2251
A whirlwind introduction to dataflow graphs
While in the middle of writing “Reading bits in far too many ways, part 3”, I realized that I had written a lot of background material that had absolutely nothing to do with bit I/O and…
Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,393 posts.
2252
An intutive counterexample to the axiom of choice
Time for some hard-core geeking-out. This comment on HN by /u/jiggawatts struck me as a brilliant idea: it's an intuitive counter-example t...
2253
Myths about Hash Tables
A hash table is data structure that is used to search for exact matches to a search key. For searching, they work like this: Take a search key (example: the word “cat”) Hash the search …
2254
What use is mental math in 2022?
The ability to quick estimates is still valuable, maybe more valuable than it used to be.
2255
The Opposite of a Bloom Filter
A Bloom filter is a data structure that may report it contains an item that it does not (a false positive), but is guaranteed to report correctly if it contains the item (“no false negatives”). The opposite of a Bloom filter is a data structure that may report a false negative, but can never report a false positive…
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2257
The examples in the textbooks are not representative of real world problems
Bill Harris points to this cartoon from Randall Munroe. I think he (Munroe) is really on to something here. Not about Bayes’s theorem but about the sorts of examples that are in textbooks.
2258
Types versus sets (and what about categories?) (2022)
A recent Twitter thread brought home to me that there is widespread confusion about what types actually are, even among the most prominent researchers. In particular: are types the same thing as sets ? At the risk of repeating some of my prior posts, perhaps it’s time for a little history about type theory, set theory…
2259
How good can you be at Codenames without knowing any words?
About eight years ago, I was playing a game of Codenames where the game state was such that our team would almost certainly lose if we didn't correctly guess all of our remaining words on our turn. From the given clue, we were unable to do this. Although the game is meant to be a word guessing game based on word…
2260
The Derivative of a Number
Are you kidding? Edward Barbeau is now a professor emeritus of mathematics at the University of Toronto. Over the years he has been working to increase the interest in mathematics in general, and e…
2261
Solving LinkedIn Queens Using Haskell
Solving LinkedIn Queens in the LogicT monad
2262
A cute proof that makes e natural
Po-Shen Loh explains why Euler's number e is natural using only precalculus: one exponential curve has tangent slope 1 at the y-axis, which leads to the compound interest limit.
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2264
You gotta think outside the hypercube
A closer look at the tesseract and the ways we can render it on the screen.
2265
Floating point from scratch: Hard Mode
Actually building floating point from scratch!
2266
The Factoring Cryptopocalypse
The key detail to understand about the work in the Joux papers is that it is limited to solving discrete logarithm problems over fields of small characteristic . As interesting as the work is, mathematically, it should not be a great surprise to cryptographers: We've known for over a decade that small-characteristic…
2267
Kolmogorov Complexity - A Primer
The Complexity of Things Previously on this blog (quite a while ago), we’ve investigated some simple ideas of using randomness in artistic design (psychedelic art, and earlier randomized css …
2268
Finding Unity in the Math Wars
I usually avoid current events, but recent skirmishes in the math world prompted me to chime in. To recap, there've been heated discussions about math…
2269
How thick is the atmosphere? A derivation of the Boltzmann distribution
Let’s talk about a small question as a way of introducing a big question. How thick is the atmosphere? How far does Earth’s atmosphere extend into space? In other words, how high can y…
2270
A group of Finnish math teachers write an open textbook in a weekend hackathon
A group of Finnish mathematics researchers, teachers and students write an upper secondary mathematics textbook in a booksprint. The event s...
2271
2272
Maze Generation: Wilson's algorithm
Algorithms, circle mazes, hex grids, masking, weaving, braiding, 3D and 4D grids, spheres, and more!
2273
My 2019 Mathematics a to Z: Linear Programming
Today’s A To Z term is another proposed by @aajohannas. I couldn’t find a place to fit this in the essay proper. But it’s too good to leave out. The simplex method, discussed with…
2274
2275
Floor, Ceiling, Bracket
The notation [x] reigned for nearly two centuries before being replaced by ⌊x⌋. Why the latter is much better and what else we might learn from its inventor.
2276
Reflections on Sudoku, or the Impossibility of Systematizing Thought
I reflect on the Entscheidungsproblem how it relates to Sudoku solvers. It's a little weird. .
2277
The Firing Squad Problem
In 1957, John Myhill first posed an interesting problem that was closely related to computer programming, but did not require any related background to solve. Dubbed the "firing squad synchronization problem," the puzzle was passed along by word of mouth and first solved by Marvin Minsky and John McCarthy. However…
2278
Supertasks
Background Reading: Earman and Norton, Infinite Pains: The Trouble with Supertasks and Comments on Laraudogoita's Supertask
2279
The birthday paradox in action: calculating the probability of a hash collision
You may feel like you've seen this before. If you have, skip to the end where I talk about a formula, and discuss the relevance to parameters in computer hashing algorithms. In particular, I'm going to talk about how large hash spaces should be to avoid collisions with a given level of probability. If there are just…
2280
An Intuitive Explanation of Bayes' Theorem
Bayes’ Theorem for the curious and bewildered; an excruciatingly gentle introduction.