Joseph, Bruno, John, List: (Both Joe's and my post are listed below.)
First, the question of relation between meaning and inductive (physical, chemical) logic. Joe, when an adjective proceeds a noun, the logical content of the noun is modified by the adjective. If the noun, "information" is modified by the adjective "physical", then the logical content of the abstract concept of information is modified by the author's intent of the meaning of "physical". If the noun, "number" is modified by the adjective "atomic", then the logical content of the abstract concept of number is modified by the authors intent of the meaning of "atomic". In the inductive argument (of Rutherford and Moseley (1911)) based on x-ray scattering data is constructed to define a logical term, "the atomic numbers", the concept of "atomic number" is based on physical arguments, that is, the set of intertwined physical suppositions that constitute the science of physics. The argument (of Rutherford and Moseley (1911)) is complete for the intended purpose. Joe, when you write, > What is eliminated is, exactly, the energetic physical properties, actual and > potential, which is the most important part of the physical information you are noting that the arguments of Rutherford and Moseley (1911) did not invoke energetic arguments per se. But certainly both energetics and motion are within the pre-suppostions of the adjective "physical" and are considered in the physical arguments used by Rutherford and Moseley (1911). Indeed, Schrodinger noted the intrinsic pre-suppositions of Rutherford and Moseley's calculations and the atomic numbers become the foundation concept for the development of grammar for describing the spatial motion of electrical systems defined by the atomic numbers, (e.g., quantum mechanics). Consequently, the puzzle, as it was stated, implicitly includes " the energetic physical properties, actual and potential," and I disagree with your assertion. Joe, you assert: > (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.) First, I choose these two particular examples, cubane and cyclo-octene, to crisply illustrate the relationships between the logics of atomic numbers, scientific induction, mathematical structures, functions as order pairs, geometry, space, physics, isomerism, and, by further induction, the isomers of relational biology. (In particular, Robert Rosen failed to grasp the significance of isomers in relational biology!) Secondly, the identity of the eight ordered pairs, (1,6), is crisply defined, as are the identity of the names and predicates of these two subjects. Thirdly, the order of the numbers within the ordered pair (1,6) is not changed during the composition of the molecular number "56" from the sum of 7+7+7+7+7+7+7+7. But note that new order relations are created! Fouthly, the addition of the numbers is simple enough for logicians and philosophers of science to fully and completely understand how the conclusions are induced from the premises. (E.G., a "tinker toy" sort of visualization of the premises and the conclusions can be, with a little effort, mentally constructed without any knowledge of graph theory (or category theory). Now, more directly to your point about other isomers of C8H8. Could you give examples supporting your assertion? (The only other C8H8 isomer that I found was styrene, which contains a 6 membered ring and a side chain. Styrene is not well suited for a crisp example that can be communicated across numerous disciplines.) Frankly, I was puzzled by your post, particularly about your notion of abstraction in mathematics and number theory relative to inductive scientific logic. Would you like to explain? Brunno: Thank you for clarification of your intent. My philosophy of mathematics, logic, computation and physics, and human mental function is radically distant from yours. I will not attempt to bridge the vast gaps, which go well beyond information theory. One relatively concrete and prominent issue is the assertion: ""It exists x such that s(s(s(s(s(s(0)))))= s(s(0)) * x". (or Ex(s(s(s(s(s(s(0)))))= s(s(0))*x)" While this is perfectly reasonable within the context you select, it does not consider the structural mathematics in the sense of "branchings". In other contexts, it fails to address the fundamental role of material identity (the inductive logic of sorts and kinds) that is foundational in the brain sciences. As illustrated in the conundrum I proposed, branching plays a critical role many areas of applied mathematics, for example molecular biology and, by induction up the molecular number ladder, mental activity. With respect to your reference to a computational hypothesis, which (whose?) are you referring to? Does your usage of the term "computational hypothesis" require mathematical closure on an exact calculation? In other words, do you get an exact answer... or another bit of philosophy? I do not understand what is unclear about the difference between electro-mechanical and electro-chemical systems. I do not think my usage of these terms is in any unusual. Finally, given the silence of many strong proponents of "physical information", I am beginning to wonder if the concept of "physical information" is another philosophical red herring, a sort of metaphysical wish to find a correspondence between a popular mechanical method of calculation and the efficient causality of motion of matter in space. Form must remain at the root of information. Cheers Jerry On Jun 7, 2012, at 1:14 PM, Joseph Brenner wrote: > 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" > <jerry_lr_chand...@me.com> > To: <fis@listas.unizar.es> > 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 > > > > > _______________________________________________ > fis mailing list > fis@listas.unizar.es > https://webmail.unizar.es/cgi-bin/mailman/listinfo/fis _______________________________________________ fis mailing list fis@listas.unizar.es https://webmail.unizar.es/cgi-bin/mailman/listinfo/fis
