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.