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Recent Comments
 tomtom2357 on Updates and errata
 Updates and errata  Complex Projective 4Space on Treefoil
 tomtom2357 on The inadequacy of SCLT
 apgoucher on The neural network of the Stockfish chess engine
 El número TREE(3) no es infinito, pero es tan grande que ni siquiera cabe en el universo  La Fragua on TREE(3) and impartial games
Author Archives: apgoucher
Hamming cube of primes
Given two nonnegative integers, m and n, we say that they are Hammingadjacent if and only if their binary expansions differ in exactly one digit. For example, the numbers 42 and 58 are Hammingadjacent because their binary expansions 101010 and … Continue reading
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Determinacy
I’d like to take this opportunity to highly recommend Oscar Cunningham’s blog. One of the posts, entitled A Better Representation of Real Numbers, describes an elegant orderpreserving* bijection between the nonnegative reals [0, ∞) and ‘Baire space‘, , the space … Continue reading
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Oneway permutations
Oneway permutations are fascinating functions that possess a paradoxical pair of properties. They are efficiently computable functions φ from [n] := {0, 1, …, n−1} to itself that are: Mathematically invertible, meaning that φ is a bijection; Cryptographically uninvertible, meaning … Continue reading
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Cyclotomic fields
The nth cyclotomic field is the field generated by a primitive nth root of unity, ζ. It is an example of a number field, consisting of algebraic numbers, and its dimension is φ(n) when regarded as a vector space over … Continue reading
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Urbit for mathematicians
The three months since the last cp4space article have largely been spent learning about an interesting project called Urbit. My attention was drawn to its existence during a talk by RivaMelissa Tez (formerly of Intel) on the importance of continued … Continue reading
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A curious construction of the Mathieu group M11
Previously, we discussed which regular polytopes have vertexsets that occur as proper subsets of the vertexset of another regular polytope in the same dimension. In particular, when there is a Hadamard matrix of order 4k, then then the (4k−1)dimensional simplex … Continue reading
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Assorted topics
This is a digest of things that have happened this month, but which are individually too small to each warrant a separate cp4space post. Firstly, there have been a couple of exciting results in the field of combinatorics: The ErdősFaberLovász … Continue reading
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Meagre sets and null sets
There are two competing notions for describing a subset of the real numbers as being ‘small’: a null set is a subset of the reals with Lebesgue measure zero; a meagre set is a countable union of nowheredense sets. Both … Continue reading
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Keep your public keys private
Yes, the title sounds very counterintuitive. After all, don’t digital signature schemes require the general public to know your public key so that they can verify your signatures? That is correct, but importantly they don’t need to know your public … Continue reading
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The neural network of the Stockfish chess engine
Last time, we briefly mentioned the highlevel differences between Stockfish and Leela Chess. To recap, Stockfish evaluates about 100 million positions per second using rudimentary heuristics, whereas Leela Chess evaluates 40 000 positions per second using a deep neural network … Continue reading
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