[Fis] Symmetry as such

Dear FISers,

let me propose a neutral and public definition of symmetry.

"Symmetry is the property of subsets of N that are generated by following
rule:
function m(n)
                local integer tmp, first, len, zero, m
                tmp = int(sqrt(n/2))
                first = 2*tmp**2
                len = 4*tmp + 2
                zero = if(n-first < len/2, first + tmp, first + len/2 + tmp)
                m = n - zero
        return(m)"

This definition allows all that Shu-Kun has wished for:
"I have been interested in a theory which can be used to both macroscopic
and microscopic levels and intermediate levels which is different
from equilibrium or nonequilibrium thermodynamics."

The two halves of the symmetric grand cyclus make an axis-symmetry, the two
halves of the small cyclus make a center-symmetry. The left and the right
halves (both small and grand cycles) are both symmetric (on M) and
assymmetric (on N).

The M axis may be used very profitably to discuss concepts related to
symmetries.

Best regards:
Karl

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Received on Tue Jul 22 19:11:45 2003