Age of information
Greek & Latin
Mind & Brain
Science & Art
☞ A Box Of Stories
Inside a mathematical proof lies literature. Some of the greatest mathematicians were also some of classical history’s most poetic storytellers
“Like novelists, mathematicians are creative authors. With diagrams, symbolism, metaphor, double entendre and elements of surprise, a good proof reads like a good story. (…) [Reviel] Netz reveals the stunning stylistic similarities between Hellenistic poetry and mathematical texts from the same era. (…) In the very layout, in the use of a particular formulaic language, in the structuring of the text (…) its success or failure depends entirely on features residing in the text itself. It is really an activity very powerfully concentrated around the manipulation of written documents, more perhaps than anywhere else in science, and comparable, then, to modern poetry. (…)
Metaphor is fairly standard in mathematics. Mathematics can only become truly interesting and original when it involves the operation of seeing something as something else – a pair of similarly looking triangles, say, as a site for an abstract proportion; a diagonal crossing through the set of all real numbers.”
☞ Oulipo - a group of writers interested in exploring the application of mathematical structures, patterns and algorithms to writing
“We now live in a world (…) increasingly run by self-replicating strings of code. Everything we love and use today is, in a lot of ways, self-reproducing exactly as Turing, von Neumann, and Barricelli prescribed. It’s a very symbiotic relationship: the same way life found a way to use the self-replicating qualities of these polynucleotide molecules to the great benefit of life as a whole, there’s no reason life won’t use the self-replicating abilities of digital code, and that’s what’s happening. (…)
In 1945 we actually did create a new universe. This is a universe of numbers with a life of their own, that we only see in terms of what those numbers can do for us. (…) And that’s not just a metaphor for something else. It actually is. It’s a physical reality. (…)
But it was Turing who developed the one-dimensional model, and von Neumann who developed the two-dimensional implementation, for this increasingly three-dimensional digital universe in which everything we do is immersed. And so, the next breakthrough in understanding will also I think come from some oddball. It won’t be one of our great, known scientists. It’ll be some 22-year-old kid somewhere who makes more sense of this. (…)
We’re seeing a fraction of one percent of it, and there’s this other 99.99 percent that people just aren’t looking at. (…)
I think they [Turing & von Neumann] would be immediately fascinated by the way biological code and digital code are now intertwined. Von Neumann’s consuming passion at the end was self-reproducing automata. And Alan Turing was interested in the question of how molecules could self-organize to produce organisms. (…) They would be amazed by the direct connection between the code running on computers and the code running in biology—that all these biotech companies are directly reading and writing nucleotide sequences in and out of electronic memory, with almost no human intervention. That’s more or less completely mechanized now, so there’s direct translation, and once you translate to nucleotides, it’s a small step, a difficult step, but, an inevitable step to translate directly to proteins. And that’s Craig Venter’s world, and it’s a very, very different world when we get there.”
“The most beautiful and satisfying experiences open to humankind are not derived from the outside, but are bound up with the development of the individual’s own feeling, thinking and acting. The genuine artists, investigators and thinkers have always been persons of this kind. However inconspicuously the life of these individuals runs its course, none the less the fruits of their endeavors are the most valuable contributions which one generation can make to its successors. (…)
Pure mathematics is, in its way, the poetry of logical ideas. One seeks the most general ideas of operation which will bring together in simple, logical and unified form the largest possible circle of formal relationships.”
(Illustration: Albert Einstein sailing his boat on Saranac Lake (Courtesy: The Fantova Collection, Princeton University)
“There is still a difference between something and nothing, but it is purely geometrical and there is nothing behind the geometry.”
“Maths and music make claims to be universal languages of sorts. Science’s base metaphors are increasingly mathematical - building conceptual models from billiard balls is a thing of the past. Some theorists (for example Wimsatt) consider metaphor central to poetry. Colin Turbayne  thinks that that science is metaphor-laden too, the metaphors dead. Waismann [quoted in 2] argues that scientific concepts are only closed in specific contexts and that they are not different in kind to the metaphors of poetry. (…)
Quantum Theory - In Quantum Theory, probabilities can be calculated but only when an observation is made can any certainty be established. Observation is said to ‘collapse the probability function.’ This has been used for an analogy to the way that a text is interpreted (dis-ambiguated) by the act of reading . (…)
Relativity - Connections are made between Einstein’s Special Relativity and analytic cubism. Awareness of the equal importance of world viewpoints, the impossibility of absolute motion and time perhaps permeated via the Zeitgeist to artists; the link came from no deep mutual understanding.
Gödel - Gödel’s findings have helped soften artists’ views on science and has removed an aim of classical science. They have only made maths more obviously like the other sciences. The gap between science and the arts hasn’t thereby been reduced.
Geometry - Mondrian is heavily geometric and minimalist. This doesn’t make him more appealing to mathematicians. Equally, the 4-colour problem in maths isn’t appealing to artists.”
“Some mathematicians are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time. (…)
Mathematics needs both birds and frogs. Mathematics is rich and beautiful because birds give it broad visions and frogs give it intricate details. Mathematics is both great art and important science, because it combines generality of concepts with depth of structures. (…)
At the beginning of the seventeenth century, two great philosophers, Francis Bacon in England and René Descartes in France, proclaimed the birth of modern science. Descartes was a bird, and Bacon was a frog. Each of them described his vision of the future. Their visions were very different. Bacon said, “All depends on keeping the eye steadily fixed on the facts of nature.” Descartes said, “I think, therefore I am.” According to Bacon, scientists should travel over the earth collecting facts, until the accumulated facts reveal how Nature works. The scientists will then induce from the facts the laws that Nature obeys. According to Descartes, scientists should stay at home and deduce the laws of Nature by pure thought. (…)
For four hundred years since Bacon and Descartes led the way, science has raced ahead by following both paths simultaneously. Neither Baconian empiricism nor Cartesian dogmatism has the power to elucidate Nature’s secrets by itself, but both together have been amazingly successful.
For four hundred years English scientists have tended to be Baconian and French scientists Cartesian. Faraday and Darwin and Rutherford were Baconians; Pascal and Laplace and Poincaré; were Cartesians. Science was greatly enriched by the cross-fertilization of the two contrasting cultures. Both cultures were always at work in both countries. Newton was at heart a Cartesian, using pure thought as Descartes intended, and using it to demolish the Cartesian dogma of vortices. Marie Curie was at heart a Baconian, boiling tons of crude uranium ore to demolish the dogma of the indestructibility of atoms.”
Michael Gove speaks to the Royal Society on maths and science
“History is driven, above all, by mathematics and the power it gives us to understand, predict and control the world.
The emergence of the first, truly great, Western civilization, in the scattered city states of Ancient Greece, was intimately connected with the first systematic thinking about reason, logic and number.
Although Pythagoras himself is a figure shrouded by myth, the Pythagorean revolution he and his disciples set in motion was the prelude to the astonishing flowering of classical philosophy which laid the foundations of the Western world.
On those first foundations men such as Euclid and Archimedes devised a means of making sense of the world which enabled their contemporaries, and successors, to master it. Greece bequeathed her mathematical heritage to Rome and the achievements of the Caesars, their imperial highways, feats of engineering and centralised accounts, were all the fruits of mathematical knowledge.
Rome’s fall was the prelude to Islam’s rise and again mathematical innovation was the leading indicator of historical progress. While Western Europe was sunk in a Dark Age of dynastic squabbling, pagan aggression and superstitious poverty the Islamic world flourished, advanced and subdued its foes while also nurturing a series of mathematical thinkers responsible for transmitting wisdom and generating great historic breakthroughs. Whether it was the establishment of Arabic numerals as the principal method of mathematical notation or the invention of algebra, Arabic and Islamic culture was the world’s forcing-house of progress for centuries.
Europe only caught up again in the sixteenth century, but when we did it was with a burst of mathematical innovation which once more moved the world on its axis. Galileo and Descartes authored advances in mechanics and geometry which were hugely ground-breaking. They were followed by the arguably even greater geniuses of Newton and Leibniz.
Newton, the greatest President this society has had - so far - was the godfather of the Enlightenment, mankind’s great period of intellectual flowering, the liberation from ignorance on which our current freedoms rest.
In the nineteenth century, the greatest mathematicians were Germans - like Karl Friedrich Gauss and Bernhard Riemann - reflecting the shift of intellectual innovation, and economic power, to central Europe.
In the twentieth century, the flight of mathematicians like Kurt Gödel from a fascist Europe sunk in a new barbarism to a new world of liberty and promise again presaged a fundamental shift in economic, political and intellectual power. (…)
Richard Feynman has described the precision of quantum mechanics as like being able to measure the distance from New York to L.A to the nearest hair’s breadth. And for those of us navigating journeys even more fraught and perilous than an odyssey across America - such as driving from West London to Westminster without hitting roadworks - the precision of GPS satellite technology can guide us - and all thanks to the extraordinary precision of relativity’s equations.”