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2017 is not just another prime number
Good bye year 2016. Hello year 2017. We all know that 2017 is a prime number, but it is more than just another prime number. 2017π (roun...
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Papers I like
This started out on Twitter and I expected having to write up maybe 50 or so, but then it made the rounds. I don’t think I have 1200+ papers that I’d recommend reading, and even if I di…
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How Shor's Algorithm works (2007)
I’ve been talking a lot recently about how quantum algorithms don’t work. But last week JR Minkel, an editor at Scientific American, asked me to write a brief essay about how quantum al…
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How Bayesian Inference Works (2016)
Bayesian inference is a way to get sharper predictions from your data. It’s particularly useful when you don’t have as much data as you would like and want to juice every last bit of predictive strength from it.
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Where Do Type Systems Come From?
Every time I want to quickly understand something about an advanced type system or programming language concept I get lost when I see something like this on Wikipedia:
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A Zero-Math Introduction to Markov Chain Monte Carlo Methods
For many of us, Bayesian statistics is voodoo magic at best, or completely subjective nonsense at worst. Among the trademarks of the…
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Golden powers are nearly integers
As n increases, the distance from phi^n to the nearest integer decreases exponentially where phi is the golden ratio.
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Category Theory for Programmers (2014)
Table of Contents Part One Category: The Essence of Composition Types and Functions Categories Great and Small Kleisli Categories Products and Coproducts Simple Algebraic Data Types Functors Functo…
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Using loaded dice to cheat at Settlers of Catan, and p-values to avoid suspicion
My copy of Settlers of Catan came with two normal wooden dice. To load these dice, I placed them in a small plate of water overnight, leaving the 6 side exposed.
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A Universe in One Line of Code with 10 PRINT
Generating a Universe with One Line of Code
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Algorithmic Solution to My Insomnia
I’ve struggled with insomnia for all of my adult life. It began in college and has waxed and waned in severity ever since, correlating with stress levels…
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Your yearly dose of is-the-universe-a-simulation
Yesterday Ryan Mandelbaum, at Gizmodo, posted a decidedly tongue-in-cheek piece about whether or not the universe is a computer simulation. (The piece was filed under the category “LOL.…
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Why isn't everything normally distributed?
Heights are normally distributed because height is determined by many factors. But why are other things with many inputs not normally distributed?
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A Pragmatic Introduction to Signal Processing
A retirement project created and maintained by Tom O'Haver , Professor Emeritus , Department of Chemistry and Biochemistry
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Designing a Tree Diff Algorithm Using Dynamic Programming and A*
During my internship at Jane Street 1 , one of my projects was a config editing tool that at first sounded straightforward but culminated in me designing a custom tree diffing algorithm using dynamic programming, relentlessly optimizing it and then transforming it into an A* accelerated path finding algorithm. This…
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Understanding the math behind 0x5f3759df and the fast inverse square root (2012)
This post is about the magic constant 0x5f3759df and an extremely neat hack, fast inverse square root, which is where the constant comes from.
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Why is the Quintic Unsolvable?
In this article, I hope to convince you that the quintic equation is unsolvable, in the sense that I can’t write down the solution to the equation \[ ax^5 + bx^4 + cx^3 + dx^2 + ex + f = 0 \] using only addition, subtraction, multiplication, division, raising to an integer power, and taking an integer root. In fact, I…
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Kalman filters and functional programming
A paper on Kalman filtering and functional folds that I alluded to previously has been split into several papers and posted online.
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