⦿ US State Department
L to R: US special envoy Steve Witkoff, US secretary of state Marco Rubio, US national security adviser Mike Waltz,
Saudi chairs, Russian foreign policy adviser Yuri Ushakov, Russian foreign minister Sergei Lavrov
 

2025 February 18

US−Russia Relations

Pjotr Sauer, Luke Harding

Top US and Russian officials met in Saudi Arabia for the most extensive negotiations between the two countries in three years. They agreed to continue planning an end to the Ukraine war and to pursue closer cooperation.
After five hours of talks, US secretary of state Marco Rubio said they had agreed to create a team to support Ukraine peace talks and to explore "economic and investment opportunities" following an end to the war.

AR Who said "stitch-up"?
 

2025 February 16

Europe: An American Colony

Bruno Maçães

At the Munich Security Conference, US defense secretary Pete Hegseth laid out US terms:
•  No Ukrainian membership of NATO
•  No American boots on the ground
•  Russia keeps stolen Ukrainian land
Trump wants a deal between Russians and Americans. He may leave Ukrainians out of negotiations. If he reaches a deal with Putin, it will let European troops secure Ukraine. Americans will sell US arms and take Ukrainian natural resources; Europe will pay to reconstruct Ukraine.
Trump wants his American empire to exploit Europe rather than to confront Russia. He wants Europe to pay for the border wars. His officials want closer interoperability with European militaries on missile systems, ammunition, AI, and cyber warfare so that European nations buy more US arms.
Europe needs independence just when it needs American power.

AR This may be the shock that Europe (including the UK) needs to get its defensive act together. Europe has numerous small forces that don't work together smoothly enough and buy nationally sourced arms and ammo. This is absurd, a recipe for defeat on the battlefield.
 

2025 February 15

Collapse of the Transatlantic Alliance

Patrick Wintour

At the Munich Security Conference on Friday, US VP JD Vance said the greatest danger to Europe was not Russia or China but the "danger from within" as an entrenched elite continued to allow mass migration and locked voters out of political debate.
For the MAGA movement, US withdrawal from Europe is an ideological break: NATO was founded to defend shared values, but if those values are no longer shared, the purpose of NATO is gone.
Vance said Germany should accept AfD populists: "If you're running in fear of your own voters, there is nothing America can do for you, nor, for that matter, is there anything that you can do for the American people."
German chancellor Olaf Scholz: "The AfD is a party from the ranks of which National Socialism and its monstrous crimes .. were trivialized."
Volodymir Zelensky: "The US vice-president made it clear .. The old days are over .. Europe needs its own armed forces."

AR Continuing mass immigration of Muslims into Europe certainly poses an existential danger to European traditions and values. But a more civilized and constructive solution is possible than encouraging the populist uprising that Vance seems to be recommending.
Europeans should recall their long heritage and end mass immigration now. They can do better than seeking to boost GDP growth by importing unskilled workers.
Is the UK's "special relationship" over? Yes.

 

The Guardian
DOGE supremo Elon Musk holds court in the Oval Office
 

2025 February 12

Musk Claims Federal Fraud

The New York Times

Elon Musk said in the Oval Office on Tuesday that he was providing maximum transparency in his sweeping claims that the federal bureaucracy had been corrupted by cheats and officials duped by fraudsters.
Answering questions as head of the Department of Government Efficiency, Musk stood next to the Resolute Desk and asserted that his work was in the interest of the public and democracy.
Musk: "If the bureaucracy's in charge, then what meaning does democracy actually have? We are actually trying to be maximally transparent .. I don't know of a case where an organization has been more transparent than the DOGE organization."
Musk appeared at a presidential signing of new executive orders related to his cost-cutting initiative. His remarks came amid criticism that he was operating with unchecked power and no accountability.
Wearing a black MAGA hat, Musk defended his team's work. As he answered questions, his 4-year-old son, X, sat on the floor. Musk rebuffed suggestions that he was operating without oversight and said he intended to bring accountability to a civil service that he claimed had gone unchecked.
Musk: "We will make mistakes. But we'll act quickly to correct any mistakes."

The Musk revolution
Rafael Behr

Germany used to be held up as a model of collective atonement for Nazi crimes. That has not thwarted the rise of Alternative für Deutschland (AfD) to second place in opinion polls going into federal parliamentary elections on February 23.
Elon Musk routinely boosts the AfD from his X platform. He has commercial and ideological incentives to meddle in German politics. The AfD is committed to low taxes and deregulation, as well as mass expulsion of migrants and rapprochement with Russia.
Musk seems attracted to the far right in Germany because that is where a breach of the cultural firebreak has the most symbolic potency. To an audience of AfD activists, he declared: "There is too much focus on past guilt. We need to move beyond that."
Palantir co-founder Peter Thiel: "There will be no reactionary restoration of the pre-internet past."
Palantir CEO Alex Karp: "There's a revolution. Some people are going to get their heads cut off."
The lessons of history may have to be relearned the hard way.

AR Ominous signs of things to come: America is on the path to becoming a rogue state that outdoes even Nazi Germany.

 

Firefly Aerospace
The Blue Ghost spacecraft has captured its first images of the Moon from the spacecraft's orbit around Earth.
Firefly released a video of Earth eclipsing the Moon. The lunar lander is expected to touch down on March 2.
 

2025 February 9

God

Ross Douthat

A compelling case for God is the evidence for cosmic design in the fundamental laws and structure of the universe and the unusual place of human consciousness within it.
The parameters of the cosmos have been apparently tuned very finely to allow for the emergence of basic order and eventually stars, planets, and complex life.
The multiverse answers the apparent odds against our own universe appearing accidentally by postulating a bazillion universes that we can't see or taste or touch. We're in a universe capable of sustaining living observers because it's the only kind where we could exist.
But we're in a universe that's deeply intelligible to us, a cosmos whose rules and systems we can penetrate, whose invisible architecture we can map, whose biological codes we can rewrite, and whose fundamental physical building blocks we can isolate.
The success of human reasoning is remarkable even if you assume that evolutionary pressure suffices to explain a modest form of successful reasoning. In many potential universes, those capacities would have hit a ceiling in terms of what they could accomplish.
The intelligibility of the cosmos is an argument not only that God exists but also that his infinite mind and our finite minds have some important connection.

God ain't human
MailOnline

In popular culture, God has long been portrayed as an old bearded man. In the Bible, God is referred to as "he" and "him" and even depicted in white robes.
Religious experts say God does not exist either as a man or as a woman, but instead exists in a subjective sense and not in a human form.
Theologian Ilia Delio: "We have anthropomorphized God − making God into a superman, the big guy in the sky we can either accept or reject .. But this is .. a projection of our need for a god .. God is not an object to argue about but the ground of all that is, not beholden to the limits of the human mind."
Anthropologist Alexandros Batalias: "There is no way to construct an argument or theory that can objectively prove the existence of God, as God is not an object to be analyzed or measured."
Many scientists agree there is no experiment that could detect God. Most agree that the universe sprang into existence with the Big Bang some 14 billion years ago.
Cosmologist Stephen Hawking: "It is not necessary to invoke God to .. set the universe going. Spontaneous creation is the reason there is something rather than nothing."
Biologist Richard Dawkins: "There is something infantile in the presumption that somebody else has a responsibility to give your life meaning and point."

AR Ross loses the argument. He's human and can't imagine how we can be so successful. Well, there are billions of us, so together we can do more, just as his brain can do more than a gnat's brain.
If there were billions more, with superhuman AI and so on, we'd be so successful it would blow his mind, but we'd still know a drop in the ocean. Being God is way beyond all that.
 

2025 February 6

Cut US$2 Trillion Nuke Plan

Dan Vergano

DOGE czar Elon Musk said he would trim $2 trillion from the federal budget. He can make the cuts on nuclear weapons.
POTUS Donald Trump called in January for talks on reducing nuclear weapons with China and Russia: "Tremendous amounts of money are being spent on nuclear, and the destructive capability is something that we don't even want to talk about .. it's too depressing."
More nuclear weapons make us less safe. A nuclear war would bring hundreds of millions of immediate deaths, followed by nuclear winter starving billions. Even a limited nuclear war would cause global famine.
China is ratcheting up its nuclear forces over fears of a US first strike. Russia has signaled it wants to head off a nuclear weapons buildup. Conditions are ripe for a Trump deal that prevents a three-way rerun of the cold war arms race.
Project 2025 called for POTUS to expand and modernize the US nuclear force, but the call wasn't in the MAGA pitch.
By nixing nuke modernization, Musk could take a $2 trillion bite out of the federal budget.

AR Perfect! Memo to Musk: Do it.
 

2025 February 4

Waves in an Impossible Sea

Andy Ross

The Higgs mechanism is responsible for the rest mass of everything in the universe. Explaining what this means is the challenge Matt Strassler sets himself in this book. So far as he can without math, he succeeds, but there are caveats.
Modern physics hangs together in a tightly woven fabric. To understand anything, you have to understand everything, at some level. But any level short of the deepest leaves big gaps and problems unanswered, and the latest level the professionals have reached leaves the worst gaps and problems of all.
Strassler is disarmingly honest about this. His presentation of the background to Newtonian physics is excellent at the "physics for poets" level, but when he tries to explain special relativity and quantum mechanics at this level, it begins to go wrong. By the time he reaches the Higgs field and its mechanism, the poets are lost. His story is better than others out there, but without the math it still makes little sense.
To tell the story even this far, Strassler takes the reader on a tour of all of modern physics, guided by what he calls Einstein's Haiku: "E equals h f, And E equals m c squared; From these seeds, the world." Charming, but explaining these two equations without math turns them into magic potions.
The book is fun to read, and I enjoyed it. Strassler knows his audience, has reader-tested the book, and writes with an engagingly light tone. The book deserves success. But don't expect to be much the wiser after reading it.
 

2025 February 2

DeepSeek AI

Melissa Heikkilä

DeepSeek adopted a series of efficient techniques to develop R1, which generates accurate answers by taking time to think about its responses.
LLMs are built in two stages: pre-training (massive data sets help models to predict the next word in a sentence) and post-training (the model is taught to follow instructions).
DeepSeek also used reinforcement learning from human feedback: Human annotators label the AI model's responses to prompts and pick the best responses. Reinforcement learning (RL) rewards the AI model for doing the right thing, but it's often slow and expensive.
DeepSeek first developed the text-predicting model V3, then used RL to reward the model. The model eventually solved problems without human supervision, re-evaluated its answers, and adjusted its processing time to solve different questions.
DeepSeek found its distilled models are strong on reasoning benchmarks.

Cheap, powerful Chinese AI for all
John Naughton

China has caught up with the leading US AI labs: DeepSeek R1 is a powerful AI assistant that's much cheaper to train and operate than the dominant models of the US tech giants.
The low costs of R1 will turbocharge US anxiety that the emergence of powerful and cheap Chinese AI could upend the economics of the industry. AI technology will be commoditized.
DeepSeek pulled this off despite the ferocious technology bans imposed by the first Trump administration. R1 is distributed under the permissive MIT licence: Anyone can use, modify, and commercialize the model without restrictions.
California venture capitalist Marc Andreessen: "DeepSeek R1 is AI's Sputnik moment .. one of the most amazing and impressive breakthroughs I've ever seen .. a profound gift to the world."

Chatbot software limitations
Anil Ananthaswamy

Transformer LLMs trained only to predict the next word in a sequence have hard mathematical bounds for compositional reasoning.
LLMs work with natural language. During training, an LLM is shown a fragment of a sentence with the last word obscured, predicts the missing information, and learns from its mistakes.
The largest LLMs train on almost all the available data on the internet. They learn the syntax and much of the semantics of written language. Such pre-trained models can be fine-tuned to complete sophisticated tasks, yet fail badly at basic multiplication.
Binghui Peng et al proved that an LLM with only one transformer layer is mathematically limited and that multilayer transformers cannot solve certain complicated compositional tasks.
One way to overcome these limitations, beyond just increasing the size of the model, is to provide a step-by-step solution of a problem within the prompt, a technique known as chain-of-thought prompting.
Haotian Ye et al modeled the behavior of transformers with and without chain-of-thought prompting and showed how chain-of-thought prompting turns a large problem into a sequence of smaller problems, enabling transformers to tackle more complex compositional tasks.
LLMs match patterns, and their abilities have mathematical boundaries: You can always find compositional tasks with complexity beyond a given system's abilities.

AR The DeepSeek team deserves our congratulations. How the Chinese or the American governments react is something else. The technology with change the world independently of anything they decide in the next few years. Let's hope AI ends up working for the good of humanity.

 

AR
Five years ago, the UK government committed Brexit.
Centre for European Reform economist John Springford: "Brexit has hurt trade and investment ..
in the long run the economy will be around 4% smaller than if Britain had stayed in."
CER director Charles Grant: "The government has not yet worked out what it wants
in terms of the economic relationship with the EU."

AR I see Brexit as an atrocious national betrayal of good friends in Europe.
The UK is not a viable loner in the modern world.
HMG: Signal the ambition to Rejoin!
 

2025 January 29

Year of the Snake

AFP

Hundreds of millions of people across Asia celebrate the lunar new year today.
 

2025 January 28

DeepSeek AI

research@deepseek.com

DeepSeek‑V3 is a strong large language model with 671 billion parameters, 37 billion activated for each token. It adopts multi-head latent attention and mixture-of-experts architectures, which were thoroughly validated in DeepSeek‑V2.
DeepSeek-V3 pioneers an auxiliary-loss-free strategy for load balancing and sets a multi-token prediction training objective for stronger performance. It is pre-trained on 14.8 trillion diverse and high-quality tokens, followed by supervised fine-tuning and reinforcement learning stages.
Comprehensive evaluations reveal that DeepSeek‑V3 outperforms other open-source models and achieves performance comparable to leading closed-source models.
Despite its excellent performance, DeepSeek-V3 requires only 2.788 million H800 GPU hours for its full training. Its training process is remarkably stable.

Chinese AI startup DeepSeek Is competing with Silicon Valley giants
Cade Metz, Meaghan Tobin

Last December, DeepSeek unveiled a new AI system. Its chatbot answered questions, solved logic problems, and wrote its own computer programs as capably as system on the market, according to American AI benchmark tests.
The Chinese engineers needed only about $6 million in compute to build their system. Experts had said no company could compete with the market leaders without spending hundreds of millions of dollars on specialized chips.
DeepSeek is known in China for scooping up talent fresh from top universities with the promise of high salaries and interesting research. It has open sourced its latest AI system.
University of California, Berkeley professor of computer science Ion Stoica: "The center of gravity of the open source community has been moving to China."
Toronto technology consultant Reuven Cohen says DeepSeek‑V3 is comparable to the latest systems from OpenAI, Google, and Anthropic − and much cheaper to use.

Nvidia sheds more than $600 billion in value as DeepSeek sparks market rout
Financial Times

DeepSeek attributes its success to methods that allow the AI model to selectively focus on specific parts of input data. For its latest R1 model, it used a reinforcement learning technique in which models teach themselves how to improve without human supervision.
Anthropic co-founder Jack Clark: "There's now an open weight model floating around the internet which you can use to bootstrap any other sufficiently powerful base model into being an AI reasoner."

Trump says DeepSeek chatbot is a 'wake-up call'
Mark Sweney

The launch of DeepSeek's R1 chatbot, built at a fraction of the cost of US competitors, wiped $1 trillion in value from the leading US tech index on Monday. Nvidia had $600 billion wiped off in the biggest one-day fall in US stock market history.
On Monday, the DeepSeek assistant surpassed ChatGPT in downloads from the Apple app store.
OpenAI CEO Sam Altman: "DeepSeek's R1 is an impressive model, particularly around what they're able to deliver for the price. We will obviously deliver much better models."

AR I could see something like this coming. Most AI systems waste resources on a prodigious scale, and huge increases in efficiency were to be expected. So investing heavily in hardware was risky.
That Chinese engineers got there first is also no surprise to me. I saw how good they could be when I was at SAP. This will be a Sputnik moment for Americans.

 

⦿ Henryk Makarewicz/United States Holocaust Memorial Museum
 

2025 Holocaust Memorial Day

Red army troops liberated Auschwitz 80 years ago today.
 

2025 January 26

Mystic Ecstasy

Rowan Williams

Simon Critchley discusses the human response to the world that is ecstasy: "It is impossible to be an atheist when listening to the music one loves."
He sees aesthetic experience and the mystical as closely aligned. The self is shown to be caught up in a patterned flow of life that shapes and suffuses the standpoint of the self.
Speaking about the divine (or the unconditioned for a Buddhist) involves accepting that it is not an object among others and cannot be included in any category of existing beings.
For Julian of Norwich, love precedes creation. To dwell in eternal love we must unravel the self. Something in us never falls away from God.

AR The divine, the unconditioned, endless love − words fail at this level.

 

Buckingham Palace
King Charles III poses with no pants on for a selfie to celebrate Burns Night, January 25
 

2025 January 24

Concept Cells

Yasemin Saplakoglu

A grandmother cell is a hypothetical neuron among the 86 billion in your brain that codes for one of your grandmothers. If you delete it, everything you know about her disappears from your brain.
Rodrigo Quian Quiroga showed patients images of places and people, including Jennifer Aniston, and found in each of their brains a neuron that responded to the actor. He found that the same neuron fired for all the Aniston photos but not for images of other actors or objects.
The brain can distinguish an estimated 20,000 semantic concepts, so millions of cells would code for every concept, and each concept cell would code for dozens of related concepts.
Christof Koch: "When your brain encounters things all the time − even high-level things like dogs and cats and people and trees and ships − we will have neurons for that."
Concept cells are not used for object recognition. They fire after a delay of about 300 ms and dip into a process forming an abstract representation informed by memory. Everyone has a different set of concepts and cells for them.
In 2012, Quiroga published his hypothesis that the brain uses concept cells to convert information from the world into memory. He proposed that concept cells might link together to form new associations and form building blocks for memories.
Concept cells may link specific objects to locations in our long-term memory. The firing patterns of concept cells and location cells correlate with the ability to remember an object's location. Concept cells are also linked to working memory.
Researchers debate how concept neurons fit in with other models of how the brain represents the external world. Concepts are represented at different scales in the brain.

AR All this seems about as I'd expect, given the overall architecture of the brain and of artificial neural networks that mimic some of its functions.
 

2025 January 22

Europe

Jakub Krupa

Polish prime minister Donald Tusk, speaking in the European Parliament: "We are dealing with an active conflict on our borders. We have to deal with technological progress .. Europe should not be fearful about its future .. what is happening around us ... is a whole new set of challenges for Europe. But Europe was created exactly to face such challenges."
German CDU leader Friedrich Merz, speaking at the WEF in Davos, on POTUS 47: "I think he'll be ready to do business, also with the Europeans. He's a dealmaker, so let's think about what we can offer .. As soon as we have a common European position we'll be seen as a strong partner."

AR Europe can face its challenges if its nation states have a common position. The UK will get nowhere with POTUS 47 on issues involving Europe, such as defending against Russian aggression, unless it aligns with the EU position. POTUS 47 will aim to divide and conquer.

 

POOL
POTUS 47 Donald Trump delivers his inaugural address in the Capitol Rotunda, Washington, 2024-01-20
 

2025 January 19

The New Overlord

Maureen Dowd

"Trump is returning as a colossus. He has brought Washington − Democrats and Republicans − to heel, teamed up with Elon Musk and slapped a gold 'Trump' sign on Silicon Valley. The lords of the cloud helped fund the coronation, and they are making a pilgrimage here to bow to their new overlord."

AR Trump has been captured by the tech bros (the billionaire cloud oligarchy) as gently as a spent SpaceX Starship booster is captured by its launch tower. America is now a plutocracy run by its big corporations for their own benefit. Perhaps the benefits will trickle down to the masses − but we've seen how trickle-down works for decades. It doesn't. Mazel tov!

 

New Scientist
 

2025 January 15

Critical Theory

Peter Gordon

Critical theory began in the Institute for Social Research, founded in Frankfurt in 1923. The theory drew on the legacy of German idealism, from Kant and Hegel, and from the materialist transformation of left Hegelianism developed by Marx.
Institute member Theodor Adorno spent the Third Reich years in California. He became skeptical about technological optimism and thought economism reflects an ideology of unfreedom by eternalizing the experience of ourselves as objects locked in a deterministic mechanism.
Adorno did not believe that current conditions permit us to grasp unblemished standards. The norms we invoke in criticism are damaged. Critical theory offers partial or incomplete insights but sustains our openness to contradiction.

AR I made a token effort to read works of critical theory by members of the Frankfurt school, though I soon decided it was a mishmash of fuzzy and tendentious thinking and abandoned the effort.
Looking back from 40−50 years on, I'm glad I wasted no more time with it. Adorno's writings had some interest, but little of value from it remains in my head.
 

2025 January 14

Stand by Ukraine

Lloyd Austin, Antony Blinken

President Vladimir Putin of Russia appalled the world with his full-scale invasion of Ukraine. He has failed to achieve any of his strategic goals.
American leadership has rallied allies and partners worldwide to help Ukraine survive. Putin assumed that the world would stand by when he sent his troops across the Ukrainian border.
Ukraine has fought brilliantly. Its success to date is a huge strategic achievement. The Ukrainian people have shown magnificent defiance.
Russia is suffering huge losses to seize small slivers of territory. Putin must either endure high casualties for minimal gains or negotiate to end his war.
We are backstopping Ukraine with economic support. Russian banks are sanctioned. Inflation in Russia is over 9% and interest rates are 21%.
A durable peace will ensure Ukrainians can deter further Russian aggression, defend their territory, and thrive as a sovereign democracy.
Pursuing a policy of peace through strength is vital.

AR Austin is US secretary of defense and Blinken is US secretary of state. They fear the incoming administration might undo all their good work with a botched peace deal that surrenders Ukraine and endangers all of us by rewarding Putin. I share their concern and their conclusion.

 

NATO
NATO Very High Readiness Joint Task Force exercise Brilliant Jump, Drawsko Pomorskie, Poland, 2024
 

2025 January 12

Raise NATO Spending

Raphael Minder

Warsaw is backing Donald Trump's demand for NATO countries to spend 5% of GDP on defence − even if it takes 10 years for some.
Polish defence minister Władysław Kosiniak‑Kamysz says Poland can be the link between Trump's challenge and its implementation in Europe. Poland will spend 4.7% of GDP for defence this year.
After Russia launched its full-scale invasion of Ukraine in 2022, Poland doubled its defence spending and ordered billions of dollars of mostly US and South Korean weapons.
Poland's six-month rotating presidency of the EU started on January 1. Poland will urge EU member states to spend €100 billion from the next common budget on defence.
Kosiniak‑Kamysz: "The EU has the capacity .. we must surely find the money to protect ourselves from war."

'Alice für Deutschland'
Laura Pitel

The co-leader of the Alternative for Germany party called for mass deportations of immigrants yesterday as the AfD launched its program for next month's nationwide elections.
In a speech in Riesa in Sachsen, Alice Weidel said that under the AfD − second in the polls with a vote share of around 20% − Germany would see repatriations on a large scale.
Weidel, the AfD candidate for chancellor in the elections, used the term "remigration" for the policy, defined as forcibly removing immigrants who break the law or refuse to integrate, regardless of their citizenship status. Critics say it is akin to ethnic cleansing.
Weidel was met with loud applause from party delegates, who shouted: "Alice für Deutschland!"
Weidel, a former Goldman Sachs analyst, is the face of a party that includes radicals classified as right‑wing extremists by the Bundesamt für Verfassungsschutz.
Weidel also called for reopening the Nord Stream gas pipeline from Russia to Germany, restarting nuclear plants, and ending gender studies programs.

AR I agree that 5% should be the target − at least until Trump has done a decent deal with Putin (which probably won't happen − unless the word "decent" changes its meaning).
As for Alice, her party still stinks. She might go down well with Trump and Musk, but she'd do a dirty deal with Putin that left Ukraine and most of eastern Europe in the lurch.
My recipe for peace in Europe: Negotiate from strength (via 5%) with the Russians.

 

Xinhua
China − workshop of the world
 

2025 January 9

China Winning

Robert D Atkinson

China aims to overtake the United States as the world's most advanced economy. American policymakers are only slowly waking up to the reality of an industrial war.
China's rate of progress in production and innovation across a wide range of industries is striking. China is weaponizing its roughly $18 trillion economy, using a vast array of policy tools to increase its relative economic power.
In such advanced industries as semiconductors, robotics, artificial intelligence, quantum computing, space, and chemicals, China is making progress toward the global leading edge of innovation. In some industries, such as electric vehicles and commercial nuclear power, Chinese companies now lead.
China installed more industrial robots last year and has more nuclear power plants under construction than the rest of the world combined. It has spent three times as much on semi­conductor subsidies as the United States and is spending more on the development of quantum technology than any other government.
America must expand its competitiveness in a range of industries. It needs closer collaboration among allied nations to push back on China's power trade practices. America depends on many industries that cannot thrive without access to global markets.
China will not end its power trade regime until it has gained dominance across a wide range of advanced industries.

AR China is well organized and its people are industrious. Good for them. Americans under the erratic and volatile leadership of Trump and Musk will be hard pressed to fight back effectively − the organizational heft and solidarity just isn't there.

 

SpaceX
Starship launches on a test flight
 

2025 January 6

SpaceX Starship

Science

The Starship rocket is a 120 m stick of stainless steel with 33 engines. Following a 420 s test flight on 2024‑10‑13, its booster stage fell out of the sky, relit some of its engines to slow itself nearly to a hover, and was retrieved by its launch tower.
SpaceX, the rocket company founded and run by Elon Musk, has already cut the price of getting cargo into orbit by about a factor of 10 with its Falcon rockets. A fully reusable Starship is expected to cut that price by another order of magnitude.
Musk aims to put people on Mars. For NASA missions, routine Starship flights will enable scientists to take more chances: not one Mars rover, but a herd of them, or a fleet of mirror segments self-assembling into a giant space telescope.

Starship rocket is beating NASA
Robin McKie

Starship is the most powerful launcher ever built, and designed to be fully and rapidly reusable. SpaceX engineers can now reclaim and reuse its main booster stage and aims to do the same for its upper stage this year.
A total of 25 flights are planned for the year ahead. Musk hopes to use his Starship to begin the colonization of Mars. He says SpaceX will launch the first uncrewed Starship missions to Mars within two years.
Astrophysicist Martin Rees: "It's a dangerous delusion to think that space offers an escape from Earth's problems .. Coping with climate change may seem daunting, but it's a doddle compared to terraforming Mars."

AR Musk the tech entreneur is a hero, Musk the political activists is a dangerous loose cannon.
His recent forays into UK politics have been impulsive and potentially damaging. In December, Musk proclaimed on X: "Free Tommy Robinson!"
If Musk's aim is to light a fuse to start a conflagration that destroys Islamism in the UK, freeing TR might be a good start. But the risk that TR will only cause chaos and mayhem is too high.
Musk's latest target is his friend Nigel Farage, whose party Reform UK he is thinking about funding in a bid to topple the present Labour government.
Musk on X: "The Reform party needs a new leader. Farage doesn't have what it takes."
I'm cheered that Musk has turned against the old Brexit warhorse, but ..

 

AR
Poole Bay in the new year, Thursday afternoon
 

2025 January 4

2025
= (20 + 25)²
= (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)²
= 1³ + 2³ + 3³ + 4³ + 5³ + 6³ + 7³ + 8³ + 9³

AR Yeah, verily!
 

2025 January 2

Finding God 2

Leopold Kronecker

Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk.

AR I read this as evidence for the introspected phenomenology of mathematics.
 

2025 January 1

Finding God

Peter Savodnik

Ayaan Hirsi Ali was born a Muslim in Somalia in 1969. She later fled to the Netherlands as a political refugee and became a famous atheist and critic of Islam.
She recalls talking with Roger Scruton in 2020. He told her: "If you don't believe in God, at least believe in beauty .. The greatest works of art have been inspired by some connection to God."
In 2023, Hirsi Ali published an essay, Why I Am Now a Christian.

Wrestling with God
Matt McManus

Jordan Peterson's book We Who Wrestle With God offers a bifurcation of the world into Cain and Abel: "The .. Jacobins who first planned the French Revolution .. were the spiritual descendants of Cain. Karl Marx is Cain to the core."
Peterson denounces the Left as resentful, genocidal, idiotic, and so on. He owes a debt to German conservative thinkers like GWF Hegel, Friedrich Nietzsche, Carl Jung, and Martin Heidegger.
For Peterson, God doesn't much like Marxists, trans people, environmentalists, atheists, materialists, wokeness, or porn. But God likes billionaires who don't love or worship money.
Peterson admires Leo Tolstoy, who underwent a conversion and developed a radical brand of Christianity that was fiercely utopian and egalitarian. Tolstoy read injunctions to turn the other cheek or give up all your wealth to the poor as requiring immense social changes.
Peterson says a person is more likely to lead a flourishing life by asking what they can do, rather than being resentful over what they can't. His new book is an opiate for the masses.

AR Fascinating .. Christianity is certainly an order of magnitude better than Islam. But Peterson's attempt to breathe new life into the Old Testament tyrant is hopeless. If this is what an anti-woke psychologist is reduced to, he'd be better off staying silent until he's learned more wisdom.

 

⦿ Damon Winter/The New York Times
Jimmy Carter, 1924−2024
POTUS 39, 1977−1981
Nobel Peace Prize, 2002
President Biden: "To all of the young people in this nation and for anyone in search of what it means to live
a life of purpose and meaning − the good life − study Jimmy Carter, a man of principle, faith and humility."
 

2024 December 31

Daniel Dennett, 1942−2024

Tim Bayne

Daniel C Dennett was a philosopher of mind who helped shift Anglo-American philosophy toward science.
Dennett went to Oxford for graduate studies in philosophy, but science grabbed him: "I ended up spending more time in the Radcliffe Science Library .. to learn about the brain."
Dennett distinguished between two images of reality, the manifest image and the scientific image. The manifest image is the everyday conception. The scientific image is from science.
The manifest image of the mind is folk psychology: We have a self with beliefs, desires, and intentions; we have voluntary control over our actions and are accountable for them; and we are conscious.
Dennett said folk psychology treats selves as centers of narrative gravity. Their intentional states help us to make sense of behavior. We display behavioral patterns that let the intentional stance get a grip.
Dennett cleared the way to a science of consciousness and rejected aspects of folk psychology.

AR Dennett means a lot to me. I've read all his books and greatly admire Consciousness Explained (1991) and Darwin's Dangerous Idea (1995). I talked with him about his work in New York in 2002 and in Oxford in 2006. For me, he's the best US philosopher of his generation and the best since the great WVO Quine, who was his undergraduate tutor.
 

2024 December 30

Donald Tusk 4 Europe

Paul Taylor

With France and Germany facing political crises and Britain sidelined by Brexit, Polish prime minister Donald Tusk may be able to convince POTUS 47 that closer European defense cooperation can strengthen NATO without harming US interests.
Poland is central to EU politics. It has revived the Weimar Triangle with Germany and France, has joined the alliance of Nordic and Baltic nations, and is in the Bucharest Nine grouping of central and eastern NATO members.
Defence ministers of Poland, France, Germany, Italy, and the UK have met as the E5 in Berlin to further European defense cooperation.

AR Good man for the job. I wish him great success. He'll need all the help we can give him.
 

2024 December 22−29

Working on Psy‑Phy ..

 

TIME
"All of us − from his most fanatical supporters to his most fervent critics − are living in the Age of Trump."
 

2024 Winter Solstice

The Year in Science

Quanta

2024 was a fruitful year for science. Some advances were big, most were incremental,
and many were made possible by the use of powerful new AI tools.

Computer science
Bill Andrews

•  Quantum computers are vulnerable to errors, but we can combine qubits to tolerate errors.
•  We can efficiently calculate the Hamiltonian for any quantum system at a constant temperature.
•  Rising temperature weakens quantum entanglement; it vanishes at a critical temperature.
•  New chatbots might understand; AI models overtrained to the point of mastery show grokking.

Physics 
Natalie Wolchover

•  A map of millions of galaxies shows how universal expansion is accelerating due to dark energy.
•  Experimenters hunting for WIMPs have hit a limit, marking the end of that dark matter search.
•  JWST images from less than 1 Gyr ABB reveal the "beautiful confusion" of that epoch.
•  JWST measurement of universal expansion rate deepens the "Hubble tension" puzzle.
•  Quantum tornadoes form when an otherwise rigid crystal of dysprosium atoms is stirred.
•  A quantum phase of matter shows the flow of emergent particles with fractional charge.
•  Neutral-atom quantum computers have achieved noise-resistant, fault-tolerant computation.
•  A "nuclear clock" transition in thorium could reveal variations in the strength of physical forces.
•  A geometric language for predicting particle interactions arises from sets of curves on surfaces.
•  Evolving understanding of entropy reframes science and our role in the universe.

Biology 
Hannah Waters

•  Google AlphaFold3 predicts the shapes of proteins as they interact with other molecules.
•  LUCA was a complex cell that likely lived in a microbial ecosystem some 4.2 Gyr BP.
•  Squeezing archaeal cells can get them to form multicellular structures.
•  Fossil traces of multicellular eukaryotes date back to 1.6 Gyr BP.
•  Phenomenal consciousness extends to insects, crabs, octopuses, fish, reptiles, and amphibians.
•  Most noncoding portions of the genome are transcribed into RNA that regulates genes expression.
•  Archaeal cells exchange noncoding RNAs in a cellular texting system.
•  A brainstem neural circuit adjusts the immune system via the levels of inflammatory molecules.
•  During sleep, the hippocampus replays neuron firing generated by experience to form memories.
•  We have a 3D map of 1 cubic mm of human brain and a map of the entire fruit fly brain.

Math 
Jordana Cepelewicz

•  The geometric Langlands conjecture, which involves sheaves, is proved.
•  AlphaGeometry can prove geometry problems nearly as well as a human IMO gold medalist.
•  AlphaProof can prove problems well enough to score a silver medal on the full Olympiad exam.
•  The universe of possible shapes is even stranger than we imagined.
•  We have new results about the distribution of prime numbers.

AR Frohe Weihnachten und guten Rutsch!
 

2024 December 19

EU Damaged by Brexit

Wolfgang Münchau

Brexit changed the way the EU has been functioning politically. The former balance between northern liberal states and the dirigiste states of the south and west shifted when the UK left. The EU single market has become less liberal.
The EU Green agenda has brought complaints from business over the sheer volume of bureaucracy it has created. EU corporate social responsibility legislation makes companies responsible for their supply chains and is a bureaucratic nightmare.
During its EU membership, the UK exerted a strong influence on EU legislation. UK civil servants made sure that draft legislation was workable and consistent with other legislation. There are inconsistencies between the EU general data protection regime, agreed before Brexit, and the more recent AI regulation.
The EU's anti-digital laws are destructive and run counter to the principle of dealing with problems after they arise. There are hardly any AI or crypto companies in Europe, and yet the EU thinks it can regulate the global tech industry.
Most of the regulatory divergence that occurred since Brexit came from the EU. There is scope for closer cooperation between the UK and the EU on foreign and security policy. But voluntary or formal alignment is a pipe dream.

EU members meet to discuss relationship with UK
Jennifer Rankin

The EU is discussing its relationship with the UK on Thursday. A senior EU official says there is "strong potential" for an EU−UK defence agreement. A first EU−UK summit is expected in March or April.
The European Commission is taking the UK to the European Court of Justice over its failure to protect the rights of EU citizens living in the UK and of failing to cancel illegal bilateral investment treaties with six EU member states.
The UK prime minister has ruled out rejoining the EU or its single market and customs union in his lifetime. The EU wants a youth experience scheme (YES) to give young people in the UK and Europe reciprocal rights to study, live, and work abroad for a few years. The UK says no.

AR I'm losing my faith in the EU dream. Brussels bureaucrats lack the skills or the vision to draft legislation relating to tech innovations or to understand how stifling their efforts are. They seem to think ignorant lawyers can write the code to rule the world. They're wrong.
Europeans need to wake up from their fatal thrall to busybody lawyers in Brussels who try to make rules for everything and who are not effectively checked by EU parliamentarians who in turn lack the ability to fight lawfare with basic common sense. Europe is not synonymous with the EU.
The Kafkaesque nightmare of an entrenched bureaucracy zealously seeking to enact naive woke ideals for the supposed benefit of EU citizens must end. Perhaps Nigel Farage can get his pals Donald Trump and Elon Musk to save us all in Europe.
 

2024 December 17

German Problems

Anna Sauerbrey

Bundeskanzler Olaf Scholz has lost a vote of confidence in the Bundestag. In 2021, Scholz had formed a coalition government. But Putin's invasion of Ukraine threw it into crisis management mode. Scholz announced a Zeitenwende and allocated €100 billion to rebuilding the Bundeswehr.
Germany is in its second consecutive year of recession. Its signature businesses are struggling. With the abrupt end of cheap Russian gas, green reforms have exacerbated the cost of energy. Carmakers are struggling to compete with Chinese imports. Public infrastructure needs more investment.
Germany is suffering a crisis of confidence, and frustration with the government is widespread. But unemployment is minimal, budgetary restrictions can be overcome, and state government continues. Most of Germany's neighbors and friends face similar troubles.

AR Europe is suffering from a dismal outlook and a looming crisis with Russia. The prospects of a boost from America or indeed China look unlikely. Political changes are needed but won't happen without a more urgent sense of the need for them. Calm before the storm.
 

2024 December 16

Mother of all Bubbles

Ruchir Sharma

Virtually every Wall Street analyst predicts US stocks will keep outperforming the rest of the world in 2025. But all this enthusiasm only tends to confirm that the bubble is at an advanced stage.
The bulls say America can remain dominant. But US earnings growth would not look so good if not for the supernormal profits of its big tech firms. Over time, supernormal profits get competed away.
Growth and profits are also getting a lift from heavy deficit spending. It now takes nearly $2 of new government debt to generate an additional $1 of US GDP growth. If any other country were spending this way, investors would be fleeing.
Analysts say America has been the world's premier market for a century. But the US stock market lagged behind the rest of the world in 6 of the last 11 decades. In the 2000s it delivered zero returns, and emerging markets tripled in value.
The US outperformance relative to other countries could end if growth slows in America, or picks up in other major powers, or for unforeseen reasons. That is often how bubbles end: unexpectedly.
The longer a trend lasts, the more confident investors get. Over the past six months US stock prices have outgained others by a wide margin. Time to bet against American exceptionalism.

AR I think big tech stocks will keep on outperforming, but who am I to say when I got suckered in the 2000s? More ominously, the Trump administration looks likely to lead to some kind of crisis. The fallout could make the financial crisis of 2008 look tame by comparison.
 

2024 December 13

Americans Are Doomsday Prepping

Robert Kirsch, Emily Ray

More than 20 million Americans engage in prepping. The Federal Emergency Management Agency (FEMA) determined in 2023 that 51% of Americans are prepared for a disaster.
Bunkerization explains prepping in the United States. The logic of the bunker shapes how Americans relate to each other, the state, and their domestic lives, as a matter of individual isolation, preparation, and savvy consumption.
Prepping is at the core of an American mythology of a frontier folk. Americans are asked to buy their way to safety. The patriotic way to be an American is to isolate oneself from other Americans in times of crisis.
During the Cold War, US citizens were urged to hunker down to show the communists that Americans were prepared to die as Americans: "Better dead than Red."
For the average prepper, stockpiling to meet FEMA recommendations for survival in the absence of state support is simply good sense. Bunkerization encourages us to see the prepping American as a responsible citizen.
A bunkerized society is in a permanent state of readiness for living in the shell of a state that takes stable infrastructure and individual welfare as market matters.

AR Sounds horrible. I'm glad I'm in Europe. We stand or fall together.
 

2024 December 12

UK−EU Free Movement

Peter Walker, Jon Henley

A majority of Britons who voted to leave the EU would now accept a return to free movement in exchange for access to the single market, says a new ECFR report.
ECFR: "There is a remarkable consensus on both sides of the Channel that the time is ripe for a reassessment of EU−UK relations."
Based on polling of more than 9,000 people across the UK, Germany, France, Italy, Spain, and Poland conducted in November, the study found that 68% of all UK voters and 54% of those who voted leave said in exchange for single market access they would now accept full free movement for EU and UK citizens.
ECFR: "The EU and the UK are both very vulnerable to prevailing global events and a reset of relations is the single most effective way to make both sides stronger."
Across the EU, 45% of Germans said they wanted closer relations with the UK, as well as 44% of Poles, 41% of Spaniards, 40% of Italians, and 34% of French people.
ECFR: "Brexit and the UK−EU future relationship matters more to UK respondents than to citizens of other states. But there is broad permission from European publics to recast relations."
Many people in the EU felt Brexit had been bad for the EU. Asked whether the UK should prioritise relations with the US or with the EU, 50% of Britons opted for the EU and 17% for the US.
ECFR: "Governments now need to catch up with public opinion and offer an ambitious reset."

AR Let's get on with it. We can't dither through another Trump presidency while the last Reform UK holdouts realise the magnitude of their error. Let's get a public groundswell movement going.
 

2024 December 11

Quantum Computers Cross Critical Error Threshold

Ben Brubaker

For quantum error correction, we coax a cluster of physical qubits to work together as a single logical qubit. Adding physical qubits makes a logical qubit better if their error rate is below a definable threshold.
Google Quantum AI have crossed the threshold. They harnessed a group of physical qubits into a single logical qubit, then showed that as they added more physical qubits, the error rate dropped exponentially.
On quantum computers, we can reduce error rates with a surface code based on two overlapping grids of physical qubits. The first grid encodes a single logical qubit. The second grid lets us check for errors.
Once the Google team could build physical qubits with low error rates, they checked whether the qubits could work together to cut the error rate. They started with a code using a 3×3 grid of physical qubits to encode one logical qubit, then they tested a 5×5 code.
They found that the error rate with the 5×5 code was slightly lower than that with the 3×3 code. After further hardware improvements, they found the error rate for the 5×5 code was cut in half. A 7×7 code again cut the error rate in half. Such exponential scaling is what theory predicts.
The Google team only demonstrated error correction using a single logical qubit. Adding interactions between multiple logical qubits will introduce new challenges.

AR This is a major development, as even daily newspapers have noted. Scalable error control is key to practical quantum computing, and this advance provides it. Quantum computing is on the way.
An expert is hopeful that powerful quantum computers may be on sale for say a billion dollars a pop within ten years. We'll need mass rollout of quantum encryption by then.
 

2024 December 9

Letters to a Christian

Sam Harris

I'm not bowled over by the idea that you were once an atheist like me, and that now, under the influence of Jordan Peterson et al, you've discovered Jesus Christ to be the savior of humanity.
There is a problem with religious fundamentalism. I'm glad to know you're worried about Islamic extremism and that we simply disagree about faith and about the validity of Christianity.
Most people use the term "faith" to indicate the acceptance of specific religious doctrines without sufficient reason. This frame of mind is antithetical to reason and conflicts with science.
Moderates tend to doubt the reality of religious lunacy. Such blindness is unhelpful, given the hideous collision between modern doubt and Islamic certainty that we are witnessing across the globe.
Scripture remains a perpetual engine of extremism. Read scripture as closely as you like, you will not find reasons for religious moderation. On the contrary, you will find reasons to live like a maniac.
I don't disdain religious moderates, but I do disdain bad ideas and bad arguments.

AR This is a topic on which oceans of ink have obscured the view for centuries, but on which now Sam Harris, the young hero of the atheist apocalypse, brings clarity and common sense.
I've read the first two chapters of Jordan Peterson's book on Old Testament myths and see the problem already. Peterson has reacted with revulsion to the modern world and ecstatically thrown his soul into the warm but polluted bath of Judaeo-Christian mythic fantasy.
His eisegesis of the old myths is fascinating but doomed. It reads like the confession of a hero so enchanted by a myth that he drowns himself in it for joy.

 

EPA
Global A-listers assembled in Notre Dame cathedral, Paris, for the grand reopening ceremony, 2024-12-07
 

2024 December 6

Transformative Experience

Alice Gregory

Yale philosophy professor Laurie Paul is the author of Transformative Experience, an investigation of personal change. Paul: "I'm totally puzzled and fascinated and disturbed by ordinary life."
Published by OUP in 2014, Transformative Experience examined the special situations that change not only what we know but also who we are. These transformative experiences provide new knowledge that previously would have been inaccessible to us.
For Paul, whether to have a child was a riddle at the limits of rationality. She explored the question via normative decision theory, but says it failed in the face of transformative experience. Choosing to undergo such an experience requires us to violate who we take our current self to be.
Paul had her first child in 2004. She gave a lecture on the experience in 2012, when she was 46 and had two children. A online draft won attention in 2013. Paul: "For many big life choices, we only learn what we need to know after we've done it, and we change ourselves in the process of doing it."
Paul had planned to be a doctor. But she enrolled at Antioch University, studied German in Berlin and Buddhist philosophy in India, returned to Antioch, applied to graduate programs, and arrived at Princeton in 1993. After a series of jobs, she won tenure at the University of Arizona in 2007.
In 2012, Paul confided to Jonathan Schaffer that she was professionally demoralized. He remembers their conversation because of its timing: "Within a year .. she became this celebrated figure. She really did not expect that kind of reception."
Paul: "The problem of other selves is just as deep and mysterious as the problem of other minds."

AR She's right about other selves − another reason to be skeptical of David Chalmers' hard problem. Continuity of the self over time is a problem I've pondered at least since Derek Parfit aired it in his 1984 book Reasons and Persons.
The conventional piety that we retain one self from birth to death raises questions about how time's arrow from a remembered past to an unknown future impacts our sense of self. This is another theme to come in Psy‑Phy.
 

2024 December 5

What Keir Starmer Should Say

Matthew d'Ancona

I want to speak about the UK's relationship with Europe. My government must act in the national interest, looking ahead, averting crisis, and ensuring the next generation has better services, better opportunities, more chances for fulfilment.
My love of Europe is deeply ingrained. I studied European law at university and even wrote a book about it. In 2016, I campaigned for Remain. As shadow Brexit secretary, I fought hard both for a second referendum and a better Brexit deal than the mess the Conservatives delivered.
Last July, I said the nation was heartily sick of Brexit and wanted to move on. But Brexit limits and infects everything we try to do. Instead of taking back control, we got more immigration and more red tape. Brexit is reducing our GDP by 4%. Its estimated cost is already well over £140 billion.
I see great potential in this country, but also huge challenges. The technological revolution. Climate change. Savage inequalities. An ageing population and a younger generation rightly demanding a fair shake. Global population movements, insecurity, and instability.
To master these challenges, we will need both statecraft and economic growth. But President-elect Trump proposes an economic strategy of tariffs and protectionism that will impact our economic fortunes. The world is changing, and we in the UK must change with it.
I propose to apply to join the European Free Trade Area. This is a precondition of our eventual entry to the single market and customs union and will require a green light from Norway, Iceland, Liechtenstein, and Switzerland, as well as the approval of the EU's 27 member states.
A majority of the public now thinks Brexit was a mistake. Since exit from the single market and customs union was not what Leavers promised in 2016, I do not plan to hold another referendum. I am thinking of the national interest.

AR The full ghost-written speech, before my short cut, is clear and persuasive. It's high time for Starmer to take courage and deliver it. How much more urging can he want?
 

2024 December 4

Popular Science, Philosophical Junk

John Dupré

In The Selfish Gene (1976), Richard Dawkins presented the evolution of life as genes striving to replicate themselves. His new book, The Genetic Book of the Dead, says an organism's genome is a palimpsest, with layers that reveal its lineage.
Dawkins remains a genetic determinist. Oxygen to breathe, parental care, and so on are background conditions that let the genes do their causal work. With the phenotype inscribed in the genes, evolution is ultimately a sequence of genomes competing with one another.
In Life as No One Knows It, Sara Imari Walker emphasizes the temporal depth of life. A lineage of structures led to any particular one out of the vast number of possible structures. Almost every possible structure will never exist. Even the macromolecules within us are enormously complex.
Walker proposes assembly theory. The complexity of an object is the number of novel steps it takes to reach the object; the smallest such number is its assembly index. The larger the assembly index, the less probable the object. Many objects with a high assembly index have a probability near zero.
Assembly theory says the existence of multiple complex objects points to a chain, a lineage, of simpler objects that can construct the later objects in the chain. An object requires such a lineage if it has an assembly index greater than 15. This helps illuminate the origins of living systems.
Dawkins maintains that the natural selection of genes is uniquely central to evolution. The market for popular science is strongly attracted to simple stories offering insight into everything by offering an illusion of understanding.
Philosophers increasingly reject the worldview in which the ultimate truth is physics. Biology shows us a world of process. Recognition of process is a prophylactic against the simplistic claims in popular science books.

AR See such popular science books in their market context. A simplistic claim must carve out mind share beside other such claims. A nuanced view would die of neglect. Philosophers may bloviate about junk, but scientists can ignore them.
The ultimate truth is not physics but mathematics, or rather the logic behind mathematics, which spawns the shapes that physicists − and in their wake applied scientists such as biologists − use to depict phenomenal reality in their own ways.
All science is simplistic in the sense that effective models of handy granularity are offered as true likenesses of an underlying reality of unfathomable depth. Assembly theory offers its quantum of illumination within a crowded landscape, and I'm grateful for its incremental glimmer.
All this is by way of preparing and defending the simplistic model I propose to add to the arsenal in my planned book Psy‑Phy.
 

2024 December 3

Incompleteness in Math and Physics

Manon Bischoff

Kurt Gödel's 1931 incompleteness theorem proved that there will always be truths that are impossible to prove in a given mathematical framework.
The incompleteness theorem is reflected in physics. New work shows that a model particle system that undergoes a phase transition has a critical parameter that cannot be calculated.
In a finite square lattice containing an arrangement of several particles that each interact with their nearest neighbor, the atoms are arranged in a regular structure, and their electrons can interact with those of the immediately surrounding atoms. In one model, the strength of the interaction between the electrons depends on a parameter φ, which sets how strongly the particles in the atomic shells repel each other.
If the repulsion φ is small, the outer electrons are mobile. The stronger φ is, the more the electrons freeze in place, as reflected in the energy of the system. If φ is very small, the total energy of the system can grow continuously, and the system conducts electricity freely. For large values of φ, the energy only increases gradually. The gap between the ground state and the first excited state makes the system a semiconductor or an insulator.
The transition between the two phases is set by a critical value of φ above which the energy spectrum of the system suddenly has a gap. The critical value of φ corresponds to a constant Ω, which cannot be calculated. There is no algorithm that outputs Ω.
Gregory Chaitin defined Ω by using Alan Turing's proof that no program exists that can decide, for all possible algorithms, whether a computer will come to a halt when executing them or not. Turing's proof is an application of Gödel's incompleteness theorem.
The Chaitin constant Ω give the probability that a Turing machine halts for some input:
Ω = Σ_p 2^−|p|
Here p ranges over all programs that halt after a finite runtime and |p| is the length of the program in bits. Calculating Ω exactly requires knowing which programs halt and which do not, which is impossible. The first few digits of Ω are 0.01574999 ..

AR I expected Gödel's result to apply in physics too, but it's good to have a specific example. I came across Chaitin's work decades ago and enjoyed his books, but the calculated value of Ω is new for me. Chaitin, who worked for IBM, made Gödel's idea seem easy for computer scientists.
For me and surely many others, Gödel's theorems are the results of the century in mathematical logic. Douglas Hofstadter's classic 1979 fugue Gödel, Escher, Bach was so glorious that it left my dream of extending my study of the theorems into a monograph in shreds.
Water under the bridge. Now I have bigger fish to fry.

 

AR