1561
Square roots and maxima
A brief numerical and graphical check on a 3Blue1Brown video.
Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,038 posts.
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Is π the Same in Every Universe?
Mathematician: That depends on what you mean by “universe.” Here’s a framing: A circle of radius R centered at a point P is the set of all points in the plane with distance R fro…
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Is running a more efficient way to travel than walking?
Is running a more efficient way to travel than walking? Does running burn less calories per distance traveled than wa...
1566
Everyone gets numbers wrong, even the New York Times
It's a shortcut to understanding, and there are no shortcuts
1567
Complexity No Bar to AI
Critics of AI risk suggest diminishing returns to computing (formalized asymptotically) means AI will be weak; this argument relies on a large number of questionable premises and ignoring additional resources, constant factors, and nonlinear returns to small intelligence advantages, and is highly unlikely.
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The Mirror Fusion Test Facility (2023)
A decade-long effort to build a machine to unlock the promise of nuclear fusion fell victim to budget constraints and competing science, and was shut down the day it was dedicated. It was never turned on.
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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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Random Points on a Sphere
John D. Cook, Greg Egan, Dan Piponi and I had a fun mathematical adventure on Twitter. It started when John Cook wrote a program to compute the probability distribution of distances $latex |xy R…
1573
How to put 170 atoms in an atom
You might already know that atoms are mostly empty space. Physical size behaves a bit weirdly at the atomic scale, but essentially the radius of an atom’s nucleus is tens of thousands of times smal…
1574
Genetics and Eugenics in Frank Herbert's DUNE
Observations on Frank Herbert’s 𝐷𝑢𝑛𝑒 series—the notes are probably overstated, the Butlerian Jihad was 𝑛𝑜𝑡 a robot uprising seeking to exterminate humanity, and precognition/prescience in the Dune universe appears to work backwards allowing for retro-causality and stable time-loops as exemplified by Leto II’s Golden…
1575
An Introduction to Lagrange Multipliers
Lagrange multipliers are used in multivariable calculus to find maxima and minima of a function subject to constraints (like "find the highest elevation along the given path" or "minimize the cost of materials for a box enclosing a given volume"). It's a useful technique, but all too often it is poorly taught and…
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A 50-year quest: My personal journey with the second law of thermodynamics
Follow Stephen Wolfram's evolution of research on the 2nd Law from early interest as a 12-year-old to his current findings in the Wolfram Physics Project. View a large collection of images of early and published works.
1577
Why are most climate models in Fortran?
An examination of the software that powers modern Climate simulations.
1578
The Hyperbolic Geometry of DMT Experiences (2016)
[Content Warning: Trying to understand the contents of this essay may be mind-warping. Proceed with caution. Featured image credit: Paul Nylander] Friends, right here and now, one quantum away, the…
1579
Where to hate daylight saving time and where to love it
Update: a newer version of this little project helps you make your complaints about daylight saving time—whether they’re for or against it—with clearer messages about whether keeping DST, abolishing it, or making it permanent would be best for your daylight preferences. Give it a whirl over at Observable.
1580
Time Travel (2006)
Last time we talked about free will, superintelligent predictors, and Dr. Evil planning to destroy the earth from his moon base. Today I'd like to talk about a more down-to-earth topic: time travel. The first point I have to make is one that Carl Sagan made: we're all time travelers—at the rate of one second per…
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Reasons why Fortran is still used (2021)
Fortran is a language that is specialized for high-performance computing. Believe it or not, it's still alive and evolving.
1582
Is Planet Nine Alone in the Outer System?
Planet 9 might be our Ultima Thule . Hell would certainly be freezing over at 700 AU. Whether this tentative observation is Planet 9 or not, it is still an interesting observation and an example, I think, of proof that AIs will not do all our science for us. (At least not LLMs).
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The Scientific Virtues: Stupidity, Arrogance, Laziness
Science education usually starts with teaching students different tools and techniques, methods for conducting research. This is wrong. Science education should begin with the scientific virt…
1584
Insert D-Wave Post Here
In the two months since I last blogged, the US has continued its descent into madness. Yet even while so many certainties have proven ephemeral as the morning dew—the US’…
1585
Neurons Gone Wild
To reject gods and spirits is easy: just bully them away in the name of science.
1586
How To Use 23andMe Irresponsibly (2014)
As you might remember, the FDA stomped on 23andMe for using too many irresponsible genetic tests that purported to tell you things about yourself and your health with limited support. They eventual…
1587
What Gives Gold that Mellow Glow? (2006)
What Gives Gold that Mellow Glow?
1588
An Adversarial Review of “Adversarial Generation of Natural Language”
Or, for fucks sake, DL people, leave language alone and stop saying you solve it.
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Not so fast, Mr. Fourier
A real explanation of discrete Fourier transform (DFT, FFT), discrete cosine transform (DCT), and their inverses.
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