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Habits of highly mathematical people
The most common question students have about mathematics is “when will I ever use this?” Many math teachers would probably struggle to give…
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The latest blog posts to take off on Hacker News. 132 posts.
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What is the roundest country?
We can define roundness in many ways. For example, as you may know, the circle is the shape that given a fixed perimeter maximizes the area. This definition has many problems. One of the problems is that countries generally have chaotic perimeters (also known as borders), so they tend to be much longer than they seem…
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Gradient Boosting Explained in 3D
Understanding gradient boosting with interactive 3d-demonstrations
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Generalized linear models, abridged
Generalized linear models (GLMs) are indispensable tools in the data science toolbox. They are applicable to many real-world problems involving continuous, yes/no, count and survival data (and more). The models themselves are intuitive and can be used for inference and prediction. A few very high quality free and open…
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The best linear algebra books
If you would follow the road to linear algebra here are some trustworthy signposts.
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Space Emerging from Quantum Mechanics
The other day I was amused to find a quote from Einstein , in 1936, about how hard it would be to quantize gravity: “like an attempt to breathe in empty space.” Eight decades later, I think we can still agree that it’s hard.
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Nearly All Binary Searches and Mergesorts Are Broken (2006)
Posted by Joshua Bloch, Software EngineerI remember vividly Jon Bentley's first Algorithms lecture at CMU, where he asked all of us incoming Ph.D. ...
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A Beginner's Guide to Understanding Convolutional Neural Networks
Engineering at Forward | UCLA CS '19
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The rectangularness of countries
What is the most rectangular country?
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Experimenting with Post-Quantum Cryptography
Posted by Matt Braithwaite, Software Engineer Quantum computers are a fundamentally different sort of computer that take advantage of aspec...
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Just A New Fractal Detail In The Big Picture (2015)
When the central heating takes effect I'll get up and make myself some tea and porridge to which I'll add some nuts and fruit. I'll switch on The World Service to hear the news, and then make a few phone calls about damp-proofing. And I'll probably plant the daffodil bulbs for Spring (it says on the packet they should…
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Feynman on Fermat's Last Theorem
I write about Startups, coding and Physics
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What is Symbolic Computation?
I've been reading a lot of Lisp books lately, some more advanced than others. All of the introductory books I've seen cover the idea of symbolic computation, but most of them breeze past it with just a few pages about "symbols" and "quoting". For many programmers coming from non-Lisp languages these are new, foreign…
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The Rule of 72 (2007)
The Rule of 72 is a great mental math shortcut to estimate the effect of any growth rate, from quick financial calculations to population estimates. Here’s…
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Why isn’t the fundamental theorem of arithmetic obvious? (2011)
The fundamental theorem of arithmetic states that every positive integer can be factorized in one way as a product of prime numbers. This statement has to be appropriately interpreted: we count the…
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Machine Learning 101: What Is Regularization?
Posts and writings by Datanice
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To approximate 52! by hand, compute 54! and divide by 3000
Some time ago I gave a talk in which I showed that something unexpected happened with a deck of playing cards. I had some volunteers try it, and while they did so I talked about just how many orderings there are for 52 cards. I computed (an approximation to) $52!$ (52 factorial) by hand. It's not so hard - you just…
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Prime After Prime
Are the prime numbers sprinkled randomly along the number line, like windblown seeds? Of course not: Primality is not a matter of chance but a product of simple arithmetic. A number is prime if and only if no smaller positive integer other than 1 divides it evenly.
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How to assign partial credit on an exam of true-false questions?
Note: the following is a record of some whimsical mathematical thoughts and computations I had after doing some grading. It is likely that the sort of problems discussed here are in fact well studi…
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Combinatorial Music Theory (1991)
graph theory, music theory
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Perlin noise
I used Perlin noise for the fog effect and title screen in Under Construction. I tweeted about my efforts to speed it up, and several people replied either confused about how Perlin noise works or not clear on what it actually is. I admit I only (somewhat) understand Perlin noise in the first place because I’ve…
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Linear algebra for game developers – Part 1 (2009)
When I posted about decals last week, a number of readers commented that they would be interested in posts about linear algebra as it…
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Solomon Golomb (1932–2016)
Stephen Wolfram shares a glimpse into his conversations with Solomon Golomb, developments on shift registers, polyominoes, scientific contributions.
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The Busy Beaver Game
This month, a bunch of ‘logic hackers’ have been seeking to determine the precise boundary between the knowable and the unknowable. The challenge has been around for a long time. But on…