(For undistored table and figures, see the attached.) Hi,
Benjamin Udell brought to our attention the following interesting article on the Borromean rings: "Physicists Prove Surprising Rule of Threes," _Wired_, May 29, 2014, by Natalie Wolchover (_Quanta Magazine_). http://www.wired.com/2014/05/physicists-rule-of-threes-efimov-trimers/ Borromean rings are a set of three rings that are interlinked in such a way that removing any one of them leads to dissolving all the links. The above cited article describes the experimental demonstration of the Borromean rings in atomic physics. I think Borromean rings are present in living cells and Peircean signs as well: (1) The Borromean rings in cell biology. There are three types of forces operating inside the living cell (see Table 1) that act as Borromean rings since removing any one of them will inevitably lead to cell death. _______________________________________________________________________ Table 1. The three types of the forces and their tokens postulated to form the Borromean rings inside the living cell: i.e., removing any one of these forces will lead to cell death. ________________________________________________________________________ Forces acting inside the Cell ________________________________________________________________________ Chemical Mechanical Osmotic ________________________________________________________________________ Examples ATP > ADP DNA supercoils ion gradients across the cell membrane _________________________________________________________________________ Mechanism electronic conformational free energy (i.e., E & S) interactions interactions gradients (Quantum (Newtonian (Termodynamics) mechanics) mechanics) _________________________________________________________________________ Alternative bond energy conformational osmotic energy Names energy (or conformons) _________________________________________________________________________ (2) The Borromean rings in semiotics: As previously maintained, the Peircean sign can be represented as a mathematical category with three sets (Object, Sign, and Interpretant), each acting as a Borromean ring due to the fact that their mappings (denoted as f, g, and k in Figure 1) obey the composition condition, i.e., f x g = k. That is, when any one of these mappings are removed, there is no triadic interactions and no mathematical category. f g Object ---------> Sign -------> Interpretant | ^ | | |__________________________________| k Figure 1. The Peircean sign as a mathematical category consisting of three Borromean rings called Object, Sign and Interpretant, the interpretant ring weaving through the other two rings consecutively following the rule that each intersection is either up or down and different from the previous one (see Figure 2). (3) Finally, it did not escape my attention that the three fields, physics (including chemistry), biology and semiotics may form Borromean rings at a higher level of organization than the level (i.e., the cellular level) discussed in Table 1, so that no higher-order life (including thinking) would be possible without all three fields mutually interacting. _____ P_____ _____B______ | | | | | __ +| _____-| |___ | |_______|____| |___|________| - | | + |_______ S ________| Figure 2. Semiotics (S) viewed as a Borromean ring in a system of inter-linked rings in which physics (P)(including chemistry) and biology (B) form its complementary Borromean rings. The symbols + and signify that the semiotic ring is passing over and under the other rings, respectively. If the above arguments are right, it may be inferred that the three concepts, Peircean signs, mathematical categories, and Borromean rings are different names for the same object, perhaps Pierces irreducible tirad(icity). With all the best. __________________________________________________ Sungchul Ji, Ph.D. Associate Professor of Pharmacology and Toxicology Department of Pharmacology and Toxicology Ernest Mario School of Pharmacy Rutgers University Piscataway, N.J. 08855 732-445-4701 www.conformon.net
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