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A reminder that proteins are highly dynamic molecules.
◼️We have made much progress in measuring & predicting static protein structures, but the dynamics that animate life remain challenging to measure & model.
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Quantum states split under magnetic fields (Zeeman effect)—the same physics fusion relies on to control charged particles. Here, color shows wave phase, brightness its strength. Microscopic rules, macroscopic power.
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UnsolvedMath - a curated list of 1000+ open math problems for AI to solve.
We've just uploaded to Hugging Face a curated set of unsolved math problems, including 600+ Erdos problems, in a machine-friendly way.
The goal is to have a proper benchmark for Reasoning Models, which can't be incorporated through training.
Any new insights are a good benchmark. Currently GPT 5.2 with Extended Thinking is the leading model by a lot. Tests and whitepaper incoming! Link below.
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I've been editing this article about "brain mapping" and connectomics, and I'm just stunned by how quickly the cost estimates to map, say, a mouse brain have plummeted in just the last couple years.
It actually seems feasible that we could map the entire human brain -- all 86 billion neurons, and their connections -- in this lifetime.
In the 1970s, Sydney Brenner started mapping all the connections between neurons in C. elegans. His team sliced the worm into thin pieces, took photos using an electron microscope, and manually traced and reconstructed each synapse for 302 neurons total. This project took more than a decade of work, and it cost about $16,500 to reconstruct each neuron. Scaling this up to a human brain boggles the mind.
Electron microscopy remained the norm in connectomics for decades, because it was the only option available to see synapses at a resolution high enough to be able to trace their paths. Each electron microscope costs several hundreds of thousands of dollars, though, and you need lots of them to map even a mouse brain in a reasonable timeframe.
In 2023, the Wellcome Trust released a report estimating how long, and how expensive, it would be to map the mouse connectome (~70M neurons). They estimated that imaging alone would cost $200-300M, and that proofreading (or ensuring that traces between neurons are correct) would cost $7-21 BILLION. (A human can only manually trace about 1 mm of neuron per hour.) Also, the images would occupy about 500 petabytes of data, and getting those data would require 20 electron microscopes running in parallel for about 5 years, continuously. They estimated the whole project would take about 17 years of work.
This is, understandably, insane. But now it seems like there's an actual path toward mapping the full mouse brain in about five years for ~$100M dollars.
There have been three major breakthroughs in the last year or so:
1/ Expansion microscopy, first developed in 2015, showed that it's possible to "enlarge" the brain by about 5x using a swellable polymer. But an improved method increases this number to >20x expansion, meaning we can now expand brains and image neurons much more easily using cheap light microscopes, rather than expensive electron ones.
2/ E11 Bio (a nonprofit research org) developed protein barcodes that get delivered into brain tissue; each neuron gets a unique combination of barcodes. These cells are then stained with colorful antibodies, which stick to a matching protein barcode, causing each neuron to light up in a distinct color. This makes tracing neurons so much easier.
3/ Google Research released PATHFINDER this May, an AI-based neuron tracing tool that can proofread about 67,200 cubic microns of brain tissue per hour, with very high accuracy. It works on electron micrographs, but something similar could be presumably be developed for the E11 / colorful tag approach.
This is an extremely exciting time for neuroscience. (C. elegans connectome below.)
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I wrote this fun interactive article explaining Isomap, a classic non-linear dimensionality reduction technique.
Isomap captures the local similarity structure of data through a graph and computes an embedding that preserves this structure.
Check it out! Link below.
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The price of everything on Earth.
This chart is all of the natural occurring elements, their occurrence rate in Earth's crust (X-axis) and their price in USD (Y-axis).
The chart illustrates three clear price regimes.
1. Yellow band is stuff that is economically priced this is within 1 order of magnitude of -1 log-log.
2. Stuff above the yellow band is expensive for its relative abundance on Earth.
3. Stuff below the yellow band is cheap for its relative abundance on Earth.
There is a by-product trap in the global economy and this is the dominant choke mechanism, many of the elements above the red line are by-products of primary processes and you can't build dedicated economies of scale for a material without a primary process. Likewise some things below the yellow band are also by-products or waste products of a primary process.
Titanium is the canonical process opportunity of the 21st Century, it sits well outside the economy for such an abundant material a clear sign that Kroll + chloride chemistry is the issue. Any viable electrolyte/plasma/FFC type route is a multi sigma unlock for humanity.
Noble gases are on the floor, they are cheap to stockpile and tied to industrial air separation processes ie oxygen and nitrogen plants.
Rare Earth sit tightly in the economically priced band, their pricing is separation process and demand mix dominated, not scarcity dominated.
The kink/flattening at high abundance shows where scarcity stops mattering, beyond circa 10^3 ppm the economy hits the energy floor and energy / logistics drive price illustrating the Earth is well below its carrying capacity for humanity.
The chart also demonstrates that national resilience lies on process capacity and not access to ore, this is quite different to the learnings of WWII. But hey, times change.
Policy should invest toward primary processes or waste stream recovery for Ga/Ge/In/Sc/Re/Te and we should be funding science for process breakthroughs in Ti/V/Nb/Ta/Hf.
On the whole, humans get a B+
(maybe we should get an A++ when you consider nobody even thinks about this stuff and we just Adam Smith our way to glory?)
Fun to plot this for other worlds and figure out what processes make sense to take there. Obviously all the prices start much higher when you start over and you have to spend a long time driving them down. The chart for Earth is mature, we've been doing this here a few thousand years now.
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12 Things Everyone Should Know About Violence: What the science really says about aggression, crime, and human nature
1. The most violent group of people in the world is... toddlers.
[Link below.]


















