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"When people talk about metabolism, they think diet and exercise - but it is deeper than that, we are actually watching your body, your cells, at work," Prof Herman Pontzer, from Duke University, told BBC News."They are incredibly busy at one year old and when we see declines with age, we are seeing your cells stopping working."

Prof Tom Sanders, from King's College London, said: "Interestingly, they found very little differences in total energy expenditure between early adult life and middle age - a time when most adults in developed countries put on weight. "These findings would support the view that the obesity epidemic is fuelled by excess food energy intake and not a decline in energy expenditure."

Prominent German Climate scientist Friederike Otto commented that "Scholz 'forgets' our worst history, dismisses every generation that comes after him as irrelevant & the audience just applauds."

"Where does one begin? In just one half-sentence, the Chancellor of the Federal Republic relativizes the Nazi regime and, in a paradoxical way, also the climate crisis," she wrote on Twitter. "He stylizes climate protection as an ideology with parallels to the Nazi regime. In 2022. Jesus. This is such a scandal."

"I have also been to events where five people sat dressed in the same way, each had a well-rehearsed stance, and then they do it again every time," he said. "And that's why I think that is not a discussion, that is not participation in a discussion, but an attempt to manipulate events for one's own purposes. One should not do this."

The chancellor leads a three-party coalition with partners the Greens and pro-business Free Democrats, and their pledge to improve climate change action was central to their campaign.

It is easy to understand the appeal of such one-sided tales. As human beings, we seem to prefer to impose clear and linear narratives on a chaotic and unpredictable reality; ambiguity and contradiction are much harder to live with.

To truly grasp the complex nature of our current time, we need first of all to embrace its most terrifying aspect: its fundamental open-endedness. It is precisely this radical uncertainty — not knowing where we are and what lies ahead — that gives rise to such existential anxiety.

Anthropologists have a name for this disturbing type of experience: liminality

liminality originally referred to the sense of disorientation that arises during a rite of passage. In a traditional coming-of-age ritual, for instance, it marks the point at which the adolescent is no longer considered a child but is not yet recognized as an adult — betwixt and between

We are ourselves in the midst of a painful transition, a sort of interregnum, as the Italian political theorist Antonio Gramsci famously called it, between an old world that is dying and a new one that is struggling to be born. Such epochal shifts are inevitably fraught with danger

the great upheavals in world history can equally be seen “as genuine signs of vitality” that “clear the ground” of discredited ideas and decaying institutions. “The crisis,” he wrote, “is to be regarded as a new nexus of growth.”

Once we embrace this Janus-faced nature of our times, at once frightening yet generative, a very different vision of the future emerges.

we see phases of relative calm punctuated every so often by periods of great upheaval. These crises can be devastating, but they are also the drivers of history.

even the collapse of modern civilization — but it may also open up possibilities for transformative change

the broad theme was clear: Social-media platforms are the main communication tools of the 21st century, and they matter.

With Trump at the center, the techlash morphed into a culture war with a clear partisan split. One could frame the position from the left as: We do not want these platforms to give a natural advantage to the most shameless and awful people who stoke resentment and fear to gain power

On the right, it might sound more like: We must preserve the power of the platforms to let outsiders have a natural advantage (by stoking fear and resentment to gain power).

the political world realized that platforms and content-recommendation engines decide which cultural objects get amplified. The left found this troubling, whereas the right found it to be an exciting prospect and something to leverage, exploit, and manipulate via the courts

Crucially, both camps resent the power of the technology platforms and believe the companies have a negative influence on our discourse and politics by either censoring too much or not doing enough to protect users and our political discourse.

one outcome of the techlash has been an incredibly facile public understanding of content moderation and a whole lot of culture warring.

Musk and Ye aren’t so much buying into the right’s overly simplistic Big Tech culture war as they are hijacking it for their own purposes; Trump, meanwhile, is mostly just mad

Each one casts himself as an antidote to a heavy-handed, censorious social-media apparatus that is either captured by progressive ideology or merely pressured into submission by it. But none of them has any understanding of thorny First Amendment or content-moderation issues.

They embrace a shallow posture of free-speech maximalism—the very kind that some social-media-platform founders first espoused, before watching their sites become overrun with harassment, spam, and other hateful garbage that drives away both users and advertisers

for those who can hit the mark without getting banned, social media is a force multiplier for cultural and political relevance and a way around gatekeeping media.

Musk, Ye, and Trump rely on their ability to pick up their phones, go direct, and say whatever they wan

the moment they butt up against rules or consequences, they begin to howl about persecution and unfair treatment. The idea of being treated similarly to the rest of a platform’s user base

is so galling to these men that they declare the entire system to be broken.

they also demonstrate how being the Main Character of popular and political culture can totally warp perspective. They’re so blinded by their own outlying experiences across social media that, in most cases, they hardly know what it is they’re buying

These are projects motivated entirely by grievance and conflict. And so they are destined to amplify grievance and conflict

That allows quantum computers to make many calculations in one pass, while digital ones have to perform each calculation separately. By speeding up computation, quantum computers could potentially solve big, complex problems in fields like chemistry and materials science that are out of reach today.

When Google researchers made their supremacy claim in 2019, they said their quantum computer performed a calculation in 3 minutes 20 seconds that would take about 10,000 years on a state-of-the-art conventional supercomputer.

The IBM researchers in the new study performed a different task, one that interests physicists. They used a quantum processor with 127 qubits to simulate the behavior of 127 atom-scale bar magnets — tiny enough to be governed by the spooky rules of quantum mechanics — in a magnetic field. That is a simple system known as the Ising model, which is often used to study magnetism.

This problem is too complex for a precise answer to be calculated even on the largest, fastest supercomputers.

On the quantum computer, the calculation took less than a thousandth of a second to complete. Each quantum calculation was unreliable — fluctuations of quantum noise inevitably intrude and induce errors — but each calculation was quick, so it could be performed repeatedly.

Indeed, for many of the calculations, additional noise was deliberately added, making the answers even more unreliable. But by varying the amount of noise, the researchers could tease out the specific characteristics of the noise and its effects at each step of the calculation.“We can amplify the noise very precisely, and then we can rerun that same circuit,” said Abhinav Kandala, the manager of quantum capabilities and demonstrations at IBM Quantum and an author of the Nature paper. “And once we have results of these different noise levels, we can extrapolate back to what the result would have been in the absence of noise.”In essence, the researchers were able to subtract the effects of noise from the unreliable quantum calculations, a process they call error mitigation.

Altogether, the computer performed the calculation 600,000 times, converging on an answer for the overall magnetization produced by the 127 bar magnets.

Although an Ising model with 127 bar magnets is too big, with far too many possible configurations, to fit in a conventional computer, classical algorithms can produce approximate answers, a technique similar to how compression in JPEG images throws away less crucial data to reduce the size of the file while preserving most of the image’s details

Certain configurations of the Ising model can be solved exactly, and both the classical and quantum algorithms agreed on the simpler examples. For more complex but solvable instances, the quantum and classical algorithms produced different answers, and it was the quantum one that was correct.

Thus, for other cases where the quantum and classical calculations diverged and no exact solutions are known, “there is reason to believe that the quantum result is more accurate,”

Mr. Anand is currently trying to add a version of error mitigation for the classical algorithm, and it is possible that could match or surpass the performance of the quantum calculations.

In the long run, quantum scientists expect that a different approach, error correction, will be able to detect and correct calculation mistakes, and that will open the door for quantum computers to speed ahead for many uses.

Error correction is already used in conventional computers and data transmission to fix garbles. But for quantum computers, error correction is likely years away, requiring better processors able to process many more qubits

“This is one of the simplest natural science problems that exists,” Dr. Gambetta said. “So it’s a good one to start with. But now the question is, how do you generalize it and go to more interesting natural science problems?”

Those might include figuring out the properties of exotic materials, accelerating drug discovery and modeling fusion reactions.

In it, Baudrillard argues that there are four phases of the image - a faithful depiction of that which really is, an unfaithful depiction of that which really is, a depiction that covers up for the fact that there is nothing which is actually being depicted, and the simulacra, which exists in a human culture of such universal equivalency that no one has the grounding necessary to know what “reality” might even be outside of equivalencies, outside of depiction

at this stage, the litbro really exists precisely within Baudrillard’s concepts - it is a representation of someone else’s representation, a second-hand depiction, an archetype that is now developed fully through reference to itself rather than to some underlying reality. Baudrillard said that the development of simulacra is “a question of substituting the signs of the real for the real.”

Another example you often hear is the 1950s diner, the joint that has the neon signs and the art deco styling and the mini jukeboxes at the tables. This classic bit of Americana is not, in fact, based on what diners were like in the 1950s; it’s someone’s idea of what 1950s diners were like, which then spread mimetically from the actual physical 1950s diners that had been built to films and television, which then acted as “proof” that the imaginary diners were real, creating a social expectation of what a diner looks like that diner owners then felt pressure to fulfill…. Eventually most people came to believe that this is what diners were like in the 1950s. The point, though, is not that this is an act of deception. The point is that the consumerist reality in which these restaurants exists obliterates any belief in a true or false depiction. (No one cares whether the classic 1950s diner actually depicts a historical truth, really

, we know from the science of linguistics and the philosophy of knowledge that they differ profoundly from how humans reason and use language. These differences place significant limitations on what these programs can do, encoding them with ineradicable defects.

It is at once comic and tragic, as Borges might have noted, that so much money and attention should be concentrated on so little a thing — something so trivial when contrasted with the human mind, which by dint of language, in the words of Wilhelm von Humboldt, can make “infinite use of finite means,” creating ideas and theories with universal reach.

The human mind is not, like ChatGPT and its ilk, a lumbering statistical engine for pattern matching, gorging on hundreds of terabytes of data and extrapolating the most likely conversational response or most probable answer to a scientific question

the human mind is a surprisingly efficient and even elegant system that operates with small amounts of information; it seeks not to infer brute correlations among data points but to create explanations

such programs are stuck in a prehuman or nonhuman phase of cognitive evolution. Their deepest flaw is the absence of the most critical capacity of any intelligence: to say not only what is the case, what was the case and what will be the case — that’s description and prediction — but also what is not the case and what could and could not be the case

Those are the ingredients of explanation, the mark of true intelligence.

Here’s an example. Suppose you are holding an apple in your hand. Now you let the apple go. You observe the result and say, “The apple falls.” That is a description. A prediction might have been the statement “The apple will fall if I open my hand.”

an explanation is something more: It includes not only descriptions and predictions but also counterfactual conjectures like “Any such object would fall,” plus the additional clause “because of the force of gravity” or “because of the curvature of space-time” or whatever. That is a causal explanation: “The apple would not have fallen but for the force of gravity.” That is thinking.

The crux of machine learning is description and prediction; it does not posit any causal mechanisms or physical laws

any human-style explanation is not necessarily correct; we are fallible. But this is part of what it means to think: To be right, it must be possible to be wrong. Intelligence consists not only of creative conjectures but also of creative criticism. Human-style thought is based on possible explanations and error correction, a process that gradually limits what possibilities can be rationally considered.

ChatGPT and similar programs are, by design, unlimited in what they can “learn” (which is to say, memorize); they are incapable of distinguishing the possible from the impossible.

Whereas humans are limited in the kinds of explanations we can rationally conjecture, machine learning systems can learn both that the earth is flat and that the earth is round. They trade merely in probabilities that change over time.

For this reason, the predictions of machine learning systems will always be superficial and dubious.

some machine learning enthusiasts seem to be proud that their creations can generate correct “scientific” predictions (say, about the motion of physical bodies) without making use of explanations (involving, say, Newton’s laws of motion and universal gravitation). But this kind of prediction, even when successful, is pseudoscienc

While scientists certainly seek theories that have a high degree of empirical corroboration, as the philosopher Karl Popper noted, “we do not seek highly probable theories but explanations; that is to say, powerful and highly improbable theories.”

The theory that apples fall to earth because mass bends space-time (Einstein’s view) is highly improbable, but it actually tells you why they fall. True intelligence is demonstrated in the ability to think and express improbable but insightful things.

This means constraining the otherwise limitless creativity of our minds with a set of ethical principles that determines what ought and ought not to be (and of course subjecting those principles themselves to creative criticism)

True intelligence is also capable of moral thinking

To be useful, ChatGPT must be empowered to generate novel-looking output; to be acceptable to most of its users, it must steer clear of morally objectionable content

In 2016, for example, Microsoft’s Tay chatbot (a precursor to ChatGPT) flooded the internet with misogynistic and racist content, having been polluted by online trolls who filled it with offensive training data. How to solve the problem in the future? In the absence of a capacity to reason from moral principles, ChatGPT was crudely restricted by its programmers from contributing anything novel to controversial — that is, important — discussions. It sacrificed creativity for a kind of amorality.

Here, ChatGPT exhibits something like the banality of evil: plagiarism and apathy and obviation. It summarizes the standard arguments in the literature by a kind of super-autocomplete, refuses to take a stand on anything, pleads not merely ignorance but lack of intelligence and ultimately offers a “just following orders” defense, shifting responsibility to its creators.

In short, ChatGPT and its brethren are constitutionally unable to balance creativity with constraint. They either overgenerate (producing both truths and falsehoods, endorsing ethical and unethical decisions alike) or undergenerate (exhibiting noncommitment to any decisions and indifference to consequences). Given the amorality, faux science and linguistic incompetence of these systems, we can only laugh or cry at their popularity.

The students who’d been told they were almost always right were, on average, no more discerning than those who had been told they were mostly wrong.

In the second phase of the study, the deception was revealed. The students were told that the real point of the experiment was to gauge their responses to thinking they were right or wrong.

Once again, midway through the study, the students were informed that they’d been misled, and that the information they’d received was entirely fictitious. The students were then asked to describe their own beliefs

The students who’d received the first packet thought that he would avoid it. The students in the second group thought he’d embrace it.

One implication of the naturalness with which we divide cognitive labor,” they write, is that there’s “no sharp boundary between one person’s ideas and knowledge” and “those of other members” of the group

Humans’ biggest advantage over other species is our ability to coöperate. Coöperation is difficult to establish and almost as difficult to sustain

Reason is an adaptation to the hypersocial niche humans have evolved for themselves

Consider what’s become known as “confirmation bias,” the tendency people have to embrace information that supports their beliefs and reject information that contradicts them

Of the many forms of faulty thinking that have been identified, confirmation bias is among the best catalogued; it’s the subject of entire textbooks’ worth of experiments

Even after the evidence “for their beliefs has been totally refuted, people fail to make appropriate revisions in those beliefs,” the researchers noted. In this case, the failure was “particularly impressive,”

reason is an evolved trait, like bipedalism or three-color vision. It emerged on the savannas of Africa, and has to be understood in that context

During our leisure time, not counting work, each of us processes 34 gigabytes, or 100,000 words, every day

The world’s 21,274 television stations produce 85,000 hours of original programming every day as we watch an average of five hours of television daily, the equivalent of 20 gigabytes of audio-video images

That’s not counting YouTube, which uploads 6,000 hours of video every hour.

We’ve created a world with 300 exabytes (300,000,000,000,000,000,000 pieces) of human-made information. If each of those pieces of information were written on a 3-by-5-inch index card and then spread out side by side, just one person’s share—your share of this information—would cover every square inch of Massachusetts and Connecticut combined.

Neurons are living cells with a metabolism; they need oxygen and glucose to survive, and when they’ve been working hard, we experience fatigue. Every status update you read on Facebook, every tweet or text message you get from a friend, is competing for resources in your brain with important things like whether to put your savings in stocks or bonds,

The processing capacity of the conscious mind has been estimated (by the researcher Mihaly Csikszentmihalyi and, independently, by Bell Labs engineer Robert Lucky) at 120 bits per second. That bandwidth, or window, is the speed limit for the traffic of information we can pay conscious attention to at any one time.

While a great deal occurs below the threshold of our awareness, and this has an impact on how we feel and what our life is going to be like, in order for something to become encoded as part of your experience, you need to have paid conscious attention to it.

What does this bandwidth restriction—this information speed limit—mean in terms of our interactions with others? In order to understand one person speaking to us, we need to process 60 bits of information per second. With a processing limit of 120 bits per second, this means you can barely understand two people talking to you at the same time

We’re surrounded on this planet by billions of other humans, but we can understand only two at a time at the most! It’s no wonder that the world is filled with so much misunderstanding.

With such attentional restrictions, it’s clear why many of us feel overwhelmed by managing some of the most basic aspects of life. Part of the reason is that our brains evolved to help us deal with life during the hunter-gatherer phase of human history

Attention is the most essential mental resource for any organism. It determines which aspects of the environment we deal with, and most of the time, various automatic, subconscious processes make the correct choice about what gets passed through to our conscious awareness. For this to happen, millions of neurons are constantly monitoring the environment to select the most important things for us to focus on.

These neurons are collectively the “attentional filter.” They work largely in the background, outside of our conscious awareness. This is why most of the perceptual detritus of our daily lives doesn’t registe

The attentional filter is one of evolution’s greatest achievements. In nonhumans, it ensures that they don’t get distracted by irrelevant things

When our protohuman ancestors left the cover of the trees to seek new sources of food, they simultaneously opened up a vast range of new possibilities for nourishment and exposed themselves to a wide range of new predators. Being alert and vigilant to threatening sounds and visual cues is what allowed them to survive; this meant allowing an increasing amount of information through the attentional filter.

Ten thousand years ago, humans plus their pets and livestock accounted for about 0.1% of the terrestrial vertebrate biomass inhabiting the earth; we now account for 98%

Humans are, by most biological measures, the most successful species our planet has seen. We have managed to survive in nearly every climate our planet has offered (so far), and the rate of our population expansion exceeds that of any other known organism

Our success owes in large part to our cognitive capacity, the ability of our brains to flexibly handle information. But our brains evolved in a much simpler world with far less information coming at us. Today, our attentional filters easily become overwhelmed.

Successful people—or those who can afford it—employ layers of other people whose job it is to narrow their own attentional filters.

The human problem-solvers — 609 high school students from 108 countries — won 58 gold medals, 123 silver and 145 bronze. The A.I. performed at the level of a silver medalist, solving four out of six problems for a total of 28 points. It was the first time that A.I. has achieved a medal-worthy performance on an Olympiad’s problems.

Nonetheless, Dr. Kohli described the result as a “phase transition” — a transformative change — “in the use of A.I. in mathematics and the ability of A.I. systems to do mathematics.”

Dr. Gowers added in an email: “I was definitely impressed.” The lab had discussed its Olympiad ambitions with him a couple of weeks beforehand, so “my expectations were quite high,” he said. “But the program met them, and in one or two instances significantly surpassed them.” The program found the “magic keys” that unlocked the problems, he said.

Haojia Shi, a student from China, ranked No. 1 and was the only competitor to earn a perfect score — 42 points for six problems; each problem is worth seven points for a full solution. The U.S. team won first place with 192 points; China placed second with 190.

The Google system earned its 28 points for fully solving four problems — two in algebra, one in geometry and one in number theory. (It flopped at two combinatorics problems.) The system was allowed unlimited time; for some problems it took up to three days. The students were allotted only 4.5 hours per exam.

“The fact that we’ve reached this threshold, where it’s even possible to tackle these problems at all, is what represents a step-change in the history of mathematics,” he added. “And hopefully it’s not just a step-change in the I.M.O., but also represents the point at which we went from computers only being able to prove very, very simple things toward computers being able to prove things that humans can’t.”

“Mathematics requires this interesting combination of abstract, precise and creative reasoning,” Dr. Davies said. In part, he noted, this repertoire of abilities is what makes math a good litmus test for the ultimate goal: reaching so-called artificial general intelligence, or A.G.I., a system with capabilities ranging from emerging to competent to virtuoso to superhuman

One approach was an informal reasoning system, expressed in natural language. This system leveraged Gemini, Google’s large language model. It used the English corpus of published problems and proofs and the like as training data.

Dr. Hubert’s team developed a new model that is comparable but more generalized. Named AlphaProof, it is designed to engage with a broad range of mathematical subjects. All told, AlphaGeometry and AlphaProof made use of a number of different A.I. technologies.

In January, a Google DeepMind system named AlphaGeometry solved a sampling of Olympiad geometry problems at nearly the level of a human gold medalist. “AlphaGeometry 2 has now surpassed the gold medalists in solving I.M.O. problems,” Thang Luong, the principal investigator, said in an email.

The informal system excels at identifying patterns and suggesting what comes next; it is creative and talks about ideas in an understandable way. Of course, large language models are inclined to make things up — which may (or may not) fly for poetry and definitely not for math. But in this context, the L.L.M. seems to have displayed restraint; it wasn’t immune to hallucination, but the frequency was reduced.

Another approach was a formal reasoning system, based on logic and expressed in code. It used theorem prover and proof-assistant software called Lean, which guarantees that if the system says a proof is correct, then it is indeed correct. “We can exactly check that the proof is correct or not,” Dr. Hubert said. “Every step is guaranteed to be logically sound.”

Another crucial component was a reinforcement learning algorithm in the AlphaGo and AlphaZero lineage. This type of A.I. learns by itself and can scale indefinitely, said Dr. Silver, who is Google DeepMind’s vice-president of reinforcement learning. Since the algorithm doesn’t require a human teacher, it can “learn and keep learning and keep learning until ultimately it can solve the hardest problems that humans can solve,” he said. “And then maybe even one day go beyond those.”

Dr. Hubert added, “The system can rediscover knowledge for itself.” That’s what happened with AlphaZero: It started with zero knowledge, Dr. Hubert said, “and by just playing games, and seeing who wins and who loses, it could rediscover all the knowledge of chess. It took us less than a day to rediscover all the knowledge of chess, and about a week to rediscover all the knowledge of Go. So we thought, Let’s apply this to mathematics.”

Dr. Gowers doesn’t worry — too much — about the long-term consequences. “It is possible to imagine a state of affairs where mathematicians are basically left with nothing to do,” he said. “That would be the case if computers became better, and far faster, at everything that mathematicians currently do.”

“There still seems to be quite a long way to go before computers will be able to do research-level mathematics,” he added. “It’s a fairly safe bet that if Google DeepMind can solve at least some hard I.M.O. problems, then a useful research tool can’t be all that far away.”

A really adept tool might make mathematics accessible to more people, speed up the research process, nudge mathematicians outside the box. Eventually it might even pose novel ideas that resonate.