# Re: Two Mathematicians in a Bunker and Existence of Pi

```On 3/5/2012 4:57 PM, Jason Resch wrote:
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On Mon, Mar 5, 2012 at 12:26 PM, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>> wrote:
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On 3/5/2012 10:03 AM, Evgenii Rudnyi wrote:

On 05.03.2012 18:29 meekerdb said the following:

On 3/5/2012 3:23 AM, Evgenii Rudnyi wrote:

The experiment takes an operational approach to what Pi means.
During the initial stage of the experiment mathematicians prove
the
existence of Pi.

When mathematicians 'prove the existence' of something they are just
showing that something which satisfies a certain definition can be
inferred from a certain set of axioms. In your example the
mathematicians may define Pi as the ratio of the circumference to
the
diameter of a circle in Euclidean geometry. But what does that mean
if geometry is not Euclidean; and we know it's not since these
mathematicians are in the gravitational field of the Earth.
Mathematics is about abstract propositions. Whether they apply to
reality is a separate question.

Brent

I agree that this assumption might not be the best one. I will think it
over.

However, I do not completely understand you. How the geometry of
physical space
in which mathematicians reside influences the definition of Pi?
Mathematicians
will consider just Euclidean geometry, that's it. In my view, whether
the
physical space Euclidean or not, does not influence the work of
mathematicians.

Exactly. Hence mathematics =/= reality.

```
This is like comparing the kidney of a whale to a liver of a whale, and deciding whale=/=whale. You can't compare one limited subset of the whole (such as the local part of this universe) with another subset of the whole (euclidean geometry), and decide that the whole (of mathematics) is different from the whole (of reality).
```
```
The same mathematicians in the same place could 'prove the existence' of the meeting point of parallel lines or that through a point there is more than one line parallel to a given line. So no matter what they measure in their bunker it will be consistent with one or the other. So you can only hold that mathematics=reality if you assume everything not self-contradictory exists in reality; but that was what the bunker thought experiment was intended to test. You've essentially made it untestable by saying, well it may fail HERE but somewhere (Platonia?) it's really true.
```
Brent

```
```

In any case, the problem remains. What is mathematics under the
assumption of
physicalism? Do you have any idea?

It's a language game.

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This is what Hilbert proposed and what others such as Bertrand Russel tried to prove, but instead the opposite was proved in 1931. Mathematical truth transcends the symbol manipulation game defined by any set of axioms.
```
Jason

Brent
A physicist goes off to a conference. After a week his suit’s gotten soiled
and
crumpled, so he goes out to look for a dry cleaner. Walking down the main
street of
town, he comes upon a store with a lot of signs out front. One of them says
“Dry
Cleaning.” So he goes in with his dirty suit and asks when he can come back
to pick
it up. The mathematician who owns the shop replies, “I’m terribly sorry,
but we
don’t do dry cleaning.” “What?” exclaims the puzzled physicist. “The sign
outside
says ‘Dry Cleaning’!” “We do not do anything here,” replies the
mathematician. “We
only sell signs!”
--- Alain Connes, in Changeux

Evgenii

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