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 7 Jun 2010 00:52 "Barb Knox" <see(a)sig.below> wrote > 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 | > ----------------------------- I don't have to redesign a digital electronic computer, data packet protocol, transmission control protocol, hypertext transfer protocol, usenet protocol, newsreader protocol, hardware, software and implementation and integration system to tell you your sig doesn't work in 99% of usenet readers because fixed width font was abandoned when Bill Gates made his first billion. I don't care how many text books in CERN prove your sig worthiness in how many standards. Also, I'm working on Winograds talking computer program from 1971, great reading (the AI's words) if you're into that. So a maths degree is not scheduled until I'm at least 200. I did find it interesting all mathematicians had tragic lives, some kind of curse I thought I would be exempt from, but the unwillingness of sci.math to use their probability theory to evaluate the natural Vs unnatural coincidence phenomena my life entails has led to 8 years of sonic torture so far. You could always answer this question Barb which would prove you all wrong in an instant, there is more than one scientific method. > 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? Still think it's paradise Barb Knocks? Herc
From: Barb Knox on 7 Jun 2010 03:59 In article <873c8lFpmfU1(a)mid.individual.net>, "|-|ercules" <radgray123(a)yahoo.com> wrote: > "Barb Knox" <see(a)sig.below> wrote [SNIP] > I did find it interesting all mathematicians had tragic lives Thaat may be interesting, but it's false. [snip] > the > unwillingness of sci.math to use their probability theory to evaluate the > natural Vs unnatural coincidence phenomena my life entails You have not had significantly more interesting coincidences in your life than anyone else has. You *have* noticed quite a few interesting things about your life; you have *not* noticed the very many more uninteresting things about your life -- that's just a fact about human cognition. Elementary Bayesian analysis of your situation would take into account the facts that: (1) The vast majority of people who think that they are very very special or have some mission from god or are themselves god are in fact wrong, and are often delusional. (2) The majority of people who get committed to a psychiatric institution for schizophrenic delusions are in fact delusional. > has led to 8 years of sonic torture so far. Oh yes, and (3) One of the more common sorts of delusion is delusion about being persecuted. -- --------------------------- | 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 | -----------------------------
From: herbzet on 7 Jun 2010 06:38 |-|ercules wrote: > "herbzet" wrote ... > > |-|ercules wrote: > >> I want to hear mathematicians explain why the nonexistence of a box that contains > >> the numbers of the boxes that don't contain their own number means that higher > >> infinity exists. > > > > Who said that? Cite, please. > > you did. > > -------------------------------------------------------------------------------- > > > Because the most widely used proof of uncountable infinity is the > > contradiction of a bijection from N to P(N), which is analagous to > > the missing box question. > > Perhaps so, but why do you ask? > > -- > hz > > ------------------------------------------------------------------------------ Then again, perhaps not. -- hz
From: herbzet on 7 Jun 2010 06:59 |-|ercules wrote: > "herbzet" wrote ... > > |-|ercules wrote: > >> "herbzet" wrote ... > >> > |-|ercules wrote: > > > >> >> I want to hear mathematicians explain why the nonexistence of a box that contains > >> >> the numbers of the boxes that don't contain their own number means that higher > >> >> infinity exists. > >> > > >> > Who said that? Cite, please. > >> > >> you did. > >> > >> -------------------------------------------------------------------------------- > >> > >> > Because the most widely used proof of uncountable infinity is the > >> > contradiction of a bijection from N to P(N), which is analagous to > >> > the missing box question. > >> > >> Perhaps so, but why do you ask? > >> > >> -- > >> hz > >> > >> ------------------------------------------------------------------------------ > > > > Then again, perhaps not. > > you can crawl back under your rock until the box question goes away. What question was that now? You keep moving the goalposts on us. Perhaps if you can manage to phrase the question with some rigor, it is possible that you would receive a concise reply. -- hz
From: herbzet on 7 Jun 2010 08:19
|-|ercules wrote: > "herbzet" wrote ... > > |-|ercules wrote: > >> "herbzet" wrote ... > >> > |-|ercules wrote: > >> >> "herbzet" wrote ... > >> >> > |-|ercules wrote: > >> >> >> "herbzet" wrote ... > >> >> >> > |-|ercules wrote: > >> >> > > >> >> >> >> I want to hear mathematicians explain why the nonexistence of a box that contains > >> >> >> >> the numbers of the boxes that don't contain their own number means that higher > >> >> >> >> infinity exists. > >> >> >> > > >> >> >> > Who said that? Cite, please. > >> >> >> > >> >> >> you did. > >> >> >> > >> >> >> -------------------------------------------------------------------------------- > >> >> >> > >> >> >> > Because the most widely used proof of uncountable infinity is the > >> >> >> > contradiction of a bijection from N to P(N), which is analagous to > >> >> >> > the missing box question. > >> >> >> > >> >> >> Perhaps so, but why do you ask? > >> >> >> > >> >> >> -- > >> >> >> hz > >> >> >> > >> >> >> ------------------------------------------------------------------------------ > >> >> > > >> >> > Then again, perhaps not. > >> >> > >> >> you can crawl back under your rock until the box question goes away. > >> > > >> > What question was that now? You keep moving the goalposts on us. > >> > > >> > Perhaps if you can manage to phrase the question with some rigor, > >> > it is possible that you would receive a concise reply. > >> > > >> > >> ok, we have boxes, all numbered from 1, 2, 3... and so on indefinitely. > >> > >> inside the boxes are some physical representations of natural numbers, > >> any finite or infinite amount of them, composed of 1 of each of 1, 2, 3... > >> > >> can any of the boxes contain only the numbers of all the boxes that don't contain > >> their own numbers? No. > >> what can you deduce from this? Among the infinite(!) number of statements I could *validly* deduce from this statement, I could deduce that (1) If there is an infinite set S, then there is a set S' of greater cardinality. -- hz |