Does God Play Dice?

[heracleitos]

This can happen even though these systems are deterministic, meaning that their future behavior follows a unique evolution[8] and is fully determined by their initial conditions, with no random elements involved.[9] In other words, the deterministic nature of these systems does not make them predictable.

What is the use of calling a system deterministic if you can't determine its action? But OK, I'll go with this definition.

- deterministic: If you take action A then consequence B will occur. Always.
- unpredictable: If event C takes place, it is not possible to determine what action caused it.

Such system is deterministic but largely unpredictable, i.e. chaotic.

The truth about natural numbers is exactly like that, i.e. chaotic:

- theorem of soundness: If you can prove proposition P from arithmetic theory, then P is true in the natural numbers.
- theorem of incompleteness: There exist true propositions in the natural numbers that cannot be proved from arithmetic theory.

You will find that the theorem of incompleteness dominates the theorem of soundness, i.e. most truth about the natural numbers cannot be proven in arithmetic theory.

You could argue the same happens to the universe but, likewise, you wouldn't be able to prove it.

It requires proving that the theory of the universe (=theory of everything, ToE) contains a copy of Robinson's fragment Q of arithmetic theory. In that case, the universe is a deterministic but chaotic system, on the condition that the ToE does not contain the definition of a true random number generator too, because in that case, it is not necessarily clear what is going on.

This brings us back to Zarathustra's dice-throwers and probability. Even if there is only one possible fate, you won't be able to determine it, hence it wouldn't be, from our point of view, deterministic. You could say that from the point of view of the universe everything is already determined, but we can't place ourselves on this point of view. Hence determinism as the idea that you can calculate and determine with 100% certainty the future is wrong.

Yes. It's like using a cryptographical PRNG (Pseudo Random Number Generator). The next number is perfectly deterministic if you know what PRNG it is, as well as the initial seed, but for someone who does not have that information, it looks indistinguishable from random.

Consider that just by the very act of measuring we already affect the outcome. We can never determine with 100% certainty the future, because we ourselves are included in the universe and affect it with our own actions.

If we truly have free will, then the theory of the universe cannot predict our actions. Otherwise, it can.

You would have to be situated "outside" the universe to be able to tell the outcome of the universe at any given point in time, but to be "outside" the universe is non-sensical. The universe is everything, you can't be "outside" everything.

If we have free will, then our action cannot be predicted from the theory of the universe. Hence, in that case, our actions are true propositions in the universe but not provable from its theory.

Since the universe expands, and on the condition that the theory of the universe is not able to predict the precise end of the universe, the Lowenheim-Skolem theorem will be provable from the theory of the potentially infinite universe. In that case, it is a multiverse. Under those conditions, there are an unlimited number of universes that interpret the theory of the universe.

Hence, the existence of free will almost surely implies that our universe is part of a multiverse. That is exactly what religion says: there is also a heaven and a hell.

It's in this sense that I say that the universe isn't deterministic.

A free-will containing Lowenheim-Skolem multiverse is still perfectly deterministic, but again chaotic.

Though, from the perspective of the universe, everything may already be determined—we just won't ever be able to determine it ourselves.

If we had a copy of the theory of the universe, then according to the theorem of soundness, every proposition about the universe that is provable from this theory, would still be true in the universe, but also in every other universe of the entire multiverse. So, it is would be deterministic. However, since the theorem of incompleteness would also be provable from this theory, there will be numerous true propositions about the universe that are unprovable from its theory. Hence the universe would also be chaotic.

The use of the words "determinism" and "deterministic" simply vanishes at this point.

No, they don't.

The theorem of incompleteness will massively dominate the theorem of soundness, but the theorem of soundness will still be perfectly provable and therefore true across the entire multiverse.

Soundness never vanishes. It just gets dominated by chaos.

[HJCarden]

Nevertheless, the issue of 'Does God Play Dice?'is seriously raised by du Sautoy. He says,
'What of the challenge to define God as the things we cannot know? Chaos theory asserts that I cannot know the future of certain systems of equations because they are too sensitive to small inaccuracies. In the past gods weren't supernatural intelligences living outside the system but were rivers, the wind, the fire, the lava...
Some religious commentators who know their science and try to articulate a scientific explanation for how a supernatural intelligence could act could act in the world have tried to use the gap that chaos provides as a space for the intelligence to affect the future'.

The existence of God and the truth of Chaos Theory do not contradict each other. I think it is inextricable from any reasonable conception of God that God exists in the same relation that we do to time. I cannot adequately defend any certain conception of God's relationship to time, but I believe it is sufficient for my reasoning to conclude that however God relates to time or if God relates to time at all, that this relation does not bear any resemblance to our subjective experience and concept of time. Therefore, I do not believe that the existence of God would carry any logical contradiction to us seeing a future that is genuinely uncertain and that does not appear to be under the control of a classically omnipotent God. If this is a compelling statement, then one should agree that there is sufficient cause to dissolve the logical contradiction between Chaos Theory and God.

[JackDaydream]

Nevertheless, the issue of 'Does God Play Dice?'is seriously raised by du Sautoy. He says,
'What of the challenge to define God as the things we cannot know? Chaos theory asserts that I cannot know the future of certain systems of equations because they are too sensitive to small inaccuracies. In the past gods weren't supernatural intelligences living outside the system but were rivers, the wind, the fire, the lava...
Some religious commentators who know their science and try to articulate a scientific explanation for how a supernatural intelligence could act could act in the world have tried to use the gap that chaos provides as a space for the intelligence to affect the future'.

The existence of God and the truth of Chaos Theory do not contradict each other. I think it is inextricable from any reasonable conception of God that God exists in the same relation that we do to time. I cannot adequately defend any certain conception of God's relationship to time, but I believe it is sufficient for my reasoning to conclude that however God relates to time or if God relates to time at all, that this relation does not bear any resemblance to our subjective experience and concept of time. Therefore, I do not believe that the existence of God would carry any logical contradiction to us seeing a future that is genuinely uncertain and that does not appear to be under the control of a classically omnipotent God. If this is a compelling statement, then one should agree that there is sufficient cause to dissolve the logical contradiction between Chaos Theory and God.

I don't think that chaos theory would involve a necessary contradiction with the existence of God. The problem may be more with the way God is seen as some seem to imagine God. I find Paul Tillich's idea of God, which is not
about God as a being but as the grounds of being. Thinking about God in such a way does allow for more fluidity than many other perspectives, especially those which are clearly anthropomorphic. Also, Teilhard de Chardin's idea of the 'omega point' is useful too as a basis for understanding the concept of 'God' in relation to science. Ideas from comparative religion, including the Tao, and Buddhism on consciousness are important here too, as trying to understand, possibly in relation to weak and strong forms of the cosmic anthropic principle.

[kaleido]

- deterministic: If you take action A then consequence B will occur. Always.
- unpredictable: If event C takes place, it is not possible to determine what action caused it.

But how do you know B will always occur? You can't know. You have to observe this occurrence continuously to be able to determine its necessity. But that doesn't mean the moment you look away it won't occur. Therefore there is no determinism, as it is usually understood. Only in the narrow confines of logic can there be determinism, for example when you say 2+2=4 is true always. But reality is a lot more than logic. Reality is not a math problem. It is unpredictable, hence not "deterministic".

The "theory of everything" as is generally understood is a stupid.

Alex Kierkegaard: "The theory "of everything". To realize how absurd the notion of such a theory is consider this: such a theory would be able to predict what you would do before you did it. You would have the prediction before you acted. In which case you could do something else and prove it wrong. The theory of everything would end up being a theory that anyone could prove wrong at any time, lol. The purported smartest theory would actually be, as is only fitting, the stupidest."

Alex Kierkegaard: "Why is the notion of a "theory of everything", the way laymen and even many scientists understand it, fundamentally erroneous? Because "everything" is not merely a "theory". It's a whole lot more than that."

The theorem of incompleteness shows that logic is circular. Wittgenstein also showed that "proof in logic is merely a mechanical expedient to facilitate the recognition of tautologies", which means truth ultimately boils down to a subject's perspective. That 2+2=4 is true for the vast majority of humanity means that we are the same species, and share similar perspectives, even though these are not exactly equal. Logic is the most egalitarian domain of mankind because it assumes the object is equally perceptible by every subject.

There is no "multiverse". That's just a word invented by scientists who don't know the definition of the word "universe" (universe = everything, including "multiverses", heavens and hells).

There is no "free will": there are only strong or weak wills (Nietzsche, BGE). Correspondingly, there is also no "unfree will" (Nietzsche, BGE).

[3017Metaphysician]

However, it is not because a system is unpredictable that it would be nondeterministic.

I don't understand this. I believe it is precisely because a system is unpredictable that it would be nondeterministic.

Incorrect:

Chaos theory is an interdisciplinary scientific theory and branch of physics focused on underlying patterns and deterministic laws, of dynamical systems, that are highly sensitive to initial conditions, that were once thought to have completely random states of disorder and irregularities.[1] Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization.[2] The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning that there is sensitive dependence on initial conditions).[3] A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause a tornado in Texas.[4][5][6]

An animation of a double-rod pendulum at an intermediate energy showing chaotic behavior. Starting the pendulum from a slightly different initial condition would result in a vastly different trajectory. The double-rod pendulum is one of the simplest dynamical systems with chaotic solutions.
Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors in numerical computation, can yield widely diverging outcomes for such dynamical systems, rendering long-term prediction of their behavior impossible in general.[7] This can happen even though these systems are deterministic, meaning that their future behavior follows a unique evolution[8] and is fully determined by their initial conditions, with no random elements involved.[9] In other words, the deterministic nature of these systems does not make them predictable.[10][11] This behavior is known as deterministic chaos, or simply chaos.

Another example, is the universe of true propositions about the natural numbers, which is deterministic but also chaotic.

The discovery of the existence of true but unprovable propositions (from arithmetic theory) about the natural numbers is exactly the breakthrough achieved by Godel in his famous incompleteness theorems.

Hence, "chaotic" does not necessarily mean "random".

No. If there was complete chaos, there would be no computers to type this message. There is both determinism (cause and effect/physical/metaphysical laws of nature) and indeterminism (QM) in the physical universe. The nature of randomness, determinate and indeterminate forces or features of existence, including chaotic systems, is all perceived by subject's who exhibit same.

Remember, chaos theory is produced by a conscious mind that is, well, chaotic too? Or do you mean in some sense illogical? You may want to qualify what you think 'chaos' actually means to all existing things. For instance, if you're trying to correspond to the reasons for existence having no explanation in the usual sense, this does not mean that the universe is absurd or meaningless. It just means that an understanding of its existence and properties lie outside the usual categories of rational human thought. Godel's theorem only warns us that the axiomatic method of making logical deductions from given assumptions cannot in general provide a system which is both provably complete and consistent. There will always be truth that lies beyond, that cannot be reached from a finite collection of axioms.

[LuckyR]

However, it is not because a system is unpredictable that it would be nondeterministic.

I don't understand this. I believe it is precisely because a system is unpredictable that it would be nondeterministic.

Incorrect:

Chaos theory is an interdisciplinary scientific theory and branch of physics focused on underlying patterns and deterministic laws, of dynamical systems, that are highly sensitive to initial conditions, that were once thought to have completely random states of disorder and irregularities.[1] Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization.[2] The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning that there is sensitive dependence on initial conditions).[3] A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause a tornado in Texas.[4][5][6]

An animation of a double-rod pendulum at an intermediate energy showing chaotic behavior. Starting the pendulum from a slightly different initial condition would result in a vastly different trajectory. The double-rod pendulum is one of the simplest dynamical systems with chaotic solutions.
Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors in numerical computation, can yield widely diverging outcomes for such dynamical systems, rendering long-term prediction of their behavior impossible in general.[7] This can happen even though these systems are deterministic, meaning that their future behavior follows a unique evolution[8] and is fully determined by their initial conditions, with no random elements involved.[9] In other words, the deterministic nature of these systems does not make them predictable.[10][11] This behavior is known as deterministic chaos, or simply chaos.

Another example, is the universe of true propositions about the natural numbers, which is deterministic but also chaotic.

The discovery of the existence of true but unprovable propositions (from arithmetic theory) about the natural numbers is exactly the breakthrough achieved by Godel in his famous incompleteness theorems.

Hence, "chaotic" does not necessarily mean "random".

No. If there was complete chaos, there would be no computers to type this message. There is both determinism (cause and effect/physical/metaphysical laws of nature) and indeterminism (QM) in the physical universe. The nature of randomness, determinate and indeterminate forces or features of existence, including chaotic systems, is all perceived by subject's who exhibit same.

Remember, chaos theory is produced by a conscious mind that is, well, chaotic too? Or do you mean in some sense illogical? You may want to qualify what you think 'chaos' actually means to all existing things. For instance, if you're trying to correspond to the reasons for existence having no explanation in the usual sense, this does not mean that the universe is absurd or meaningless. It just means that an understanding of its existence and properties lie outside the usual categories of rational human thought. Godel's theorem only warns us that the axiomatic method of making logical deductions from given assumptions cannot in general provide a system which is both provably complete and consistent. There will always be truth that lies beyond, that cannot be reached from a finite collection of axioms.

Just a point of clarification: what is the difference (if any) in your mind between randomness (which is by definition unpredictable) and the indeterminate (which is also unpredictable by your definition)? And where would Free Will fit in (if it existed) in relation to the other two?

[3017Metaphysician]

I don't understand this. I believe it is precisely because a system is unpredictable that it would be nondeterministic.

Incorrect:

Chaos theory is an interdisciplinary scientific theory and branch of physics focused on underlying patterns and deterministic laws, of dynamical systems, that are highly sensitive to initial conditions, that were once thought to have completely random states of disorder and irregularities.[1] Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization.[2] The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning that there is sensitive dependence on initial conditions).[3] A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause a tornado in Texas.[4][5][6]

An animation of a double-rod pendulum at an intermediate energy showing chaotic behavior. Starting the pendulum from a slightly different initial condition would result in a vastly different trajectory. The double-rod pendulum is one of the simplest dynamical systems with chaotic solutions.
Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors in numerical computation, can yield widely diverging outcomes for such dynamical systems, rendering long-term prediction of their behavior impossible in general.[7] This can happen even though these systems are deterministic, meaning that their future behavior follows a unique evolution[8] and is fully determined by their initial conditions, with no random elements involved.[9] In other words, the deterministic nature of these systems does not make them predictable.[10][11] This behavior is known as deterministic chaos, or simply chaos.

Another example, is the universe of true propositions about the natural numbers, which is deterministic but also chaotic.

The discovery of the existence of true but unprovable propositions (from arithmetic theory) about the natural numbers is exactly the breakthrough achieved by Godel in his famous incompleteness theorems.

Hence, "chaotic" does not necessarily mean "random".

No. If there was complete chaos, there would be no computers to type this message. There is both determinism (cause and effect/physical/metaphysical laws of nature) and indeterminism (QM) in the physical universe. The nature of randomness, determinate and indeterminate forces or features of existence, including chaotic systems, is all perceived by subject's who exhibit same.

Remember, chaos theory is produced by a conscious mind that is, well, chaotic too? Or do you mean in some sense illogical? You may want to qualify what you think 'chaos' actually means to all existing things. For instance, if you're trying to correspond to the reasons for existence having no explanation in the usual sense, this does not mean that the universe is absurd or meaningless. It just means that an understanding of its existence and properties lie outside the usual categories of rational human thought. Godel's theorem only warns us that the axiomatic method of making logical deductions from given assumptions cannot in general provide a system which is both provably complete and consistent. There will always be truth that lies beyond, that cannot be reached from a finite collection of axioms.

Just a point of clarification: what is the difference (if any) in your mind between randomness (which is by definition unpredictable) and the indeterminate (which is also unpredictable by your definition)? And where would Free Will fit in (if it existed) in relation to the other two?

Randomness and indeterminism is the same for me. Mainly because it relates to the causes and effects of stuff. Take for instance your stream of conscious thoughts, ideas and feelings. They occur at random (unpredictable which thoughts will occur next) and are indeterminate as to which thoughts you will apprehend the flow of with your undecided attention of the Will. In other words, the independent flow of ideas only you decide to stop with your Will and give it whatever attention it needs to do its job.

To that end, your question of how free Will fits in, is that it is free to select from that randomness or parade of flowing thoughts, ideas and feelings. The more intriguing questions might be where the instructions for that sense of independent self-organized flow, and does the subconscious mind control such ideas... . Beyond hardwiring, instinct, innate ideas, and such, what purpose do those parade of ideas have in survival of the fittest?

[LuckyR]

Incorrect:



Another example, is the universe of true propositions about the natural numbers, which is deterministic but also chaotic.

The discovery of the existence of true but unprovable propositions (from arithmetic theory) about the natural numbers is exactly the breakthrough achieved by Godel in his famous incompleteness theorems.

Hence, "chaotic" does not necessarily mean "random".

No. If there was complete chaos, there would be no computers to type this message. There is both determinism (cause and effect/physical/metaphysical laws of nature) and indeterminism (QM) in the physical universe. The nature of randomness, determinate and indeterminate forces or features of existence, including chaotic systems, is all perceived by subject's who exhibit same.

Remember, chaos theory is produced by a conscious mind that is, well, chaotic too? Or do you mean in some sense illogical? You may want to qualify what you think 'chaos' actually means to all existing things. For instance, if you're trying to correspond to the reasons for existence having no explanation in the usual sense, this does not mean that the universe is absurd or meaningless. It just means that an understanding of its existence and properties lie outside the usual categories of rational human thought. Godel's theorem only warns us that the axiomatic method of making logical deductions from given assumptions cannot in general provide a system which is both provably complete and consistent. There will always be truth that lies beyond, that cannot be reached from a finite collection of axioms.

Just a point of clarification: what is the difference (if any) in your mind between randomness (which is by definition unpredictable) and the indeterminate (which is also unpredictable by your definition)? And where would Free Will fit in (if it existed) in relation to the other two?

Randomness and indeterminism is the same for me. Mainly because it relates to the causes and effects of stuff. Take for instance your stream of conscious thoughts, ideas and feelings. They occur at random (unpredictable which thoughts will occur next) and are indeterminate as to which thoughts you will apprehend the flow of with your undecided attention of the Will. In other words, the independent flow of ideas only you decide to stop with your Will and give it whatever attention it needs to do its job.

To that end, your question of how free Will fits in, is that it is free to select from that randomness or parade of flowing thoughts, ideas and feelings. The more intriguing questions might be where the instructions for that sense of independent self-organized flow, and does the subconscious mind control such ideas... . Beyond hardwiring, instinct, innate ideas, and such, what purpose do those parade of ideas have in survival of the fittest?

I'm glad I asked, since I was not getting that from your postings. In that case (though I typically de-emphasize the specific process of decision making) I don't disagree with both your theory on the details of the process and (more importantly from my perspective) the implications on human decision making, as pertains to Free Will.

[3017Metaphysician]

No. If there was complete chaos, there would be no computers to type this message. There is both determinism (cause and effect/physical/metaphysical laws of nature) and indeterminism (QM) in the physical universe. The nature of randomness, determinate and indeterminate forces or features of existence, including chaotic systems, is all perceived by subject's who exhibit same.

Remember, chaos theory is produced by a conscious mind that is, well, chaotic too? Or do you mean in some sense illogical? You may want to qualify what you think 'chaos' actually means to all existing things. For instance, if you're trying to correspond to the reasons for existence having no explanation in the usual sense, this does not mean that the universe is absurd or meaningless. It just means that an understanding of its existence and properties lie outside the usual categories of rational human thought. Godel's theorem only warns us that the axiomatic method of making logical deductions from given assumptions cannot in general provide a system which is both provably complete and consistent. There will always be truth that lies beyond, that cannot be reached from a finite collection of axioms.

Just a point of clarification: what is the difference (if any) in your mind between randomness (which is by definition unpredictable) and the indeterminate (which is also unpredictable by your definition)? And where would Free Will fit in (if it existed) in relation to the other two?

Randomness and indeterminism is the same for me. Mainly because it relates to the causes and effects of stuff. Take for instance your stream of conscious thoughts, ideas and feelings. They occur at random (unpredictable which thoughts will occur next) and are indeterminate as to which thoughts you will apprehend the flow of with your undecided attention of the Will. In other words, the independent flow of ideas only you decide to stop with your Will and give it whatever attention it needs to do its job.

To that end, your question of how free Will fits in, is that it is free to select from that randomness or parade of flowing thoughts, ideas and feelings. The more intriguing questions might be where the instructions for that sense of independent self-organized flow, and does the subconscious mind control such ideas... . Beyond hardwiring, instinct, innate ideas, and such, what purpose do those parade of ideas have in survival of the fittest?

I'm glad I asked, since I was not getting that from your postings. In that case (though I typically de-emphasize the specific process of decision making) I don't disagree with both your theory on the details of the process and (more importantly from my perspective) the implications on human decision making, as pertains to Free Will.

Sure. There may be things that go beyond randomness or indeterminism relative to how things in nature emerge. Weather would be a good example there. No current model predicts with absolute certainty what the weather will do. And that kind of goes back to Godel and Heisenberg....

Yet another way to think about free Will and randomness or indeterminism, is our understanding of what it means to accidently do something or, something accidently happens to you that is unplanned. At face value, whether it is an illusion or not, our perception or observation of it (those effects) appear at random, but the nature of those existing phenomena may not necessarily be random. Meaning, there could be, like a lottery, a design for randomness like anything that appears to us, or emerges in nature (QM, etc.). Kind of like playing the odds. Something can be designed to have such a cause and effect. A perceived random effect.

But since we cannot know the true nature of reality (its instructions/information-we don't know where Singularity came from), we have concepts that rationalize the behavior, like human belief systems, in whatever form we perceive as necessary (i.e., scientific theories). Kind of like playing by the rules of the game. We didn't make the rules of nature, we just try to describe it/to a lesser degree explain it. Existentially it just is.

To that end, perhaps the more intriguing/existential part of randomness is trying to parse meaning from it. Like say we're walking down a city street in a large crowd of people during lunch. You bump into someone you hadn't seen in years. By all appearances or observation, it appears completely at random. But is it really... . Those kinds of concerns can easily correspond to 19th century Voluntarism which has its origin in Kant, particularly his doctrine of the "primacy of the practical over the pure reason." Intellectually, humans are incapable of knowing ultimate reality, but this need not interfere with the duty of acting as though the 'spiritual character' of this reality were certain. Kind of like the causal powers of the mind. We've seen in 'practical' applications where people have a Will to believe certain things, and somehow, they come into existence. We've seen it in sports, technological advances, medicine, inventions, and a whole host of other fields and other areas of life. And of course, imaginative leaps, often are the actual cause of great discoveries throughout the history of mankind.

In any case, it is logically necessary to have that forgoing stream of random conscious/subconscious ideas, thoughts and feelings that are necessary for us to effect meaning from our lives. It seems we need it for both Being and becoming, and to affect our quality of life. But intellectually, like antinomy, we need at least two opposite forces to effect choice. And we use the randomness of those possible choices to select stuff to do. Many situations in which the existence or identity of a thing depends on the co-existence of at least two conditions, which are opposite to each other yet dependent on each other, are always at work in nature (hot/cold, good/bad, sun/rain, ad nauseum). Whether it's an illusion or not, really doesn't matter...we can never know what an illusion really is or what's ultimate reality. Remember, science only has theories. Afterall all, what is Time/Relativity(?).

Anyway, too much coffee, feel free to poke holes...

[3017Metaphysician]

Don't always agree with Sean Carrol, but I'm pretty much 100% on this one. Particularly relative to neurons not having Agency (materialism is nonsensical vis a vis the Will). Enjoy!!

/yid]