Thirteenth of October two thousand and twenty.
1. There is randomness without design.
2. If something is possible given infinite time it must happen.
3. Nietzsche's idea of the eternal return, also found in modern physics, John Barrow, Max Tegmark... Roger Penrose. There is no final state, things will eventually repeat.
4. In Nietzsche's cosmos time is infinite, events (space in which changing matter resides) are not.
5. This means given infinite time events will repeat infinitely. The Eternal return of the Same.
6. This will never reach a fixed and final state, as if it could, given an infinite past it would, must have, occurred.
7. The throw of a dice will repeat numbers. (Nietzsche's example). There is a probability that a number will repeat. A throw of 6, will repeat if one keeps throwing the die. There is a probability that a sequence will repeat, again Nietzsche's cosmos.
8. But this applies to any sequence. 3456134562... but also 11111... 33333... etc. (… = recurring infinitely)
9. 1111.... and 5555.... are contradictory. In Nietzsche's universe repetition occurs when all the possible variations are completed, so a complete repetition has to occur. Yet there is no reason why a day, this day cant repeat precisely, or this second. These are final states, but as is the repetition of all possibilities. That these other repetitions haven't occurred is ruled out as they obviously have not. So the whole set repeats but no subset. But given probability these subsets being possible MUST occur.
10. A contradiction is avoided by the idea of the identity of indiscernibles. If there is no way, physical or temporal to differentiate two events, they must be the same event. In the dice throw 111111... each 1 is identical. (to see them as not is to temporally space these, by physically spacing. But there is no way to do this within a universe.
11. Perfect Being and perfect Nothing cannot alter. (Hegel) Are delimited and fixed. This is the state that Nietzsche argues can't occur because it hasn't. However as above any repetition or a set of events is likewise no alteration if it is identical. The eternal return of the SAME. There is as above no reason why one identical repetition given infinite time will not prevail to the elimination of any other possibility, and this then contradicts other possibilities. That the whole set must repeat to exclusion of others, subsets endlessly repeating is a contradiction solved by the identity of indescribables, in which case nothing repeats. (we cannot step outside the universe to recognise this repetition, to count it.) A repetition of the same is impossible.
12. If the set of things is infinite, as well as time, then in such a universe endless repetition of the process can occur, as no identical repetition occurs but each repetition is novel. If the events of that process are also infinite they will be different. Deleuze's repetition of difference. In such a universe each repetition in its novelty will ensure a universe which becomes more complex, more sophisticated, i.e. 'develops'..
i.e. A simple universe of 2 bits.
Has 4 possible states before 1 or more will repeat.
Has two levels of 'sophistication'
(simple variation 2)
Three bit universe
So using binary an infinite set of binary numbers
would have an infinity of variations, some being more varied, complex, than others.
Just as Real numbers on a number line have infinite repeating non identical numbers.
1.5687566... 4763... an irrational number – the numbers after the decimal point go on forever. In any section of a number line there is an infinity of irrational numbers.
If numbers are not helpful much the same applies in language. A simple vocabulary will allow only simple statements, the more the vocabulary grows the more sophisticated the possible texts.
The cat sat on the mat.
The marmalade cat carefully made a place to rest on the Persian rug.
13. Whether the world (totality of possible infinite events) can be expressed in number or not, this process produces non repeating unique events which in this infinite process will become more varied in the type of events as it 'develops' it's 'sophistication'. Thus it will have a direction, it will evolve more complex events, and forms. Here the absolute is an infinite process, ever increasing in sophistication. The development of the atomic elements, of life and consciousness being good examples.
Simple randomness produces nothing sophisticated. Infinite randomness does. This is a kind of reverse of thermodynamics in that entropy is sophistication.