List, John: The issue of chirality is a critical issue in scientific philosophy. The logic of chirality is vastly more perplex than the simple logic of mathematics or physics because it is necessary to invoke the logic of multiple scientific symbol systems in a coherent manner such that the predicates of the entity are coherent in all the relevant systems of logic. CSP recognized this. (EP2:159)
Your brief geometric explanation was “spot on” from the mathematical perspective of space and motion. For a book-length inquiry into the relationship between mathematical graph theory of knots and chirality, see: “When Topology Meets Chemistry” CUP, Flapan, 2000. (Minor technical errors, but very sound over all.) But, chemical chirality, in CSP’s lifespan, was defined in terms of Pasteur’s (1822-1895) separation of two crystalline forms of tartaric acid (from wine residues.) The sole difference between the two forms of the tartaric acid were two geometric forms, VISIBLE to the naked eye and the rotation of polarized light. The two forms were identical in all other aspects; in chemical composition (carbon, hydrogen and oxygen), molecular weight, chemical reactivity and chemical reaction product and in physical attribute, melting point, etc. In the 1870’s, Van’t Hoff and LaBell, proved that this was only possible if the central carbon atoms organized the four substituents in a form of a tetrahedron. This requires that the four substituents must be separate and distinct from each other. If the four substituents are non-identical to each other, then, if one observes the order FROM ANY of the FOUR corners of the tetrahedron, then the arrangements of the other three will be either a clock-wise or counterclockwise in the two crystal forms AND will rotate plane polarized light in OPPOSITE directions. The BIG question to CSP was how was this possible? He deemed it critical for scientific philosophy of matter. For example, in his lecture on phenomenology, (EP2, 159), ends with a discussion of chirality and the laws of motion (Right—handed and Left-handed screws) “There, then, is a physical phenomena absolute inexplicable by mechanical action. This single instance suffices to overthrow the corpuscular philosophy.” Thus, I think the notion of chirality was a significant factor in his mistaken beliefs about the Boscowitz hypothesis. I would note two further facts that are important in assessing the scientific importance of chirality. 1. Virtually all biological molecules are chiral because virtually all the chemical building blocks fro constructing the anatomy of living beings are chiral. 2. Even the induced “taste” of chiral molecules differ. We can compare the mathematical perspective of chirality with the chemical perspective of chirality, because of the difference between geometric logic and chemical logic, very roughly speaking: 1. The scaling of circles is not a possible logical action on atoms or molecules, that is, atoms and molecules are not scalable in the mathematical sense of topology. 2. The logical origin of chemical chirality is not the direction of motion of a point on the circle, but, roughly speaking, the order of substitution of structurally distinct radicals on a points of a tetrahedron, all bonded to a central ligand. Finally, I would note that the entire collection of facts about chemical isomers (see Jeff D. post) illustrate the deep mathematical distinctions between the meaning of chemical and physical symbols. Cheers jerry BTW, see the book by the nobel laureate, R. Hoffmann for a deeper look on the meaning of “isomers”. The Same and Not the Same > On Dec 19, 2017, at 12:43 PM, John F Sowa <s...@bestweb.net> wrote: > > On 12/17/2017 3:24 PM, Helmut Raulien wrote: >> Now, do you think that there is chirality also in other contexts than >> molecules, e.g. in signs? > > To illustrate that issue, consider the analogs in 2 dimensions > and 3 dimensions. > > For example, any circle on a plane can be made congruent with any > other circle by two transformation: movement and size. > > Given two circles A and B, move A to B so that the center point > of A coincides with the center point of B. Then enlarge or contract > the radius of A until its circumference coincides with B. > > But if you put an arrowhead on A that points clockwise and > an arrowhead on B that points counterclockwise, there is no > way to make A and B congruent by those two transformations: > the arrows will always point in opposite directions. > > However, if you're allowed to move A out of the plane into > 3-D space, you can flip it over, put it back on the plane, > and make it congruent with both the circle and arrow of B. > > The same issue holds for chiral pairs in 3-D space: there is > no transformation by movement and size that can make your left > and right hands coincide. But if you could move out of 3-D > space into 4-D space, it would be possible to "flip" your left > hand to give yourself two right hands. (But don't do that. > It would have bad effects on the rest of your body.) > > To generalize: In a space of any number of dimensions, > the operations of movement and size can be specified by a > dyadic relation of A to B. But the operation of "flipping" > requires some space (a Third) that cannot be specified within > the original space. > > John > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu > . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu > with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at > http://www.cspeirce.com/peirce-l/peirce-l.htm . > > > >
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