Author Archives: apgoucher

Self-replicator caught on video

In a previous article, an announcement was made of a complex self-replicating machine (known as the 0E0P metacell) in a simple 2-state cellular automaton. In the interim between then and now, Thomas Cabaret has prepared a most illuminating video* explaining … Continue reading

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Five-input 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 n-input m-output 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 Box-Müller 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 self-directed replication

A new form of artificial life has been born — and there are no doubts that it directs its own self-replication: 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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6-colourings 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 6-colour 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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