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

`On Mon, Mar 5, 2012 at 7:24 PM, meekerdb <meeke...@verizon.net> wrote:`
```
>  On 3/5/2012 4:57 PM, Jason Resch wrote:
>
>
>
> On Mon, Mar 5, 2012 at 12:26 PM, meekerdb <meeke...@verizon.net> wrote:
>
>> 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
>

Okay.

> but that was what the bunker thought experiment was intended to test.
>

I fail to see how the bunker experiment tests this.  The bunker experiment
seems to assume that mathematical reality is or depends upon a physical
representation.

> You've essentially made it untestable by saying, well it may fail HERE but
> somewhere (Platonia?) it's really true.
>

People used to say Darwin's theory was untestable, because evolution was
such a slow process they thought it could never be observed.  Some on this
list have argued that the hypothesis has already survived one test: the
unpredictability in quantum mechanics.  If instead we found our environment
and observations of it to be perfectly deterministic, this would have ruled
out mechanism+a single or finite universe.  Further, there is a growing
collection of evidence that in most universes, conscious life is
impossible.  This can also be considered as confirmation of the theory that
there exists a huge diversity in structures that have existence.  Just
because one proposed test will not work should not imply a theory is
untestable.

A final thought: Consider what our universe would look like if you were a
being outside it.  You would not be affected by the gravity of objects in
our universe, for gravity only affects physical objects in this universe.
You could not see the stars or galaxies of our universe, for photons never
leave it.  There would be no relativity of size, or time, or distance
between your perspective and that within our universe.  You could not say
what time it happened to be in our universe, or whether the world had even
formed yet or long ago ended.  You could in no way make your presence known
to us in this universe, for our universe is bound to follow certain fixed
laws.  In summary, outside our universe there is no evidence we even exist;
our entire universe is merely an abstract, immutable and timeless
mathematical object.  From the outside, one could study our universe
through the window of math and computer simulation, but observation through
your senses or any measurement apparatus would never reveal its existence.

Jason

>
> 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.
>>
>>
>  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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