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On consciousness and choice. A set of axioms


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1st axiom: Consciousness (as a subset of all its elements A) exists in the the universe B

A ⊆ B

2nd axiom: An element in A can be written as

a ∈ A

Such that two choices for a conscious decision, depends on

1 ∈ {1,2}

And 

2 ∈ {1,2}

3rd axiom: Before either choice 1 or choice 2 and so on (1,2.... N) has been consciously made, both possibilities should exist in a superposition such that 1 + 2 is an undecided set S. In example, the choices we have is like a wave of possibilities found in quantum mechanics. The ability then to choose would be equivalent to a collapse in the wave function where either decision, 1 or 2 has been made.

4th axiom: It would follow then it is a linear function that would satisfy the ordinary definition of

f{x(1) + x(2)} = f{x(1)} + f{x(2)} 

= f(ax) =a(fx)

From additivity with (a) as a scalar.

5th axiom: If choices are determined analogous to a probability wave, then it's theoretically plausible that both possible choices intefere with each other before it has been determined. So the choice we make, either by 1 can be affected by the decision making of 2 just as the decision 2 may affect our decision of choice 1. This invites an idea of constructive and destructive interference of choice making.

6th axiom: If choice can be approximated in a similar fashion to the linear superposition of two possible states contained in a wave function, a choice would exist in a choice of states may be roughly expressible as a ket with uppercase psi notation |Ψ> where the possible choices are denoted in the lowercase as , |ψ1>,  |ψ2>... |ψN> which are available in decision making. Because of this we would write under conventional notation 

|Ψ> =Σ c_i|ψ_i>

such that choice, or the theory decide for another phrase is still given by the square of the moduli

<Ψ|Ψ> = Σ |c_i|² = 1

so that the decision has been decided to only one outcome, or unity of one choice.

 

Preliminary conclusions: I'm going to return to this later, but what I am suggesting is that consciousness exists as a subset of spacetime and decision making may be closely inspected by a superposition of possibilities that is no different largely in theory from the wave function of possible states we deal with in quantum mechanics. I do not mind any harsh criticism, as this is a bit speculative, I'll try and continue this hypothetical model when concerning choice theory later. I have modelled it like this thus far, because some scientists do take it seriously that perhaps consciousness itself may arise from a collapse in the wave function. Some evidence already appears to point to this when we discovered that microtubules appear to show quantum effects after Penrose and Hameroff suggested a model to explain how consciousness might arise inside a warm wet brain. It's quite rudimentary to start, but I intended it to be like this, knowing the proper model is probably more complex.

Edited by Dubbelosix
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Ignoring for a moment microtubules, or other interesting organisms like Centrioles (which are little machines made of a collection of microtubules) why should the first axiom hold? If the first axiom does not hold, then the rest cannot simply follow, we state that consciousness is a subset inside the universe. This axiom itself depends crucially on the model we may chose in physics, whether it be a finite space or an infinite Hilbert space, but for reasons clear, choices presented to us cannot be infinite per se, because of at least one main reason, that being we would need to be consciously aware of infinite choices for an infinite amount of time, and those steps can never reach a determinable choice. You may think you have an infinite amount if choices, but this is purely imaginary. In physics we also deal with real and imaginary dimensions. The terminology may be very solid in the sense that time could be something we have invented to make sense of the notion of change around us. On the other hand, while time is an imaginary dimension (in the mathematical sense) it may still be "real" in a physical sense. It will always be difficult to ever try and prove either way. What is interesting, is we can state that consciousness still, is a subset if all real dimensions and that the sense if time, very crucial to consciousness in any model, is itself a subset of real space R^3. This model is not new as viewed in this sense as it is itself an axiom from computer theory. 

"In fact, it is known that time(t(n)) is a strict subset of space(s(n)) for space 

constructible s(n) ≥ n" 

What it means is that you have a process of time for a machine (and yes we too are machines) for any given natural n. It's interesting that time is the subset of space in this sense and not the other way around because this model as we understand it mathematically can hold important consequences to how we view the world, and the models we have been convincing ourselves that we hold true about physical reality. A good example, is the theory of relativity because from it we knew that time and space was fundamentally woven together in some way - now scientists are wondering if space is not fundamental, but instead perhaps the big bang happened more in time than it did space. I don't believe this personally, but if space is emergent it would mean the basic premise of time being a subset of space would be wrong in computer theory.

https://cs.stackexchange.com/questions/92102/why-does-spacen-timen-imply-that-timefn-is-a-subset-of-spacefn

Edited by Dubbelosix
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I don't want marks, honestly I don't. Perhaps no one replies often because it is very theoretical. Perhaps there's no objections. If there are at least good objections, no one should hold back. Besides, my posts aren't over, I'm just covering the essential topics of the axioms I chose so that it has a bit more basis for any future discussion. The first post I started off by saying consciousness is a subset of the universe. I haven't defined properly yet in what sense it is a subspace. Hopefully from the last post, the universe is a set B existing in the real configuration complete space R^3 where consciousness is like the dimension of time, where events are computed as processes that define choice from our frame of reference. So while the posts are slowly disecting this, we can hopefully soon build a better picture for choice theory. While consciousness and time are certainly linked, we have to still speak of ourselves in computer language. It's a work in progress.

Edited by Dubbelosix
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I'm going to provide some reading material, the following link I'd like people to familiarise themselves with universe in set theory, especially the Von Neumann universe 

https://en.m.wikipedia.org/wiki/Universe_(mathematics)

And the basic ideas which preexisted my own independent model of axioms for choice and set theory

https://brilliant.org/wiki/axiom-of-choice/

Though be careful. I've highlighted a good objection to infinite choices. It would also be good to read

https://en.m.wikipedia.org/wiki/Choice_theory

And hopefully we can remodel the basis of the theory in the Op for a rational reinterpretation for a finite set of choices, for a finite machine.

 

 

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