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Posts Tagged ‘optics

“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In 1936, the economist John Maynard Keynes purchased a trove of Isaac Newton’s unpublished notes.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.”

John Ciardi

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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).

A portrait of a 17th-century man with long curly hair, wearing a red robe and white lace cravat, posing with a serious expression.
Rasmus Bartholin (source)

“Truth is ever to be found in the simplicity, and not in the multiplicity and confusion of things”*…

Knots with 8 crossings

From Kim (Scott) Morrison‘s and Dror Bar-Natan‘s, The Knot Atlas, “a complete user-editable knot atlas, in the wiki spirit of Wikipedia“– a marvelous example of a wide-spread urge in mathematics to find order through classification. As Joseph Howlett explains, that quest continues, even as it proves vexatious…

Biology in the 18th century was all about taxonomy. The staggering diversity of life made it hard to draw conclusions about how it came to be. Scientists first had to put things in their proper order, grouping species according to shared characteristics — no easy task. Since then, they’ve used these grand catalogs to understand the differences among organisms and to infer their evolutionary histories. Chemists built the periodic table for the same purpose — to classify the elements and understand their behaviors. And physicists made the Standard Model to explain how the fundamental particles of the universe interact.
 
In his book The Order of Things, the philosopher Michel Foucault describes this preoccupation with sorting as a formative step for the sciences. “A knowledge of empirical individuals,” he wrote, “can be acquired only from the continuous, ordered and universal tabulation of all possible differences.”
 
Mathematicians never got past this obsession. That’s because the menagerie of mathematics makes the biological catalog look like a petting zoo. Its inhabitants aren’t limited by physical reality. Any conceivable possibility, whether it lives in our universe or in some hypothetical 200-dimensional one, needs to be accounted for. There are tons of different classifications to try — groups, knots, manifolds and so on — and infinitely many objects to sort in each of those classifications. Classification is how mathematicians come to know the strange, abstract world they’re studying, and how they prove major theorems about it.

Take groups, a central object of study in math. The classification of “finite simple groups” — the building blocks of all groups — was one of the grandest mathematical accomplishments of the 20th century. It took dozens of mathematicians nearly 100 years to finish. In the end, they figured out that all finite simple groups fall into three buckets, except for 26 itemized outliers. A dedicated crew of mathematicians has been working on a “condensed” proof of the classification since 1994 — it currently comprises 10 volumes and several thousand pages, and still isn’t finished. But the gargantuan undertaking continues to bear fruit, recently helping to prove a decades-old conjecture that you can infer a lot about a group by examining one small part of it.
 
Mathematics, unfettered by the typical constraints of reality, is all about possibility. Classification gives mathematicians a way to start exploring that limitless potential…

[Howlett reviews attempts to classify numbers by “type” (postive/negative, rational/irrational), and mathematical objects by “equivalency” (shapes that can be stretched or squeezed into the other without breaking or tearing, like a doughnut and and coffee cup (see here)…]

… Similarly, classification has played an important role in knot theory. Tie a knot in a piece of string, then glue the string’s ends together — that’s a mathematical knot. Knots are equivalent if one can be tangled or untangled, without cutting the string, to match the other. This mundane-sounding task has lots of mathematical uses. In 2023, five mathematicians made progress on a key conjecture in knot theory that stated that all knots with a certain property (being “slice”) must also have another (being “ribbon”), with the proof ruling out a suspected counterexample. (As an aside, I’ve often wondered why knot theorists insist on using nouns as adjectives.)

Classifications can also get more meta. Both theoretical computer scientists and mathematicians classify problems about classification based on how “hard” they are.
 
All these classifications turn math’s disarrayed infinitude into accessible order. It’s a first step toward reining in the deluge that pours forth from mathematical imaginings…

The Never-Ending Struggle to Classify All Math,” from @quantamagazine.bsky.social.

* Isaac Newton

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As we sort, we might spare a thought for the author of our title quote, Sir Isaac Newton; he died in this date in 1727. A polymath, Newton excelled in– and advanced–  mathematics, physics, and astronomy; he was a theologian and a government offical (Master of the Mint)… and a dedicated alchemist. He was key to the Scientific Revolution and the Enlightenment that followed.

Newton’s 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 (e.g., the Laws of Motion and the principle of universal gravitation). He also made seminal contributions to optics, and shares credit with German mathematician Gottfried Wilhelm Leibniz for formulating infinitesimal calculus.  Indeed, Newton contributed to and refined the scientific method to such an extent that his work is considered the most influential in the development of modern science.

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Written by (Roughly) Daily

March 20, 2025 at 1:00 am

“The structure of the universe- I mean, of the heavens and the earth and the whole world- was arranged by one harmony through the blending of the most opposite principles”*…

Two diagrams from Agrippa’s De occulta philosophia (1533) demonstrating the proportion, measure, and harmony of human bodies — Source: left, right

… And as we undertake to understand that structure, we use the lens– the mental models and language– that we have. The redoubtable Anthony Grafton considers and early 16th century attempt: Heinrich Cornelius Agrippa‘s De Occulta Philosophia libri III, Agrippa’s encyclopedic study of magic that was, at the same time, an attempt to describe the structure of the universe, sketching a path that leads both upward and downward: up toward complete knowledge of God, and down into every order of being on earth…

Heinrich Cornelius Agrippa’s manual of learned magic, De occulta philosophia (1533), explicated the ways in which magicians understood and manipulated the cosmos more systematically than any of his predecessors. It was here that he mapped the entire network of forces that passed from angels and demons, stars and planets, downward into the world of matter. Agrippa laid his work out in three books, on the elementary, astrological, and celestial worlds. But he saw all of them as connected, weaving complex spider webs of influence that passed from high to low and low to high. With the zeal and learning of an encyclopedist imagined by Borges, Agrippa catalogued the parts of the soul and body, animals, minerals, and plants that came under the influence of any given planet or daemon. He then offered his readers a plethora of ways for averting evil influences and enhancing good ones. Some of these were originally simple remedies, many of them passed down from Roman times in the great encyclopedic work of Pliny the Younger and less respectable sources, and lacked any deep connection to learned magic.

[Grafton describes the many dimensions of Agrippa’s compilation of the then-current state of magic…]

But few of the dozens of manuscript compilations that transmitted magic through the Middle Ages reflected any effort to impose a system on the whole range of magical practices, as Agrippa’s book did. He made clear that each of the separate arts of magic, from the simplest form of herbal remedy to the highest forms of communication with angels, fitted into a single, lucid structure with three levels: the elementary or terrestrial realm, ruled by medicine and natural magic; the celestial realm, ruled by astrology; and the intellectual realm, ruled by angelic magic. Long tendrils of celestial and magical influence stitched these disparate realms into something like a single great being…

Agrippa offered, in other words, both a grand, schematic plan of the cosmos, rather like that of the London Underground, which laid out its structure as a whole, and a clutch of minutely detailed local Ordinance Survey maps, which made it possible to navigate through any specific part of the cosmos. Readers rapidly saw what Agrippa had to offer. The owner of a copy of On Occult Philosophy, now in Munich, made clear in his only annotation that he appreciated Agrippa’s systematic presentation of a universe in which physical forms revealed the natures of beings and their relations to one another: “Physiognomy, metoposcopy [the interpretation of faces], and chiromancy, and the arts of divination from the appearance and gestures of the human body work through signs.” Agrippa’s book not only became the manual of magical practice, but it also made the formal claim that magic was a kind of philosophy in its own right…

A 16th century attempt to understand the structure of the universe: “Marked by Stars- Agrippa’s Occult Philosophy,” from @scaliger in @PublicDomainRev.

* Aristotle

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As we take in the totality, we might send more modern birthday greetings to a rough contemporary of Agrippa’s, Evangelista Torricelli; he was born on this date in 1608. Even as Agrippa was trying to understand the world via magic, Torricelli, a student of Galileo, was using observation and reason to fuel the same quest. A physicist and mathematician, he is best known for his invention of the barometer, but is also known for his advances in optics, his work on the method of indivisibles, and “Torricelli’s Trumpet.” The torr, a unit of pressure, is named after him.

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“I’ve been making a list of the things they don’t teach you at school”*…

You can learn to make these at a terrariums workshop

It’s that time again

In Warsaw’s Gruba Kaśka water plant there are eight clams with sensors attached to their shells. If the clams close because they don’t like the taste of the water, the city’s supply is automatically shut off. [Judita K]

When bar codes were patented in 1952, they were round [Sarah Laskow]

A 70% dilution of isopropyl alcohol is better at killing bacteria, fungi, and viruses than ‘pure’ 99% isopropyl alcohol, for several distinct reasons. [Mitch Walleser]

Epidemiologists at Emory University in Atlanta believe that raising the mimimim wage in the US by $1 would have prevented 27,550 suicides since 1990. [John A Kaufman & Co, via The Economist]

Games Workshop, owner of Warhammer, is worth more than Centrica, owner of British Gas. [Allister Thomas]

Numbers 30-34 of this year’s list from Tom Whitwell of Fluxx: “52 things I learned in 2020.”

* Neil Gaiman, The Kindly Ones

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As we have fun with facts, we might send fascinatingly-illustrated birthday greetings to David Brewster; he was born on this date in 1781. A physicist, inventor, author, and academic administrator, he is best remembered for his work in optic (especially the phenomenon of polarization). Brewster was a pioneer in photography; he invented an improved stereoscope, which he called “lenticular stereoscope” and which became the first portable 3D-viewing device. He also invented the binocular camera, two types of polarimeters, the polyzonal lens, the lighthouse illuminator, and (perhaps most relevantly to today’s post) the kaleidoscope. For this work, William Whewell dubbed him the “father of modern experimental optics” and “the Johannes Kepler of optics.”

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Written by (Roughly) Daily

December 11, 2020 at 1:01 am

“It’s fine to celebrate success, but it is more important to heed the lessons of failure”*…

 

If you ever wanted a glimpse into what dooms startups, look no further than autopsy.io, a website that lists the reasons why many newborn tech firms imploded. The website offers entrepreneurs the ability to self-explain why their startup didn’t quite make it; in a bid to separate real-life stories from entertaining fictions, the application form asks for a link to a blog post or medium article “that tells the story of the failure,” along with the founder(s) Twitter handle and Crunchbase or Angel.co profile. Some of the reasons listed for failure are maddeningly opaque, such as UniSport’s “for a number of reasons” or PlayCafe’s “we didn’t reach enough users.” Others are bleakly hilarious; as the founders of Zillionears, self-billed as a “creative pre-sale platform for musicians,” confessed: “People really didn’t really LIKE anything about our product.” If you’re thinking of launching your own company, or you work for a wet-behind-the-ears startup, it’s worth scanning the list to see if any of these potential crises are brewing in your setup.

Via Nerval’s Lobster at Slashdot.

* Bill Gates

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As we dust ourselves off, we might spare a thought for Roger Bacon; he died on this date in 1292.  A philosopher and Franciscan friar, Bacon was one of the first to propose mathematics and experimentation as appropriate methods of science.  Working in mathematics, astronomy, physics, alchemy, and languages, he was particularly impactful in optics: he elucidated the principles of refraction, reflection, and spherical aberration, and described spectacles, which soon thereafter came into use. He developed many mathematical results concerning lenses, proposed mechanically propelled ships, carriages, and flying machines, and used a camera obscura to observe eclipses of the Sun.  And he was the first European give a detailed description of the process of making gunpowder.

He began his career at Oxford, then lectured for a time at Paris, where his skills as a pedagogue earned him the title Doctor Mirabilis, or “wonderful teacher.”  He stopped teaching when he became a Franciscan.  But his scientific work continued, despite his Order’s restrictions on activity and publication, as Bacon enjoyed the protection and patronage of Pope Clement…  until, on Clement’s death, he was placed under house arrest in Oxford, where he continued his studies, but was unable to publish and communicate with fellow investigators.

Statue of Roger Bacon in the Oxford University Museum

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Written by (Roughly) Daily

June 11, 2015 at 1:01 am