On 12/17/2013 1:51 AM, Bruno Marchal wrote:
On 17 Dec 2013, at 02:03, meekerdb wrote:
On 12/16/2013 4:41 PM, LizR wrote:
On 17 December 2013 13:07, meekerdb <[email protected]
<mailto:[email protected]>> wrote:
In a sense, one can be more certain about arithmetical reality than the
physical
reality. An evil demon could be responsible for our belief in atoms, and
stars,
and photons, etc., but it is may be impossible for that same demon to give
us the
experience of factoring 7 in to two integers besides 1 and 7.
But that's because we made up 1 and 7 and the defintion of factoring.
They're our
language and that's why we have control of them.
If it's just something we made up, where does the "unreasonable effectiveness" come
from? (Bearing in mind that most of the non-elementary maths that has been found to
apply to physics was "made up" with no idea that it mighe turn out to have physical
applications.)
I'm not sure your premise is true. Calculus was certainly invented to apply to
physics. Turing's machine was invented with the physical process of computation in mind.
Absolutely not. The "physical" shape of the Turing machine was only there for
pedagogical purpose.
Are you denying that Turing wanted to reason about realizable computation?? Of course his
reasoning itself was abstract and led to a mathematical theorem. But Liz was asking about
the unreasonable effectiveness of mathematics. I don't think you can say that Turing, or
Babbage or Post or Church just became interested in sequences of symbol manipulation
because they dreamed about it. They were concerned with real instances of inference and
calculation, from which they abstracted recursive functions and Turing machines.
the discovery of universal machine is a purely mathematical, even arithmetical,
discovery. "physical implementation" came later (if you except Babbage, but even Babbage
will discover the mathematical machine (and be close to Church thesis), when he realized
that his functional description language (intended at first as a tool for describing his
machine) was a bigger discovery than his machine.
The discovery of the universal machine is the bigger even discovery made by nature. It
is even bigger than the big bang. And nature exploit it all the time, and with comp we
understand completely why.
I agree with the first sentence. I don't understand the second.
That discovery is a theorem of elementary arithmetic, and has nothing to do with the
physical, except that with comp, we get the explanation of the physical as a consequence
of that theorem in arithmetic.
Non-euclidean geometry of curved spaces was invented before Einstein needed it, but it
was motivated by considering coordinates on curved surfaces like the Earth. Fourier
invented his transforms to solve heat transfer problems. Hilbert space was an
extension of vector space in countably infinite dimensions. So the 'unreasonable
effectiveness' may be an illusion based on a selection effect.
This beg the question, of both the existence of math, and of a primitive physical
reality (and of the link between).
So what's your answer to Wigner? Is it just an accident that the math the universe
instantiates, out of all mathematical universes Tegmark contemplates, happens to use the
same math we discovered?
Brent
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