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### Mathematicians on wikipedia display liberal bias

Posted: Sun Jul 13, 2008 11:10 am UTC
Conservapedia wrote:Mathematicians on Wikipedia distort and exaggerate Wiles' proof of Fermat's Last Theorem by (i) concealing how it relied on the controversial Axiom of Choice and by (ii) omitting the widespread initial criticism of it.

Seriously though, can anyone explain to me how this demonstrates liberal bias?

### Re: Mathematicians on wikipedia display liberal bias

Posted: Sun Jul 13, 2008 11:39 am UTC
Oh, man, Conservapedia is brilliant.

See also their article on Elementary proofs. Pshh, you only get an honorary silver plate, Wiles. No Fields medal for you, YOU DIRTY LIBERAL.

(Subtly ignoring the fact that he was outside the age restriction for the Fields).

### Re: Mathematicians on wikipedia display liberal bias

Posted: Sun Jul 13, 2008 11:55 am UTC
Ended wrote:Oh, man, Conservapedia is brilliant.

See also their article on Elementary proofs. Pshh, you only get an honorary silver plate, Wiles. No Fields medal for you, YOU DIRTY LIBERAL.

(Subtly ignoring the fact that he was outside the age restriction for the Fields).

That is the most absurd misrepresentation of what an elementary proof is that I have ever seen. If you consider that Wiles was born in '53, that the medal was awarded in '90 and '94 and that his first claim of a proof was in '93, its impossible for him to have been awarded a medal.

Conservapedia claims that the existence of a nonmeasurable set is equivalent to choice. You tools, you absolute tools!!

### Re: Mathematicians on wikipedia display liberal bias

Posted: Sun Jul 13, 2008 12:08 pm UTC
I'm not familiar enough with Wiles' proof to know whether/how it used the "disfavored"[1] AoC, but as was pointed out elsewhere[2], it can't possibly rely on it:

If Fermat's last theorem is false, it is refutable, since there would be a counterexample. The axiom of choice is consistent with the other axioms, so it can't be used to prove anything which can be refuted from the other axioms. (Assuming, of course, that ZF is consistent.)

### Re: Mathematicians on wikipedia display liberal bias

Posted: Sun Jul 13, 2008 12:13 pm UTC
Can someone clarify, is conservipedia a joke site like uncyclopedia etc or is it serious?

### Re: Mathematicians on wikipedia display liberal bias

Posted: Sun Jul 13, 2008 12:33 pm UTC
skeptical scientist wrote:If Fermat's last theorem is false, it is refutable, since there would be a counterexample. The axiom of choice is consistent with the other axioms, so it can't be used to prove anything which can be refuted from the other axioms. (Assuming, of course, that ZF is consistent.)

It could be undecideable without choice.

SimonM wrote:Can someone clarify, is conservipedia a joke site like uncyclopedia etc or is it serious?

### Re: Mathematicians on wikipedia display liberal bias

Posted: Sun Jul 13, 2008 1:02 pm UTC
jestingrabbit wrote:
skeptical scientist wrote:If Fermat's last theorem is false, it is refutable, since there would be a counterexample. The axiom of choice is consistent with the other axioms, so it can't be used to prove anything which can be refuted from the other axioms. (Assuming, of course, that ZF is consistent.)

It could be undecideable without choice.

Perhaps, but we'd know it's true the same way we know Godel's sentence G is true, whether or not you accept choice as valid. We know it's not refutable, and if false it would be refutable, so it's true.

### Re: Mathematicians on wikipedia display liberal bias

Posted: Sun Jul 13, 2008 6:25 pm UTC
I heard that Obama has never gotten a Fields Medal, either.

### Re: Mathematicians on wikipedia display liberal bias

Posted: Sun Jul 13, 2008 6:51 pm UTC
Oh, come on. It is a wiki. You know what to do.

Btw, if you want to know more, http://rationalwiki.com/wiki/Conservape ... athematics

### Re: Mathematicians on wikipedia display liberal bias

Posted: Sun Jul 13, 2008 7:43 pm UTC
SimonM wrote:Can someone clarify, is conservipedia a joke site like uncyclopedia etc or is it serious?
As a wiki, that just depends on who's editing it. I personally know somebody who likes to insert subtle or not-so-subtle inaccuracies into the articles on there.

### Re: Mathematicians on wikipedia display liberal bias

Posted: Sun Jul 13, 2008 8:03 pm UTC
Since no one has mentioned it yet, the liberal bias claim most likely comes from the fact that conservative mathematicians do not accept the Axiom of Choice. In fact, most of them are notoriously Anti-Choice, claiming that people never have the right to choose to abort a baby one element from each set in a collection.

### Re: Mathematicians on wikipedia display liberal bias

Posted: Sun Jul 13, 2008 8:12 pm UTC
Pathway wrote:Oh, come on. It is a wiki. You know what to do
Since you've linked to rationalwiki, you will be aware of Conservapedia's policy of burning the evidence.

### Re: Mathematicians on wikipedia display liberal bias

Posted: Sun Jul 13, 2008 10:05 pm UTC
Pathway wrote:Oh, come on. It is a wiki. You know what to do.

I could fix it, but I don't want to fix it. I want them to sound as idiotic as possible. I regard the whole excercise of "Conservapedia" as preposterous, and the more they want to shoot themselves in the foot by making blatantly ignorant comments, the better.

Also, I couldn't even if I tried. Conservapedia requires that users be logged in to edit, and to be allowed to create accounts in Conservapedia you have to log in and have the appropriate permissions.

### Re: Mathematicians on wikipedia display liberal bias

Posted: Mon Jul 14, 2008 2:10 am UTC
skeptical scientist wrote:
Conservapedia wrote:Mathematicians on Wikipedia distort and exaggerate Wiles' proof of Fermat's Last Theorem by (i) concealing how it relied on the controversial Axiom of Choice and by (ii) omitting the widespread initial criticism of it.

Seriously though, can anyone explain to me how this demonstrates liberal bias?

They don't say it demonstrates liberal bias. Check it out:

the link wrote:The following is a growing list of examples of liberal bias, deceit, silly gossip, and blatant errors on Wikipedia.

... they're using it as an example of bias exhibited by the writers of Wikipedia articles, not of specifically liberal bias.

### Re: Mathematicians on wikipedia display liberal bias

Posted: Mon Jul 14, 2008 9:09 am UTC
That rationalwiki site is just as awful (but on the opposite side), assuming most of their articles are as bad as the featured one on Peer Review (http://rationalwiki.com/wiki/Peer_review) and http://rationalwiki.com/wiki/Scientific_method

An entire site full of Dawkinian e-atheists :(((

### Re: Mathematicians on wikipedia display liberal bias

Posted: Mon Jul 14, 2008 9:24 am UTC
poohat wrote:edit: why cant I link URLs like this on this forum?

fix'd

### Re: Mathematicians on wikipedia display liberal bias

Posted: Mon Jul 14, 2008 9:29 am UTC
poohat wrote:edit: why cant I link URLs like [url="www.google.com"]this[/url] on this forum?

To do [url]-tagging you don't need to add inverted commas ("...") to your web-address in the [url= ... ] section. So [url=http://www.google.com] works.
[quote] needs "..." on it to add a specific person or object as a source for the quote though.
Hope that makes sense.

### Re: Mathematicians on wikipedia display liberal bias

Posted: Mon Jul 14, 2008 1:06 pm UTC
poohat wrote:That rationalwiki site is just as awful (but on the opposite side), assuming most of their articles are as bad as the featured one on Peer Review (http://rationalwiki.com/wiki/Peer_review) and http://rationalwiki.com/wiki/Scientific_method

An entire site full of Dawkinian e-atheists ((

Are you objecting to the tone or the content of those articles?

### Re: Mathematicians on wikipedia display liberal bias

Posted: Fri Jul 18, 2008 3:03 am UTC
poohat wrote:An entire site full of Dawkinian e-atheists :(((

You say it like it's a bad thing.

### Re: Mathematicians on wikipedia display liberal bias

Posted: Fri Jul 18, 2008 4:23 am UTC
This wiki hurts me.

Conservapedia - article on Evolution wrote:The great intellectuals in history such as Archimedes, Aristotle, St. Augustine, Francis Bacon, Isaac Newton, and Lord Kelvin did not propose an evolutionary process for a species to transform into a more complex version.

### Re: Mathematicians on wikipedia display liberal bias

Posted: Fri Jul 18, 2008 6:18 am UTC
I love the elementary proofs page for the following sentence: "Elementary proofs cannot be broken down into smaller proofs of the same proposition."

As opposed to all other proofs, which are required by law to be redundant.

### Re: Mathematicians on wikipedia display liberal bias

Posted: Fri Jul 18, 2008 12:33 pm UTC
Charlie! wrote:I love the elementary proofs page for the following sentence: "Elementary proofs cannot be broken down into smaller proofs of the same proposition."
Yeah, the person responsible for that little gem is the friend I mentioned above. I'll let him know that people appreciate his efforts.

### Re: Mathematicians on wikipedia display liberal bias

Posted: Sat Jul 19, 2008 12:53 am UTC
skeptical scientist wrote:
jestingrabbit wrote:
skeptical scientist wrote:If Fermat's last theorem is false, it is refutable, since there would be a counterexample. The axiom of choice is consistent with the other axioms, so it can't be used to prove anything which can be refuted from the other axioms. (Assuming, of course, that ZF is consistent.)

It could be undecideable without choice.

Perhaps, but we'd know it's true the same way we know Godel's sentence G is true, whether or not you accept choice as valid. We know it's not refutable, and if false it would be refutable, so it's true.

True doesn't mean theorem (provable), and undecidable doesn't mean true (whatever that means ). Godel's sentence wasn't proven true because you can accept it or deny it, but rather a much more clever self-referential argument (which actually showed why it can't be true). And how did we know that Fermat's last theorem was not refutable before it was proved true? I thought that we were unsure whether it was undecidable or provable.

### Re: Mathematicians on wikipedia display liberal bias

Posted: Sat Jul 19, 2008 3:02 pm UTC
skeptical scientist wrote:
jestingrabbit wrote:
skeptical scientist wrote:If Fermat's last theorem is false, it is refutable, since there would be a counterexample. The axiom of choice is consistent with the other axioms, so it can't be used to prove anything which can be refuted from the other axioms. (Assuming, of course, that ZF is consistent.)

It could be undecideable without choice.

Perhaps, but we'd know it's true the same way we know Godel's sentence G is true, whether or not you accept choice as valid. We know it's not refutable, and if false it would be refutable, so it's true.

I thought that in GEB he constructed a Godel sentence in peano arithmetic and then demonstrated that you can either assume that the statement is formally true or formally false. When you assume that it is formally false (i.e. there exists a truth) you can construct infinite numbers that represent proofs of G.

Or am I remembering that wrong?

### Re: Mathematicians on wikipedia display liberal bias

Posted: Sat Jul 19, 2008 11:01 pm UTC
vega12 wrote:
skeptical scientist wrote:Perhaps, but we'd know it's true the same way we know Godel's sentence G is true, whether or not you accept choice as valid. We know it's not refutable, and if false it would be refutable, so it's true.

True doesn't mean theorem (provable), and undecidable doesn't mean true (whatever that means ).

I am well aware of the difference between "true", "provable", and "undecidable". "Truth" is determined by your model. For example, the statement "1+1=0" is true in some models of the theory of fields (fields of characteristic 2) and not in others. With PA, we have a standard model in mind, (N,0,S,+,*,<). So when I say "true", I mean true in that model. We know that Godel's sentence G is true in the standard model, because in the standard model it can be interpreted as saying "there is no formal derivation of G from the axioms of PA", and if it were false, there would be a formal derivation of G, contradicting the fact that the axioms of PA are true, and can therefore only be used to derive true statements. We also know that there is no formal derivation of G, and thus (by the completeness theorem), G must be false in some models of the axioms of PA. One consequence of this is that there is no finite (or even computably enumerable) collection of axioms which characterize the theory of natural numbers, and there will always be nonstandard models of such a collection of axioms. (Actually if this was all we cared about there would be a much easier proof using compactness; Godel's theorem tells us a lot more.)

Godel's sentence wasn't proven true because you can accept it or deny it, but rather a much more clever self-referential argument (which actually showed why it can't be true).

I think you mean "provable" here, rather than true. The self-referential argument showed that G could not be formally derived from the axioms of number theory. It also, as I explained above, showed that it must be true (since what it says is exactly that it can't be formally derived from the axioms of number theory; or rather, that's what it says if your background model is actually the natural numbers.)

And how did we know that Fermat's last theorem was not refutable before it was proved true? I thought that we were unsure whether it was undecidable or provable.

We didn't. My point is that by proving FLT by assuming the axiom of choice, we prove that FLT is consistent (in ZF, i.e. set theory without choice), since choice is known to be consistent with ZF. Since if false, FLT would be refutable (by providing a counterexample an+bn=cn), this implies that it must be true, whether or not you accept choice.

----------------------------

dadaMathematician wrote:I thought that in GEB he constructed a Godel sentence in peano arithmetic and then demonstrated that you can either assume that the statement is formally true or formally false. When you assume that it is formally false (i.e. there exists a truth) you can construct infinite numbers that represent proofs of G.

Or am I remembering that wrong?

No you are correct. In the latter case, you are no longer working in the natural numbers, but in some nonstandard model of number theory, where you can construct "infinite" natural numbers. (I.e. there is a "natural number" x with x>1, x>2, x>3, x>4, etc. In other words, your model is "non-Archimedean".)

### Re: Mathematicians on wikipedia display liberal bias

Posted: Sun Jul 20, 2008 9:35 am UTC
GMontag wrote:
poohat wrote:That rationalwiki site is just as awful (but on the opposite side), assuming most of their articles are as bad as the featured one on Peer Review (http://rationalwiki.com/wiki/Peer_review) and http://rationalwiki.com/wiki/Scientific_method

An entire site full of Dawkinian e-atheists ((

Are you objecting to the tone or the content of those articles?

Both, theyre horrible. This sort of rabid science-fanboyism is almost as dumb as theology.

Because obviously anyone who believes theres problems with the peer-review system, or thinks that the 'scientific method' isnt as clearly defined as non-philosophers often think, is a closet Creationist.

### Re: Mathematicians on wikipedia display liberal bias

Posted: Mon Jul 21, 2008 10:15 pm UTC
JCCyC wrote:
poohat wrote:An entire site full of Dawkinian e-atheists ((

You say it like it's a bad thing.

It kinda is.

### Re: Mathematicians on wikipedia display liberal bias

Posted: Tue Jul 22, 2008 12:13 am UTC
As Stephen Colbert once said, "Reality has a notorious liberal bias."

### Re: Mathematicians on wikipedia display liberal bias

Posted: Mon Jul 28, 2008 2:46 pm UTC
I don't know what this says about me, but I find this discussion in itself to be one of the funniest things I've ever seen... And I havn't even followed the links yet.

Ed. With regard to the Fermat's last theorem article, I find it abhorrent that they imply mathematical proof is flawed because someone with a high IQ score says it is (and called savant? She must have picked that name herself for publicity reasons). What's their problem with non euclidean geometry anyway? We live on a surface with a non euclidean geometry for goodness sake.

poohat wrote:Because obviously anyone who believes theres problems with the peer-review system, or thinks that the 'scientific method' isnt as clearly defined as non-philosophers often think, is a closet Creationist.

I'm not altogether sure what you mean by this, but doesn't it occur to you that denying that there could be problems with the peer-review system is not a scientific approach?

### Re: Mathematicians on wikipedia display liberal bias

Posted: Mon Jul 28, 2008 4:32 pm UTC
Generally speaking, if someone on the internet starts a sentence with "Because obviously," he or she is being sarcastic.

Marilyn vos Savant's mother's maiden name was also vos Savant, I think. That said, her objections (later retracted) to Wiles's proof were ridiculous.

### Re: Mathematicians on wikipedia display liberal bias

Posted: Mon Jul 28, 2008 7:18 pm UTC
Nodnod. MvS takes her last name from her mother, who was a vos Savant. She didn't make it up just to sound smarter. ^_^

However, I can understand her objections to Wiles Theorem. As her Wikipedia entry states, she responded to her critics that she felt Fermat's Last Theorem was an intellectual challenge to attempt to prove it with Fermat's tools. Wiles' proof centers around many mathematical concepts that did not exist at that time, and so she did not feel it was an adequate answer to the problem; this is supported by her argument about why we don't accept it when people "square the circle" using hyperbolic geometry - the circle-squaring problem is meant to be solved in euclidean geometry (and is, of course, impossible in that geometry). She did, however, grant that simply solving the problem with any tools was still an interesting result.

### Re: Mathematicians on wikipedia display liberal bias

Posted: Mon Jul 28, 2008 10:24 pm UTC
Xanthir wrote:this is supported by her argument about why we don't accept it when people "square the circle" using hyperbolic geometry - the circle-squaring problem is meant to be solved in euclidean geometry (and is, of course, impossible in that geometry).
Yeah, but that was a bad analogy. The problem with switching to hyperbolic geometry when squaring the circle is that you're changing the rules, and the solution you get isn't what the original problem was talking about. Wiles's proof used different tools than Fermat might have expected, but it never changed the rules of the original problem. Almost all proofs do this: to prove the thing you want to prove, you reach into some not-so-obviously related field. These connections might seem weird to those not familiar with the subject matter, but that doesn't mean there's anything wrong with the proof.

Marilyn's complaint is along the lines of someone asking me to prove a Fibonacci identity, then objecting when I start talking about domino tilings. Just because the tools look unrelated doesn't mean they don't work.

### Re: Mathematicians on wikipedia display liberal bias

Posted: Mon Jul 28, 2008 11:50 pm UTC
No it's not. Like I said, she believed the point of the FLT was proving it with Fermat's tools (or alternately, proving that it was impossible with the mathematics Fermat had at the time). Thus she felt that Wiles' work was a bit of a cheat.

It's true that the analogy could be improved. A better one would be something like making a transatlantic flight in a jetliner. It's impressive that we can do that now, but it's got nothing on Charles Lindburgh.

I'm not saying that the tools don't work, I'm saying that using them goes against the spirit of the challenge (as MvS imagined them).

Note: I don't feel anything like MvS, though someone succeeding at her version of the challenge would be pretty cool.

### Re: Mathematicians on wikipedia display liberal bias

Posted: Tue Jul 29, 2008 12:49 am UTC
Xanthir wrote:No it's not. Like I said, she believed the point of the FLT was proving it with Fermat's tools (or alternately, proving that it was impossible with the mathematics Fermat had at the time). Thus she felt that Wiles' work was a bit of a cheat.

That may be what she feels now, but this sounds like after-the-fact weaseling to cover real errors to me. I haven't read her book, but I did read this review, which makes it quite clear that the book was arguing that the proof itself was incorrect, and not merely "a bit of a cheat".

### Re: Mathematicians on wikipedia display liberal bias

Posted: Wed Jul 30, 2008 5:47 am UTC
>>No it's not. Like I said, she believed the point of the FLT was proving it with Fermat's tools (or alternately, proving that it was impossible with the mathematics Fermat had at the time). Thus she felt that Wiles' work was a bit of a cheat.

Then she's an idiot (spare me her high IQ ratings). Furthermore you can't "prove that it was impossible with the mathematics Fermat had at the time". You might be able to come up with a proof that much more in the style Fermat would have likely envisioned. However, in a sense, Wiles did come up with a proof which Fermat could have come up with using the tools he had at the time. As Buttons pointed out, we're still doing math here, we just know more about the structure of it, having followed different trails of logic for three hundred years. It's not exactly plausible, but that's not what she said. If she wants a Mathematical Proof that Fermat could not have plausibly†† done what he said, it's clear that's she's completely talking out of her ass.

Gah.
†But it IS consistent with his comment about not being able to fit in a margin
††Defined how exactly? How plausible is it that he was in fact a time traveler, but had exhausted his time perturbation credit?

### Re: Mathematicians on wikipedia display liberal bias

Posted: Wed Jul 30, 2008 10:06 am UTC
archgoon wrote:>>No it's not. Like I said, she believed the point of the FLT was proving it with Fermat's tools (or alternately, proving that it was impossible with the mathematics Fermat had at the time). Thus she felt that Wiles' work was a bit of a cheat.

Then she's an idiot (spare me her high IQ ratings). Furthermore you can't "prove that it was impossible with the mathematics Fermat had at the time". You might be able to come up with a proof that much more in the style Fermat would have likely envisioned. However, in a sense, Wiles did come up with a proof which Fermat could have come up with using the tools he had at the time. As Buttons pointed out, we're still doing math here, we just know more about the structure of it, having followed different trails of logic for three hundred years. It's not exactly plausible, but that's not what she said. If she wants a Mathematical Proof that Fermat could not have plausibly†† done what he said, it's clear that's she's completely talking out of her ass.

Gah.
†But it IS consistent with his comment about not being able to fit in a margin
††Defined how exactly? How plausible is it that he was in fact a time traveler, but had exhausted his time perturbation credit?

I've read all this, and what you're saying about her is fine by me, having not read her stuff.

But there is still the question "is Fermat's last theorem a theorem of Peano arithmetic?" which was a question that was asked about the prime number theorem (PNT). This is basically where the whole discussion about elementary proofs comes from. It was believed that PNT required complex analysis and a whole lot of stuff by people like Hardy. It was later shown that it was in fact a theorem of Peano arithmetic.

There is something to be said here about elementary proofs, but conservapaedia completely misses the point.