The following example concerning the fundamental theory of information in 
chemistry and physics puzzled me. Logical analyses of this puzzle from longtime 
participants would be welcomed.  

Consider any pair of atomic numbers. (Recall that the concepts of atomic 
numbers were established by physical measurements (Rutherford, Moseley, 
(1911)).  Because the conundrum is a question of meaning, I will select the two 
numbers 1 and 6. As atomic numbers, these two numbers represent all of the 
physical information contained in the respective atoms.  The QM equations for 
these two numbers (e.g., hydrogen and carbon) are well studied. And, the 
respective geometries of the orbitals are well studied.

Next consider exact 8 pairs of these two numbers, 16 integers in all.  (Could 
we write a string:
6,1,6,1,6,1,6,1,6,1,6,1,6,1,6,1) that would represent the 16 physical sets of 
The sum of these atomic numbers is 56  (= 8 x7)

First question: How much physical information is in the number 56?

Let us call the sum of the atomic numbers the molecular number.
Two separate and distinct chemical molecules can be composed from the this 
partition of the molecular number of 56 into 8 separate but physically 
identical pairs of atomic numbers.

One molecular number 56 is called "cubane". The geometry of cubane is that of a 
cube, with each corner of the cube having the number 6 and each of the number 
"1"s projecting outside the cube as one node of a tetrahedron.  (Do Not 
conflate this geometry of a physical tetrahedron with the tetrahedron of a 
categorical representation of commutativity.)

A second molecular number 56 is called cyclo-octene  (or, more exactly, 
1,3,5,7, tetra-dehydro-cyclo-octene.  The geometry of cyclo-octene  is that of 
an octagon with each angle of the octagon having the number 6 and each of the 
number "1"s projecting outside the octagon.

Note that both chemical representations of molecular number 56 are symmetric 
graphs composed from the same multi-sets of atomic numbers.

Questions: Is the physical information content of molecular number 56 the same 
in cubane and cyclo-octene?

How much information is the molecular number?

What is the physical basis for calculating the information content of molecular 
number 56?

When would the amount of information represented in this molecular number be 
the same?

What is necessary and what is sufficient to calculate meaningful physical 

Have fun! 

(Thanks to Joseph Brenner for calling this line of reasoning to my attention!)



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