Every particle is also a wave, presenting much the same problems in defining its location as the ripple in the coffee in the first place. And whatever definition or convention one eventually adopts for the "exact" location raises the question of whether the universe's computations are employing the same one.
I certainly agree with you that quantum physics says that particles aren't exactly where they are ... rather, each particle is a probability wave of where in the universe it might be.
I did mention earlier that this is the philosophical problem of whether quantum randomness was an ontological or an epistemological problem. Is quantum randomness a feature of the universe? Or is it only a limitation of our knowledge?
I think if nothing else, it's clear that the current state of physics doesn't allow anyone to say with certainty whether the mind is a computation or not. I don't see how anyone could claim certainty of anything. Yet so many people do.
I didn't state it at all. I stipulated to its irrelevance.
The universe does not have to "solve" the halting problem to run as we see it run, whether or not it is - in principle - "computable".
I don't follow this. Nobody said the universe solves the halting problem. I never said that. The entire point is that IF the universe is a computation, THEN it cannot solve the halting problem.
But frankly I never brought up the halting problem. You did. If I misunderstood your intention, my apologies. That said, I don't understand how the remark you made bears on anything I said. Perhaps we're talking past each other. I think we're mostly in agreement.
The only reason it has to halt in a finite number of steps is that human engineering limitations require each step to take a certain amount of time.
Not true. The reason is that our
knowledge of fundamental physics does not allow us to physically instantiate infinitary models of computation.
When I say that a computation is required to halt in order for its output to be called a computable object (real number, state of the universe, whatever), that is not my opinion.
It's the official technical definition. It drives me a little nuts when you make up your own science. The Wiki links are all out there. It's like if I said gravity is an attractive force and you say no it's not, it's repulsive. You don't get to say that. Because it's already an established technical term in physics. Likewise, what it means for an object to be computable. It means that this object is the output of a Turing machine program that halts after finitely many steps.
This isn't a matter of opinion.
We can certainly talk about infinitary models of computation. They are very interesting and there are a number of different approaches. But none of them are implementable in the physical world
according to our contemporary physics.
If you want to agree with me that we need new physics, then we're in agreement. But if you want to argue with me that current physics allows infinitary computation, that's just wrong.
I hope at least I've made my position as clear as I possibly can. If we disagree, I wish you'd tell me why.
That would not apply to a universe that is producing time itself via its computations, and taking its steps on a rational number line. (Note: countability preserves computability, in principle - the rationals can be put into 1-1 correspondence with the integers).
The integers and the rationals are isomorphic as sets, but not as ordered sets or topological spaces. Cardinality is a very weak metric for trying to say anything meaningful. There are some very wild countable sets.
I don't see how the rational numbers have anything to do with this. When you say "countability preserves computability," I would challenge you to provide either a formal proof or a reference. It doesn't seem particularly meaningful to me; and to the extend it's meaningful, it's wrong.
But like I say I'm just really trying to understand why you seem to be disagreeing with things I think we fundamentally agree on. Does that make sense?
The universe may very well be capable of taking its steps in infinitesimal "time"
Yes yes it MAY WELL be capable of that, and SOMEDAY physicists may figure it out. But RIGHT NOW, contemporary physics has a thing called Planck time, which is the
smallest interval of time we can meaningfully talk about. Below that there may be infinitesimal bits of time, and Zeno may live there, and so might Tinker Bell. As far as contemporary physics is concerned, any question or discussion about any interval of time smaller than the Planck time is meaningless.
So you are AGREEING with me that we need NEW PHYSICS in order to get a better theory of infinitary computation that explains some of these mysteries.
I think we're really in agreement on this point. We need new physics to get a new theory of computation that goes beyond Turing machines. This is something I do believe. We have to figure out how the universe might do an infinitary computation. Our current physics does not afford us such a theory.
, and with infinitesimal spacing. At least, there is no obvious reason to assume otherwise, eh?
No reason at all, except for
what contemporary physics says about the subject. Past that, one is engaging is scientific speculation.
You are dealing with a version of Zeno's Paradox, here. The arrow does move.
That's right. But our physics has no answers. Remember that the mathematical real numbers are not the same as the physical universe. We don't know if there are dimensionless points. We don't know anything below the Planck length and the Planck time. There could be dancing sprites down there, or Leibniz's monads. Nobody knows.
It's speculation. And speculation is good, but let's label it as such.
Exact positions, velocities, and times, probably do not exist as properties of "particles".
Metaphysical speculation. Perfectly fine, when labeled as such. "Probably do not exist." How would you know? How would I know? These are things nobody knows. Speculation.
More likely, like temperatures and densities, they are human abstractions and heuristics whose usefulness emerges at appropriate scales of inquiry.
Sure but now you're arguing that the universe is random and the order that we see around us is an illusion, like seeing hunters in the sky. You just said, if I understood you correctly, that the qualities and attributes we see in the objects around us, are artifacts of our minds and not inherent in the objects themselves. Did I understand you correctly?
