Conservapedia:Conservapedian mathematics

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The folks that create Conservapedia's "content" sometimes go off in fascinating directions other than the usual relentless attacks against anything that doesn't fit their strange reactionary and fundamentalist mindset.

In the case of articles relating to science and math, Conservapedia's's charter is often less than clear. Their front page seems to specify "educational, clean, and concise entries", and states that it "is rapidly becoming one of the largest and most reliable online educational resources of its kind."^[1]

But guess what? They rape mathematics just as much as history, and sanity in general.

[edit] The general state of affairs

Students in school (including the much-beloved home-schooled ones) seem to be interested in mathematics and science, so Conservapedia sort of has to support it. In fact, the much-touted industrial might of the United States depends on our superb math and science educational system. And, in a way, Conservapedia does have what might pass for student-oriented math and science articles. While it's true that a blind anti-science hysteria often appears on their front "news" page,^[2] and their anti-evolution hysteria is well known, they do have quite a number of articles on science and math, a few of which might actually be helpful to students.

But the Conservapedia powers-that-be are in rather unfamiliar territory when dealing with science and math, so they often don't seem to know how to proceed. The usual rhetorical devices so loved by Andy don't work in this area — even he knows better than to argue mathematical points by questioning whether the other party supports school prayer. Though he does occasionally dip his toe into the water of this type of insanity, as when he asserts (see below) that "Liberals don't want to admit [that Wiles' proof is not elementary]." Because of this unfamiliarity, the Conservapedia mathematics articles are riddled with ignorance and completely inappropriate expository levels. Much of this seems to stem from the "cut and paste" mentality that runs rampant there. Many articles are totally useless stubs that appear to have been copied from some textbook's glossary, and many contain ignorance that goes uncorrected because ... well, because all the important Conservapedia editors are just plain ignorant — or off editing a homosexuality-related article, and the few that are intelligent and well-intentioned don't last long.

[edit] Andy's abysmal arrogance, ignorance, hubris, and general delusions of grandeur

[edit] The "Critical Thinking in Math" class

Andrew Schlafly, the owner of the site, personally sets the tone for all of this, naturally. Perhaps the most telling bit of ignorance and delusional thinking can be found in the "Critical Thinking in Math" class that he seems to want to teach on the webshite. The announcement sets the bar quite high — it's on the main page, along with the courses on American Government and the Supreme Court. The stated goals include "awakening mathematical interest in students" (a laudable goal, of course), and "fending off mental decline" in adults. The objectives are unbelievably ambitious — with no tools beyond ninth grade math (and accessible to even younger people if they are motivated), he wants to cover such things as the axiom of choice, Gödel's incompleteness theorems, formal logic, Wiles' proof of Fermat's Last Theorem, the Twin Primes Conjecture, Goldbach's conjecture, the Prime Number Theorem, and the definition/construction of the integers and transcendental numbers.

We can certainly allow for the possibility that some of these topics could be reasonably treated in a superficial way, as in: "Goldbach's conjecture says that every even number greater than 2 is the sum of two primes. As simple as this sounds, it remains unproven after 250 years." And there is certainly a lot of mathematical history, biography, and folklore that can be treated in this way. But many of the stated goals of the course admit no such folkloric treatment. The axiomatic construction of the integers and reals, the axiom of choice, Gödel's incompleteness theorems, and Hilbert's program all require very careful thinking.

Aside from the outlandish goals, Andy's ignorance and bizarre notions show up in the proposed curriculum. He wants to cover "controversy about proof by contradiction", even though proof by contradiction has been a staple of mathematics for 2300 years. He also wants to discuss the notion of "elementary proof". His obsession with elementary proofs, and complex numbers, will be discussed in more detail below. The curriculum also lists the concept of "additive factoring", with no evidence that Andy has any idea what it is, or why it would be appropriate for a course of this type.

The class was announced in early August, 2007, with the actual startup proposed for September (of that year). By late August, four people had expressed interest, but Andy still had high hopes and much enthusiasm:

We don't have a lot of students yet but it is still only August. We plan to start mid-September, and I welcome your input on the curriculum. I expect the interest in this to grow as it has in the American Government course (now up to 45 participants). Much will be accomplished by this math course for the immense benefit of the participants.

In late August (2007), someone ("Robert") signed up, offering his services as an instructor, but expressing reservations about the ambitiousness of the curriculum. A couple of weeks later, he posted a detailed analysis of his reservations on the talk page. Andy responded, positively and briefly at first, and shortly thereafter, in a rambling and obnoxious way. Mixed in with the irrelevancies about "the view that more abstraction is better", "yield[ing] to popular opinion", and "inject[ing] a degree of accountability", there is the bizarre statement that "Proof by contradiction was disfavored, for obvious reasons, by many mathematicians as recently as 30 years ago. That you [Robert] are completely unaware of it merely underscores the need for this course." Robert responded by asking for textbook recommendations on these points. No response was forthcoming. We still don't know what those "obvious reasons" are, or why they escaped the notice of Euclid, Euler, Gauss, Fermat, and Leibnitz.

As of August 2008, this "course" shows no signs of having been offered (or even constructed), for free or for USD250 per student.

[edit] A digression on complex numbers

At about this time, Andy's fanatical views about "elementary proofs" came to the forefront on the page about bias in Wikipedia. The discussion is classic Andy, of the sort that one normally sees when he is spouting his delusions on political topics. But it is all the more amazing in a mathematical discussion.

In order to understand (as well as one can possibly understand his thought processes) Andy's notions about elementary proofs, we need to examine his views on complex numbers. He is curiously opposed to them, and heaps scorn on them at every opportunity. We have no idea why—they are a staple of mathematics, and learning about them typically begins somewhere in high school or junior high. Andy seems to have some kind of preposterous belief that there is a unique pitfall in the choice of the imaginary unit. He must have really disliked his teacher. Oh, we're sorry. Was he homeschooled?

Brief technical digression: complex numbers are the set of numbers defined with a special item called "i" (for "imaginary"). The complex numbers are set up so that every non-zero number has a square root (or cube root, etc.), even negative numbers. Two square roots, in fact. The two square roots of 1 are +1 and -1, and the two square roots of -1 are +i and -i. The choice of the word "imaginary" may have been unfortunate for Andy's mathematical well-being. Be that as it may, complex numbers, and the field of "complex analysis" that it engenders, constitute an extremely important, and well-accepted, branch of mathematics.

Complex analysis is incredibly useful in many places in mathematics, even places that deal only with "real" numbers. For example, complex analysis easily explains the interval of convergence of many functions' power series on the "real line". As such, the question of whether a theorem that, on the face of it, does not involve complex numbers, can be proved without using complex analysis, is a somewhat interesting mathematical oddity. Such proofs—not using complex analysis in a theorem whose statement does not involve complex numbers—are sometimes called "elementary proofs". A famous case of this is the proof of the Prime Number Theorem. The details aren't important, but a classic proof using complex analysis was formulated in 1896. The question of whether an elementary proof existed touched on some interesting issues of the philosophy of mathematics in the early 20th century, and, in 1949, elementary proofs were published by Atle Selberg and Paul Erdös.^[3]

But to Andy, this question is of cosmic importance, and illuminates the world of liberal deceit that lives within his mind. In the page about bias in Wikipedia, he asserts that politically motivated censorship was involved in the Wikipedia page on the subject. He goes on and on about this, with such classic gems as "many of the recent claims of proofs, such as Wiles' proof of Fermat's Last Theorem, are not elementary proofs and liberals don't want to admit that."^[4] He goes off into religion, of course, with "Liberals prefer instead to claim that mathematicians today are smarter than the devoutly Christian mathematicians like Bernhard Riemann and Carl Gauss." And the usual "liberals detest accountability". One correspondent asks:

• Can you explain again what is liberal about the omission of elementary proof?
• Can you name anybody who would not admit that Wiles proof is not elementary?
• Does it say anything about the political and religious orientation of Bernhard Riemann that he used his [complex] Zeta function in a non-elementary proof of the prime number theorem?
• Does it say anything about the political and religious orientation of Paul Erdös that he found an elementary proof for the prime number theorem?

Andy's reply does not address those questions, but does say:

Yes, many liberals do resist characterization of Wiles proof as not being elementary.

Andy's attempts to attach ideology to mathematics bears frightening analogy to the "German mathematics" movement in Nazi Germany, substituting "conservative-Christian" for "German".

Andy's perverse disdain for complex numbers is also on display in his own edits (later reverted by others!) to the Conservapedia pages for Imaginary number, where he asserts that the square root of -1 is "non-existent", and Elementary proof, where he asserts that "Elementary proofs are preferred because they 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."

• By whom are they "preferred"?
• What are the "additional assumptions"?
• What is the requirement that there be a "unique square root of -1"? Minus one, like all nonzero numbers, has two square roots; there is no "uniqueness problem".
• What are the "inconsistent results"?

There had been an earlier archive of the same page, going over the same issues.

Conservapedia's "Elementary proof" page gives two definitions for it—the common "intuitive" notion of simplicity (misstated as inability to be broken down into smaller proofs), and the more formal notion discussed above. (The notion in terms of simplicity was not created by Andy.)

[edit] Critical Thinking in Math: the criticism becomes serious.

Robert must have looked around at the complex analysis material discussed above, and a number of other examples of Andy's insanity, because, a few weeks later, he posted this. He takes Andy to task for a great many instances of insanity, challenging him on the various points about complex analysis and elementary proofs, as well as:

• Andy's completely ridiculous statement that the Continuum Hypothesis is equivalent to the Axiom of Choice, which cited nothing more than some radio program.
• Andy's claim that proof by contradiction "was disfavored, for obvious reasons, by many mathematicians as recently as 30 years ago", pointing out that it has been widely accepted and used for 2300 years.
• Andy's completely spurious source for statements about Wiles' use of the Axiom of Choice in Fermat's Last Theorem.
• Andy's statement that Wiles' proof has been criticized on the internet, citing a crackpot web site that also happens to claim proofs of the Twin Primes Conjecture and Goldbach's conjecture.

Robert concludes by asking "Are these things the standard of veracity, trustworthiness, and verifiability that you uphold for Conservapedia? Are these things appropriate for an encyclopedia that prides itself on not being the 'National Enquirer of the internet'"?

Andy makes a rather weak reply to a few of the (easier) criticisms, and then stops.

Rob Smith then briefly blocks Robert, for "disruption".

Robert comes back more strongly a couple of weeks later here, asking about the remaining issues. Then, having been alerted to the previous blocking, issues an (apparently final) blast here. Andy is apparently left speechless at this point.

We should point out that, in apparent preparation for this class, Andy did ask his brother Roger (a Ph.D. in mathematics) whether he had a proof of the Twin Primes Conjecture. Roger replied, quite sensibly, that he believes it is true, but has no proof.

Another person has raised reservations about the appropriateness of the curriculum for high-school-level students.

Also, a few people have raised questions on various talk pages, along the lines of "Andy, when are you going to answer the math questions?" Such things are quickly burned, and the individuals banned. It appeared for a while that this might become another FBI Incident in miniature, but it seems to have passed.

Scheduled to start in September 2007, we're still looking forward to the "Critical Thinking in Math" class. As of February March April May, August 2008, nothing has happened, and it seems to have three students - we look forward to the first anniversary of this course not occurring.

All of the CP items noted above have been saved to prevent them from being burned. If deleted, we will recreate them here.

[edit] What the heck is Stone–Čech compactification?

While not as notorious as the copying of the U.S. Navy Ships Registry during the second "article creation drive" (can someone produce a citation? Has it been documented in WIGO?) many mathematics articles appear to have been mindlessly copied out of some textbook glossary. (We have not located the precise source. Might be just mangled versions of the Wikipedia articles' lead paragraphs.) A particularly good illustration of this may be found by perusing the topology category. It is filled with articles that make no sense in the context of high-school level mathematics, or, for that matter, any educational context at all.

Are there meaningful things that one can say about topology to high-school students? Certainly. (Mobius strips and Klien bottles rule!) Are there things that one can say that go beyond simple statements that "topology is the study of how coffee cups are similar to donuts"? Yes, if one puts a great deal of care into it, and the students are seriously motivated.

So how does Conservapedia rise to the challenge? Let's start with the article on Stone–Čech compactification. If that sounds a bit esoteric, it's because it is. It's not the sort of thing that I would put into any mathematics site aimed at high-school-level students. Be that as it may, let's look around.

Most of what we will look at is in fact quite advanced, because topology is an advanced topic within mathematics. That's what makes it so challenging to present this material in an educational way. The reader is not expected to understand all these terms. But, if you wish, you can follow along by looking them up in Wikipedia, as long as you are not offended by their DeceitfulLiberalBias. One thing you will find is that topology, done right, really is a very advanced subject.

• Stone–Čech Compactification—This is defined in terms of a Completely Regular Space. OK.
• Completely Regular Space—This is defined in terms of Normal Space, Continuous Function, Separated, Singleton set, and Closed Set, the last three of which are not wikilinked or defined.

• (undefined) Closed Set— The definition of open and closed sets, and that they are complements of each other, is central to basic topology. You can't do anything, much less Stone–Čech Compactification, if you don't know what they are.

• Normal Space—This refers to Completely Regular Space, Hausdorff Space, Urysohn's Lemma, and the concepts of Countable, Basis, Disjoint, and Neighborhood. The latter two are not wikilinked or defined.

• (undefined) Neighborhood— The concept of a "Neighborhood" is absolutely crucial to an understanding of topology in terms of concepts that the student will know. For example, an "open set" will be found to be one that "contains a neighborhood of each of its points".

• Continuous Function—This refers to Compact, Open Set, Inverse Image, Net, and Filter. The latter three are not wikilinked or defined anywhere.
• Urysohn's Lemma—This refers to several other things. If those things didn't lead to dead ends, this might be OK.
• Open Set—This is defined in terms of the notion of a "ball", plus some handwaving. It is also not in the Topology category. The page has also been vandalized. The concept of Open Set is about as crucial to topology as anything can be. You can't begin to talk about anything in topology without discussing the central role of open sets. Nebulous talk about "all points sufficiently close to it are also contained" won't do. You need a precise formulation of what "sufficiently close" means. That's what topology is about. By the way, the "topological space" article, does mention "open sets", but it does so in the plural, so the wikilink to the singular "open set" is red.

• (undefined) Inverse Image—< The definition of Continuous Function, as one for which the Inverse Image of any open set is an open set, is absolutely critical. Establishing that this is equivalent to the more common definition of continuity (in terms of epsilons and deltas), is the crown jewel of elementary topology. You can't discuss continuity without carefully discussing what an inverse image is. And if you don't do that, you have missed the point entirely. Neither Stone–Čech Compactification, nor anything else, will make sense.
• (undefined) Net—Not a problem; must have been in the glossary that this stuff was cribbed from.
• (undefined) Filter—Ditto.

• Compact—This is defined in terms of Open Cover (not defined), and refers to Complete and Totally Bounded.

• (undefined) Open Cover— The concept of compactness, and of Open Cover, are crucial. We're 95% certain that the book whose glossary all this was cribbed from actually said something about it.

• Hausdorff—This is defined in terms of all the usual undefined things, like Disjoint, Open, Net, and Filter. Just showing off.
• Totally Bounded—This is defined in terms of Metric Space, Cover, and the rather nebulous notion of "any fixed size".
• Metric—This is OK.
• Metric Space—This is defined in terms of Metric and Topology, but leaves out the crucial connection between the two. The connection is that the Topology must have, as its basis, all Neighborhoods of all points. But, since they didn't say what a Neighborhood is, this is probably the best they can do.
• Complete—This is defined in terms of Cauchy Sequence and Converge.
• Cauchy Sequence—This one is actually OK. It's in terms of Metric. Deleted see Inability to contribute
• Converge—This is is mostly OK, but the statement "Similar definitions can be made for convergence of functions" glosses over the whole topic of functional analysis.
• 2nd-Countable Space—This is OK, but unmotivated. It is in terms of Countable and Basis.
• Countable—This is defined in terms of Bijection, which is not defined. Bijection not defined? How are you going to define Homeomorphism?
• Basis—This is sort of OK.
• 1st-Countable Space—This states that every point has a countable basis. Points don't have bases. Look it up.
• Homeomorphism— This is crucial to what topology is about. Alas, without defining Bijection, you can't really talk about this, so they define it in terms of some baloney about "such that f(f^-1) is the identity function". But all is not lost! Andy himself added the business about coffee cups and donuts.

And there are many other topological delights—Frechet Space, Kolmogorov Space, Boundry [sic], Paracompact Space, ....

Finally, speaking of showing off, this one is not in the topology category, but is too delicious to pass up:

• "2-category is a category with morphisms in between morphisms. It is defined as a category enriched over the category of categories and functors, with the monoidal structure induced by the composition."

Yummm!

[edit] Infinity

Another source of amusement is the article on infinity. From the edit history, one can see that many CP editors have had their hand in this, trying to get it to the present pinnacle of confusion. I'd quote the first sentence here, but that wouldn't do it justice. Go see for yourself. Much of the foolishness comes from that paragon of clear expository writing for students, Ed Poor.

[edit] How long does it take to earn $40?

Conservapedia's article of "conservative parables" (as of this revision) tells the story of a teenager who received $40 from his father but then lost it out of his car. The kid obsesses with the lost cash for a while. Years later, he comes to his senses and realized that if he had just worked a few extra hours, at $8 per hour, he could have replaced that $40.

The question is: If you make $8 per hour, how long does it take you to earn $40? The first answer to this question was "about 6 hours". The second answer was 5 hours, but it was later reverted to 6 hours with the explanation, "removed mistake inserted by Ferno... ever hear of taxes, folks?" Then, another user corrected it to 5.6 hours citing current tax rates. This was undone. So, by fiat, it takes six hours of working at $8 per hour to replace $40.

The first version of this parable said that the minimum wage is $8 per hour, which is optimistic. According to the US Department of Labor, the minimum wage was $5.85 per hour effective July 24, 2007, increasing to $6.55 per hour effective July 24, 2008 and to $7.25 per hour effective July 24, 2009. Andrew later realized this.

[edit] Cellular automata

The John Conway article claims that

The game [of life] is probably the clearest example of the falsehood of natural evolution, as the slightest change in self-sustaining patterns like glider guns usually destroys them. Only those patterns created by human beings (or discovered and preserved by them) have any chance of being perpetuated.

In fact, the opposite is true. Random patterns in the Game of Life frequently produce both gliders and stationary self-sustaining patterns. ^[5] The "glider gun" pattern is rather complex, but, like all Life patterns, can be created by random occurrence.

[edit] Axiom of choice

Conservapedia also give us this "Conservative Insight" into the axiom of choice,

The Axiom of Choice has many equivalent statements, such as the Tychonoff theorem, the Well-Ordering Theorem, the existence of cardinal numbers, the existence of a basis for every vector space, and the existence of subsets of the real line which do not have a well-defined Lebesgue measure. In algebra it is common to use Zorn's Lemma (also equivalent to the Axiom of Choice) to study ideals in infinite Noetherian rings.^[6]

Whilst the axiom of choice can be used to construct non-Lebesgue measurable sets, cardinal numbers, however, exist by virtue of the existence of the natural (counting) numbers - it is attempts to continue aleph numbers that require the axiom of choice. The Tychonoff theorem is not equivalent to the axiom of choice, but all five known proofs use the axiom of choice at some point. The existence of a basis for every vector space is an interesting on. If it is a Schauder basis then it is countable and so does not require the axiom of choice. If it is the more conventional Hamel basis then the proof that all vector space have as basis require the axiom of choice. It is correct to state that the axiom of choice is equivalent to the well-ordering theorem and Zorn's Lemma. It is important to note the difference between, is used in the proof and is equivalent to.

[edit] Inability to contribute

A trend started around July 2008 where Ed Poor, an alleged math teacher^[7] , would block or threaten to block anybody who would contribute to mathematics and physics articles by adding content he personally does not understand, with the excuse that it's not suitable for Conservapedia's reading level (apparently students who are studying for the SAT test^[8]) - such as in the block of Lemonpeel on July 8, 2008^[9]. It should be noted however that as of August 21, 2008 no such article or guidelines exists. This has occurred both when the material is appropriate for high school students, despite Ed's lack of understanding (example: derivative), and where the nature of the subject makes it unsuitable - if not impossible - to adjust the article for those not in college (example: Quantum mechanics). As a result many mathematics articles were left in shambles with vague, informal definitions and outright incorrect statements.

Not content with merely reverting edits Ed has also been known to delete entire articles because he is unfamiliar with the content. As of August 24, 2008 the victims of his ignorance have been:

• Derivative^[10] - Deleted (restored by Andy)
• Natural logarithm - Deleted
• Radioactivity - Deleted
• Line - Blanked and (we will be generous) rewritten
• Probability - Deleted and apparently restored (with no history)
• Quantum mechanics - Mutilated
• Real line^[11] - Deleted
• Cauchy sequence^[12] - Blanked then deleted

This whole trend makes contributing to Conservapedia with halfway decent mathematical content impossible.

The situation became so bad an editor named SamHB wrote an open letter to Ed Poor. Ed replied on SamHB's user page (not talk page) halfway through the letter.

Ed then put SamHB on probation^[14].

A similar attempt to contact Andy was made via email, we do not know what came of this.

To give you an idea of what Ed is striving for with his "reading level", let's look at the edits made by the man himself. Ed thinks this is a complete article on a math topic.

As further evidence that Ed Poor is not qualified to teach math at any level, upon seeing that a Conservapedia article used the formula R=V/I, Ed stated he heard a completely different definition: V=R*I, and asked if it was accurate. This, of course, is the equivalent of asking if 3=6/2 is contradicted by 6=3*2. No one who pretends to be a math teacher should ever ask such a question.

[edit] Casualties

• Mathoreilly - Blocked once for removing irrelevant content from the Theory of Relativity article, then permanently by Karajou, with many contributions reverted for suspected parody.^[15]
• Lemonpeel - Refused to explain Quantum mechanics in terms children would understand.^[16]
• SamHB - For not pretending that the math articles are fine ^[17]
• Fantasia - For acting according to consensus when said consensus didn't include Ed. ^[18]
• Wandering - For criticizing Fantasia's block above.^[19]
• Foxtrot (the creator of most of CP's mathematics article and disliker of the Axiom of Choice, only a light casualty) - For clearing up one of Ed's earlier, paranoid driven, mistakes^[20] and then trying to explain why Ed was wrong on the talk page^[21].

Following the updating of this article, on August 26, 2008 SamHB wrote another letter to Ed, making reference to this site and possibly this article^[22]. In this letter SamHB stated:

We here at RationalWiki stand by our belief Ed Poor is an ignoramus and a bully. His behavior at both Conservapedia and Wikipedia lend support to this theory and all evidence is laid out, in full, at Conservapedia:Sysops/Ed Poor.

[edit] See also

• Conservapedia:Probability

[edit] Notes and references