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

`On Mon, Mar 5, 2012 at 10:42 PM, meekerdb <meeke...@verizon.net> wrote:`
```
>  On 3/5/2012 8:28 PM, Jason Resch wrote:
>
>
>
> 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.
>
>
> 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.  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?

>
>
>  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.  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.
>
>
No, it doesn't prove they all exist, just that there are perhaps infinitely
many universes almost exactly like this one.  Which, while not proving
everything exists, is certainly something we would expect to find if indeed
everything exists.

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?

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

That we cannot affect them from our current location does not make them any
less real.  That our universe is an immutable, abstract, timeless object to
a being in a different universe does not imply we are any less real, 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, 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.  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.

Jason

> Brent
>
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