tag:blogger.com,1999:blog-8148573551417578681.post2514936033190642324..comments2020-09-29T19:28:06.601-07:00Comments on Dark Buzz: Bad argument that math is scienceRogerhttp://www.blogger.com/profile/03474078324293158376noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-8148573551417578681.post-58956426633014933202015-01-16T08:06:40.889-08:002015-01-16T08:06:40.889-08:00(Part 2)
Let me also mention a parallel line of r...(Part 2)<br /><br />Let me also mention a parallel line of reasoning to your refutation of Einsteinian armchair theorizing. I often see the remark that it was modern mathematics that created digital computers. Not so! The papers of Turing and Gödel had little to do with modern computers. That's the revisionism of sloppy historians. Universal computation is a theoretical construct that gives few hints when building practical computers and new "biological" chips are making this even more irrelevant. For instance, the Z3 wasn't even proved to be Turing-complete until 1998. The real contributions were more from the field of logic and engineering. Atanasoff, Berry, Eckert, or Mauchly didn't know much about Turing. Claude Shannon was an MIT electrical engineer that looked to apply 19th century logic of Boole.<br /><br />"The idea that von Neumann was some kind of torch carrier who convinced the world that computers were important just does not wash with the facts. It does, apparently, sell books." (Bill Mauchly)<br /><br />The Z3 and Colossus weren't even generally known to exist until the 1970s. The ABC was dismantled by Iowa State, after Atanasoff went to do physics research for the U.S. Navy. The ENIAC was the real game changer.<br /><br />The theorist's phony reading of history breaks down over and over again.Matthew Corynoreply@blogger.comtag:blogger.com,1999:blog-8148573551417578681.post-66169237338504895282015-01-16T08:03:51.006-08:002015-01-16T08:03:51.006-08:00Concerning mathematics, arguments about Platonism ...Concerning mathematics, arguments about Platonism are red herrings because we at least strive for consistency in mathematical systems. They are only a map. The philosophy is quite pointless blather. However, the one aspect in which the methods of scientific discovery and theoretical deduction concur is the notion of burden of evidence. Popper never realized that he provided no way of choosing what to falsify but starts history where it's convenient. We cannot falsify every claim and this would force us to assume an endless number of mutually exclusive theories at the same time. The philosopher David Stove does a nice job refuting the irrationalism of Karl Popper, Thomas Kuhn, Imre Lakatos, and Paul Feyerabend.<br /><br />One of the worst abuses of mathematical abstraction results from infinity, which is self-contradictory and a great deal of impredictive mathematics has been built on top of it. The problem is that it's shifting the burden of evidence to have people disprove it. A sensible notion of finite might have its complement as zero or empty, for instance. We all know that when you get a repeated decimal then you can get a terminating one in a different base and the square root of two is not a problem if your protractor measures spread instead of a ridiculous arc length that requires transcendental functions. Intension is different from extension. Irrational numbers can never be expressed in extension but they simply don't exist except as algorithms, making them pseudo-numbers. Dedekind cuts and Cauchy sequences are riddled with logical contradictions. The proofs simply fail.<br /><br />Cantor was and confused multiple generations of mathematicians. Now we have the incomprehensible "continuum," "infinities" and "real" numbers. Cantor can shove his "transfinite numbers," Turing can shove his "infinite tape" and Gödel can shove his "for all." It's all meaningless. The law of the excluded middle is nonsense. Or did you stop beating your wife? Colorless green ideas sleep furiously (grammatical but meaningless). What the hell is so profound about finding out that a system could not prove its own consistency when you suspected it to begin with? Why assume infinite runnable programs but not infinite running computers? As for P vs NP, finding a needle in a haystack is hard work but it certainly isn't puzzling that it isn't hard to check that it's a needle once you found it. It's axiomatic! Zeilberger: “The vast majority of Boolean functions require exponentially many gates (as was first noted by Claude Shannon), the probability that any one specific function (e.g. SAT) will require only polynomially many gates is miniscule.” <br /><br />Mathematicians love to exaggerate the post-modern results of non-Euclidean geometry but Poincare knew they were merely matters of convention. Mathematicians try to go down one-way streets with set theory and wonder why they lose information. Set theory was not the source of mathematics but an a posteriori sideshow. A proper theory of algorithms is a better foundation than most set theory because it doesn't do math backwards and puzzle, like a behaviorist, at the asymmetries. You can't tell me with absolute certainty what is in a black box by only studying its output. The pathologies of Bourbaki are apparent here. This idea also extends to their absurd notions of proof where mathematicians refuse to understand the existence of irreducible complexity and think that all proofs can be “from the book.” Most proofs are probably longer than any human being could survey but what is wrong with uncertainly on the order of 1*10^-100? Such is life.<br /><br />Mathematicians hate computers and automation of their boring jobs and try to come up with math that is supposedly above procedure. Physicists regress into primary narcissism with escapist science fiction and untestable theories. Neither want to face the limits to knowledge or consistency imposed by logical thinking or experiment.Matthew Corynoreply@blogger.comtag:blogger.com,1999:blog-8148573551417578681.post-7368127308560904182014-08-27T05:24:49.489-07:002014-08-27T05:24:49.489-07:00>> I could test "1+1=2" by laying ...>> I could test "1+1=2" by laying 2 1-foot pieces of string together, and measuring the length. If so, I am likely to get 2.01 or something else not exactly 2.<br /><br />That's funny. I imagined you laying out pieces of string on the floor, quite unable to decide. 2, or 2.01?Jon Burdickhttps://www.blogger.com/profile/02548776058585897717noreply@blogger.comtag:blogger.com,1999:blog-8148573551417578681.post-18216064937815474812014-08-23T21:15:17.774-07:002014-08-23T21:15:17.774-07:00"The professors act as if a proof is some sor..."The professors act as if a proof is some sort of mysticism or voodoo with no applicability."<br /><br />In the corporate world, they are probably right.<br /><br />"They are more like people playing Dungeons & Dragons in their own imaginary universe"<br /><br />Now they are claiming they are ready to conquer condensed matter and overthrow the incompetent incumbentsAnonymousnoreply@blogger.com