So apparently the geometry department wants a word.
Something about me โdefacingโ the sacred halls of Euclid with a claim that \(S^2\) doesnโt actually need three coordinates to exist.
Donโt worry โ the cameras were rolling.
Weโve got the whole thing: the accusation, the replay, and the quiet moment when everyone realizes the wall was blank all along.
Three PDFs, three acts:
๐ Act I โ The Note: On the Minimal Abstract Space Required to Contain \(S^2\)
๐ https://carlostomas49.github.io/S2-Trilogy/OnMinimalSpaceforS2.pdf
๐ Act II โ The Orthodox Reply: No, \(S^2\) Does Not Live in Two Dimensions
๐ https://carlostomas49.github.io/S2-Trilogy/act2.pdf
๐ Act III โ My Answer: On Mistaking a Coordinate System for a Concept
๐ https://carlostomas49.github.io/S2-Trilogy/act3.pdf
The rest is geometry trying to explain away its own handwriting.
If the language feels dense, thatโs fine, grab your nearest ๐ฎ๐ฉ๐ฉ๐๐ซ-๐๐ข๐ฏ๐ข๐ฌ๐ข๐จ๐ง ๐ฆ๐๐ญ๐ก๐๐ฆ๐๐ญ๐ข๐๐๐ฅ๐ฅ๐ฒ-๐ฆ๐ข๐ง๐๐๐ ๐๐ซ๐ข๐๐ง๐ and have them walk you through it.
Just make sure that when theyโre done, they donโt sound like the person from Act II.
๐
Because hereโs the thing โ everyone makes mistakes.
Even the giants who once defined the tone of mathematics itself.
And thatโs what makes this moment worth living through: a small correction echoing through a weary decade thatโs relearning how to think, together.
A quiet fix to a loud assumption, happening out in the open, in the mid-2020s โ post-pandemic, post-certainty โ with the chalk dust still hanging in the air.
Stay safe, and cheers ๐ฅ๐
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