Saturday, January 11, 2025

Volume Relation

In culty backwaters, or call it a swamp, where the sausage gets made, we have our little niche controversies. 

Perhaps goaded by Braingate, the controversy swirling around the two elderly gangsta presidents (were their faculties still intact?), and the subsequent coverups (not really, at least in Biden's case), some latecomers to our party have decided to retell our own story about Bucky. 

According to them, our guy was too Alzheimery by the 1970s to really know what he meant in Synergetics, which means the rest of us have been engaged in a coverup, trying to make Synergetics seem more coherent than it really is.

This new "Bucky was senile" faction that wants to purge S3 (an important constant) from the future curriculum, to spare people the need to understand what it's all about. 

Because Bucky was close to senile by the time those two volumes were published, he was able to confuse himself about this number (~1.06066... or 2nd root of 9/8).

But was he really that confused? We're talking about two conceptions of unit volume and comparing them. Both the cube and the tetrahedron will need a size when the other is unit. 

If the tetrahedron's edges are twice the cube's, then that difference, one of proportion between volumes, is S3. So it's like a currency conversion constant, with Tetrahedron Dollars versus Cube Dollars. The difference is only about 6%.

I think what makes readers doubt the sense of Synergetics is that what it does to the cube seems too drastic. A cube of edges 1 no longer has a rational whole number volume. That can't seem right to anyone brainwashed to think "right angles rule", the predominant orthodoxy. Surely you're joking Mr. Fuller!