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Life lessons from differential equations (2015)
Some problems simply have no solution. Some problems have no simple solution. Some problems have many solutions. ...
Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,851 posts.
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Nonnegative matrix factorization
The why and how of nonnegative matrix factorization Gillis, arXiv 2014 from: ‘Regularization, Optimization, Kernels, and Support Vector Machines.’ Last week we looked at the paper ‘Beyond news cont…
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Collatz's Ant
This is a brief continuation of a previous post ( Repo ), which introduced such visualization for collatz sequences based on Langton’s Ant .
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Beautiful plots of roots of polynomials
Click on the picture for bigger view. Roots of quadratic polynomials are in grey; roots of cubics are in cyan; roots of quartics are in red and roots of quintics are in black. The horizontal axis of symmetry is the real axis; the vertical axis of symmetry is the imaginary axis. The big hole in the middle is centered…
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VP trees: A data structure for finding stuff fast
<img src="http://stevehanov.ca/wavelet/cup.png"/> Let's say you have millions of pictures of faces tagged with names. Given a new photo, how do you find the name of person that the photo most resembles? <p> In the cases I mentioned, each record has hundreds or thousands of elements: the pixels in a photo, or patterns…
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Automating xkcd Diagrams: Transforming Serious to Funny
Read Wolfram's latest announcements, events, news and developer insights. In-depth highlights of Wolfram technologies used across industry, research, education.
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Flipping until you are lost
Start with any triangulation of a convex polygon, and then repeatedly choose a random diagonal and flip it, replacing the two triangles it borders with two d...
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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…
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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...
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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 …
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What use is mental math in 2022?
The ability to quick estimates is still valuable, maybe more valuable than it used to be.
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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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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.
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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…
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Girls Need Math
The other day a programmer-friend sent an e-mail to me and three other women. It read:
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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…
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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…
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Solving LinkedIn Queens Using Haskell
Solving LinkedIn Queens in the LogicT monad
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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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You gotta think outside the hypercube
A closer look at the tesseract and the ways we can render it on the screen.
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Floating point from scratch: Hard Mode
Actually building floating point from scratch!
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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…
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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 …