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.