Modern AI systems approach tasks like recognising objects in images and predicting the 3D structure of proteins as a diligent student would prepare for an exam. By training on many example problems, they minimise their mistakes over time until they achieve success. But this is a solitary endeavour and only one of the…
Using the power of randomness to answer scientific questions.
Andrej has invited me to write about certain surprising functional programs. The first program, due to Ulrich Berger (1990), performs exhaustive search over the “ Cantor space ” of infinite sequences of binary digits. I have included references at the end. A weak form of exhaustive search amounts to checking whether…
We describe a set of very unusual dice, and a two player game where you will always have the advantage. You can even teach your opponent how the game works, yet still win again! Finally, we will describe a new game for three players where you can expect to beat both players at the same time! Watch James Grime and…
Machine learning systems thrive on finding and exploiting statistical regularities. This is why they can't do causal reasoning.
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Stephen Wolfram considers if numbers are actually required, the use of symbolics and the potential for the growing role of computational irreducibility.
One of the easiest ways to start a (friendly) fight in a group of mathematicians is to bring up the axiom of choice. I'll explain what it is, why it's so controversial, and hopefully shed some light on how we choose axiomatic systems and what that means for the math we do.
Stephen Wolfram shares a glimpse into his conversations with Solomon Golomb, developments on shift registers, polyominoes, scientific contributions.
Programming in logic can help you produce better optimized, more secure, bug-free code … if only you knew how to do it.
Blog of Raph Levien.
Cutting-edge cyber security research from NCC Group. Find public reports, technical advisories, analyses, & other novel insights from our global experts.
A bloom filter is one of those data structures you are probably already aware of, or have at least heard about. For those looking for a simple recap, they are a probabilistic data structure which can …
Learn how time-weighted averages are calculated and why they’re so powerful for data analysis. Read the full article on the Tiger Data blog.
This post explores some concepts behind Gaussian processes, such as stochastic processes and the kernel function. We will build up deeper understanding of Gaussian process regression by implementing them from scratch using Python and NumPy.
The python code that goes along with this blog post can be found at To evaluate the quality of a blue noise texture, you can analyze it in frequency space by taking a discrete Fourier transform. Wh…
TL;DR: How to reason about people who are smarter than you. A few proposals, interspersed with reinforcement learning and humorous fiction. Ending on a surprising connection to logical inductors.
This paper shows that models which result from gradient descent training (e.g., deep neural nets) can be expressed as a weighted sum of simi...
OK, since no one is posting, you get to endure another Monopoly post! After our recent attempt to play the shortest actual game of Monopoly on record, we started to wonder about what the shortest T…
EDIT: I never expected this post to garner so much interest. Just to be clear, using the constant is a very bad idea in almost every situation I can think of. Even instructions like RCPSS should only be used by people who are convinced that the tradeoffs are worth it (or don’t have any other choice). Subtracting from…
I’ve supervised a lot of great student projects in my nine years at MIT, but my inner nerdy teenager has never been as personally delighted by a project as it is right now. To…
There’s an old theory that memory is actually encoded in part in RNA. The argument is pretty simple: there’s no obvious way for all that sensory data to be captured in synapses as long …
Problem: Show that all horses are of the same color. “Solution”: We will show, by induction, that for any set of $ n$ horses, every horse in that set has the same color. Suppose $ n=1$, this is obviously true. Now suppose for all sets of $ n$ horses, every horse in the set has the same color. Consider any set $ H$ of…
Robert Vanderbei has written a beautiful series of articles and talks about a method for finding the radius of the earth based on a single photograph of a sunset over a large, calm lake.
Can high school students really learn algebraic geometry? And what could it teach us about mathematics education?
[Photo by Alejandra Mavroski.] Myrtle called it The article that launched a thousand posts…, and counting comments on this and several other blogs, that may not be too much of an exaggeration…
The Book of Why: The New Science of Cause and Effect is a collaborative effort aimed at a general audience by Judea Pearl , a professor of computer science at UCLA, and Dana Mackenzie , a science writer. As a medical student with a laughably poor formal education in statistics, I believe I qualify as a card-carrying…
