Description comes from decay

international | sci-tech | opinion/analysis Sunday April 09, 2006 11:49 by Seán Ryan

A discussion of the God-like properties of Mathematics.

Chapter 3 of Book II

Imagine if Bob were the last human alive.

Imagine that his last coherent thought is the last ordered statement in the universe before Heat Death or whatever.

Imagine Adam, the first human and imagine that his first coherent thought is the first ordered thought in the universe.

Now imagine the whole scenario in reverse. From dust of maximum entropy, man is formed, after some thought man again becomes part of the dust of maximum entropy. If we look at this picture forwards through time we get the exact same picture.

What this says about entropy (to me) is that thought and entropy can be equated.

In a state of maximum entropy, time has no meaning or at least is not relative. In a state of maximum entropy Relativity ceases to exist.

There must exist an equation that allows maximum entropy to give rise to consciousness which in turn collapses back into maximum entropy. There is symmetry here.

I'm simplifying here when I suggest maximum entropy to consciousness and back to maximum entropy again. What I mean is consciousness and the rest of the multiverse. But consciousness is the strange one here in that consciousness by nature is never static. A consciousness may observe or interact with a static system provided it is not part of the system itself. After such an observation the system will no longer be static. The interesting consequence being that the system after being observed has its overall entropy increased but the consciousness has increased its knowledge base of the former system.

If we simplify this even further by dealing in terms of information the picture becomes very illuminating.

The static system contains information. In general terms this information would contain a description of the system. A single and simple quantum fluctuation (this can occur with or without the presence of a universe) alters this information.

The information content of a static system would never remain static and therefore the static system itself would become motive. Time and entropy would be created. The information content of this system would be dependant on conditions imposed by its previous information content. The system in other words would be dependant on its past (this is similar to memory) but at the same time not utterly bound by it.

Relativity is introduced because the system uses the knowledge of the past to illuminate the present and the future.

Or could it be that we are looking at two peaks and a trough on a sine wave?

When we look at a two dimensional sine wave we see a strange duality. We see that energy forever fluctuates and that we can calculate a value of the wave at any particular point by describing the height or the depth of that point. But we also note that the wave passes through many zero points.

We look at electricity in this fashion. In Ireland Alternating Current (AC) is fed into our homes at 220 volts. Its frequency is 50hz, this means that it will switch off and on fifty times a second.

This two dimensional sine wave is a very good representation of what is happening with an electrical voltage. Any information that is needed about this voltage can be derived from the sine wave that represents it.

There is however a problem with all of this. The problem is of course the zero points on the sine wave. Zero is nothing and nothing is an absolute and an absolute cannot exist in a relative universe.

This problem is resolved looking at it in higher dimensions. The addition of a single dimension allows us to look at the sine wave as a spring. If we held this spring beside a projection screen and shone a light at it, its shadow would be a two dimensional sine wave. If we rotated the spring so that the light was to shine through it we would have a shadow that depicted a two dimensional circle.

By viewing the process in higher dimensions the zero point is explained and it is shown not to be an absolute after all.

Let's take a look at mathematics.

Mathematics is a system that is governed by an inviolable set of laws. And it is an entity that remains a constant in a universe that does not allow for it, in that change is the nature of the universe. The laws of mathematics exist independently of existence itself.

Mathematics deals in absolute quantities that remain constant irregardless as to the motion of the observer. This in itself is important as it shows that mathematics is not bound by relativity and yet relativity can be described in mathematical terms.

For this and many other good reasons lots of people are coming to the belief that the idea of God is in fact mathematics.

At first this seems a preposterous idea and I suppose to some it must seem sacrilegious.

If some simple examples are looked at however, the more obvious of counter arguments can be obliterated.

If mathematics is God then mathematics is responsible for creation, and its fingerprint should be on each and every creation.

Any individual component or system within creation can only be described in terms of quantity. How much mass does it have, what is its momentum, where's it going, what colour is it, how many friends does it have etc.

The most simple of concepts, the concept of one's self.

I.

It even looks like a 1.

How about the ultimate in complexity, using just simplicity; the concept of the universe existing without me existing to conceptualise it. Nothing, zilch, nada or zero even.

Two numbers who are absolute in construction.

They can be expressed it terms of utmost simplicity; 1+0 =1.

Or they can be expressed in terms that cannot be understood; 1/0=?

It would seem that mathematics lie outside the bounds of reason, and that they probably define it.

The universe is a chaotic process rather than a random one. A chaotic process is a process that has a sensitive dependency on its initial starting conditions (the point of origin itself is a label that must be judged and applied by a conscious agent and it can be placed anywhere) but one that nonetheless becomes more complex with time and defies long term predictability. Randomness on the other hand implies no dependencies, sensitive or otherwise. Not only does a random number defy prediction, it defies generation. Simply put, a random number would be conditional on the terms that generate it and because this is so it cannot be random. It is no more possible to generate a random number that it is to predict one, this is the case because prediction is generation.

Sometimes our familiarity with numbers blinds us to some of their more Godlike or absolute qualities. For example, if I have an apple and I add another one I will have two apples, and yet the apples may not be similar, one might be red and the other green. One skyscraper plus one outhouse equal two buildings. Numbers in themselves try to be absolute descriptions but when we use them to try to describe anything we must introduce relativity. From this it can be seen that if there is a description that fits and sums the cosmos, that it must indeed be a mathematical one.

Try to imagine a universe that has no associated mathematical description. Try to imagine an event that has no mathematical component. Try to imagine the sum of your own knowledge without categorizing, counting or understanding. The very act of understanding, is itself a mathematical function, it is a summing of remembered pertinent knowledge followed by reduction and deduction.

Try to imagine a God without numbers. This would truly be a God without description. The bible does this a number of times; it describes God as a being with no beginning and no end. This is a creature that cannot be summed. Interestingly I think this way of looking at God should be used as an atheist's proof that God does not exist; that which has never existed has no beginning, and similarly that which has never existed has no end, everything else oscillates to a mathematical tune. Of course it might just be a three-dimensional look at a higher-dimensional structure. In order for creation to have happened, mathematics needs to have pre-existed and to have existed independently of creation. Mathematics exists without creation but creation cannot exist without mathematics.

If E = mC2 is an honest simplification and underlying explanation of the universe, then surely the concept that is God is an honest simplification and underlying explanation of mathematics.

This is all fine and cosy until one remembers that unlike God, the concept of that which is mind defies mathematical description. My comprehension of self pre-exists my mathematical comprehension and does so independently of numbers. Consciousness needs to have pre-existed mathematics. Mathematics has no independent existence outside realisation. Description has no meaning outside realisation and is in itself a thing from the past that has finally caught up with the observer.

Description either comes from decay or causes it.

Our old friend the electron via its quantum mechanical description can be described by a static model. We could describe it as being everywhere at every time and that only once it is observed does it appear to be a motive point particle that has definitely existed at a specific time and place.

Physicists tell us that an electron is a probability wave. They rate the chances of an electron being observed in terms of probability. However if there were no observer the chances of an observation being made is zero. An electron can be found at any point in space and time to some degree of probability. You could pick any point in space and time and you would never know for certain whether an electron was there until you looked for it. You could not decide there was zero probability of an electron being there before making an observation.

We consider zero in an absolute sense, but intuitively we understand its true relativistic meaning. Zero or nothing is the point at which some process or event evades detection by awareness, or in other words, it lies beyond the threshold of awareness. A consequence of this is that over time and similar to if indeed not because of entropy it will change. Science has regularly proved this by having to redefine the playing field many times over with new discoveries in particle physics. The ultimate aim of science is to prove nothing is impossible. It is my humble opinion that if this were taken as a given and the concept of limits be redefined or scrapped, that Science would make a lot more sense.

It often strikes me as funny that many excellent writers on the subject of Quantum Mechanics, tell us that it is a subject that is composed of some very counter-intuitive ideas and processes. This seems to say that the relativistic laws and laws of mathematics behave in a very logical fashion. It seems to me that it is the usage of mathematics and the relativistic laws that follows a logical pathway, but that the core subjects themselves have the same ethereal or wave-like qualities of Quantum Mechanics.

In a relativistic universe or multiverse, any reference phenomena at any time can be considered "The" absolute reference point in the universe or multiverse, and that everything else behaves relatively towards it. Mathematics for us is this absolute reference point and it's simply a universal case of tough shit that it possesses no meaning other than those we help define with its usage. And when you think about it, it too helps illustrate that the idea of God and Mathematics are similar. In that both are some kind of universal reference point that allow us to define ourselves and everything else.

Some might argue that what I have said so far might suggest that God has will but that mathematics has not and that this proves that God and Mathematics are not the same.

I'll not use logic to counter this argument. I'll simply refer to reality, the reality we observe and interact with, the reality that can be explained mathematically. I think mathematics has spoken much and that we have yet much to hear. I think mathematics though it be an abstract is nonetheless a facet of reality or more correctly a facet of consciousness. The fact it recognises no higher truth than itself is consistant with the idea of God rather than contrary and is in itself a fundemental act of self awareness.