Randomness and infinity

What is randomness? It is the inherent property of nature where a given function has the ability to output one output or another without any sort of predictability whatsoever. Randomness also has roots in reality. Why is reality what it is and not something else? It randomly “chose” to be this instead of being something else.

In this article I want to explore something I like to call “Elimination based thinking” to explain the connection of randomness to infinity. This is the idea where one eliminates all that can be eliminated, and then one is only left with something that can hold its stance without any subjective aspects by considering all that can be considered and by leaving space for the addition or subtraction of logic without necessarily making a theory deficient. 

When it comes to metaphysics or anything at all, there are logical steps one can take that have the ability to be both simultaneously true and false. The most notable example of this would be the idea of God. There is just as much of a possibility of there being no God as there is for God existing. For this specific reason, there is no benefit to using God in a theory, and it easily falls apart when considering the possibility that God does not exist. 

Similarly, ideas such as Panpsychism, Idealism, Physicalism, The One or Nous in Neoplatonism, Jung’s Collective Unconscious, the Mind at Large, all fall apart, since there are no logical steps one can take towards any of these without taking a “step of faith” which then can be true or false. 

I, however, propose a different way of thinking, one that does not involve logic that is left for faith but rather uses only fundamental aspects of logic to question the fundamentals themselves. To give you an example, in my “Quantification-Based Metaphysics” theory I used this idea by eliminating all that can be eliminated and considering the things that absolutely must be given in any sort of logical framework. 

1. If there is something, there can be something else.

2. If there is something else, there can be nothing/everything.

   
   

Though these arguments look absolute, they can function in the same logical framework without the need to depend on others. If we remove the first statement from the quantification theory, we remove the randomness I am about to explain in this theory, and we remove the idea of there being any other reality than what there is. If we remove the second statement from the quantification theory, we are left with the idea that there is no unquantifiable state and there are only the quantified states, though an infinite number of them, we are only subjected to one. If we remove both of these statements, we’re left with the fact that there is nothing other than the quantified states of things or rather, something. However, the idea that something interacts with something through changing not it in itself but its properties remains throughout, and by asking why the same conclusions I reached in the theory remain about how reality can be subjective and how consciousness must exist in a different “layer” and the quantified state.

So this is elimination-based thinking, the idea that one can eliminate one’s own axioms and still have a theory that is sound, or when one considers all subjective angles that can be considered, the theory still remains intact.

So what is this randomness the first axiom brings up? And why is this randomness a basic aspect of reality? And why does this randomness essentially prove the first axiom? Though it seems like a circular argument, the dual causality can go both ways and can stand on its own. Randomness can prove the axiom, and the axiom can prove the randomness, but they do not need to exist together to function. 

There is a very basic question when it comes to reality. Why are the laws of reality what they are? For example, why is F = ma and not F = 2ma? Why is the permittivity of free space what it is and not a value higher or lower? It could have easily been different, though it is measured with arbitrary measurements we have already set up, meters, kilograms, seconds, it could have easily been higher or lower given the same arbitrary measurements we use. 

So given these brute facts of reality and the premise that those facts could have been something else, the fact that they are what they are has to be questioned. This is where randomness comes in, since they randomly chose to be what they are. 

So where does infinity come in when it comes to randomness? In a finite system, there can only be a finite number of outputs that can be modeled. Though the actual output that presents itself is subjected to probability. In mathematics, true randomness can only emerge from systems that consider infinite limits due to this very reason, since a predictable number of outcomes can be approximated.

When it comes to infinite sets, however, probability seems to act in strange ways. Bertrand’s paradox says that depending on the point of view, the probability of something changes. His famous circle and line probability example demonstrates this effect well. But to give an example that is easier to understand, imagine a fair coin, and it was tossed an infinite times. If one were to look at a finite subset of this infinite set, in that subset, there might be more heads than tails or more tails than heads. 

Finite sets therefore make randomness depend on the choice of the said random set. Making randomness inherently part of free will, as I have discussed before. Though there is another argument against this theory. It says that this perspective probability is irrelevant, as essentially if one considers the “true” probability and the infinite set itself, it will be 50/50. 

The connection of randomness to infiniteness is essentially there, but also I believe there has to be another connection to infinite even in finite sets and the outcomes of those finite predictable systems. At any given moment in time, there can be only one outcome to any predictable system, and though it depends on a predictable probability, there has to be a reason why only 1 is outputted at any given moment.

To give an example of this, I can use the same coin flip outcome set. There is a ½ probability that it can land on heads, and there is a ½ probability that it can land on tails. If we toss it up 3 times, there can only be 8 sets of outcomes. But after conducting this experiment, we can only get 1 outcome from it. Why is this? And how is this outcome “chosen”?

There is a relative probability we can get out of this that seems illogical but is perfectly reasonable. The idea that, given any output, there is only a 50% chance that a different set may have been the set that was outputted. Imagine this, there are 8 balls in a bag, 7 of them blue and one of them red. You are told that there are 2 different colors of balls in the bag, and you are told to pick a ball out of the bag without looking in. Now to you, the probability of the ball being red or blue is 50/50, though someone with more information than you might think it’s got a ⅞ chance to be a blue ball, this probability is irrelevant when it comes to what you may guess the ball’s colour to be. Now imagine there are infinite balls in this bag instead of 8, and the person who sees 8 is just as “wrong” as the person who doesn’t see inside the bag. Meaning that probability was also “wrong” and probability breaks down when it comes to infinite sets.

So there is only one set that is outputted when the coin is tossed up 3 times, and there are no infinite sets that can be outputted when it comes to outputs of 3 coin tosses, though the fact remains that somehow, 1 was chosen, how? If there is a set of outcomes that can be outputted from a collection of finite sets it must be that said outcome must only happen because there is an infinite chance of it being something else than what it is, since if one repeats this experiment infinitely the probabilities become infinite. Meaning that if HHH is the set one observes after tossing up the coin 3 times the reason why this set was the one observed is because the probability function collapsed down to 1 outcome infinitely, making the probability of ⅛ irrelevant. Meaning the idea of there only being 8 sets that one can get out of a coin being tossed up 3 times is irrelevant to the probability of the set that was outputted.

It sounds illogical from a mathematics point of view but I want to explain it in a philosophical sense to further make sense of this idea. The idea is that there can only be one thing that can essentially make something something, given any random chance of output. Meaning for any given system, whatever chance it may have of outputting something is essentially irrelevant when looked at through a lens of a retrospective perspective. So even if something has a chance of being true of 1 out of 1000, if in retrospect it turned out to be true, it means there was no chance for it to be wrong in the first place. Meaning that randomness is a quality of ignorance, thus further adding to the idea that randomness is a matter of perspective. 

So though there is a ⅞ chance that the outputted set may have been different, the fact that it wasn’t means that there was no chance for it to be at all in the first place, since somehow reality itself “chose” it to be HHH instead of anything else, making probability only a way to approximate reality but never understand it. 

So how does infinity necessarily help along randomness? The idea is that since we live in a reality with limits, there must be an underlying infinite probability basis for randomness to truly emerge out of reality, just as how when we choose different perspectives the probabilities shift, there has to be some sort of pool of infinity that reality puts limits on, and depending on those limits and where and when they are put, randomness emerges. I’ll give another example, just to make it more clear. Imagine there is a choice you have to make between 1 and 2, i.e., {1, 2}. The choice you make is only a limitation of all the other choices you can make, have made, and will have made. There is a sequence of choices that you can make that can go something like {... , 1,2,1,1,1,2,1,2,1,2, …}, and the choice you make, either 1 or 2, is a limitation that looks like this {... , 1,2,1,1, {1} ,2,1,2,1,2,, …}, due to whatever the circumstance is. But if there was only a finite output that you could give, this means there was no choice to begin with. Like the case with AI.

The idea of ignorance was pointed out to me by ChatGPT. Though I had all the necessary ideas, the usage of that word by ChatGPT when I was trying to test holes in this theory really put everything together. Now I have to wonder, how come this AI isn’t truly conscious if it can make observations like that? Free will, the ability to choose, and the fundamental lack of connection to the infinite. Though they might be connected, AI doesn’t necessarily get to put limits on any ideas, only convey them as they are. Like water flowing down a hill, the only limitation that was done to the infinite was done before (i.e., laws of physics), and it has no other connection to the infinite, and therefore there cannot be anything for it to choose from, as choice requires an infinite number of possibilities that can be (as demonstrated in the 1 and 2 examples above). Meaning it cannot be random and therefore cannot even mimic conscious beings in the truest sense, i.e., randomness. Though I believe it can do this if we somehow connect it to the inherent randomness of the universe, perhaps through QM, such as quantum random number generators.

So, “What appears as randomness is, epistemically, a consequence of our ignorance, but metaphysically, it reflects the way infinite possibility collapses into finite actuality. How did elimination-based thinking help me reach this conclusion? Because without it, this idea makes no coherent sense. The theory avoids subjective assumptions and stands on the notion that infinity is a required component, though it might appear to be a brute logical axiom.

However, let's try removing infinity from the theory. If we reduce it to a framework of purely finite sets, we again confront the same issue: limitations only appear random because they reflect a deeper, unaccounted infinity. As shown in the {1, 2} example, any finite set of possibilities ends up pointing back toward an infinite context in which limitation makes sense.

In this way, even when we strip the theory down, it reflexively rebuilds itself by reintroducing the very idea we tried to eliminate. It behaves like a self-preserving structure, a “living idea”, which is exactly what elimination-based thinking reveals. We are left not with a circular argument, but with a self-consistent one that continues to function even when its components are temporarily removed and re-examined.

That said, this is not the final version of the idea. It's how I understand it now, and it may evolve into something stronger and more refined in the future.