The Rest Is Science Paradoxes Of Infinity
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Mar 24, 2026 They tumble into the paradoxes around infinity, from Hilbert's Hotel to Zeno's motion puzzles. They trace the history and symbols behind the infinite and revisit Pythagorean fears about non-finite numbers. They unpack calculus, limits, and mind-bending thought experiments like Thompson's lamp and the Ross-Littlewood jar.
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Hilbert's Hotel Reveals Strange Arithmetic Of Infinity
- Infinity behaves like a quantity you can manipulate with clever reindexing rather than ordinary arithmetic.
- Hilbert's Hotel shows a full infinite hotel can admit one guest by shifting n→n+1 and admit countably infinite buses by mapping n→2n or primes→powers.
Origins Of The Lemniscate Symbol
- The infinity symbol's origin is uncertain but likely evolved from older numeric notation.
- John Wallis used the lemniscate in 1655 and it may echo Roman parenthetical numerals (thousand/millennium) or Greek omega imagery.
Pythagoreans Rejected Irrational Numbers
- The Pythagoreans prized numerical harmony and opposed the infinite as disorderly.
- Hippasus allegedly discovered √2 was irrational and was ostracized or drowned for introducing incommensurable (infinite) quantities into their worldview.
