Probability, chaos and the nature of creation

Probability and an elementary, almost axiomatically governing rule of the universe (thoughts given through the analogy of a complex puzzle)

I will attempt in this article to describe my views on how probability plays an intrinsic role in the governing of chaos and the universe as we know it.
Many subscribe to the belief that the universe is fundamentally predictable through mathematics. In fact Einstein once famously said that "God does not play dice with the universe". It turned out, in a sense, that Einstein was wrong. But he was wrong only in the sense that betting companies are wrong to hedge their bets with making money through gambling. The only thing that makes betting companies money is that a probability describing a single event never has a certain outcome, but is in fact a way of describing a myriad of many complex factors which are all mathematical and will hence yield the same result in a great enough sample. Remember that if anything can be conceived to possibly (or impossibly) happen it is possible. It is just that the more likely events occur a higher proportion of the time. Just as we must define limits for integration, without which the sum of any specific value is zero, probability is meaningless when applied to single values. Probabilities are proportions of a sample on a large scale. As the sample size tends to infinity, it is 100% certain that the probabilities will also tend to the actual proportions obtained from the infinite sample.
In fact, the classical mechanics of the universe are simply a large scale description of predictable patterns in probability on a very large scale: the laws which govern these mechanics provide the footholds for mathematics and are maths' only claim to validity. Force is equal to mass multiplied by acceleration because of a repertoire of different subatomic forces, energies, masses - among other things - that all interplay to produce this predictable pattern on the larger scale. At the smallest scale the universe is in fact still affected by what goes on around it. So, in fact one day we might in fact realise - if such a statement is true - that the quantum mechanics are in fact affected by the large scale mechanics of physics and visa versa.
This might be another "strange loop" which could further support Hofstadter's opinion/hypothesis that strange loops are very important. In fact, they might prove to be a stepping stone in understanding how patterns in the universe arise.
On to my main point - an essay to describe evolution in terms of an infinitely complex puzzle and to attempt to shed some of my self-validated insight on intelligence's origins and nature.
Think of an infinitely complex maze, further convoluted by the fact that the maze is affected in strange ways by the way you move through it, so going through the maze to a certain spot - you may only return to your original state through backtracking your steps and actions exactly to your starting point. This can be likened to travelling back in time. You cannot take shortcuts through the maze. Think of intelligence as one possible location in the maze. The achievement of reaching this location (creating intelligence) is only possibly attained through one single route, since there is only one possible route to any single place in the maze. Even if two different routes are exactly the same but for one footstep for example taking a step with the right foot rather than the left foot, this small effect will produce a butterfly effect, meaning that a difference between the two paths will arise which shall become more and more pronounced as you progress further and further away from the location at which you committed this deed.
In fact, the pathways can be thought of as progress through time and the different pathways, in this case, as evolutionary branches on the evolutionary tree of life. In fact, there are many other situations in which this analogy applies anywhere where probability and infinite possibilities play a key role.
Evolution follows the concept of probability. It was infinitely unlikely that "intelligence" as we know it should ever have been developed. In fact, intelligent humans (homo sapiens) have only existed for the equivalent of the blink of an eye in the timeline of the universe, even in the comparatively minute period of existence of life on earth. Had one idiosyncratic genetic mutation not occurred at exactly the right time and place in the past, intelligence might never have existed - or perhaps existed but in an altered form. In fact, we also have to think outside of the internal development of humans. For instance, what could have happened if the individual human or lifeform in which this mutation occurred was killed before it could reproduce. That lifeform would never have passed on the line of material necessary for humans to develop. Therefore the events in the past leading up to this were all important in the timeline in which intelligence was created. In fact, the external effect need not be as extreme as death, but only a small interaction occurring in a different way. Generally - as I alluded to earlier through mentioning the butterfly effect - the further back a change occurs in timelines, the more exponential its effects will become in the future. This is simply due to the nature of chaos.
Chaos is a thing we use to describe infinitely complex physical - or other - processes which we cannot possibly predict - since such an attempt would be paradoxical. This would be because in the act of trying to assess the future of a chaotic system, we ourselves would be changing its course, and would have to include the act of our own prediction in the context: the instrument affects the experiment. It is in fact impossible to ever conduct any "experiment" whether that be a thought experiment or a physical experiment, without in fact affecting the outcome itself. Such an experiment would need to infinitely recurrently apply corrections to the experiment to account for the influence of the experimenting tools themselves. One such thing is the theoretical model of the universe in a computer, which would have to include the computer itself and its effects. This is my view of what we mean by relativity in the universe, and why I believe constancy is the only possible perspective which could help us truly understand how the universe works.
If the impossibility of this supposed trial by error (natural selection in other words) method of obtaining a pathway to intelligence seems too unlikely, then consider this: intelligence did not in fact exist until the moment it was created. We only place such a high value on intelligence because it mystifies us: we do not fully understand the universe or intelligence, because we are using intelligence itself to understand it. In fact, it is questionable whether 'understanding' is something inherent in the universe, or simply another function of intelligence itself - something created from nothing. This also goes for mathematics, science and the content of this article, all of which are functions or consequences of intelligence.
It is almost certain that something infinitely more amazing than intelligence could have been created through natural selection, and that something infinitely more amazing than that could also have been created ad infinitum. There will always be a better possibility for perfection would imply that there are a finite number of outcomes. This can be explained through the nature of creating something from nothing: that something is not defined and so we assume it has "infinite value" - because 'something' is every possibility ever conceived or not conceived. That is the brilliance of creation and possibly why mathematics has evolved as a tool used to describe the universe:
I believe explanation of the power of mathematics can be found through starting with the simple statement 0=0. The rules of algebra dictate that we may apply any transformation to either side as long as we apply it to the other. In the mathematical sense, we might add 2 to either side to give 2=2. But this could also be written 1+1=2. I firmly subscribe to the belief that every action has an equal and opposite reaction is an underlying principle in the creation of the universe. If something is created, its equal and opposite must also be created. Through various transformations things might appear not to sum to 0 in the universe: there are a growing multitude of different physical phenomena that we must look at and consider in describing the universe. Yet, I believe that if all things are reduced to their simplest form - rearranging the equation - this will not result in a solvable equation with universal variables, but a simple statement that can be reduced to 0=0. Of course you would have to "solve simultaneous equations on a grand scale" to achieve this, but in doing so would better understand the patterns of the universe. I think that you must think of forces, energy, fields etc. to all be intrinsically linked and to be of the same sort of substance (i.e. things which exist in this universe the traditional sense) in order for this to be possible, however the universe as we know it is such a complicated soup of all these things that it becomes difficult, almost impossible, to make sense of it in this fashion. I also believe that relativity arises from everything having an equal and opposite as shown by the diagram below, which I shall leave for the reader to consider:

Do you believe in fate?

We oftentimes hear about the suggestion that there is such a thing as "fate", "destiny", a "plan" for humankind. These words are tossed around in everyday speech in a myriad of different contexts, whether it be the often religious notion that God has a plan for humanity and that things were set out for us from the very start or perhaps the astrological notion that the stars dictate the way different sorts of people will act each day due to various 'correlations'. Personally, I don't put much faith in astrology, but others do and recently I have come to see reason for them to do so. Why, you may ask, would any extra-terrestrial happening dictate what I might feel like eating for breakfast tomorrow. Well, perhaps these things don't affect each other directly. It is the notion of cause and effect and there is often a misnomer about what people mean when they say two different events are related to each other. In the case of the positions of the planets and the stars, what is to say that certain movements of these objects in space could actually be related to the actions of is on earth, not because they themselves caused them, but because there is a meta-cause of both these things. It is the same problem as the idea of the number of drownings going up at the same time as ice cream sales. This does not mean that one causes the other, but that a higher-order cause was involved in bringing about both, namely the fact that both these statistics peak in the summer because more people go to the seaside when the weather is hotter and swim as well as being more inclined to buy a nice, cold ice-cream cone.

Consequently you might question what this higher-order cause might be, and it is a very good question to ask. Perhaps it is a very complicated cause to do with time. Time is one of the only things that links everything in the universe with everything else, among other theories of humans such as the idea of the three spacial dimensions. Perhaps, the pseudoscientific notion of biorhythms comes into play and means that each month the stars will be in certain positions and at the same time, purely on the basis of the regular rhythm of life, you will also be full of a certain hormone which makes you more likely to feel a certain way. In this sense looking at the stars to determine our fate is completely redundant, we may as well make less work for ourselves by analysing what time it is and our past history to determine a more accurate and less confusing view of why we might feel a certain way, rather than simply because 'the moon has passed close to the line of the equator'.

Everything in the world, and in the universe as a whole for that matter, obeys a regular rhythmic pattern dictated by the forces and objects around it. These ideas stem from the most basic physical principles we regard as 'most likely true based upon our current knowledge', and were discovered by scientists like Newton and Einstein among many many others. This is why we can predict the position of the earth at a certain time, or the position of another planet relative to the earth at that time. We would see it as strange to think that tomorrow Mars would suddenly, without reason, be moving much faster around the sun than it was today. We would have to see evidence for this, otherwise we would have to probably rethink the most basic, axiomatic principles governing the physical universe.

In fact this idea of these firstmost principles is very interesting. It is strange nowadays to use the word 'theory' to describe such things as gravity and atoms for example, since these 'theories' have become so well accepted, and seem so true that they are now almost always referred to as 'facts of life'. But of course, they are facts, but only in the realms of our own understanding. We have built other theories upon them and other theories came before them that they had to in some way agree with in order to be seen as credible. But the limit of our ability to test theories we make to determine whether they are true or not comes when we hit the barrier of what we are able to observe by any means about the universe around us. If we could in some way 'observe' time in some way then I am sure we would have a very different system of physics at the present moment. However much you think about it physics is at its roots a human explanation for something we do not fully understand and possibly never will. Just because something seems to fit, however well, with our understanding, in actuality it is never good enough to be regarded as real 'fact' since somewhere along the line, often at the very beginning we had to make an assumption, or a 'given statement' such as "all things fall down on earth". What is to say that they do? All that we have to observe is five basic senses at the end of it (not even in agreement with the number of recommended senses for something to be objective and not simply down to mere coincidence), and to be honest those alone will never be good enough to say for certain that all things fall down, or in fact that the objects and systems we interact with in everyday life are really what we see them as. At the end of it they are only viewed from our biased points of view. So where does the real truth lie? Well, in actual fact until the real truth - if there is one - is discovered for certain we have to believe every theory to be true in its own right, however crazy it might sound, since at the end of it everything is still only subjective to how credible we as a population think it to be, and that never equals certainty. For now however, I suppose our theories about life, mathematics, the universe and everything are all in actual fact true, since the concept of truth is, if you think about it, as much of a human invention as anything else. It belongs to the concept of logic and lies within the same thought system as Newton's laws of motion, Einstein's theory of relativity and the laws of thermodynamics and so all these things are true in that sense.

Coming back to my original idea about fate, there is a flaw in cause and effect - that is expressed as the very weird and wonderful notion of the human brain and consciousness. If everything, as most people believe it does, follows the currently accepted physical laws, then true randomness is in theory impossible, since everything must follow a rigid and structured system. By these premises that must mean that human thought is simply a direct result of the atoms and chemicals in our brains interacting with electrical signals in a complicated yet theoretically predictable manner meaning that fate has always been decided for us. This would also mean that if we were able to computer-generate a model of a human brain at a specific moment in time with every detail included, and programmed it using all the physical laws then this should mean the brain would work almost exactly as that of the person who's 'brain snapshot' was taken (this is a similar notion to modelling the atmosphere to predict the weather), give or take a few differences resulting from the absence of the external factors the person was subjected to: stimuli. But these differences are of course very important since in the long run they might add up to make for completely different paths of events. Of course, these stimuli would theoretically come from other predictable physical events and objects causing them which in theory could also be programmed into the computer. But of course these stimuli were in theory caused by other stimuli and so on and so forth until eventually you realise that to obtain an accurate model of what that person's brain would be doing at a certain time you would need to program the entire universe into the computer. Now, here comes the big problem - what about the computer itself, it of course is an external stimulus and part of the universe, so how do we program it into the equation? Well, as you may have guessed you would now need an infinite number of computer simulations each inside of one another to do this, much as you get with two mirrors placed in front of each other forming an infinite number of images within one another, which of course is impossible. But perhaps there is some truth in this: perhaps we ourselves are just one of an infinite number of sub and meta universes each inside each other in a never-ending chain. However, as we have seen with this theoretical computer simulation of the universe, there is perhaps a beginning. What could this beginning be? God perhaps? Well, again we are jumping to conclusions - my theory could possibly be false from it's very origins and therefore further reasoning would be futile, but it could just as well be true for all anyone knows. In a sense it is actually true by definition in the strange way I described before - true just as every other theory is. It just goes to show that seeing isn't actually believing, but the other way round. If you believe something, then it true by your own definition since the universe is a very, very relative place. What might be true for you may not be true for others. Because of my computer argument I can see how fate might simultaneously exist and not exist. To predict it all you would need would be a brain of infinite capacity - God as some might describe it. You might say this is impossible, but of course so was motion according to Zeno of Elea in his Achilles and the Tortoise paradox. What is impossible for someone may not be in another situation or train of thought for reasons that people are still trying to understand. That, I believe, is one of the beauties of life and consciousness.

Credit to Wikipedia for this image of an extract from the page on axioms... Just something to think about, is this truly true?

Credit to Godel Escher Bach among other things for inspiring me to write this article.