Conservapedia talk:Conservapedian mathematics/Archive1

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Coffee

I got the coffee cup - donut but could you just go on from there please, please? Susan^{... miaow ...} 16:15, 21 November 2007 (EST)

What needs to be done here? airdish 16:32, 22 November 2007 (EST)

category theory

we really need something about this. the complete lack of reference in the "added reference to abstract nonsense" is particularly special. in my opinion, he's read an article about Paul Erdös (pronounced airdish(!)) and his concept of "proofs from the book", ie that the best proofs were simple and beautiful and had vast and powerful ramifications, and twisted it to the nth degree (but kept it in the real numbers). airdish 03:35, 23 November 2007 (EST)

Wow, circular definition much? That's an awesome (pair of) link(s) (if you click on the abstract nonsense link), and belongs not only in WIGO, methinks, but "best of CP" as well. human 14:40, 25 November 2007 (EST)

I'll do that now. airdish 03:20, 28 November 2007 (EST)

Thanks! human 16:08, 28 November 2007 (EST)

As a side note, the Erdos entry is quite funny as well. They are desperate to hold up examples of successful homskullers. But they make only a passing, half joking, mention that he was an atheist, and don't make any mention that he was a homeless drug-addict. All three not very high on the list of things CS likes.Antifly 16:22, 29 June 2008 (EDT)

Complex numbers

Someone else seems to have a beef with them. Unless this is Andy's sock. The objection seems to be related to this.--Bayes^update 15:19, 25 January 2008 (EST)

Probably a psrodtst channeling teh assfly. Andy thinks complex numbers are teh ebil because they steam up his glasses, no matter how many times teh roger assfly explains them to him. human 16:34, 25 January 2008 (EST)

OK, having an EE background Andy S's gripes with complex numbers simply blows my mind. The article says they're used in Fourier analysis ... true enough, but Andy's lunacy is deeper than that, because they're used in elementary AC circuit analysis. I mean, Andy's like a plumber who's decided to lash out at pipe wrenches. MrG 71.208.28.238 (talk) 01:10, 23 May 2011 (UTC)

Proof by Contradiction

I can kind of see Andy's point about proof by contradiction. I mean, proving something by showing that it's opposite is NOT true? That's just crazy. On the other hand, Andy seems to have dedicated his life to proving creationism by disproving Darwinism. TWIST! User:64.106.84.253

Proof by contradiction works by showing that denying the hypothesis leads to contradictions, not necessarily (though usually) its opposite. Example. NightFlare^{Speak, mortal} 18:06, 26 January 2008 (EST)

It was just over 30 years ago when my Uni Math tutor criticised my use of Proof by Contradiction, saying that Proof by Contradiction was only used as a last resort for a reason which would apply to any proof, not just for existential claims. It is that it requires the conjecture to be proved to be either true or false, whereas it might be meaningless. The classic example: Take the propositions, A: B is true and B: A is false . What are their truth values? There is no combination of True or False that can be attached to them that does not generate a contradiction. A non-exhaustive examination of deductions however, could apparently spuriously "prove" one of them by contradiction. Unsigned below seems much more knowledgeable than me but I think their argument is flawed. As they correctly observe, a PBC that works proving P by showing that P' => Q' where Q is known to be true is indeed no more "dangerous" than a normal proof and a proof may always be possible directly. However, what about a PBC that proves P by assuming P' but then nevertheless deducing P from it? This kind of proof is subject to the kind of objection above,and also it may be possible to furnish a proof in this fashion where this none, or at least none discovered, by any other method, not least in the case of meaningless conjectures such as the above. This surely is the kind of PBC that all the fuss is about, and which I at least hope Andy is objecting to. (Am i naive!). PardreObe (talk) 17:32, 15 December 2009 (UTC)

There actually have been serious philosophical discussions in the foundations of mathematics, both about proof by contradiction and about elementary methods. Proof by contradiction is generally disfavored by mathematicians (at least for proofs of existential claims), for the obvious reason that a proof of an existential claim by contradiction generally gives no information relevant to an actual construction of the object that is proven to exist. However, for about 99% of mathematicians, this is just a mild sort of disfavoring. There is a school of (mainly Dutch) mathematicians called "constructivists" or "intuitionists" who follow Brouwer (and Kronecker before him), and to some extent also the famous French analysts Borel, Lebesgue, and Hadamard, in rejecting non-constructive proofs of this sort, on the grounds that mathematics is about constructions (since it clearly isn't about physical objects) and therefore an existence proof must be constructive. Most mathematicians reject these claims about the subject matter of mathematics (instead treating math either as a purely formal game with symbols, or as being about an independently existing but totally abstract realm) and therefore are fine with non-constructive proofs, even though constructive ones are often more illuminating. So there is a real controversy here, but it's not exactly central.

As for elementary methods, people have at various points considered this a very important idea in mathematics. Certainly in the 19th century, people were often quite surprised when statements not involving the complex numbers seemed to effectively require complex numbers in their proofs. (Technically the complex numbers aren't required, because they are a conservative extension of the real numbers, but duplications of Riemann and Chebyshev's famous arguments basically repeat the complex number constructions in a slightly more complicated way.) So there was a lot of anticipation of some day finding an elementary proof of the Prime Number Theorem - but when Selberg and Erdös finally gave one, people realized that it was really no more illuminating than the complexified argument was. I believe there are some interesting research programs around the notion of elementary proofs, but certainly nothing very mathematically central. For further reference on the topic, I would look at the work of the philosophers of mathematics Andrew Arana, and Mic Detlefsen.

Finally, there is one sense in which the complex numbers are a strange structure - there is no mathematical property belonging to i that doesn't also belong to -i. Therefore, there is no way to pick out which one is which, which causes problems for a theory of reference, if we think mathematical language somehow refers to independently existing entities. One way around this is to work with a particular construction of the complex numbers (say, as ordered pairs of reals), which gives us non-mathematical properties that distinguish i and -i. But this is fairly inelegant. The complex numbers are however far from unique in this way - just consider the free group on a single generator, and realize that there is no distinguishing g and -g in this group. Or better yet, consider the unique group of 7 elements, and notice that no non-zero element in this group is distinguished from any other. But since we normally work with particular instantiations of this group structure, rather than the abstract group, this doesn't cause any actual mathematical problems.

I think this article could do a lot better in defending proof by contradiction than it does at the present. Saying it has been accepted for a long time and is widely accepted today are strong arguments but I think we can do more. I freely admit that I am no expert on logic and may well have this wrong but I think that there is no essential difference in proof by contradiction and any other kind of proof. If you prove a statement P by contradiction you assume the converse of P, P' say and you get a contradiction, i.e. you get P' => Q' where Q' is known to be false (Q is true) hence P must be false by the truth table for =>. Now any argument like this can be turned into a normal proof by taking contrapositives, so we know Q is true, we use the reverse argument to get Q => P. using contrapositives we have (P' => Q') <=> (Q => P). So these arguments are equivalent, one cannot be more contravertial than the other. In fact, contradiction is only used for ease, in some cases it is easier to write P' => Q' than Q => P. There is no such thing as a theorem which can only be proved by contradiction, the ones that are proved using it are just easier to write that way.

Andy stated his objection to proof by contradiction was that as ZFC might be inconsistent, so any contradiction reached might not mean the assumption is false. i.e. we have P' => Q', Q' is false so we conclude P is true, however, unknown to us Q' is also true (it is a contradicion) so our conclusion is false. This isn't as dangerous as it seems, from experience of assuming false things by mistake, making false conclusions usually leads you to the mistake (or contradiction in this case) faster. Anyway, as I mentioned before this difficulty is not unique to contradiction. If we assume Q and prove P as in a normal proof, nut Q' is also true then our conclusion is again false and normal proofs are just as dangerous. Again, we have Andy talking with authority and jumping to conclusions about things he is ignorant of.

Perhaps someone more concise than me could add this to the article.

On the point, of constructivism, that is in the realm of the philosophy of maths as to what sorts of proofs are acceptable. It is a perfectly valid opinion but most mathematicians don't accept it and I think that is the correct decision to make. Again the problem has nothing to do with contradiction anyway. If you prove that something exists by showing that its non-existance leads to a contradiction then that is equivalent to assuming the converse of the contradiction and working back to the conclusion that this thing exists. You still have a non-constructive proof of existence but without using contradiction.

About complex numbers, the canonical way to define them is with ordered pairs of reals, this puts them on a footing as well defined and rigorous as any set and is a very elegant way to do it. Saying i is a "number" such that i^2 = -1 and letting complex numbers be a+bi is not a rigorous construction of C and shouldn't be used in formal books. Under this construction there is a difference between i and -i, Im(i) = 1, Im(-i) = -1. If you think this is artificial then you could say the same about 1 and -1. No set is well defined up to a relabelling of its elements anyway. Consider f:R->R f(x) = -x. We relabel R by swapping the sign so we can't "really" tell which number "is" 1 and which "is" -1. Anything you can say about iR you can say about R because iR is just a relabeling of R. In this respect we can't tell the difference between 1 and i. These kind of uniqueness issues aren't a problem for any mathematicians as we always aork up to isomorphism.

Rant over. Sorry! ^{— Unsigned, by: 195.112.46.6 / talk / contribs}

Hey, I never gave thanks for this insight, so... thank you! Flare^Talk 21:20, 11 June 2009 (UTC)

In computer science there is a thing called the Curry-Howard correspondence, according to which many notions in logic have a precise counterpart in the realm of typed lambda calculus. Most fundamentally, propositions are types, and proofs are programs. Each type system corresponds to a different logic. Most functional languages correspond to inconsistent logics because every type has a corresponding term, even the always-false proposition $\bot$ - this is actually what allows them to have unrestricted recursion and thus be Turing-complete. But there are type systems that correspond to predicate logic, such as Martin-Löf's "intuitionistic type theory" (also called Martin-Löf type theory, or sometimes even, rather pretentiously, just "type theory"), and (technically non-Turing-complete) programming languages that use it. For example, if you had a type representing the real numbers (not just IEEE floating point numbers but actual arbitrary precision real numbers), you could write a program of the type

$\prod _{l:list(\mathbb {R} )}\prod _{countable(l)}\sum _{n:\mathbb {R} }n\notin l$

The Πs correspond to universal quantifiers, and the Σs to existential quantifiers. The whole type corresponds to the proposition "for every countable sequence of real numbers, there exists a real number n such that n is not in that sequence", i.e. Cantor's diagonalization theorem. A lambda term of that type would correspond to a constructive proof of the theorem - but it's also a program, specifically, it's a function whose arguments are a sequence of real numbers and a proof that that sequence is countable, and whose result is a pair of 1) the number that isn't in the sequence and 2) a proof that it isn't in the sequence. The important point is that the proof is constructive. The logic doesn't include a primitive (i.e. axiom) of the type

$\prod _{P:Set}\prod _{\prod _{\prod _{P}\bot }\bot }P$

(or more simply $\forall P.((P\rightarrow \bot )\rightarrow \bot )\rightarrow P$, i.e. double negation elimination) because there is no way, in general, to produce a $P$ from a $\neg (\neg P)$. There might be, for some $P$, but not without knowing anything about $P$. As a consequence, it's impossible to formulate proofs by contradiction in intuitionistic type theory.

Now there are proof assistants that allow you to assume double negation elimination and/or excluded middle as an axiom, but using it removes the possibility of creating a program from such a proof. Most mathematicians aren't intuitionists and will be happy to write proofs using double negation elimination, as long as the proof isn't needed in the computation. Thrawcheld (talk) 00:56, 10 February 2016 (UTC)

Conway's Game of Life

I think this section needs a little rewriting. For one thing, the Conservapedia quote is partially correct, in that "the slightest change in self-sustaining patterns... usually destroys them." Sufficiently complex structures like guns and rakes generally aren't created with random patterns--in fact, it is quite difficult to create prior states ("synthesis") for most of these complex structures at all! And, as they state, once these complex structures are created, an interaction with a glider can often take them down.

On the other hand, our sentence following this, which states that "[r]andom patterns in the Game of Life frequently produce both gliders and stationary self-sustaining patterns," is true, because those objects are very, very simple. A glider, for instance, consists of only five lit cells, as opposed to the more complex structures CP describes, which typically sport dozens, if not hundreds, of lit cells moving in a precise fashion.

Furthermore, the Game of Life being described by both parties cannot be used to make an accurate statement about biological evolution at all, because (aside from random initial configurations), it does not invoke randomness at all! Much more useful for such a demonstration would be a probabilistic version of the Game (I found one here, though it seems to have since been taken down), in which probabilistic "cell has 70% chance of staying lit"-type rules simulate the randomness of mutations. Then, of course, we'd need something to model natural selection, but that's beyond me... Anyway, I thought I'd point this out. 71.50.80.77 20:14, 5 August 2008 (EDT)

I think the argument we are making is with the sentence "Only those patterns created by human beings (or discovered and preserved by them) have any chance of being perpetuated." emphasis mine. I gotta go check that link now, adding random mutations and selection pressure (other than the human observer saying "that's pretty!") to life is a neat idea... ħuman 20:21, 5 August 2008 (EDT)

Dead link, can you help? ħuman 20:22, 5 August 2008 (EDT)

Unfortunately not. It was the only probabilistic version I found after hours of Googling one boring day earlier this summer, and I don't know of any other such sites. Sorry. 71.50.80.77 20:35, 5 August 2008 (EDT)

Dang, thanks anyway. One of these days I need to delete the 90% of my thousands of bookmarks that are probably dead, too... ħuman 21:00, 5 August 2008 (EDT)

At LemonPeel or whoever knows

Does anybody know exactly what was added to the natural logarithm page that got it deleted? Does anyone mind asking LemonPeel at CP? I've been curious. NightFlare^{i haz a talk page.} 06:42, 21 August 2008 (EDT)

I am about 95% certain that Lemonpeel is the same person as Mathoreilly so try hitting him on his talkpage here. $\approx$$\pi$ 06:58, 21 August 2008 (EDT)

Done. NightFlare^{i haz a talk page.} 07:34, 21 August 2008 (EDT)

I'm pretty sure he is not. Gauss 20:44, 3 September 2008 (EDT)

This article is great

That is all. <font=""; face="Comic Sans MS">Jellyfish!^{Sleepy Jack the fire drill} 10:09, 21 August 2008 (EDT)

Roots of zero

A while ago I added "non-zero" to the part that said every number had two square roots but, on second thought, zero might be included for a reason I don't understand and a few minutes of searching doesn't give a specific answer to this, so whoever knows better please say if it's better or not. I'm leaving the "non-zero" there only because it's technically correct either way. Thanks in advance. NightFlare^{i haz a talk page.} 10:58, 21 August 2008 (EDT)

Whatever the answer is, it's also there at the end of the section. NightFlare^{i haz a talk page.} 11:20, 21 August 2008 (EDT)

You were correct in the change you made. Gauss 21:11, 28 August 2008 (EDT)

A victory for intuition! NightFlare^{i haz a talk page.} 00:00, 2 September 2008 (EDT)

I remember before being introduced to the concept of complex numbers, learing that a quadratic had zero, one, or two roots, depending on whether the determinant was -ve, 0, or +ve. A friend who knew about them, said a quadratic always had two roots: if the determinant was -ve, the roots were complex. "What if the determinant is zero, doesnt it still have just one root?" "No, then they're identical." The idea of one equation having two solutions, it's just that they are identical, is reminiscent of things like triune gods and such. Like angels on a pinhead, couldnt there be a thousand on there, all just happening to be identical? The idea of a quadratic always having two roots, but in the case of a zero determinant their being identical, actually necessitates the concept of all numbers having two square roots, just in the case of zero, they are identical.... PardreObe (talk) 16:54, 15 December 2009 (UTC)

Too much serious

Here, have some geometry humour. --Kels 23:17, 28 August 2008 (EDT)

I laffed. ħuman 00:05, 29 August 2008 (EDT)

multiplication

I don't know where else PeD may have done this, but the gross simplification and stupidification of the multiplication article should be mentioned... ħuman 21:07, 3 September 2008 (EDT)

FBI incident redux

I am starting to feel like this is heading the direction the FBI incident did, with people going over there, taunting Ed getting banned to see themselves added here or adding themselves here. If it is alright with everyone I will remove the latest blocks and unless there is some major event, the topology category disappears or something this needs no more updating unless what occurs is Ed's doing. $\approx$$\pi$ 06:30, 4 September 2008 (EDT)

I suspect EPauper, Belgian (and HPoirot, HerculeP, EdmundP, EdwardP,...) to be the same and one user (me perhaps?), who got mad at Ed for reasons not related to the Mathematics articles. He had no aspiration for being mentioned here or in WIGO, I think he didn't even know about this article. I agree that they shouldn't be mentioned.

Instead JohnI is a wonderful parodist (and not me). He should be mentioned: his block's edit summary by Ed Poor wonderfully contrasts with "building on JohnI's last entry - thanks, John!" by the same Ed Poor, for this parody. Editor at CP^{Liar at RP!} 06:57, 4 September 2008 (EDT)

I hope JohnI is a parodist that statement he wrote is incorrect in so many ways. Ed is not qualified to teach even addition to 5 year olds if he calls multiplication a function and thinks there are only two commutative operators. $\approx$$\pi$ 07:03, 4 September 2008 (EDT)

If this is not a parodist, I don't know who is... His maths entries are so incorrect indeed - and Ed can't be qualified to teach maths to anybody, no way. I hope it's just his CP-Wiki-impersonification and he doesn't really teach anybody. Maybe he's just envious of Andy's 56 homeschoolers. Editor at CP^{Liar at RP!} 08:32, 4 September 2008 (EDT)

Ooo big mistake. Less than 50 edits and is already throwing liberal around. Don't people relies the best way to allay suspicion is get your self known around the place then slowly start using the lingo as though it is growing on you. You shouldn't start the liberal and the this is our site crap until you have been there about a month. $\approx$$\pi$ 09:03, 4 September 2008 (EDT)

Tychonoff

The Tychonoff theorem implies the AC, as shown by Kelly. Have a look here. --LArron 08:26, 5 December 2008 (EST)

Thanks didn't know the other way bit. - User $\scriptstyle -i\ln(-1)$ 08:32, 5 December 2008 (EST)

just some notes

OK I just wanted to add that this sentence: "In fact, the much-touted industrial might of the United States depends on our superb math and science educational system." is honestly (at least on secondary education level) ..er.. slightly exaggerated. The US falls in the PISA studies constantly behind most other developed nations and is in none of the three categories (Math, Science, and Reading) in the top 20. Oh and as a student that has experienced the German educational system for years (and has minor experiences with other European schooling systems) and is currently studying at an US high school; it just does not compare (jop even AP courses).

Please don't be offended (weird how Americans take criticism often too personally), I just wanted to spread the truth. Postsecondary institutions are world-class and often on the same or better niveau than leading European and Asian colleges and universities.

OK, I've changed it. (No, I'm not offended.) The intention was not to say that our educational system is superior (which, of course, it isn't) but to say that this alleged superiority is a central tenet of the CP mindset. Gauss 17:49, 14 February 2009 (EST)

--"CUR^talk 17:59, 14 February 2009 (EST)

Nice catch, although I removed the rather-long parenthetical you added. I think the "much-touted" part takes care of the "exaggeration"? IOW, it's a little sarcastic. ħuman 19:30, 14 February 2009 (EST)

Some other guesses why he hated complex numbers

• With his putative electrical engineering background (one wonders how he works with stuffs with electrical engineering without complex numbers), i is reserved for current, j is for current density, k is for some arbitrary constants, so all the alphabets used by a quaternion (and as such, complexnumbers) are used for something else (mostly it is i or j for the unit imaginary vector). Thieh 15:18, 1 May 2009 (UTC)

Good point, although many engineers manage to avoid reality in their schooling and training. Engineers make some of the worst amateur scientists due to this. They think they have "learned" how science works, but they have never done any science. Anyway, yes, good point, you can't do any AC engineering without ω. ħuman 02:59, 2 May 2009 (UTC)

Interesting idea. My father was an electrical engineer, keen amateur mathematician, and almost professional religious maniac, and so perhaps was in some ways not dissimilar to Andy, and I can remember him telling me of the different uses of "i" - although isnt current normally represented by capital I? I realize that I am in the company of much sharper mathematical minds than mine, but I cant help wondering that though Andy's wording might be poor, his comments might get harsher treatment than they deserve. His references "a unique root of -1", "consistent results" etc. It is routine when referring to roots of positive reals to ask "What is the root of..." and to answer only giving the +ve root, as if there were only one, and he is essentially only following that convention. The "consistent results" is just another way of questioning the legitimacy of the concept, and the reference to "assumptions" is referring to the fact that an elementary proof dispenses with the need for the concept. Please dont slay me - - I'm just being 'liberal' and going easy on the guy. :) PardreObe (talk) 16:41, 15 December 2009 (UTC)

Re: How long does it take to earn $40?

The answers/edits on CP has been removed. may need images as backup. Thieh 01:44, 2 May 2009 (UTC)

If they're gone it's too late (try the wayback machine?). We learned eventually to screencap everything due to this evidence burning habit they have. ħuman 02:56, 2 May 2009 (UTC)

Can we just vape the section? It's just random, unsourced trivia. Peter ^{tanquam ex ungue leonem} 05:49, 7 April 2012 (UTC)

Cover story status

This article has may have degenerated somewhat, but I don't know why this is a cover story. Its formatting is all over the place, it has external links that should be ref not in the article itself, and it generally reads badly. Can we recede its status pending a rewrite? - π 13:01, 14 May 2010 (UTC)

I am against on the general principle that it is a CP: article. Should we be saying this wherever it was first discussed? ħuman 08:32, 29 May 2010 (UTC)

Apparently it was never discussed. Thumbs down, says me, anyway. ħuman 08:33, 29 May 2010 (UTC)

Also, Pi, note that (as far as I can see) the link to the abstract is borken here. ħuman 08:34, 29 May 2010 (UTC)

Ah that is the namespace. I would like to see this restored to Cover story status, but a rewrite would be needed. - π 08:35, 29 May 2010 (UTC)

Nice work on fixing coverstory so the link to abstract works. This will need a lot of work to make coverstory I think. Can we "unapprove" it for now and discuss what it will take to get it there? ħuman 08:39, 29 May 2010 (UTC)

If people do get around to rewriting this, an explanation on how imaginary numbers relate to, and can be extended into, real numbers needs to happen. Just posting Euler's formula and Euler's identity should be good enough. The wikipedia on both of these and imaginary numbers are pretty easy for non-mathematicians to grasp. Imaginary numbers have a place any time you are expressing anything in polar cordinates or working with trigonometry at all; they aren't limited in usefulness to just Fourier transforms as the article seems to imply.^{— Unsigned, by: 173.26.196.66 / talk / contribs}

Bump. - π 12:34, 19 August 2010 (UTC)

I have had vague intentions for a while to go through this one. The section straight after the intro should be Schlafly's seven crank delusions, as listed by some RW user on their user page. What page was that? - David Gerard (talk) 14:32, 19 August 2010 (UTC)

Ah, User:SamHB - David Gerard (talk) 15:33, 20 August 2010 (UTC)

Is there a good place to put "39+4=44"....

In this article or elsewhere? Source^img. [[User:K61824|]][[User_talk:K61824|]] 07:41, 14 September 2010 (UTC)

Fuck's sake

I was about to "de-bronze" this crap when I realized why I clicked it into a tab - cover story? This is shite, and boring shite at that. 24 hours of conversation before I demote it to no metal brains (since it is lame, and CP-centric) and kill the cover story thing. Please convince me. ħuman 06:54, 24 September 2010 (UTC)

I think this ties in with the de-CPing of RW. It's a bit tl;dr. I have no prob with it being de-brained. --PsyGremlin말하십시오 07:11, 24 September 2010 (UTC)

It should be downgraded to silver, at least. It might be extensive and well-documented but I could care less about a relatively minor CP event. Blue (pester) 20:09, 16 May 2011 (UTC)

Silver is fine. But this is a useful and important article that I use to cite to outsiders on just how incredibly on crack Conservapedia is - David Gerard (talk) 10:22, 17 May 2011 (UTC)

When I read about Andy's take on math, I keep thinking of the words "Time Cube" for some reason. DataSnake (talk) 22:10, 8 November 2011 (UTC)