“Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.”*…
No scripture is as old as mathematics is. All the other sciences are younger, most by thousands of years. More than history, mathematics is the record that humanity is keeping of itself. History can be revised or manipulated or erased or lost. Mathematics is permanent. A² + B² = C² was true before Pythagoras had his name attached to it, and will be true when the sun goes out and no one is left to think of it. It is true for any alien life that might think of it, and true whether they think of it or not. It cannot be changed. So long as there is a world with a horizontal and a vertical axis, a sky and a horizon, it is inviolable and as true as anything that can be thought.
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As precise as mathematics is, it is also the most explicit language we have for the description of mysteries. Being the language of physics, it describes actual mysteries—things we can’t see clearly in the natural world but suspect are true and later confirm—and imaginary mysteries, things that exist only in the minds of mathematicians. A question is where these abstract mysteries exist, what their home range is. Some people would say that they reside in the human mind, that only the human mind has the capacity to conceive of what are called mathematical objects, meaning numbers and equations and formulas and so on—the whole glossary and apparatus of mathematics—and to bring these into being, and that such things arrive as they do because of the way our minds are structured. We are led to examine the world in a way that agrees with the tools that we have for examining it. (We see colors as we do, for example, because of how our brains are structured to receive the reflection of light from surfaces.) This is a minority view, held mainly by neuroscientists and a certain number of mathematicians disinclined toward speculation. The more widely held view is that no one knows where math resides. There is no mathematician/naturalist who can point somewhere and say, “That is where math comes from” or “Mathematics lives over there,” say, while maybe gesturing toward magnetic north and the Arctic, which I think would suit such a contrary and coldly specifying discipline.
The belief that mathematics exists somewhere else than within us, that it is discovered more than created, is called Platonism, after Plato’s belief in a non-spatiotemporal realm that is the region of the perfect forms of which the objects on earth are imperfect reproductions. By definition, the non-spatiotemporal realm is outside time and space. It is not the creation of any deity; it simply is. To say that it is eternal or that it has always existed is to make a temporal remark, which does not apply. It is the timeless nowhere that never has and never will exist anywhere but that nevertheless is. The physical world is temporal and declines; the non-spatiotemporal one is ideal and doesn’t.
A third point of view, historically and presently, for a small but not inconsequential number of mathematicians, is that the home of mathematics is in the mind of a higher being and that mathematicians are somehow engaged with Their thoughts. Georg Cantor, the creator of set theory—which in my childhood was taught as a part of the “new math”—said, “The highest perfection of God lies in the ability to create an infinite set, and its immense goodness leads Him to create it.” And the wildly inventive and self-taught mathematician Srinivasa Ramanujan, about whom the movie “The Man Who Knew Infinity” was made, in 2015, said, “An equation for me has no meaning unless it expresses a thought of God.”
In Book 7 of the Republic, Plato has Socrates say that mathematicians are people who dream that they are awake. I partly understand this, and I partly don’t.
Mathematics has been variously described as an ideal reality, a formal game, and the poetry of logical ideas… an excerpt from “What is Mathematics?” from Alec Wilkinson— eminently worthy of reading in full.
* Albert Einstein
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As we sum it up, we might send carefull-calcuated birthday greetings to Georgiy Antonovich Gamov; he was born on this date in 1904. Better known by the name he adopted on immigrating to the U.S., George Gamow, he was a physicist and cosmologist whose early work was instrumental in developing the Big Bang theory of the universe; he also developed the first mathematical model of the atomic nucleus.
But mid-career Gamow began to shift his energy to teaching and to writing popular books on science… one of which, One Two Three… Infinity, inspired legions of young scientists-to-be and kindled a life-long interest in science in an even larger number of other youngsters (like your correspondent).
“The challenge is not so much to change the sound. The challenge is to connect and to create something special.”*…
How dare these women take such liberties with Vivaldi and other greats?! I’m shocked … SHOCKED I tell you!
In honesty, I’m quite impressed. The women of Salut Salon quartet — Angelika Bachmann (violin), Iris Siegfried (violin and vocals), Anne-Monika von Twardowski (piano) and Sonja Lena Schmid (cello) — combine virtuosity, acrobatics and a sense of fun in their performances. The result is surprising, enchanting and overall, entertaining.
According to their official bio, the Salut Salon musicians “share the same humor. They love to laugh, they laugh a lot, especially at the things that go terribly wrong, even in front of an audience.”
As this video shows, they’re not afraid to take risks — in fact, they seem absolutely fearless on stage…
“Are these women the Harlem Globetrotters of piano quartets?“
* Gustavo Dudamel
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As we fondly remember Victor Borge, we might recall that it was on this date in 1931 that Cab Calloway recorded “Minnie the Moocher,” the first jazz record to sell one million copies and the song that cemented the popularity of “scat” singing (which had been first popularized in 1926 by Louis Armstrong’s “Heebie Jeebies.”)
“What is research but a blind date with knowledge?”*…
Science at work: a fascinating interactive visualization of every paper ever published in Nature.
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As we interpret influence, we might spare a thought for Neil Arnott; he died on this date in 1874. A physician and inventor, he created one of the first forms of the waterbed, the Arnott waterbed for the comfort of patients during prolonged illness. He also invented the economical Arnott stove (which he called a thermometer-stove), which featured a self-regulating fire. And in 1852, he won the Rumford Medal for the construction of the smokeless fire grate, as well as other improvements to ventilation and heating.
“Be a good ancestor”*…
The Greek philosopher Plato once imagined a city that provides full justice to its citizens. Setting out his ideas in the Republic almost 2500 years ago, Plato did not, however, think that such a city could ever be realized. Radical (and surely unachievable) transformations in education, culture and government would be required to establish and sustain it. “Ridiculous,” Plato concluded.
In a similar vein, the US cultural anthropologist Vincent Ialenti envisions a fictional city whose citizens have been trained to think so that humans don’t need to flee the planet to survive. So utopian is the picture that Ialenti – writing in his new book Deep Time Reckoning – calls it “absurd”. Yet that notion is no less absurd, he continues, than the way humans are now acting, “careening toward an Anthropocene cliff”.
Based at George Washington University, Ialenti developed this picture by drawing on three years of fieldwork in Finland, where he’d studied experts who were evaluating the risks of a permanent repository for nuclear waste…
The Finnish experts developed various strategies to envision “deep time”. For example, they implemented unusual computer modelling methods to integrate a variety of datasets, scenarios, maps and reports over an unprecedented range of issues, including climate change, geological events, shorelines, human demographics, vegetation growth and ecosystems. For clues on the long-term evolution of materials and planetary landscapes, they studied everything from ancient Roman nails and 2100-year-old Chinese cadavers to cannons from a sunken 17th-century Swedish warship and traces of a crater in Finland caused by a meteor 73 million years ago.
Ialenti is fully aware of the deficiencies and partialities of the Finnish project and of his own study…
Climate-change predictions, even for 2050, seem hopelessly far in the future, and tainted by politics, guesswork and subjectivity. Thinking about the present seems more do-able, while thinking about tens or hundreds of thousands of years in the future appears starry-eyed and abstract. But Ialenti believes the exact opposite is true. What’s abstract (in the sense of detached from reality) is what Ialenti calls “a manic fixation on the present”, and not being able to think about humanity thousands of years hence.
Ialenti is less interested in the conclusions reached by the Finnish experts than by their audacious aims, which are to develop methods to break free from what he calls our “shallow time discipline”. He then tries to devise ways to retrain our habits to encourage humans to think long-term; for him, Deep Time Reckoning is not a stale academic treatise but more of a “practical toolkit”.
This toolkit includes high-school civics classes devoted to teaching long-term developments: of the universe since the Big Bang 13.8 billion years ago; of Earth since 4.5 billion years ago; of Earth’s life, dinosaurs and humans; and of the evolution of languages and technologies. It envisions school pupils reading about futuristic visions by Ray Kurzweil and Marxist descriptions of world utopias.
Ialenti even asks his university students to examine the tools that the insurance industry uses to protect companies against future calamities, and the methods that the Catholic Church uses to maintain institutional continuity. Practiced over generations, Ialenti thinks, such an education would eventually make deep time thinking “less wacky and aloof”, and more second-nature…
Plato meant the Republic to be a beacon for humans to think about justice in the present, not as the blueprint for an actual city to be realized in the future. After all, if you head straight towards a lighthouse, you usually end up on the rocks.
Somewhere in deep time looms a catastrophe that we don’t yet have the imagination to envision, nor the will to confront. Ialenti thinks he finds in the Finnish nuclear-risk experts glimmerings of what it might take to cultivate the human behaviour needed to do so. Humanity’s long-range hope, Ialenti suggests, hangs on what we might call the Finlandization of the planet.
Professor Robert P. Crease (@rcrease) explains how a nuclear-waste program in Finland can help us to envisage the world thousands of years from now: “Very Deep Thinking.”
See also Ingrid Burrington‘s interview with Yale architecture and design professor Keller Easterling, “How to Design Better Systems in a World Overwhelmed by Complexity, ” and Jeremy Lent‘s “What Does An Ecological Civilization Look Like?“
* Marian Wright Edelman
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As we play the long game, we might spare a thought for Alfred Habdank Skarbek Korzybski; he died on this date in 1950. Trained as an engineer, he developed a field called general semantics, which he viewed as both distinct from, and more encompassing than, the field of semantics. He argued that human knowledge of the world is limited both by the human nervous system and the languages humans have developed, and thus no one can have direct access to reality, given that the most we can know is that which is filtered through the brain’s responses to reality.
Korzybski was influential in fields across the sciences and humanities through the 1940s and 50s (perhaps most notably, gestalt therapists), and inspired science fiction writers (like Robery Heinlein and A.E. van Vogt) and philosophers like Alan Watts.
His best known dictum is “The map is not the territory.”
“Electricity is really just organized lightning”*…
In Mary Shelley’s Frankenstein, written in 1818, the young Victor Frankenstein becomes obsessed with the idea that electricity is a kind of fluid that endows living things with their life force. This obsession leads to tragedy.
Shelley’s view of electricity was, in fact, not an uncommon perspective at the time: just a few decades earlier the Italian scientist Luigi Galvani had shown that a shock of static electricity applied to the legs of a dismembered frog would cause the legs to kick. Galvani concluded that there existed a kind of “animal electric fluid” that was responsible for the animation of living creatures.
In the two hundred years since Frankenstein our view of electricity has certainly evolved, as has our ability to generate and control electric currents. But do we really understand what we’re doing? Do we even know what electricity is?
Physicist Brian Skinner (@gravity_levity) explains “Here’s why we don’t understand what electricity is.”
Pair with “Bruno Latour, the Post-Truth Philosopher, Mounts a Defense of Science.”
* George Carlin
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As we plug in, we might send really fast birthday greetings to Leon Cooper; he was born on this date in 1930. A physicist, he shared the Nobel Prize in 1972 (with John Bardeen and John Robert Schrieffer) for contributing the concept of Cooper electron pairs which forms the basis of the BCS (their initials) theory of superconductivity. He is also one of the the namesakes and co-developers of the BCM theory of synaptic plasticity.
He went on to become a cofounder and co-chairman of Nestor, Inc., a company that applies neural-network systems to complex applications. The company built computer-based adaptive pattern-recognition and risk-assessment systems that could, for example, accurately classify complex patterns in sonar, radar or imaging systems. He also founded and was director of Brown University’s Institute for Brain and Neural Systems, which develops cognitive pharmaceuticals and intelligent systems for electronics, automobiles and communications.
The character “Sheldon Cooper” in Big Bang Theory is partially named for Cooper.
