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Complex Projective 4-Space
Personal blog · cp4space.hatsya.commathscience
Complex Projective 4-Space is a personal blog at cp4space.hatsya.com about math and science. Since 2020, 16 different Hacker News readers have linked it 23 times, most often “Discovery of a single tile that tiles the plane only aperiodically”. It is still writing: the last post was on 2026-05-03, and you can follow it by feed.
Where exciting things happen
Most-linked posts?
- Discovery of a single tile that tiles the plane only aperiodically3 people · 3 mentions · first linked 2023-03-21
- The neural network of the Stockfish chess engine2 people · 2 mentions · first linked 2021-01-13
- Urbit for Mathematicians2 people · 2 mentions · first linked 2021-06-19
- Shallow trees with heavy leaves (2020)2 people · 2 mentions · first linked 2020-12-14
- 4-input 2-output Boolean circuits (2020)2 people · 2 mentions · first linked 2025-06-23
What Hacker News says?
We also know the optimal circuits if you want to compute two boolean functions from four variables at the same time: https://cp4space.hatsya.com/2020/06/30/4-input-2-output-bool... .
Comment linking /2020/06/30/4-input-2-output-boolean-circuits/
on “Minimal Boolean Formulas (2011)”Submitted The neural network of the Stockfish chess engine as a story · 355 points
HN discussionThey missed the opportunity to call it 'Conway's Life of Games'! There are many open problems about Life that universality doesn't answer, such as whether there exists an oscillator of every period. There was a problem posed by Conway himself that was solved just this year! https://cp4space.hatsya.com/2022/01/14/conway-conjecture-set...
Comment linking /2022/01/14/conway-conjecture-settled/
on “Conway's Game of Life – Mathematics and Construction [pdf]”Submitted 29-year-old Conway conjecture settled as a story · 230 points
HN discussionIf I recall (previously-submitted article - https://cp4space.hatsya.com/2023/03/21/aperiodic-monotile/ ), the shape has to be flipped upside down some fraction of the time. So you'd either need two tile shapes for a real bathroom, or your tiles would be a compromise between "both faces are easily cleaned" and "both faces stick firmly to the mortar".
Comment linking /2023/03/21/aperiodic-monotile/
on “Mathematicians discover shape that can tile a wall and never repeat”Submitted The exceptional Jordan algebra (2020) as a story · 108 points
HN discussionAn example is efficient prime-field arithmetic: https://cp4space.hatsya.com/2021/09/01/an-efficient-prime-fo... > If A happened to be larger than C, and therefore the result of the subtraction underflowed, then we can correct for this by adding p to the result. [...] we can multiply B by 2^32 using a binary shift and a subtraction, and then add it to the result. We might encounter an overflow, but we can correct for…
Comment linking /2021/09/01/an-efficient-prime-for-number-theoretic-transforms/
on “Git Security Vulnerabilities Announced”Submitted Every finite phoenix has period 2 as a story · 19 points
HN discussionSee also the @p encoding system used in urbit: https://cp4space.hatsya.com/2021/05/12/urbit-for-mathematici... https://github.com/urbit/urbit-ob > ob.patp('0') '~zod' > ob.patp2dec('~nidsut-tomdun') '15663360' > ob.hex2patq('010203') '~doznec-binwes' > ob.patq2hex('~marned-wismul-nilsev-botnyt') '01ca0e51d20462f3' > ob.isValidPatq('~marned-wismul-nilsev-botnyt') > true Each byte is converted to a three letter syllab…
Comment linking /2021/05/12/urbit-for-mathematicians/
on “Sing-song: a speakable encoding for long numbers and keys”Submitted Shallow trees with heavy leaves (2020) as a story · 11 points
HN discussionPrime numbers with practical applications do get discovered. Most notably, I suppose: 2^64 - 2^32 + 1: https://cp4space.hatsya.com/2021/09/01/an-efficient-prime-fo... There are annual prizes on performing certain computations efficiently in prime fields for this prime: https://www.zprize.io/ But if there is a practical application to very large primes: I don’t know. 40 million digits sounds very inefficient unless y…
Comment linking /2021/09/01/an-efficient-prime-for-number-theoretic-transforms/
on “New largest prime number found See all 41,024,320 digits [video]”Submitted Shallow Trees with Heavy Leaves as a story · 8 points
HN discussion"While all agreed "the hat" was the first einstein, its mirror image was required one in seven times to ensure that a pattern never repeated." The article has a small error here - it should say approximately 7. The ratio between the tiles and their mirrors is phi^4. https://cp4space.hatsya.com/2023/03/21/aperiodic-monotile/
Comment linking /2023/03/21/aperiodic-monotile/
on “UK hobbyist stuns math world with 'amazing' new shapes”Submitted Urbit for Mathematicians as a story · 7 points
HN discussionyes https://cp4space.hatsya.com/2021/01/08/the-neural-network-of...
Comment linking /2021/01/08/the-neural-network-of-the-stockfish-chess-engine/
on “DeepMind has open-sourced the heart of AlphaGo and AlphaZero”Submitted Training a Random Gaussian Generator as a story · 3 points
HN discussionOh wow! I wasn’t expecting to see this on HN. I’m one of the authors of the paper, and I’m happy to answer any questions. (I’m sorry I didn’t see it earlier, it was posted in the middle of my night.) First of all, to clear up a possible misunderstanding: this new formula will not help you to compute determinants more quickly. The number of terms still grows a lot faster than polynomial, and if you just want to compu…
Comment linking /2022/07/02/a-combinatorial-proof-of-houstons-identity/
on “A New Formula for the Determinant”Submitted Schanuel's Conjecture and the Semantics of Triton's FPSan as a story · 2 points
HN discussionSubmitted Every finite phoenix has period 2 (Conway's Game of Life) as a story · 2 points
HN discussionSubmitted Keep your public keys private as a story · 2 points
HN discussionSubmitted Subsumptions of Regular Polytopes as a story · 2 points
HN discussionSubmitted 4-input 2-output Boolean circuits (2020) as a story · 1 points
HN discussionSubmitted Discovery of a single tile that tiles the plane only aperiodically as a story · 1 points
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