On 6/13/2020 1:22 PM, Telmo Menezes wrote:
Am Sa, 13. Jun 2020, um 05:01, schrieb Brent Meeker:
On 6/12/2020 9:25 PM, Telmo Menezes wrote:
Am Sa, 13. Jun 2020, um 04:08, schrieb Brent Meeker:
On 6/12/2020 8:12 PM, Telmo Menezes wrote:
Am Fr, 12. Jun 2020, um 18:39, schrieb 'Brent Meeker' via
Everything List:
On 6/12/2020 2:55 AM, Telmo Menezes wrote:
Hello all,
I've been reading here often the claim that physics is about the
"real stuff" and math is a human construction that helps us make
sense of the real stuff, but it is just an approximation of
reality. So here's a thought experiment on this topic.
Let us imagine I program a digital computer to keep iterating
through all possible integer values greater than 2 of the
variables a, b, c and n. If the following condition is satisfied:
a^n + b^n = c^n
then the computer turns on a light. I let it run for one year.
Will the light turn on during that year?
So my questions are:
(1) Can you use theoretical physics to make a correct prediction?
Yes. Theory of theoretical physics includes arithmetic and in
fact your question assumes it.
So we can conclude that arithmetic is part of physical reality,
No, you can conclude it's part of /*theories*/ of physics.
It points to underlying reality at least as much as a physical
theory does, that's my point.
I agree. But what points is distinct from the thing pointed to.
at least as much as any other thing that physics talks about?
(2) Can you use math to make a correct prediction?
Not unless the math can predict how fast the computer runs
It doesn't matter how fast the computer runs, and we know this
thanks to a mathematical proof, not a theory in physics. And
that's how we know how this particular physical system will behave.
No we don't. What happens when you runs out of registers to
contain the numbers?
In that case an exception is triggered and nothing happens. The
light doesn't turn on. Will it turn on before exhausting whatever
memory space is available?
Not if it perfectly reliable. But then why not just postulate a
computer whose light is burned out? Is there something special
about Fermat's last theorem, now that we know the answer? You've
made it seem profound, but it's logically equivalent to a program
that says, "Don't turn on the light."
I'm not trying to sound profound. What I am trying to do is to
confront the idea that empiricism is the only way to figure out a
world where the only real things are the ones that "kick back". As far
as I can tell, this very real question can only be solved in the
platonic realm. No actual experimentation will help settle it --
although I concede that it will help adjust your bayesian priors. I
think this is interesting.
When Andrew Wiles proved Fermat's last theorem, was he doing physics?
- If yes, then he provided an answer for a question about systems that
"kick back" without any empirical grounding whatsoever.
The empirical grounding was implicitly assumed in supposing that the
computer implemented the computation as mathematicians intended so that
Wiles proof could be translated into some conclusion about the physical
process. It's really no different than any other testing of mathematics
by running a computer. On the math-fun list, to which I subscribe,
there is a discussion right now of whether one should define 0^0=1. I
pointed out that in Lisp (expt 0 0) returns 1. Does that prove that
Lisp is doing physics? or that the computer programmer made some
assumption about mathematical axioms?
Brent
- If no, then physics has to share the stage with math.
Do you believe I am missing an option?
and how reliable it is.
If we use Newton's laws to predict the movement of a ball, we
assume that someone will not show up and kick it around, that the
ball is not unbalanced, etc.
Newton also assumed physics was deterministic.
What's your point?
Newton was wrong. As far as we know now, nothing can be perfectly
reliable because all physical processes include some randomness.
Are you sure? I don't possess your level of sophistication in
theoretical physics, but as far as I understand, there are two types
of randomness:
(1) Non-linear dynamics. In such cases, it's not that we cannot write
laws that perfectly describe the system, but in practice we would need
extremely high to infinite precision to be sure about the outcome
(e.g. weather prediction, throwing dice, etc). I assume we all agree
on this, and it doesn't make Newton wrong -- perhaps only a bit
ignorant, but we can forgive him given that he lived a long time ago.
(2) Fundamental / primary randomness as a brute fact of reality. This
is kind of this topic of this mailing list, right? If MWI is correct,
then this sort of randomness is, in a sense, an illusion created by
our limited perception of all there is. There is no definite answer to
this question, correct?
So, if we agree that we only care about (2) here, I would say that I
do not share your certainty.
Maybe I can suggest a system with an uneven number of redundant
computers and such a simple voting mechanism that a probability of
failure is infinitesimal, like NASA used to do.
An idealization.
Language itself is an idealization. This sort of refutation is
applicable to anything one can say.
Exactly so. Which is why you should no more confuse arithmetic with
reality than you do Sherlock Holmes.
The only reality that you and me have access to is idealized. Is there
such thing as a non-idealized reality? This is a metaphysical
question. I won't bother you with discussion on the ontological status
of Sherlock Holmes.
Telmo
Brent
As far as the laws of mathematics refer to reality, they are not
certain, and as far as they are certain, they do not refer to
reality.
-- Albert Einstein
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