## Monday, January 11, 2016

### Randomness sprinkled over the determinism

I posted yesterday about confusion over luck, and now I have another example.

Physicist Sabine Hossenfelder is also confused about randomness:
I wish people would stop insisting they have free will. It’s terribly annoying. Insisting that free will exists is bad science, like insisting that horoscopes tell you something about the future – it’s not compatible with our knowledge about nature. ...

There are only two types of fundamental laws that appear in contemporary theories. One type is deterministic, which means that the past entirely predicts the future. There is no free will in such a fundamental law because there is no freedom. The other type of law we know appears in quantum mechanics and has an indeterministic component which is random. This randomness cannot be influenced by anything, and in particular it cannot be influenced by you, whatever you think “you” are. There is no free will in such a fundamental law because there is no “will” – there is just some randomness sprinkled over the determinism.

In neither case do you have free will in any meaningful way.
Lubos Motl rebuts this, and endorses this comment:
Hossenfelder: "I wish people would stop insisting they have free will."

Stor: How could they, if they have no free will! :)
Motl cites the Free Will Theorem and argues for operational free will, but I don't think he gets to the heart of the matter.

People are really confused about probability and randomness.

Hossenfelder argues that our physical theories do not allow for free will. But if one did, what would it look like? For one thing, certain microscopic processes would be unpredictable. Just like quantum mechanics.

So how is quantum mechanics not the perfect theory for allowing a belief in free will?

Hossenfelder has her own proposal for a physical theory with free will. She says:
we need a time evolution that is neither deterministic nor random. ...

What we need in order for this evolution to not be random is a function F(ti) hat we can call the “free will function” that at any time ti returns a specific choice, ...

The function F should not be forward deterministic itself, otherwise we would be back in the block universe with Laplace’s demon. Neither should it be a random
process. ...

All examples that allow for free will have in common that the free will function cannot be a solution (at least piecewise) to a differential equation for if it was it could be evolved forward by use of this equation.
It is hard to make any sense of this. She seems to have in mind an F that is determined by knowledge that is only known to the person with the free will.

She writes:
The sensible consequence to draw from this "free will theorem" is of course that neither particles nor humans have free will. I don't know why you believe their argument implies I am wrong. The very opposite is the case, it supports my argument. Do you really want to argue that particles have free will? Seriously?
The authors of that theorem (Conway, Kochen) say that the sensible conclusion is that both humans and particles have free will. Electrons seem to have free will in the sense that if you align their spin in one direction, and then measure spin in a transverse direction, the electrons seem to decide on their own whether to have spin up or down. When we try to predict, all we can say is that we see a 50-50 chance of each possibility. Some people say that this is proof of true randomness, but it makes just as much sense to say that the electron has a mind of its own.

Saying that an electron has free will is essentially the same as saying that the electron appears to make choices that are not predictable by any external data. It does not mean that the electron has consciousness, and physicists do not know how to define that concept. Quantum mechanics textbooks do not say that the electron makes choices, because that would be anthropomorphizing it. But they make equivalent statements about it being unpredictable.

George Musser said: Many people may seek free will out of religious (not political) motivations, but in most cases I think it's simpler: we observe we have free will, and the purpose of science is to explain observations. Our observations might be illusory, but then we need to account for the illusion.

Hossenfelder: Since this comment section is suffering from an extraordinary influx of mostly ill-informed, impolite, and entirely superfluous submissions that clog my inbox, I am closing this comment section.

1. Amusing!

---

BTW, I haven't gone through her paper (and in fact am not likely to completely read it), but looking at the way she uses words, I think there is something mathematically interesting here.

She speaks of a solution (at least piecewise) to a differential equation.''

She seems to make a fundamental breach between piecewise solutions and the normal (or the usual) solutions (i.e. the single-function solutions).

Ummm... Suppose I have a finite set of subdomains, and I have simple polynomials within each subdomain, their collection acting as a piecewise solution to a differential equation. By way of a concrete example, let's take Helmholtz' equation (standing waves). The normal solution consists of the series: $\sum_{n} A \sin (nkx) + B \cos (nkx)$; $n$ an integer. Assume a simple enough boundary condition that the solution has a finite number of sines and cosines, not infinite.

Now, coming back to the piecewise (approximate) solution, suppose I keep increasing the order of each polynomial, even though the number of polynomials (i.e. no. of subdomains) remains the same.

In the limit that the number of terms in each polynomial tends to infinity, are there any fundamental mathematical differences between the usual solution and this piecewise solution? (I mean some fine differences that are not even touched on in the usual engg texts on FEM or Galerkin's method etc.?)

As to me, I would think that in the passage to infinity, the piecewise solution would lose its piecewise-ness, and would in fact become one of a piece'' (so to speak). I mean, it would become indistinguishable from the usual solution (sines and cosines) even if the number of subdomains were to remain constant (i.e. *finite*) throughout. For convenience, take just two subdomains. If the usual solution is analytic (and the sines and cosines are), then an infinite power series could represent it, and the fact that the overall solution was initially stitched at the inter-sub-domains boundary would cease to have any impact, because the solution would no longer carry any discontinuity of any higher order.

But is this supposition mathematically rigorous?

I take it that it has been demonstrated that increasing the number of subdomains does converge to the true solution. However, my point here is about what happens in the limit of the increasing degree of the polynomials---not the number of subdomains. In the language of FEM, I am looking for the p-refinement and a finite number of subdomains, not the h-refinement (i.e. an infinitely fine mesh with a finitely long polynomial within each).

Do you know something about this topic? If so, can you point out any good references? Or should I go ahead and raise it at iMechanica or Maths StackExchange?

I don't know if physicists are well-familiar with such things.

Just a thought that crossed my mind looking at her usage of the words...

Best,

--Ajit
[E&OE]

1. One of the major problems with contemporary physics is the problem with classical math. Infinite series and infinite mesh are meaningless terms and don't reveal the implicit finite reasoning. It's all outdated twaddle. People that write these papers are failing to update their approach. Convergence is mystical nonsense. These people use mathematics that is so old, it was created back when people had animal trials.

2. The whole idea that free will is somehow encapsulated by a piecewise smooth function is silly. I guess she thinks that a human decision must be a discontinuity in the derivative of some function. But humans take at least several seconds to make the simplest decisions. No one can make an instantaneous decision, and there is no reason to expect a discontinuity.

3. Coming to free will, it's an attribute of consciousness, and consciousness is orthogonal to physicality. You can't characterize your mind, consciousness or soul, in terms such as length, mass, time, etc.; the mind has no extension, weight, duration etc.

A living being has a consciousness. The fact that a living being also has material attributes does not mean that you can start with the concepts that subsume only the material attributes, and use them to describe consciousness. Once a living being dies, the material constituents remain (mass is conserved), but the life-principle is no longer associated with the now dead matter. Clearly, material concepts would therefore fail to describe anything meaningful about consciousness (and concepts related to it).

Now, maths describes the quantitative aspects of the physical (inanimate) world (or only the inanimate aspects of living beings), and so, an attempt to use maths to describe consciousness basically goes in the same category as above.

If someone wants to describe the connection or the integration (Sanskrit: yoga'') between the two, it is clear that the enterprise wouldn't be successful without making reference to both. A mathematical function is a fundamentally inadequate concept to use for describing consciousness or free will.

Physicists qua humans could of course study consciousness. But they should not try to bring the tools of their specific trade when they study consciousness, because of this fundamental difference between the two aspects. (It's one thing to use maths in zoology and sociology, or to use statistics in psychological experiments, and it's another thing to use the formalism of a 1:1 mapping between two sets (quantitative descriptions of something) to describe the functioning of the human mind. For building theories of consciousness, what they instead need to do is to begin their studies completely ab initio, starting with such terms as are suitable to psychology. Only then are they likely to succeed.

Otherwise, a person like me is left wondering: If mental changes are being described by a function, what is the space in which this function exists? Is it adequate to capture all the mental changes to be described? Answers: no idea, and can't possibly be so.

Bye for now.

--Ajit
[E&OE]

2. As if God isn't intervening! I'm not going to even stoop to their level to debate them. The whole discussion speaks to their autism and inability to detect patterns. They are so brain-damaged and caught in the left-brain that thy call the rest of us schizos. I say they are the result of too much inbreeding.