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Types versus sets in math and programming languages
For several years I have been designing and implementing a functional teaching language especially for use in the context of a Discrete Mathematics course. The idea is for students to be exposed to…
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The Joy of Condensed Matter
I published a slightly different version of this article in Nautilus on February 24, 2021. Everyone seems to be talking about the problems with physics: Woit’s book Not Even Wrong, SmolinR…
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Evaluating Search Algorithms
The three-step framework Shopify's Data Science & Engineering team built for evaluating new search algorithms.
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Understanding Multiple Neighbourhood Cellular Automata
Multiple Neighborhood Cellular Automata (MNCA) produce complex and robust emergent structures not commonly seen in simpler models
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JPEG XL would be Turing-complete without the 1024×1024 pixel limitation
You can construct the Rule 110 cellular automaton in JPEG XL.
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Entropy and Algebra and Topology = ?
Today I'd like to share some math connecting ideas from information theory, algebra, and topology. It's all in a new paper I've recently uploaded to the arXiv (https://arxiv.org/abs/2107.09581), which describes a correspondence between Shannon entropy and functions on topological simplices that obey a version of the…
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Computing the number of digits of an integer even faster
I my previous blog post, I documented how one might proceed to compute the number of digits of an integer quickly. E.g., given the integer 999, you want 3 but given the integer 1000, you want 4. It is effectively the integer logarithm in base 10. On computers, you can quickly compute the integer logarithm … Continue…
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Finite State Machines
To infinity and beyond!
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Floor, Ceiling, Bracket
The notation [x] reigned for nearly two centuries before being replaced by ⌊x⌋. Why the latter is much better and what else we might learn from its inventor.
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