Epstein Secrets

eoretical footing. In the late 19" century, most mathematicians thought infinity was a curious idea with no proper place in mathematics. They treated Cantor's attempts to make it into a real mathematical object with contempt. This affected Cantor’s morale and caused him to suffer several bouts of deep dep

ou try it on your computer, you will get the not terribly useful, #DIV/0! Error. That’s progress I guess! Zero had been tamed. What about infinity? Cantor showed that while you could think of infinity as a number, it might not be just one number. He proposed there are many infinities. In fact, there are

ents believe making a thinking machine is just a matter of building a really large, fast neural network and working out how to train it efficiently. Quantum Brains Conventional wisdom says each brain cell is a single processing unit making an on-off decision — fire, or don't fire - depending on the state

t with cardinals. Statisticians probably do it. Topologists do it openly, in multiply connected domains Variationists do it locally and globally. Cantor did it diagonally. Fermat tried to do it in the margin, but couldn't fit it in. Galois did it the night before. Mobil's always does it on the same

hematical physicists understand the theory of how to do it, but have difficulty obtaining practical results. Pure mathematicians do it rigorously. Quantum physicists can either know how fast they do it, or where they do it, but not both. Real analysts do it almost everywhere EFTA_R1_01490133 EFTA0242

n't have to worry about turning the page or working in two dimensions. If you are worried that a tape is less powerful than a sheet of paper remember Cantor’s theorem: an infinite plane is the same as an infinite line. The use of a tape massively simplified the mathematics, and subsequently many early com

itatively different to a traditional computer in order to break the Turing limit. The obvious place to turn is the quantum world. Quantum Computers Quantum computers have had an extraordinary run in the press recently. It has been variously claimed they offer limitless computing power and can break all k

he first two infinities; counting numbers and the continuum of real numbers. HOUSE_OVERSIGHT_016092 10. 11. 12. 13. 14, Index of Theorems 403 Cantor’s First Infinity Theorem — The infinite plane is the same infinity as the infinite line. . Known Unknowns Gédel’s Incompleteness Theorem — Mathemat

of the philosophical argument. I also avoid a strongly historical narrative, but if you enjoy the history of science I recommend, The Missing 4%, and Quantum for a really clear exposé of the issues HOUSE_OVERSIGHT_016087 398 Are the Androids Dreaming Yet? around quantum mechanics, relativity and cosmolo