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

```On 3/5/2012 9:34 PM, Jason Resch wrote:
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On Mon, Mar 5, 2012 at 10:42 PM, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>> wrote:
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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:

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.

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.
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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.

```
The existence of all mathematical structures implies the existence of all programs, which is observationally indistinguishable from Bruno's result taking only the integers to exist.
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That they are observationally indistinguishable is vacuously satisfied by them both being unobservable.
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I find the existence of all consistent structures to be a simpler theory. If the integers can exist, why cant the Mandlebrot set, or the Calabiâ€“Yau manifolds?
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I didn't say that things descriable by those mathematics *can't* exist. I just said I don't believe they do. Yaweh *could* exist (and according to you does) but I don't believe he does.
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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.
```
```
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 Bruno's theory, "physical universes" are considered observations of minds.
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Hmm? Is that right? The UD* certainly must generate lots of programs without human-like consciousness, e.g. this universe in which dinosaurs weren't killed off. So I'm not clear on why there wouldn't be infinitely many universes without conscious beings.
```

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```Where I use the term, I refer to independent structures (both seen and unseen).

In any case it doesn't warrant the conclusion that all possible universes
exist.

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No, it doesn't prove they all exist, just that there are perhaps infinitely many universes almost exactly like this one.
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Maybe I'm not understanding what you mean by "independent structures". Independent of what? I don't see that referring to independent structures has anything to do with whether they exist.
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Which, while not proving everything exists, is certainly something we would expect to find if indeed everything exists.
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Of course it is trivial to say that an everything theory successfully predicts the existence of what we observe to exist. The question is whether it does the converse. Can it predict that we don't see some (almost all) things.
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There are all these reasons and arguments that are compatible with and suggestive of the idea that all is out there. I haven't seen one offered piece of evidence from you that would suggest the idea of mathematical reality is false. So tell me: for what reason(s) do you reject the hypothesis?
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I don't reject it; I just don't accept it.  It seems to ill defined to be
testable.

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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.

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.

```
```      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.

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Clearly we will not get proof of the mathematical universe hypothesis by seeing other universes and mathematical objects through telescopes. Different universes are independent in such a way that we can only access them as we access all other mathematical structures.
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Ask yourself WHY they are inaccessible. Isn't it because if they were accessible then there would be contradictory facts in the world. And why can't there be contradictory facts? Because ex falso quodlibet. But "quodlibet" is what has already been hypothesized. (on the other hand see Graham Priest's "In Contradiction").
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Also, if your model is perfect, there should be no difference between studying the model and the object it represents. In the future, we will be able to discover, emulate, and visit other universes by discovering them in math, and using sufficiently powerful simulations, know what it is like there, or whether or not life is possible.
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Except if we are studying them or simulating them, then we can interact with them and (necessarily?) change them.
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That we cannot affect them from our current location does not make them any
less real.
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"Affect" and "observe" are two different things (at least classically) and if we can neither affect or observe that makes them rather like Russell's teapot. We can't be sure it doesn't exist, but there's no reason to think it does.
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That our universe is an immutable, abstract, timeless object to a being in a different universe does not imply we are any less real,
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I'm not sure what being "an abstract object to a being" means, but I don't think it implies we are any more real.
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that our experiences don't matter, or that the existence of the structure that is our universe is without consequence. Immutability says nothing about an objects reality; we cannot affect the past,
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Unless the past was identical with the present then something has mutated.

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or portions of our universe sufficiently far away, yet most would say these exist. Moreover, that other universes are currently inaccessible to us does not necessarily imply that they will always be immutable and inaccessible to us. There is always some non-zero possibility that when you wake up tomorrow, you won't find yourself in this universe, but one very far away.
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So you say, but I'm betting not...and so are you.

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The existence of all structures reconfirms, in a stronger senses, quantum immortality. If all the other universes are out there, then given mechanism, a we are all immortal. Unlike the immortality implied by quantum immortality, we can even survive destruction of this universe, waking up in a different one where the present one was just a very long dream.
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I'm not sure I've survived the past year.

Brent
The person I was when I was 3 years old is dead. He died because
too much new information was added to his brain.
-- Saibal Mitra

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