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30, 49, 295-312, 297 art and 304 being appreciated 142 computer and 132, 257, 309 convergent thinking 300 design tradeoff 311 divergent thinking 298 Eureka moment 302 incubation 301 innovator’s dilemma 306 intimation 301 John Cleese on 303 knowledge and 141 mathematical creativity 309 mechanical steps 14
Center 5 equivalence 200 Ericsson, Anders 37 Ernd 169 Escher, MC 346 and Penrose Steps 51 Essential Complexity 231 Euclid’s proof 156 Euler 157, 202 Eureka moment 302 Everett, Hugh 328 experiments 1 exponent 241 expression analysis 84 eyes 108 color perception 110 fovea centralis 112 resolution of 112 F
7 Oxford English Dictionary 86 Oxford University xi, 50, 149, 205, 282 P paperclip test 298 paper tape 221 paradox xi, 68, 70, 114, 153, 203, 326 Barber paradox 155 EPR paradox 332 false 155 Kochen-Specker paradox 345 liar’s paradox 154 Russell paradox 155 Wiles paradox 247 Zenoss paradox 154 parallel
count up starting at 1 then 2, 3, 4, 5, and so on until I try every number. Will this eventually get to the War and Peace number? The answer is yes. Eureka! All of human knowledge is computable. I have written this computation out as a simple computer program below. It says, in plain English, start at ze
ime intervals then I may indeed reach it. On the other hand, some series never converge. I will never reach infinity how ever many steps I take. The Barber Paradox Now, for a slightly harder paradox, let’s suppose there is a town with just one barber. In this town, every man keeps himself clean-shaven b
e problem, my brain continued to work on it. I was not conscious of this, I was only aware that failing to solve the problem annoyed me. I then had a Eureka moment. Although I couldn't prove a piece of music was non-computational, I could make one! - a piece that could not have been created using computat
sh into itself? Does Crash halt if it runs with the input Crash? This creates a paradox; there is no solution which makes sense. It’s similar to the Barber Paradox of earlier. Since a paradox is created there must be a fault in our original theory. The error is the existence of Crash. Since Crash cannot
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