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 01:13 "Transfer Principle" <lwalke3(a)lausd.net> wrote .. > On Jun 5, 8:20 pm, 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. > > 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 proof is essentially a computer program. I'm giving you a description of my 4 algorithms, but you keep asking what syntax and computer I'm using. I'm pointing out your trivial obvious errors, I'm not defining a new branch. But instead off calling you all wrong, I will just say your results are meaningless. Higher infinities and incompleteness and most of your uncomputable claims are just platonic drivel. Mathematics is a machine, so is a turnip incinerator. Herc
From: Transfer Principle on 6 Jun 2010 01:54 On Jun 5, 10:13 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > "Transfer Principle" <lwal...(a)lausd.net> wrote .. > > 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" What does Herc mean by "factual" here? Does he mean that classical mathematics doesn't prove anything about the real world. If so, then I agree with Herc to some extent. It is true that "ZFC proves that N and R do not have the same cardinality" is indisputable, since it does follow from the axioms of ZFC. Yet one will be hard-pressed to find an uncountable object in the real world. Indeed, some physicists wonder whether length, time, etc., can be quantized (Planck units), which would imply that there's no real-world example of an _infinite_ object, much less an uncountable object. It is precisely for this reason that I am open to reading about alternate theories, as long as those theories don't contradict empirical evidence. Thus, even I won't defend a theory which seeks to prove that 2+2 = 5, since one can prove in the real world that 2+2 = 4, not 5. But since the real world can't prove anything about infinity, I'm open to many different theories about infinity, including NFU, PST (Pocket Set Theory), intuitionism, as well as finitist set theories like ZF-Infinity in which one can't necessarily prove that infinite sets exist. I am even somewhat open to _ultrafinitist_ theories where there's an upper bound on the largest natural number that exists, as long as that upper bound is larger than any number that can describe objects in the real, physical world. > Higher infinities and incompleteness and most of your uncomputable claims are just > platonic drivel. I agree (except for the word "drivel").
From: Marshall on 6 Jun 2010 09:06 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. 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. 3) "disagree" insofar as this one is provably false. 4) Never was clear on what this was claiming. If it's claiming that the real numbers are countable, then disagree. > 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. Marshall
From: Marshall on 6 Jun 2010 09:13 On Jun 5, 10:54 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > Yet one will be hard-pressed to find an uncountable > object in the real world. You'll never find a three in the real world either, but that doesn't mean that three is therefore a somehow problematic concept. > Indeed, some physicists > wonder whether length, time, etc., can be quantized > (Planck units), which would imply that there's no > real-world example of an _infinite_ object, much less > an uncountable object. Sure; so what? The point of math isn't to exactly faithfully model the universe. There is exactly and precisely only one *complete* model of the universe; that is the universe itself. Any other model is necessarily leaving something out. (Probably quite a lot in fact.) > > Higher infinities and incompleteness and most of your uncomputable claims are just > > platonic drivel. > > I agree (except for the word "drivel"). And yet there is no bijection between the natural numbers and the real numbers. You might be able to make up a theory in which you can prove that there is, but you won't be able to demonstrate it, because it doesn't exist. (And from there a trivial application of the pigeonhole principle shows the existence of uncomputable reals.) Marshall
From: FredJeffries on 6 Jun 2010 13:10
On Jun 5, 10:54 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > Yet one will be hard-pressed to find an uncountable > object in the real world. Indeed, some physicists > wonder whether length, time, etc., can be quantized > (Planck units), which would imply that there's no > real-world example of an _infinite_ object, much less > an uncountable object. You would be hard pressed to find a 7-dimensional object in your real world either. But the mathematics of more-than-three dimensional spaces is used all the time in economics, programming, meteorology, agriculture, war, advertising, ... and give accurate useful answers and predictions. Are all of these answers and predictions invalidated because the scientists and engineers used illegitimate mathematics? There's no such thing as a seventh dimension in the real world. So all the bridges and buildings start falling down? You're taking set theory too rigidly by insisting that the only possible real world application is to collections of tangible objects. If hyper-mahlo demi-measureable non-inaccessible sub-cardinalities are ever found in the "real world" it will be in some area hitherto not well modeled mathematically like psychology, ethics, linguistics, swearing, deodorants, ... > > It is precisely for this reason that I am open to > reading about alternate theories, as long as those > theories don't contradict empirical evidence. Thus, > even I won't defend a theory which seeks to prove > that 2+2 = 5, since one can prove in the real world > that 2+2 = 4, not 5. But there's a great yet-to-be-discovered cryptographic system based on a system where 2 + 2 = 5. Not to mention rabbit breeding or bowling (I get 6 pins with my first ball, 4 with my second, 8 with my third and roll a gutter ball with my fourth. What's my score?). > But since the real world can't > prove anything about infinity, Your real world doesn't prove anything about anything. It is human minds who sift through their sense impressions, highlighting some, discarding others, who decide what is to be proved, what constitutes a proof and whether a proposed proof really is a proof of what it alleges to prove. > I'm open to many > different theories about infinity, including NFU, > PST (Pocket Set Theory), intuitionism, as well as > finitist set theories like ZF-Infinity in which one > can't necessarily prove that infinite sets exist. I > am even somewhat open to _ultrafinitist_ theories > where there's an upper bound on the largest natural > number that exists, as long as that upper bound is > larger than any number that can describe objects in > the real, physical world. Theories don't describe objects in the real, physical world. People describe. And one of the tools people use in making descriptions is mathematics. Someday a brilliant scientist uses an ultrafinitist theory with an upper bound on the largest natural number that exists (lets call it W) to give a unified theory-of-everything which is able to be used to predict everything about the universe, solve all of our problems and establish world peace. Except flightless waterfowl. To explain penguins he needs to use W + 274 but the ultrafinitist theory with an upper bound of W + 274 doesn't work for the rest of the universe. So you would not be open to that theory? Not even somewhat? |