A definition of free will

[Qeidx]

It's fun to try to create dry definitions, but an example is useful as an illustration. Let's say that I make a choice between A) having a sandwich before going to bed and B) not having a sandwich before going to bed.

How is that choice between A and B an act of my own free will? A choice is a transition from uncertainty to certainty. So what I'm doing is simply reducing the state A&B to only either A or B. What determines the actual outcome is my free will.

Wouldn't you be reducing it not from A & B but from A v ~A?

What I mean is:
"having a sandwich before going to bed"
and
"not having a sandwich before going to bed"

The second is just the negation of the first. So, you could just symbolize the one sentence as A, then use its negation ~A. Then you'd have A or not A, which is a fair bit simpler.
We couldn't say "and" for the first state, as, we don't have both
"having a sandwich before going to bed"
and
"not having a sandwich before going to bed".
If we say we have both, we'd be contradicting ourselves.
We can say A v ~A, though. This would perfectly capture your state. Then we go from that to A alone, or ~A alone.

I'm not criticizing what you said, just trying to make your example a bit more accurate as far as logic goes.

 

[Paulhoff]

If there is an all knowing god, which some believe, then there is no free will.

Paul

 

[Anders Lindman]

Wouldn't you be reducing it not from A & B but from A v ~A?

What I mean is:
"having a sandwich before going to bed"
and
"not having a sandwich before going to bed"

The second is just the negation of the first. So, you could just symbolize the one sentence as A, then use its negation ~A. Then you'd have A or not A, which is a fair bit simpler.
We couldn't say "and" for the first state, as, we don't have both
"having a sandwich before going to bed"
and
"not having a sandwich before going to bed".
If we say we have both, we'd be contradicting ourselves.
We can say A v ~A, though. This would perfectly capture your state. Then we go from that to A alone, or ~A alone.

I'm not criticizing what you said, just trying to make your example a bit more accurate as far as logic goes.

Yes, that looks like a more correct notation. By 'and' I meant that the state contains both the possibility for A and for B, but in logic notation what you wrote would be more correct I guess.

 

[Brian-M]

It's fun to try to create dry definitions, but an example is useful as an illustration. Let's say that I make a choice between A) having a sandwich before going to bed and B) not having a sandwich before going to bed.

Of course, in real life it's never a simple choice between two options. More like a choice between an endless variety of options, most of which never occur to us. For example...

BEFORE GOING TO BED

1. Nothing, go directly to bed.
2. Have a sandwich.
3. Have a glass of milk.
4. Have a glass of water.
5. Have a glass of bleach.
6. Stay up and watch TV for five hours.
7. Smash the TV to pieces.
8. Set fire to the couch.
9. Run naked screaming through the street.
10. None of the above, do something else.

The choice is a subprocess within the process of me as a person which in turn is a subprocess within the universal process. Therefore, what runs the actual process of the choice-making is the universal process.

If by this you mean, the same laws of physics that apply to the rest of the universe also apply to myself and the processes by which I make decisions then yes, I agree.

So it's me who makes the choice with my own free will.

That's pretty much the underlying concept of free will. If it wasn't you making the choices on how you act, you wouldn't have free will.

And the choice is a true free will choice since not even the universe knows what the choice will be.

Of course the universe doesn't know what the choice will be. The universe doesn't know anything. Unless you're arguing that the universe is an intelligent entity?

Only when I have made my choice is the outcome determined.

Umm.... no. That would only apply if the decision-making process were non-deterministic.

If a fragile glass has been knocked off a table and is rapidly falling towards a hard tile floor, and nobody present has the capacity to intercept the glass, the outcome of the glass breaking is determined even before it strikes the floor, because because there is no other outcome possible.

If your decision-making process is based on the physical processes of your brain, and is not influenced by randomness, then the outcome of your decision is determined even before the decision is made. As with the glass, no other outcome is possible.

ETA: And if your decision-making process is influenced by randomness, then it's not deterministic.

My choice cannot be fully predicted in a general sense even by the universe itself knowing all the positions of all existing particles! This is so because of the computational irreducibility.

Please tell us more about this computational irreducibility. It sounds... interesting.

 

[Brian-M]

If there is an all knowing god, which some believe, then there is no free will.

Why not?

 

[Anders Lindman]

If there is an all knowing god, which some believe, then there is no free will.

Paul

Good point. I see 'God' as the universe and the universe as a computationally irreducible process, so not even 'God' can fully predict the future. Some things can be predicted very accurately, such as the motions of the planets, but many things cannot be predicted, not even in theory because of the computational irreducibility.

A simple example of computational irreducibility is pi: 3.1415926535897932...

For sufficiently large decimal position of pi the numerical value for that position is unknown and the only way to know what the number is is to ACTUALLY perform the calculations required.

 

[Anders Lindman]

Of course, in real life it's never a simple choice between two options. More like a choice between an endless variety of options, most of which never occur to us. For example...

Yes, I was thinking of using another example to make it more clear. That example was:

I am watching television and will make a choice between A) switching off the TV or B) not switching off the TV within 10 minutes. That is a clear choice between only two options.

 

[Brian-M]

Some things can be predicted very accurately, such as the motions of the planets, but many things cannot be predicted, not even in theory because of the computational irreducibility.

Such as?

A simple example of computational irreducibility is pi: 3.1415926535897932...

For sufficiently large decimal position of pi the numerical value for that position is unknown and the only way to know what the number is is to ACTUALLY perform the calculations required.

So, it's computationally irreducible because the only way to get the answer is to compute it? That seems to makes no sense.

Can you define the phrase "computationally irreducible" for me? I take it to mean "cannot be reduced to a computable algorithm". If something can be computed, then by definition it is not "computationally irreducible".

What do you take the phrase to mean?

 

[Anders Lindman]

Umm.... no. That would only apply if the decision-making process were non-deterministic.

But you are thinking about simple Lapacian type of determinism here. Computational irreducibility means that the outcome isn't known even in theory beforehand, and the only way to know the answer is to actually perform the process needed to come up with the result. And choice-making is included in that. Only after I have made the choice with my free will is the actual choice known. There is no way to predict in a general sense what my choice will be EVEN when the universe is a deterministic process because of the computational irreducibility.

 

[Anders Lindman]

Such as?



So, it's computationally irreducible because the only way to get the answer is to compute it? That seems to makes no sense.

Can you define the phrase "computationally irreducible" for me? I take it to mean "cannot be reduced to a computable algorithm". If something can be computed, then by definition it is not "computationally irreducible".

What do you take the phrase to mean?

Such as the price of an Apple Inc. share one week from now. That's probably computationally irreducible.

Computational irreducibility makes sense in that it allows for free will to be deterministic yet real in the sense that the free will cannot be determined. Consider if that was not the case, then with extremely powerful computers the future could be predicted and even people's individual choices could be predicted, which would be rather nasty. With computational irreducibility it is IMPOSSIBLE, even in theory, no matter how much computing power one has (no computer can be more powerful than reality itself), to fully predict the future.

 

[Brian-M]

Computational irreducibility means that the outcome isn't known even in theory beforehand, and the only way to know the answer is to actually perform the process needed to come up with the result.

In that case, computational irreducibility doesn't mean that the outcome is not determined. For the case with calculating a new digit of pi, there's only one possible outcome for the calculation, even though nobody knows in advance what that outcome will be.

In the case of you making a decision (via deterministic processes), there is only possible outcome for what that decision will be, even though nobody knows in advance what that decision will be.

These things are determined, but unknown.

For the case with calculating the new digit of pi, you could figure out what computer A will give you by getting a faster computer B to run the same program.

If this is done, the result from computer A is already known in advance. The outcome has already been determined by computer B.

But what if someone ran computer B, but left the display turned off, so they couldn't read the result? No-one would know what the answer from computer A will be, but the answer would still have been determined by computer B.

But what if computer B has a flaw that means that sometimes it freezes up and never produces an answer? But since the display is off, nobody would be able to tell if computer B has already determined the answer A will give or not?

Is the result from computer A determined or not?

Not necessarily determined by computer B, but when we talk about an outcome being determined (or pre-determined), we generally mean something that can be theoretically determined in advance.

Whether or not computer B even exists, the outcome from computer A is already determined.

Only after I have made the choice with my free will is the actual choice known. There is no way to predict in a general sense what my choice will be EVEN when the universe is a deterministic process because of the computational irreducibility.

What if someone had a giant supercomputer that could perfectly simulate a small area of reality, with an exact simulation of you inside? (The simulated version of you has no knowledge that it's a simulation.)

By speeding up the rate of time in the simulation, they'd be able to predict what you're going to do.

 

[Brian-M]

Such as the price of an Apple Inc. share one week from now. That's probably computationally irreducible.

Theoretically, you could model the behavior of... everyone. With an absurdly powerful computer.

Computational irreducibility makes sense in that it allows for free will to be deterministic yet real in the sense that the free will cannot be determined. Consider if that was not the case, then with extremely powerful computers the future could be predicted and even people's individual choices could be predicted, which would be rather nasty. With computational irreducibility it is IMPOSSIBLE, even in theory, no matter how much computing power one has (no computer can be more powerful than reality itself), to fully predict the future.

But you wouldn't have to simulate all of reality, just small parts of it. For example, a Jupiter-sized computer simulating a single household.

 

[Paulhoff]

Why not?

The outcome is known. Yes it is that simple.

Paul

 

[Qeidx]

The outcome is known. Yes it is that simple.

Paul

And let's say there is no God, could we also, by the same reasoning, argue that "because we can determine our own decision - there is no free will"?

 

[Anders Lindman]

Theoretically, you could model the behavior of... everyone. With an absurdly powerful computer.



But you wouldn't have to simulate all of reality, just small parts of it. For example, a Jupiter-sized computer simulating a single household.

The universal process is running all of reality so it's not possible to create a completely isolated system. Every particle is connected to all other particles via gravity for example. So to simulate a whole household would require a simulation of the whole universe since the change in direction of a single particle in another galaxy could affect the choices made by the members of that household (the so-called butterfly effect in chaos theory). And to simulate the entire universe would require more computing power than the universe itself.

 

[Anders Lindman]

These things are determined, but unknown.

No, not determined. Deterministic yet not determined yet. That's the trick of computational irreducibility. Let's say that we don't know the trillionth decimal of pi yet, yet in another galaxy another civilization has already calculated the trillionth decimal of pi, then that decimal is actually determined even if we here on Earth don't know the answer yet. As another example, let's say that nobody in all of existence has calculated the gazillionth decimal of pi yet, then that number is undetermined! The underlying process for calculating that number is deterministic, yet the actual number for that particular decimal is as yet unknown.

 

[Brian-M]

The universal process is running all of reality so it's not possible to create a completely isolated system. Every particle is connected to all other particles via gravity for example. So to simulate a whole household would require a simulation of the whole universe since the change in direction of a single particle in another galaxy could affect the choices made by the members of that household (the so-called butterfly effect in chaos theory). And to simulate the entire universe would require more computing power than the universe itself.

Not true. I'm not even sure where to begin...

In fact, I won't. If you want to believe that our decision making processes are extremely chaotic, and so incredibly sensitive to outside influence that a single particle changing direction in another galaxy can [somehow] influence the outcome of a person's decision, that's fine by me. There's a point beyond which rational discussion is futile.

 

[Brian-M]

The outcome is known. Yes it is that simple.

How does someone knowing in advance what you're going to decide make your decision less "free"?

 

[Anders Lindman]

Not true. I'm not even sure where to begin...

In fact, I won't. If you want to believe that our decision making processes are extremely chaotic, and so incredibly sensitive to outside influence that a single particle changing direction in another galaxy can [somehow] influence the outcome of a person's decision, that's fine by me. There's a point beyond which rational discussion is futile.

My free will is a subprocess within the universal process and the universal process is determined by the universal wave function in quantum mechanics.

"Since the universal validity of the state function description is asserted, one can regard the state functions themselves as the fundamental entities, and one can even consider the state function of the entire universe. In this sense this theory can be called the theory of the "universal wave function," since all of physics is presumed to follow from this function alone." -- http://en.wikipedia.org/wiki/Universal_wavefunction

So the entire universe is one SINGLE quantum state. One of the reasons why quantum computing is so difficult is what is called quantum decoherence.

"One of the greatest challenges is controlling or removing quantum decoherence. This usually means isolating the system from its environment as interactions with the external world causes the system to decohere." -- http://en.wikipedia.org/wiki/Quantum_computer#Quantum_decoherence

The whole universe basically is one big quantum computer, so you can imagine how complicated the movement of even a single atom in reality is. There are no completely separate objects.

 

[Anders Lindman]

Let's say that it's possible to look at a person's choices in isolation, totally separate from the rest of the world. I don't believe that's possible in reality, but just to make an extreme case just to cover all ground.

Then the question is: is the thinking activity which is the person's choice-making a computationally irreducible process in the physical body of that person? I haven't looked at that yet but I suspect that the case can easily be made that this is in fact the case, that the neural activities in a person is a computationally irreducible process, since even very simple physical processes can be computationally irreducible.

An example of an extremely simple physical process (such as the motion of only three particles) that is computationally irreducible is the three-body problem.

"Unfortunately, when we add a third body to our equations of motion, such as a spacecraft lost in space between the Earth and the sun, we can no longer find an analytical solution. The equations are unsolvable. This problem is known as the three body problem of celestial mechanics and remains the subject of research today." -- http://plus.maths.org/content/mathematical-mysteries-three-body-problem

But what if we had a very powerful computer simulating the entire nervous system for a person? Couldn't then the choices that person will make be predicted beforehand? I doubt it, but let's say that they can. Then it would only be possible to do so as long as the person remains totally isolated! Because if the person receives information from the outside world, such as reading a newspaper, then immediately the simulation becomes invalid.

Then let's say that we have an even more powerful computer that can simulate not only one person but the entire planet Earth. That would still not be enough since Earth is very much affected by the activity of the sun. And if we include the sun in the simulation then not even that is enough since the sun is affected by the activity in the Milky Way galaxy.