On 6/13/2020 1:29 PM, Telmo Menezes wrote:
Am Sa, 13. Jun 2020, um 08:07, schrieb Jason Resch:
On Fri, Jun 12, 2020 at 4:56 AM Telmo Menezes <[email protected]
<mailto:[email protected]>> 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?
(2) Can you use math to make a correct prediction?
Notice that I am asking a question that is as hard-nosed as it
can be. No metaphysics, just a question about an observable event
in a physical system during a well-defined time period. Will the
light turn on?
What gives?
Excellent question Telmo! I arrived at a very similar
thought-experiment in the past, writing:
In fact, incompleteness is not limited to mathematics and
mathematical problems, but extends into physical systems too.
Consider an intricate arrangement of dominoes. The question of
how long it takes for the last domino to fall after the first is
toppled is a purely physical question having some definite answer.
Dominos is an an excellent idea for this, much better than mine.
Likewise, a physical computer is a physical system, and questions
about its future behavior can be framed as a physical problem.
For example, we could ask how long after pushing the power button
will it take for the screen to light up. But things get murky in
the case the computer runs a computation before turning the
screen on.
Let’s say the computer runs a search for a proof of some unproven
statement when it is turned on, and only when it completes does
it light up the screen. Now the physical question of how long it
takes for this physical light to switch on is reduced to a
mathematical problem.
Only by (the sometimes wrong) assumption that the computer will
implement the mathematics you assume.
Brent
Where things become very unclear is when due to incompleteness,
the computer might never find such a proof.
It turns out that some physical questions cannot be answered
without solving fundamental problems in the foundation of
mathematics.
So where things get hairy is when the computer is not only looking
for some example which may or may not exist, but a proof which may
not doesn't exist in the generally assumed/accepted system of axioms.
Then if we want to answer this purely physical question of "will this
light ever turn on?", we need to delve into foundations of
mathematics. We get dragged into the mathematical debate of what
system of axioms allows a proof to be found, and is that system of
axioms consistent?
There's no way of escaping it that I see.
Exactly. There is something truly bizarre and at the same time
unescapable about this.
Telmo
Jason
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it,
send an email to [email protected]
<mailto:[email protected]>.
To view this discussion on the web visit
https://groups.google.com/d/msgid/everything-list/CA%2BBCJUhL%3DSq0QFes7hffhXGtOdemSgMLigyu5uLzHvsFKSafYw%40mail.gmail.com
<https://groups.google.com/d/msgid/everything-list/CA%2BBCJUhL%3DSq0QFes7hffhXGtOdemSgMLigyu5uLzHvsFKSafYw%40mail.gmail.com?utm_medium=email&utm_source=footer>.
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send
an email to [email protected]
<mailto:[email protected]>.
To view this discussion on the web visit
https://groups.google.com/d/msgid/everything-list/d3e946e8-3491-4eef-bd4b-b6c70c0768ee%40www.fastmail.com
<https://groups.google.com/d/msgid/everything-list/d3e946e8-3491-4eef-bd4b-b6c70c0768ee%40www.fastmail.com?utm_medium=email&utm_source=footer>.
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To view this discussion on the web visit
https://groups.google.com/d/msgid/everything-list/b9d4ea32-444a-f363-83c8-df652da40b99%40verizon.net.
