The Pub - Discuss Anything

[Vesper 28,499]

Weekend shoulder of pork

Serves 6
Prep: 10 minutes. Cook: 4 hours

Shoulder of pork does great things given time in the oven — crackling and tender pullable meat, joy.

Ingredients

• 2 tsp fennel seeds
• 2kg shoulder of pork, bone out
• Olive oil
• 6 jacket potatoes
• 6 onions
• 6 bay leaves
• 2 eating apples
• 160g watercress
• Red wine vinegar
• Mustard, to serve

Method

1. Preheat the oven to 220C fan/gas 9. Bash the fennel seeds in a pestle and mortar until fine. Sit the pork in a large roasting tray and randomly score the skin all over, rub with olive oil, the fennel, sea salt and black pepper, then roast for 1 hour. Halve the potatoes, and peel and halve the onions.

2. Remove the tray from the oven and baste the pork with the tray juices, then remove it to a plate for a moment. Add the potatoes and onions to the tray and carefully toss with the bay leaves, 2 tablespoons of red wine vinegar and a pinch of salt and pepper, then sit the pork on top.

3. Return the tray to the oven, reduce the temperature to 160C fan/gas 4 and roast for 3 hours, basting the pork and tossing the veg halfway, also adding a splash of water occasionally to prevent it from drying out, if needed.

4. Matchstick the apples, toss with the watercress, a little extra virgin olive oil, a swig of red wine vinegar and seasoning. Shred the pork and onions to your liking, then serve everything with the potatoes and a dollop of your favourite mustard on the side.

[Vesper 28,499]

Gnarly lamb Madras traybake

Serves 8
Prep: 9 minutes. Cook: 5 hours

Get this in the oven in no time, then sit back and enjoy the cooking aromas — perfect food to share.

Ingredients

• 1 x 2kg lamb shoulder, bone in
• 1 x 180g jar of Madras curry paste
• 250g yellow split peas
• 4 red onions
• 1 potato
• 4 tomatoes
• 6cm piece of ginger
• 1 bulb of garlic
• Half a bunch of coriander (15g)
• 12 cloves
• Olive oil

Method

1. Preheat the oven to 170C fan/gas 5, and boil the kettle.

2. Lightly score the skin side of the lamb all over in a criss-cross fashion, then season with sea salt and black pepper and rub with half of the curry paste.

3. Place the yellow split peas in your largest high-sided roasting tray, then peel, halve and add the onions and potato. Halve the tomatoes, peel and chop the ginger, break up the garlic bulb and roughly chop the coriander (stalks and all), then add everything to the tray, along with the remaining curry paste.

4. Stir in 1.2 litres of boiling kettle water, then sit the lamb on top, scatter over the cloves, tightly cover the tray with oiled tin foil and carefully transfer to the oven to roast for 4½ hours, or until the lamb is super-tender and melt-in-your-mouth — there’s no need to check it, just let the oven do its thing.

5. Remove the foil, baste the lamb well with the juices from the tray, and cook for a final 30 minutes, or until golden and gnarly.

6. Pull off chunks of meat and divide between serving plates, discarding any bones. Break up the potato, squeeze out the soft garlic and stir both through the split peas and veg, then plate up, along with some of the tasty juices.

[Vesper 28,499]

Roasted Med veg and feta traybake

Serves 4
Prep: 5 minutes. Cook: 30 minutes

Hero-ing those genius bags of mixed roasted veg from the freezer saves big on the prep time here.

Ingredients

• 300g couscous
• 1 x 400g tin of chickpeas
• 700g frozen chargrilled Mediterranean veg
• 1 heaped tbsp harissa paste
• 200g block of feta cheese
• 1 lemon
• 1 heaped tsp dried oregano
• Olive oil

Method

1. Preheat the oven to 200C fan/gas 7. Tip the couscous into a 25cm x 35cm roasting tray, then mix in the chickpeas, juice and all.

2. Toss the frozen veg with the harissa and a pinch of sea salt and black pepper, then layer on top of the couscous and chickpeas.

3. Quarter the feta and arrange on top, then halve the lemon, place half in the middle, and squeeze the other half over everything. Sprinkle over the oregano and drizzle with 2 tablespoons of olive oil.

4. Roast for 30 minutes, or until everything’s beautifully golden. Fork up the couscous, use tongs to squeeze over the jammy roasted lemon and serve. Delicious with a seasonal salad on the side.

Easy swaps
If you can’t get hold of frozen chargrilled Mediterranean veg, simply chop your favourite seasonal veg into 2cm chunks instead.

[Vesper 28,499]

Golden miso salmon

Serves 4
23 minutes

Going hard and fast with the grill adds an extra dimension of flavour, creating a satisfying meal.

Ingredients

• 500g asparagus
• 320g sugar snap peas
• Olive oil
• 1 tbsp dark miso
• 2 tbsp low-salt soy sauce
• 1 tbsp sesame oil
• 2 limes
• 4 x 130g salmon fillets, skin on, scaled, pin-boned
• 1 tbsp sesame seeds
• 1 carrot
• 2 spring onions
• 4 radishes
• 4 sprigs of fresh mint

Method

1. Preheat the grill to high. Snap the woody ends off the asparagus and place it in a 25cm x 35cm roasting tray with the sugar snap peas, then drizzle with 1 tablespoon of olive oil and shake to coat.

2. Mix the miso, soy and sesame oil in a shallow bowl, then finely grate in the zest of 1 lime and squeeze in the juice to make a marinade. Slice the salmon fillets in half lengthways, toss in the marinade, then drape over the veg in the tray, drizzling over the excess marinade. Scatter over the sesame seeds.

3. Grill for 12 minutes, or until the greens are blistered and the salmon is golden and just cooked through.

4. To make a quick pickle, peel and matchstick the carrot, trim and finely chop the spring onions, finely slice the radishes, pick and roughly chop the mint leaves, then dress it all with lime juice, sea salt and black pepper.

5. Scatter the pickle over the salmon in the tray, and serve. Delicious with noodles or fluffy rice on the side.

[Vesper 28,499]

Summery salmon traybake

Serves 4
20 minutes

Knowing something so colourful and beautiful can be on the table in just 20 minutes is joyful.

Ingredients

• 1 x 567g tin of peeled new potatoes
• Olive oil
• 4 x 150g salmon fillets, skin on, pin-boned
• 400g ripe cherry tomatoes, on the vine
• 100g black olives, pitted
• 1 heaped tbsp baby capers in brine
• Half a bunch of oregano (10g)
• 1 lemon
• 4 slices of prosciutto
• 4 heaped tsp pesto

Method

1. Preheat the grill to high. Drain the potatoes, place in a 25cm x 35cm roasting tray, toss with 1 tablespoon of olive oil, then place on the hob over a medium heat for 5 minutes, or until the potatoes begin to get golden.

2. In a bowl, mix the salmon, vine tomatoes, olives and capers with the oregano leaves, 1½ tablespoons of oil and half the lemon juice. Pull out the salmon fillets and wrap in the prosciutto, then pour the contents of the bowl into the tray and sit the salmon on top, skin side down.

3. Grill for 10 minutes, or until golden and the salmon is just cooked through.

4. Dollop over the pesto and serve with lemon wedges, for squeezing over.

Easy swaps
Green beans, runner beans, asparagus and sprouting broccoli would all be delicious here. Tinned potatoes are brilliant for quick cooking, but you could also swap in shop-bought potato gnocchi.

[Vesper 28,499]

Christopher Columbus was Spanish and Jewish, documentary reveals

Fifteenth century explorer’s true origins revealed after DNA analysis from samples buried in Seville Cathedral

https://www.theguardian.com/world/2024/oct/13/christopher-columbus-was-spanish-and-jewish-documentary-reveals

A view of the mausoleum of Christopher Columbus in the cathedral of Seville, Spain. A documentary has revealed the explorer was Jewish and from Spain. Photograph: Marcelo del Pozo/Reuters

The centuries-old mystery over Christopher Columbus’s nationality has been revealed by scientists in a Spanish TV documentary after using DNA analysis.

The 15th explorer was Jewish and from Spain, according to Columbus DNA: His True Origin, a programme broadcast on national broadcaster RTVE on Saturday to mark Spain celebrating its national day and commemorating Columbus’s arrival in the New World.

Researchers led by forensic expert Miguel Lorente tested tiny samples of remains buried in Seville Cathedral, long marked by authorities there as the last resting place of Columbus, although there had been rival claims. The team compared them with those of known relatives and descendants.

Countries have long argued over the origins and the final resting place of the divisive figure who led Spanish-funded expeditions from the 1490s onward, opening the way for the European conquest of the Americas.

Many historians have questioned the traditional theory that Columbus was from Genoa in north-west Italy. Other theories ranged from him being a Spanish Jew, Greek, Basque or Portuguese.

Lorente, briefing reporters on the research on Thursday, had confirmed previous theories that the remains in Seville belonged to the explorer.

He said: “Today it has been possible to verify it with new technologies, so that the previous partial theory that the remains of Seville belong to Christopher Columbus has been definitively confirmed.”

Research on the nationality had been complicated by a number of factors including the large amount of data but “the outcome is almost absolutely reliable,” Lorente added.

Columbus died aged 55 in the northwest Spanish city of Valladolid in 1506 but wished to be buried on the island of Hispaniola that is today shared by the Dominican Republic and Haiti.

His remains were taken there in 1542, then moved to Cuba in 1795 and then, it had been long thought in Spain, to Seville in 1898.

In 1877, workers found a lead casket buried behind the altar in a cathedral in Santo Domingo, the capital of the Dominican Republic, containing a collection of bone fragments the country says belong to Columbus.

Lorente said both claims could be true as both sets of bones were incomplete.

 

Read more:

 

 

DNA study confirms Christopher Columbus’s remains are entombed in Seville

 

[Vesper 28,499]

Stars behaving absurdly

For centuries, the only way in which to illuminate the mysteries of black holes was through the power of mathematics

https://aeon.co/essays/mathematics-is-the-only-way-we-have-of-peering-into-a-black-hole

A 3,000-light-year-long jet of plasma blasting from the M87 galaxy’s 6.5-billion-solar-mass central black hole, captured by the Hubble Space Telescope, September 2024. Courtesy NASA/ESA/STSCI

As celestial entities go, black holes are, paradoxically, both commonplace and extraordinary. They could be seen as commonplace due to their general ubiquity. Astrophysicists now believe that giant black holes – each with the mass of millions or billions of suns – inhabit the centres of practically every large galaxy, where they exert a powerful influence over star formation and other processes. There are more than 200 billion such galaxies, according to estimates, each thought to harbour about 100 million stellar- or star-sized black holes. Adding that up, we’re talking about something on the order of 10¹⁹ – or 10 billion billion – black holes. And far into the future, when the Universe is three times its current age (or about 40 billion years old), black holes will be all that’s left. That prediction was made in an analysis by the astrophysicists Fred C Adams and Gregory Laughlin in 1997 who concluded that, in the distant future, ‘the only stellarlike objects remaining [will be] black holes of widely disparate masses.’

 

The Event Horizon Telescope provided the first direct visual evidence of the supermassive black hole in the centre of Messier 87 and its shadow. Courtesy Wikipedia

On the other hand, black holes are also extraordinary. They’re the densest known objects in the Universe. The Sun, for instance, would be a black hole if all its matter were squeezed into a radius of less than 3 kilometres, rather than its actual radius of about 700,000 kilometres – a hypothetical compacting that would make our host star more than 10 quadrillion times denser than it is right now. Because matter in a black hole is, by definition, compressed into a relatively tiny space, its gravitational field is so strong that not even light can escape its indomitable grip. And that is why such an object is called ‘black’. Light cannot get out from the interior of a black hole, which means there is no possible way to look inside.

In view of the ineluctable opacity of black holes, one might wonder how we’ve managed to learn anything about them – especially when it comes to insights regarding their interior structure. While it’s certainly true that vital clues have been obtained from observational data, empirically obtained information has become available only in recent decades. However, for a period of about 200 years prior to that, all we had to rely on were physical theories and mathematics, and that’s the story we are telling here. From the late 18th century to the present day, mathematicians have tackled questions about these enigmatic objects that are beyond the range of any telescope yet devised – questions limited only by the reach of human imagination.

The very concept of black holes was invented through mathematics by the visionary, if little-known, scientist John Michell in 1783 (though he did not call them black holes at the time). In 1750, this low-profile rector of a small English village (Thornhill, 20 miles south of Leeds) demonstrated that the force between two magnetised objects drops off with the square of the distance between them – which was about three decades before the French scientist Charles-Augustin de Coulomb established that same fact. And in 1755, Michell proposed that earthquakes generate waves that propagate through the earth, ‘thereby helping establish the field of seismology’, according to the American Physical Society. Michell was the first to use statistical methods to demonstrate that stars often group together in binary pairs or in larger assemblages. He also conceived of a device for measuring the strength of gravity between two objects, which was used in a renowned experiment by Henry Cavendish in 1798, five years after Michell’s death.

 

Mitchell’s November 1783 letter to Cavendish and published in Philosophical Transactions, as ‘On the means of discovering the distance, magnitude, &c. of the fixed stars, in consequence of the diminution of the velocity of their light, in case such a diminution should be found to take place in any of them, and such other data should be procured from observations, as would be farther necessary for that purpose.’ By the Rev. John Michell, B.D. F.R.S. Courtesy the Royal Society, London

Michell was ahead of his time on all these fronts, but the ideas he conveyed in a 1783 letter to Cavendish – published a year later in the journal Philosophical Transactions – were more than a century ahead of the curve. Michell was originally motivated to devise a technique for determining the mass of a star. He subscribed to a theory, first advanced by Isaac Newton, that light consisted of a stream of particles known as corpuscles. He surmised that the gravitational pull of a star would slow the motion of these light particles. And if the star was big enough – ‘more than 500 times the diameter of the Sun’, he calculated – ‘all light emitted from such a body would be made to return towards it, by its own proper gravity.’ The gravitational field in such a case would be so strong that it would overcome the escape velocity of light itself, Michell proposed.

Their escape velocities are, indeed, greater than the speed of light

Any light produced by a star would be trapped inside, making the star invisible, but there still might be a way to detect its presence, he suggested: ‘If any other luminous bodies should happen to revolve about them, we might still perhaps from the motions of these revolving bodies infer the existence of the central ones with some degree of probability.’

In his remarkably discerning presentation, Michell got many things right about what we now call black holes. Their escape velocities are, indeed, greater than the speed of light, and the presence of many black holes has been deduced by scrutinising the motions of the luminous bodies that fall under their gravitational spell.

Through no fault of his own, however, Michell got many of the particulars wrong. We now know that the crucial determinant as to whether a star is destined to become a black hole depends on its density, not its diameter. Moreover, it was not until 1905 that Albert Einstein postulated the notion – supported by experiments both before and since – that light travels at a constant velocity and cannot be slowed down by the influence of gravity (as Michell and other 18th-century scholars had supposed). Optical experiments carried out by Thomas Young in 1801 bolstered the proposition that light had wave-like properties – evidence that led to the eventual downfall of Newton’s corpuscular theory of light.

Few scientists of Michell’s era were able to comprehend his arguments about dark, invisible stars, and his ideas consequently attracted little notice. To gain a detailed understanding of the curious objects that Michell conjured up, an entirely new way of thinking about matter, gravity, light and energy was required. That is just what Einstein provided on 25 November 1915 when he supplanted Newton’s then 230-year-old law of universal gravitation with the introduction of his own brainchild – the general theory of relativity.

Einstein offered a novel description of gravity that was, at its heart, geometrical. Gravity, he said, was not an attractive force exerted between two or more massive objects, as Newton had maintained centuries earlier. Instead, the phenomenon arose from the fact that a massive object curves the space and time around it. In this theory, space and time meld together to form the concept of ‘spacetime’ – and the curvature of spacetime, in turn, relates directly to its shape or geometry. According to Einstein’s view, it is the curvature of spacetime induced by a massive object like the Sun that holds other objects – such as the planets in the solar system – in its gravitational sway. This notion was summed up decades later by the physicist John Wheeler in his oft-cited statement: curved spacetime tells matter how to move; matter tells spacetime how to curve.

It took Einstein 10 long years to arrive at this result – during which, by his own admission, he worked harder than ever before in his life. And the outcome of this pursuit – which characterised gravity as a geometric effect – was somewhat ironic, given that Einstein had previously not held mathematics in high regard, nor had he devoted much effort to that subject area as a student. He knew little about geometry when he set out to formulate his general theory, and he had not even heard about the geometry of curved spaces invented in 1854 by the mathematician Bernhard Riemann, upon which his theory ultimately was based.

Einstein’s contribution here can be encapsulated within a single mathematical equation that might appear to be quite simple: G_ij = T_ij. The curvature of spacetime on the left side of this expression is equal to the distribution of matter and energy on the right. However, the letters G and T represent complex mathematical constructs known as tensors, which are 4-by-4 arrays of numbers and functions. What looks like a single equation above is, in fact, 10 linked ‘field’ equations. Each one of these equations would be difficult to solve on its own and, to make things harder, all 10 of them have to be solved simultaneously.

As the radius goes to zero, the pressure and density would approach infinity

Einstein did not know whether an exact solution to his field equations could ever be obtained. And when he used his equations to address a longstanding problem regarding Mercury’s anomalous orbit around the Sun, he sought and eventually found only approximate solutions.

Fortunately, Einstein’s paper of 25 November 1915 made its way into the hands of the physicist Karl Schwarzschild, who was then a 42-year-old soldier in the German army, assigned to the Russian front during the First Word War. Schwarzschild somehow found time during breaks in the military action not only to read Einstein’s paper but also to pursue his own ideas, which culminated in the first exact solution to the field equations of general relativity. The solution in question – which Schwarzschild sent to Einstein in a letter dated 22 December and published a month later – described the geometry of spacetime around a spherical, non-rotating star. Based on his determination of the geometry, Schwarzschild was able to work out the precise mechanics of Mercury’s orbit around the Sun, providing a mathematical description that had proven elusive until that time.

Karl Schwarzschild, early 20th C. Courtesy the AIP Emilio Segrè Visual Archives

In February, Schwarzschild published a second paper in which he explored, again mathematically, the interior of such a star. Using an argument reminiscent of the approach Michell had pursued some 130 years earlier – though propped up this time by the framework of Einstein’s new gravitational theory – Schwarzschild showed that, if enough mass were packed into a small enough radius, any light produced by the star would be stuck inside. This radius, known as the Schwarzschild radius, marks the boundary of what we now call the event horizon – the point of no return, or actually the surface of no return surrounding a black hole, beyond which any light or particles cannot get out.

Of perhaps even greater interest was what Schwarzschild found at the centre of his hypothetical sphere-like star. As the radius goes to zero, the pressure and density would approach infinity. Such a point would be called a singularity – a place where the laws of general relativity would break down and its predictions would go haywire. Schwarzschild, in other words, had identified some of a black hole’s key features back when the theory of general relativity was just a few months old.

Einstein, the author of that theory, doubted that the objects that sprung from Schwarzschild’s equations could actually exist. ‘If this result were real, it would be a true disaster,’ Einstein commented, reflecting his sense that the appearance of singularities would have a pathological effect on his newly unveiled theory.

Schwarzschild considered his solution an important theoretical contribution, but he too was unsure of the physical reality of the objects that his calculations gave rise to – objects that would be called black holes 50 years later. One of his qualms was that he couldn’t think of a viable mechanism for how such things could be formed, nor did he believe that the predicted infinite pressures could ever be realised. Schwarzschild, sadly, was unable to carry this work further, as he died a few months later, in May 1916, from a disease he contracted during the war.

Although mathematical analyses, drawing on Einstein’s theory, had raised the possibility of black holes, the concept remained an abstraction until persuasive arguments could be made as to how objects of this sort might actually materialise in the real world.

Some of the earliest inklings that black holes might be real came in 1930 when a 19-year-old Indian student, Subrahmanyan Chandrasekhar, travelled by ship from Madras to Southampton. Chandrasekhar was headed for the University of Cambridge, where he would pursue graduate studies in astrophysics. It was a long journey to England and, to pass the time, his thoughts turned – as many a young man’s mind might – to white dwarfs, a kind of star he’d become interested in after reading a book on the subject by Arthur Eddington, who was then a professor at Cambridge, as well as one of the world’s most esteemed astronomers. A white dwarf is the dense core of a star (roughly the size of the Sun) that is no longer ‘shining’, having exhausted its nuclear fuel and expelled almost all of its outer layer. Chandrasekhar wanted to know how big (or massive) a white dwarf could be without collapsing uncontrollably to a singularity of infinite density. He determined during this voyage that such a gravitational instability would occur in a white dwarf of 1.44 solar masses – a threshold that’s now called the Chandrasekhar limit.

Attendees of the Astrophysical Conference on Novae and White Dwarfs in Paris, 1939. Subrahmanyan Chandrasekhar is back row, second from right, Arthur Eddington front row, second from right. Courtesy the AIP Emilio Segrè Visual Archives

He presented this result at a meeting of the Royal Astronomical Society of London, but his findings were challenged by Eddington, who declared that Chandrasekhar’s ideas – based, as they were, solely on mathematics – bore no relation to the physical world. There ought to be a law of nature, Eddington said, ‘to prevent a star from behaving in this absurd way’. Any claims to the contrary, he added, were tantamount to ‘stellar buffoonery’.

Subrahmanyan Chandrasekhar and his wife Lalitha at the McDonald Observatory in 1939. Courtesy of Special Collections Research Center, University of Chicago Library

Chandrasekhar was ultimately vindicated. He won the 1983 Nobel Prize in Physics for this and related work on stellar evolution – the same year that he published a 672-page book, The Mathematical Theory of Black Holes. History, meanwhile, has proven Eddington wrong on this point: it turns out that our laws of nature do permit stars to behave in ‘such an absurd way’. And much of that was demonstrated by the physicist J Robert Oppenheimer and his colleagues in the late 1930s.

Oppenheimer generalised Chandrasekhar’s results on mass limits to stars other than white dwarfs – specifically to neutron stars, the cores of collapsed stars that are so dense, their electrons and protons get crushed together to form neutrons. (A tiny chunk of a neutron star, the size of a sugar cube, would weigh a billion tons.) Working with George Volkoff, Oppenheimer showed that a neutron star of more than about three solar masses will inexorably collapse into a black hole.

Einstein’s arguments were eventually refuted, and he never wrote another paper on black holes

And he went further still. In a separate paper in September 1939 with his then-graduate student Hartland Snyder, Oppenheimer filled in a key part of the picture that Chandrasekhar had not addressed, supplying a step-by-step mathematical account of the process whereby a star implodes to form a black hole. The mathematician Demetrios Christodoulou regarded this achievement as ‘very significant, being the first work on relativistic gravitational collapse’. By showing how a black hole can be formed, guided by Einstein’s equations, Oppenheimer and Snyder brought the product of Schwarzschild’s wartime musings much closer to plausibility.

Ironically, one month later, in October 1939, Einstein published a paper in The Annals of Mathematics in which he claimed to have set forth ‘a clear understanding as to why the “Schwarzschild singularities” do not exist in physical reality’ – essentially challenging a prediction that was borne of his own equations. Einstein’s arguments were eventually refuted, and he never wrote another paper on black holes.

Oppenheimer did not undertake any additional work on the subject either – despite the important contributions he’d already made. By 1942, he had other weighty matters on his mind, as he was asked to join the Manhattan Project that year. In 1943, he was named director of the Los Alamos Laboratory where the atomic bomb was being developed, and that work – for obvious reasons – overshadowed his prior theorising about black holes.

Another momentous breakthrough on the mathematics front came in 1963 when Roy Kerr, a New Zealander then based at the University of Texas, addressed a major shortcoming of the Schwarzschild solution: it applied only to spherical black holes that are stationary – a problem, given that every star and planet ever observed rotates to some extent. And rotating objects are not perfectly round; they have bulges at the centre. Kerr’s colleague at Texas, Alan Thompson, warned Kerr not to waste his time and effort on spinning black holes, because a new paper by the physicist Ezra Newman and two co-authors had just concluded that no solutions could be found for them.

Upon identifying a flaw in the paper by Newman et al, Kerr forged ahead. However, in order to make progress, he had to adopt two simplifying assumptions: first, that the black holes are rotating at a constant rate so that nothing in this scenario changes in time and, second, that even though the black holes were not perfect spheres, they were still symmetrical around a vertical axis – in the same way that an upright cylinder is nonspherical yet symmetrical around its vertical axis. With these assumptions, he soon hit upon a solution to the Einstein equations that applied to rotating black holes – or Kerr black holes, as they were soon called.

Kerr’s paper, which was published in July 1963, was just a page-and-a-half long, but it was considered a huge advance because he had furnished the best mathematical representation yet of a physically realistic black hole.

Chandrasekhar praised the accomplishment, saying that Kerr’s description applied flawlessly to ‘untold numbers of massive black holes that populate the Universe’.

In the fall of 1963, the mathematical physicist Roger Penrose came as a visiting professor to the University of Texas, where he engaged in many conversations with Kerr. One thing Penrose wondered about was whether the singularities that arose in Schwarzschild and Kerr black holes would also arise in objects that lacked those same symmetries. His answer came in his 1965 singularity theorem – and in other theorems that followed (some carried out with Stephen Hawking) – which earned Penrose a Nobel Prize in Physics in 2020. To explore this question, he developed new mathematical tools from geometry and the related subject of topology (the study and classification of the general, as opposed to exact, shape of objects). In 1965, Penrose proved that the event horizon of a Schwarzschild and Kerr black hole is something called a closed trapped surface – a surface whose curvature is so intense that even outward-pointing light beams get wrapped around and forced inward. Once a closed trapped surface is formed, he demonstrated, the collapse to a singularity is inevitable, regardless of symmetry considerations.

When Penrose gave a talk at Princeton about his theorem shortly after his January 1965 paper came out, the physicist Robert Dicke told him he’d ‘shown [that] general relativity is wrong’. There was no problem with the theory, Penrose countered, ‘[b]ut you do have to have singularities’ – which was a point that many physicists, including Einstein, had been hesitant to accept.

A complementary piece of this puzzle came in a 1979 theorem (published in 1983) by the mathematicians Richard Schoen and Shing-Tung Yau. Although Penrose had proved that a closed trapped surface will evolve (or devolve) to an object with a central singularity, he did not say how a closed trapped surface could be created in the first place. Schoen and Yau spelled out the precise conditions: when the matter density of a given region is twice that of a neutron star, a trapped surface will form, and that object will collapse directly to a black hole.

Their work, now referred to as the black hole existence proof, came out at a time when the existence of black holes was still open to debate. But by then, the evidence was starting to build. In the 1970s, astronomers proposed that a bright X-ray source called Cygnus X-1 was a stellar-sized black hole, and that the galaxy M87 harboured a supermassive black hole with the mass of billions of suns. And by the 1990s, a case was starting to be made that a supermassive black hole resided at the centre of practically every large galaxy.

Mathematicians still have a big role to play in unravelling the elusive properties of black holes

The case for the physical reality of black holes was dramatically strengthened on 14 September 2015, when detectors from the LIGO Observatory in Louisiana and Washington state intercepted gravitational waves for the first time in history – the product, scientists asserted, of the violent collision of two black holes, each with the mass of about 30 suns, which took place about 1.3 billion light-years from Earth (and hence about 1.3 billion years ago). Gravitational waves from roughly 100 other collisions and mergers – involving black holes and their ultra-dense kin, neutron stars – have since been detected.

In 2019, a global network of radio telescopes that collectively comprise the Event Horizon Telescope captured an image of the outer edge of an enormous black hole (with the mass of billions of suns) lying in the centre of the M87 galaxy. In 2022, the Event Horizon Telescope obtained an image of the ‘supermassive’ black hole in the centre of our own galaxy, the Milky Way, with the mass of 4 million suns.

In view of this and other compelling evidence, the existence of black holes is no longer a matter of dispute among astrophysicists. But that should not be taken to mean that our understanding of these objects is complete. Nothing could be further from the truth. And mathematicians still have a big role to play in unravelling the elusive properties of black holes.

To cite a recent example, in 2022, the mathematicians Elena Giorgi, Sergiu Klainerman, and Jérémie Szeftel proved that slowly rotating Kerr black holes are stable, meaning that if you perturb a Kerr black hole in a gentle way, by giving it a little ‘bump’, it will settle down and behave in just the way the Kerr solution prescribed. In 2023, Marcus Khuri and Jordan Rainone proved that an infinite family of black holes, configured in a variety of elaborate shapes, are mathematically possible in higher-dimensional spaces that extend beyond the three familiar dimensions. While such exotic entities are by no means certain to exist, there is nothing in mathematics that rules them out.

Meanwhile, there are several open problems concerning black holes that have kept mathematicians busy for more than half a century. One is the cosmic censorship conjecture, first posed by Penrose in 1969, which holds (in one of its various forms) that singularities must be concealed behind an event horizon. Or, to put it more starkly, there are no ‘naked’ singularities. The second problem relates to the no-hair theorem (or actually conjecture), which posits that black holes can be fully characterised by their mass, spin and charge. Restating that in slightly different terms, there is no way to distinguish between two black holes that have the same mass, spin and charge. Special cases have been solved for both of these enduring problems, but there are no complete solutions for either of them.

Scientists still have deeply profound questions about black holes. And though technology has finally enabled us to glimpse the tumultuous exteriors of these objects, mathematics is often all we have to illuminate those places that our instruments cannot penetrate – including the shadowy realm, deep inside a black hole, that is otherwise obscured by an event horizon.

This essay was adapted from The Gravity of Math: How Geometry Rules the Universe (Basic Books, 2024) by Steve Nadis and Shing-Tung Yau.

[Vesper 28,499]

The tentacles of language are always on the move

An evolutionary biologist explains how human language can shift as slowly or rapidly as organisms adapting to life on Earth

https://psyche.co/ideas/the-tentacles-of-language-are-always-on-the-move

 

As an evolutionary biologist, I see the history of species in my own body. In my spinal cord, I see half a billion years of evolution, starting with the flexible cord of a tiny proto-fish in the ancient Cambrian period; I see the steps backwards from my brain to the mere subtle thickening of the nerve cord at the front end of that same proto-fish.

In contrast with evolutionary biology, I have little formal training in linguistics beyond two classes in artificial intelligence approaches to language at the University of Vienna. The classes predated ChatGPT by decades and were held in a building that once housed a late-medieval monastery, which seems fitting in retrospect; the computer science of two decades ago feels akin to the Middle Ages.

Evolution is more like human language than computer science. It produces major changes in the lineages of animals and plants over hundreds of millions of years, and then occasionally goes into sprint mode, such as in the great African Rift lakes, where a rainbow of new species has evolved in only hundreds of thousands of years. The grand developments of human languages, likewise, can seem impossibly slow – and then suddenly race ahead. The early Indo-European and major language groups of modern Europe and South Asia saw slow, grand developments, yet they too can shift in a lifetime or less. I’m exhibit number one. My exceedingly international biography, with time spent living in Austria, the UK, Germany, the US, Japan, Australia and the Philippines, helped me see such shifts, and gives me more food for linguistic thought than a more stationary human language-user would ever see.

I’ll start with German, the official language of Austria, where I grew up. German in Austria is by no means a ‘pure’ Germanic language, but rather a mix of German, south-Slavic vocabulary and, especially in the Viennese dialect, Yiddish, the German dialect of the Jewish diaspora that emerged in the later Middle Ages.

Knowing a language provides the speaker with insights a native speaker might miss because their language production will be too automatic

Yiddish is an especially interesting input into the body of Viennese German: the language developed as a Germanic tongue more than 1,000 years ago as displacements of the Jewish people split it into eastern and western branches. The eastern branch of the Yiddish language developed in relative isolation from the rest of the Germanic languages. Then, in the 19th century, the pogroms in eastern Europe led many speakers of eastern Yiddish back to central Europe, where their vocabulary entered Viennese German. At a heavy metal concert, when my teenage self remarked at the kieberer (a Yiddish word loaned into Viennese for ‘police’, versus the ‘polizei’ of straight-up German), I was invoking a millennium of European language mixing.

I grew up speaking German, but it wasn’t quite my ‘mother tongue’. My mother is a (now retired) high-school English teacher, and her love always lay more with Shakespeare’s language than with Schiller’s. I enjoyed reading in English from a young age, and we spent a semester in England when I was seven years old. While I have an accent in my pronunciation of spoken English, it never felt like a foreign language to me. This turned out to be a good starting point for writing scientific manuscripts and popular science articles. Knowing a language in depth (while not being exposed to it in the critical period of language acquisition at the beginning of life) provides the speaker and writer with insights an actual native speaker might miss because their language production will be too automatic. While I am certainly not putting myself near the pantheon of Joseph Conrad and Vladimir Nabokov – both literary greats in a language of which they were not native speakers – I am almost sure they profited from the distance I mention above.

A few years ago, I decided to move to the Philippines. There are a number of pleasant aspects to life in this archipelago of 7,000-plus tropical islands and, for the fish biologist, there is no better place to stick your head underwater. Fish biodiversity is stunningly high around the coral reefs of the Philippines and, after a decade of diving the islands’ waters, I still find fish species new to me.

I spent a lot of time underwater, but not all. Love struck, and with it came the unique chance to learn one of the many Filipino languages from a native speaker up close.

My spouse grew up with Bisayan, the main language spoken in the central and southern Philippines. At its core, Bisayan is an Austronesian language, related to Indonesian and the languages of the Pacific Islands. However, centuries of Spanish colonial rule added a rich Romance language vocabulary – in unusual ways. Nouns were imported without adapting the Spanish grammar for creating plurals or adding articles. The Bisayan word for table is lamesa – the Spanish mesa, fused to la, the Spanish feminine definite article. Hence, ‘The table is high’ in Bisayan is ‘Taas ang lamesa’ – a sentence with the Austronesian article ang followed by the Romance article la, which was swallowed by the Spanish noun when it became a Bisayan word.

The ATM machines often give the language options as ‘English’ and ‘Taglish’

Conversely, there is still a Spanish creole language in the Philippines, Chavacano, which is spoken in the south of the island of Mindanao. This is a language akin to 19th-century Spanish, with a grammar different from modern Castilian Spanish, but nevertheless a Romance language. Separating Chavacano and Bisayan is a lengthy ferry ride and a day of travel over mountains and through areas not particularly safe for the outsider due to the decades-long religious-political strife for Muslim independence. The broken-up geography and politics of the Philippines has certainly contributed to the country’s great diversity in languages.

Since the Philippines were a US territory from 1898 to 1946, the English language gained a strong foothold in the country, extending US culture and soft power. The Filipinos, pragmatic people in action and word, liberally mix English into Tagalog (the national language of the Philippines) and Bisayan. The ATM machines often give the language options as ‘English’ and ‘Taglish’, the crossover idiom of English and Tagalog, instead of offering to show the menu in pure Tagalog.

English is the second official language of the Philippines, alongside Tagalog. As the language of the economically and politically powerful Americans, it has gained an especially strong following among the upper-middle and upper classes of the country. Well-off friends of mine speak to their children exclusively in English. If you listen to an interview with a celebrity actress in the capital Manila, you will hear agitated chatter in Tagalog, interspersed with phrases and half-sentences in English. I assume it’s the details of the history of a region that make communities of speakers either open to foreign influences, or dogmatic and insular when it comes to modifying their native language, such as the French-speaking Canadians, who strive to keep English out, even with legal means.

Just as Austrian German is distinct from German, Philippine English is a separate dialect, on a par with Australian, South African or American English. I would argue that due to its constant contact with a wide variety of Austronesian languages (there are hundreds more in addition to Tagalog and Bisayan), it’s more derived than these variants of English. In several cases, somewhat unusual uses of verbs were turned into nouns, creating newly coined words, proper neologisms. For example, while a ‘holdup’ is, comprehensible to any native speaker of English, a robbery, in Philippine English, a ‘holdupper’ became a term for a robber.

My favourite term in Philippine English is ‘double dead’. If your cow dies from pneumonia (dead once) and you don’t want to waste the meat, you just slaughter it anyway (dead twice), and cut it into steaks. The practice happens among the poor country folk who can’t afford to waste the effort they put into raising such a big animal. The term is honest and descriptive. It couldn’t be any clearer that the animal’s life is over; it’s dead not only once but twice. This is in stark contrast to many more recently coined terms in standard or American English: an ‘unsheltered person’ does nothing to paint a picture of a man with psychiatric problems, poor hygiene and no cash left in his pockets who was abandoned by his family and society. The term obfuscates, while ‘double dead’ vividly describes.

If one of the three languages lacks a trick available in another, he adds it

During the first three years of my son’s life, Austrian German from the southward movement of ancient Germanic tribes and borrowed Yiddish from the East converged with Bisayan, including the adoption of American and Spanish vocabulary in his mind.

At age three, he is comfortable in German, and somewhat less in Bisayan and English. If one of the three languages lacks a trick available in another, he adds it. He assigns new grammatical constructs to languages that don’t have them. Bisayan doesn’t have grammatical genders like German; there is only one gender-neutral article. This doesn’t deter our son: he made the Bisayan worm (das ulod) neutral, in an interesting contrast with the German worm (der Wurm, masculine). Once you start learning to speak German, you feel the urgent need to add gendered articles to words!

And Bisayan also received some Anglo-Saxon tenses from him: hilak, the Bisayan word for ‘crying’, became hilak-ing. There is no such verb form in Bisayan, to my knowledge. But just like with the German gendered articles, anyone who had got the taste for using the English ‘ing’ form in communicating will want to use it in any language they speak.

The scholarly literature on bilingualism is home to an agitated discussion of the benefits or harms of bringing up a child with two or more languages. Ideological divisions run deep in this literature. In my experience, children are extremely keen to express themselves, by whatever means possible, and they will handle more than one language quite naturally. To come back to our son, he knows, at age three, which set of grandparents to speak to in which language. The development of languages, with their mixing and reshuffling over the course of centuries, almost certainly builds on the dynamics of multilingual families.