You start on an enclosed lawn, surrounded by four walls with a doorway in one of them. If you go in and explore, you might begin to feel trapped. You'll find you can visit five different rooms in the house, or go back outside to the lawn, but there's no way to go anywhere else. It's not because there are walls…
Our office chair, the air we breathe, the stars in the night sky: they are all made of atoms, which in turn are composed of electrons, protons and neutrons. Electrons are negatively charged; according to current knowledge, they have no expansion, but are point-like. The positively charged protons are different …
Category theory is a domain of mathematics that exerts a strange influence over programmers. One thing that can be said for sure about category theory is tha...
Posted by Nick Johnson | Filed under python , tech , coding , damn-cool-algorithms
Looking at Taylor series as streams of real numbers, solving differential equations becomes as easy as writing them.
We built a neural theorem prover for Lean that learned to solve a variety of challenging high-school olympiad problems, including problems from the AMC12 and AIME competitions, as well as two problems adapted from the IMO.
Hey all, I’ve been enjoying wordle, the puzzle game recently but also wondered how a program might do at it.
Today's date is a good excuse to memorize a few more digits of 3.1415926 53589793 23846264 33832795....
This is going to be a somewhat experimental post. In class, I mentioned that when solving the type of homework problems encountered in a graduate real analysis course, there are really only about a…
Note: The full source code for this article can be found here (summarized version). Individual sections contain references to specific code snippets below.
The above is the title of a talk by computer scientist Cynthia Rudin. here’s the abstract:
These algorithms aren't magic – but combined they can save over 90% of storage costs and speed up queries. Here’s how 5 common ones work.
Gödel’s first incompleteness theorem states that there are mathematical statements that can neither be proven or disproven. His proof is fairly difficult to ...
Timsort: A very fast , O(n log n), stable sorting algorithm built for the real world — not constructed in academia. Timsort is a sorting algorithm that is efficient for real-world data and not created in an academic laboratory. Tim Peters created Timsort for the Python programming language in 2001.
However, no experiment with actual coin-tosses has been done to investigate whether the predicted effect is empirically observed. Diaconis et al noted, correctly, that to estimate the probability with a S.E. of 0.1% would require 250,000 tosses, but this seems unnecessarily precise. Let's work with numbers of tosses…
The source code implementing the projections below is only available on request for a small fee. It includes a demo application and an invitation to convert an image of your choice to verify the code does what you seek. For more information please contact the author .
Summary: it is possible to play Tetris and guarantee that you will score at least one line, no matter which pieces are given to you, i.e., even assuming they are chosen adversarially.
I. Allan Crossman calls parapsychology the control group for science. That is, in let’s say a drug testing experiment, you give some people the drug and they recover. That doesn’t tell …
You may be familiar with the term “hockey stick curve,” used describe a trend that has been flat/stable for a very long time, but shoots up at the end of the series in dramatic fashion, resembling the shape of a hockey stick. Hockey can be a violent sport, and it’s easy to get hurt by even one well-aimed swing…
In the past few months, I’ve twice injured the same ankle while playing with my kids. This, perhaps combined with covid, led me to several indisputable realizations: I am mortal.Despite my se…
What was once a pre-market morning newsletter became an afternoon newsletter, 12 seconds at a time
W hat happens, if 100 persons in a room are given $100 each and give away a Dollar to one randomly chosen person in this room each tick of the clock? How is wealth distributed over time by pure chance?
I saw a math puzzle the other day on Hacker News. It reads as follows: Two numbers are chosen randomly, both are positive integers smaller than 100. Sandy is told the sum of the numbers, while Peter is told the product of the numbers. Then, this dialog occurs between Sandy and Peter: Peter: I don’t know the numbers…
A lot of modern cryptography builds on insights from number theory, which has been studied for centuries.
AnyLeaf Articles: Quaternions: A practical guide
Faizan Muhmmad is a Software Engineer at Google
