Now two mathematicians have proved Hawking and his colleagues wrong. The new work—contained in a pair ofrecent papers by Christoph Kehle of the Massachusetts Institute of Technology and Ryan Unger of Stanford University and the University of California, Berkeley—demonstrates that there is nothing in our known laws of physics to prevent the formation of an extremal black hole.
Their mathematical proof is “beautiful, technically innovative, and physically surprising,” said Mihalis Dafermos, a mathematician at Princeton University (and Kehle’s and Unger’s doctoral adviser). It hints at a potentially richer and more varied universe in which “extremal black holes could be out there astrophysically,” he added.
That doesn’t mean they are. “Just because a mathematical solution exists that has nice properties doesn’t necessarily mean that nature will make use of it,” Khanna said. “But if we somehow find one, that would really [make] us think about what we are missing.” Such a discovery, he noted, has the potential to raise “some pretty radical kinds of questions.”
The Law of Impossibility
Before Kehle and Unger’s proof, there was good reason to believe that extremal black holes couldn’t exist.
In 1973, Bardeen, Carter, and Hawking introduced four laws about the behavior of black holes. They resembled the four long-established laws of thermodynamics—a set of sacrosanct principles that state, for instance, that the universe becomes more disordered over time, and that energy cannot be created or destroyed.
Christoph Kehle, a mathematician at the Massachusetts Institute of Technology, recently disproved a 1973 conjecture about extremal black holes.
Image: Dan Komoda/Institute for Advanced Study
In their paper, the physicists proved their first three laws of black hole thermodynamics: the zeroth, first, and second. By extension, they assumed that the third law (like its standard thermodynamics counterpart) would also be true, even though they were not yet able to prove it.
That law stated that the surface gravity of a black hole cannot decrease to zero in a finite amount of time—in other words, that there is no way to create an extremal black hole. To support their claim, the trio argued that any process that would allow a black hole’s charge or spin to reach the extremal limit could also potentially result in its event horizon disappearing altogether. It is widely believed that black holes without an event horizon, called naked singularities, cannot exist. Moreover, because a black hole’s temperature is known to be proportional to its surface gravity, a black hole with no surface gravity would also have no temperature. Such a black hole would not emit thermal radiation—something that Hawking later proposed black holes had to do.
In 1986, a physicist named Werner Israel seemed to put the issue to rest when he published a proof of the third law. Say you want to create an extremal black hole from a regular one. You might try to do so by making it spin faster or by adding more charged particles. Israel’s proof seemed to demonstrate that doing so could not force a black hole’s surface gravity to drop to zero in a finite amount of time.
As Kehle and Unger would ultimately discover, Israel’s argument concealed a flaw.
Death of the Third Law
Kehle and Unger did not set out to find extremal black holes. They stumbled on them entirely by accident.
They were studying the formation of electrically charged black holes. “We realized that we could do it”—make a black hole—“for all charge-to-mass ratios,” Kehle said. That included the case where the charge is as high as possible, a hallmark of an extremal black hole.
After proving that highly charged extremal black holes are mathematically possible, Ryan Unger of Stanford University is now trying to show that fast-spinning ones are, too. But it’s a much harder problem.
Photograph: Dimitris Fetsios
Dafermos recognized that his former students had uncovered a counterexample to Bardeen, Carter, and Hawking’s third law: They’d shown that they could indeed change a typical black hole into an extremal one within a finite stretch of time.
Kehle and Unger started with a black hole that doesn’t rotate and has no charge, and modeled what might happen if it was placed in a simplified environment called a scalar field, which assumes a background of uniformly charged particles. They then buffeted the black hole with pulses from the field to add charge to it.
The first human implanted with a Neuralink brain chip can control a computer mouse with their thoughts, Elon Musk claimed in an X Spaces event Monday. The anonymous patient has recovered fully, according to Musk, after having a Neuralink chip implanted into their brain just a few weeks ago.
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“Progress is good, patient seems to have made a full recovery … and is able to control the mouse, move the mouse around the screen just by thinking,” said Musk in a conversation on X Monday night.
Neuralink is working with the patient to get as many “button presses” as possible, purely by thinking, according to Musk. These include the patient moving a mouse around, clicking, and dragging a cursor solely with their brain. There is no evidence for these claims besides what Musk is announcing in brief snippets on X, so these claims should be taken with a grain of salt. However, if true, Neuralink’s advancements would be a major step forward for technology.
In late January, Musk announced that the first human patient had received a Nueralink implant via a tweet on X. The experimental surgery installs a microchip into the top layer of a person’s skull. Musk revealed little else about the identity of the initial patient.
Neuralink’s first product is called “Telepathy,” according to Musk, and it’s specifically designed for people who have lost the use of their limbs. The cursor movement described by Musk appears to be the very first progress on Neuralink’s Telepathy.
“Imagine if Stephen Hawking could communicate faster than a speed typist or auctioneer,” said Musk in a tweet. “That is the goal.”
“Opening up the brain of a living human being to insert a device, particularly someone with serious medical problems, deserves more than a two-sentence report on what is, in effect, a proprietary social media platform not distinguished for its reliability where facts are concerned,” the Center said.
The Hastings Center noted that Neuralink has not publicly shared what it plans to do if things go wrong, nor has the company shared the findings of its animal research that justified this experiment in the first place.
Despite the novelty of this human experiment from Musk and Neuralink, we still don’t know much. The company continues to only share bits of information through Musk’s X account, which is highly unusual for the scientific community but is par for the course from Musk.
IT has been a terrible week for a string of disgraced paedophile Jeffrey Epstein’s pals and associates who have been exposed in a cache of newly unsealed court docs.
The splew of unsealed docs have exposed Jeffrey Epstein’s inner circle and further detail of his depraved sexual crimes he committed alongside disgraced British socialised, Ghislaine MaxwellCredit: The Mega Agency
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The new files reveal an alleged plot to blackmail Prince Andrew over his alleged sexual encounter with Virginia GiuffreCredit: Jae Donnelly
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Former President Bill Clinton (pictured with Epstein and Maxwell) has also been dragged into the spotlight with allegations he likes girls ‘young’Credit: The Mega Agency
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Giuiffre has alleged she was trafficked by Epstein and given to Andrew and ‘two of the world’s most respected politicians’Credit: PA
Delivered in several anticipated drops, the files have revealed the inner-workings of Epstein’s world – while dragging a sprinkling of previously unmentioned celebrities and politicians into the mix.
The docs have made public the lurid details of a string of sexual allegations made against Prince Andrew, former presidents Bill Clinton and Donald Trump, physicist Stephen Hawking and A-list celebrities.
1. Andrew, Clinton & Branson’s ‘sex tapes’
Epstein victim Sarah Ransome wrote emails to a reporter in 2016 claiming the duke, Bill Clinton and billionaire businessman Sir Richard Branson were filmed having sex by Epstein on separate occasions.
READ MORE ON EPSTEIN DOCS
She later retracted the claims and told the New Yorker in 2019 “she had invented the tapes to draw attention to Epstein’s behaviour, and to make him believe that she had ‘evidence that would come out if he harmed me’”.
All of the above have always vehemently denied any wrongdoing over their association with Epstein and no tapes have ever emerged publicly.
A spokesman for Branson blasted the claims as “baseless and unfounded”.
2. Stephen Hawking’s ‘underage orgy’
The doc drop revealed an email that had been sent from Epstein to Maxwell that showed the billionaire asking her to “issue a reward” to any of Giuffre’s friends who “come forward and help prove her allegations are false”.
Among the allegations listed by Epstein in the email were a “Clinton dinner” and a claim that Stephen Hawking “participated in an underage orgy”.
In the message, Epstein suggested Giuffre had made claims about both the British scientist and former US President Bill Clinton.
The email read: “You can issue a reward to any of Virginia’s friends, acquaints, family that come forward and help prove her allegations are false.
In 2015, photos emerged showing Hawking, who died in 2018 aged 76, being hosted on Epstein’s private Caribbean island before he was first charged in 2006.
The internationally renowned physicist was pictured at a barbecue on Little St James, often referred to as Epstein’s “Paedo Island”.
He was part of a group of 21 scientists attending a conference in March 2006, which Epstein had funded.
3. Duke of York’s ‘underage orgy’
A woman named only as Jane Doe 3 alleged she was “forced” into sexual relations with “a member of the British Royal Family, Prince Andrew (a/k/a Duke of York)”.
In 2019, Clinton’s spokesman said he knew “nothing about the terrible crimes Jeffrey Epstein pleaded guilty to” and that the pair had not spoken “in over a decade”.
6. Giuffre ‘trafficked’ to Andrew and ‘two of world’s most respected politicians’
In an email exchange with journalist Sharon Churcher in May 2011, Giuffre said she was concerned about speaking out after Clinton had allegedly “threatened them not to write sex-trafficking articles” about Epstein.
In a follow up email, Churcher said it would be a “gamble” for Giuffre to not have more to say about how she was “sex-trafficked to PA [Prince Andrew] and other men including two of the world’s most respected politicians”.
The names of the two politicians in the email remain redacted.
In Giuffre’s deposition released on Tuesday, she alleged she had sex with New Mexico Governor Bill Richardson who passed away in September and another “prominent US politician” when she was 17.
Asked how many times she allegedly had sex with the unnamed official, she replied “twice that I can recall.”
7. Donald Trump’s sex with ‘many girls’
Ransome also claimed that “many girls” had sexual relations with former US president Donald Trump, including her friend who wasn’t named.
In an email written to a journalist in 2016 and filed in court papers, Ransome said: “She confided in me about her casual ‘friendship’ with Donald. Mr. Trump definitely seemed to have a thing for her and she told me how he kept going on about how he liked her ‘pert nipples,’”.
The claims were also flagged by Dershowitz in his letter which attempted to prove the Epstein victim lacked credibility.
Provisional search terms used by lawyers to find relevant files on Maxwell’s computers were also disclosed in the documents.
Amongst the terms on a list were “Andrew”, “Prince”, “Royal”, “PA”, “Kensington”, “Duke” and “York”.
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A picture of Ransome on Epstein’s island included in the newly unsealed files
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Sarah Ransome doubled down on her previous sex tape claims this weekCredit: Netflix
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She also alleged Epstein raped her ‘three times’ in a single dayCredit: AFP
9. Duke and Duchess of York ‘friends’ with Epstein
Epstein’s former housekeeper Juan Alessi claimed Andrew had “daily massages” while he stayed at the paedophile financier’s Florida home.
During his video-taped interview under oath in 2009, Alessi said Sarah, Duchess of York, only paid a short visit to Epstein, but the duke “spent weeks with us”.
The disgraced financier pleaded the fifth amendment eight times as he was quizzed during a former trial against his ex-lover, Maxwell.
He was directly asked whether he and Maxwell instructed Giuffre to have sex with Andrew and whether he had asked her to gather a “full report” to be later used as “blackmail material”.
He was also questioned over whether Andrew had sex with Giuffre “several times” and if the information gathered for the trial had “the potential to affect the reputation” of the duke.
To each targeted question, Epstein exercised his right to the fifth amendment – refusing to answer to avoid incriminating himself.
Andrew’s accuser has previously claimed he sexually assaulted her in a Victorian-style bath at Ghislaine’s mews house in Belgravia in March 2001.
Monday’s drop of documents revealed Maxwell’s lawyer had claimed that Giuffre lied about having sex with Andrew because he was “too big for the bath”.
The prince strenuously denies any wrongdoing.
However, the late Queen’s second son stepped down from public life after the furore over his friendship with Epstein, and paid millions to settle a civil sexual assault case with Giuffre – a woman he claimed never to have met.
11. Maxwell’s fears over links to Andrew
Maxwell could be seen sending an email in January 2015, shortly after a civil claim had been filed against her, in which she described herself as “out of my depth”.
The socialite said: “I have already suffered such a terrible and painful loss over the last few days that I can’t even see what life after press hell even looks like – statements that don’t address all just lead to more questions… what is my relationship to Clinton? Andrew on and on.”
Maxwell has been imprisoned since July 2020 despite attempts by her defence counsel to have her released on bail.
She was sentenced to 20 years in prison at the federal court in the Southern District of New York in June 2022.
Epstein was found hung in a prison cell in New York on August 10, 2019, while awaiting trial for a range of offences, including trafficking minors for sex, and multiple rapes.
How you can get help
Women’s Aid has this advice for victims and their families:
Always keep your phone nearby.
Get in touch with charities for help, including the Women’s Aid live chat helpline and services such as SupportLine.
If you are in danger, call 999.
Familiarise yourself with the Silent Solution, reporting abuse without speaking down the phone, instead dialing “55”.
Always keep some money on you, including change for a pay phone or bus fare.
If you suspect your partner is about to attack you, try to go to a lower-risk area of the house – for example, where there is a way out and access to a telephone.
Avoid the kitchen and garage, where there are likely to be knives or other weapons. Avoid rooms where you might become trapped, such as the bathroom, or where you might be shut into a cupboard or other small space.
If you are a victim of domestic abuse, SupportLine is open Tuesday, Wednesday and Thursday from 6pm to 8pm on 01708 765200. The charity’s email support service is open weekdays and weekends during the crisis – messageinfo@supportline.org.uk.
Women’s Aid provides a live chat service – available weekdays from 8am-6pm and weekends 10am-6pm.
You can also call the freephone 24-hour National Domestic Abuse Helpline on 0808 2000 247.
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Most of Epstein’s sexual crimes took place on ‘Paedo island’ – Little Saint James in the US Virgin IslandsCredit: AP:Associated Press
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Dozens of haunting photos taken at Epstein’s ‘Paedo Island’ show him and Maxwell hosting famous pals and scantily-clad young girls and womenCredit: The Mega Agency
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A new cache of allegations against the Duke of Yorke have been unsealed – he denies wrongdoingCredit: PA
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Victims of Jeffrey Epstein – Sarah Ransome, Virginia Roberts Giuffre, and Marijke ChartouniCredit: Alamy
AI is coming to games, whether you like it or not. Last night’s Nvidia keynote showed just how powerful—and devastating—that’s going to be. The company’s CEO, Jensen Huang, showed off how its freshly announced “Omniverse Avatar Cloud Engine” (ACE) can create real-time interactive AI NPCs, complete with improvised voiced dialogue and facial animation.
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While the focus of AI’s incursion into gaming spaces has perhaps so far been mostly on the effects for artists, it’s writers who should already have the most to fear. Given how mediocre the standards are for NPC dialogue and quest texts in games, it’s absolutely inevitable that the majority of such content will be AI-written in the near future, despite the potential fury and protests that will come in its wake. But Nvidia’s reveal last night suggests that the consequences could be far farther-reaching, soon replacing voice actors, animators, lighting teams, the lot.
ACE is Nvidia’s “suite of real-time solutions” for in-game avatars, using AI to create characters who can respond to unique player interaction, in character, voiced, and with facial expressions and lip-syncing to match. To see it in action (or at least, in purported action—we’ve no way of verifying the footage the company played during the Computex 2023 keynote), take a look at this. It should start at 25 minutes, the clip starting at 27:
NVIDIA Taiwan
So what you’re seeing here is an in-game character responding in real-time to words the player says out loud, uniquely to how they phrased the questions, with bespoke dialogue and animation. The character has a backstory, and a mission it’s compelled to impart, but beyond that the rest is “improvisation,” based on the words the player says to it.
This is the most immediately obvious use of ChatGPT-like AI as we currently understand it, which is essentially a predictive text model writ large. It’s ideal for creating characters able to say coherent, relevant conversational dialogue, based on inputs.
Now, there are two very obvious issues to mention straight away, the first being how awful and flat the character’s performance is in this clip. But remember, this is the first iteration of this tech, and then put it in the context of how, until about ten minutes ago, computer-generated voices all sounded like Stephen Hawking. This’ll advance fast, as AI models better learn to simulate the finer nuances of human speech.
The second issue is that absolutely no one playing a game like this would stick to the script as happens in this clip. In fact, the first thing just about everyone would say to such an NPC would be something about fucking. For reference, see all text adventure players ever in the early 1980s. That’s going to be the more difficult aspect for games to overcome.
Screenshot: Nvidia / YouTube / Kotaku
Of course, application of the tech is going to be viewed as far less important in the face of just how many jobs ACE is looking to replace. Huang so nonchalantly mentions how the AI is not only providing the words and voice, but is doing the animation too. And this is in the wake of his previously explaining how AI is being used to generate the lighting in the scene, and indeed improve the processing power of the graphics technology that’s creating it all.
There’s no version of reality where this doesn’t see a huge number of people in games development losing jobs—albeit most likely those who haven’t gotten said jobs yet. Why hire new animators for your project when the AI will do it for you, backed up by the dwindling team you’ve already got? Who’s going to look for new lighting experts when there’s a lighting expert living inside your software? Let alone the writers who currently generate all the dialogue you currently skip past.
And this isn’t futuristic stuff to concern ourselves with somewhere down the line: it already exists, and it’s going to be appearing in games that release this year. With the announcement of ACE, this is all going to be exacerbated a lot faster than perhaps anyone was expecting.
For game studios, this is great news! The potential for such technology is incredible. Games that are currently only achievable by teams of hundreds will become realistically achieved by teams of 10s, even individuals. We, as players, will soon be playing games where we can genuinely roleplay, talk directly to in-game characters in ways the likes of Douglas Adams fantasized about and failed to achieve forty years ago.
