1 kg vs a GOOGOLPLEX kg: How Many Clacks?

A 1 kg block, a wall, and a block that gets 100 times heavier every round. Count every hit (block on block, and block on wall) and you get 3, 31, 314, 3,141 … the digits of π. So we kept going: the Moon, the Sun, the Milky Way, a googol kilograms, the Feynman point, a googolplex, and Graham's number. Every count in this video is exact. Up to 100 trillion kg we simulate every collision. Beyond that nobody can, so the count comes from the exact formula N = ⌈π / arctan(√(m/M))⌉ − 1, worked out with 3,200-digit arithmetic, and the motion is shown compressed in time. We checked every ×100 step up to 10^3200 kg: each one adds exactly one digit of π. The model is 1-D, frictionless and perfectly elastic, with classical physics only (no gravity, no relativity). Closest gaps assume the small block starts 1 m from the wall. Chapters 0:00 1 kg vs a googolplex kg 0:20 1 kg vs 1 kg: 3 clacks 0:28 100 kg: 31 0:37 10,000 kg: 314 0:46 1,000,000 kg: 3,141 0:56 100,000,000 kg: 31,415 1:06 1 billion kg: where did π go? 1:19 10 billion kg: 314,159 1:29 1 trillion kg: 3,141,592 1:39 100 trillion kg: 31,415,926 1:50 10^16 kg: nobody can simulate every hit 2:22 10^30 kg: half the Sun, a proton-sized gap 2:47 10^62 kg: you asked 2:56 10^70 kg: below the Planck length 3:05 A googol kg: 51 digits of π 3:35 The Feynman point: 999999 4:05 A googolplex kg: 5 × 10^99 digits 4:45 Graham's number 5:10 Back to 3 Why π? Watch the full explanation:    • Why Do Colliding Blocks Count π? (31,415,9...   From YOU to the SUN (how many clacks does everything make?):    • From YOU to the SUN: How Many Clacks Does ...   Can the small block EVER win? (5-round fight):    • Видео   10^1,000,000 kg and 500,001 digits of pi:    • Видео   Does speed change the number of clacks?:    • Видео   Credits: Gregory Galperin, "Playing pool with π" (2003). 3Blue1Brown made this puzzle famous. All simulations are exact event-driven physics rendered by TumbleWorks. No voiceover, just the clacks. What mass should we try next? Tell us in the comments. ——— About TumbleWorks: maths and physics simulations computed from the real equations, never keyframed. Collisions that count the digits of pi, chaos in double pendulums, the golden ratio in sunflowers, light in curved mirrors. Each one asks a question and lets the physics answer it. New simulation every day. Subscribe:    / @tumbleworks   #physics #math #pi