In yesterday’s blog entry, Hobbes Squares the Circle, a video clip from YouTube, “Squaring the Circle with Gaddy’s Pi” was featured. Looking at that video clip more than once, it at least *seems* that the circle has indeed been squared using only a straight-edge and a compass.

As for today’s video clip (top), well, it gave me a good laugh.

But who is this “Gaddy” mentioned yesterday? From what I can find, “Gaddy” is or was Dan W. Gaddy, a high school teacher of mathematics who had spent several years working out his method of squaring the circle which then showed PI to be equal to the square root of 2 plus the square root of 3. [1] (The square root of 2 plus the square root of 3 equals 3.1462… Pi (π) equals 3.1415…)

Gaddy somehow connects with Ralph René, now deceased. “René was not himself a mathematician, but he apparently got at least some of his ideas from a mathematician by the name of Dan W. Gaddy, who reportedly authored a book called Quadrature of the Circle.” [2]

Ralph René is “formally critiqued”, beginning with “he is best known as a cofounder of the moon hoax movement…” [3] Since Ralph René has passed away, a 12 page pamphlet purporting to show details of Gaddy’s method may or may not still be available. (Further info at http://ralphrene.com/circle_squared.html).

“Scientists once proved that bumblebees can’t fly,” is the claim, but snopes.com denies this. The “old line about scientists having proved that the bumble-bee cannot fly” is just “a much loved piece of urban folklore.” [4]

But who is this Snopes? As nearly as I can tell, Snopes is Barbara and David Mikkelson. And – get this – Snopes “is just a mom-and-pop operation that was started by two people who have absolutely no formal background or experience in investigative research.” [5]

So we are right back where we started: either the scientists did or did not once prove that the bumble-bee cannot fly.

Bear this “bumble-bee cannot fly” in mind when I tell you that supposedly the scientists have proved that the circle cannot be squared. In 1882, a mathematician named Ferdinand von Lindemann reportedly proved that the number π (Pi) is not an algebraic number. Instead, said von Lindemann, π (Pi) is “transcendental”. From this is supposed to follow that “a line of length π cannot be constructed by compass and straightedge, and the squaring of the circle is impossible.” [6]

But what if π (Pi) is not what von Lindemann thought but is the value found via Dan W. Gaddy’s effort: the square root of 2 plus the square root of 3?

The point in all this is how Thomas Hobbes believed unless the circle could be squared, this implied dark corners where the light of reason does not shine. (Like Baltimore, for instance.) This in turn seemed to undermine the edifice of Euclidean geometry, “the unassailable bastion of reason itself.” (Background: Hobbes Squares the Circle, Ersjdamoo’s Blog, May 2, 2015.)

Two forces were at work: traditional mathematics and new-fangled ideas based on the method of the little pebbles, the Calculus. One seemed to lead to law and order in the universe; the other to increasing chaos. Dame Frances Yates (1899 – 1981, image above) caused a stir when, in 1964, she published *Giordano Bruno and the Hermetic Tradition*. Yates pictured Giordano Bruno not as a martyr for the progress of science but as a magus, whose program of religious and cultural reform, rooted in the Hermetic texts, was retrograde rather than progressive. [7]

Giordano Bruno was burned at the stake in 1600 in Rome, Italy. That, of course, was going too far, even if Bruno was an Hermetic magus. Italy was the land of the fabulous occult library of Cosimo de’ Medici. Progress in the “little pebbles” and the undermining of Euclid was halted in Italy by the Jesuits. Maybe “Snopes” can tell us definitively whether the Jesuits were right or wrong about disliking the “Indivisibles” and “Infinitesimals” of Calculus. Myself, I cannot say for sure.

——- Sources ——-

[1] http://concen.org/oldforum/thread-30417.html

[2] “counter-apologetics archive of Ben Wallis”, March 14, 2013. http://benwallis.blogspot.com/2013/03/happy-pi-day.html

[3] “A Formal Critique of ‘On Squaring the Circle’ by Ralph Rene, Part 1”. http://transcriptvids.com/v/OlMh_ihqEQI.html

[4] “Bumblebees Can’t Fly”, http://www.snopes.com/science/bumblebees.asp

[5] “Snopes Got Snoped”, May 31, 2013. http://accuracyinpolitics.blogspot.com/2013/05/snopes-got-snoped.html

[6] *Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World*, by Amir Alexander. Scientific American / Farrar, Straus and Giroux; April 8, 2014.

[7] “Natural magic, hermetism, and occultism in early modern science”, by Brian P. Copenhaver. http://tinyurl.com/klyjwfo