Good Math, Bad Math

Conservapedia and Math

Many of my fellow SBers have been mocking the recently unveiled Conservapedia. Conservapedia claims to be a reaction to the liberal bias of Wikipedia. Ed, PZ, Afarensis, Tim, John, and Orac have all piled on already. But why should they get to have all the fun?

Conservapedia has an extensive list of what they claim to be examples of the liberal bias of Wikipedia. My SciBlings have already covered most of the nonsense to be found within, but one point is clearly mine to mock: grievance number 16:

Wikipedia has many entries on mathematical concepts, but lacks any entry on the basic concept of an elementary proof. Elementary proofs require a rigor lacking in many mathematical claims promoted on Wikipedia.

There is currently an entry on “Elementary Proof” on Wikipedia, but to be fair, it was created just two weeks ago, most likely in response to this claim by conservapedia.

But that’s trivial. The important thing here is that the concept of “elementary proof” is actually a relatively trivial one. It’s sometimes used in number theory, when they’re trying to pare down the number of assumptions required to prove a theorem. An elementary proof is a proof which makes use of the minimum assumptions that describe the basic properties of real numbers. And even in the case of number theory, I don’t think I’ve ever heard anyone seriously argue that an elementary proof is more rigorous than another proof of the same theorem. Elementary proofs might be easier to understand – but that’s not a universal statement: many proofs that make use of things like complex numbers are easier to understand than the elementary equivalent. And I have yet to hear of anything provable about real numbers using number theory with complex numbers which can be proven false using number theory without the complex – proofs about real numbers that use complex are valid, rigorous, and correct.

And that’s not even mentioning the minor fact that the vast majority of the math articles on wikipeidia are not about simple real number theory. According to Wikipedia’s mathematics portal, wikipedia currently has 16,093 articles on mathematics. Of those, 182 are an number theory. Conservapedia’s complaint thus makes no sense whatsoever
for 98.9% of Wikipedia’s math articles.

But in fact, it gets worse than that. Here’s the Conservapedia entry on
“elementary proof”
:

The term “elementary proof” or “elementary techniques” in mathematics means use of only real numbers rather than complex numbers, which relies on manipulation of the imaginary square root of (-1). Elementary proofs are preferred because they are do not require additional assumptions inherent in complex analysis, such as that there is a unique square root of (-1) that will yield consistent results.

Mathematicians also consider elementary techniques to include objects, operations, and relations. Sets, sequences and geometry are not included.

The prime number theorem has long been proven using complex analysis (Riemann’s zeta function), but in 1949 and 1950 an elementary proof by Paul Erdos and Atle Selberg earned Selberg the highest prize in math, the Fields medal.

Sets are not part of “elementary proofs” in mathematics, according to Conservapedia. But relations are. What’s a relation? That terrible biased wikipedia says:

Definition 1. A relation L over the sets X1, …, Xk is a subset of their cartesian product, written L ⊆ X1×…;× Xk. Under this definition, then, a k-ary relation is simply a set of k-tuples.

Wikipedia’s other definition is similar. According to wikipedia, a relation is a kind of set. But we know that Wikipedia is biased, right? So lets check a different source. Wolfram’s Mathworld is an excellent source of information on mathematical definitions. Let’s see how they define “relation”:

A relation is any subset of a Cartesian product. For instance, a subset of AxB, called a “binary relation from A to B,” is a collection of ordered pairs (a,b) with first components from A and second components from B, and, in particular, a subset of AxA is called a “relation on A.” For a binary relation R, one often writes aRb to mean that (a,b) is in R.

Uh-oh. “Houston, we have a problem.”.

So… The conservapedia can’t even write a consistent definition of elementary proof. It’s not too surprising – when you read their stuff on math, you get the definite idea that they really don’t have a clue of what the heck they’re talking about. Just take another look at their definition of “elementary proof”, where they’re trying to disparage the poor square root of -1.

As I’ve said before, i is not imaginary. It’s an important number, and it does exist in mathematics – as I’ve explained in the linked post, there are a lot of very important and very real phenomena that we experience in the real world that mathematically require i to be described.

The “uniqueness” of i is also not an assumption. It’s required by the fact that the complex numbers are a field. To create the two-dimensional complex number space – the one that we know describes real-world phenomena – we require a unique i – otherwise, we don’t get that plane.

What does conservapedia have to say about complex numbers, and their use?

Complex numbers is a branch of mathematics based on the assumption that one can manipulate a unique, imaginary number defined as:

i = \sqrt{-1}

In real numbers the square root of negative one does not exist.

That’s it. The whole shebang. Wikipedia is “liberal biased” because it doesn’t use “elementary proofs” in most of its math articles, even though the whole idea of elementary proof is inapplicable in over 98% of the articles. But Conservapedia just blindly rejects things that they don’t like, regardless of whether they’re important, real, or useful.

The conservapedia babble about “i” is just babble. It’s pretty clear that they’re yet another gaggle of bozos who are upset about the idea that math is more than the simple arithmetic they learned in elementary school, and want to find some way of throwing out everything that makes them uncomfortable.

Sorry guys. Math is more than you think it is. And nobody cares whether you like that fact.

Comments

  1. #1 Blake Stacey
    February 21, 2007

    I’m glad to see your appraisal agrees with mine (two comment threads ago).

    So, who’s up for fixing the Wikipedia article on “elementary proof”?

  2. #2 Sceptical Chymist
    February 21, 2007

    I find it ironic that conservapedia seems to prefer the elementary proof of the prime number theorem by Paul Erdos and Atle Selburgh since Paul Erdos always referred to God as “The Supreme Fascist” or “SF”! One of the French Postmodernists, whose name I forget, equated i with the erect male organ! Perhaps that’s why conservapedia doesn’t like i.

  3. #3 Tam
    February 21, 2007

    The problem with them is, they don’t go far enough. I think we should limit our math to the counting numbers and not even introduce this weird number “0” that is supposedly a unique number representing nothingness. How can nothingness be unique? Having no towels is not the same as having no oranges. That’s just basic algebra.

    Damned liberals are just trying to confuse us with their fancy-pants math as part of their efforts to destroy common sense.

  4. #4 Paul Carpenter
    February 21, 2007

    The article on Real Numbers is even more ridiculous.
    “Real numbers are comprised of all positive and negative values and zero, including rational, irrational and infinite values. Real numbers exclude the imaginary square roots of all negative numbers.”

  5. #5 Blake Stacey
    February 21, 2007

    Sceptical Chymist:

    The French postmodernist you seek is Jacques Lacan. This is the remark which prompted Alan Sokal and Jean Bricmont to say that it was “distressing” to see their erectile organs equated with an imaginary quantity.

  6. #6 Blake Stacey
    February 21, 2007

    Paul Carpenter:

    That’s so. . . breathtaking I had to look for myself. Sure enough, Andrew Schafly went out of his way to include “infinite” in the list.

  7. #7 Joshua
    February 21, 2007

    Wait a second. If i is an erect male organ, what the heck does that make j?

  8. #8 Blake Stacey
    February 21, 2007

    I think I just discovered a quantitative measure of authoritarian, creationist stupidity. Andrew Schafly complains that the GNU Free Documentation Licence (GFDL) is “another complex and arbitrary set of rules to be enforced at whim”. At 1600 words, it’s too long and complicated for him to figure out!

  9. #9 Walker
    February 21, 2007

    Re relations

    To be fair, some mathematical philosophers object to defining relations as sets; they claim that they are primitive objects in themselves. However, other than using category theory as foundational (Sanders MacLane spent years struggling against the tyranny of set theory), they have never really formalized a better alternative. I kind of doubt that level of sophistication is going on here.

    Anyway, I am a logician and I still am not sure what you mean by “elementary proof” here. By pairing down the number of assumptions, do you mean this is like reverse mathematics in that I am trying to identify the minimum collection of axioms for a proof? I don’t see how axiom minimization is at all related to readability.

    I could maybe see them bitching about “proof-by-picture” which happen a lot in well established areas with geometric visualization. But it does not sound like that is what is going on here.

  10. #10 Blake Stacey
    February 21, 2007

    Conservapedia’s entry on the “Theory of Relativity” is so jaw-droppingly crackpot that it’s worth quoting in entirety:

    Unlike most advances in physics, the theory of relativity was proposed based on mathematical theory rather than observation. The theory rests on two postulates that are difficult to test, and then derives mathematically what the physical consequences should be. Those two postulates are that the speed of light never changes, and that all laws of physics are the same in every (inertial) frame of reference no matter where it is or how fast it is traveling. This theory rejects Isaac Newton’s theory of gravitation and replaces it with a concept that there is a continuum of space and time, and that large masses (like the sun) bend space in a manner similar to how a finger can depress an area of a balloon. From this proposed bending of space the expression arose that “space is curved.” But experiments later proved that space is flat overall.

    Nothing useful has even been built based on the theory of relativity. Albert Einstein’s work had nothing to do with the development of the atomic bomb, contrary to popular opinion. Only one Nobel Prize has ever been given (in 1993) that relates to relativity, and the validity of that particular award is questionable. Many things predicted by the theory of relativity, such as gravitons, have never been found despite much searching for them. Many observed phenomenon, such as the bending of light passing near the sun or the advance of the perihelion in the orbit of Mercury, can be also predicted by Newton’s theory.

    British Historian Paul Johnson declares the turning point in 20th century to have been when fellow Brit Sir Arthur Eddington, the top English astronomer, ventured out on a boat off Africa in 1919 to observe the bending of starlight around the sun during a total eclipse. The theory of relativity predicts twice the bending of light around massive objects compared to Newton’s theory, and an eclipse is required to darken the sun so that the starlight may be seen in proximity to the sun. Eddington liked publicity and probably dreamed of winning a Nobel Prize, and upon his return to England declared that his observations proven the theory of relativity. That was good enough for reporters and historians, but the Nobel committee was not impressed and declined to give him an award. Recent analysis of Eddington’s work revealed that he was biased in selecting his data, and that overall his data was inconclusive about the theory of relativity.

    Eddington next promoted the theory of relativity to the English-speaking world in his Mathematical Theory of Relativity (1923). As the title suggests, this theory was more a mathematical vision of how the universe should be, rather than what it actually was. When a reporter asked Eddington whether only three people even understood the theory, Eddington supposedly retorted, “Who’s the third?”

    Just as “social Darwinism” arose from Darwinism, many seized upon the theory of relativity to apply it in a vague way to morality and social issues. “All things are relative” became popular as atheists and others used relativity to attack Christian values. There remains enormous political support for the theory of relativity that has nothing to do with physics, and Congress continues to spend billions of dollars unsuccessfully searching for particles predicted by the theory of relativity.

    I’d try to count the flaws, but this is the crackpot physics equivalent of a Gish gallop. For starters, it misrepresents where special relativity came from, confuses special relativity with general, GPS wouldn’t work without general relativity, GR has been tested in other and more reliable ways than the 1919 eclipse measurement, etc., etc. It’s worth noting that everything except the last paragraph was written by Andrew Schafly, the project founder (and rather fractured ceramic vessel) himself.

  11. #11 Sean Schmidt
    February 21, 2007

    The good thing about all this is that at least we’ll all be able to clearly reference the right’s thoughts and arguments on topics. Just imagine, you can look at Wikipedia and then Conservapedia and easily identify the points of difference and where the faults are.

  12. #12 egro
    February 21, 2007

    If i is the erected male organ, obviously 0 is a female organ.
    Then I don’t know what the heck e^(i*Pi)+1=0 can be, but I don’t want to miss such a crazy party :))

  13. #13 Walt
    February 21, 2007

    Walker: In this context, “elementary proof” is a term in number theory. It means a proof that does not rely on complex analysis.

  14. #14 Blake Stacey
    February 21, 2007

    egro:

    That’s so fantastic I’m going to have to steal it. :-)

  15. #15 Zombie
    February 21, 2007

    Wow… I can understand how a “conservapedia” would get evolution wrong, and there are some funny, foolish ideas about relativity floating around, but I had no idea that complex numbers were considered politically disloyal.

    The inherent humor of the situation notwithstanding, this is somewhat terrifying: there’s no safe subject with these people, and one can be denounced as a political enemy for the most innocuous of reasons…

  16. #16 mrc
    February 21, 2007

    You gotta love the fact that they use the MediaWiki software to run the whole thing. Open source is at its finest hour when your opponents can freely use your technology to make fools of themselves.

  17. #17 Zombie
    February 21, 2007

    I like the last tacked on bit of the Relativity article that equates it with relativism, as if the two had anything even remotely to do with each other outside the name. (Which was, of course, a genuine English word well before either Einstein or the relativists.)

  18. #18 SLC
    February 21, 2007

    The stupidity of these clowns is mind boggling.

    1. As a for instance, it is impossible to understand why a Taylor series expansion of the function 1/(1+x^2) diverges for x >= 1 without going to the complex plane.

    2. The statement made that there is no experimental verification of the GTR is total crap. GTR is required to correctly predict the precession rate of the orbit of the planet Mercury. This has been known since 1920.

    3. GTR has nothing to do with gravitons. Gravitons are a consequence of quantum mechanics, not GTR or STR.

    4. STR predicts time dilation which was observed in the decay of muons in the early 1950s.

    5. These a**holes don’t even understand Newtonian mechanics. The laws of physics in non-relativistic mechanics are also invariant in frames of reference moving at constant speeds relative to each other. The group theoretical description is referred to as Galilean invariance (the relativistic counterpart is referred to as Lorentz invariance).

  19. #19 Mark VandeWettering
    February 21, 2007

    Dear Lord. I knew that Andy Schlafly was a dim bulb (try reading his postings to talk.origins around 2000-2001 if you need examples) but arguing that imaginary numbers are some kind of liberal subterfuge? For crying out loud…

    For fun, try this particularly dim example.

  20. #20 rehana
    February 21, 2007

    The entry on quantum mechanics is surprisingly sane, though short. The entry on string theory, on the other hand, carefully avoids mentioning relativity: “The hope is resolve conflicts between gravity and quantum mechanics in existing models of physics.”

  21. #21 Pseudonym
    February 21, 2007

    Amusingly, even their short entry on complex numbers is wrong. Even in the complex numbers, there is no square root of -1. Rather, i is a number such that i^2 = -1.

    (There are, in general, many objects which square to -1 in maths. One example is the matrix [ [ 0 -1 ] [ 1 0 ] ] and another is any unit quaternion with no real part.)

  22. #22 Roy
    February 21, 2007

    At this moment, Crapapedia has no entry for ‘infinity’. Ordinary innumerate people get into trouble with the concept, so can anyone imagine what these bozoids would do with it?

    So, please, keep it a secret. I’m sorry, but right now secrecy by security is the only protection we’ve got.

  23. #23 Roy (again)
    February 21, 2007

    I loved the relativity mythology. I’ve said it before and I’ll say it again, religion is for people who find fault with reality. It’s just not to their taste, period. So they improvise.

  24. #24 XPM
    February 21, 2007

    The irony should be quite excruciatingly apparent to any who have read Zamyatin’s We.

  25. #25 wintermute
    February 21, 2007

    Ummmm… Wow. I just clicked on “random page”, and it took me to http://www.conservapedia.com/HIV

    You just know it’s going to be bad, right? Well, you don’t know the half of it…

    HIV stands for Human Immunodeficiency Virus. It is transmitted through sodomy. Its main effect is to destroy T-cells, which causes a decreased resistance to infections such as pneumonia.
    It is a commonly held belief that God created this disease to punish people for the sin of sodomy.

    Crackpots indeed…

  26. #26 Jonathan Lubin
    February 21, 2007

    A mathematician sees the Conservapedia entry as total bunk, but I’m not all that happy with Mark’s demolition of it, either. On the “unique” property of i: when you get down to it, -i is just as good a square root of -1, and replacing the one by the other is simply the familiar process of complex conjugation. So i isn’t unique at all, and mathematicians don’t make any claim that it is.
    And when I saw Mark’s use of the expression “simple real number theory”, I shuddered. “Number Theory” means the theory of whole numbers, and this seems to be what the poor benighted Conservapedists meant by the term. Analysis, the study of the geometric or fine-structure properties of the real numbers, may or may not be of use in Number Theory. But Real Analysis and Number Theory are two different, mutually impinging but basically separate fields within mathematics.

  27. #27 jayinbmore
    February 21, 2007

    I did a search on Conservapedia for “Computer Science” and the first hit was an aritcle on John von Neumann. Compare with Wikipedia’s. According to Conservapedia, all of von Neuman’s technical and scientific achievments rate only slightly above the two ideologically pleasing facts that he was proud of having helped invent the nuclear bomb, and that, while on his deathbed, he asked for a Catholic priest. They even go so far as to mention his retort to Oppenheimer. So they include one physicist’s bitchy reply to another, while complaining that Wikipedia is all gossip.

    What I found most strange was the lack of an article on Donald Knuth. You’d think they’d be only too happy to include an entry on a computer scientist who wrote a whole book about his faith. Hmm….

  28. #28 Davis
    February 21, 2007

    On the “unique” property of i: when you get down to it, -i is just as good a square root of -1, and replacing the one by the other is simply the familiar process of complex conjugation.

    You beat me to it. This bothered me, too — I actually think of this as a major point that is oft-overlooked in studying complex numbers. Recognizing that there are two equally good square roots of -1 gives us a general reason to expect results like “complex solutions to polynomials with real coefficients occur in conjugate pairs.”

  29. #29 Antendren
    February 21, 2007

    Concerning the comments on relations and sets, it sounds like they’re trying to distinguish first order logic from higher order logics.

    While it contains functions and relations, which may be implemented as sets in the meta universe, in FOL it’s not possible to quantify over sets or sequences.

  30. #30 Jonathan Vos Post
    February 21, 2007

    The elementary proof (so designated at inception) by Paul Erdos and Atle Selberg earned Selberg the highest prize in math, the Fields medal. Yes, but the fight over priority and coauthorship soured their relationship forever. People still take sides. Not Left versus Right.

    It is elementary but not simple, correct.

    “Proofs from the Book” — as Erdos puts it.

    In one sense, an odd thing to do, like that novel which noplace uses the letter “e.” In another sense, a tour de force of making do with a lesser set of axioms and methodologies.

    I’m baffled that this is thought to have anything to do with politics, other than the personality issues.

    Do they reject the co-founder of modern French Left activism, a certain Grothedieck? Just wondering…

    Like Nazis rejecting Special Relativity as by a Jew, or Stalin rejecting Darwin in favor of Lamarck for ideological reasons…

  31. #31 JP
    February 21, 2007

    Complex numbers is a branch of mathematics

    These people are idiots.

    Thanks to the commentor that pointed out that an ‘Elementary Proof’ is not one that avoid complex numbers, but one that avoids complex analysis.

    From an algebraic stand point, there is no reason to distinguish ‘i’ from any other any other non-rational square root. You might be uncomfortable with the fact that it is not the length of anything (unlike rationals and pi). But, throwing ‘i’ (and all roots) in with the rationals is fundamentally much less crazy than building the real numbers from the rational. But, somehow they don’t seem to have a problem with the real numbers.

  32. #32 Torbjörn Larsson
    February 22, 2007

    The relativity article is hilarious. I also like that the “experiments [that] later proved that space is flat overall” wouldn’t have happened without relativity in the first place. Or that other useful technologies which depend on relativity are particle accelerators – but it so happens that “Congress continues to spend billions of dollars unsuccessfully searching for particles predicted by the theory of relativity”.

    Now, if we could rally remaining forces to contribute to Crackpedia, and Crackpedia only…

  33. #33 Davis
    February 22, 2007

    But, throwing ‘i’ (and all roots) in with the rationals is fundamentally much less crazy than building the real numbers from the rational.

    Indeed; I’ve had a hard time really getting this across to people, but 2pi is profoundly stranger than 2+i. Non-mathematicians tend to think real numbers are elementary, but only because they envision rationals and certain basic irrationals when they think “real.”

  34. #34 Chris' Wills
    February 22, 2007

    Joshua asked: Wait a second. If i is an erect male organ, what the heck does that make j? ^>>

    A. Glad you aren’t an electrical engineer :o)

    I wonder if the reason they have such a hard time with
    i^2=-1 is because the result is called imaginary?

    This would also answer the question why they have no problems with the reals. They think that because they are called real they are the only real numbers.

    Perhaps Mark can mention the transcendental and supernatural numbers to them; heavenly numbers no doubt.

  35. #35 Arno Verweij
    February 22, 2007

    The entry in Crackpedia on Real numbers has been changed just today! Seems to me to be a little more “biased” as it does not mention anything imaginary anymore. And note the pain the author felt while cleaning it up, as he stated in his change commentary :-)
    But according to the “commandments” of Crackpedia, this entry still complies to their rules. I wonder how long it stays unaltered…

  36. #36 keiths
    February 22, 2007

    Is Andy Schlafly related to Phyllis? It would certainly explain a lot.

  37. #37 ben
    February 22, 2007

    But at least they didn’t actually say pi=3.

    Well, they did have to mention it though. There ought to be a law. What? There there almost was? Oh.

  38. #38 False Dog
    February 22, 2007

    Having one towel is not the same as having one orange, so how can “1” be unique?

  39. #39 Chris' Wills
    February 22, 2007

    Keiths asked: Is Andy Schlafly related to Phyllis? It would certainly explain a lot.>>

    A. Only by birth (though the idea of Phyllis having sexual congress does seem strange), Andy is Phyllis’ son.

    He is also a lawyer which might explain his facility at expounding untruth.

    He also has a brother called Roger, they used to be a pair of jesters on talk origins

    http://www.cinam.net/son3-3-cp.html
    scroll to bottom of screen.

    Roger appears to have an anti-vaccine site; strange family.
    Oh bad, Roger has a PHd in mathematics and lets his brother run a site posting such rubbish.

    Is there a Mr Schlafly (i.e. a natural sperm delivery system) associated with Phyllis or are the boys virgin births?

  40. #40 Jud
    February 22, 2007

    Torbjörn Larsson said: “…’experiments [that] later proved that space is flat overall’….”

    Always look forward to your comments, Torbjörn, and glad to see you were mentioned as a candidate for a commenter award over at Pharyngula.

    About the above, my impression is that the overwhelming weight of observational evidence appears to restrict the possible curvature of the universe pretty tightly to values near zero. Is this what is meant by experiments proving that space is flat, or something else? (I’d be quite happy to find out the latter, since it is always delightful to learn something new.)

  41. #41 Jud
    February 22, 2007

    Jud said: “…to values near zero….” Sorry, that should be omega ~1.

  42. #42 cleek
    February 22, 2007

    it’s probably safe to assume a lot of these truly ridiculous things are spoofs.

  43. #43 SteveM
    February 22, 2007

    < ...>A mathematician sees the Conservapedia entry as total bunk, but I’m not all that happy with Mark’s demolition of it, either. On the “unique” property of i: when you get down to it, -i is just as good a square root of -1, and replacing the one by the other is simply the familiar process of complex conjugation. So i isn’t unique at all, and mathematicians don’t make any claim that it is.

    You are kidding right? Holy smack, -2 is just as good a square root of 4 as 2 is, so 2 is not unique!

  44. #44 vbp
    February 22, 2007

    Y’know I do think they are trying to make an alternate reality by manipulating an encyclopedia. Tlon, Uqbar, Orbis Tertius made flesh!

    Wow.

    Although, I now see many articles are better, or at least less bad, then they used to be. I guess I should be pleased but they do lose that alternate-universe tinge. Pity. And I was going to edit the Relativity article to chronicle the contributions of Dr. Calvin and Prof. Hobbes, too. Ah well.

  45. #45 Spaceman Spiff
    February 22, 2007

    As if the “elementary proof” entry was not loopy enough… Check on some of the biographies of famous mathematicians. The entirety of the article on G.H. Hardy reads:

    “Godfrey Harold “G.H.” Hardy (1877-1947) was an atheistic British mathematician who felt that the approach of the elementary proof lacked the “depth” needed to solve difficult math problems. He was shown to be wrong when Paul Erdos devised an elementary proof to the Prime Number Theorem, which has only been proven using non-elementary complex analysis.”

    Do they really need the second sentence. I mean, he was “an atheistic,” so he must be wrong. Also it would seem that the Prime Number Theorem is the only “difficult math problem.”

  46. #46 Nat Whilk
    February 22, 2007

    Walker wrote: Re relations To be fair, some mathematical philosophers object to defining relations as sets; they claim that they are primitive objects in themselves.

    That’s right. In fact, it wasn’t until 1914 that someone (Wiener, and then, more neatly, Kuratowski in 1921) showed how the theory of relations could be reduced to that of classes, so the notion that one can be ontologically committed to relations without being similarly committed to sets is not only not laughable but is supported by heaps of empirical evidence.

    And treating Wikipedia and MathWorld as authoritative sources? Please. In the frenzy to shoot fish in a barrel, try to avoid shooting yourself in the foot.

  47. #47 gg
    February 22, 2007

    Lots of people have commented on the utter idiocy of the relativity article, so I won’t say too much about it, even though I teach the subject and the article makes my teeth hurt. A few comments:

    “Nothing useful has even been built based on the theory of relativity. Albert Einstein’s work had nothing to do with the development of the atomic bomb, contrary to popular opinion.”

    Is this a sort of ‘conservative Freudian slip’? The author seems to be implying that atomic bombs are ‘useful’, which is not a wording most sane people would apply. (“Handy little tool, this apocalyptic weapon.”) Oh, and of course E=mc^2 is pretty much essential to doing any meaningful nuclear physics calculations.

    “Many observed phenomenon, such as the bending of light passing near the sun or the advance of the perihelion in the orbit of Mercury, can be also predicted by Newton’s theory.”

    Utter, utter nonsense. Oh, and one more prediction of GR that has been observed is gravitational lensing.

  48. #48 Nat Whilk
    February 22, 2007

    gg wrote: “Is this a sort of ‘conservative Freudian slip’? The author seems to be implying that atomic bombs are ‘useful’, which is not a wording most sane people would apply.

    Harry Truman seemed to find the Bomb useful. All 8 or 10 members of the Nuclear Club seem to find them useful, otherwise they wouldn’t have them. Are they all insane?

  49. #49 gg
    February 22, 2007

    Nat wrote: “Harry Truman seemed to find the Bomb useful. All 8 or 10 members of the Nuclear Club seem to find them useful, otherwise they wouldn’t have them. Are they all insane?”

    I was more taking issue with the rather casual use of the word ‘useful’ in association with nuclear weaponry. Most people would say they are definitely a mixed bag in terms of being a benefit. Personally, I don’t like to talk about a weapon that can kill millions and summarize it by a single positive word.

    The word isn’t really accurate, either, since nuclear weapons have only been actually used once, by Truman. I would say that deterrence is actually an indirect use of the technology. And, actually, I do find that a desire to acquire nuclear weapons is not exactly indicative of a healthy mind. The most recent entries, or wannabies, into the nuclear club, Pakistan, North Korea, and Iran, don’t have leadership that inspire me with their sensibility. (Neither does the U.S. right now, but that’s another story.)

  50. #50 Davis
    February 22, 2007

    You are kidding right? Holy smack, -2 is just as good a square root of 4 as 2 is, so 2 is not unique!

    Re-read the original statement:

    there is a unique square root of (-1) that will yield consistent results.

    There is not a unique square root of -1, nor is there a unique square root of any non-zero (complex or real) number.

  51. #51 Davis
    February 22, 2007

    As an addendum to my previous comment, I’ll note that deciding i=sqrt(-1), instead of -i=sqrt(-1) is pretty much an arbitrary choice. With real numbers, we set 2=sqrt(4) instead of -2 so that properties like sqrt(x)sqrt(y)=sqrt(xy) hold (this would be false if sqrt(x) denoted the negative root). However — this property is problematic regardless of whether you set sqrt(-1)=i or -i. Assuming that property holds:

    sqrt(-1)sqrt(-1)=sqrt((-1)^2)=sqrt(1)=1≠i2.

  52. #52 Neil, Just Neil.
    February 22, 2007

    I can’t believe you guys fell for such an obvious ruse perpetrated no doubt by one of your own. The site is an obvious lure for scientists, atheists and other liberal/socialist types for the sole purpose of getting each other riled up into a frenzy. And it appears to have worked! I can almost smell the sweat steaming off your heads as you pound away on your keyboards trying to denounce the site as a delusional series of rants by idiots out to prove God exists and math is a joke! I have no comment to make about the site as I will not lower myself to that level even for the humor I would gain from it.
    This is hilarious on a grand scale! I haven’t laughed this hard in a long time!
    Think about it, it has succeeded hasn’t it?

  53. #53 David Cantrell
    February 22, 2007

    Conservapedia just blindly rejects things that they don’t like, regardless of whether they’re important, real, or useful

    Well duh. They’re Conservatives.

  54. #54 Davis
    February 22, 2007

    Neil, the WHOIS info on Conservapedia supports the notion that this is indeed in earnest. (Look up “Andrew Schlafly” on Google.)

    It’s incredibly difficult to distinguish between parody and actual far-right-wing creations.

  55. #55 Blake Stacey
    February 22, 2007

    Earlier today, Conservapedia had 306 registered users, 166,630 page views and 14,283 edits (I checked at 1:32 PM and posted the results at Pharyngula). Just now, at 3:55, their statistics page shows 335 users, 175,220 page views and 14,426 edits. This is what being ScienceBlogged (SciBled?) will do to you!

    The next question is whether those new contributors are sincere “conservatives”, parodists looking for a giggle or — sssh! — truth-loving folk who want to subvert the system from within.

  56. #56 Torbjörn Larsson
    February 22, 2007

    Jud:

    Always look forward to your comments, Torbjörn, and glad to see you were mentioned as a candidate for a commenter award over at Pharyngula.

    Thank you, and thank you! It seems I missed quite a party there.

    Posthumously I would like to nominate all Good Math aficionados, Pharyngulates, … but I see I will get new chances later. Oh, and I can correct the nasty rumor banded about there: I’m not a norwegian, but a swede. (The spelling should tip people off: Torbjörn vs Torbjørn; http://www.nordicnames.de/pojk_t/Torbjorn.html )

    Is this what is meant by experiments proving that space is flat, or something else?

    Yes, I think they refer to the overall curvature of the universe. As you say, the mass-energy density for the universe is close to the critical, ie it is 1 in the current Lambda-CDM model. As I understand it, from that the modelers extract a spatial curvature that is close to 0 when they relax conditions. (See for example, well, the liberal Wikipedia for references. :-)

    Interestingly, the resulting curvature looks slightly negative, which AFAIK in the simplest inflationary setting would indicate that we live in a multiverse. I hope the upcoming Planck probe will constrain this parameter more.

  57. #57 Joseph Hertzlinger
    February 22, 2007

    The most important reason to read leftist blogs is to find out what blithering idiots who call themselves conservatives are saying. This isn’t covered very well at National Review Online or Instapundit.

    Meanwhile, in order to judge the claim that the mathematical articles in Wikipedia are biased, we should find out if Wikipedia discusses left adjoints more often than right adjoints…

  58. #58 Dustin
    February 22, 2007

    For Torbjörn & Mark C.C., I made the following:
    http://www.conservapedia.com/Momentum_%28operator%29
    Check it out before they send it to the memory hole.

  59. #59 Michael Saelim
    February 23, 2007

    There’s only one valid conclusion:

    Math has an inherent liberal bias and therefore must be cast out of all thought.

    Oh noes, I’m majoring in paganism! :O

  60. #60 Martin DeMello
    February 23, 2007

    “i is an erect male organ” is the kind of statement that mathematicians call a phallusy.

  61. #61 Blake Stacey
    February 23, 2007

    Dustin:

    Well, it takes ~45 seconds to load each equation, but I have to admire your handiwork! For convenience’s sake, you should link your article to the “elementary proof” page. [[Elementary Proof|definition of elementary]] will make the words “definition of elementary” a wikilink to the Elementary Proof article.

    The Conservapedia server is so thoroughly SciBled that it took me about ten minutes to load the page history of their “Judicial Activism” article and find out just who wrote what. As it turns out, both Ed Brayton and Andrew Schlafly fell for a Pharyngula commenter’s joke.

    The satire is now the object of ridicule; the map is now the territory. Oh, if Social Text had been a wiki, and Alan Sokal a blogger. . . .

  62. #62 muppt
    February 23, 2007
  63. #63 Torbjörn Larsson
    February 23, 2007

    For Torbjörn & Mark C.C., I made the following

    Davis, I thoroughly enjoyed your effort!

    Of course, we don’t know if operators will be sanctioned (probably, seems like a good conservative thingie), nor brakets (probably not, must be some evil liberal misspieling).

  64. #64 Blake Stacey
    February 24, 2007

    Conservapedia will probably start censoring Dirac notation and forcing us to write everything in terms of wavefunctions. Kets are probably fine, but no innocent child should be forced to see (gasp!) a bra.

    Thank you, thank you, I’ll be here all week. . . .

  65. #65 Jonathan Vos Post
    February 24, 2007

    Ira M. Gessel [Brandeis], “Is Analysis Necessary”, Abstracts of AMS, Vo. 27, No. 4, Issue 146, p.637

    “Analytic techniques are often used to prove results, such as combinatorial identities, whose statement involves no analysis. I will discuss the question of whether analysis is really necessary to prove such results, with examples involving integration, residues, P-recursive sequences, and asymptotic series.
    [received 3 Sep 2006]

    ===========

    “Is analysis worthwhile? Is the theatre really dead?” song lyrics for reader identification

  66. #66 Alexei K
    February 24, 2007

    Are we sure this isn’t a mirror for Wikiality?

    http://www.wikiality.com/Main_Page

  67. #67 Torbjörn Larsson
    February 24, 2007

    I guess the following non-conservapedia operation makes sense to Blake:

    <0|.|i> = <0|i> = *

    You naughty boy!

  68. #68 Torbjörn Larsson
    February 24, 2007

    That wasn’t so naughty. Let me try with HTML instead:

    I guess the following non-conservapedia operation makes sense to Blake:

    <0|.|i> = <0|i> = *

    You naughty boy!

  69. #69 Dustin
    February 25, 2007

    One thing I can’t abide is relativity denial. The conservapedia entry on “relativity” said there was no evidence whatsoever supporting the theory. I thought it was vandalism, but still added something to their page (they only have one, and don’t seem to recognize that there is a distinction between the special and general theories) mentioning that GPS satellites have to make relativistic corrections in order to function because of the curvature of space caused by the earth.

    That addition was removed… by the administrator. I guess he can’t handle those inconvenient facts. That’s just downright Orwellian. Heh, Conservapedia doesn’t need vandalism to be discredited, they’re doing a fine job on their own.

  70. #70 Jonathan
    February 25, 2007

    Happily innumerate libertarian leftist on deck,

    Reading your comments here is hilarious even if I don’t understand 90%+ of your arguments.

    Just in case some of you hard scientists might be interested in what a soft scientist has to say about why many conservatives are so improbably resistant to facts and logic I thought I would show you this link to Dr Bob Altemeyer’s online book _The Authoritarians_. A rather casual examination for the layman of what Dr Altemeyer calls “the authoritarian follower” or “right wing authoritarian”. Based on quite a few years of Dr Altemeyer’s research into the authoritarian personality it is an illuminating study of a psychological or personality type that non authoritarians have a very hard time understanding.

    RWAs do not desire or seek power for themselves, rather they desire a strong leader to tell them what and how to think and to reinforce their biases.

    http://home.cc.umanitoba.ca/~altemey/

    From the introduction of _The Authoritarians_

    The second reason I can offer for reading what follows is that it is not chock full of opinions, but experimental evidence. Liberals have stereotypes about conservatives, and conservatives have stereotypes about liberals. Moderates have stereotypes about both. Anyone who has watched, or been a liberal arguing with a conservative (or vice versa) knows that personal opinion and rhetoric can be had a penny a pound. But the arguing never seems to get anywhere. Whereas if you set up a fair and square experiment in which people can act nobly, fairly, and with integrity, and you find that most of one group does, and most of another group does not, that’s a fact, not an opinion. And if you keep finding the same thing experiment after experiment, and other people do too, then that’s s a body of facts that demands attention. Some people, we have seen to our dismay, don’t care a hoot what scientific investigation reveals. But most people do. If the data were fairly gathered and we let them do the talking, we should be on a higher plane than the current, Sez you!

  71. #71 Mumon
    February 25, 2007

    I just came across your post. I too, was similarly amused, as you can see from my diary on Kos.

    Yes, they at Conservapedia are suspicuous of the poor old square root of -1 (of course, to me, it’s j not i, but I digress…)

    And I guess cell phones.

    And DSL and cable modems…

    And wireless LANs…

  72. #72 C. Dunn
    February 26, 2007

    If i is an erect male organ, then j is clearly a Pfizer customer.

  73. #73 Anonymous
    February 26, 2007

    “Is analysis worthwhile? Is the theatre really dead?” song lyrics for reader identification

    Posted by: Jonathan Vos Post | February 24, 2007 01:16 PM

    Jonathon, are you asking for someone to identify the lyrics?
    They’re from “The Dangling Conversation” by Simon & Garfunkel from the Parsley Sage Rosemary & Thyme album (1966)

    And the lyrics go “Can analysis be worthwhile?/Is the theater really dead?”.

  74. #74 Anonymous
    March 9, 2007

    Idiots… But at least they are using their stupidity for a good cause… Amusing us!!!

  75. #75 Tom Stockton
    March 9, 2007

    It appears that Conservapedia is a project for ultra-orthodox Christian home-schoolers. Unlike Wikipedia, it can only be edited by a chosen few (because of the problem with an arboreal octopus?). Don’t fault the entries too much, since many are edited by children who are just beginning to learn the material. The real issue might be whether Conservapedia constitutes a form of child abuse – Is this the material they’re actually being taught? The USA already has trouble maintaining a technological lead, so this could bring about our Age of Unlightenment if it becomes widely used.
    Nevertheless, it is a hoot & I can’t wait to have twice the fun with Liberalpedia.

  76. #76 Gry Heidi Nordhagen
    March 17, 2007

    I decided to have a bit of fun this weekend. I have entered various concepts in mathemathics and physics into the search field on Wikipedia (and followed links; _I_ am certainly no mathematician or physicist!). The results were truly … interesting. Usually, the Conservapedia didn’t have an equivqalent entry to the one in Wikipedia. When it did, the Conservapedia entry was positively skeletal compared to the Wiki one.

    Then I decided to get a bit further afield. I decided to look up various political and religious topics, as well as the sort of knowledge any person who should call herself (or himself) educated really should know about!), such as Buddhism, Palestine, Taoism, Odin, Christianity, love, hate, compassion, empathy, Europe, periodic table, stone age, ice age, dinosaur(_do_ look this one up!), pregnancy, feminism, Science Fiction, Fantasy, Isaac Asimov, War, Peace, immune system, satellite, (Mahatma) Gandhi, virus, ethics, Descartes, logic, contraception, ecology, intelligence, fascism, Habeas Corpus, computer, Hinduism, ahimsa and a number of other subjects.

    The results were … interesting.

    If Conservapedia had an entry at all, it was positively anorectic, if not downright slanted (misleading, to the less discriminating reader.

    If I want to look up _facts_, I know where I will go. Despite the subtle indications that since “anyone can add to or edit the content on Wikipedia” – direct quote from the Conservapedia entry, hinting that the contents _must_ be inaccurate or slanted) does not compare well to what I found as the “header” on Concervapedia: “Minors under 16 years use this site. Posting of obscenity here is punishable by up to 10 years in jail under 18 USC § 1470. Vandalism is punishable up to 10 years in jail per 18 USC § 1030. We will trace your IP address and give it to authorities if necessary.” (this is also a direct quote)

    I have bookmarked Wikipedia in my “frequent use” folder, although I might also have put it in Science despite looking up lots of stuff that has nothing at all to do with science.

    Concervapedia I have put in “Politics”.

  77. #77 Will, no last name
    June 26, 2009

    Wow, i would consider myself a conservative and conservapedia still looks like a bunch of regressive fear-mongering zealots, where do they find these guys?

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