The intuitive physicists were triumphant on many more occasions. Like Richard Feynman, who, from his wild imagination of virtual particles, wrote down outrageously ill-defined integral overall paths of virtual particles and fields through space and time.20 At the level of perturbation theory, that is, pretending that the quantum was infinitesimal, Feynman’s path integral is nothing more than a mathematical trick that helps with organizing calculations. In fairness, it was a damn fine trick. It helped predict the magnetic dipole moment of the electron to eleven digits, while also helping to solve difficult mathematical problems from the topological invariants of knots to the deformation quantization of Poisson manifolds.21
These crypto currencies have been hot topic of discussion recently with the success of Ethereum. Today’s needull tries to explain what these are and the differences between Bitcoin and Ethereum.
The Ethereum blockchain is much faster than that of Bitcoin. The delay between two blocks in the bitcoin system is around 12 seconds. The propagation time of a block through the network, understandably, poses de facto new challenges. The Ethereum protocol provides solutions in both cases. Moreover, and this is the great innovation of this platform, one can arbitrarily store data on the blockchain—by which I mean smart-contracts—that are, in fact, programs written in a complete Turing language. There is thus no restriction on the complexity of programs that can be deposited on this particular blockchain.
This would probably be my third needull on Ramanujan. This mathematician fails to amaze me every time I read about him. Although, I do not understand many of his proofs and theorems (very few people do) but there is something very pristine about him. A natural talent like Mozart, we keep discovering in layers. It won’t be incorrect to say that he was touched by divine.
In the last months of his life, Ramanujan frequently asked his wife Janaki Ammal for loose sheets of paper to record new results. Following Ramanujan’s death, Janaki, who had no formal education, delivered the papers to the University of Madras. They were subsequently forwarded to Hardy, who passed them on to G. N. Watson, the world’s premier authority in the field of special functions. After Watson’s death in 1965, the papers, comprising eighty-seven pages of handwritten results and more than six hundred formulas, were placed in storage at the Trinity College Wren Library. Forgotten by the mathematical world, the papers became known as “The Lost Notebook.” They were rediscovered by George Andrews in 1976 and have been the focus of intensive research ever since.6 The Lost Notebook and Other Unpublished Papers was finally published in 1987, in honor of the Ramanujan Centennial.7