Mark E Curtis

The geometry of DNA: a structural revision

- the appliance of critical reason to Crick and Watson’s proposal - 

Euclid

"It is of course not surprising that, in these days of short cuts, there should have arisen a movement to get rid of Euclid and to substitute a “royal road to geometry”; the marvel is that a book which was not written for schoolboys but for grown men should have held its own as a school-book for so long…


It was with reference to such a danger that Dionysius Lardner wrote in 1846:


“Euclid once superseded, every teacher would esteem his own work the best, and every school would have its own class book. All that rigour and exactitude which have so long excited the admiration of men of science would be at an end. These very words would lose all definite meaning. Every school would have a different standard; matter of assumption in one being matter of demonstration in another; until, at length, GEOMETRY, in the ancient sense of the word, would be altogether frittered away or be only considered as a particular application of Arithmetic and Algebra.”


It is, perhaps, too early yet to prophesy what will be the ultimate outcome of the new order of things; but it would at least seem possible that history will repeat itself and that, when chaos has come again in geometrical teaching, there will be a return to Euclid more or less complete for the purpose of standardising once more...


Euclid’s work will live long after all the text-books of the present day are superseded and forgotten. It is one of the noblest monuments of antiquity…"


Sir Thomas L. Heath - 'Euclid - The Thirteen Books of the Elements' Vol I ‘preface’ Nov 1908

I heartily concur with Sir Thomas Heath’s prophetic observation and Dionysius Lardner's 1846 statement regarding the dangerous confusions and misunderstandings that the abandonment of Euclid will lead us toward. At the time of his writing, Sir Thomas can have had no conception that the ‘chaos’ he prophesied in mathematics was likely to permeate the relatively modern science of ‘biochemistry’. Sad to say, since 1953, biochemistry’s understanding of DNA structure has single handedly sent education and knowledge throughout the world on a wrong headed trajectory. To coin a phrase, we have all been right royally led up the garden path and thereby humanity finds itself in this present all consuming state of scientific, cultural, and educational dystopia.


The ancient practice of ‘geometry' that so many people find dry, dull and difficult actually served the key purpose of opening and exercising the mind in an incredibly stringent manner - similar to that which today we might ascribe to the good of physical exercise on the body.


To the biochemist who questions the importance of geometry and places all their emphasis on the chemistry of molecules I can but press them to contemplate the spacial illustration on the cover of one of their own Bibles (below). An atom is, by its very nature, a ‘monad’ and ‘compound groups of monads’ create molecules of both 2 and 3-dimensional geometric space and structure. It is not unreasonable to argue that both the proportions and regularity exhibited by the DNA super-molecule are in large part accounted for by geometric shape and not only by the chemical attractions and interactions of its parts. 


Furthermore, if geometry really doesn’t play a part in the architecture of molecules and subsequent super-molecules, I would ask how it is that many viruses, phytoplankton and diatom’s accurately exhibit structural combinations and variations of just such pure geometric architecture. 

Tetrahedron        -        Octahedron        -        Cube        -        Icosahedron        -        Dodecahedron


Platonic Solids





Zika Virus

Icosahedron & Dodecahedron

Yellow Fever Virus

Icosahedron

Cowpea Mosaic Virus

Icosahedron

Foot & Mouth Virus

Icosahedron & Dodecahedron

Nematode Orsay Virus

Truncated Icosahedron

Grouper Nervous Necrosis Virus

Truncated Icosahedron

Polio Virus

Icosahedron & Dodecahedron

Noro Virus

Variation

West Nile Virus

Variation

Covid 19

Truncated Icosahedron

Human Papillova Virus

Truncated Icosahedron

Tetrahedron        -        Octahedron        -        Cube        -        Icosahedron        -        Dodecahedron


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