09-14-2016, 05:21 PM

TR wrote: I rejoice that it is not so hard to understand!

Note, I said physics is easy for a competent physicist. Not, in general, me! IOW physics is easy for those for whom physics is easy ;-)

Anyway I see what you're getting at. It's basically Christian's point. Since motions in space, in particular rotations, are reversible, it makes sense that we should use a simply connected model. Christian might say, colorfully, that if nature used SO(3) we'd all experience gimbal lock. Since we don't nature must use SU(2). That's plausible, and (as I said long ago when I first glanced at the paper) it's worth pursuing. However the problem comes when, willy-nilly, we assume SU(2) and thus prove that classical experiments can violate Bell-type inequalities. That's not true, as far as I can tell.

TR wrote: Time flows in reverse. We can’t experience time flow in reverse, however, because our brains process data digitally. Or at least, we think that brains process data digitally; after all, we can convert wavelike information into digital data, and make sense of it.

no question there is a digital aspect to the brain. But it's not simply a bunch of digital neurons which either fire or don't (binary 1 / 0) depending on the firing status of their inputs (other neurons connected along the dendritic network). Today we know it's a lot more complex, and includes analog operations as well. So you can't explain the psychological arrow of time that easily.

TR wrote: Sense seems always well ordered, so obviously so that we construct an axiom – the axiom of choice – to guarantee it. The axiom of choice is equivalent to free will.

Yes, sense seems well-ordered in time; Zorn may be relevant, I suppose. Axiom of choice (AC) is not necessarily related to free will. AC is required only for choosing an element from an infinite set. On the face of it the "free choice" involved in (hypothetical) free will is among a finite set of alternatives, so AC is not needed.

TR wrote: What if randomness is built into the system, such that nature makes random choices continuously in a way that makes our own choices only seem random or non-random?

Nature does make random choices - if you want to put it that way - in QM (not, of course, in classical physics). Free will can be defined as the ability to make a truly random choice, unpredictable no matter how much information we have regarding brain state. Note, I'm not claiming such free will exists; I really don't know. But if it does evidently it must involve QM. No other part of physics implements essential unpredictability.

TR wrote: ... an arbitrary choice of endpoints in an ordered prime sequence, or in a finite set of primes, allows us to answer from Zorn’s Lemma, or the Axiom of Choice (which are equivalent).

No, AC is not required to choose from a finite set.

TR wrote: ... is nature well ordered in principle? We know that it is not.

Right. But our senses seem to be.

TR wrote: Now I'll deal with the counter-arguments:

These weren't counter-arguments, per se, against Lamport's essential idea: that Buridan's Principle is valid and interesting. I agree with that. Rather I was just pointing out a couple minor mistakes in his presentation.

TR wrote: There are stable equilibria, too. They are just less numerous than unstable states.

When balancing on a knife edge there's only one equilibrium point and it's unstable.

TR wrote: Lamport is saying that perfect information -- such as the numbers imprinted on the sides of a die -- leads to perfect knowledge.

True but he's also saying (well, implying) that such perfect info is possible - theoretically if not practically - for "the positions and velocities of all atoms in the universe". But that contradicts Uncertainty Principle.

Note, I said physics is easy for a competent physicist. Not, in general, me! IOW physics is easy for those for whom physics is easy ;-)

Anyway I see what you're getting at. It's basically Christian's point. Since motions in space, in particular rotations, are reversible, it makes sense that we should use a simply connected model. Christian might say, colorfully, that if nature used SO(3) we'd all experience gimbal lock. Since we don't nature must use SU(2). That's plausible, and (as I said long ago when I first glanced at the paper) it's worth pursuing. However the problem comes when, willy-nilly, we assume SU(2) and thus prove that classical experiments can violate Bell-type inequalities. That's not true, as far as I can tell.

TR wrote: Time flows in reverse. We can’t experience time flow in reverse, however, because our brains process data digitally. Or at least, we think that brains process data digitally; after all, we can convert wavelike information into digital data, and make sense of it.

no question there is a digital aspect to the brain. But it's not simply a bunch of digital neurons which either fire or don't (binary 1 / 0) depending on the firing status of their inputs (other neurons connected along the dendritic network). Today we know it's a lot more complex, and includes analog operations as well. So you can't explain the psychological arrow of time that easily.

TR wrote: Sense seems always well ordered, so obviously so that we construct an axiom – the axiom of choice – to guarantee it. The axiom of choice is equivalent to free will.

Yes, sense seems well-ordered in time; Zorn may be relevant, I suppose. Axiom of choice (AC) is not necessarily related to free will. AC is required only for choosing an element from an infinite set. On the face of it the "free choice" involved in (hypothetical) free will is among a finite set of alternatives, so AC is not needed.

TR wrote: What if randomness is built into the system, such that nature makes random choices continuously in a way that makes our own choices only seem random or non-random?

Nature does make random choices - if you want to put it that way - in QM (not, of course, in classical physics). Free will can be defined as the ability to make a truly random choice, unpredictable no matter how much information we have regarding brain state. Note, I'm not claiming such free will exists; I really don't know. But if it does evidently it must involve QM. No other part of physics implements essential unpredictability.

TR wrote: ... an arbitrary choice of endpoints in an ordered prime sequence, or in a finite set of primes, allows us to answer from Zorn’s Lemma, or the Axiom of Choice (which are equivalent).

No, AC is not required to choose from a finite set.

TR wrote: ... is nature well ordered in principle? We know that it is not.

Right. But our senses seem to be.

TR wrote: Now I'll deal with the counter-arguments:

These weren't counter-arguments, per se, against Lamport's essential idea: that Buridan's Principle is valid and interesting. I agree with that. Rather I was just pointing out a couple minor mistakes in his presentation.

TR wrote: There are stable equilibria, too. They are just less numerous than unstable states.

When balancing on a knife edge there's only one equilibrium point and it's unstable.

TR wrote: Lamport is saying that perfect information -- such as the numbers imprinted on the sides of a die -- leads to perfect knowledge.

True but he's also saying (well, implying) that such perfect info is possible - theoretically if not practically - for "the positions and velocities of all atoms in the universe". But that contradicts Uncertainty Principle.