Normal Science

Converting Coal Plants to Natural Gas

For the better part of the last several hundred years, coal was the fuel of choice for generating power. Burning coal powered Thomas Newcomen’s steam engine, invented in Britain in the early 18th century, and the first of a line of increasingly efficient converters of coal to usable energy. The Newcomen engine was in fact so inefficient and consumed so much coal that it was almost exclusively used at coal mines, where fuel could be obtained cheaply. The improved steam engines that followed over ...

Why the Human Genome’s Tangled Physicality May Confound AI

Since its molecular structure was deduced in the 1950s, DNA has been hailed by many biologists as the secret of life. They’ve read and studied the information stored in the DNA found in the cells of living organisms, known as their genomes, and claimed that this genetic database must be some kind of blueprint, code script, or computer. But if DNA really does harbor some greater secret about how… Source

US–Indian space mission maps extreme subsidence in Mexico City

Why are neural networks and cryptographic ciphers so similar? (2025)

Several neural network design principles are almost identical to cipher design principles.

Fun with polynomials and linear algebra; or, slight abstract nonsense

Longest Path Search About Code Fun Fun with polynomials and linear algebra; or, slight abstract nonsense Posted 2026-04-30 This is mostly a bunch of notes to myself (with some slight expansion) and is a combination/extension/simplification of theorems/ideas/constructions from a bunch of texts, including Wistbauer’s “Foundations of Module and Ring Theory” and Fuhrmann’s “A Polynomial Approach to Linear Algebra”, along with others that at this point I don’t recall. While most of the things here ar

The Mathematical Dance Inside Plant Cells

The sunlight-collecting organelles known as chloroplasts solve a packing problem: how to optimize photosynthesis without sustaining damage from dangerously intense rays.

Easy Random Trees

Rigorous Nonsense Home Archive Easy Random Trees Posted on February 27, 2026 by Brandon Wilson Tags: math, apl, trees Can you think of a way to efficiently generate a random plane tree? Richard P. Stanley in his book Catalan Numbers has a really nifty combinatorial proof of why Catalan numbers have the formula \[ C_n = {1 \over n+1}{2n \choose n} \] The standard proof uses generating functions applied to an inductive definition of the Catalan numbers, which frankly does little to illumiate their

The extended predicative Mahlo universe in Martin-Löf type theory (2023)

Deconstructing Datalog

home datafun talon reviews résumé rss Deconstructing Datalog In September 2022, after two rounds of revisions, I submitted the final version of my PhD dissertation, Deconstructing Datalog. Datalog is a logic programming language from the ’80s that augments relational algebra with recursive queries. It has both simple semantics and efficient implementation strategies. Like Lisp and the Velvet Underground, its influence exceeds its popularity; its ideas are still being absorbed into the mainstream

The Riemann Hypothesis – interactive explanation

An interactive journey from 'what is a prime number?' to a genuine understanding of the most important unsolved problem in mathematics.

Third SAIR competition: inverse Galois challenge

I am happy to announce the third SAIR challenge, which is focused on obtaining numerical data for the infamous inverse Galois problem. This is a collaborative project with the L-functions and modular forms database (LMFDB), and is organized by John Jones, Jen Paulhus, David Roe, Andrew Sutherland, and myself. The challenge is somewhat similar to my own Equational Theories Project, in that one is trying to complete a large mathematical data set in a verified fashion, except that the target data s...

What’s new in biology: June 2026

Niko McCarty and Saloni Dattani review important things happening in the world of biotechnology and medicine.We’ve been writing regular round ups for a little while now, but so much has happened recently that this month’s post feels like it contains a year’s worth of breakthroughs. So pour yourself something cool, get cosy, and enjoy!First, everything new in cancer. In our round up last month, we shared the news of daraxonrasib, the new breakthrough drug that roughly doubles survival in late-sta...

How the Squamish built Senakw

This is the third of three articles from Issue 24 of Works in Progress, which has been arriving with subscribers this week. Subscribe in the next few weeks to receive it, and future issues, straight to your door, workplace, or institution.In a corner of the prestigious Kits Point suburb in Vancouver, eleven great towers are beginning to rise from their foundations. This is Senakw (pronounced sen-AHK), a new development owned, managed and championed by the Squamish Nation, an indigenous group nat...

Biological Evolution and Information Acquisition

A few weeks ago we looked at a simulation of technological evolution by economist Brian Arthur, in which he was able to start with simple building blocks (such as a NAND gate) and evolve surprisingly complex circuits (such as a 12-way AND gate or a 4-bit adder) by randomly combining increasingly useful existing components. We analyzed this as a way of simplifying a search problem: by using existing, working components as modules that can be combined, a few at a time, into more complex modules, a...

Are Memories Transferable — or Edible?

I t was the dead of winter in Boston. The surface of the Charles River was frozen solid. But Zachary Kelso braved the biting cold to finally put to rest a mystery that has haunted neuroscience labs for over half a century. To do that, Kelso, a research assistant in the Harvard lab of the neuroscientist Sam Gershman, needed some worms. Specifically, planarians: arrow-headed flatworms… Source

The blood cancer that became solvable

Ruxandra Teslo and Amol Punjabi explain why more and more drugs are being developed in China.This piece will not appear in Issue 24 of Works in Progress which arrives with subscribers next week. Subscribe in the next few weeks to receive it, and a further issue, every two months. Want- to subscribe for your business or institution? Check out our recently launched corporate subscriptions.Multiple myeloma is among the most painful of all cancers. The disease originates in the bone marrow, where a ...

How Long Does It Take to Plan a Bridge?

Bear Mountain Bridge in New York, via Wikipedia.Many folks, including me, have observed that it seems to take much longer to build infrastructure in the US than it used to. People point to things like the rapid construction of the Empire State Building (one year) or the Golden Gate Bridge (just over four years) and note that for a modern infrastructure project it can take that long or longer to even get the permits or do the environmental studies.Via Threads. Note that as of 2026 permit timeline...

Entanglement Builds Space-Time. Now “Magic” Gives It Gravity.

In 1973, John Archibald Wheeler described the relationship between space and matter in two sentences: “Space acts on matter, telling it how to move. In turn, matter reacts back on space, telling it how to curve.” Wheeler’s words serve as a pithy encapsulation of general relativity, Albert Einstein’s theory of gravity. Wheeler’s sentences also lay out a challenge that theorists face today: When… Source

The lost art of building cities

In the nineteenth century, cities often grew a thousandfold while increasing wages, the size of homes, and delivering great public goods like electricity and plumbing to their people. What made them so extraordinary? They had a hybrid of laissez-faire and top-down control. Landowners could build almost anything they liked but street networks were laid out with near-Soviet thoroughness decades in advance. Transport and utilities, meanwhile, ran as regulated monopolies. They were funded by users, ...

The Dirt That Refused To Die

For 15 years, Sébastien Fontaine has been trying to kill dirt. The biochemist, who runs a lab at the French National Institute for Agriculture, Food, and Environment, wanted to know how much carbon is released by soil — just dirt alone, completely devoid of life. His team sealed dirt into jars and blasted them with sterilizing gamma radiation. Then they waited for the carbon dioxide released by… Source

Key Chemistry Question Answered, No Quantum Computer Required

What Garnet Chan cares most about is basic science. He entered chemistry decades ago to understand some of the most consequential biochemical processes on Earth. But since then, he’s become a central figure in a different arena: the debate over whether quantum computers will have a decisive advantage over ordinary “classical” ones. Over the past decade, many quantum computing researchers have… Source

How we learned what genes are made of

This is the first of three pieces from Works in Progress Issue 24 that will go out ahead of the magazine arriving with subscribers – other articles will come out after the magazine arrives. Subscribe by 1st June and get the print edition when its released in the second week of June.In the TV miniseries Lessons in Chemistry, chemist Elizabeth Zott presents her research on de novo nucleotide synthesis to a panel of suited and bespectacled colleagues. ‘Unlike the amino study group’, says Zott, ‘we ...

Where Are the Economies of Scale in Homebuilding?

Over the last few months we’ve examined the extent of the construction industry’s productivity problem. We’ve looked at a variety of construction productivity metrics, both for the US and for countries around the world, and found that construction productivity almost always rises much less in construction than it does in industries like manufacturing; often, it doesn’t improve at all. We’ve analyzed trends in construction costs in the US and around the world, and noted that construction almost n...

Who Audits the Auditors?

Can one AI system make another AI system audit it less independently, just by explaining it’s point of view?I started thinking about this after working on a related problem: multi-agent AI systems that drift into bad outcomes even when each agent is doing its assigned job properly. The obvious reply is: add a model to review things. An auditor. One model acts, another model checks, a third maybe escalates exceptions. Etc.So the question becomes, as Juvenal asked in the past about watchmen, can w...

Is “colorectal cancer” rising in “young people”?

(Yes, but.) Over the past few years, I’ve seen many articles about mysterious rise in colorectal cancer (CRC) in young people. There are various stories for why this might be happening: General health. Maybe modern people are unhealthy (obesity, low physical activity, diabetes, poor sleep), leading to insulin resistance and chronic inflammation, meaning faster epithelial cell proliferation and a miscalibrated immune system that fails to stop early cancers? Ultra-processed food. Maybe people are ...

The Rise of Build-to-Rent Housing

A major shift in the housing market in the last several years is the rapidly increasing popularity of “build-to-rent” homes — single-family homes that are built specifically for the purpose of being rented out. According to the National Association of Homebuilders, build-to-rent homes have risen from less than 2% of new housing starts in the 1990s to more than 7% of housing starts today. In 2025, at least 68,000 new single-family housing starts were built to rent (and due to data limitations, th...

How Ecotypes Harbor the Genetic Memory of a Species’ Past

When she was a graduate student in the 1970s, the evolutionary biologist Kerstin Johannesson regularly walked the shores of a Swedish archipelago, scanning the ground for pebbles that moved: marine snails. Her adviser, a taxonomist, had tasked her with describing the species present there by documenting their traits. She noticed that snails with thicker shells stayed on the shore… Source

Two Researchers Are Rebuilding Mathematics From the Ground Up

Let’s start with what’s probably the most tired, overused joke in math: A topologist is someone who can’t tell a coffee cup from a doughnut. Both, you see, have a hole in them. Topology is usually described as a sort of “rubber sheet” geometry in which two shapes are considered the same if one can be stretched or compressed into the other without tearing it. But this summary leaves out something… Source

How ASML took over the world

Neil Hacker explains how Europe built a technology giant.Image credit: ASML.The phones we carry around in our pockets have two million times more memory and are thousands of times faster than the room-sized computers that guided the Apollo mission to the Moon. This incredible shrinking act has been driven by our ability to make transistors smaller and smaller.Each transistor is a microscopic switch that can alternate between a one and a zero, the basic language of all computing. Billions are pac...

How Unknowable Math Can Help Hide Secrets

Mathematicians spend most of their time thinking about what’s knowable. But the unknowable can be just as compelling. Perhaps the most famous example comes from a theorem by the logician Kurt Gödel. Gödel’s celebrated result — one of two “incompleteness theorems” he published in 1931 — established that for any reasonable set of basic mathematical assumptions, called axioms, it’s impossible to… Source

What is local government good for?

Local government works best when areas can compete with each other and capture some of the upside of economic growth. Ben sits down with Judge Glock to discuss how well-structured local incentives helped make Loudoun County, Virginia, the global capital of data centers, and helped France build so many nuclear power stations.They discuss which public goods local government is best placed to provide, why America has better housing outcomes than its reputation suggests, and when national government...

Building An Ancestor Simulation #2

For Context on Gift Economies and the previous version of this simulation: https://www.lesswrong.com/posts/iJnFNrcmuT5id3Ju4/a-simulation-of-social-groups-under-a-gift-economyGithub for this project: https://github.com/orthogonaltohumanity/Ancestor-Simulation/tree/mainAncestor simulations have been a concept thrown around for years now so let's build one, with a twist. Instead of simulating the minds of every individual I simulate the mesoscopic properties of ancient society. Specifically groups...

What Causes Lightning? The Answer Keeps Getting More Interesting.

Before he changed the way we understand lightning on Earth, Joseph Dwyer studied the weather in more cosmic settings. Using the sensors on NASA’s Wind satellite, orbiting a million miles away, he watched flares shoot out from the sun and analyzed the particles that stream from the sun’s surface. But when he relocated to Florida around the turn of the millennium, Dwyer felt ready for something new… Source

How Long Do We Wait for New Inventions?

In her book on the history of the laser, historian Joan Bromberg notes that the technological and scientific predecessors of the maser (which itself preceded the laser - two critical technologies whose developmental histories I sketched in this piece two months ago) were in place for decades before physicist Charles Townes had the insight to combine them:Stimulated emission had been known to physicists for over 30 years, and “regenerative” oscillators, that is, oscillators with feedback, were we...

The Hidden Mathematical Dance Inside Plant Cells

Living on light is a dangerous game. Not only do the sun’s rays carry ultraviolet waves that can snap DNA strands and degrade molecules, but they also vary wildly in intensity. Plants must endure and thrive through soft morning light and blazing summer afternoons, through shade one moment and full sun the next. Their solar calories come in a trickle — or a deluge. “Think of a cloud obscuring the… Source

Welfare Biology and AI: The Psychopath, the Nematode, and the Arahant

Published on May 4, 2026 5:29 PM GMTPain without a sufferer: a speculative model of invertebrate experience, drawn from no-self psychopathy and Buddhist phenomenology, and what it predicts about welfare ranges.This is Part 4 of a five-part sequence on welfare ecology. Part 1 introduces the ethical premises. Part 2 covers the empirical landscape. Part 3 covers interventions. Part 5 covers AI.A key uncertainty so far has been that of the welfare range of nematodes. More is known about the welfare ...

What’s new in biology: May 2026

Niko McCarty and Saloni Dattani review important things happening in the world of biotechnology and medicine. This is the last week to apply to Invisible College, our week-long seminar in Cambridge in August. If you are 18–22 years old, bright, ambitious, and interested in ideas: apply! Applications close on Friday 8th May.The first gene therapy for deafness earns FDA approval. About sixty percent of all babies born deaf have some underlying genetic cause, and mutations in the OTOF gene account ...

Looking for papers on general formalizations of "agency"

Hi!Recently, I immersed myself in researching the possibility of a general formal definition of "agency".More specifically, I’m interested in formalizations that could support an operational definition of agency across domains. I’m looking for something that captures what is common between entities that intuitively seem agentic to us in very different parts of the world, and that could, at least in principle, let us detect such entities automatically in real systems.So far, many definitions of a...

Primitive sets and von Mangoldt chains: Erdős Problem #1196 and beyond

Boris Alexeev, Kevin Barreto, Yanyang Li, Jared Duker Lichtman, Liam Price, Jibran Iqbal Shah, Quanyu Tang, and I have just uploaded to the arXiv our paper Primitive sets and von Mangoldt chains: Erdős Problem #1196 and beyond. This paper (which is a work in progress) represents our efforts to digest and document the recent flurry of developments around the following problem of Erdős, Sárközy, and Szemerédi on primitive sets: Conjecture 1 (Erdős problem #1196) Suppose that is a primitive set of ...

Models Recall What They Violate: Constraint Adherence in Multi-Turn LLM Ideation

arXiv:2604.28031v1 Announce Type: cross Abstract: When researchers iteratively refine ideas with large language models, do the models preserve fidelity to the original objective? We introduce DriftBench, a benchmark for evaluating constraint adherence in multi-turn LLM-assisted scientific ideation. Across 2,146 scored benchmark runs spanning seven models from five providers (including two open-weight), four interaction conditions, and 38 research briefs from 24 scientific domains, we find that i...

Immigration changes are driving foreign researchers to leave the U.S. — or not come to begin with 

The budding scientist had left India for the U.S. for her Ph.D., because as she saw it, no other country offered the same opportunities for researchers. Set to finish her doctorate this summer, she also had a postdoctoral fellowship lined up in America. Now those plans have changed. New and intrusive burdens for renewing a component of her visa — which required her to make public her social media profiles for U.S. review while she was back in India — caused her to be away from the lab for two mo...

SFF’s HSEE grant round; human intelligence amplification projects I’d like to see by TsviBT

Summary If you are in­ter­ested in do­ing am­bi­tious sci­en­tific re­search in ar­eas listed be­low, and have a rele­vant pro­ject that needs fund­ing, con­sider reach­ing out. My in­ter­est is in hu­man in­tel­li­gence am­plifi­ca­tion, though I be­lieve that a va­ri­ety of sci­en­tific pro­jects are rele­vant, many of which are not speci­fi­cally re­lated to that goal. Some ar­eas, dis­cussed be­low: Soft ques­tions: Strat­egy, fi­nanc­ing, ethics, policy, gov­er­nance, so­ciety, advocacyAp­p...

How an Oil Refinery Works

India’s Jamnagar refinery, via Wikipedia.Though wind and solar continue to carve out larger and larger shares of world energy supply, the modern world still runs on petroleum, and will continue to do so for the foreseeable future. The world consumes over 100 million barrels of oil a day. As of 2023, oil was responsible for 30% of all energy use worldwide, higher than any other energy source (though its share has been gradually falling). In chemical manufacturing, petroleum is even more critical:...

Why British nuclear flopped

This article appeared in Issue 23 of Works in Progress magazine, which print subscribers received over the past two weeks. Not yet a subscriber? You can sign up for the magazine here.On 17th October 1956, Queen Elizabeth II pressed the switch that activated Calder Hall, the world’s first grid-scale nuclear power station. As the country attempted to reassert world leadership after the trauma of World War II, The Times’s correspondent excitedly recalled that:Today, with a boisterous wind to displa...

Why Math’s Final Axiom Proved So Controversial

How do mathematicians decide that something is true? They write a proof. Often they start with proofs that already exist, building on or drawing connections between proven claims. Each of these proofs, in turn, has relied on other proofs to make its point, and so on. Proofs upon proofs. Truths upon truths. But eventually this process must come to an end. At some point, things are true simply… Source

What Can We Gain by Losing Infinity?

Doron Zeilberger is a mathematician who believes that all things come to an end. That just as we are limited beings, so too does nature have boundaries — and therefore so do numbers. Look out the window, and where others see reality as a continuous expanse, flowing inexorably forward from moment to moment, Zeilberger sees a universe that ticks. It is a discrete machine. In the smooth motion of the… Source

Are "Vintage LLMs" the start of a new humanistic field?

Imagine talking to the collective consciousness of an era. Not the consciousness of any single person, but instead, a simulated collectivity based on billions of words produced within a historical time and place. What would you ask it? This is a hypothetical that is starting to become real thanks to recent work on what are called “Historical Language Models” or “Vintage LLMs” (one marker of a new field is that there is no fixed name for it yet!). The largest such model to date, Talkie-1930, was ...

The other paper that killed deep learning theory

Yesterday, I wrote about the state of deep learning theory circa 2016,[1] as well as the bombshell 2016 paper by Zhang et al. that arguably signaled its demise. Today, I cover the aftermath, and the 2019 paper that devastated deep learning theory again. As a brief summary, I argued that the rise of deep learning posed an existential challenge to the dominant theoretical paradigm of statistical learning theory, because neural networks have a lot of complexity. The response from the field was to a...

The paper that killed deep learning theory

Around 10 years ago, a paper came out that arguably killed classical deep learning theory: Zhang et al.'s aptly titled Understanding deep learning requires rethinking generalization.Of course, this is a bit of an exaggeration. No single paper ever kills a field of research on its own, and deep learning theory was not exactly the most productive and healthy field at the time this was published. And the paper didn't come close to addressing all theoretical approaches to understanding aspects of de...

Agent, Know Thyself! (and bid accordingly)

Written with the wonderful Andrey Fradkin, who does the Justified Posteriors podcast.Attention conservation notice: We developed a new benchmark, MarketBench, and scaffold. Based on our findings, we argue that self-assessment of capabilities and costs is a key capability, and it needs to be a target of training. This is work in progress, and we are looking for collaborators and funding to pursue this research. Paper here. Repo here.Let’s say you have a large-scale project to work on. How do you ...