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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