Dear Jerry,
I am afraid I have forgotten exactly what it was I said that caused you to
embark on this line of reasoning. Be that as it may, there is one part of it
that I wish to distance myself from.
You wrote: "As atomic numbers, these two numbers represent all of the
physical information contained in the respective atoms."
I respectfully disagree. A number is one (abstract) thing and an atom is
another (non-abstract) thing. I consider this form of analysis, which you
have used also in your "Perplex Number" discussion, as eliminative. What is
eliminated is, exactly, the energetic physical properties, actual and
potential, which is the most important part of the physical information that
is characteristic of an atomic or molecular structure. It is this that
determines the angles between atoms.
That numbers, from whatever source, can be combined in various ways is
clear. To call this 'physical information', fundamental to information
theory in chemistry and physics, that provides any /new/ facts or insights
into what, say, cyclooctene is and/or can become seems inappropriate to me.
(By the way, there are several additional linear, non-cyclic, assymmetrical
"56" structures, with methyl groups and double and triple bonds that you can
write that correspond to the formula C8H8.)
Best regards,
Joseph
- Original Message -
From: "Jerry LR Chandler"
To:
Sent: Thursday, June 07, 2012 5:11 PM
Subject: [Fis] Physical information is WHAT? A Puzzle.
FISers:
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 information.)
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
information?
Have fun!
(Thanks to Joseph Brenner for calling this line of reasoning to my
attention!)
Cheers
Jerry
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