Tuesday, 20 September 2011

Do Mathematicians have hearts – or – from Bucky Fuller to I-Ching

A nonsensical Twitter exchange with a nice chap from that cold watery waste north of the USA, @JohnJGeddes.
It meandered from this:
@JohnJGeddes: “we are the sum of our loves, so a great writer must have a great heart.” Retweeted to one of my friends, @1_Lovelife
to which I responded: “What does that make a great mathematician?”
He: “The sum of his other sides :)”
I: “He is the Hippopotamus in the Room: in his squareness being the sum of the squares of his bottom- and back-sides!”
He: “my best friend in Scotland is a Mathematician - I know you Math people have great hearts :) ”
I: “I knew one once with a great heart – gave him lift from airport to lecture to Royal Society (?) – Bucky Fuller.”
He: “Oh, wow! Yeah, a good guy :)”
I: “Bucky was a phenomenon! I frivolously worked out that his Vector Equilibrium reconciled east and west. How?”
He: “I'll”
I: “1. Individuating West (points as opposed to connections). Represent a one-frequency VE as twelve points around a focus – Christ”
I: “2. Relational East. Within 2-frequency VE can be found the eight great hexagrams (paired orthog. helixes)+56 lesser hexagrams…”
I: “… of the I-Ching! (Each hexagram/tetrahedron is of two opposite handed orthogonal helixes, each of three lines)”
I: “Which brings us to my Minorbore’s secondary riddle: How did the Ring square up to the three Axes?”
I: “In a dual, of course! Bucky’s (VE) cuboctahedral dual, rhombic dodecahedron in spherical guise is the shape left by…”
I: “… the orthogonal intersection of three identical diameter rings or tubes (the three axes). OK enough, ed.”
He: “that's a really elegant solution, Allan* - the Math I mean - well, the drink too, I suppose :)”

[*I guess they spell Alan with two ells over there – to make it go further – they have such vast distances to cover, you see]

I add a few diagrams ‘borrowed’ from the web (I hope with no offense, since there is no commercial purpose to this) to help explain the figures.

The spheres (vertices) represent the individuated West and 12 closest pack around a central to form a frequency 1 Vector Equilibrium or Jesus and the Twelve disciples of Christianity.
The edges (connecting lines) represent the inter-relational East and a 2-frequency Vector Equilibrium has 8 Great (2-frequency) Tetrahedra (Hexagrams) and 56 lesser (1-frequency) Tetrahedra, making the 64 hexagrams of the I-Ching.

This raises the vexed question of why 13 is considered unlucky in the West, whereas 7, the closest packing of circles around a central circle, is considered lucky. Mathematically, both should be lucky (because stable).

1 comment:

  1. It’s nice to see Russian finding this article!
    вектор еквилибриум on search.