91
A trip through the Graphics Pipeline
Welcome. This is the index page for a series of blog posts I’m currently writing about the D3D/OpenGL graphics pipelines as actually implemented by GPUs. A lot of this is well known among gra…
92
Bad but interesting mathematical notation idea
From the highly eclectic blog of Mark Dominus
93
Explained from scratch: private information retrieval and homomorphic encryption
This is a from-scratch explanation of private information retrieval built using homomorphic encryption. I try to assume only a general math / computer science background. To simplify things, my explanations may not always match academic definitions. You can check out this paper or code for more.
94
95
Experiment with Penrose Tilings and other patterns
Create And Share Mathematical Tiling Patterns
96
Visualizing Bayes Theorem (2009)
I recently came up with what I think is an intuitive way to explain Bayes’ Theorem. I searched in google for a while and could not find any article that explains it in this particular way.
97
When Double Precision Is Not Enough
Using greater than double precision to calculate the eigenvalues of the lesp matrix.
98
99
What Are the Odds?
An unusual lottery result made the news recently: on October 1, 2022, the PCSO Grand Lotto in the Philippines, which draws six numbers from $latex {1}&fg=000000$ to $latex {55}&fg=000000$ a…
100
Vintage-Style Map of the Mandelbrot Set
Bill Tavis designed this lovely vintage-style map of the familiar fractal shape, the Mandelbrot set. He is selling a poster version of the map, starting at the
101
Einstein-Bohr debate settled once and for all
In Steven Pinker’s guest post from last week, there’s one bit to which I never replied. Steve wrote: After all, in many areas Einstein was no Einstein. You [Scott] above all could speak…
102
Efficient simulation through linear algebra
I spent a lot of time working on a project in which physically plausible simulation of soft materials with pressure chambers was a key part, and in doing so, we managed to improve a part of our simulation by a significant amount. I was very happy with how this small part of the whole system turned out, and I've been…
103
The Algorithm for Hard Problems: Shake and Pull Gently
(Or, “regularized greedy algorithms and their applications.”) James Gilles “Algorithm” is one of those words that sounds fancier than it really deserves. We hear all the time about the “facebook algorithm”, the “youtube algorithm”, “high frequency trading algorithms”, “artificial intelligence algorithms”, and so on…
104
Busy Beaver Updates: Now Even Busier
Way back in the covid-filled summer of 2020, I wrote a survey article about the ridiculously-rapidly-growing Busy Beaver function. My survey then expanded to nearly twice its original length, with …
105
Hardy, Ramanujan and Taxi No. 1729
In his book Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, G. H. Hardy tells this famous story: He could remember the idiosyncracies of numbers in an almost uncanny way. It …
106
How thick is a three-sided coin?
Matt Parker, employing the enviably pithy prose typical of a content creator forged on the unforgiving fires of social media, asked the simple question back in 2018: > How thick is a three-sided coin? Translated into mathematician-ese, this means > What aspect ratio of a flipped coin leads to the chance of landing on…
107
Ssss: Shamir's Secret Sharing Scheme (2006)
Shamir's Secret Sharing Scheme
108
109
Ramanujan Factorial Approximation (2012)
Ramanujan came up with an approximation for factorial that resembles Stirling's famous approximation but is much more accurate. As with Stirling's approximation, the relative error in Ramanujan's approximation decreases as n gets larger. Typically these approximations are not useful for small values of n. For n = 5…
110
A pair of dice which never roll 7 (2004)
Some friends of mine play the board game Settlers Of Catan . In this game, each player rolls two ordinary dice on their turn, and the number which comes up determines what resources people get for the turn. When a seven is rolled, something special happens: no resources are generated, and instead a robber moves on the…
111
Things I would like to see in a computer algebra system
If I were to design a computer algebra system (CAS) from scratch today, I would try to achieve the following goals. Several ideas have already been implemented in one system or another, but certainly not all at once. Some ideas could be adopted by existing CASes; others would require fundamentally different designs or…
112
I disagree with Turing and Kahneman regarding statistical evidence (2014)
It’s funny. I’m the statistician, but I’m more skeptical about statistics, compared to these renowned scientists.
113
A step by step backpropagation example (2015)
Background Backpropagation is a common method for training a neural network. There is no shortage of papers online that attempt to explain how backpropagation works, but few that include an example…
114
Twenty questions is a weird game
Let’s play a game. I’m thinking of a number from 1 to 100. You guess, and I tell you whether my number is higher or lower.
115
Let's Talk SkipList
the forgotten data structure (not really)
116
Degenerate matter: How reality deals with uncertainty
Casual introduction to the uncertainty principle from quantum mechanics and how it leads to neutron stars and superfluids
117
Math on GitHub: Following Up
About six weeks ago, on May 19, 2022, GitHub released Math support on Markdown. At the time of the release, it received criticism for being ill-designed and buggy. I, too, wrote a blog post about it.
118
Understanding Convolutions in Probability
In this post we take a look a how the mathematical idea of a convolution is used in probability. In probability a convolution is a way to add two random variables. Using a slightly ridiculous, mad-science, example we walk through multiple way to compute a convolution and ultimate arrive at the formu
119
Visualizing Diffs: The Myers difference algorithm (2020)
In 1986, Eugene Myers published An O(ND) Difference Algorithm and Its Variations , which unified the problems of finding the longest common subsequence of two sequences (the LCS of "driftwood" and "artwork" is "two") and finding the shortest edit script for transforming one sequence into another. Myers showed that…
120
Juris Hartmanis 1928–2022
A sure foundation for Computational Complexity source—wonderful 2015 CACM interview Juris Hartmanis passed away this morning. He was a professor in Cornell’s computer science department…