Six Impossible Things: Issue 2

March 17, 2024. In the first issue of 6IT: the mathematics of supervising children; unreliably clairvoyant demons; why the sky is blue (and why it isn’t); a Poisson process for primes; sychronizing fireflies; and quantum error correction from Penrose tilings.

β€œThere's no use trying, ” she said. β€œOne can't believe impossible things.” β€œI daresay you haven't had much practice,” said the Queen. β€œWhen I was your age, I always did it for half-an-hour a day. Why, sometimes I've believed as many as six impossible things before breakfast.”
β€” Lewis Carroll, Through the Looking Glass

Inspired by one of my heroes, John Baez, I’m planning to blog about β€œfinds” in the hard sciences on a semi-regular basis. These may be papers, favourite theorems, new discoveries, or shower thoughts; I’m hoping to be brief and nerdily enthusiastic rather than thorough and technically deep. Either way, I hope it’s fun to read. Let’s see how it goes!

Contents

  1. The obstructed supervision theorem
  2. Zermelo’s demon and the axiom of choice
  3. Why the sky is blue
  4. A game of primes
  5. The firefly effect
  6. Quantum error correction from Penrose tilings

https://arxiv.org/pdf/2403.03340.pdf

https://www.researchgate.net/profile/Michael-Jones-66/publication/2246342_Regularization_Theory_and_Neural_Networks_Architectures/links/02bfe50d33d1a45e52000000/Regularization-Theory-and-Neural-Networks-Architectures.pdf

https://www.stat.cmu.edu/~ryantibs/papers/sparsitynn.pdf

https://arxiv.org/pdf/2404.07905.pdf

https://en.wikipedia.org/wiki/Carter_constant

https://arxiv.org/pdf/2204.02063.pdf

https://arxiv.org/abs/1610.09702

https://arxiv.org/pdf/2301.10191

https://arxiv.org/pdf/2405.10958

1. The obstructed supervision theorem