intro’d to Henri while reading Nassim‘s black swan:
Henri Poincaré, in spite of his fame, is regularly considered to be an undervalued scientific thinker, given that it took close to a centruy for some of his ideas to be appreciated. he was perhaps the last great thinking mathematician (or possibly the reverse, a mathematical thinker). every time i see a t-shirt bearing the picture of the moder icon Albert Eisntein, i cannot help thinking of Poincaré – Einstein is worthy of our reverence, but he has displace many others. there is so littel room in our consciousness; it is winner-take-all up there.
.. Poincaré’s essays, not just for their scientific content, but for the quality of his french prose. the grand master wrote these wonders as serialized articles and composed them like extemporaneous speeches. ….. he seemed in a hurry… in such a rush that he did not bother correcting typos and grammatical errors in his text, even after sotting them, since he found doing so a gross misuse of his time….
… he angrily disparages the use of the bell curve.
.. i can hardly imagine him on a t-shirt, or sticking out his tongue like in that famous picture of Einstein. there is something non-playful about him,…
… many claim that Poincaré figured out relativity before Einstein – and that Einstein got the idea from him – but that he did not make a big deal out of it…. Poincaré was too aristocratic in both background and demeanor to complain about the ownership of a result.
..Poincaré is central to this chapter because he lived in an age when we had made extremely rapid intellectual progress in the fields of prediction – think of celestial mechanics. the scientific revolution made us feel that we were in possession of tools that would allow us to grasp the future. uncertainty was gone. the universe was like a clock and, by studying the movements of the pieces, we could project in the future.
Poincaré was the first known big-gun mathematician to understand and explain that there are fundamental limits to our equations. He introduced nonlinearities, small effects that can lead to severe consequences, an idea that later became popular, perhaps a bit too popular, as chaos theory. What’s so poisonous about this popularity? Because Poincaré’s entire point is about the limits that nonlinearities put on forecasting; they are not an invitation to use mathematical techniques to make extended forecasts. Mathematics can show us its own limits rather clearly. There is (as usual) an element of the unexpected in this story.
… was about the stability of the solar system, … a calculation error, …. led to the opposite conclusion – unpredictability.. or, more technically, nonintegrability.
Jules Henri Poincaré (French: [ʒyl ɑ̃ʁi pwɛ̃kaʁe]; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and a philosopher of science. He is often described as a polymath, and in mathematics as The Last Universalist by Eric Temple Bell, since he excelled in all fields of the discipline as it existed during his lifetime.
In 1881–1882, Poincaré created a new branch of mathematics: the qualitative theory of differential equations. He showed how it is possible to derive the most important information about the behavior of a family of solutions without having to solve the equation (since this may not always be possible). He successfully used this approach to problems in celestial mechanics and mathematical physics.
It was Albert Einstein’s concept of mass–energy equivalence (1905) that a body losing energy as radiation or heat was losing mass of amountm = E/c2 that resolved Poincaré’s paradox, without using any compensating mechanism within the ether. The Hertzian oscillator loses mass in the emission process, and momentum is conserved in any frame. However, concerning Poincaré’s solution of the Center of Gravity problem, Einstein noted that Poincaré’s formulation and his own from 1906 were mathematically equivalent.
Poincaré and Einstein
Einstein’s first paper on relativity was published three months after Poincaré’s short paper, but before Poincaré’s longer version. Einstein relied on the principle of relativity to derive the Lorentz transformations and used a similar clock synchronisation procedure (Einstein synchronisation) to the one that Poincaré (1900) had described, but Einstein’s was remarkable in that it contained no references at all. Poincaré never acknowledged Einstein’s work on special relativity. Einstein acknowledged Poincaré posthumously in the text of a lecture in 1921 called Geometrie und Erfahrung in connection with non-Euclidean geometry, but not in connection with special relativity. A few years before his death, Einstein commented on Poincaré as being one of the pioneers of relativity, saying “Lorentz had already recognised that the transformation named after him is essential for the analysis of Maxwell’s equations, and Poincaré deepened this insight still further ….”
Poincaré’s work habits have been compared to a bee flying from flower to flower. Poincaré was interested in the way his mind worked; he studied his habits and gave a talk about his observations in 1908 at the Institute of General Psychology in Paris. He linked his way of thinking to how he made several discoveries.
The mathematician Darboux claimed he was un intuitif (intuitive), arguing that this is demonstrated by the fact that he worked so often by visual representation. He did not care about being rigorous and disliked logic. (Despite this opinion, Jacques Hadamard wrote that Poincaré’s research demonstrated marvelous clarity. and Poincaré himself wrote that he believed that logic was not a way to invent but a way to structure ideas and that logic limits ideas.)
We have learned that no real measurement is infinitely precise. All measurements necessarily include a degree of uncertainty.
But the tiniest puff of wind can make all the difference.
This was the birth of the concept that is called the “Butterfly Effect”. Poincaré may have been ahead of his time when it comes to the scientific community but his timing was perfect when it comes to the international community of artist residing in Paris in 1907. His ideas had a profound impact on the conversations in the cafes of his hometown. The interest in Poincaré’s concepts was a major influence on many painters and poets. Among them was Pablo Picasso, with his cubist paintings.
We need informed imagination.
Narratives and pictures may matter more than we think. Life is a non-discrete system. Evolution is not an algorithmic process. The processes of life are contextual, continuously varying, unpredictable and complex. The philosopher E. F. Schumacher wrote poetically: “The power of the Eye of the Heart, which produces insights, is vastly superior to the power of thought, which produces opinions”
why rev of everyday life matters…
let’s do this first: free art-ists.
John Hagel (@jhagel) tweeted at 7:09 AM – 21 Nov 2018 :
Exploring some of the early investigators of chaos theory – embarking on a quest to extract ordered structures from a sea of chaos. Surprised it does not mention the Santa Fe Institute where much of this work is done today https://t.co/5fFPSmILdD(http://twitter.com/jhagel/status/1065245789809713154?s=17)
Poincaré identified the unpredictability of the system and wrote: “It may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible.”
Chaos theory became the perfect mathematical tool to extract ordered structures from a sea of chaos. It is based on two main ideas: 1) even complex systems contain an underlying order, and 2) in these systems, small differences in initial conditions (e.g. small temperature variations) produce very divergent results, which means that, in general, the prediction of their long-term behaviour is impossible (mathematically, we say that the system has a strong dependence on the initial conditions).
This happens even though the behaviour of these phenomena is completely determined by their initial conditions, without involving any type of random elements. In other words, the deterministic nature of these systems does not make them predictable, although, at the very least, thanks to chaos theory it is possible to analyse their unpredictability from a strategic point of view.