The Gordian Knot and String Theory*
By R. D. Flavin


“Alexander Cutting the Gordian Knot” by Fedele Fishetti (1732-1792).

“Alexander could find out no way to loosen the cord and yet was unwilling to allow it to remain unloosened, lest it should exercise some disturbing influence upon the multitude, he struck the cord with his sword and cut it through, saying that it had been untied by him. But Aristobulus says that he pulled out the pin of the wagon-pole, which was a wooden peg driven right through it, holding the cord together. Having done this, he drew out the yoke from the wagon-pole. How Alexander performed the feat in connection with this cord, I cannot affirm with confidence. At any rate both he and his troops departed from the wagon as if the oracular prediction concerning the untying of the cord had been, fulfilled (Arrian 1884, p. 84).”

     'String Theory,” a model which suggests a gravitational basis for quantum field theory, as part of theoretical physics, is fine in an imaginary mathematical playground, but fails the scientific method as it can't be tested. Of course, much of so-called quantum mechanics is untestable and answers of 'yes', 'no', 'maybe,' and 'yes and no and maybe' at the same time is a Gordian Knot awaiting to be either unraveled or split (that is, abandoned or dismissed). Though, with CERN's Large Hadron Collider up and running again and the discovery of the Higgs boson (or particle), further study of elementary particles may be able to 'test' some aspects of quantum field theory.

     Prof. Neugebauer (Brown, History of Mathematics Department) most excellently drew our attention to the 'exact' sciences of mathematics and astronomy as practiced by the ancients (Neugebauer 1951), while already theory was being practiced in such disciplines and pursuits as planetary orbits, the nature of mass as consisting of 'atoms', and the ridiculous fraud pulled off by Galen for passing off the 'anatomy' of monkeys and pigs as human. The unobservable is often untestable and we've been doing such for a good span – there's a tad of time 'tween Newton and Hawkings.

     BTW, I don't consider myself a 'good' writer or even mediocre... However, I don't strive for such. Rather, for many years I've tried to be a conduit (i.e., a bridge, an alternative voice which doesn't speak DOWN, but speaks best he can) and my success I'll leave to others to decide. Sigh, getting back to 'string theory' and putting a century of theoretical physics in words an average reader MIGHT comprehend. Fearless. Challenge accepted. And let's get on with it...

     By the time of the early Bronze Age, we (Eastern and possibly small communities in Western Asian civilizations) had achieved math, fairly accurate geography, observational and testable practices which helped develop the 'modern' scientific method. Yet, we still had and have theory and both unobservable and untestable models, such as in theoretical physics and specifically quantum mechanics and all its designer baggage. Ever striving for the skinny (read: simplest answer or cause), much like Alfred Russel Wallace shared his idea of the 'Natural Selection' explanation for 'evolution' with Darwin, so too did Theodor Kaluza write Einstein and only published on his own several years later (Kaluza 1921), and soon afterward Oskar Klein complimented and extended Kaluza (Klein 1926a, 1926b). Others, naturally, followed, both terming the work of Kaluza and Klein as the 'Kaluza-Klein Theory', but also ...greatly expanded on the possibilities of more than one universal dimension, gravitational obligations, and models for such proposed behavior for elementary particles, as well as the emergence of a 'possible' higher spatial dimension which was postulated to account for certain behaviors in electromagnetism and gravitation. By way of a sad contemporary analogy – much like certain intoxicants (hard alcohol and marijuana) are regarded by some as “gate-way drugs” leading to abuse, so too did a serious suggestion of a higher spatial 'dimension'. The Heisenberg's uncertainty principle (Heisenberg 1927) and the challenge of Schrödinger's Cat (Schrödinger 1935), was what jazz and blues is to rock and roll – influence. As quantum mechanics didn't emerge in a vacuum (or as some Zen kōan like the”sound of one hand clapping), so too did the Danish physicist, Niels Bohr (who won the Nobel Prize in Physics in 1922), greatly conributed to the growing field of speculative quantum theory. Later, when the youngsters like Richard Feyman and Steven Hawking showed up (along with a host of others, quantum mechanics and string (or 'superstring') theory became commonplace. Though remaining purely theoretical...

The formula for the Bekenstein–Hawking entropy (S) of a black hole, which depends on the area of the black hole (A). The constants are the speed of light (c), the Boltzmann constant (k), Newton's constant (G), and the reduced Planck constant (ħ).

     While Hawkings has recently cast doubt upon his earlier theory about 'black holes', the arguments both for and against the existence of the one-dimensional objects called 'strings' continue. I have likened such to the classic Gordian Knot, as most understand the 'legend' one way, though other interpretations exist and are still debated (was the 'knot' a metaphor or cipher, etc.), and I opine theoretical quantum mechanics is in a similar situation. As a 'metaphor', fine, if put forth as an aspect of mathematics, then prove it. So much for the 'exact' sciences...


Arrian of Nicomedia. 1884. The Anabasis of Alexander; or, The History of the Wars and Conquests of Alexander the Great. Literally translated, with a commentary, from the Greek of Arrian the Nicomedian. By E. J. Chinnock, M.A., LL.B., London, Rector of Dumfries Academy. London: Hodder and Stoughton, 27, Paternoster Row, MDCCCLXXXIV. Butler & Tanner, The Selwood Printing Works, Frome, and London. See: Book II/Chapter III, p.84.

Kaluza, Theodor. 1921. "Zum Unitätsproblem der Physik." Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin. Vol. Unknown: 966-972.

Klein, Oskar. 1926a. "Quantentheorie und fünfdimensionale Relativitätstheorie." Zeitschrift für Physik. 37, 12: 895–906. doi:10.1007/BF01397481.

Klein, Oskar. 1926b. "The Atomicity of Electricity as a Quantum Theory Law." Nature. 118: 516. doi:10.1038/118516a0.

Heisenberg, W. 1927. “Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik.” Zeits Physik. 43: 172–198.

Neugebauer, Otto. 1951. The Exact Sciences in Antiquity (Vol. IX of Acta historica scientiarum naturalium et medicinalium). Copenhagen, E. Munksgaard; Princeton, N.J., Princeton University Press.

Schrödinger, Erwin. 1935. "Die gegenwärtige Situation in der Quantenmechanik (The present situation in quantum mechanics)." Naturwissenschaften. 23, 49: 807–812. doi:10.1007/BF01491891.

*Written at the request of my cousin, Steve Peslak.

Tying an Angler's knot,

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