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I immediately thought of Plato and western esotericism. These look magical. Plato's atomic theory in Timaeus was that atoms should be the simplest geometric for
by dr_dshiv 5y ago
I immediately thought of Plato and western esotericism. These look magical. Plato's atomic theory in Timaeus was that atoms should be the simplest geometric forms possible. These are what we now call the Platonic forms: the tetrahedron, the cube, the isocahedron, the octohedron and the dodecahedron. Plato associated each with an element, based on the intrinsic material properties of the geometric shape. For instance, earth was cubic because cubes stack well and fire was tetrahedric because the sharpness of the pyramid-shape was destructive like fire.
Dodecahedra were the 5th element, the quintessence, which was the aether beyond air. Totally magical. These things would have impressed people and communicated philosophical prowess.
- berkeleynerd 5y agoAnyone interested in this kind of stuff (i.e., the Western Esoteric Tradition) would enjoy The Secret History of Western Esotericism podcast. Lots of great scholars and scholarship on this understudied aspect of Western civ. https://shwep.net/ https://shwep.net/
- dr_dshiv 5y agoSecond. It's the best thing on the internet.
- ddalex 5y agoOk what's the first best thing on the internet?
- aptsurdist 5y agoThanks so much for this link, I started listening and I immediately love it.
- wincy 5y agoWeird that these are the exact dice used to play a game of Dungeons and Dragons.
- ravi-delia 5y agoNot so weird, you want your dice to be maximally symmetric for fairness. When you add easy manufacture to the qualifications, only the platonic solids will do.
- dragonwriter 5y agoThe d10 is not a platonic solid.
- ravi-delia 5y agoThat is correct, I'm an idiot. Almost only the platonic solids will do? Honestly it seems like the platonic solids are the easiest to work with, except percentile dice are nice for people using base-10 so you have to throw in a 10-sided die too. There are non-platonic versions of the other dice too, but you don't see them I assume because they're harder to manufacture. Less cut and dry than I though though!
- gweinberg 5y agoThe original D&D dice were the 5 platonic solids, the 10s were added later. But there are lots of shapes that can be "fair". You can stick 2 pyramids with any number of sides together, you can make a long prism with any number of sides since it will never land on the long ends, a coin can be considered to be a 2 sided die. I seem to recall somebody made a 30 sided die where the sides were parallelograms, although I never had one.
- dragonwriter 5y ago> The original D&D dice were the 5 platonic solids, the 10s were added later. True; IIRC, the rules used d10 but it was a way of reading the d20 before d10s were manufactured.
- monkeywork 5y ago
- kortex 5y agoThe pentagon and dodecahedron are also very interesting mathematically. Squares and triangles tile the plane, and have nice "round" number angles 90° and 60°. Pentagons don't tile and feature 108° angles. The diagonals of a convex regular pentagon are in the golden ratio to its sides. The inscribed pentagram has a very recursive feel for this reason, "tiling" (nesting) off to infinity.
- anigbrowl 5y agoI'd have to go looking for the paper now but this is fascinatingly true of some kinds of viral envelopes.
- prox 5y agoWeren’t the Pythagoreans complete number worshippers? Maybe they are related to them?
- dr_dshiv 5y agoYes, like Max Tegmark, they believed the world was made of math. Where harmony means wholeness, they believed in harmonies in numbers (1+2+3+4=10), harmonies in numbers in space (geometry), harmonies in numbers in time (musical ratios) and harmonies in numbers in space and time (astronomy; harmonies of the spheres). They also conducted the first hypothesis driven experiment in western science when they cast bronze chimes with corresponding ratios of thickness (1:2, 2:3) to see if the pythagorean tuning of strings was a generalizable property. Plato extended pythagoreanism to make the world of math into the world of pure forms—a universal, immortal realm. He also continued the esoteric tradition of the pythagoreans, who had to keep their practices secret because they kept getting slaughtered. It's just the best history. Pythagoras was also gender inclusive—not only were there many female pythagorean philosophers, he also (according to aristoxenus) openly credited his moral doctrines to Themistoclea. For integrating science and spirituality at the start of western civ, pythagoreanism is pretty much the coolest.
- prox 5y agoIt’s interesting that such a “scientific” group was readily persecuted. Power fears knowledge it seems. However very interesting group! Wish they were still around :)