Bruno,

Actually it is not a joke. I guess it is my first step toward Platonia. As I am a chemist by background, the problem might be not mathematically correct indeed. Yet, if you could help, we could improve it in this respect.


The background is as follows. I am a chemist and I am still at the level of what you refer to as physicalism or mechanism. Before I consider your theorem, first I would like to understand better in my own terms what physicalsim and mechanism mean and what are the limits. When you talk about this, it is too fast for me.

According to a common view in natural sciences, a human being (and hence mind) has been created during evolution. Right now however, after following discussion here, I have a problem with mathematics along this way. Science has been pretty successful with mathematical models in physics, chemistry and even in biology. Yet, according to my current view, mathematics has been created by the mankind. Thereafter I have got suddenly a question, why mathematical models (physical laws) are working at all to describe the Universe when there was no mind. The mathematics, it seems, was not there at the times of Big Bang.

We cannot repeat Big Bang to understand this. According to the current economic situation, it is highly unlikely that taxpayers are ready to spend money on bigger and bigger particle accelerators. Hence my proposal. If we cannot repeat Big Bang, then for a relatively small budget we could make easily a local heat death of a small Universe with two mathematicians and see what happens with mathematics there. In a way, we repeat evolution in the reverse direction.

It would be nice to exclude mind out of consideration at all but as this is impossible my goal was to reduce its role as possible. We know that mathematics is what mathematicians do. Pi is a nice number and most of taxpayers have heard about it. In the experiment we could allow mathematicians to write the prove that Pi exists on a paper, it would be even simpler. If you think that some other mathematical object would be nicer, please make your suggestion.

So, at the beginning of the experiment we have mind (two working brains of mathematicians) and they prove on the paper that a given mathematical object exists. An open question to discuss is what happens with this mathematical object at the end of the experiment.

Evgenii


On 04.03.2012 14:39 Bruno Marchal said the following:

On 04 Mar 2012, at 13:27, Evgenii Rudnyi wrote:

An experiment to perform in order to prove experimentally whether
Pi exists independently from the mind

The idea came during discussion on embryophysics list

http://groups.google.com/group/embryophysics/t/419d3c1fec30e3b5

Below there is a description of the experiment that one could think
of to check the relationships between Mathematics, Mind and Nature
(the MMN experiment). In my view this could be done as a real
experiment (so this is actually not a thought experiment) provided
we find two mathematicians who agree to sacrifice their life for
science. I believe that this should be not that difficult provided
the importance of the experiment for the modern science.

Let us take a completely isolated bunker where the experiment
begins. The initial conditions are enough so that mathematicians
can comfortably chat for awhile with each other about Pi and prove
that it exists. Eventually the oxygen in the bunker will run over
and both mathematicians die. From a viewpoint of a natural science,
we have a dynamical system that eventually comes to the equilibrium
state. I assume that at the beginning when mathematicians prove
that Pi exists we have a consequence of physical states where Pi
exists indeed. If you are in doubt, please suggest any other
physical states where you say that Pi exists. The goal of the
experiment is to establish what happens with Pi at the end when the
system reaches the stationary state.

Because of experimental settings, we can neglect the interaction
with environment and I hope that this could be done even for the
quantum mechanics treatment.

Before the experiment will be perform in real, you can take your
bet on whether Pi is retained after the death of mathematicians or
not.

I confess I cannot make any sense of what you say here. What do you
mean by "Pi is retained", how do you verify this (after the death of
the mathematicians)?

Also, what is the initial theory that you have to use to interpret
the experience?

I have no clue of the meaning of "I assume that at the beginning when
 mathematicians prove that Pi exists we have a consequence of
physical states where Pi exists indeed". "consequence of physical
states where Pi exists" contains too many vague abuse of languages.

When mathematicians proves that Pi exists, they assume a lot (real
numbers, circles, length of enough smooth curves, set theory, etc.).

Usually, they don't prove that Pi exist, they assume that all Cauchy
 sequences define some number, called "real number", and they show
that curves sufficiently smooth have a length definable by such a
sequence. Then they define Pi, by the ratio of the length of a circle
with its diameter, and build the Cauchy sequence defining it.

And also, why those two poor mathematicians have to die? Is not Earth
 close enough, and the death of Archimedes enough? (assuming the rest
 makes sense).

You might just be joking, perhaps.

Bruno

http://iridia.ulb.ac.be/~marchal/




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