Mark C.

I have been laughing at this entirely too long...

@pickover n =b-1 for any base b

Mathematics. Are you able to solve this equation just by looking at it, without using a pen and paper to solidify your thinking process? (Similar kinds of math problems circulate widely on the Web.)

Do you own books about electronics, but could never make it all click? Do you know what a resistor does, but still get stumped designing your own circuits? If yes, I wrote "The Secret Life of Circuits" with you in mind. All chapters available now: lcamtuf.coredump.cx/blog/secret/

@lukOlejnik It's literally a subset the complex numbers you can calculate/compute - and equivalent to a system due to Chow (1999). Real question becomes if this is enough for science, or do we need all the incomputable stuff inbetween? Cf: arxiv.org/abs/2605.01636…

Physicist has written a fascinating big beautiful paper.Let’s not be afraid to call it what it is - groundbreaking. For hundreds of years, mathematics had dozens of “basic” functions: sine, cosine, logarithm, square root, exponential. You know these from school. Everyone does. Now it turns out that all of it is one single operator: E(x, y) = exp(x) - ln(y), and the constant 1. Sin, cos, π - everything follows from this neatly , just nest it properly. Nature hid the simplest possible description of reality. And it was just been found. The whole thing is beautiful and remarkable, here the word “groundbreaking” is not a marketing buzzword. For instance, instead of writing π or 3.14, one can now elegantly write E(E(E(1,E(E(1,E(1,E(E(1,E(E(1,E(E(1,E(1,E(E(1,1),1))),1)),E(E(E(E(E(1,E(E(1,E(1,E(E(1,E(E(E(1,E(E(1,E(1,E(E(1,1),1))),1)),E(E(1,E(E(1,E(E(1,E(E(1,1),1)),E(E(E(1,E(E(1,E(1,E(E(1,1),1))),1)),E(1,1)),1))),1)),1)),1)),1))),1)),E(E(E(1,E(E(1,E(1,E(E(1,1),1))),1)),E(E(1,E(E(1,E(1,E(E(1,E(E(1,E(E(1,E(1,E(E(1,1),1))),1)),E(1,1))),1))),1)),1)),1)),1),1),1))),1))),1)),E(E(E(1,E(E(1,E(1,E(E(1,1),1))),1)),E(E(1,E(E(1,E(1,E(E(1,E(E(1,E(E(1,E(1,E(E(1,1),1))),1)),E(1,1))),1))),1)),1)),1)),1) arxiv.org/abs/2603.21852

@skdh You only get a subset of the computable complex numbers. Fine if that's what you need, but I'd consider 'full-fat' physics might need more. (cf: arxiv.org/abs/2605.01636… )

A mathematician has come up with a new way to derive all mathematical operations from merely one. I've had a look at the paper.

@mathandcobb @skdh For reference - I found these substitutions work best (and are minimal by exhaustive search) when reconstructing Chow's subfield of \mathbb{C} to prove EML = EL numbers: gist.github.com/unprovable/766…

@mathandcobb @skdh EML's totally equivalent to Chow's EL numbers (1999). You need to take the workings of the principal branch carefully - used Weihrauch (2000) in this to show the EML/EL are contained in the computable complex numbers: arxiv.org/abs/2605.01636…

@nasqret @mathandcobb @skdh how far did you get?

@mathandcobb @skdh Working on this with Lean and Mathematica!

Est-ce que quelqu’un organise des meet-ups plutôt techniques autour des LLMs à Paris ? Pas besoin d’en faire souvent mais on a le talent pour les remplir.

@halvarflake Running @quantum_village with @V__Wave, I can attest it really is not...

"I work for a non-profit" is the way to riches, clearly.

Today I have open sourced my Xbox 360 XL storage patches that raise the limits from 2 TB to 16 TB. This was one of the most complex projects I have worked on in recent years, and now you can see how it all works! fatxplorer.eaton-works.com/2026/05/04/xbo…

@__paleologo For the complexity theory historical account, I can't wait to read the chapter on Levin.

Down the memory lane. In the late 1980s "Fuzzy Logic" was all the rage. Popular articles, serious papers. It seemed to be a revolution in logic, control theory, AI. IEEE even created an "IEEE Transactions on Fuzzy Systems" in 1992 (there are about 120 IEEE transactions journals in total). Then, nothing. In the past 25 years, I haven't heard fuzzy logic/systems once. Google Trends bears this out: nice exponential decay curve. Interest seems to have waned. The IEEE journal has still an impact factor of 11.9, but it's sort of misleading (because mediocre authors cite mediocre authors. IEEE Transactions on Information Theory has 2.9! Really?) It seems to have experienced a mild resurgence last year. The point being, fads exist. We just barely remember them. At some point, someone has to write a story of "complexity theory as fad".

But do you know what coreutils are a fertile ground for? Race conditions around file creation, deletion, permission setting, and so on. The original code accounted for decades of hard-learned lessons in that space. The Rust rewrite did not: seclists.org/oss-sec/2026/q…

they call them crisps there

I thank the Institute for Theoretical Physics at the California Institute of Technology [@Caltech] for having invited me to give a seminar on my work on timelike Liouville field theory, a recent work done in collaboration with @Bruno_Sivilotti, a bright young colleague.

A cryptographer found a hidden fingerprint in Bitcoin’s earliest blocks that proves ONE person mined 1.1 MILLION BTC and never spent a single coin That stash is worth over $115 BILLION today In 2013 a researcher named Sergio Demian Lerner was studying the very first blocks ever mined on Bitcoin. He noticed something nobody else had spotted in 4 years Every Bitcoin block contains a small data field called the ExtraNonce. It’s a number that gets incremented every time a miner generates a block. Different miners produce different ExtraNonce sequences Lerner mapped the ExtraNonce values from the first 50,000 blocks and discovered something incredible When you plot them on a graph they form slopes. Each slope represents a single miner There were dozens of slopes. But ONE dominated everything A single slope appeared across approximately 22,000 of the first 36,000 blocks ever mined. Perfectly consistent timing, identical software behavior, no overlap with itself, and a self imposed limit Lerner named this miner “Patoshi” The math became obvious. Patoshi mined approximately 1.1 MILLION Bitcoin during 2009 and the first half of 2010 That’s 5.7% of every Bitcoin that will ever exist. Mined by one person before almost anyone else knew what Bitcoin was Satoshi’s mining code incremented the ExtraNonce field differently than any other miner’s which was an unintentional fingerprint built into the original Bitcoin client itself Through cross referencing with known transactions between Satoshi and early developers like Hal Finney, the cryptography community concluded the Patoshi miner was almost certainly Satoshi Nakamoto The wildest part is what Patoshi DIDN’T do He could have mined far more. The Bitcoin network in 2009 had so few participants that Satoshi’s hardware was effectively the entire network. He could have captured close to 100% of all blocks for months Instead the pattern shows Patoshi deliberately throttled his hash rate to roughly 50% of his actual capability. He was leaving room for other miners to win blocks Patoshi also stopped mining at the same time every day. The on/off pattern looks more like one person running a computer in their study than an industrial operation Around April 2010 the Patoshi pattern stops appearing entirely. Satoshi never mined another block Over a year later in April 2011 he sent his last public message and disappeared forever The 1.1 MILLION BTC is still sitting in approximately 20,000 separate addresses across the chain It has not moved in 16 YEARS The single largest dormant fortune in human history measured by current value. Worth more than the GDP of most countries and owned by an identity nobody has ever confirmed The Patoshi pattern is the closest thing we have to evidence that Bitcoin was created by an individual rather than a state actor or organization The mining patterns show one person, one timezone, one consistent personality taking breaks like a normal human If they ever sell, the entire crypto market would have to absorb the largest single liquidation in financial history If they never sell, those 1.1 MILLION BTC are effectively burned forever making Bitcoin’s true circulating supply much smaller than people think Both outcomes are world changing. The decision rests with one person who hasn’t been seen since 2011 The person it points to is gone

Arithmetic. Vision. Navigation. Planning. What if they're all the same task? We introduce group composition as a unifying abstraction for many learning problems & show neural networks crack it using Fourier! Led by @KuninDaniel @giovannimarchet @AdeleMyersPhD @hopfbifurcator🌟

I beep therefore I am...

@littmath I have a preprint using some computable analysis and it was just wrong about the computable bits (niche field) but totally up to speed on subtleties of the principal branch cut in complex nat log.

@littmath I honestly think it's to do with surface area of available training data for the subjects at hand? I've had a clanger point out some nice corrective subtleties, but completely miss a typo'd index...

TBC the models are very rapidly improving and I often find them very useful; capabilities are way ahead of where they were even a few months ago. Just still interested in understanding why there seems to be some delta here.