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pavpanchekha.com | ||
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www.forwardscattering.org
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| | | | | [AI summary] Nicholas Chapman proves that it is decidable to find the fastest Turing machine for computing functions defined on a finite domain by limiting the search space to machines with a finite number of states based on a reference solution's runtime. | |
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njwildberger.com
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| | | | | There are several approaches to the modern theory of "real numbers". Unfortunately, none of them makes complete sense. One hundred years ago, there was vigorous discussion about the ambiguities with them and Cantor's theory of "infinite sets". As time went by, the debate subsided but the difficulties didn't really go away. A largely unquestioning uniformity... | |
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jeremykun.wordpress.com
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| | | | | We assume the reader is familiar with the concepts of determinism and finite automata, or has read the corresponding primer on this blog. The Mother of All Computers Last time we saw some models for computation, and saw in turn how limited they were. Now, we open Pandrora's hard drive: Definition: A Turing machineis a... | |
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www.jeremykun.com
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| | | Last time we investigated the naive (which I'll henceforth call "classical") notion of the Fourier transform and its inverse. While the development wasn't quite rigorous, we nevertheless discovered elegant formulas and interesting properties that proved useful in at least solving differential equations. Of course, we wouldn't be following this trail of mathematics if it didn't result in some worthwhile applications to programming. While we'll get there eventually, this primer will take us deeper down the rabbit hole of abstraction. | ||
