– Feynman: “Feynman on Averaging: This question of trying to figure out whether a book is good or bad by [either] looking at it carefully or by taking the reports of a lot of people who looked at it carelessly is like this famous old problem: Nobody was permitted to see the Emperor of China, and the question was, What is the length of the Emperor of China’s nose? To find out, you go all over the country asking people what they think the length of the Emperor of China’s nose is, and you average it. And that would be very “accurate” because you averaged so many people. But it’s no way to find anything out; when you have a very wide range of people who contribute without looking carefully at it, you don’t improve your knowledge of the situation by averaging.”
– Bohr: “One of the favorite maxims of my father was the distinction between the two sorts of truths, profound truths recognized by the fact that the opposite is also a profound truth, in contrast to trivialities where opposites are obviously absurd.”
– Leibniz: “There are two famous labyrinths where our reason very often goes astray. One concerns the great question of the free and the necessary, above all in the production and the origin of Evil. The other consists in the discussion of continuity, and of the indivisibles which appear to be the elements thereof, and where the consideration of the infinite must enter in.”
– Born: “Chance is a more fundamental conception than causality.”
– ensemble of decision trees in deep learning
– http://en.wikipedia.org/wiki/Minimum_description_length
– spectra of graphs: http://onionesquereality.wordpress.com/2011/06/30/summerreadings/
– Fermat’s Last Theorem is not strong enough to imply the irrationality of
– Kolmogorov: “Information theory must precede probability theory and not be based on it. By the very essence of this discipline, the foundations of information theory have a finite combinatorial character.”
– Valiant: “Changing or increasing functionality of circuits in biological evolution is a form of computational learning”
– Antoine necklase was studied by Louis Antoine who was blind
– Sossinsky: ““It is not surprising at all that almost all blind mathematicians are geometers. The spatial intuition that sighted people have is based on the image of the world that is projected on their retinas; thus it is a two (and not three) dimensional image that is analysed in the brain of a sighted person. A blind person’s spatial intuition on the other hand, is primarily the result of tile and operational experience. It is also deeper – in the literal as well as the metaphorical sense. […]”
– “The Minimum Description Length principle is a formalization of the Occam’s Razor and is one of the most beautiful and powerful methods for inductive inference.”
– Tao: “Perhaps the most fundamental differential operator on Euclidean space is the Laplacian”
– Kolmogorov: “The applications of probability theory can be put on a uniform basis. It is always a matter of consequences of hypotheses about the impossibility of reducing in one way or another the complexity of the descriptions of the objects in question. Naturally this approach to the matter does not prevent the development of probability theory as a branch of mathematics being a special case of general measure theory. The concepts of information theory as applied to infinite sequences give rise to very interesting investigations, which, without being indispensable as a basis of probability theory, can acquire a certain value in investigation of the algorithmic side of mathematics as a whole.”
– ML insight exploiting graph laplacians http://www.cse.ohiostate.edu/~mbelkin/papers/SSL_ML_04.pdf
– Gowers on Szemeredi uniformity lemma: http://link.springer.com/article/10.1007%2FPL00001621
– Schroedinger claimed DNA contains not only information (input) but also instructions for the automata, not likely the case
– quotation from Ramanujan:” Thought is the only way that leads to life. All else is hollow spheres Reflecting back In heavy imitation And blurred degeneration A senseless image of our world of thought.. Man thinks he is the thought which gives him life. He binds a sheaf and claims it as himself. He is a ring through which we pass swinging ropes. Which merely move a little as he slips.. The Ropes are Thought. The Space is Time.”

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