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Why does quantum mechanics use complex numbers extensively? Why is the inner product of a Hilbert space antilinear in the first argument? Why are Hermitian operators important for representing observables? And what is the i in the Schrödinger equation doing? This post explores these questions through the framework of groupoid...
Past years: 2023 2024 Continuing a yearly tradition, I evaluate AI predictions from past years, and collect a convenience sample of AI predictions made this year. I prefer selecting specific predictions, especially ones made about the near term, enabling faster evaluation. Evaluated predictions made about 2025 in 2023, 2024, or...
David Chalmers describes the inverted qualia thought experiment, in The Conscious Mind, as an argument against logical supervenience of phenomenal experience on physical states: > one can coherently imagine a physically identical world in which conscious experiences are inverted, or (at the local level) imagine a being physically identical to...
Why are linear functions between finite-dimensional vector spaces representable by matrices? And why does matrix multiplication compose the corresponding linear maps? There's geometric intuition for this, e.g. presented by 3Blue1Brown. I will alternatively present a category-theoretic analysis. The short version is that, in the category of vector spaces and linear...
I present a step-by-step argument in philosophy of mind. The main conclusion is that it is probably possible for conscious homomorphically encrypted digital minds to exist. This has surprising implications: it demonstrates a case where "mind exceeds physics" (epistemically), which implies the disjunction "mind exceeds reality" or "reality exceeds physics"....
Sometimes, a philosophy debate has two basic positions, call them A and B. A matches a lot of people's intuitions, but is hard to make realistic. B is initially unintuitive (sometimes radically so), perhaps feeling "empty", but has a basic realism to it. There might be third positions that claim...
It is analytically useful to define intelligence in the context of AGI. One intuitive notion is epistemology: an agent's intelligence is how good its epistemology is, how good it is at knowing things and making correct guesses. But "intelligence" in AGI theory often means more than epistemology. An intelligent agent...