The ten CGB Mathematical Depositions, brought to motion. Each formula and its plain-language reading are free to read; the living animation is the viewing.
“You are purchasing the ability to view these animations. Not the underlying inventions or mathematics.”
Add 1 + 1/4 + 1/9 + 1/16 + … forever and you get a piece of π-squared. Separately, watch a ringing bell fade as it oscillates — that fade is governed by the same ratio. Counting and dying waves, one structure.
The disorder in a message, the irreversibility of heat, and the stiffness of free energy are the same inequality in different clothes. Shannon proved it for bits, Clausius for engines, Helmholtz for reactions — and they never met.
A chip voxel vibrates at many frequencies at once; distance from its neighbours damps the signal like a bell curve. The seed’s matrix determinant scales everything — if det = 0 the voxel is dead, if large it screams.
A single photon carries data in three channels: colour, spin angle, and brightness. Count the bits in each and a good visible photon holds about 24 bits — the chromosome of light.
Grow a chip like a tree and every branch splits into sub-branches; the total gate count at any depth follows a predictable ceiling. Too many wires vs gates is a losing design — the theorem tells you which regime you’re in.
Empty space vibrates at every frequency; the total is infinite. But 1+2+3+… secretly equals −1/12, and with that the infinite vacuum energy collapses to a tiny real force pulling metal plates together. Measured in the lab.
The golden ratio shows up in sunflowers and galaxies — and in chip design: the ideal wiring fraction is 38.2%, exactly 1/φ². Deviate and you either starve for wires or waste silicon on empty metal.
A quantum chip holds a million answers at once, but you see only one when you look. The trick is rotating the hidden answer into view with exactly the right number of nudges — too few and it’s wrong, too many and you overshoot.
Physics says erasing one bit costs a minimum energy — about 3 billionths of a trillionth of a joule at room temperature. Divide your power budget by that and you have the absolute maximum computations per second any computer can ever reach.
A circle has area πr², a sphere volume 4/3πr³. Go higher and the volume grows, peaks at dimension 5, then shrinks to zero. A 100-dimensional ball is almost empty — everything hides at the surface.