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

```On 3/5/2012 8:28 PM, Jason Resch wrote:
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On Mon, Mar 5, 2012 at 7:24 PM, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>> wrote:
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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:

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).
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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;

Okay.

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

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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.
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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.
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That specific retrodiction came from Bruno's hypothesis which is that universes are generated by computation. What is computable is much less than all mathematics.
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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.
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There's a popular idea that most possible universes are inhospitable to conscious life: a theory that might well be false under Bruno's hypothesis in which consciousness and universes are both realized by computation. In any case it doesn't warrant the conclusion that all possible universes exist.
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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.
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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.
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That's a complete non sequitur.

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From the outside, one could study our universe through the window of math and computer simulation,
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I could study a mathematical or computational representation, but that's not the same as studying our universe - unless you beg the question.
```
Brent

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