Group items matching

in title, tags, annotations or url

Because right-wing commentators aren’t the only ones who think Biden’s mind is basically gone—lots of voters think so too

Since mainstream media venues by and large epistemically rely on the views of the masses to supply journalists with their coverage frames, news operations end up treating popular concerns about Biden’s age as a kind of sacrosanct window into reality rather than as a hype cycle perpetually fed into the ambient collective consciousness by anti-Biden voices intending to sink his reelection chances.

By contrast, most of the news sources the right sees as hyperpartisan Biden spin machines actually strain at being fair-minded and objective, which disinclines them toward producing any sort of muscular pushback against the right’s relentless mischaracterizations.

Of course, a major reason why the public thinks this is because the entirety of the right-wing information superstructure is devoted, on a daily basis, to depicting Biden as severely cognitively compromised

even if we grant every single concern that Klein and others have voiced, it is indisputably true that Joe Biden remains an intellectual giant next to Donald Trump

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

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.

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.

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.

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.

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.