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The Greedy Doctor Problem
TL;DR: How to reason about people who are smarter than you. A few proposals, interspersed with reinforcement learning and humorous fiction. Ending on a surprising connection to logical inductors.
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Gradient Descent Models Are Kernel Machines
This paper shows that models which result from gradient descent training (e.g., deep neural nets) can be expressed as a weighted sum of simi...
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0x7FDE623822FC16E6: A magic constant for double float reciprocal (2011)
EDIT: I never expected this post to garner so much interest. Just to be clear, using the constant is a very bad idea in almost every situation I can think of. Even instructions like RCPSS should only be used by people who are convinced that the tradeoffs are worth it (or don’t have any other choice). Subtracting from…
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The 8000th Busy Beaver number eludes ZF set theory (2016)
I’ve supervised a lot of great student projects in my nine years at MIT, but my inner nerdy teenager has never been as personally delighted by a project as it is right now. To…
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RNA Memory Hypothesis
There’s an old theory that memory is actually encoded in part in RNA. The argument is pretty simple: there’s no obvious way for all that sensory data to be captured in synapses as long …
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All Horses Are the Same Color
Problem: Show that all horses are of the same color. “Solution”: We will show, by induction, that for any set of $ n$ horses, every horse in that set has the same color. Suppose $ n=1$, this is obviously true. Now suppose for all sets of $ n$ horses, every horse in the set has the same color. Consider any set $ H$ of…
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Sunset Geometry (2016)
Robert Vanderbei has written a beautiful series of articles and talks about a method for finding the radius of the earth based on a single photograph of a sunset over a large, calm lake.
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Computational algebraic geometry for high school students
Can high school students really learn algebraic geometry? And what could it teach us about mathematics education?
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What’s Wrong with “Multiplication Is Repeated Addition”? (2008)
[Photo by Alejandra Mavroski.] Myrtle called it The article that launched a thousand posts…, and counting comments on this and several other blogs, that may not be too much of an exaggeration…
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Review: The Book of Why
The Book of Why: The New Science of Cause and Effect is a collaborative effort aimed at a general audience by Judea Pearl , a professor of computer science at UCLA, and Dana Mackenzie , a science writer. As a medical student with a laughably poor formal education in statistics, I believe I qualify as a card-carrying…
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Does having prime neighbors make you more composite?
Babylonian accountants and land surveyors did their arithmetic in base 60, presumably because sexagesimal numbers help with wrangling fractions. When you organize things in groups of 60, you can divide them into halves, thirds, fourths, fifths, sixths, tenths, twelfths, fifteenths, twentieths, thirtieths, and…
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How to average floating point numbers (2015)
When it comes to accuracy, how you add a series of arbitrary values together, and average them still matters.
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Learning with Not Enough Data: Semi-Supervised Learning
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Speech to Birdsong Conversion
A blog about signals, programming, music, and other stuff.
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Peter M. Neumann has died
Memories from Oxford days Mathematical Institute src Peter Neumann, Professor of Mathematics at Queen’s College, Oxford University, passed away two weeks ago. Last Monday would have been his …
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Using Benford’s Law to Detect Bitcoin Manipulation
Economist Gary Smith sends along this post with the above title and the subtitle, “Market prices are not invariably equal to intrinsic values.” Here’s Smith:
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Cleaner parallel curves with Euler spirals
Blog of Raph Levien.
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Signed integers are asymmetrical
An edge case in integer safety.
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Donut.c Without a Math Library
My little donut.c has been making the rounds again, after being featured in a couple YouTube videos (e.g., Lex Fridman and Joma Tech ). If I had known how much attention this code would get over the years, I would have spent more time on it.
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Implementing strict three-point perspective
Implementing strict three point perspective is ridiculous. You’ll never need it. Let’s do it anyway.
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The Poincaré Conjecture, Explained
Poincaré began working on what is now considered to be the foundation of topology and algebraic topology in the 1890s with the work Analysis Situs (1895) and five later supplements (1899; 1900, 1902a, 1902b, 1904).
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Trapped priors as a basic problem of rationality
P(A|B) = [P(A)*P(B|A)]/P(B), all the rest is commentary.
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Evolution of Random Number Generators
Prime powers have a kinda chaotic pattern in their bits. We bootstrap this idea into a good random number generator, recapitulating history.
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Rolling hash; Rabin-Karp string search
This is yet another string search algorithm. (Previously my readers have read about Knuth-Morris-Pratt .)