tag:blogger.com,1999:blog-20067416.post3247155692738613702..comments2022-05-10T03:49:17.107-04:00Comments on Recursivity: Kirk Durston Does Mathematics!Unknownnoreply@blogger.comBlogger15125tag:blogger.com,1999:blog-20067416.post-33668240684308689502015-01-05T07:47:09.150-05:002015-01-05T07:47:09.150-05:00dimethyl....
Have you actually read the papers yo...dimethyl.... <br />Have you actually read the papers you are citing? <br />This rant against real numbers (and infinities) is unjustified. No concrete, simple, alternative has ever been proposed. <br />I'm not sure if Cantor was a religious crank. Maybe he was. But do what? So was Newton. <br />From your phrase "you mathematicians try to go down one-way streets..." I infer that (a) you are not a mathematician and so you may not be able to understand those finite and transfinite numbers and their significance/users, and (b) you have a false impression about what mathematicians do. They don't *try* to go down one-way streets. Sometimes they do, but they don't do it on purpose. Most of the time, however, they go down streets full of interesting questions and problems and, to be sure, aiming at understanding what's out there. Takis Konstantopouloshttps://www.blogger.com/profile/14675216467783238403noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-2806700274049477132015-01-04T21:18:49.623-05:002015-01-04T21:18:49.623-05:00What a confused post. Cantor was a religious crank...What a confused post. Cantor was a religious crank who brought the contradictory mathematics of infinity into set theory FOR RELIGIOUS PURPOSES (read about him before commenting) and confused multiple generations of mathematicians. You are clearly ignorant of the fact that modern mathematics, with its incomprehensible "continuum," "infinities" and real numbers, is a complete mess.<br /><br />Tell Cantor to shove his "transfinite numbers," tell Turing to shove his "infinite tape" and tell Godel to shove his "for all." It's all meaningless! These people just hate computers and automation of their boring jobs. We compute with symbols just fine and refuse to do this with runtime logic errors! The law of the excluded middle is nonsense: colorless green ideas sleep furiously. What the hell is the profound nature of finding out that a system could not prove its consistency when you assumed you didn't trust it to start with? This modern theoretical "math" is so BOOOORRRRRRING!!!<br /><br />Alan J. Hu - Automatic Formal Verification of Software: Really! <br />https://www.youtube.com/watch?v=_LEkTEJWOeU<br /><br />(demonstrates the triviality of meaningless computational limits in actual practice)<br /><br />Real fish, real numbers, real jobs<br />http://link.springer.com/article/10.1007%2FBF03024838<br /><br />Doron Zeilberger that this anti-computer mathematics is a joke:<br />http://www.math.rutgers.edu/~zeilberg/Opinion68.html<br /><br />http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/real.html<br /><br />Norman Wildberger has a great series on YouTube about this issue:<br />https://www.youtube.com/user/njwildberger<br /><br />A True History of Strict Finitism<br />http://www.math.uni-hamburg.de/home/loewe/HiPhI/Slides/bendegem.pdf<br /><br />Solomon Feferman has proved that modern mathematics does not need Cantor's work: <br />http://www.amazon.com/In-Light-Logic-Computation-Philosophy/dp/0195080300<br /><br />And he knows the continuum hypothesis is bunk:<br />http://logic.harvard.edu/EFI_Feferman_IsCHdefinite.pdf<br /><br />Zenkin:<br />http://projecteuclid.org/euclid.rml/1203431978<br />http://www.researchgate.net/publication/255490016_CANTOR%27S_DIAGONAL_ARGUMENT_A_NEW_ASPECT<br /><br />Mueckenheim:<br />http://arxiv.org/pdf/math/0306200<br /><br />How real are real numbers? (Chaitin)<br />http://arxiv.org/pdf/math/0411418v3<br /><br />You mathematicians try to go down one-way streets with set theory and wonder why you lose information. The theory of algorithms is the future of math and not fuddy duddy set theory that does math backwards and puzzles, like a behaviorist, at the asymmetries.<br /><br />The negation of finite is nothing and not "infinity."Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-20067416.post-29302034034813364322014-12-03T10:54:38.516-05:002014-12-03T10:54:38.516-05:00I thought Durston claimed a biology background? w...I thought Durston claimed a biology background? why do so many creationists fancy themselves expert on everything?nmanninghttps://www.blogger.com/profile/14767343547942014627noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-25900600322133767492014-11-24T07:09:33.859-05:002014-11-24T07:09:33.859-05:00I loathe people who use "mathematics" to...I loathe people who use "mathematics" to "prove" their religious claims. Kirk Durston is not the worst. At least, one can argue, he doesn't know mathematics. But there are others, veritable mathematicians who keep blowing the horns of mathematics as evidence (or "proof") for the existence of (their) god. Example: John Lennox.<br /><br />Both types are much worse and much more dangerous than your typical religionist. The latter appeals to the church-goers. The former aspires to attract larger sets of people, those who accept as proof as an argument coming from authority. If only they could understand that Kirk Durston, John Lennox, Jerry Falwell and Jim Jones have similar "logic", they wouldn't be that deluded.Takis Konstantopouloshttps://www.blogger.com/profile/14675216467783238403noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-27927843377875796592014-11-21T13:32:32.348-05:002014-11-21T13:32:32.348-05:00Sounds like Durston must be one of those guys I...Sounds like Durston must be one of those guys I've seen on the Internet arguing against the proposition that <br /><br />0.9999... = 1<br /><br />I've noticed that those folks seem to see the ellipsis as a process, getting closer and closer but never reaching the limit, instead of a completed infinite sequence.Curt Cameronhttps://www.blogger.com/profile/08048312089881459521noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-21972294695596685602014-11-19T19:54:58.251-05:002014-11-19T19:54:58.251-05:00I agree that "count to a completed infinity&q...I agree that "count to a completed infinity" is meaningless, but it is trivial to formalize the notion of counting the elements of an infinite set in a finite amount of time.<br /><br />To make the notion of counting as concrete as possible, imagine the sequence of positive integers in order, as recited by Count von Count of Sesame Street.<br /><br />If the Count simply says each number 1% faster than its predecessor (which, while impossible for me, may well be within the powers of a muppet vampire) then the total time should converge (note that the time to recite each integer grows roughly logarithmically so it's a not quite a geometric series) to a finite limit.<br /><br />For any given integer, it is possible to determine the time at which the Count said it, and all of them would be done in time to complete the episode.<br /><br />I'm unfamiliar with the philosophical distinction between potential and completed infinity but I don't see how the above example would be considered anything other than a completed infinity.Paulhttps://www.blogger.com/profile/05140694525853737770noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-91503770322280889902014-11-17T09:09:57.016-05:002014-11-17T09:09:57.016-05:00If you want to see how an actual mathematician app...If you want to see how an actual mathematician approaches the same question (with tongue firmly in cheek) see R.K. Meyer, God Exists!, Nous, Vol 21, 1987 -- available on JSTOR. Meyer made many great contributions to systems of "relevant" logic, and always wrote with style and very dry wit.Jeffohttps://www.blogger.com/profile/06989946392105339862noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-1917423115657164392014-11-16T06:49:48.164-05:002014-11-16T06:49:48.164-05:00Yes, you're right. In that paragraph you quot...Yes, you're right. In that paragraph you quoted, Durston makes the mistake of thinking that the "universe with an infinite past" model entails the creation of the universe at some time t = ∞. But this is clearly erroneous. It just means that at every time t there exists a time t-1 at which the universe existed.Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-35529513984894802492014-11-15T23:59:03.563-05:002014-11-15T23:59:03.563-05:00So Kirk says he got his ridiculous claims from a m...So Kirk says he got his ridiculous claims from a mathematician, not a philosopher...thus he attempts argument from authority. As if that changes the fact that Kirk's writings are full of self-contradictions, contradictions of his own premises, as Jeff has shown. As if a mathematician defines a potential infinity as a "procedure", that makes it OK when Durston cites, then CONTRADICTS, the "procedure" definition. As if it's OK now that Kirk switched the cardinality of a set and the elements in it. As if it changes the fact that the distinction between "potential infinity" and "completed infinity" is still a distinction without a difference, and was still concocted by philosophers, a distinction never derived mathematically from any set of axioms, nor as an axiom ever shown to be useful to derive accurate results. In other words, it's still not a mathematical distinction or concept.<br /><br />At any rate, here's a previous bit of Kirk's misunderstandings of the basic features of set theory, from his blog.<br /><br />Kirk Durston: <i>"...let us pretend that the past was actually infinite. Now let us take a quantum leap infinitely far back into the past to some actual past time t. Let us call it t minus infinity. Since we are imagining that the real physical world had an infinite past, that time t minus infinity would actually have had to occur infinitely long ago. Now let us imagine doing what history is supposed to have actually done, and count down from t minus infinity to t now … t minus infinity, t minus infinity plus 1, t minus infinity plus 2, t minus infinity plus three, and so on. When would we arrive at t now? The answer is never. No matter how long we counted down from t minus infinity, there would always be an infinite number of seconds still to go before we got to t now."</i><br /><br />Jeff, I think you can catch the problem there: in the infinite set he is considering, he assumes it has element(s) that are infinite. As I pointed out at his blog, the set contains no infinite elements, all elements in it are finite; but the cardinality of the set is infinite. Basic error.<br /><br />All of this BS because William Lane Craig and Durston require an asymmetry between past and present, hoping to prove by thought alone (no observations) that the past is finite, which then "proves" that God created the universe; but the future is infinite, so they can live forever singing an infinite number of religious hymns in Heaven. Having their cake and eating it too.<br />Diogeneshttps://www.blogger.com/profile/15551943619872944637noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-5977203986598880032014-11-15T23:27:55.873-05:002014-11-15T23:27:55.873-05:00I see this load of garbage from Schechter:
"...I see this load of garbage from Schechter:<br /><br />"Nearly all research-level mathematicians today (I would guess 99.99% of them) take for granted both "potential" and "completed" infinity, and most probably do not even know the distinction indicated by those two terms."<br /><br />Wrong, Eric. 100% research-level mathematicians know there is no such garbage in real serious mathematics as "potential infinity" or "complete infinity" and hence no distinction between them. They are both garbage.<br /><br />I disagree slightly with Dr Shallit: I think wikjpedia is actually an amazingly good source for reading mathematics.<br /><br />But, as with all things, one must learn by doing, not just reading.Anonymoushttps://www.blogger.com/profile/07799396263113135068noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-9377792627091446492014-11-15T20:05:47.893-05:002014-11-15T20:05:47.893-05:00Oh, and a tip: when you want to understand a math...Oh, and a tip: when you want to understand a mathematical topic, I'd suggest reading a textbook on the subject, instead of relying on random web pages that have not been peer-reviewed.Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-57358556851311495742014-11-15T19:42:45.938-05:002014-11-15T19:42:45.938-05:00Thanks for the tacit admission that you are unable...Thanks for the tacit admission that you are unable to defend your arguments.Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-27514509400339501902014-11-15T18:59:14.335-05:002014-11-15T18:59:14.335-05:00I will leave it to the reader to read, in this rec...I will leave it to the reader to read, in this recommended order, Mathematician <a href="http://www.math.vanderbilt.edu/%7Eschectex/courses/thereals/potential.html" rel="nofollow">Eric Schechter's article</a>,then <a href="http://p2c.com/sites/default/files/documents/blogs/kirk/On%20the%20infinite%20past%20v.%203.pdf" rel="nofollow">my article</a> and then yours.Anonymoushttps://www.blogger.com/profile/00286138236210323687noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-79260237460437180582014-11-15T18:45:16.639-05:002014-11-15T18:45:16.639-05:00Nice try, Kirk. You're the one who wrote the ...Nice try, Kirk. You're the one who wrote the article; whether you cited or copied or plagiarized the definitions is not my concern. <br /><br />Why not address the arguments I made, instead of pretending you didn't rely on those definitions?Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-3653859254543172912014-11-15T18:20:12.711-05:002014-11-15T18:20:12.711-05:00Jeffrey, thank you for taking the time to critique...Jeffrey, thank you for taking the time to critique my short article. In reading your critique, I wondered if you had checked the links/references I provided. You will see that some of your key concerns are not with me but with Mathematician <a href="http://www.math.vanderbilt.edu/%7Eschectex/courses/thereals/potential.html" rel="nofollow">Eric Schechter's essay</a>. For example, the word 'procedure' is not mine, but part of his definition of a potential infinity. Also, the definitions and concepts you credit me with are not mine, but Schechter's and I have linked and referenced each one to them. Both you and Schechter are mathematicians, so much of your concern seems to hinge on a disagreement primarily between mathematicians.Anonymoushttps://www.blogger.com/profile/00286138236210323687noreply@blogger.com