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I am the founder of Hatsya Limited, which provides mathematical and technological solutions to realworld problems.

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Author Archives: apgoucher
Selfreplicator caught on video
In a previous article, an announcement was made of a complex selfreplicating machine (known as the 0E0P metacell) in a simple 2state cellular automaton. In the interim between then and now, Thomas Cabaret has prepared a most illuminating video* explaining … Continue reading
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Fiveinput Boolean circuits
Over the past few weeks, I’ve been investigating Boolean optimisation. That is to say, given some circuit of logic gates that implements a particular ninput moutput function, find a more efficient circuit that implements the same function. In practical applications, … Continue reading
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(W^2 + X^2) / (W^2 + X^2 + Y^2 + Z^2)
The BoxMüller transform is a method of transforming pairs of independent uniform distributions to pairs of independent standard Gaussians. Specifically, if U and V are independent uniform [0, 1], then define the following: ρ = sqrt(–2 log(U)) θ = 2π V … Continue reading
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Complexity of integer multiplication almost solved
Whilst not quite as close as the proofs of the ternary Goldbach conjecture and bounded gaps between primes, there has been a quick succession of two important and somewhat complementary breakthroughs on the computational complexity of integer multiplication: Afshani, Freksen, … Continue reading
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Fully selfdirected replication
A new form of artificial life has been born — and there are no doubts that it directs its own selfreplication: So, what exactly is happening? At 0:06, the organism begins to sequentially construct four identical copies of itself. At … Continue reading
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6colourings of subsets of the plane
There has been further recent activity on the Chromatic Number of the Plane problem, with an eleventh research thread being spawned. Philip Gibbs has been able to 6colour a large disc (with diameter slightly greater than 4), and Aubrey de … Continue reading
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Atiyah’s problem
At the Heidelberg Laureate Forum three years ago, I took lots of selfies with Fields medallists, Abel prizewinners and Turing laureates. This included having a dinner in a castle with Leonard Adleman, pioneer of asymmetric cryptography: …and Endre Szemeredi of … Continue reading
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