Mark E Curtis

The geometry of DNA: a structural revision

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“Euclid once superseded, every teacher would esteem his own work the best, and every school would have its own class book.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Euclid’s work will live long after all the text-books of the present day are superseded and forgotten.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, Heath can have had no conception that the ‘chaos’ he prophesied in mathematics was likely to permeate this relatively modern science of ‘biochemistry’, and which has unfortunately, since 1953, sent education and knowledge on a wrong headed trajectory, completely at odds to that which it ought, and thereby led the planet into an all consuming state of scientific, cultural, and educational dystopia.

The ancient practice of ‘geometry' that many people find so dry and dull, actually served a 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 biochemist’s who question the import of geometry and place 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 very own bibles (below). An element, or perhaps I should say atom, is by its very nature a ‘monad’, and compound groups of monads create molecules of both 2 and 3-dimensional geometric space. It really is not unreasonable to argue that both the proportions and regularity exhibited by the DNA super-molecule are in part accounted for by geometric shape and not only 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. To put such structural accuracy down to coincidence and chance is not scientific.

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