Web sites about mathematics should help people understand and appreciate mathematics, not confuse the crap out of them with misinformation. Unfortunately, Wolfram Mathworld does the latter.

Example 1. MathWorld explains here that “The numbers of palindromic numbers less than a given number are illustrated in the plot [below].”


So the left plot tells us that there are about 100 palindromes less than or equal to 20. But there are only 21 nonnegative integers less than or equal to 20, so there can’t be 100 palindromes among them. In fact, there are 11 palindromes less than or equal to 20: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 11. My guess is that the left plot illustrates the n-th palindromic number as a function of n. In any case, it’s not what MathWorld describes.

MathWorld begins its list of the “first few palindromic numbers” with 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 (these 10 numbers are palindromes and are all less than 10), but in the next paragraph, MathWorld states that the number of palindromic numbers less than 10 is 9. There are 9 if you don’t count zero for some strange reason, but if you don’t intend to, give a definition that excludes it (MathWorld’s definition is less than clear), and then don’t list it.

Still confused? Read the Wikipedia article.

Example 2. Pascal’s Triangle shouldn’t be hard to screw up, right? Wrong. Here’s MathWorld’s Pascal’s Triangle:


This triangle needs to go to the shop for an alignment. The numbers are neither lined up in columns nor staggered (the latter being the usual presentation). What are the numbers in the column containing the rightmost 4? What numbers are along the diagonal through the top? (1, 1, 1, 1, 1, 5, 6?) As shown, MathWorld’s anyway-ill-worded “each subsequent row is obtained by adding the two entries diagonally above” is meaningless.

Example 3. In its article on Mersenne numbers (numbers that are one less than a power of two), MathWorld attempts to explain why “[i]n order for the Mersenne number [2n-1] to be prime, n must be prime.” MathWorld’s justification: “This is true since for composite n with factors r and s, n = rs. Therefore, 2n1 can be written as 2rs1, which is a binomial number and can be factored.” That’s sloppy to say the least. First, if a composite number n has factors r and s, it’s not necessarily the case that n = rs. Furthermore, the fact that a number can be factored doesn’t prove it’s composite. Every Mersenne number 2n1 can be factored. It’s just that when n is composite, there’s definitely a factorization into positive integers neither of which equals 1. Explaining it isn’t hard: In order for 2n-1 to be prime, n must be prime. For if not, n = rs where r and s are integers greater than 1 and less than n; then 2n1 = 2rs1 has a factor between 1 and 2n1, namely 2r1.

Example 4. MathWorld describes prime numbers as “numbers that cannot be factored.” Prime numbers, like all integers, however, can be factored, and elsewhere, MathWorld gives the factorization of several prime numbers, such as 7: 7 = 7×1.

Example 5. Any of MathWorld’s articles on statistics.

In the article on the Central Limit Theorem, what is lowercase n? What is f? The “limiting cumulative distribution function” of Xnorm is limiting in the sense of what approaching what? (It’s not clear to me that MathWorld’s statement of the theorem is even correct, but it’s clearly unclear.)

The article “explaining” the p-value has perhaps the worst definition of p-value I’ve ever seen when not grading exams. MathWorld says it’s “[t]he probability that a variate would assume a value greater than or equal to the observed value strictly by chance: P(z > zobserved)” (wrong). Wikipedia says “In statistical hypothesis testing, the p-value is the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true” (right).

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In the wake of today’s incident in Times Square, the second in barely as many days, Joe Lieberman, the Idiot from Connecticut, is expected to introduce idiotic revisions to the Enemy Belligerent, Interrogation, Detention, and Prosecution Act of 2010 (EBIDPA). The revised legislation will define water bottles, books, and several other items as “suspicious” and impose severe penalties on persons leaving them unattended in public places. The Department of Homeland Security will be charged with maintaining the secrecy of the list of suspicious items, revising it as needed. In an attempt to prevent EBIDPA from becoming politicized, Lieberman is adding language to restrict what information can be provided about the Act and its enforcement to Democratic and Republican members of Congress.

Anyone suspected of violating the new provisions would be classified as an enemy belligerent and immediately lose his or her U.S. citizenship. In addition, arresting officers would be prohibited from mirandizing suspected violators. Local and state governments will have until June 1, 2010 to enter fingerprints, iris scans, and DNA samples from all U.S. residents into a national database.

Rudolph Giuliani, former mayor of New York, and several world leaders, including Kim Jong-Il and Robert Mugabe, praised Lieberman for his patriotism.


Idiot with bottled water (2006 photo).

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Clay and his partner of 20 years, Harold, lived in California. Clay and Harold made diligent efforts to protect their legal rights, and had their legal paperwork in place—wills, powers of attorney, and medical directives, all naming each other. Harold was 88 years old and in frail medical condition, but still living at home with Clay, 77, who was in good health.

One evening, Harold fell down the front steps of their home and was taken to the hospital. Based on their medical directives alone, Clay should have been consulted in Harold’s care from the first moment. Tragically, county and health care workers instead refused to allow Clay to see Harold in the hospital. The county then ultimately went one step further by isolating the couple from each other, placing the men in separate nursing homes.

They weren’t finished there: to pay for the bills, the county decided that Clay and Harold’s house and all its contents would be auctioned off. And three months later, Harold died, alone.

Thanks to my friend Andy for posting the outrage. Thanks also to Ashley, whom I don’t know but whose blog Google helped me find, for her summation: Why I hate you if you voted Yes on 8.

UPDATE (July 24, 2010) Clay Green and Sonoma County have settled the case, and this PBS report of the settlement suggests both parties are happy with the outcome (not to mention Green’s lawyers, who should also be satisfied). Green and his partner’s estate receive cash compensation for the county’s actions, Green’s lawyers get paid, and the county alters its policies for property disposition and case management.

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