around the sun at the two equinoxes, let's define a line from the center of the sun to the center of the earth, and continuing on into space, at the vernal equinox (first day of northern hemisphere spring) as celestial east (for Easter), and an opposite line at the autumnal equinox as celestial west.
The earth's surface is two-dimensional, while space is three-dimensional. This means that we require another line to express a point in space. This can only be a line from the earth's center at summer solstice, through the center of the sun, to the earth's center at winter solstice from the point of view of either one of the hemispheres. Let's call this the solstice line, it is perpendicular to both the polar axis and the equinox line.
To avoid confusion and errors, let's refer to the two opposite directions on the solstice line simply as celestial june and celestial december, since this is when the solstices fall. Use of three coordinates in space can precisely define any point in neighborhood of the solar system. Maybe the Celestial Meridian can be used for deeper space.
The orbit of any body in the solar system can be easily described mathematically by use of such a grid system. we could easily plot relative positions of planets and other objects for any given time. The grid locator system can be centered on either the earth or the sun, or any point for that matter such as a spaceship, with a constantly varying conversion factor between the two. This system could also benefit from the 180 degree trigonometric function that I described in the posting "New Trigonometric Functions" on this blog.
Human Language Compilation
I believe that computers should make translation of documents from one language to another simple, quick and, easy.
Computers do not actually work with our letters and words. All that they understand is the alignment of magnetic bits to represent either a 1 or a 0. But if we group such bits into groups of eight, known as a byte, we have 256 possible combinations because each os the eight bits can be magnetically set to represent either a 1 or a 0, two possible combinations, and two multiplied by itself eight times is 256.
In a code system known by it's acronym of ASCII, each letter of the alphabet, lower case and caps, as well as numbers, puncuation and, control characters, are each represented by one of the 256 possible combinations that make up a byte.
In the programming of computers, special languages are developed as a link between the tasks that humans want to computer to do and the opcodes (operational codes) that are wired into the processor of the computer. The processor in a typical computer might have several hundred opcodes, representing the tasks that are wired into it.
Opcodes are used in combination to create a vast number of possible language commands. They are distinguished by hexidecimal code. This is a numbering system based on sixteen, rather than ten. It uses the digits 0 through 9, followed by the letters a through f. This base is used because a unit of four bits (a nibble) can be made into sixteen possible combinations. This numbering system is used for such things as memory addresses in the computer, as well as opcodes.
Computer programming languages fall into two broad categories, those that are interpreted and those that are compiled. Simple web scripts such as Javascript and ActiveX controls are interpreted by the browser line by line and are not compiled. BASIC (Beginners All-purpose Symbolic Instruction Code) was originally designed as an interpreted language so that programming students could write a program and watch it being run line by line.
In high-level languages that are compiled, such as C++, a special program must be written to link the language with each processor that enters the market. This is because each and every processor has it's own set of opcodes. This special program is called a compiler and it goes over the program and, in several steps, breaks it down into the opcodes of the particular processor on the computer on which it is being run.
In assembly language, which is a low-level computer language only a step above the computer's machine code, or opcodes, another type of compiler, an assembler, is used to translate the commands into the machine code that the processor can work with. Such a low-level language as assembly language is arduous to write, but it used when a very short program that can run very quickly is required.
There are computer languages which are neither compiled or interpreted. The popular Java uses a "virtual machine" on the computer to enable it to operate across all computer platforms. Java makes use of "Java Byte Code", which is a "p-code" for pre-compiled code.
What I want to ask is why can't we write a compiler for human languages? If compilers are special programs that break the commands of high level computer languages into the opcodes that are wired into the processor of the computer, then the next step should be a compiler for any written language. The compiler could scan each sentence and break it down into numeric code.
A compiler could be written to link each human language to this code so that a document in one human language could be easily translated into another, as long as a compiler had been written for both languages.
The roadblock to an accomplishment such as this is, as I pointed out in the posting "Numbered Sentences" on my progress blog, that the word is not the primary unit of human communication when we are concerned with translating one language into another. Working with letters and words is fine as long as we will remain within one language. But it is the sentence, not the word, which must be translated from one language to another. A word-for word translation usually produces little more than gibberish simply because grammar and syntax differ from one language to another.
Such a coding system does not yet exist. It would be similar in concept to ASCII, but would require us to break down every possible sentence and, after eliminating redundancies, assign each a numeric code that would be the same regardless of what human language it was in. It would be fairly simply to assign nouns and verbs a place in a language tree structure. Spell check and grammar checking software is already widely-used and this is the next logical step.
My vision for the next breakthrough in the progress of computers lies not in technology, but in how we approach language. I have written about this topic already on the progress blog. The great limitation is that we are still using the ASCII system of coding that has been in use since 1968, when available computer memory was maybe one-thousandth of what it is now.
Basically, computer storage revolves around magnetic bits. Each bit can be either a 1 or a 0, on or off, so that there are only two possible states for each bit. This means that eight such bits have 256 possible combinations, which is ideal to encode all of the alphabet, lower case and capitals, numbers, punctuation, as well as unprinted controls such as carriage return and space. This is the system that we use, reading computer memory in the groupings of eight bits that is referred to as a "byte".
Computers only deal with numbers, while we communicate mostly with words. This means that we have to create artificial languages to communicate with computers, and to instruct them what to do. There are several hundred opcodes, or basic instructions, wired into each computer processor. Machine code tells the computer what we want it to do by combining the instructions in these opcodes.
This machine code, which is expressed in a so-called hexidecimal number system consisting of the numbers 0-9 and the letters A-F, is actually the most fundamental level computer language. One step up from this is assembly language, this is expressed in simple letter instructions and works by combining machine code instructions to the processor.
We can build higher level computer languages from this, all of which work by combining the instructions of lower-level languages. Some languages, such as those for web scripting, are interpreted in that they are simply read by the browser line-by-line. Most must have a compiler written to link each computer language to each new processor that comes on the market. The great advantage of higher-level languages is that the programmer does not have to understand exactly how the processor works in order to write instructions.
I find this system to be inefficient in the extreme for modern computing, as described on the progress blog. This is another example of how we have a way of becoming technically forward, but system backward.
For one thing, with the spell-check technology available nowadays, there is no need to encode capital letters. We can shorten the bytes that will speed computers by encoding all letters in lower case and letting spellcheckers capitalize the appropriate letters at the receiving end.
For another thing, I had the idea that we could just consider all letters, numbers, punctuation and, controls as one big number. This would mean considering it as a base-256 number, instead of the base-ten system that we are used to. But this relatively simple change would greatly multiply both the storage space and the speed available by compressing any document, as described in "The Floating Base System" on this blog.
Today I would like to write more about what should definitely be the next frontier in computing, reforming the basic system of encoding.
There are three possible ways to encode written information in a computer, by letters, by words or, by sentences. The way it is done now is still by letters, which is by far the most primitive and inefficient of the three and is a reflection of the strict memory limitations of 1968. The real unit of communication is actually the sentence, as we have seen on the progress blog, in "Human Language Compilation" and "Numbered Sentences". Notice that languages must be translated from one to another by the sentence, not by the word. This is because grammar and syntax differ from language to language, and word for word translations usually produce little more than gibberish.
To encode by sentences, we could scan the dictionary for sensible combinations of words that make sentences and then eliminate redundancies, or sentences that mean the same thing. This would give us a few million sentences that are used in communication. There would also be special pointers to names, place names, and culturally specific words. This would not only make storage and transmission of information many times more efficient, but would also facilitate easy translation from one language to another because all sentences could already be pre-translated.
The user would type a sentence, and then pick the one that came up from the database that was most like the one that was typed. Each one of these would have a pre-assigned bit code, similar in concept to the present ASCII.
There is yet another approach to better integrating the ordinary language that we communicate with and computers that I have not written about yet. This approach involves words, rather than sentences, and is will be more complex and difficult than numbering sentences, but will be the ultimate in language-computer integration and is what I want to add today.
Words are actually codes, which is why we have dictionaries for words but not for numbers. A word serves to differentiate something that exists from everything else, this fits with that all-pervasive pattern that I termed "The One And The Many", as described in the posting by that name on the patterns blog.
Since we are more complex than our inanimate matter surroundings, there is not enough complexity for everything that we could conceive of to actually exist. So, words also define for us that which does exist from that which doesn't. This is why we require words, as well as numbers, only a fraction of what could exist, from our complexity perspective, actually does exist.
Words, as codes, are far more complex than numbers. Although it may not seem like it, there is a vast amount of complexity packed into each and every word. All of the complexity of the pre-agreed upon meaning is contained in a word. Words can be thought of a a kind of "higher-level" of numbers in a way similar to that of computer languages.
Numbers differ from words in that everything is basically numbers being manifested. They exist in the universe of inanimate space and matter, while words don't. Numbers are less complex than words, but are not required to differentiate that which exists from that which doesn't as words are.
We must completely understand something in order to describe it with numbers, although that is not the case with less-precise words. (In "The Progression Of Knowledge", on the progress blog, I explained how this can give us an idea of where we stand as far as how the volume of knowledge that we have now compares with all that we can possibly know).
We cannot determine the complexity of the words that we must fall back on because if we could, we could continue our description of reality with numbers and would not need the words. We know what words mean, or else they would not be useful, but we do not know how much actual complexity the word contains in it's meaning because if we did, we could express it's meaning with numbers and would no longer really need the word.
In "Outer Mathematics" on either this or the patterns and complexity blog, we saw how numbers are all that there really is. Everything is actually numbers being manifested. This means that there must be a formula for everything that exists. But because of our complexity level, we are unable to discern formulae about ourselves or things more complex than us.
We can only arrive at a formula for something that is less complex than our brains, which have to figure it out and completely understand it. To derive a formula about ourselves or things more complex than us, we would have to be "smarter than ourselves", which is impossible. We could take the communications systems of animals and break it down into numbers, but cannot do that with our own. So, we can only rely on words for such descriptions.
But if there must be a formula for everything, even if it is hidden from us by our complexity perspective, that must also include words. Out there somewhere, there must be a way to substitute a number or a formula for every word in our language. If only we could arrive at this, it would be possible to construct a very complex system of numbers and formulae that would parallel the words that we use to communicate.
If we could only accomplish this, we would have the numbers that computers can deal with. Computers could deal directly with ordinary words, at least the ones that we had incorporated into this matching structure of numbers and formulae, and these artificial computer languages would no longer be necessary. We cannot see this, at our complexity level, because we are up against our own complexity and we cannot be "smarter than ourselves".
In the universe of inanimate matter, there is only quantity. In other words, everything is really numbers but with inanimate matter these numbers and formulae that describe everything are only one-dimensional. When we deal with living things, particularly ourselves, we have to deal with quality as well as quantity.
We can differentiate between the two by describing quantity as one-dimensional and quality as multi-dimensional. Quality forms a peak, which is the intersection of at least two slopes, while quality forms a simple slope. Quality is not simply "the more, the better", but is a peak factor. This is why we are so much more complex than the surrounding inanimate reality.
I explained a simple version of structuring words like numbers in "The Root Word System" on this blog.
So, just as we did the Human Genome Project and the Sloan Sky Survey, let's get powerful supercomputers to work developing the structure that must exist to incorporate every word that we use so that each word that we use can be expressed as a number or formula in the overall structure. Computers will then be capable of dealing with ordinary human language. All that we would have to do is to tell the computer what we wanted it to do, and they would be unimaginably more useful and easy to use than they are now.
Computers do not actually work with our letters and words. All that they understand is the alignment of magnetic bits to represent either a 1 or a 0. But if we group such bits into groups of eight, known as a byte, we have 256 possible combinations because each os the eight bits can be magnetically set to represent either a 1 or a 0, two possible combinations, and two multiplied by itself eight times is 256.
In a code system known by it's acronym of ASCII, each letter of the alphabet, lower case and caps, as well as numbers, puncuation and, control characters, are each represented by one of the 256 possible combinations that make up a byte.
In the programming of computers, special languages are developed as a link between the tasks that humans want to computer to do and the opcodes (operational codes) that are wired into the processor of the computer. The processor in a typical computer might have several hundred opcodes, representing the tasks that are wired into it.
Opcodes are used in combination to create a vast number of possible language commands. They are distinguished by hexidecimal code. This is a numbering system based on sixteen, rather than ten. It uses the digits 0 through 9, followed by the letters a through f. This base is used because a unit of four bits (a nibble) can be made into sixteen possible combinations. This numbering system is used for such things as memory addresses in the computer, as well as opcodes.
Computer programming languages fall into two broad categories, those that are interpreted and those that are compiled. Simple web scripts such as Javascript and ActiveX controls are interpreted by the browser line by line and are not compiled. BASIC (Beginners All-purpose Symbolic Instruction Code) was originally designed as an interpreted language so that programming students could write a program and watch it being run line by line.
In high-level languages that are compiled, such as C++, a special program must be written to link the language with each processor that enters the market. This is because each and every processor has it's own set of opcodes. This special program is called a compiler and it goes over the program and, in several steps, breaks it down into the opcodes of the particular processor on the computer on which it is being run.
In assembly language, which is a low-level computer language only a step above the computer's machine code, or opcodes, another type of compiler, an assembler, is used to translate the commands into the machine code that the processor can work with. Such a low-level language as assembly language is arduous to write, but it used when a very short program that can run very quickly is required.
There are computer languages which are neither compiled or interpreted. The popular Java uses a "virtual machine" on the computer to enable it to operate across all computer platforms. Java makes use of "Java Byte Code", which is a "p-code" for pre-compiled code.
What I want to ask is why can't we write a compiler for human languages? If compilers are special programs that break the commands of high level computer languages into the opcodes that are wired into the processor of the computer, then the next step should be a compiler for any written language. The compiler could scan each sentence and break it down into numeric code.
A compiler could be written to link each human language to this code so that a document in one human language could be easily translated into another, as long as a compiler had been written for both languages.
The roadblock to an accomplishment such as this is, as I pointed out in the posting "Numbered Sentences" on my progress blog, that the word is not the primary unit of human communication when we are concerned with translating one language into another. Working with letters and words is fine as long as we will remain within one language. But it is the sentence, not the word, which must be translated from one language to another. A word-for word translation usually produces little more than gibberish simply because grammar and syntax differ from one language to another.
Such a coding system does not yet exist. It would be similar in concept to ASCII, but would require us to break down every possible sentence and, after eliminating redundancies, assign each a numeric code that would be the same regardless of what human language it was in. It would be fairly simply to assign nouns and verbs a place in a language tree structure. Spell check and grammar checking software is already widely-used and this is the next logical step.
My vision for the next breakthrough in the progress of computers lies not in technology, but in how we approach language. I have written about this topic already on the progress blog. The great limitation is that we are still using the ASCII system of coding that has been in use since 1968, when available computer memory was maybe one-thousandth of what it is now.
Basically, computer storage revolves around magnetic bits. Each bit can be either a 1 or a 0, on or off, so that there are only two possible states for each bit. This means that eight such bits have 256 possible combinations, which is ideal to encode all of the alphabet, lower case and capitals, numbers, punctuation, as well as unprinted controls such as carriage return and space. This is the system that we use, reading computer memory in the groupings of eight bits that is referred to as a "byte".
Computers only deal with numbers, while we communicate mostly with words. This means that we have to create artificial languages to communicate with computers, and to instruct them what to do. There are several hundred opcodes, or basic instructions, wired into each computer processor. Machine code tells the computer what we want it to do by combining the instructions in these opcodes.
This machine code, which is expressed in a so-called hexidecimal number system consisting of the numbers 0-9 and the letters A-F, is actually the most fundamental level computer language. One step up from this is assembly language, this is expressed in simple letter instructions and works by combining machine code instructions to the processor.
We can build higher level computer languages from this, all of which work by combining the instructions of lower-level languages. Some languages, such as those for web scripting, are interpreted in that they are simply read by the browser line-by-line. Most must have a compiler written to link each computer language to each new processor that comes on the market. The great advantage of higher-level languages is that the programmer does not have to understand exactly how the processor works in order to write instructions.
I find this system to be inefficient in the extreme for modern computing, as described on the progress blog. This is another example of how we have a way of becoming technically forward, but system backward.
For one thing, with the spell-check technology available nowadays, there is no need to encode capital letters. We can shorten the bytes that will speed computers by encoding all letters in lower case and letting spellcheckers capitalize the appropriate letters at the receiving end.
For another thing, I had the idea that we could just consider all letters, numbers, punctuation and, controls as one big number. This would mean considering it as a base-256 number, instead of the base-ten system that we are used to. But this relatively simple change would greatly multiply both the storage space and the speed available by compressing any document, as described in "The Floating Base System" on this blog.
Today I would like to write more about what should definitely be the next frontier in computing, reforming the basic system of encoding.
There are three possible ways to encode written information in a computer, by letters, by words or, by sentences. The way it is done now is still by letters, which is by far the most primitive and inefficient of the three and is a reflection of the strict memory limitations of 1968. The real unit of communication is actually the sentence, as we have seen on the progress blog, in "Human Language Compilation" and "Numbered Sentences". Notice that languages must be translated from one to another by the sentence, not by the word. This is because grammar and syntax differ from language to language, and word for word translations usually produce little more than gibberish.
To encode by sentences, we could scan the dictionary for sensible combinations of words that make sentences and then eliminate redundancies, or sentences that mean the same thing. This would give us a few million sentences that are used in communication. There would also be special pointers to names, place names, and culturally specific words. This would not only make storage and transmission of information many times more efficient, but would also facilitate easy translation from one language to another because all sentences could already be pre-translated.
The user would type a sentence, and then pick the one that came up from the database that was most like the one that was typed. Each one of these would have a pre-assigned bit code, similar in concept to the present ASCII.
There is yet another approach to better integrating the ordinary language that we communicate with and computers that I have not written about yet. This approach involves words, rather than sentences, and is will be more complex and difficult than numbering sentences, but will be the ultimate in language-computer integration and is what I want to add today.
Words are actually codes, which is why we have dictionaries for words but not for numbers. A word serves to differentiate something that exists from everything else, this fits with that all-pervasive pattern that I termed "The One And The Many", as described in the posting by that name on the patterns blog.
Since we are more complex than our inanimate matter surroundings, there is not enough complexity for everything that we could conceive of to actually exist. So, words also define for us that which does exist from that which doesn't. This is why we require words, as well as numbers, only a fraction of what could exist, from our complexity perspective, actually does exist.
Words, as codes, are far more complex than numbers. Although it may not seem like it, there is a vast amount of complexity packed into each and every word. All of the complexity of the pre-agreed upon meaning is contained in a word. Words can be thought of a a kind of "higher-level" of numbers in a way similar to that of computer languages.
Numbers differ from words in that everything is basically numbers being manifested. They exist in the universe of inanimate space and matter, while words don't. Numbers are less complex than words, but are not required to differentiate that which exists from that which doesn't as words are.
We must completely understand something in order to describe it with numbers, although that is not the case with less-precise words. (In "The Progression Of Knowledge", on the progress blog, I explained how this can give us an idea of where we stand as far as how the volume of knowledge that we have now compares with all that we can possibly know).
We cannot determine the complexity of the words that we must fall back on because if we could, we could continue our description of reality with numbers and would not need the words. We know what words mean, or else they would not be useful, but we do not know how much actual complexity the word contains in it's meaning because if we did, we could express it's meaning with numbers and would no longer really need the word.
In "Outer Mathematics" on either this or the patterns and complexity blog, we saw how numbers are all that there really is. Everything is actually numbers being manifested. This means that there must be a formula for everything that exists. But because of our complexity level, we are unable to discern formulae about ourselves or things more complex than us.
We can only arrive at a formula for something that is less complex than our brains, which have to figure it out and completely understand it. To derive a formula about ourselves or things more complex than us, we would have to be "smarter than ourselves", which is impossible. We could take the communications systems of animals and break it down into numbers, but cannot do that with our own. So, we can only rely on words for such descriptions.
But if there must be a formula for everything, even if it is hidden from us by our complexity perspective, that must also include words. Out there somewhere, there must be a way to substitute a number or a formula for every word in our language. If only we could arrive at this, it would be possible to construct a very complex system of numbers and formulae that would parallel the words that we use to communicate.
If we could only accomplish this, we would have the numbers that computers can deal with. Computers could deal directly with ordinary words, at least the ones that we had incorporated into this matching structure of numbers and formulae, and these artificial computer languages would no longer be necessary. We cannot see this, at our complexity level, because we are up against our own complexity and we cannot be "smarter than ourselves".
In the universe of inanimate matter, there is only quantity. In other words, everything is really numbers but with inanimate matter these numbers and formulae that describe everything are only one-dimensional. When we deal with living things, particularly ourselves, we have to deal with quality as well as quantity.
We can differentiate between the two by describing quantity as one-dimensional and quality as multi-dimensional. Quality forms a peak, which is the intersection of at least two slopes, while quality forms a simple slope. Quality is not simply "the more, the better", but is a peak factor. This is why we are so much more complex than the surrounding inanimate reality.
I explained a simple version of structuring words like numbers in "The Root Word System" on this blog.
So, just as we did the Human Genome Project and the Sloan Sky Survey, let's get powerful supercomputers to work developing the structure that must exist to incorporate every word that we use so that each word that we use can be expressed as a number or formula in the overall structure. Computers will then be capable of dealing with ordinary human language. All that we would have to do is to tell the computer what we wanted it to do, and they would be unimaginably more useful and easy to use than they are now.
The Root Word System
I was looking up a word in the dictionary when a thought came into my mind. A dictionary is actually a symptom of how inefficient our language is.
A perfect language, if it could exist, would actually resemble the number system that we use. Our number system is far more efficient than our word system. Numbers are self-explanatory, while words are not.
You do not need a dictionary to tell you the meaning of a number, because there is really no way to define a number better than the number itself. But suppose we used a different system and the symbol for the number 357 was completely different from the number 358. You would then need to carry a number dictionary around.
Of course, such a system would be highly illogical. But, this is the way words operate. Two closely similar words can mean completely different things in the same way that two similar things may be described by totally different words. In contrast we know that two similar numbers, such as the 357 and 358, must mean close to the same thing.
Unlike numbers, words were thrown together haphazardly over the centuries. Words are organized as verbs, nouns, pronouns, adverbs and, adjectives. But reality is fundamentally numbers and is ordered like our numbering system. We could have taken great advantage of this, except that the words were already in existence.
Words are different from numbers in that only a tiny fraction of the things that could potentially exist actually do exist and need to be assigned a word. In contrast, every number is known to exist whether it is manifested or not. It would make no sense to imagine things that do not exist and assign words to them.
Humans used symbols to represent words long before the idea of alphabets came along. Letters of the alphabet were used to represent spoken sounds and, written words were grafted onto spoken words.
Then I got to wondering, what if letters had come first so that they could have been used from the beginning to represent words, using an alphabet? We could have structured words like numbers and they would be just about as self-explanatory as numbers. Words could have successive roots and, building words would be like building molecules from atoms.
For example, the word "atom" could be such a root word so that anything associated with atoms, such as the component electrons, neutrons and, protons, would be assigned words with the root "atom-". Another such root word could be "house-", and anything associated with a house would be assigned words built on this root word. Root words could be combined together, if necessary, with the most fundamental one coming first.
We could even make the system still more efficient by assigning root words by which letter of the alphabet they begin with, so that related or similar things would be assigned similar words. We would start with dividing all words into the parts of speech: verbs, nouns, etc.
The incredible efficiency that would have been possible with such a word system can be extended to sentences. The fundamantal unit of communication is really the sentence, rather than the word. But we are forced to revolve communication around the word, due to this great inefficiency. It would often be possible to crunch sentences together into a single word. This would be extremely useful digitally.
Such a root word system to make words operate in the same way as the number system would bring us almost unfathomable advantages. For one thing, it would make learning immeasurably easier. Students would need to learn only a relatively few root words. Also the more fundamantal the word was, and thus the more frequently it is likely to be used, the shorter the word would be.
Not only would the Root Word System be incredibly efficient, it would make it a simple matter to translate between languages. It would be so easy for any document to be analyzed by computer because it would essentially be a program in itself and the compiler would only have to parse the root words.
Even if you do not think that the Root Word System is a practical idea at this point, because it would involve creating a whole new human language, it could start off as a computer language.
A perfect language, if it could exist, would actually resemble the number system that we use. Our number system is far more efficient than our word system. Numbers are self-explanatory, while words are not.
You do not need a dictionary to tell you the meaning of a number, because there is really no way to define a number better than the number itself. But suppose we used a different system and the symbol for the number 357 was completely different from the number 358. You would then need to carry a number dictionary around.
Of course, such a system would be highly illogical. But, this is the way words operate. Two closely similar words can mean completely different things in the same way that two similar things may be described by totally different words. In contrast we know that two similar numbers, such as the 357 and 358, must mean close to the same thing.
Unlike numbers, words were thrown together haphazardly over the centuries. Words are organized as verbs, nouns, pronouns, adverbs and, adjectives. But reality is fundamentally numbers and is ordered like our numbering system. We could have taken great advantage of this, except that the words were already in existence.
Words are different from numbers in that only a tiny fraction of the things that could potentially exist actually do exist and need to be assigned a word. In contrast, every number is known to exist whether it is manifested or not. It would make no sense to imagine things that do not exist and assign words to them.
Humans used symbols to represent words long before the idea of alphabets came along. Letters of the alphabet were used to represent spoken sounds and, written words were grafted onto spoken words.
Then I got to wondering, what if letters had come first so that they could have been used from the beginning to represent words, using an alphabet? We could have structured words like numbers and they would be just about as self-explanatory as numbers. Words could have successive roots and, building words would be like building molecules from atoms.
For example, the word "atom" could be such a root word so that anything associated with atoms, such as the component electrons, neutrons and, protons, would be assigned words with the root "atom-". Another such root word could be "house-", and anything associated with a house would be assigned words built on this root word. Root words could be combined together, if necessary, with the most fundamental one coming first.
We could even make the system still more efficient by assigning root words by which letter of the alphabet they begin with, so that related or similar things would be assigned similar words. We would start with dividing all words into the parts of speech: verbs, nouns, etc.
The incredible efficiency that would have been possible with such a word system can be extended to sentences. The fundamantal unit of communication is really the sentence, rather than the word. But we are forced to revolve communication around the word, due to this great inefficiency. It would often be possible to crunch sentences together into a single word. This would be extremely useful digitally.
Such a root word system to make words operate in the same way as the number system would bring us almost unfathomable advantages. For one thing, it would make learning immeasurably easier. Students would need to learn only a relatively few root words. Also the more fundamantal the word was, and thus the more frequently it is likely to be used, the shorter the word would be.
Not only would the Root Word System be incredibly efficient, it would make it a simple matter to translate between languages. It would be so easy for any document to be analyzed by computer because it would essentially be a program in itself and the compiler would only have to parse the root words.
Even if you do not think that the Root Word System is a practical idea at this point, because it would involve creating a whole new human language, it could start off as a computer language.
Human Formulae
Euclidean geometry is based on an axiom that cannot be mathematically proven. On a plane with a line and a point outside the line, there is one and only one line which can be drawn through the point that will be parallel to the line.
However, this axiom is considered to be so self-evident that it really does not need to be proven. Just the fact that this system of geometry has served satisfactorily for nearly 3,000 years can be considered as proof enough of it's truth.
Today, I would like to introduce an axiom. Although the axiom cannot actually be proven, I consider it to be self-evident in it's truth. It is that any given system can be described by a mathematical formula, as long as the system is of less than infinite complexity. A formula exists to describe any system, either in it's present state or how it was formed, whichever is more compact.
Since there is a finite amount of space and matter in the universe, it must be of less than infinite complexity and thus there is a formula out there somewhere that describes the entire universe.
There is a clear rule that I can see regarding the derivation of formulae (the plural of formula is formulae). To discern a formula in some process, the observer must necessarily have more complexity in their mental processes than is present in the process being observed. In other words, the formula governing the process will only be apparent to the observer if the observer is "smarter" than the process being observed.
Another obvious requirement regarding the derivation of formulae is that the process be completely understood. It is not possible to attach a precise mathematical formula to a process unless that process is thoroughly understood. In the posting "The Progression Of Knowledge" on this blog, I explained how the difference between science and mathematics is that science concerns that which we partially understand while the realm of mathematics is that which is completely understood.
We do just fine at deriving formulae for scientific processes and the behavior (behaviour) of inanimate matter. But what about our understanding of human beings?
Humans are extremely complex. But while we are extremely complex, we are not infinitely complex. Somewhere out there is a formula that accurately describes anything to do with humans, not in the general terms of philosophy but in a precise mathematical equation.
But if we try to derive it, we run into the roadblock of the fact that we cannot be smarter than ourselves and we would have to be to derive such a formula. So while the formula must exist, because we are of less than infinite complexity, not only can we not be smarter than ourselves, we certainly cannot be smarter than everyone else combined. So, the formula remains out of reach.
But what about supercomputers, or networks of supercomputers? Or grid computing, harnessing the processors of thousands of desktop computers? What if we had such computing power working for weeks or months on deriving formulae that might be out of the reach of ordinary human minds?
This would be particularly useful in languages. The bottleneck of computer processing is the information that we have to give the computer to work with. But that would not be a factor with language analysis. I have written previously about possible ways to translate between languages on this blog and in my book "The Patterns Of New Ideas" but previous concepts all involve pre-translation of sentences.
Providing a word-for-word translation between two languages is fairly simple. But that is only the beginning of actual translation because grammar and syntax is different from one language to another. Chances are that a word-for-word translation would produce little but gibberish.
Word usage is different. In a simple example, if we wanted to know how a machine operated in English, we would ask "How does it work?". But in French, we would have to ask the equivalent of "How does it walk?".
But if computer compression software routinely examine text and graphics, looking for patterns in the data so that it can be compressed for more efficient storage and faster download, then why not examine entire languages and break down all the rules of grammar and syntax into formulae? Combine this with a simple word-for-word dictionary and it should be simple for computers to provide translation from one language to another.
Even with all that computers are doing now, there is certainly much more that they could be doing but which has not yet been thought of and derivation of human formulae is certainly among them.
There is a general agreement among physicists that all that exists is really numbers and mathematics. Everything is numbers being manifested in some way, there are no exceptions. An obvious example is the chemical elements. An element is defined by the number of protons in it's nucleus, as displayed on the periodic table.
There is a simple, yet far-reaching implication of everything really being numbers. This must mean that every system and every process in the universe could potentially be expressed as a mathematical formula. There can never be anything that does not have a formula describing it.
My thought is that the next major frontier in science is how we fit into the universe. Remember how I have described in the cosmology blog that we see and experience the universe the way we do not just because of what it is, but also because of what we are. The next step is to get a look at the universe from "outside ourselves".
The way to go about this is with the knowledge that everything that exists can be broken down into a formula. The trouble is that we are of a certain level of complexity, and we can only analyze things enough to break them down into formulae if they are less complex than we are. We are not able to understand those things that may be more complex than we are, at least not enough to derive a formula. Just as the average cat does not understand the processes of planetary formation, there must be some things about the universe that are simply beyond us.
If everything that exists can be broken down into a formula, that must mean that somewhere out there there is a formula that precisely describes and predicts our behavior (behaviour). We cannot arrive at this formula because to do this, we would have to be "smarter than ourselves", which is impossible.
We saw in "The Progression Of Knowledge", on this blog, that to describe something with mathematics it is necessary to completely understand it. Mathematics is the realm of that which we completely understand, while science is the realm of that which we partially understand. We get still more subjective, and further away from mathematics, when we describe something as "it's an art, not an exact science".
But what is mathematics, what is science, and what is an art, depends on what we could call our "complexity perspective". We have a certain level of complexity, which is much higher than that of our surrounding environment of inanimate matter but is still limited. There are actually formulae for everything, but many of these particularly for those concerning ourselves and our nature, are beyond our reach due to our complexity perspective. I have written about this previously, in "Human Formulae" on this blog, but today I want to add more to it.
These unreachable formulae, which can describe everything that there is, are what I call "outer mathematics". The inner formulae are the ones that are within our reach by observation and reasoning. Once in a while, someone has a leap of insight that takes us beyond our usual limits and leads us to a new formula such as Einstein's E = MC squared, describing the apparent amount of energy contained in matter.
Complexity is a related topic. On the patterns and complexity blog, I have described what a tremendous advantage it would be to us if we could begin quantifying complexity. This means putting an actual number on the complexity of something, not just expressing it in subjective terms such as "less complex than" or "much more complex than".
But, once again, complexity is a matter of our perspective resulting from our own complexity. Complexity is not something that we can measure with a ruler or a meter, I explained how it will require novel ways of measurement.
For example, we know that the more complex something is the more there is that can potentially go wrong with it. Thus, we could measure the complexity of the human body by going through medical journals and counting all of the things that can possibly go wrong with the body. This would not, however, give us the absolute complexity of the body but only the complexity level relative to that of the surrounding inanimate matter.
As another example, we could put a number on the relative complexity of a society in the year 1900, in comparison with today, by counting the total number of job descriptions in the society. The more complex the society, the more different jobs there would be.
What about time? Since we can now see that the passage of time is something within ourselves and our nature, as described in detail on the cosmology blog, http://www.markmeekcosmology.blogspot.com/ , there must be a formula somewhere describing how our consciousness moves along the strings of matter composing our bodies and brains at what we perceive as the speed of light. If we could just obtain this formula, we might be able to do all kinds of things with time.
It has been said that, with regard to science, the Nineteenth Century was the century of chemistry, the Twentieth Century was the century of physics and the Twenty-First Century will be the century of biology.
The processes of living things have not yet been broken down into formulae in anything like the same way as chemical processes or the forces of nature. This is simply because of the limitations of our complexity perspective, we are living things ourselves and we cannot be "smarter than ourselves" so that we can derive the formulae that define and describe us.
It seems clear to me that the next frontier in science is to put the ever-more powerful supercomputers to work to give us a view of the universe, and how we are a part of it, that we cannot see because of our complexity perspective in the same way that the powerful telescopes of the Twentieth Century gave us a view of the physical universe that we could not see with our eyes alone. Just as there was a universe of galaxies that we cannot see on our own, there is a realm of "outer mathematics" that we cannot access on our own but can only access from outside ourselves.
However, this axiom is considered to be so self-evident that it really does not need to be proven. Just the fact that this system of geometry has served satisfactorily for nearly 3,000 years can be considered as proof enough of it's truth.
Today, I would like to introduce an axiom. Although the axiom cannot actually be proven, I consider it to be self-evident in it's truth. It is that any given system can be described by a mathematical formula, as long as the system is of less than infinite complexity. A formula exists to describe any system, either in it's present state or how it was formed, whichever is more compact.
Since there is a finite amount of space and matter in the universe, it must be of less than infinite complexity and thus there is a formula out there somewhere that describes the entire universe.
There is a clear rule that I can see regarding the derivation of formulae (the plural of formula is formulae). To discern a formula in some process, the observer must necessarily have more complexity in their mental processes than is present in the process being observed. In other words, the formula governing the process will only be apparent to the observer if the observer is "smarter" than the process being observed.
Another obvious requirement regarding the derivation of formulae is that the process be completely understood. It is not possible to attach a precise mathematical formula to a process unless that process is thoroughly understood. In the posting "The Progression Of Knowledge" on this blog, I explained how the difference between science and mathematics is that science concerns that which we partially understand while the realm of mathematics is that which is completely understood.
We do just fine at deriving formulae for scientific processes and the behavior (behaviour) of inanimate matter. But what about our understanding of human beings?
Humans are extremely complex. But while we are extremely complex, we are not infinitely complex. Somewhere out there is a formula that accurately describes anything to do with humans, not in the general terms of philosophy but in a precise mathematical equation.
But if we try to derive it, we run into the roadblock of the fact that we cannot be smarter than ourselves and we would have to be to derive such a formula. So while the formula must exist, because we are of less than infinite complexity, not only can we not be smarter than ourselves, we certainly cannot be smarter than everyone else combined. So, the formula remains out of reach.
But what about supercomputers, or networks of supercomputers? Or grid computing, harnessing the processors of thousands of desktop computers? What if we had such computing power working for weeks or months on deriving formulae that might be out of the reach of ordinary human minds?
This would be particularly useful in languages. The bottleneck of computer processing is the information that we have to give the computer to work with. But that would not be a factor with language analysis. I have written previously about possible ways to translate between languages on this blog and in my book "The Patterns Of New Ideas" but previous concepts all involve pre-translation of sentences.
Providing a word-for-word translation between two languages is fairly simple. But that is only the beginning of actual translation because grammar and syntax is different from one language to another. Chances are that a word-for-word translation would produce little but gibberish.
Word usage is different. In a simple example, if we wanted to know how a machine operated in English, we would ask "How does it work?". But in French, we would have to ask the equivalent of "How does it walk?".
But if computer compression software routinely examine text and graphics, looking for patterns in the data so that it can be compressed for more efficient storage and faster download, then why not examine entire languages and break down all the rules of grammar and syntax into formulae? Combine this with a simple word-for-word dictionary and it should be simple for computers to provide translation from one language to another.
Even with all that computers are doing now, there is certainly much more that they could be doing but which has not yet been thought of and derivation of human formulae is certainly among them.
There is a general agreement among physicists that all that exists is really numbers and mathematics. Everything is numbers being manifested in some way, there are no exceptions. An obvious example is the chemical elements. An element is defined by the number of protons in it's nucleus, as displayed on the periodic table.
There is a simple, yet far-reaching implication of everything really being numbers. This must mean that every system and every process in the universe could potentially be expressed as a mathematical formula. There can never be anything that does not have a formula describing it.
My thought is that the next major frontier in science is how we fit into the universe. Remember how I have described in the cosmology blog that we see and experience the universe the way we do not just because of what it is, but also because of what we are. The next step is to get a look at the universe from "outside ourselves".
The way to go about this is with the knowledge that everything that exists can be broken down into a formula. The trouble is that we are of a certain level of complexity, and we can only analyze things enough to break them down into formulae if they are less complex than we are. We are not able to understand those things that may be more complex than we are, at least not enough to derive a formula. Just as the average cat does not understand the processes of planetary formation, there must be some things about the universe that are simply beyond us.
If everything that exists can be broken down into a formula, that must mean that somewhere out there there is a formula that precisely describes and predicts our behavior (behaviour). We cannot arrive at this formula because to do this, we would have to be "smarter than ourselves", which is impossible.
We saw in "The Progression Of Knowledge", on this blog, that to describe something with mathematics it is necessary to completely understand it. Mathematics is the realm of that which we completely understand, while science is the realm of that which we partially understand. We get still more subjective, and further away from mathematics, when we describe something as "it's an art, not an exact science".
But what is mathematics, what is science, and what is an art, depends on what we could call our "complexity perspective". We have a certain level of complexity, which is much higher than that of our surrounding environment of inanimate matter but is still limited. There are actually formulae for everything, but many of these particularly for those concerning ourselves and our nature, are beyond our reach due to our complexity perspective. I have written about this previously, in "Human Formulae" on this blog, but today I want to add more to it.
These unreachable formulae, which can describe everything that there is, are what I call "outer mathematics". The inner formulae are the ones that are within our reach by observation and reasoning. Once in a while, someone has a leap of insight that takes us beyond our usual limits and leads us to a new formula such as Einstein's E = MC squared, describing the apparent amount of energy contained in matter.
Complexity is a related topic. On the patterns and complexity blog, I have described what a tremendous advantage it would be to us if we could begin quantifying complexity. This means putting an actual number on the complexity of something, not just expressing it in subjective terms such as "less complex than" or "much more complex than".
But, once again, complexity is a matter of our perspective resulting from our own complexity. Complexity is not something that we can measure with a ruler or a meter, I explained how it will require novel ways of measurement.
For example, we know that the more complex something is the more there is that can potentially go wrong with it. Thus, we could measure the complexity of the human body by going through medical journals and counting all of the things that can possibly go wrong with the body. This would not, however, give us the absolute complexity of the body but only the complexity level relative to that of the surrounding inanimate matter.
As another example, we could put a number on the relative complexity of a society in the year 1900, in comparison with today, by counting the total number of job descriptions in the society. The more complex the society, the more different jobs there would be.
What about time? Since we can now see that the passage of time is something within ourselves and our nature, as described in detail on the cosmology blog, http://www.markmeekcosmology.blogspot.com/ , there must be a formula somewhere describing how our consciousness moves along the strings of matter composing our bodies and brains at what we perceive as the speed of light. If we could just obtain this formula, we might be able to do all kinds of things with time.
It has been said that, with regard to science, the Nineteenth Century was the century of chemistry, the Twentieth Century was the century of physics and the Twenty-First Century will be the century of biology.
The processes of living things have not yet been broken down into formulae in anything like the same way as chemical processes or the forces of nature. This is simply because of the limitations of our complexity perspective, we are living things ourselves and we cannot be "smarter than ourselves" so that we can derive the formulae that define and describe us.
It seems clear to me that the next frontier in science is to put the ever-more powerful supercomputers to work to give us a view of the universe, and how we are a part of it, that we cannot see because of our complexity perspective in the same way that the powerful telescopes of the Twentieth Century gave us a view of the physical universe that we could not see with our eyes alone. Just as there was a universe of galaxies that we cannot see on our own, there is a realm of "outer mathematics" that we cannot access on our own but can only access from outside ourselves.
Thursday, June 18, 2009
The Progression Of Knowledge
I have developed a way of thinking about how society progresses in the quest for scientific knowledge. Have you ever wondered about why mathematics and science are two separate subjects in school? Here is my version of the progression of knowledge.
Mathematics is for the things that we fully understand and science is for the things that we only partially understand. It is only when we fully understand the way something operates, such as a process in nature, that we describe it in terms of mathematics. Of course, science and mathematics fit closely together, the backbone of any of the physical sciences is mathematics. I define science as that which we cannot yet describe completely with mathematics because we do not have a complete understanding of it.
The difference between mathematics and science is the same as the difference between words and numbers. Words are science and numbers, of course, are mathematics. Words are less precise than numbers but have much greater flexibility and subjectivity that is necessary to describe that which is not completely understood. To make possible a description of something in terms of mathematics, all relevant factors must be thoroughly understood. When this is not the case, when it is only partially understood, it is the realm of science and words rather than mathematics.
Everything is really mathematics at it's most fundamental level, it is when we do not thoroughly understand it's workings that we classify it as science. The word "science" means "knowledge" but I think it could better be defined as "in the process of being understood". It is when we can apply definite numbers to a process that we really understand it.
Here is my definition of the knowledge progression: Information moves from the unknown or from superstition to the realm of science as it becomes understood and from there to the realm of mathematics as it becomes completely understood. Unknown - Science - Mathematics.
The chemical elements, for example, can be easily described in terms of mathematics because the very definition of a particular element is the number of protons in the nucleus. The calendar, the course of a year as the earth moves around the sun, was once the realm of science but is now that of mathematics because it is thoroughly understood. The measurement of the height of a tower by the length of it's shadow would also be considered as mathematics because there is no mystery to the process, it is well understood. We do not yet thoroughly understand why like electric charges repel and unlike charges attract so although this seems like it could be described easily mathematically, it is still considered as science.
All we have to do to tell how far along we are in understanding the nature of reality is to look inside a school. As long as science and mathematics are considered as separate subjects, it goes to show that we do not fully understand the operation of reality. When we do fully understand the operation of reality, it will be described primarily in mathematical terms and science will become one with mathematics.
Suppose there was a math book illustrating all mathematical processes and all relevant examples of each process and also a science book describing the sum of scientific knowledge. As knowledge advanced, the science book would decrease while the math book increased but the science book would decrease faster than the math book increased.
This also goes to validate my Theory of Primes, that all of reality consists of fundamental patterns. The way I see it, the categorization of the physical sciences into chemistry, physics, astronomy, etc. is also evidence of our incomplete knowledge. If we did have complete knowledge, these fields would merge together and into mathematics. When we get closer to complete understanding, specialization of topic will give way to categorization by pattern as is done in mathematics books. There will be no more chemistry, physics and, astronomy but only mathematical patterns.
On my patterns and complexity blog, http://www.markmeekpatterns.blogspot.com/ , I pointed out how coincidences that we observe can be a powerful tool to measure complexity in certain circumstances. The complexity section of that blog is about the tremendous benefits that we would gain if we could only quantify complexity. That is, put an actual numerical measurement on it instead of describing it in vague and subjective terms.
My definition of coincidence is a random reduction in apparent complexity, as seen by the observer. A reverse coincidence is a random increase in apparent complexity. Each coincidence must be balanced by a reverse coincidence that is equal in magnitude.
The ideal example of coincidence could be a call center. Suppose the call center has one hundred operators, but that you get the same few operators every time you call. This would be a coincidence that causes you to perceive the center as being less complex than it actually is. But if you called a hundred times and got a different operator every time, this would be a reverse coincidence that might make you think that the center was actually much more complex than it actually is.
There is actually no such thing as either a coincidence or a reverse coincidence. Both are only a matter of our perspective of incomplete understanding. Coincidences are somewhat like a mirage, the shimmering water mirage seen ahead in the distance on a hot day on flat ground. There appears to be water but when you arrive at where the water appears to be, it has moved further back.
Likewise, the more understanding we have of whatever system we are observing, the fewer coincidences and reverse coincidences we will observe. Neither actually exist and once we understand everything about a system of some kind, we will observe no more of either coincidences or reverse coincidences.
There is no such thing as a coincidence because any coincidence must be balanced by a reverse coincidence somewhere else in the system. If we do not see this balance, then we do not completely understand the system. Coincidences and reverse coincidences are perspective illusions which indicate that we have less than complete understanding of the system being observed.
A coincidence exists only when we do not fully understand it. Suppose we had four people walk in the same direction with equal space between them. Now suppose that someone happened to be walking by on the opposite side of the road. They might think "What a coincidence, those people walking just happen to have equal space between them".
If we could really develop an eye for coincidences, they would also be a powerful measurement tool in the progression of knowledge. We know what we know, but usually do not know what we don't know. When observing a system of some type, such as a galaxy or a bee hive, suppose we could keep a close count of every coincidence and reverse coincidence that we see and, if possible, put some value on it. When we got to the point where we saw none of either coincidences or reverse coincidences, we would know that we then knew about all that we could practically know about that system.
This concept makes partial values useful. If, when observing a system of some kind, we observed a certain value of coincidences and a certain value of reverse coincidences. First, we would know that we could assume the higher value of the two for both because coincidences and reverse coincidences must balance out.
Then, if we learned more about the system and then made another observation and this time logged only half the previous value for coincidences and reverse coincidences, we would know that we had progressed halfway in the progression of knowledge.
PART TWO
Since the universe is not infinite, the body of knowledge that we can possibly have cannot be infinite either. There must be a day in our future when, at least theoretically, we will reach the point where we know all that we can practically know. The question is: where do we, with our present accumulation of knowledge, stand with regard to that point?
In Part One, there are two possible methods described for answering this question. One, that more and more of our knowledge will be expressed as mathematics rather than as words and two, the use of apparent coincidences as a measurement of where we stand with regard to knowledge.
Today, I would like to describe another possible way to measure our progression of knowledge.
Humans began to learn and record knowledge. At first, every new fact would be something completely new. But as time went on, there would be an increasing proportion of newly-learned facts that are not totally new, but are a previously-unseen connection between facts that are already known. The more facts that we have already, the higher the likelyhood that a new fact will be a connection between two already-known facts, rather than something totally new.
We could call this first- and second-tier learning. But this is only an illusion of our perspective. There are no such tiers of facts in absolute reality.
As an example, the discovery of electrons was a totally new fact even though we already knew about the atoms of which electrons are a part. Their discovery was not a connection between previously-known facts, this was first-tier learning. Now, suppose that it was discovered that zebras like pumpkins. This would be second-tier learning, since it would be a connection between two entities that we already know about.
If we could get used to dividing newly-discovered facts into these two categories, this should give us a good idea about where we stand in the progression of knowledge. As we move along, an increasing proportion of newly-discovered facts should be second-tier, a connection between two previously-known facts. As we near the maximum potential of our practical knowledge, virtually every new fact should be a connection between two previously-known facts rather than a fact that is totally new to us.
Thus, this can be used as a measurement tool.
Mathematics is for the things that we fully understand and science is for the things that we only partially understand. It is only when we fully understand the way something operates, such as a process in nature, that we describe it in terms of mathematics. Of course, science and mathematics fit closely together, the backbone of any of the physical sciences is mathematics. I define science as that which we cannot yet describe completely with mathematics because we do not have a complete understanding of it.
The difference between mathematics and science is the same as the difference between words and numbers. Words are science and numbers, of course, are mathematics. Words are less precise than numbers but have much greater flexibility and subjectivity that is necessary to describe that which is not completely understood. To make possible a description of something in terms of mathematics, all relevant factors must be thoroughly understood. When this is not the case, when it is only partially understood, it is the realm of science and words rather than mathematics.
Everything is really mathematics at it's most fundamental level, it is when we do not thoroughly understand it's workings that we classify it as science. The word "science" means "knowledge" but I think it could better be defined as "in the process of being understood". It is when we can apply definite numbers to a process that we really understand it.
Here is my definition of the knowledge progression: Information moves from the unknown or from superstition to the realm of science as it becomes understood and from there to the realm of mathematics as it becomes completely understood. Unknown - Science - Mathematics.
The chemical elements, for example, can be easily described in terms of mathematics because the very definition of a particular element is the number of protons in the nucleus. The calendar, the course of a year as the earth moves around the sun, was once the realm of science but is now that of mathematics because it is thoroughly understood. The measurement of the height of a tower by the length of it's shadow would also be considered as mathematics because there is no mystery to the process, it is well understood. We do not yet thoroughly understand why like electric charges repel and unlike charges attract so although this seems like it could be described easily mathematically, it is still considered as science.
All we have to do to tell how far along we are in understanding the nature of reality is to look inside a school. As long as science and mathematics are considered as separate subjects, it goes to show that we do not fully understand the operation of reality. When we do fully understand the operation of reality, it will be described primarily in mathematical terms and science will become one with mathematics.
Suppose there was a math book illustrating all mathematical processes and all relevant examples of each process and also a science book describing the sum of scientific knowledge. As knowledge advanced, the science book would decrease while the math book increased but the science book would decrease faster than the math book increased.
This also goes to validate my Theory of Primes, that all of reality consists of fundamental patterns. The way I see it, the categorization of the physical sciences into chemistry, physics, astronomy, etc. is also evidence of our incomplete knowledge. If we did have complete knowledge, these fields would merge together and into mathematics. When we get closer to complete understanding, specialization of topic will give way to categorization by pattern as is done in mathematics books. There will be no more chemistry, physics and, astronomy but only mathematical patterns.
On my patterns and complexity blog, http://www.markmeekpatterns.blogspot.com/ , I pointed out how coincidences that we observe can be a powerful tool to measure complexity in certain circumstances. The complexity section of that blog is about the tremendous benefits that we would gain if we could only quantify complexity. That is, put an actual numerical measurement on it instead of describing it in vague and subjective terms.
My definition of coincidence is a random reduction in apparent complexity, as seen by the observer. A reverse coincidence is a random increase in apparent complexity. Each coincidence must be balanced by a reverse coincidence that is equal in magnitude.
The ideal example of coincidence could be a call center. Suppose the call center has one hundred operators, but that you get the same few operators every time you call. This would be a coincidence that causes you to perceive the center as being less complex than it actually is. But if you called a hundred times and got a different operator every time, this would be a reverse coincidence that might make you think that the center was actually much more complex than it actually is.
There is actually no such thing as either a coincidence or a reverse coincidence. Both are only a matter of our perspective of incomplete understanding. Coincidences are somewhat like a mirage, the shimmering water mirage seen ahead in the distance on a hot day on flat ground. There appears to be water but when you arrive at where the water appears to be, it has moved further back.
Likewise, the more understanding we have of whatever system we are observing, the fewer coincidences and reverse coincidences we will observe. Neither actually exist and once we understand everything about a system of some kind, we will observe no more of either coincidences or reverse coincidences.
There is no such thing as a coincidence because any coincidence must be balanced by a reverse coincidence somewhere else in the system. If we do not see this balance, then we do not completely understand the system. Coincidences and reverse coincidences are perspective illusions which indicate that we have less than complete understanding of the system being observed.
A coincidence exists only when we do not fully understand it. Suppose we had four people walk in the same direction with equal space between them. Now suppose that someone happened to be walking by on the opposite side of the road. They might think "What a coincidence, those people walking just happen to have equal space between them".
If we could really develop an eye for coincidences, they would also be a powerful measurement tool in the progression of knowledge. We know what we know, but usually do not know what we don't know. When observing a system of some type, such as a galaxy or a bee hive, suppose we could keep a close count of every coincidence and reverse coincidence that we see and, if possible, put some value on it. When we got to the point where we saw none of either coincidences or reverse coincidences, we would know that we then knew about all that we could practically know about that system.
This concept makes partial values useful. If, when observing a system of some kind, we observed a certain value of coincidences and a certain value of reverse coincidences. First, we would know that we could assume the higher value of the two for both because coincidences and reverse coincidences must balance out.
Then, if we learned more about the system and then made another observation and this time logged only half the previous value for coincidences and reverse coincidences, we would know that we had progressed halfway in the progression of knowledge.
PART TWO
Since the universe is not infinite, the body of knowledge that we can possibly have cannot be infinite either. There must be a day in our future when, at least theoretically, we will reach the point where we know all that we can practically know. The question is: where do we, with our present accumulation of knowledge, stand with regard to that point?
In Part One, there are two possible methods described for answering this question. One, that more and more of our knowledge will be expressed as mathematics rather than as words and two, the use of apparent coincidences as a measurement of where we stand with regard to knowledge.
Today, I would like to describe another possible way to measure our progression of knowledge.
Humans began to learn and record knowledge. At first, every new fact would be something completely new. But as time went on, there would be an increasing proportion of newly-learned facts that are not totally new, but are a previously-unseen connection between facts that are already known. The more facts that we have already, the higher the likelyhood that a new fact will be a connection between two already-known facts, rather than something totally new.
We could call this first- and second-tier learning. But this is only an illusion of our perspective. There are no such tiers of facts in absolute reality.
As an example, the discovery of electrons was a totally new fact even though we already knew about the atoms of which electrons are a part. Their discovery was not a connection between previously-known facts, this was first-tier learning. Now, suppose that it was discovered that zebras like pumpkins. This would be second-tier learning, since it would be a connection between two entities that we already know about.
If we could get used to dividing newly-discovered facts into these two categories, this should give us a good idea about where we stand in the progression of knowledge. As we move along, an increasing proportion of newly-discovered facts should be second-tier, a connection between two previously-known facts. As we near the maximum potential of our practical knowledge, virtually every new fact should be a connection between two previously-known facts rather than a fact that is totally new to us.
Thus, this can be used as a measurement tool.
Subscribe to:
Posts (Atom)