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, 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.

An aperiodic tiling displays no such “translational symmetry,” and mathematicians have long sought a single shape that could tile the plane in such a fashion. This is known as the einstein problem.

black and white squares also can make weird nonperiodic patterns, in addition to the familiar, periodic checkerboard pattern. “It’s really pretty trivial to be able to make weird and interesting patterns,” he said. The magic of the two Penrose tiles is that they make only nonperiodic patterns — that’s all they can do.“But then the Holy Grail was, could you do with one — one tile?” Dr. Goodman-Strauss said.

now a new paper — by Mr. Smith and three co-authors with mathematical and computational expertise — proves Mr. Smith’s discovery true. The researchers called their einstein “the hat,

“The most significant aspect for me is that the tiling does not clearly fall into any of the familiar classes of structures that we understand.”

“I’m always messing about and experimenting with shapes,” said Mr. Smith, 64, who worked as a printing technician, among other jobs, and retired early. Although he enjoyed math in high school, he didn’t excel at it, he said. But he has long been “obsessively intrigued” by the einstein problem.

Sir Roger found the proofs “very complicated.” Nonetheless, he was “extremely intrigued” by the einstein, he said: “It’s a really good shape, strikingly simple.”

The simplicity came honestly. Mr. Smith’s investigations were mostly by hand; one of his co-authors described him as an “imaginative tinkerer.”

When in November he found a tile that seemed to fill the plane without a repeating pattern, he emailed Craig Kaplan, a co-author and a computer scientist at the University of Waterloo.

“It was clear that something unusual was happening with this shape,” Dr. Kaplan said. Taking a computational approach that built on previous research, his algorithm generated larger and larger swaths of hat tiles. “There didn’t seem to be any limit to how large a blob of tiles the software could construct,”

The first step, Dr. Kaplan said, was to “define a set of four ‘metatiles,’ simple shapes that stand in for small groupings of one, two, or four hats.” The metatiles assemble into four larger shapes that behave similarly. This assembly, from metatiles to supertiles to supersupertiles, ad infinitum, covered “larger and larger mathematical ‘floors’ with copies of the hat,” Dr. Kaplan said. “We then show that this sort of hierarchical assembly is essentially the only way to tile the plane with hats, which turns out to be enough to show that it can never tile periodically.”

some might wonder whether this is a two-tile, not one-tile, set of aperiodic monotiles.

Dr. Goodman-Strauss had raised this subtlety on a tiling listserv: “Is there one hat or two?” The consensus was that a monotile counts as such even using its reflection. That leaves an open question, Dr. Berger said: Is there an einstein that will do the job without reflection?

“the hat” was not a new geometric invention. It is a polykite — it consists of eight kites. (Take a hexagon and draw three lines, connecting the center of each side to the center of its opposite side; the six shapes that result are kites.)

“It’s likely that others have contemplated this hat shape in the past, just not in a context where they proceeded to investigate its tiling properties,” Dr. Kaplan said. “I like to think that it was hiding in plain sight.”

Incredibly, Mr. Smith later found a second einstein. He called it “the turtle” — a polykite made of not eight kites but 10. It was “uncanny,” Dr. Kaplan said. He recalled feeling panicked; he was already “neck deep in the hat.”

Dr. Myers, who had done similar computations, promptly discovered a profound connection between the hat and the turtle. And he discerned that, in fact, there was an entire family of related einsteins — a continuous, uncountable infinity of shapes that morph one to the next.

this einstein family motivated the second proof, which offers a new tool for proving aperiodicity. The math seemed “too good to be true,” Dr. Myers said in an email. “I wasn’t expecting such a different approach to proving aperiodicity — but everything seemed to hold together as I wrote up the details.”

Mr. Smith was amazed to see the research paper come together. “I was no help, to be honest.” He appreciated the illustrations, he said: “I’m more of a pictures person.”

There were plenty of books about Black people, but they tended to be about poor or working-class Black people and often depicted Black lives proscribed by discrimination and inequality

I was aware of two instances of myself in fiction of the time. One was the nerdy teenage middle-class Black girl in Louise Fitzhugh’s “Nobody’s Family Is Going to Change.” Then there was “Sarah Phillips” by Andrea Lee in 1984. That one was a near-sacred experience for me, in depicting a middle-class Black girl who grew up outside Philadelphia, went to Harvard and then moved to Europe. Here was someone I could have been, a variation on some people I knew

But I neither needed nor sought out more such books. How much me did I need? I read to learn about what I didn’t know.

when I started my graduate study, I explicitly did not want to study Black English. It was too close to home.

What fascinated me, and still does, are languages utterly unlike the one I grew up with. This is what I do my academic work on. I am happy to write about Black English, but I do it out of civic duty. What first hooked me on languages was hearing someone speak Hebrew

This idea that one, if brown, is to seek one’s self in what one reads and watches gets around quite a bit.

But still, the idea that Black people are deprived in not exploring what they already relate to is not as natural as it sounds.

This position is rooted, one suspects, as a defense against racism, in a sense that learning most meaningfully takes place within a warm comfort zone of cultural membership. But it’s a wide, wide world out there, and this position ultimately limits the mind and the soul.

I question its necessity in 2023. The etymology of the word “education” is related to the Latin “educere,” meaning to lead outward, not inward.

It can be especially ticklish to hear white people taking up the idea that Black people stray from their selves when taking up things beyond Blackness

I sense the idea that real Blackness means ever seeking yourself in your reading and viewing is a post-1966 thing, to refer to what I wrote here last week.

W.E.B. Du Bois had no such idea. He wrote: “I sit with Shakespeare, and he winces not. Across the color line I move arm in arm with Balzac and Dumas, where smiling men and welcoming women glide in gilded halls. From out the caves of evening that swing between the strong-limbed Earth and the tracery of the stars, I summon Aristotle and Aurelius and what soul I will, and they come all graciously with no scorn nor condescension.”

Du Bois adapted these “white” works to his own needs and predilections. Even the naked racism he lived with daily did not lead him to draw a line around “white” things as something alien to his essence

Rather, he insisted that these works were, in fact, part of his self, regardless of how wider society saw that self or how figures like Shakespeare and Aristotle would have seen him.

Du Bois, in this, was normal. Today I sit with “Succession,” Steely Dan and Saul Bellow, and they wince not. I see myself in none of them. Yes, Bellow had some nasty moments on race, such as a gruesomely prurient scene in “Mr. Sammler’s Planet.” But I’m sorry: I cannot let that one scene — or even two — deprive me of the symphonic reaches of “Herzog” and “Humboldt’s Gift.” What they offer, after all, becomes part of me along with everything else.

the truth is that characters I can see as me are now not uncommon on television in particular. Andre Braugher’s Captain Holt on “Brooklyn Nine-Nine” was about as close to me as I expect a sitcom character ever to be, for example. That was fun. But honestly, I didn’t need it. I live with me. I watch TV to see somebody else.

In the summer of 2020, “public-health experts” decided that racism is a public-health crisis comparable to the coronavirus pandemic. It was therefore, they claimed, within their purview to express public support for the Black Lives Matter protests following the murder of George Floyd and to argue that the benefits of such protests outweighed the increased risk of spreading the disease. Those supposed experts actually knew nothing about the likely effects of the protests. They made no concrete predictions about whether they would in any way ameliorate racism in America, just as Nature can make no concrete predictions about whether its political endorsements will actually help a preferred candidate without jeopardizing its other important goals. The political action was expressive, not evidence-based...

as is often the case, a debate which appears to be about the neutrality of institutions is not really about neutrality at all... Rather, it is about whether there is any room left for soberly weighing our goals and values and thinking in a measured way about the consequences of our actions rather than simply reacting to situations in an impulsive and expressive manner, broadcasting our views to the world so that people know where we stand.

Our goals and values might not be “neutral” at all, but they might still be best served by procedures, institutions, and even individuals that follow neutral principles.

Musk seems willing to grant this power to racists, conspiracy theorists, and trolls. This isn’t great for reasonable people who want to have nuanced conversations on social media, but the joke has always been on them. Twitter isn’t that place, and it never will be.

one of Musk’s first moves after taking over was to fire the company’s head of policy—an individual who had publicly stated a commitment to both free speech and preventing abuse.

On Friday, Musk tweeted that Twitter would be “forming a content moderation council with widely diverse viewpoints,” noting that “no major content decisions [would] happen before that council convenes.” Just three hours later, replying to a question about lifting a suspension on The Daily Wire’s Jordan Peterson, Musk signaled that maybe that wasn’t exactly right; he tweeted: “Anyone suspended for minor & dubious reasons will be freed from Twitter jail.” He says he wants a democratic council, yet he’s also setting policy by decree.

Perhaps most depressingly, this behavior is quite familiar. As Techdirt’s Mike Masnick has pointed out, we are all stuck “watching Musk speed run the content moderation learning curve” and making the same mistakes that social-media executives made with their platforms in their first years at the helm.

Musk has charged himself with solving the central, seemingly intractable issue at the core of hundreds of years of debate about free speech. In the social-media era, no entity has managed to balance preserving both free speech and genuine open debate across the internet at scale.

Musk hasn’t just given himself a nearly impossible task; he’s also created conditions for his new company’s failure. By acting incoherently as a leader and lording the prospect of mass terminations over his employees, he’s created a dysfunctional and chaotic work environment for the people who will ultimately execute his changes to the platform

Just like midlife, quarterlife can bring its own crisis — trying to separate from your parents or caregivers and forge a sense of self is a struggle. But the generation entering adulthood now faces novel, sometimes debilitating, challenges.

Many find themselves so mired in day-to-day monetary concerns, from the relentless crush of student debt to the swelling costs of everything, that they feel unable to consider what they want for themselves long term

“We’ve been constrained by this myth that you graduate from college and you start your life,” she said. Without the social script previous generations followed — graduate college, marry, raise a family — Ms. Byock said her young clients often flailed around in a state of extended adolescence.

nearly one-third of Gen Z adults are living with their parents or other relatives and plan to stay there.

Many young people today struggle to afford college or decide not to attend, and the “existential crisis” that used to hit after graduation descends earlier and earlier

Ms. Byock said to pay attention to what you’re naturally curious about, and not to dismiss your interests as stupid or futile.

Experts said those entering adulthood need clear guidance for how to make it out of the muddle. Here are their top pieces of advice on how to navigate a quarterlife crisis today.

She recommends scheduling reminders to check in with yourself, roughly every three months, to examine where you are in your life and whether you feel stuck or dissatisfied

From there, she said, you can start to identify aspects of your life that you want to change.

“Start to give your own inner life the respect that it’s due,”

But quarterlife is about becoming a whole person, Ms. Byock said, and both groups need to absorb each other’s characteristics to balance themselves out

However, there is a difference between self-interest and self-indulgence, Ms. Byock said. Investigating and interrogating who you are takes work. “It’s not just about choosing your labels and being done,” she said.

Be patient.

Quarterlifers may feel pressure to race through each step of their lives, Ms. Byock said, craving the sense of achievement that comes with completing a task.

But learning to listen to oneself is a lifelong process.

Instead of searching for quick fixes, she said, young adults should think about longer-term goals: starting therapy that stretches beyond a handful of sessions, building healthy nutrition and exercise habits, working toward self-reliance.

“I know that seems sort of absurdly large and huge in scope,” she said. “But it’s allowing ourselves to meander and move through life, versus just ‘Check the boxes and get it right.’”

take stock of your day-to-day life and notice where things are missing. She groups quarterlifers into two categories: “stability types” and “meaning types.”

“Stability types” are seen by others as solid and stable. They prioritize a sense of security, succeed in their careers and may pursue building a family.

“But there’s a sense of emptiness and a sense of faking it,” she said. “They think this couldn’t possibly be all that life is about.”

On the other end of the spectrum, there are “meaning types” who are typically artists; they have intense creative passions but have a hard time dealing with day-to-day tasks

“These are folks for whom doing what society expects of you is so overwhelming and so discordant with their own sense of self that they seem to constantly be floundering,” she said. “They can’t quite figure it out.”

That paralysis is often exacerbated by mounting climate anxiety and the slog of a multiyear pandemic that has left many young people mourning family and friends, or smaller losses like a conventional college experience or the traditions of starting a first job.

Stability types need to think about how to give their lives a sense of passion and purpose. And meaning types need to find security, perhaps by starting with a consistent routine that can both anchor and unlock creativity.

perhaps the prototypical inspiration for staying calm in chaos: Yoda. The Jedi master is “one of the few images we have of what feeling quiet amid extreme pain and apocalypse can look like,

Even when there seems to be little stability externally, she said, quarterlifers can try to create their own steadiness.

establishing habits that help you ground yourself as a young adult is critical because transitional periods make us more susceptible to burnout

He suggests building a practical tool kit of self-care practices, like regularly taking stock of what you’re grateful for, taking controlled breaths and maintaining healthy nutrition and exercise routines. “These are techniques that can help you find clarity,”

Don’t be afraid to make a big change.

It’s important to identify what aspects of your life you have the power to alter, Dr. Brown said. “You can’t change an annoying boss,” he said, “but you might be able to plan a career change.”

That’s easier said than done, he acknowledged, and young adults should weigh the risks of continuing to live in their status quo — staying in their hometown, or lingering in a career that doesn’t excite them — with the potential benefits of trying something new.

quarterlife is typically “the freest stage of the whole life span,

Young adults may have an easier time moving to a new city or starting a new job than their older counterparts would.

Know when to call your parents — and when to call on yourself.

Quarterlife is about the journey from dependence to independence, Ms. Byock said — learning to rely on ourselves, after, for some, growing up in a culture of helicopter parenting and hands-on family dynamics.

there are ways your relationship with your parents can evolve, helping you carve out more independence

That can involve talking about family history and past memories or asking questions about your parents’ upbringing

“You’re transitioning the relationship from one of hierarchy to one of friendship,” she said. “It isn’t just about moving away or getting physical distance.”

Every quarterlifer typically has a moment when they know they need to step away from their parents and to face obstacles on their own

That doesn’t mean you can’t, or shouldn’t, still depend on your parents in moments of crisis, she said. “I don’t think it’s just about never needing one’s parents again,” she said. “But it’s about doing the subtle work within oneself to know: This is a time I need to stand on my own.”

This is the danger of the American dream when you scale it down from the national to the individual level. You risk devoting your life to wanting something because it’s what you’ve been told you should want. Everybody loves a Cinderella story, but sometimes your dream, in reality, is just a wish somebody else’s heart made.

Like all of these books, it is about the power and untrustworthiness of written texts—history texts in particular. These various strands don’t always cohere. The question of who killed Bonkowski Pasha is part of the main story of the novel, and yet it disappears for chapters at a time. Perhaps more seriously, the postmodern elements sometimes sit uncomfortably with the torrents of historical and sensory detail

You can think of Musk’s acquisition of Twitter as the latest sortie, a takeover of the ultimate wordcel site by the world’s most successful shape rotator.

more likely, he fell prey to a different delusion, one in which the shape rotators and the wordcels are united: thinking of Twitter in terms of words and arguments, as a “digital public square” where vital questions are hashed out. It is that, sometimes, but that’s not what it’s designed for. It’s designed to maximize engagement, which is to say, it’s an addiction machine for the highly verbal.

Both groups theoretically understand what the machine is doing — the wordcels write endless articles about bad algorithms, and the shape rotators build them. But both nonetheless talk as though they’re saving the world even as they compulsively follow the programming. The shape rotators bait the wordcels because that’s what makes the machine spit out more rewarding likes and retweets. We wordcels return the favor for the same reason.

Musk could theoretically rework Twitter’s architecture to downrank provocation and make it less addictive. But of course, that would make it a less profitable business

More to the point, the reason he bought it is that he, like his critics, is hooked on it the way it is now. Unfortunately for Tesla shareholders, Musk has now put himself in the position of a dealer who can spend all day getting high on his own supply.

a 2022 Reuters investigation found that some American clinics were quite aggressive with treatment: None of the 18 U.S. clinics that Reuters looked at performed long assessments on their patients, and some prescribed puberty blockers on the first visit.

As Cass writes in her report, “The toxicity of the debate is exceptional.” She continues, “There are few other areas of health care where professionals are so afraid to openly discuss their views, where people are vilified on social media and where name-calling echoes the worst bullying behavior.”

The report’s greatest strength is its epistemic humility. Cass is continually asking, “What do we really know?” She is carefully examining the various studies — which are high quality, which are not. She is down in the academic weeds.

he notes that the quality of the research in this field is poor. The current treatments are “built on shaky foundations,” she writes in The BMJ. Practitioners have raced ahead with therapies when we don’t know what the effects will be. As Cass tells The BMJ, “I can’t think of another area of pediatric care where we give young people a potentially irreversible treatment and have no idea what happens to them in adulthood.”

She writes in her report, “The option to provide masculinizing/feminizing hormones from age 16 is available, but the review would recommend extreme caution.

her core conclusion is this: “For most young people, a medical pathway will not be the best way to manage their gender-related distress.” She realizes that this conclusion will not please many of the young people she has come to know, but this is where the evidence has taken her.

In 1877 a British philosopher and mathematician named William Kingdon Clifford published an essay called “The Ethics of Belief.” In it he argued that if a shipowner ignored evidence that his craft had problems and sent the ship to sea having convinced himself it was safe, then of course we would blame him if the ship went down and all aboard were lost. To have a belief is to bear responsibility, and one thus has a moral responsibility to dig arduously into the evidence, avoid ideological thinking and take into account self-serving biases.

“It is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence,” Clifford wrote

A belief, he continued, is a public possession. If too many people believe things without evidence, “the danger to society is not merely that it should believe wrong things, though that is great enough; but that it should become credulous, and lose the habit of testing things and inquiring into them; for then it must sink back into savagery.”

Since the Trump years, this habit of not consulting the evidence has become the underlying crisis in so many realms. People segregate into intellectually cohesive teams, which are always dumber than intellectually diverse teams. Issues are settled by intimidation, not evidence

Our natural human tendency is to be too confident in our knowledge, too quick to ignore contrary evidence. But these days it has become acceptable to luxuriate in those epistemic shortcomings, not to struggle against them. See, for example, the modern Republican Party.

It is reasonable to imagine that Rife thinks his audience processes his Black English usage as a warm method of interpersonal bonding in the same way he seems to. In fact, a tweet of his suggests that he hadn’t even been conscious of what he was doing until apprised, and doesn’t even think of himself as shifting into something “Black” at all.

Rife is not posing or ridiculing; he’s connecting. Linguists call it accommodation. A non-Black speaker these days may do it with a Black audience.

reflecting in language exactly what we were supposed to be going for: interracial harmony.

Except that these days, that ideal may seem a tad 1.0. Under the new identitarian mind-set, where we cherish coming together less than we cherish a diversity of identities, many see someone like Rife as culturally appropriating Black speech, something that isn’t his. “Mimesis is a kind of negation,”

There is simply no way that whiteness and Blackness will mingle as they have in music, cuisine, gesture, greeting styles, dating, matrimony and multiracial identity, and yet for some reason be halted at language.

The horse has been out of the barn ever since white kids embraced Jay-Z and Tupac.

style-shifting is humans’ linguistic default, not a pose or party trick.