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:
