Give me ONE digit position of any real that isn't computable up to that digit position!
in [Math]
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From: |-|ercules on 6 Jun 2010 13:39 "Marshall" <marshall.spight(a)gmail.com> wrote > On Jun 5, 8:45 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: >> "Marshall" <marshall.spi...(a)gmail.com> wrote.. >> >> > On Jun 5, 8:12 pm, Transfer Principle <lwal...(a)lausd.net> wrote: >> >> >> But this all goes back to the question that I've been >> >> asking this past fortnight or so, ever since Herc >> >> started this recent posting spree. Is Herc really >> >> trying to introduce a new theory (or "theories"), or is >> >> he trying to prove that classical ZFC is "wrong"? >> >> > Neither one. >> >> > He's using the word "theory" to mean "theorem." >> > What he's trying to do is prove some established >> > theorems false. >> >> Right! >> >> 1/ I designed the simplest computer fetch cycle >> >> 2/ I proved Godel's proof places no bounds on knowledge >> >> 3/ I proved the possible existence of an effective halt algorithm >> >> 4/ I showed that higher infinities are thought to be implied by the non existence >> of a box that contains the numbers of the boxes that don't contain their own number >> >> No-one has agreed or disagreed with 1 - 3, a couple have disagreed with 4 without >> substantiating why. > > For what it's worth: > > 1) Is uninteresting to me; neither agree nor disagree. The simplest computer model is uninteresting? > 2) The way you phrased it in this post is sorta weird, but in > other posts you've said this one says that a computer and > a human are on equal footing with regards to Incompleteness; > I agree. Does "this statement has no proof" limit the boundaries of your comprehension? > 3) "disagree" insofar as this one is provably false. Do you think the following is flawed? --------------------------------------------------------- Once there was no polynomial time algorithm to determine if a number is prime. However Rabin found a probabilistic solution based on witnesses to compositeness. Over half of numbers from 1 to any composite number are witnesses so they are easy to find. If you run 100 iterations of the algorithm and no witness is found, the number is prime with probability 1 - (1/2)^100. P(x is prime) = 99.9999999999999999999999999999999999%. Such an attack could be used for a halting algorithm, add a parameter to the probabilistic Halt function which has 3 outcomes. pHalt(program, input, p) = {Halts | NotHalts | DontKnow} If half of values of p produce the correct result Halts or NotHalts, then performing numerous iterations would give an effective procedure to determine if a program halts or not. --------------------------------------------- > 4) Never was clear on what this was claiming. If it's claiming > that the real numbers are countable, then disagree. So you think the nonexistence of a box that contains the numbers of all the boxes that don't contain their own number implies higher infinities? > >> Aatu said they were all wrong then disappeared to work on >> his *informal proof* of the incontrovertible fact that all informal proofs can be formalized. > > Disagree. So you agree with Aatu his "demonstration of incontrovertible fact" was of a non-mathematical nature and not in the scope of it's own demonstrated assertion? Herc
From: Marshall on 6 Jun 2010 22:11 On Jun 6, 10:39 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: > "Marshall" <marshall.spi...(a)gmail.com> wrote > > On Jun 5, 8:45 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > >> "Marshall" <marshall.spi...(a)gmail.com> wrote.. > >> > On Jun 5, 8:12 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > >> >> But this all goes back to the question that I've been > >> >> asking this past fortnight or so, ever since Herc > >> >> started this recent posting spree. Is Herc really > >> >> trying to introduce a new theory (or "theories"), or is > >> >> he trying to prove that classical ZFC is "wrong"? > > >> > Neither one. > > >> > He's using the word "theory" to mean "theorem." > >> > What he's trying to do is prove some established > >> > theorems false. > > >> Right! > > >> 1/ I designed the simplest computer fetch cycle > > >> 2/ I proved Godel's proof places no bounds on knowledge > > >> 3/ I proved the possible existence of an effective halt algorithm > > >> 4/ I showed that higher infinities are thought to be implied by the non existence > >> of a box that contains the numbers of the boxes that don't contain their own number > > >> No-one has agreed or disagreed with 1 - 3, a couple have disagreed with 4 without > >> substantiating why. > > > For what it's worth: > > > 1) Is uninteresting to me; neither agree nor disagree. > > The simplest computer model is uninteresting? That's right. Uninteresting. The TM is already too simple to be of much interest to me. What is done with it could be done with any model of computation; TMs are adequate for what we do with them but they are horrifically awful by almost any metric I can think of. My opinion here is a minority one, though. Are you claiming your model is the simplEST possible? Or just that it's simpler than TMs? > > 2) The way you phrased it in this post is sorta weird, but in > > other posts you've said this one says that a computer and > > a human are on equal footing with regards to Incompleteness; > > I agree. > > Does "this statement has no proof" limit the boundaries of your comprehension? I'm not certain but I think we're in agreement on this issue. > > 3) "disagree" insofar as this one is provably false. > > Do you think the following is flawed? I must be if it says a halting algorithm is possible. > > 4) Never was clear on what this was claiming. If it's claiming > > that the real numbers are countable, then disagree. > > So you think the nonexistence of a box that contains the numbers of all the boxes > that don't contain their own number implies higher infinities? I don't know what that means. But I know there is no bijection between the naturals and the reals. > >> Aatu said they were all wrong then disappeared to work on > >> his *informal proof* of the incontrovertible fact that all informal proofs can be formalized. > > > Disagree. > > So you agree with Aatu his "demonstration of incontrovertible fact" was of a non-mathematical > nature and not in the scope of it's own demonstrated assertion? I disagree that Aatu said what you characterize him as saying. Marshall
From: herbzet on 6 Jun 2010 22:38 |-|ercules wrote: [...] > 4/ I showed that higher infinities are thought to be implied by the > non existence of a box that contains the numbers of the boxes that > don't contain their own number > > [...] a couple have disagreed with 4 without substantiating why. You seem to have forgotten that I did just that: news:4C09C6CC.4A8B8EB(a)gmail.com . So also did William Hughes: news:e11507ed-53f6-4e70-9332-f2f4cf24830d(a)k39g2000yqb.googlegroups.com You also seem to have forgotten that in your thread "SCI.MATH POLL - uncountable infinity" you specifically requested that responders *not* substantiate their replies: "No explanations or you will spoil the poll, just TRUE or FALSE." So -- que voulez-vous? What do you want? -- hz
From: |-|ercules on 6 Jun 2010 22:58 "Marshall" <marshall.spight(a)gmail.com> wrote >> So you think the nonexistence of a box that contains the numbers of all the boxes >> that don't contain their own number implies higher infinities? > > I don't know what that means. But I know there is no > bijection between the naturals and the reals. Given a set of labeled boxes containing numbers inside them, can you possibly find a box containing all the label numbers of boxes that don't contain their own label number? > > >> >> Aatu said they were all wrong then disappeared to work on >> >> his *informal proof* of the incontrovertible fact that all informal proofs can be formalized. >> >> > Disagree. >> >> So you agree with Aatu his "demonstration of incontrovertible fact" was of a non-mathematical >> nature and not in the scope of it's own demonstrated assertion? > > I disagree that Aatu said what you characterize him as saying. Can you paraphrase what Aatu said? Herc
From: Barb Knox on 6 Jun 2010 23:44
In article <870p4oFkopU1(a)mid.individual.net>, "|-|ercules" <radgray123(a)yahoo.com> wrote: > "Transfer Principle" <lwalke3(a)lausd.net> wrote .. > > On Jun 5, 8:20 pm, Marshall <marshall.spi...(a)gmail.com> wrote: [snip] > >> What he's trying to do is prove some established > >> theorems false. > > > > Thanks for the clarification. So Herc is trying to > > prove that established theorems (of ZFC) are false. > > > > According to Knox, Herc is trying to prove that > > classical mathematics is "wrong." And like Knox, I > > wish that Cooper would just consider an alternate > > theory (she mentioned intuitionism) if he doesn't > > like classical mathematics that much. > > > It's hard to prove classical mathematics is wrong when every time > I dispute your claims you jump back to shore and say "nahh nahh > we didn't claim anything factual we just have some axioms and derivations" <a penny begins to drop> But that is *precisely* all that modern mathematics *does* claim. Really. From Euclid until relatively modern times, "axioms" were considered to be "obvious truths" about the real world, from which theorems were derived which also necessarily applied to the real world. But the success of non-Euclidean geometries fatally wounded that idea, and most modern mathematicians agree with Einstein that: As far as the propositions of mathematics refer to reality they are not certain, and so far as they are certain, they do not refer to reality. A lot of folks (including some very clever ones such as Lewis Carroll and Goedel) have found this view very hard to digest. So, it seems your quarrel is not so much with the content of (modern) mathematics, but with the historical turn that changed the entire focus of the enterprise from "real world" axioms to arbitrary axiom systems (some of which happen to do a fine job of describing some useful structures in the "real world"). Note that that these days "applied mathematics" is the branch that does focus on "real world" systems. You might enjoy looking into this area. Also, I expect you would benefit from reading about the Euclidean / non-Euclidean controversy that raged (and I do mean raged) at the time. Any decent text on the history of mathematics will cover this. > A proof is essentially a computer program. Almost true, but not quite, and the difference is crucial. A proof is essentially the *output* of a (metaphorical) machine that crunches axioms into theorems. This logical *machinery* (and there are several to choose from) is a METAMATHEMATICS, and the *objects* that it manipulates internally are its mathematics. You are absolutely correct that the machinery of a metamathematics is essentially finite a computer program. But the objects it manipulates can represent *anything*, including higher infinities. For example, there are popular computer games that deal with all sorts of non-real-world objects and situations (such as aliens, FTL travel, getting another life after you get shot). The game system is the metamathematics; the content of the game is the mathematics. Metamathematics seems to be the sort of thing you would find congenial. Perhaps some others here can recommend a good introductory text. [snip] > Higher infinities and incompleteness and most of your uncomputable claims are > just platonic drivel. Note that platonism is only one view of the ontology of mathematics. Equally compelling is "nominalism", which basically says that just because we can write down an expression (a "name") does not imply that there is a real "something" "somewhere" that corresponds to that name. So the fact that ZFC has an expression for "the power-set of the set of all natural numbers" does *not* give that name any magical power of creating existence in the "real world" or any other reality. It's like a game, or a story. Humans have a long history of using word magic, where manipulating the name of something or someone is thought to affect that thing or person. The modern description for such a belief is "hogwash". Saying "Bloody Mary" 3 times in a mirror will *not* conjure up someone who will kill you. The name "Santa Claus" exists in the real world; the named person does not. > Mathematics is a machine, so is a turnip incinerator. Nooooo!! METAMATHEMATICS is the machine, mathematics is the turnips (or integers or sets or higher infinities or uncomputable reals or whatever or whatever). In conclusion, please have a look at some of the following topics: History of the non-Euclidean geometry controversy Applied mathematics Metamathematics Nominalism I strongly expect that you will find ideas there that are quite compatible with your preferred beliefs. Pax. -- --------------------------- | BBB b \ Barbara at LivingHistory stop co stop uk | B B aa rrr b | | BBB a a r bbb | Quidquid latine dictum sit, | B B a a r b b | altum videtur. | BBB aa a r bbb | ----------------------------- |