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The Busy Beaver Game
This month, a bunch of ‘logic hackers’ have been seeking to determine the precise boundary between the knowable and the unknowable. The challenge has been around for a long time. But on…
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Zero-allocation Trie Traversal
As part of a demonstration in an upcoming article , I wrote a simple trie implementation. A trie is a search tree where the keys are a sequence of symbols (i.e. strings). Strings with a common prefix share an initial path down the trie, and the keys themselves are stored implicitly by the structure of the trie. It’s…
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Computing primes with CSS
I’ve been working on a redesign of this site, so doing more CSS, finally internalizing Sass, etc. During my reading, the nth-child pseudo-class caught my eye.
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The Holy Trinity: Logic, Languages, Categories (2011)
The Christian doctrine of trinitarianism states that there is one God that is manifest in three persons, the Father, the Son, and the Holy Spirit, who together form the Holy Trinity. The doctrine…
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Toward an exploratory medium for mathematics
The world's oldest complete piece of surviving music is the 3,400-year-old Hurrian cult hymn . The hymn was found inscribed on clay tablets excavated from the ancient city of Ugarit, in modern-day Syria. Sometime after the hymn was composed, the idea of using notation to record music was lost. Writing two millennia…
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The best linear algebra books
If you would follow the road to linear algebra here are some trustworthy signposts.
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Solomon Golomb (1932–2016)
Stephen Wolfram shares a glimpse into his conversations with Solomon Golomb, developments on shift registers, polyominoes, scientific contributions.
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Gradient Boosting Explained in 3D
Understanding gradient boosting with interactive 3d-demonstrations
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Generalized linear models, abridged
Generalized linear models (GLMs) are indispensable tools in the data science toolbox. They are applicable to many real-world problems involving continuous, yes/no, count and survival data (and more). The models themselves are intuitive and can be used for inference and prediction. A few very high quality free and open…
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Fast Fibonacci Algorithms (2015)
Definition: The Fibonacci sequence is defined as \(F(0) = 0\), \(F(1) = 1\), and \(F(n) = F(n-1) + F(n-2)\) for \(n ≥ 2\). So the sequence (starting with \(F(0)\)) is 0, 1, 1, 2, 3, 5, 8, 13, 21, ….
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The Relativistic Rocket
Thanks to Alan R. Wilson for correcting a two-word typo involving GPS satellites. Thanks to Aron Yoffe for suggesting the newtonian comparison. Thanks to Tom Fuchs for suggesting the analogy to the stone thrown upwards. Fuel numbers added by Don Koks, 2004. Updated by Phil Gibbs, 1998. Thanks to Bill Woods for…
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What if You Only Invested at Market Peaks?
What happens when you only invest at the peaks of the market by being the world's worst market timer.