Babylonian accountants and land surveyors did their arithmetic in base 60, presumably because sexagesimal numbers help with wrangling fractions. When you organize things in groups of 60, you can divide them into halves, thirds, fourths, fifths, sixths, tenths, twelfths, fifteenths, twentieths, thirtieths, and…
Physicists have proved that a subatomic particle can switch into its antiparticle alter-ego and back again, in a new discovery revealed today. An extraordinarily precise measurement made by Oxford researchers using the LHCb experiment at CERN has provided the first evidence that charm mesons can change into their…
When it comes to accuracy, how you add a series of arbitrary values together, and average them still matters.
<meta http-equiv=
Deep neural networks have long been considered too complex to understand from first principles — but new research does just that, presenting a theoretical framework for DNNs.
A blog about signals, programming, music, and other stuff.
Memories from Oxford days Mathematical Institute src Peter Neumann, Professor of Mathematics at Queen’s College, Oxford University, passed away two weeks ago. Last Monday would have been his …
Economist Gary Smith sends along this post with the above title and the subtitle, “Market prices are not invariably equal to intrinsic values.” Here’s Smith:
Blog of Raph Levien.
An edge case in integer safety.
My little donut.c has been making the rounds again, after being featured in a couple YouTube videos (e.g., Lex Fridman and Joma Tech ). If I had known how much attention this code would get over the years, I would have spent more time on it.
Implementing strict three point perspective is ridiculous. You’ll never need it. Let’s do it anyway.
Poincaré began working on what is now considered to be the foundation of topology and algebraic topology in the 1890s with the work Analysis Situs (1895) and five later supplements (1899; 1900, 1902a, 1902b, 1904).
Erdős posed and solved problems in number theory and other areas and founded the field of discrete mathematics.
P(A|B) = [P(A)*P(B|A)]/P(B), all the rest is commentary.
Prime powers have a kinda chaotic pattern in their bits. We bootstrap this idea into a good random number generator, recapitulating history.
This is yet another string search algorithm. (Previously my readers have read about Knuth-Morris-Pratt .)
This comes from a question posed to me and others in 2019 by Stefan Langerman, a computational geometer who also happens to be a diamond dealer. The classic ...
papad Hard to believe Sanjeev Arora and his coauthors consider it “a basic tool [that should be] taught to all algorithms students together with divide-and-conquer, dynamic programming, and random sampling.” Christos Papadimitriou calls it “so hard to believe that it has been discovered five times and forgotten.” It…
The intended audience for this article is undergrad students who already have a good grasp of Java, or seasoned Java developers who would like to explore an in-depth analysis of various hash table implementations that use Open Addressing. The reader should be familiar with Java generics, collections, basic data…
Here are the slides of my talk “The dawn of formalized mathematics” from the 8th European Congress of Mathematics , which is taking place online and in Protorož, Slovenia, from June 20 to 26, 2021:
Or, “how not to GIS”.
The ubiquitous IEEE floating-point standard defines two numbers to represent zero, the positive and the negative zeros. You also have the positive and negative infinity. If you compute the inverse of the positive zero, you get the positive infinity. If you compute the inverse of the negative zero, you get the negative…
Most of us learn how to write technical articles by osmosis. After reading a hundred or so papers, we unconsciously pick up the common patterns of the field and begin to imitate them. This phenomenon is largely beneficial, but there are several truly odious habits that are almost universally and inadvertently adopted…
Ensemble averages and time averages
An interactive, illustrated timeline of historic moments in humankind's quest for information. With annotations by Jeremy Norman.
