Leibniz’s harmonic triangle in 3D
John D. Cook wrote about Leibniz’s harmonic triangle last week (Cook 2026). The first column is the harmonic series, and each entry is the difference of the entries to its west and northwest: which…
HP Lattice Folding: Simplified Protein Structure Prediction
Proteins fold into specific 3D structures, and that structure determines their function. Predicting structure from sequence is one of the grand challenges of computational biology. While AlphaFold…
EMR isn’t only for slowing down patient care
American Chemical Society. “Forget LASIK: Safer, cheaper vision correction without lasers or incisions.” ScienceDaily, 29 September 2026.…
Lecture on Debye model for solids
I just finished preparing my undergraduate lecture on the Debye model for solids. Here are my slides . The course is a third-year course on statistical mechanics. In the previous lecture, they…
Economist Robin Hanson did not invent the Great Filter
Humanity seems to have a bright future, i.e., a non-trivial chance of expanding to fill the universe with lasting life. But the fact that space near us seems dead now tells us that any given piece of…
Dynamics 2021+
A couple of songs to start this unit. I think we should start all topics with a song. Hot off the press for 2025 Updated booklets from the wonderful Mr Cunningham. I am sure there are more to come.…
Intro to Replicator Dynamics
Part Of: Biology sequenceRelated To: Population Genetics, Natural Selection, Fitness SeascapesContent Summary: 4400 words, 22 min read Introduction In January 2021, the Alpha variant of SARS-CoV-2…
Measles Infections Keep Rising Rapidly In Pennsylvania
The US is now in the middle of a measles outbreak, with Pennsylvania currently experiencing the most cases. The Pennsylvania Department of Health said that as of October 16, there have been 1260…
El Nino, Sea Level, and Kelvin Waves
The media recently reported on oceanic Kelvin waves and their connection to El Nino. See samples below. Some of the information is correct; some is problematic or exaggerated (samples below). <a…
Series Summation Methods
Here, we will maintain a list of series summation methods. Methods currently covered: Operator method Euler transform for alternating series Borel trick Shanks transform Method 1: Operator method The…
Sunlight for Sale: Reflect Orbital Illumination Test
Reflect Orbital continues to make progress on placing giant mirrors in Earth orbit to produce and sell sunlight after dark. On October 10, the space startup set up spotlights near Lone Pine,…
Verastem's VS-7375: The New Kid On The KRAS Block
VS-7375, an oral KRAS G12D ON/OFF inhibitor, reached a confirmed ORR of 9 of 22 (41%) at 900 mg in 2L+ mPDAC. How might this ORR translate into survival, and how does VS-7375 compare with…
Predictions Made By Renowned Climate Proifessor Over Past Decades Have Been Proven To Be Poor
The following YouTube vidfeo lists the climate predictions and public statements associated with alarmist German meteorologist and oceanographer Prof. Dr. Mojib Latif across the specified…
Notice: Upcoming HAARP ionospheric tests from Alaska - 20th to 24th Oct 2026
The High-frequency Active Auroral Research Program (HAARP) is based in Alaska and it's a high-power, high frequency (HF) transmitter for studying the ionosphere. The principal instrument is a phased…
A transcript of Sarnak's latest talk
In exploring various ways to leverage these new AI capabilities for human understanding, one small experiment I did was to transcribe Sarnak's wonderful lecture from the Serre birthday…
Robust Lyapunov Exponents
Abstract: the upper envelope of the Lyapunov exponent functional on SL(2,R) cocycle A over an automorphism T of a probability space can be estimated below by the Herman functional H(A) which is the…
NGC 891
The thin edge-on galaxy NGC 891 and its dark central dust lane amid foreground stars
In domain theory, there is only partial and co-partial
In domain theory, partial maps f\colon A \rightharpoonup B take on a topological dimension: for example, we might require that the support be an open subspace of the domain, or that it be a closed…
SHORTS (2) ‘Deflating Gödelised Physics, With Stephen Hawking’
A short analysis and summary of my essay. (2) Photo by the author. Source <a class="au tf" href="https://www.flickr.com/photos/193304911@N06/55519067491/in/dateposte" rel="noopener ugc nofollow"…
Lamentation on AI in Mathematical Research
A month ago, I received an email out of the blue from someone named Ioannis Tsiokos. He said that he had achieved a breakthrough in tiling theory: he had discovered a strongly aperiodic monotile in…
Orbital Propellant Depot: 1971
In order to get anywhere in the solar system, we’re going to need to study, test and perfect orbital refueling operations. And in order to do that, we’ll need orbital fuel depots. This is…
Notes on the complex roots of unity
One of the most wonderful aspects of math is how deep we can get by studying seemingly trivial questions. Consider the roots of unity, where "unity" simply means the number 1. Basics: roots…
Flashed Face Distortion
What: The Flashed Face Distortion is one of the creepier ones on the site, and honestly one of my favorites. As you focus on the cross in the middle, the faces on the left and right start to…
Müller-Lyer Illusion
What: The Müller-Lyer illusion (pronounced roughly MEW-ler LEER) is one of the absolute classics, you’ve probably seen it in a textbook at some point. Two lines, exactly the same length, one…
Dear Mathematicians
Dear Mathematicians, First, no AI was used in the writing of this message. Second, I’m pretty envious of you guys. If all my problems, or at least a bunch of them, suddenly got solved, I would be…
Spinformation: do gravitational-wave events carry information beyond effective spins?
The name says it all: spinformation! Measuring spins in gravitational-wave events is a tricky business. There are two spins, so 6 numbers (both are vectors), but we actually mostly measure some…
Today I learned why sausage splits lengthwise
As a chemical engineering student, I never expected to learn the physics behind why sausages usually split lengthwise. Sausages are actually very similar to pipes, and I learned about pipes. A…
The Musaicum East Africa
Today i introduce another important milestone in my Musaicum satellite image mosaic series – the Musaicum East Africa. The Musaicum images are a series of regional satellite image mosaics based…
A Light Switch for the Brain (Optogenetics 3D)
Borrowing light-gated ion channels from green pond algae to turn living neurons on and off with blue light pulses. An interactive 3D simulation of optogenetics and the 2026 Nobel Prize in Physiology…
Another Eukaryotic Gene Regulator Turns up in Archaea
Leucine zipper proteins as gene regulators in Archaea, regulated by nutrient-binding PAS domains. In this day of AI, it is a pleasure to read an elegantly constructed and written paper that breaks…
[UPDATED] KOSMOS 2612 and ICEYE-X36: a worrisome cat-and-mouse-game in Space
click diagram to enlarge (update at end of post) A worrisome cat-and-mouse-game is happening in Space as we speak. The Russian military satellite KOSMOS 2612 (2026-083H) which was launched from…
WEEKEND WEATHER FORECAST
#Philadelphia #weather #PAwx #PhillyWx #wx Originally Posted —Last night’s frontal passage didn’t create locally severe weather, nor did the rain pass through here as fast as had…
Air Pollution in Thailand
Thailand: Comprehensive National Policy Framework: PM2.5 and PM10 Suppression 1. Actual Impact of Particulate Matter Pollution Particulate matter (PM2.5 and PM10) represents one of Thailand’s most…
Fluids, Heat, and Linear Algebra in 1950
In 1944 Los Alamos was focused on fluids and heat transfer, the same types of problems worked by Humble Oil and David Young in the following years. Stan Frankel became the first patient infected with…
Little Dumbbell Nebula - M76
The compact blue-green and reddish lobes of M76 in a dense star field
Math review: week 5
Math Review Week 5 Highlights of what I (re)learned in week #5 of my math studies. Shorter week due to traveling.
Phosphate: All hopes for food and LFP batteries rest on Morocco with up to 85% of remaining reserves
Phosphate is absolutely essential for both plants and animals. It’s estimated that Morocco has of 75-85% of phosphate reserves. How long reserves will last depends on being economic. So if the…
ARMA: Auto Regressive Moving Average
ARMA(1,1) time series modelXt = 0.5 Xt-1 + Zt + 0.7 Zt-1ARMA(1,1) Time Series EquationAR order: p = 1MA order: q=1Stationarity: |0.5|<1Invertibility: |0.7|<1Assuming Zt is white noise, the model
Weekly Rainfall Reports
No rain this week. He had some beautiful weather
The algebraic structure of regular expressions
Converting NFAs to regular expressions by solving linear systems of equations
Math 2.0 Gets an Operating System: Can Open Math OS Build Mathematics Beyond the Theorem Factory?
An architectural and evidence-bounded analysis of Open Math OS as a possible foundation for Math 2.0.
Jolly Rancher fluorescence
It turns out Jolly Rancher candies light up strongly under UV illumination. I advance some theories as to why.
Archimedes, Barenblatt, and Sato-Tate
Mathematics is also the art of quantitative proportions in action. Who knows, nowadays, that the Fields medal depicts an exceptional antic geometric probability theorem? I…
A potential cause of idiopathic seizures in dogs
By Carol Beuchat PhD Slow whelping caused by of uterine inertia is common in dogs. It can stretch out a process that should take only an hour or two to many hours or even days. Prolonged labor is…
Milgrom's Latest MOND Paper
Mordehai Milgrom, who invented MOND, has long been ambivalent about whether this is really a modification of gravity or a modification of inertia. In his latest paper, he considers the possibility…
The Coinductive Characterization of Lambda Terms
This post shows how to use a type of infinitary trees to characterize the behavior of lambda terms.
Duplex Ultrasound For DVT: How Does It Work?
Admit it. You’re curious. You order this test for your trauma patients all the time but you’ve never seen it done. It’s simple and noninvasive, but it does require access to all areas to be…
Mathslopocalypse
I once asked a specialist in a particularly obscure mathematical subdiscipline how many people in the world could understand her work. “Maybe 20 or 30,” she said. I thought it sounded…
Measuring the brain's long-term memory forming latency
I've got an amusing little essay for you, to sweeten your weekend. 'Tis a semi-scientific article about my experiment of measuring brain latency in forming long-term memories from short-term ones…
Three Standard Ways to Factor a Quadratic
Last time, we looked at some non-recommended ways to factor a quadratic trinomial. Here we’ll explore several recommended methods (the basic case, trial-and-error, and ac-grouping), looking…