Conservapedia:Conservapedian mathematics

Is this a true statement:

$\Delta E + d-T = hc$

Where $E$ is an elephant, $h$ is the act of the elephant hanging off $c$ (a cliff) while gripping $d$ (a dandelion) with $t$ (its trunk). Math can "prove" just about anything; if you want to balance a battleship on the spout of a tea kettle, math will "prove" to the world it can be done. But actually seeing it is something else. The battleship's anchor alone would crush that tea kettle, and the elephant will fall to the bottom of the cliff, taking the dandelion with it. Your math is not matching up with what everyone is actually seeing on a daily basis. You are not correct.

Set theory and the Bible is an approach that seeks to understand both mathematics and the Bible by viewing them through set theory. Georg Cantor championed this approach as a way of understanding eternity in the Bible, an his work yielded profound new insights for mathematics.

The Parable of the Vineyard Workers at Matthew 20:1-16 is difficult to understand under conventional approaches, but is straightforward when the workers are viewed as one set, and the master as a different set.

A geometric rate of growth occurs when a series increases in proportion to its current value, as in doubling per century in the case of Best New Conservative Words. Symbolically, this could be written as

$\mathrm{Conservative \, Words \, Today} = \mathrm{Original \, Conservative \, Words}\times 2^{\frac{\mathrm{time}}{\mathrm{100 \, years}}}$

where $\mathrm{time}$ is the amount of time since the $\mathrm{Original \, Conservative \, Words}$ were counted (perhaps the year 1600 as described in the above article).|4=Conservapedia's article on "Geometric rate", which references Conservapedia's Law. |undefined

The folks who write Conservapedia don't just attack anything different from them in the realms of politics or religion. Science that conflicts with their religion obviously comes in for a drubbing, even as lip service is paid to the idea that science is good. But they also get weird about mathematics itself.

The general state of affairs
Students are expected to learn about mathematics, so Conservapedia had to support it. And, in a way, Conservapedia does have what might pass for student-oriented math and science articles. While blind anti-science hysteria often appears on their front page, 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 theoretically be helpful to students, if they squint.

Unfortunately, any potential helpfulness is ultimately negated as articles based in reality are freely mixed with articles written from misunderstood sources and articles that are complete fabrications by Schlafly. For example, the page on the Fourier transform, while poorly explained, is approximately correct &mdash; but the article on relativity mindlessly denies its correctness, predictive power and impressive accuracy.

Conservapedians are in unfamiliar territory when dealing with science and math. The usual rhetorical devices don't work in this area &mdash; even Schlafly 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]," or when he claims "college math is not completely immune to liberal influences that have destroyed other subjects like physics." Because of this, the Conservapedia mathematics articles are riddled with ignorance and completely inappropriate expository levels. Much of this seems to stem from a "cut and paste" mentality. Many articles are hopelessly useless stubs that appear to have been copied from a textbook glossary, and many contain ignorance that goes uncorrected because all the important Conservapedia editors are just plain ignorant &mdash; or off editing a homosexuality-related article &mdash; and the few that are intelligent and well-intentioned never last long before being deleted, and all contributors involved getting banhammered.

The "Critical Thinking in Math" class
Another example is the difficulty that uneducated people feel about hypotheses. [...] For this reason, reductio ad absurdum is a form of argument that is repugnant to those that are not familiar with logic or mathematics; if the hypothesis is going to be proved false, they cannot make themselves hypothetically entertain it. Perhaps the most telling example was the "Critical Thinking in Math" class Schlafly planned for 2007. The announcement set the bar quite high &mdash; it was on the main page, along with the courses on American Government and the Supreme Court. The stated goals included "awakening mathematical interest in students" (a laudable goal, of course), and "fending off mental decline" in adults (also a laudable goal).

The objectives were unbelievably ambitious: with no tools beyond 9th grade math (and accessible to even younger pupils if they are motivated), he wanted 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 and construction of the integers and transcendental numbers.

Some of these topics could be reasonably treated in a superficial way, e.g.: "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 manner. But 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 wanted to cover "controversy about proof by contradiction", even though proof by contradiction has been a staple of mathematics for 2300 years. He also wanted to discuss the notion of "elementary proof". The curriculum also listed the concept of "additive factoring", with no evidence that Andy has any idea what this is, or why it would be appropriate for a course of this type.

The class was announced in early August 2007, to start in September of that year. In late August, someone ("Robert") signed up, offering his services as an instructor, but expressing reservations about the ambition 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 Leibniz.

On September 13th, 2008, Schlafly wrote "I've found greater interest in American History right now, so it's taken first priority. It's unfortunate that some who have math skills seem resistant to looking at math critically," deftly ignoring the enormous quantities of criticism he received for his asinine ideas.

A digression on complex numbers
Around this time, Andy's 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 from him on political topics. It is all the more amazing in a mathematical discussion.

Andy is curiously opposed to complex numbers, and heaps scorn on them at every opportunity (remember, a complex number is a constant, plus a constant times i). The reason is unclear &mdash; they are a staple of mathematics and learning about them typically begins somewhere in high school or junior high. Additionally, Andy would have learnt and used them extensively back when he was studying and working in electrical engineering, as they are the basis of Fourier frequency-domain analysis, which in turn is pretty much the heart and fiber of analog electronics and signal processing. It's as if a plumber decided to lash out at pipe wrenches.

Andy seems to have some kind of preposterous belief that there is a unique pitfall in the choice of the imaginary unit. The choice of the word "imaginary" (originally coined by Descartes as a criticism of the concept) may have been unfortunate for Andy's mathematical well-being. Nevertheless, complex numbers, and the field of "complex analysis" that it engenders, are extremely important and well-accepted in 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 does not involve complex numbers can be proved without using complex analysis is a somewhat interesting mathematical oddity. Such proofs &mdash;that do not use complex analysis to prove a theorem whose statement does not involve complex numbers &mdash; are sometimes called "elementary proofs". A famous case 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 Erdős.

To Andy, this question is of cosmic importance, and illuminates his concept of liberal deceit. He asserts that politically-motivated censorship was involved in the Wikipedia page on the subject, 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." He goes off into religion, no less, with "Liberals prefer instead to claim that mathematicians today are smarter than the devoutly Christian mathematicians like Bernhard Riemann and Carl Gauss." Furthermore, "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 Erdős 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 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 (i and -i); 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.)

Critical Thinking in Math: the criticism becomes serious
Robert must have looked around at the complex analysis material discussed above, because, a few weeks later, he posted this. He takes Andy to task for a great many of Andy's 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.

A few people raised questions on various talk pages, along the lines of "Andy, when are you going to answer the math questions?" Another person raised reservations about the appropriateness of the curriculum for high-school-level students.

In apparent preparation for this class, Andy did ask his brother Roger (who is also a conservative fundamentalist, but has 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.

Political examples
There are cases in which the Nash equilibrium is a counter-intuitive outcome (and where the intuitive outcome is not a Nash equilibrium). The reason for this is the assumption that a participant assumes that nobody except for him will change strategies. If two very unlikely or disadvantageous strategies are best responses to each other, it is a Nash Equilibrium, but it may not be the most desirable outcome. For example, if you prefer a Republican government, but more people are voting Democratic, voting Democratic or abstaining are among your best responses, since your vote will not be able to affect the outcome. This may be part of the reason why countries sometimes elect liberal governments, even though most rational and logical people are conservative. If the media is able to convince people that most others are voting for a left-wing party, some would-be conservatives might get discouraged and not vote, or even vote for the left-wing party because they think it is what everyone else is doing, with disastrous implications.

Andy also manages to interject politics and his personal obsessions into mathematics by giving questionable insane examples of mathematical "applications". For example, the following is the only application noted by Andy in the CP article on 'linear algebra':


 * An n x m matrix can be developed using observed incidents of liberal style in Wikipedia entries, and that data can then be simplified to draw conclusions about liberal style can mislead viewers. The n rows can represent different elements of liberal style, while the m columns can represent different types of entries on Wikipedia.

There are certainly much clearer and more important examples of the linear algebra applications that a person with a degree in electrical engineering should be able to come up with (e.g., circuit analysis, matrix differential equations, etc.). A vaguely defined matrix almost certainly made up on the spot clearly doesn't belong in an educational work.

On the CP article on 'Set' Andy gives the following as an "application":


 * There is the set of unborn children who were aborted about which striking conclusions can be drawn. Given the large and diverse number of elements of this set, it would likely include many who could surpass existing athletic and intellectual achievements.  Indeed, many of the world records and Nobel Prize achievements recognized today would have been outdone by members of this set.

The concept of a 'set' plays a fundamental role in modern mathematics. Indeed, many mathematicians look to set theory as the foundations of the field itself. There are numerous applications and examples of sets that even an interested high school student can give. However, from ignorance or an obsessional mindset, Andy goes into a bizarre diatribe against abortion. Even accepting his argument, it can also be said that many criminals and murderers would also be "members of this set".

Andy has difficulty even writing about mathematics without bringing politics into the discussion.

What the heck is was Stone–Čech compactification?

 * On Aug. 29, 2008, Ed Poor deleted the "Stone–Čech compactification" article. It's good to know what an avid reader of RationalWiki he has become.

While not as notorious as the copying of the U.S. Navy Ships Registry during the second "article creation drive", many mathematics articles appear to have been mindlessly copied out of some textbook glossary. (We have not located the precise source; it might be just mangled versions of the Wikipedia articles' lead paragraphs.) A particularly good illustration of this may be found by perusing the category topology. 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. (Möbius strips and Klein 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 Deceitful Liberal Bias. One thing you will find is that topology, done right, really is a very advanced subject.


 * Stone–Čech Compactification&mdash;This is defined in terms of a Completely Regular Space. OK.
 * Completely Regular Space&mdash;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&mdash; 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&mdash;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&mdash;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&mdash;This refers to Compact, Open Set, Inverse Image, Net, and Filter. The latter three are not wikilinked or defined anywhere.
 * Urysohn's Lemma&mdash;This refers to several other things. If those things didn't lead to dead ends, this might be OK.
 * Open Set&mdash;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&mdash;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&mdash;Not a problem; must have been in the glossary that this stuff was cribbed from.
 * (undefined) Filter&mdash;Ditto.


 * Compact&mdash;This is defined in terms of Open Cover (not defined), and refers to Complete and Totally Bounded.
 * (undefined) Open Cover&mdash;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&mdash;This is defined in terms of all the usual undefined things, like Disjoint, Open, Net, and Filter. Just showing off.
 * Totally Bounded&mdash;This is defined in terms of Metric Space, Cover, and the rather nebulous notion of "any fixed size".
 * Metric&mdash;This is OK.
 * Metric Space&mdash;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&mdash;This is defined in terms of Cauchy Sequence and Converge.
 * Cauchy Sequence&mdash; This one is actually OK. It's in terms of Metric. Oops, this was deleted in
 * Converge&mdash;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&mdash;This is OK, but unmotivated. It is in terms of Countable and Basis.
 * Countable&mdash;This is defined in terms of Bijection, which is not defined. Bijection not defined? How are you going to define Homeomorphism?
 * Basis&mdash;This is sort of OK.
 * 1st-Countable Space&mdash;This states that every point has a countable basis. Points don't have bases. Look it up.
 * Homeomorphism&mdash; 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&mdash;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!

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. Following the CP link Math and the Bible the reader gets quite a few treats. It opens with: "The Bible was the inspiration for set theory and other accomplishments in math." After a lot of biblical references, poor Cantor is slandered: "Modern understanding of the full nature of infinity is based on the work of devout Christian Georg Cantor, who studied infinity as a way to understand God better." Leaving Cantor's beliefs and sometimes frail mental state aside, most people regard him as a genius who studied infinity since he was a mathematician.

Quotes of infinite wisdom
The Parable of the Vineyard Workers conveys truths about mathematical logic unknown at the time of Christ. In a mere sixteen verses at Matthew 20:1-16, Jesus explains surprising truths about infinity, zero, and set theory. It would take nearly 20 centuries before mathematicians caught up.

Only in set theory is it true that "the last will be first, and the first last," as stated by the conclusion of the parable. Outside of set theory that statement ostensibly appears to be false.

Only if infinity exists can a master pay everyone the same wage, no matter how hard or little they work. Infinity is synonymous with God.

The existence of infinity in turn implies the existence of zero, based on the inability to diminish infinity by anything more than zero. Zero -- the zero difference between the "wages" paid, and the jealousy that results -- is synonymous with the lack of God in this story.

A silver lining to the parable is how it demonstrates that communism can create more jealousy than capitalism does, through the jealousy of those who work less and yet get paid as much.

Negative infinity has an existence implied by infinity, as its negative. Negative infinity is not the additive inverse of positive infinity, because their sum does not equal zero.

Although negative numbers were not accepted by mathematicians until the 1600s, negative infinity is logically implied by the existence of Hell as described frequently in the Gospels. Also, the existence of an infinitely good God implies the existence of an infinitely bad evil that rejects God.

Negative infinity is difficult to define with independent terminology. Taking a cue from negative infinity as a representation of Hell, negative infinity is the lowest value possible.

Zero was introduced conceptually by Jesus before mathematicians recognized it. His parable of about the repeated yield of zero in connection with the sower of the seed is an explanation of logic in how everything times zero is zero, and how infinity divided by anything is still infinity. This same parable is retold in all three synoptic Gospels, at Matthew 13:1-23, Mark 4:1-20, and Luke 8:1-15.

Rejected by ancient Greek philosophers and mathematicians, infinity is a significant part of the logic of Jesus.

[...]

Infinity is depicted by both the Multiplication of the loaves, the master's estate in the Prodigal Son, and the parable of the vineyard workers. Also, one's soul is of infinite value to him and cannot be exceeded in value by anything else, as explained by Matthew 16:26.

Jesus taught the existence of infinity in multiple ways. Indeed, the Gospels and Epistle to the Hebrews are like a book of logic about infinity. This was contrary to the views of the greatest Greek mathematician and philosopher, Pythagoras and Aristotle, who both incorrectly rejected that infinity could exist. The Old Testament has only indirect references to infinity.

In addition, recognition of infinity — such as infinite time or infinite strength — is helpful on a personal level in dealing with adversity. Jesus emphasized the concept of infinity often in his miracles and parables. He rejected the mistaken view of the ancient Greeks that infinity is non-existent and unintelligible.

Infinity and zero are two intertwined opposites that can be played off each other logically in ways that seem paradoxical at first. They are related in that infinity can never be diminished or increased by more than zero, while zero is the result of making something infinitely small.

The Parable of the Vineyard Workers is perfectly logical but initially seems paradoxical. The master has infinite resources, and pays the workers the same wage no matter how much or little they work. This enrages the workers who toil longer, even though they were fully paid, because there is zero difference between their wages and that of workers who toiled little. Yet there is nothing for any of the workers to be angry about.

Neither infinity nor zero were accepted by thinkers at the time of Christ, and the parables did much to explain the logic of these two intertwined opposites. Shakespeare frequently used infinity in his plays.

The Multiplication of the loaves and fish is an enigmatic sign (miracle) by Jesus, the only one that is reported in all four Gospels: Matthew 14:13–21, Mark 6:31-44, Luke 9:10-17 and John 6:5-15. Its frequent reference in the Gospels, including twice by Mark, suggests that Jesus performed this work more than once. This sign by Jesus indicates that scarcity is due to a lack of faith, not a lack of resources. This work illustrates the existence of infinity, which Greek philosophers and mathematicians had denied. It is strikingly similar to the Banach-Tarski Paradox in mathematics.

This paradox—or insight—bears a striking resemblance to the multiplication of the loaves, which is the only miracle described in all four Gospels.

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.

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.

While Life patterns are extremely fragile (the presence or lack of a single cell can utterly destroy virtually any complex pattern), they are not a valid comparison to biological evolution: if a cell is hit by a wayward photon, it does not explode. A better comparison is to the "Evoloop" cellular automaton, in which self-replicating loops interact and mutate. Over time, this produces a dramatic change in the loops: as the only resource is space, the population becomes dominated by ever-smaller loops. An animation of this can be found here.

It is also worth noting that if the game of life demonstrates the falsehood of evolution, then it demonstrates the plausibility of abiogenesis, since it is common for random patterns to give rise to "organised" patterns like gliders.

Axiom of choice
Conservapedia also provides us with 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.

Whilst the axiom of choice can be used to construct non-Lebesgue measurable sets, it can also be done with a weaker theorem. Cardinal numbers 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 existence of a basis for every vector space is an interesting one. 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 only known proofs 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, Tychonoff theorem and Zorn's Lemma. It is important to note the difference between "is used in the proof" and "is equivalent to".

In November 2008 three seemingly qualified editors set about trying to correct these statements. They were quickly met by the only person who edits mathematics articles at Conservapedia, Foxtrot, and AndyJM was blocked for removing information from the articles despite explaining why first. Foxtrot made it very clear that he would not tolerate any edits that said the axiom of choice (AC) did anything other than yield strange results.

Alan, the Axiom of Choice yields many strange behaviors in mathematics. That's why it is still questioned and debated. If the statement is not equivalent to AC (which I will have to look deeper into to believe), then the correct behavior is not to remove the statement altogether but to change it to an implication. Edits that whitewash the Axiom of Choice's questionable role in mathematics are the sort of behavior you see at Wikipedia, not here (see Conservapedia:Critical Thinking in Math for a guide to our positions). I am reinstating the fact, but will tentatively change it to just a consequence of AC instead of an equivalence.

Andy opposes the axiom because it leads to what he considers paradoxical results. Of course, he also rejects proof by contradiction, in which one can prove a proposition P by showing that the falsity of P would lead to paradoxical results.

The massacre of 2008
A major catastrophe occurred in the summer of 2008, during which Ed Poor, an alleged math teacher, nearly single-handedly destroyed Conservapedia's math (and general science) offerings.

It started around July 2008, when Ed would block or threaten to block anybody who would contribute to mathematics and physics articles by adding content he personally did not understand, with the excuse that it was not suitable for Conservapedia's reading level (apparently students who are studying for the SAT test ) &mdash; such as in the block of Lemonpeel on July 8, 2008. It should be noted however that as of August 21, 2008 no such article or guidelines existed. 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 &mdash; if not impossible &mdash; 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's rampage included the deletion of entire articles because he was unfamiliar with the content. As of August 24, 2008 the victims of his ignorance were:


 * Derivative &mdash; Deleted (restored by Andy)
 * Natural logarithm &mdash; Deleted
 * Radioactivity &mdash; Deleted and since been restored.
 * Line &mdash; Blanked and (we will be generous) rewritten
 * Probability &mdash; Deleted and apparently restored (with no history)
 * Quantum mechanics &mdash; Mutilated
 * Real line &mdash; Deleted
 * Cauchy sequence &mdash; 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.

Your mischaracterization of my goals and actions makes a bad start. I never opposed those who were trying to improve math and education articles. Rather, I found that too much of the edits were misleading or confusing readers.

Articles should be accessible to homeschoolers. They need a simple introduction, and then can build on the basics to discuss advanced topics. Launching right into graduate-school or PhD. level verbiage from the start is a blatant disregard of policy and is not an improvement of anything. You may as well drop the pretense now, or you simply won't be allowed to contribute to this project.

Ed then put SamHB on "probation".

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 and at the same time considers this quote &mdash; an incomplete definition with an unnecessarily complex (and barely related) explanation about a simple concept &mdash; appropriate for students.

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.

Casualties

 * Mathoreilly &mdash; Blocked once for removing irrelevant content from the Theory of Relativity article, then permanently by Karajou, with many contributions reverted for suspected parody.
 * Lemonpeel &mdash; Refused to explain quantum mechanics in terms children would understand (as if anyone likely could).
 * SamHB &mdash; For not pretending that the math articles are fine
 * Fantasia &mdash; For acting according to consensus when said consensus didn't include Ed.
 * Wandering &mdash; For criticizing Fantasia's block above.
 * Foxtrot (the creator of most of CP's mathematics article and disliker of the Axiom of Choice, only a light casualty) &mdash; For clearing up one of Ed's earlier, paranoia driven, mistakes and then trying to explain why Ed was wrong on the talk page.
 * DiEb &mdash; Part of his problem relates to the Radioactivity article (described in SamHB's open letter) and part to having been caught up in the JasonH spoofing incident. Apparently either Ed never figured out what happened or he didn't like somebody saying he should know about Peano axioms.

Aftermath
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. In this letter SamHB stated: A recurring claim, both here and, especially, at that other site, is that you are an ignoramus and a bully. I don't agree. After very careful reading of your edits, it is clear that you do know the material, and do have good judgement (see my comments above) about pitching it correctly to the target audience. While we respect diversity of opinion, we here at RationalWiki generally stand by our belief Ed Poor is both 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.

Finally on August 28, 2008 Ed Poor penned his piece Relevance of articles, in which he defended his lack of math teaching skills by saying it is irrelevant to the topics at hand. He also finally admitted to what everyone had until this point been saying, that Conservapedia lacks in even the most basic mathematical concepts. If only he had come to this realization two months and seven editors ago he would have some help to do this now.

On August 29, 2008, Ed started his deletion spree again:
 * Peano's Axiom &mdash; The one he was taunted by JasonH for knowing nothing about
 * Number theory &mdash; "content was no better than a mere definition &mdash; try again"
 * Stone–Čech compactification &mdash; Our favorite article.

As of the end of August, Ed threatened to delete all of the topology articles, and Foxtrot was pleading with him not to. Mentioning articles here or at Conservapedia in relation to Ed seemed to be enough to warrant their deletion as Ed continued to stew in his ignorance, insecurity, and paranoia.

What happened to the Riemann Integral Article?
As an example of the high regard Conservapedia sysops have for maintaining high quality mathematics articles, one of their best articles, the Riemann Integral, was destroyed by sysop TK in April 2009, apparently in a fit of rage against user SamHB. Prior to that, it had actually been nominated as a Featured Article. It has now been deep-burned and salted. SamHB's proposed improvements to it are not lost, however; they may be found at A Storehouse of Knowledge, to which Sam repaired after this incident.

ConservaMath Medal








To promote the progress of mathematics, Conservapedia announced its intention to award a ConservaMath Medal. This is in response to speculation that the Fields Medal that is about to be awarded to a woman, or a communist-trained Obama supporter, and was intended to be awarded at the same time as the rival medal. No information on the design has been created, although one may be recycled. Nominees for the award were based on merit, while winners were expected to be chosen based on politics.

After several months, and no further announcements about the ConservaMath Medal, it is widely assumed the award has been abandoned, likely due to Schalfly's short attention span.