This goes against a lot of what scientists believe, that we are measuring what's "out there."
What matters in the end is not what scientists believe, or even assert, but the scientific theories they produce and whether they are predictive. Different scientists will believe different things but they have to come to a consensus at some point as to what works and that will put what they believe into perspective.
I think the argument against the physical existence of noncomputable quantities is an argument against the CUH and the Church-Turing-Deutsch thesis. You noted earlier that these aren't necessarily true, and I agree. But a lot of people believe them; and to the extent that people believe them, it's fair to note that the idea of computability and the idea of continuity are somewhat at odds.
The universe might be computable and yet contains some infinite elements, like space perhaps. Energy is quantified per QM but I don't think anyone has managed to measure what would be the smallest quantity of energy that would be physically possible if quantities of energy were effectively finite.
And I also already pointed out that an infinite universe would anyway be computable using an infinite computing power. So, this issue is similar to the issue computable/non-computable numbers in that the so-called non-computable numbers are only so if you try to express them in terms of rational numbers. In reality, they are expressible in terms of each other, so they are effectively computable. So, I think you need to be careful in drawing conclusions from mathematical theorems. They usually are true within a very restrictive set of conditions.
Further, scientists are at liberty to express beliefs that go beyond what scientific theories can support. So, here again, you need to take what these guys say with a pinch of salt, not least because they quickly tend to disagree with each other on these issues.
Good point, if we agree that science doesn't describe reality, it's only something we're making up about things we can never name or understand. Your viewpoint is extreme here. Not wrong of course, but it will put you into some trouble with those who think science is about studying what's "out there." If we can't apply everyday notions of mathematics to the world, that undermines all of science. You should think about this and tell me if you take this as a reasonable criticism.
No, I'm perfectly in line with the scientific outlook. Perhaps just a little bit ahead.
Yes but I'm lost because you just denied that concepts like rationality or being an integer even apply to the real world. I hope you see that while you might be right, that position undermines science. You have to make sure you understand the implications of your own idea.
I definitely didn't say or suggest that the notion of rational or integer numbers doesn't apply to the real world. You seem to have a tendency to interpret what people say in terms of black and white. What I said is much more nuanced than that. You'd need to watch yourself.
If the noncomputability lies only in our minds or labeling or notation, no difference at all. So if math is only in our minds and not in the objects themselves, you are going to have an army of scientists to argue with. I'll just sit back and watch.
I don't need to quarrel with anyone. You should read again my first posts in this thread. I said something to the effect that we should let scientists to decide how best to represent the physical world, if need be using the notion of infinity, and let experience be the judge. Plus, personally, I really don't care if scientists wrongly claim infinities exist as long as this doesn't affect the predictive power of their theories. Newton also made metaphysical assumptions. He was wrong and experience proved him wrong. So, what matters is science, not individual scientists.
Now you're joining me in arguing against Tegmark. I suspect your viewpoint and mine are not that far apart.
You should pay more attention to what people say. My criticism of Tegmark started way back in this thread. I tried to discuss this with Write4U for a while but had to give up since he doesn't seem able to explain himself.
I tend to agree. But Tegmark and many others think the math is "real" in some way. I'm arguing against that point of view and now you're arguing with me, so I'm pretty confused. But your points in this post are correct, or at least valid.
My criticism of Tegmark is that his view doesn't make sense.
That being said, I already said I am perfectly comfortable with the idea that the evolution of the universe could be entirely and exactly represented using a mathematical model. Might never happen but I'm fine with this idea in principle.
If there's a physically intantiated noncomputable quantity, we could never measure it and we could never even write a program to approximate it.
I don't think you should assert that. The question seems more complicated that what you make it out to be.
I agree with most of what you said here.
That's certainly a relief.
EB
