Posts Tagged ‘Isaac Newton’
“Here comes the sun”*…
Further, in a fashion, to last Wednesday’s post… We’ve looked before (e.g., here) at the potential havoc that solar storms could wreak on our electified lives. Now, as Paul Voosen reports, scientists are speculating on a defense, suggesting that gases released from satellites could slash the threat of severe “space weather”…
When violent eruptions from the Sun slam into Earth’s magnetic field, they do more than paint aurorae across the night sky. They can scramble the electronics of satellites and induce powerful ground currents that knock out electrical grids. It’s been estimated that a one-in-a-100-year solar storm like the 1859 Carrington Event could cause more than $3 trillion of damage to the power grid alone. [See here.]
Yet for decades, society’s only defenses have been better space weather forecasts and more durable technology on the ground and in space. Now, a small group of space physicists says humanity should intervene and weaken solar storms in real time. In a study published [recently] in Space Weather, the researchers describe a provocative proposal called “StormWall”: a fleet of satellites that would release hundreds of tons of gases into space just before a solar storm strikes Earth. Computer simulations suggest the artificial cloud could cut the intensity of a major solar storm by half or more. “It’s as if you could install an airbag in the magnetosphere,” says Daniel Welling, a co-author and space physicist at the University of Michigan.
Call it “helioengineering”—a deliberate intervention in the near-Earth space environment. But unlike controversial geoengineering proposals to mitigate global warming, which would inject long-lived Sun-blocking particles into the atmosphere, StormWall’s protective gases would dissipate within hours, says Brian Walsh, the study’s lead author and a space physicist at Boston University. “It’s waiting for us to do some temporary modification.”
The proposal would require more extensive simulations and testing. But it is “highly innovative and appears to be quite feasible in the near term,” says Allison Jaynes, a space physicist at the University of Iowa. It’s a “laudable idea,” adds Gurudas Ganguli, a space physicist at the U.S. Naval Research Laboratory (NRL)…
[Voosen explains the technology proposed and considers the challenges in its implementation…]
… Of course, like an airbag, StormWall would have to be replaced if deployed. But just as NASA and other space agencies are studying how to protect the planet from asteroids [and here], Walsh says there’s a good argument for fortifying an electronics-dependent society against massive solar eruptions. “If we lose all our power grids and can’t use the internet for 6 years, it would be traumatic.”
“Radical proposal would block solar storms with orbital ‘airbag’” from @science.org.
* George Harrison
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As we apply sunscreen, we might send bright birthday greetings to Godfried Wendelen; he was born on this date in 1580. And astronomer (and Catholic priest) known as “the Ptolemy of his time.” Despite the tenets of his church, Wendelen was an audacious proponent of the Copernican theory that the planets orbit around the sun. He made more accurate measurements of the distance to the sun than those previously made by Aristachus (2,000 years earlier) from the geometrical relationships at the exact time of a half-moon.
Wendelen is considered by many as a precursor of Kepler and Newton, and was in fact cited by Newton in his Principia. The crater Vendelinus on the Moon is named after him
“Something that doesn’t actually exist can still be useful”*…
Gregory Barber on ultrafinitism, a philosophy that rejects the infinite. Ultrafinitism has long been dismissed as mathematical heresy, but it is also producing new insights in math and beyond…
Doron Zeilberger is a mathematician who believes that all things come to an end. That just as we are limited beings, so too does nature have boundaries — and therefore so do numbers. Look out the window, and where others see reality as a continuous expanse, flowing inexorably forward from moment to moment, Zeilberger sees a universe that ticks. It is a discrete machine. In the smooth motion of the world around him, he catches the subtle blur of a flip-book.
To Zeilberger, believing in infinity is like believing in God. It’s an alluring idea that flatters our intuitions and helps us make sense of all sorts of phenomena. But the problem is that we cannot truly observe infinity, and so we cannot truly say what it is. Equations define lines that carry on off the chalkboard, but to where? Proofs are littered with suggestive ellipses. These equations and proofs are, according to Zeilberger — a longtime professor at Rutgers University and a famed figure in combinatorics — both “very ugly” and false. It is “completely nonsense,” he said, huffing out each syllable in a husky voice that seemed worn out from making his point.
As a matter of practicality, infinity can be scrubbed out, he contends. “You don’t really need it.” Mathematicians can construct a form of calculus without infinity, for instance, cutting infinitesimal limits out of the picture entirely. Curves might look smooth, but they hide a fine-grit roughness; computers handle math just fine with a finite allowance of digits. (Zeilberger lists his own computer, which he named “Shalosh B. Ekhad,” as a collaborator on his papers.) With infinity eliminated, the only thing lost is mathematics that was “not worth doing at all,” Zeilberger said.
Most mathematicians would say just the opposite — that it’s Zeilberger who spews complete nonsense. Not just because infinity is so useful and so natural to our descriptions of the universe, but because treating sets of numbers (like the integers) as actual, infinite objects is at the very core of mathematics, embedded in its most fundamental rules and assumptions.
At the very least, even if mathematicians don’t want to think about infinity as an actual entity, they acknowledge that sequences, shapes, and other mathematical objects have the potential to grow indefinitely. Two parallel lines can in theory go on forever; another number can always be added to the end of the number line.
Zeilberger disagrees. To him, what matters is not whether something is possible in principle, but whether it is actually feasible. What this means, in practice, is that not only is infinity suspect, but extremely large numbers are as well. Consider “Skewes’ number,” eee79. This is an exceptionally large number, and no one has ever been able to write it out in decimal form. So what can we really say about it? Is it an integer? Is it prime? Can we find such a number anywhere in nature? Could we ever write it down? Perhaps, then, it is not a number at all.
This raises obvious questions, such as where, exactly, we will find the end point. Zeilberger can’t say. Nobody can. Which is the first reason that many dismiss his philosophy, known as ultrafinitism. “When you first pitch the idea of ultrafinitism to somebody, it sounds like quackery — like ‘I think there’s a largest number’ or something,” said Justin Clarke-Doane, a philosopher at Columbia University.
“A lot of mathematicians just find the whole proposal preposterous,” said Joel David Hamkins, a set theorist at the University of Notre Dame. Ultrafinitism is not polite talk at a mathematical society dinner. Few (one might say an ultrafinite number) work on it. Fewer still are card-carrying members, like Zeilberger, willing to shout their views out into the void. That’s not just because ultrafinitism is contrarian, but because it advocates for a mathematics that is fundamentally smaller, one where certain important questions can no longer be asked.
And yet it gives Hamkins and others a good deal to think about. From one angle, ultrafinitism can be seen as a more realistic mathematics. It is math that better reflects the limits of what people can create and verify; it may even better reflect the physical universe. While we might be inclined to think of space and time as eternally expansive and divisible, the ultrafinitist would argue that these are assumptions that science has increasingly brought into question — much as, Zeilberger might say, science brought doubt to God’s doorstep.
“The world that we’re describing needs to be honest through and through,” said Clarke-Doane, who in April 2025 convened a rare gathering of experts to explore ultrafinitist ideas. “If there might only be finitely many things, then we’d better also be using a math that doesn’t just assume that there are infinitely many things at the get-go.” To him, “it sure seems like that should be part of the menu in the philosophy of math.”
For mathematicians to take it seriously, though, ultrafinitists first need to agree on what they’re talking about — to turn arguments that sound like “bluster,” as Hamkins puts it, into an official theory. Mathematics is steeped in formal systems and common frameworks. Ultrafinitism, meanwhile, lacks such structure.
It is one thing to tackle problems piecemeal. It is quite another to rewrite the logical foundations of mathematics itself. “I don’t think the reason ultrafinitism has been dismissed is that people have good arguments against it,” Clarke-Doane said. “The feeling is that, oh, well, it’s hopeless.”
That’s a problem that some ultrafinitists are still trying to address.
Zeilberger, meanwhile, is prepared to abandon mathematical ideals in favor of a mathematics that’s inherently messy — just like the world is. He is less a man of foundational theories than a man of opinions, of which he lists 195 on his website. “I cannot be a tenured professor without doing this crackpot stuff,” he said. But one day, he added, mathematicians will look back and see that this crackpot, like those of yore who questioned gods and superstitions, was right. “Luckily, heretics are no longer burned at the stake.”…
Read on for the history of ultrafinitism, the critical dialogue surrounding it, and its implications: “What Can We Gain by Losing Infinity?” from @gregbarber.bsky.social in @quantamagazine.bsky.social.
* Ian Stewart (whose point was somewhat different from Zeilberger’s :-), Infinity: A Very Short Introduction
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As we engage the endless, we might spare a thought for a man whose work touched on the infinitesimal, Isaac Barrow; he died on this date in 1677. A theologian and mathematician, he played a key role in the development of infinitesimal calculus (in particular, for a proof of the fundamental theorem of calculus). Barrow was the inaugural holder of the prestigious Lucasian Professorship of Mathematics at the University of Cambridge, a post later held by his student, Isaac Newton (who, of course, shares primary credit for the development of calculus with Gottfried Wilhelm Leibniz).
“The bigger, the better”*…
Thea Applebaum Licht with a reminder that, when it comes to size, Texas has got nothing on California…
Between about 1905 and 1915, the United States entered a golden age of postcards. Cheaper and faster mail service, the advent of “divided back” cards (freeing the entire front for images), and improved commercial printing all drove a new mass market for collectible communication. It was at this same moment that a craze for “tall-tale” or “exaggeration” postcards reached its peak. By cutting, collaging, and re-photographing images, artists created out-of-proportion illusions. One of the most popular genres was agricultural goods of fantastic dimensions.
Nowhere were such postcards more popular than in the western states. There, in the heart of the tough business of agriculture, illustrations of folkloric American abundance were understandable favorites. Pride and place were tied up with the prodigious crops. Supersized fruits and vegetables were often accompanied by brief captions: “How We Do Things at Attica, Wis.”, “The Kind We Raise in Our State”, or “The Kind We Grow in Texas”. Photographers like William “Dad” H. Martin and Alfred Stanley Johnson Jr. captured farmers harvesting furniture-sized onions and stacking corn cobs like timber, fisherman reeling in leviathans, and children sharing canoe-like slices of watermelon.
In the series of exaggeration postcards [produced in the run-up to the postcard boom, then published during it] collected [here], it is California that takes center stage. Produced by the prolific San Francisco–based publisher Edward H. Mitchell, each card features a single rail car rolling through lush farmland. Aboard are gargantuan, luminous fruits and vegetables: dimpled navel oranges, a dusky bunch of grapes, and mottled walnuts. Placed end-to-end, the cards would make a colorful train crossing California’s fertile valleys. Unlike other, more action-packed “tall-tale” cards — filled with farmers, fisherman, and children for scale — Mitchell’s series is restrained. Sharply illuminated, the colossal cargo lean toward artwork rather than gag. “A Carload of Mammoth Apples”[here], green-yellow and gleaming, could have been plucked from Rene Magritte’s The Son of Man [here].
Fabulous fruit and vegetables: “Calicornication: Postcards of Giant Produce (1909),” from @publicdomainrev.bsky.social.
In other art-related news: (very) long-term readers might recall that, back in 2008, (R)D reported that London’s Daily Mail believed that it had tracked him down, and that he is Robin Gunningham. Now as Boing Boing reports:
Anyone reading Banksy’s Wikipedia article at any point since a famous Mail on Sunday exposé in 2008 would likely get the impression the secretive stenciler is probably Robin Gunningham or Robert Del Naja, artists who came from the Bristol Underground. Reuters, having conducted extensive research into their movements, finds both men present at critical moments, but only one at all of them: an arrest report from New York City puts Gunningham firmly in the frame, and recent public records from Ukraine put it beyond doubt.
We later unearthed previously undisclosed U.S. court records and police reports. These included a hand-written confession by the artist to a long-ago misdemeanor charge of disorderly conduct – a document that revealed, beyond dispute, Banksy’s true identity. … Reuters presented that man with its findings about his identity and detailed questions about his work and career. He didn’t reply. Banksy’s company, Pest Control, said the artist “has decided to say nothing.”
His long-time lawyer, Mark Stephens, wrote to Reuters that Banksy “does not accept that many of the details contained within your enquiry are correct.” He didn’t elaborate. Without confirming or denying Banksy’s identity, Stephens urged us not to publish this report, saying doing so would violate the artist’s privacy, interfere with his art and put him in danger.
Del Naja (better known for other work) evidently participates in painting the murals and is perhaps the stencil draftsman (Banksy: “he can actually draw”). Banksy’s former manager, Steve Lazarides, organized a legal name change for Gunningham after the Mail on Sunday item, which successfully ended records for Banksy’s movements under his birth name and stymied researchers—until Reuters figured out the new one by poring through Ukrainian public records on days Del Naja was there. Gunningham used the name David Jones, among the most common in the U.K. If it rings a bell, you might be thinking of another famous British artist was who obliged by his record company to find something more unique.
* common idiom
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As we live large, we might spare a thought for Isaac Newton; he died on this date (O.S.) in 1727. A polymath who was a key figure in the Scientific Revolution and the Enlightenment that followed, Newton was a mathematician, physicist, astronomer, alchemist, theologian, author, and inventor. He contributed to and refined the scientific method, and his work is considered the most influential in bringing forth modern science. His book Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687, achieved the first great unification in physics and established classical mechanics. He also made seminal contributions to optics, and shares credit with the German mathematician Gottfried Wilhelm Leibniz for formulating infinitesimal calculus. (Newton developed calculus a couple of years before Leibniz, but published a couple of years after.) Newton spent the last three decades of his life in London, serving as Warden (1696–1699) and Master (1699–1727) of the Royal Mint, a role in which he increased the trustworthiness/accuracy and security of British coinage in a way crucial to the rise of Great Britain as a commercial and colonial power.
Newton, of course, had a famous relationship with fruit:
Newton often told the story that he was inspired to formulate his theory of gravitation by watching the fall of an apple from a tree. The story is believed to have passed into popular knowledge after being related by Catherine Barton, Newton’s niece, to Voltaire. Voltaire then wrote in his Essay on Epic Poetry (1727), “Sir Isaac Newton walking in his gardens, had the first thought of his system of gravitation, upon seeing an apple falling from a tree.” – source
Newton’s apple is thought to have been the green skinned ‘Flower of Kent’ variety.
“Alchemy. The link between the immemorial magic arts and modern science. Humankind’s first systematic effort to unlock the secrets of matter by reproducible experiment.”*…
As (AI/tech pro and writer) Dale Markowitz explains, for scientists of yore anything—from mermaids to alchemy—was on the table…
In 1936, the economist John Maynard Keynes purchased a trove of Isaac Newton’s unpublished notes. These included more than 100,000 words on the great physicist’s secret alchemical experiments. Keynes, shocked and awed, dubbed them “wholly magical and wholly devoid of scientific value.” This unexpected discovery, paired with things like Newton’s obsession with searching for encrypted messages in the Bible’s Book of David, showed that Newton “was not the first of the age of reason,” Keynes concluded. “He was the last of the magicians.”
When it came to fascination with the occult, Newton was hardly alone. Many contemporary scientists may cast aspersions on spells, mythical tales, and powers of divination. Not so for many of the early modern thinkers who laid the foundations of modern science. To them, the world teemed with the uncanny: witches, unicorns, mermaids, stars that foretold the future, base metals that could be coaxed into gold or distilled into elixirs of eternal life.
These fantastical beliefs were shared by the illiterate and educated elite alike—including many of the forebears of contemporary science, including chemist Robert Boyle, who gave us modern chemistry and Boyle’s law, and biologist Carl Linnaeus, who developed the taxonomic system by which scientists classify species today. Rather than stifling discovery, their now-arcane beliefs may have helped drive them and other scientists to endure hot smoky days in the bowels of alchemical laboratories or long frigid nights on the balconies of astronomical towers.
To understand the role of magic in spurring scientific progress, it helps to understand the state of learning in Europe in those times. Throughout the Middle Ages, many scholars were fixated on the idea that knowledge could only be gleaned from ancient texts. Universities taught from incomplete, often poorly translated copies of Aristotle, Ptolemy, and Galen. To stray from the giants was a crime: In 14th-century Oxford, scholars could be charged 5 shillings for contradicting Aristotle. Curiosity was considered a sin on par with lust. A powerful motivator was needed to shuck off ancient thinking.
One of the first influential thinkers to break with the old ways was the 16th-century Swiss-German physician Paracelsus. The father of toxicology, known for his pioneering use of chemicals in medicine, Paracelsus was among the first of his time to champion the importance of experimentation and observation—a philosophy which would set the foundations for the scientific method. Paracelsus showed the scholars what he thought of their old books by publicly burning his copies of Galen and Avicenna.
But what led him to this experiment-first approach? Perhaps it was because, to Paracelsus, experimentation was a kind of magic. His writing fuses scientific observation with the occult. To him, medicine, astrology, and alchemy were inextricably linked—different ways of unveiling sacred truths hidden in nature by God. Paracelsus considered himself a kind of magus, as he believed Moses and Solomon had been, as Newton would view himself 150 years later. Paracelsus believed, though, that divine knowledge could be gained not just by studying scripture, but also by studying nature. The alchemical workbench, the night sky—these were even surer routes to God than any dusty old textbook…
[Markowitz recounts the stories of Tycho Brahe [almanac entry here], his patron Holy Roman Emperor Rudolf II, Robert Boyle, William Harvey, and Linnaeus [here], who, in 1749, urged the Royal Swedish Academy of Sciences to launch a hunt for mermaids…]
… To our contemporary ears, most all of this may sound fairly ridiculous. But as Edward Donlick puts it in The Clockwork Universe, “The world was so full of marvels, in other words, that the truly scientific approach was to reserve judgment about what was possible and what wasn’t, and to observe and experiment instead.” To the 17th-century scientist, anything was on the table, so long as it could be experimentally studied.
Today, we know how the story ends: Belief in astrology, alchemy, and witchcraft declined in places where empiricism and skepticism became cornerstones of science. But perhaps early scientists’ fascination with the occult should remind us of other tenants of discovery: open-mindedness and curiosity. Witches, mermaids, and the philosopher’s stone may not have survived modern scrutiny, but it was curiosity about them that drove real progress and allowed early thinkers to stray from established norms. In this sense, curiosity is a kind of magic…
“How the Occult Gave Birth to Science,” from @dalequark.bsky.social in @nautil.us.
See also: “The importance of experimental proof, on the other hand, does not mean that without new experimental data we cannot make advances” and “Everyone knows Newton as the great scientist. Few remember that he spent half his life muddling with alchemy, looking for the philosopher’s stone. That was the pebble by the seashore he really wanted to find.”
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As we think about transmutation, we might spare a thought for a rough contemporary (and fellow-traveler) of Newton’s, Rasmus Bartholin; he died on this date in 1698. A physician, mathematician, and physicist, he is best known for his discovery of the optical phenomenon of double refraction. In 1669, Bartholin observed that images seen through Icelandic feldspar (calcite) were doubled and that, when the crystal was rotated, one image remained stationary while the other rotated with the crystal. Such behaviour of light could not be explained using Newton’s optical theories of the time. Subsequently, this was explained as the effect of the polarisation of the light.
Bartholin also wrote a several mathematical works and made astronomical observations (including the comets of 1665). And he is famed for his medical work, in particular his introduction of quinine in the fight against malaria.
(Bartholin’s family was packed with pioneering scientists, 12 of whom became professors at the University of Copenhagen; perhaps most notable, his elder brother Thomas, who discovered the lymphatic system in humans and advanced the theory of “refrigeration anesthesia”(being the first to describe it scientifically).
“Where all think alike there is little danger of innovation”*…
Last week, Northwestern Professor Joel Mokyr was awarded a half-share in The Nobel Prize in Economic Sciences (AKA The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel) “for having identified the prerequisites for sustained growth through technological progress.” Anton Howes explains why this is noteworthy…
Among today’s winners of the Nobel prize in Economics is Joel Mokyr, the professor at Northwestern whose name is indelibly associated with the primacy of innovation to modern economic growth – the gradual, sustained, and unprecedented improvement in living standards that first Britain, and then country after country, have enjoyed over the past few hundred years. It was reading Mokyr’s The Enlightened Economy that first opened my eyes to the importance of studying the history of invention to explaining the causes of the Industrial Revolution, which I have since made my career.
What makes this Nobel win so remarkable, and so pleasantly surprising, is that Mokyr’s work is not the kind that is often published by economics journals, or even many economic history journals anymore. Over the past few decades, journal editors and peer-reviewers have increasingly insisted that papers must present large datasets that have been treated using complex statistical methods in order to make even the mildest claims about what caused what. Although Mokyr is a master of such methods – he was one of the early pioneers of economic history’s quantitative turn – the work for which he has won the prize is firmly and necessarily qualitative.
Mokyr’s is the economic history that gets written up in books – his classics are The Lever of Riches, The Gifts of Athena, The Enlightened Economy, and A Culture of Growth – and in readable papers shorn of unnecessary formulae. His is history accessible to the layman, though rigorously applying the insights of economics. The prize is a clear signal from the economics profession that it doesn’t just value the application of fancy statistical methods; its highest prize can go to works of history.
Whereas most of the public, and even many historians, think of the causes of modern economic growth – the beginnings of the Industrial Revolution – as being rooted in material factors, like conquest, colonialism, or coal, Mokyr tirelessly argued that it was rooted in ideas, in the intellectual entrepreneurship of figures like Francis Bacon and Isaac Newton, and in the uniquely precocious accumulation in eighteenth-century Britain of useful, often mechanically actionable knowledge. Britain, he argued, through its scientific and literary societies, and its penchant for publications and sharing ideas, was the site of a world-changing Industrial Enlightenment – the place where progress was thoughtpossible, and then became real.
One of Mokyr’s big early insights, first appearing in Lever of Riches, was that many inventions could not be predicted by economic factors. Society could enjoy remarkable productivity improvements from simply increasing the size of the market, leading to division of labour and specialization – what he labelled ‘micro-inventions’ – in the vein popularised by Adam Smith. But this could not explain an invention that appeared out of the blue, like Montgolfier’s hot air balloon in the 1780s – what he called a ‘macro-invention’, not for the magnitude of its impact, but for its novelty. Macro-inventions often required further development to make them important, but the original breakthrough could not be predicted by looking at changes in prices or the availability of resources. It ultimately came down to advances in our understanding of the world. Mokyr put the Scientific Revolution – and the factors that contributed to it – on the economist’s map.
Mokyr also looked at the relationship between different kinds of knowledge. A scientist might know, through observation, that the air has a weight. A craftsman might know, through long training and experience with glass, how to make a long glass tube. Each could not get far alone. But combining them, by creating means to ensure that scientists and craftsmen talked with one another and collaborated – through connecting their propositional and prescriptive knowledge, their heads and hands – very quickly led to the invention of thermometers, barometers, and much more besides, in an ever expanding field of knowledge. What Mokyr taught economists is that it’s not knowledge per se that makes the difference, but the way it is organized. Much of his later work has shown just how deep a pool Britain’s scientists could draw on, of skilled artisans.
In a way, Mokyr himself has practised what he preached. As editor of Princeton University Press’s book series on the Economic History of the Western World, Mokyr has for decades provided an all-important space for economists and historians to write the kinds of research that would never have been publishable in economics journals – including of explanations of the Industrial Revolution that are the polar opposite to his own. He helped keep the connection between history and economics alive.
Mokyr’s case for the primacy of knowledge and ideas was not an easy one to make to economists. They are naturally drawn to data that can be counted, and not to narrative, often no matter how well evidenced. But it appears that Mokyr’s persistence, elevated by his infectious, irrepressible sprightliness, has paid off. His prize is a long overdue recognition of the historyin economic history, and a remarkable testament to the power of ideas to persuade…
A triumph for history and the importance of ideas: “Joel Mokyr’s Nobel,” from @antonhowes.bsky.social.
See also: “Why Joel Mokyr deserves his Nobel prize,” gift article from The Economist.
* Edward Abbey, Desert Solitaire
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As we ponder the process of progress, we might send creative birthday greetings to one of the subjects Mokyr’s study, Sir Christopher Wren; he born on this date in 1632. A mathematician and astronomer (who co-founded and later served as president of the Royal Society), he is better remembered as one of the most highly acclaimed English architects in history; he was given responsibility for rebuilding 52 churches in the City of London after the Great Fire in 1666, including what is regarded as his masterpiece, St. Paul’s Cathedral, on Ludgate Hill.
Wren, whose scientific work ranged broadly– e.g., he invented a “weather clock” similar to a modern barometer, new engraving methods, and helped develop a blood transfusion technique– was admired by Isaac Newton, as Newton noted in the Principia.
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