Category Archives: Bad Math

Your Funny for Today

This one comes from Ellen Wulfhorst on the Reuters wire:

Unlike traditional, mainstream media, blogs often adopt a specific point of view. Critics complain they can contain unchecked facts, are poorly edited and use unreliable sources.

I sense a great disturbance in the Schwartz, as if a million monitors were just sprayed with soda. (Well, no, I don’t have that many readers, but Dave Neiwert, Athenae and Coturnix have already picked up on it.) And here’s another puzzling statement from the same piece, describing the poll which found that “a majority of Americans do not read political blogs.”

The poll was conducted online from January 15 to January 22 among 2,302 adults. Harris said it does not calculate or provide a margin of error because it finds such figures can be misleading.

Is anyone else concerned by the sampling bias which this procedure could entail? If you ask people online what websites they read, you’re going to get (at best) a measure of what people who spend time online read, not what Americans in general are reading. Sure, that’ll probably increase the percentage of blog readers, skewing the poll towards “new media,” but it’s still bias. (They claim to have used “propensity score weighting” to “adjust” for this.)

On their website, Harris Interactive lays out their rationale for not reporting margins of error. Basically, they assert that people are too poorly educated to know what “margin of error” means: people don’t know that the phrase refers only to sampling error, not to other possible sources of obfuscation (which are harder to get a quantitative handle on). Therefore, people will assume that polls are more accurate than they really are; to avoid this problem, and to save the wear-and-tear on a newscaster’s mouth which the tediously long phrase “margin of sampling error” would produce, Harris will not admit fallibility at all.

Gee, how nice of them to make that decision for us, so that even the people who know statistics can’t get the figures. I just loooove suffering for the sins of innumerate America.

UPDATE: I also get a kick out of this:

Just one in ten (19%) Echo Boomers (those aged 18-31) regularly read a political blog

One in ten. Nineteen percent. Oops.

Yet Another Relativity Denier

BPSDBExercise: find the mistake in this attempt to challenge Einstein. Hint: if an observer in one Lorentz frame measures the position of a particle to be changing as [tex]x = ct[/tex], then that particle is traveling at the speed of light, and all observers in other Lorentz frames will agree.

Bonus point: explain the difference between the speed of light in a vacuum and the speed of light as measured when light is passing through matter.

(Thanks to the reader who noticed the “relativity challenge” Google ad in my sidebar. You know, it’s not quite cricket for me to plead that the Gentle Reader click on those links, but I can’t help it if other people appreciate the irony of pseudoscience making micropayments to science.)

Shorter Uncommon Descent

BPSDBTyler DiPietro finds a fresh example of steaming creationist nonsense at the weblog of Dembski and sycophants, Uncommon Descent. I summarize for the busy reader:

Because running an image of a face through a software filter makes it look less like a face, Darwin was a fuddy-duddy and materialism is on its last leg.

The cream on the cocoa is, however, this bit, from a commenter:

I’m not sure about the CSI [complex specified information] decreasing, however. Anyone able to get values of the CSI for each picture?

Gee, given that “complex specified information” has never been consistently defined, I wonder how one could compute it.

An Item of Prime Importance

I was busy with something or other, so I didn’t get to see the event Dennis Overbye describes in the New York Times, where the director and the star of the new film Jumper chatted with MIT professors Ed Farhi and Max Tegmark before a live audience in lecture hall 26-100. Not having been there, I don’t have very much to say, but I do feel the need to quote one paragraph of Overbye’s article and add just a tiny bit of emphasis:

The real lure, [Farhi] said, is not transportation, but secure communication. If anybody eavesdrops on the teleportation signal, the whole thing doesn’t work, Dr. Farhi said. Another use is in quantum computing, which would exploit the ability of quantum bits of information to have different values, both one and zero, at the same time to perform certain calculations, like factoring large prime numbers, much faster than ordinary computers.


In any other circumstance, I’d probably pontificate on how exponential parallelism is not the source of quantum computing’s calculation-fu, but I think we have a few other points to address first. . . .

Attentive readers will recall that Dr. Farhi was the guy who signed my paperwork when I was an undergraduate. For an amusing story from those days, see my post of last November, “Pay No Attention to the Man.”

(Tip o’ the fedora to Dave Bacon.)


When the bus is stuck in traffic, or when I’m curled restlessly in bed during the darkest hours of morning when sleep will not come and all the old wounds on my heart ache like they were newly made, I sometimes think back over my education and add up all the time my teachers wasted. The worst, perhaps, was the mathematics, for which entire years of schooling went for naught. “Pre-Calculus”? Pfft. AP Computer Science? Pfft++. All in all, I’d say that upwards of a third of my mathematics schooling before university was a waste of time, and another third was so incompetently done that any student who hadn’t already been hooked on science and learning would have been completely sunk.

So, I find it easy to sympathize with people who say that math education needs a severe overhaul. I’m willing to contemplate big curriculum changes, but of course, you have to convince me that the specific changes you have in mind will actually do any good. When a proposal comes down the wire to eliminate fractions, I reserve the right to chortle and guffaw.
Continue reading Fractions

One Small Step for Mismeasuring Man

There are only 1.27 times as many straight people as gay people in the world, and most people aren’t either.

How do I know? Google says so. Just count the hits.

porn: 227,000,000
lesbian porn: 9,930,000
straight porn: 610,000
heterosexual porn: 360,000
homosexual porn: 284,000

Now that I’ve gotten Science After Sunclipse banned from every school room in America (oh, like it wasn’t already, me being an ill-tempered, illiterate evilutionist and all), you can just go about your business. Or you can hang around while Windy and I resolve the group selection controversy.


Isabel finds a curmudgeonly 1842 quotation from Augustus de Morgan, about the way we write factorials:

Among the worst of barabarisms is that of introducing symbols which are quite new in mathematical, but perfectly understood in common, language. Writers have borrowed from the Germans the abbreviation n! to signify 1.2.3.(n – 1).n, which gives their pages the appearance of expressing surprise and admiration that 2, 3, 4, &c. should be found in mathematical results.

You know, I’d always thought the formula for “n choose k” was a little, well, enthusiastic:

[tex]\left(\begin{array}{c} n \\ k \end{array}\right) = \frac{n!}{k!(n-k)!}.[/tex]

n! k! n minus k!! You gotta believe me, guys!”

Still, though, if I saw de Morgan’s way of writing the factorial of n, I’d read it as

[tex]1 \cdot 2 \cdot 3 \cdot (n-1) \cdot n,[/tex]

which is only the factorial of n when n is 5. I guess there’s little point in pleasing the dead. . . .

Varieties of Wall-Banging Experience

When traveling through the Internet, one often encounters crackpot physics, and after some familiarity with the genus, one begins to organize the specimens into species. I often find myself remarking upon a particular characteristic of pseudo-physics: the use of verbal instead of mathematical arguments. Instead of positing a premise and doing the math to deduce consequences of that premise, we get a whole pile of jargon, pulled from different sources and decorated with equations to disguise the fact that the “arguments” are essentially plays on words, with the whole thing bent towards bolstering some pre-established conclusion. What do you do in order to debunk this kind of nonsense? One option is to focus on a few highlights and show that they lack validity; however, addressing all the points may balloon out into a full physics course of its own.

This problem is accentuated when a single piece of crankery indulges in misunderstandings of quantum mechanics, special relativity, general relativity and other fields, all together in a single vessel of fractured ceramic. The anti-Einstein polemic recently unearthed by PZ Myers is a good example of such a “target-rich environment,” as was biocentrism woo. Another example, currently unfolding before our cybernetic eyes, is Salvador Cordova’s ongoing misunderstanding of quantum mechanics (commentary here, here, here, here, here and now at Tyler’s new place too — and we’ve hardly gotten started).

When I have an idle moment, I might pull the thoughts I’ve scattered around my fellow skeptics’ blog threads into a unified post, but for now, I’ll just refer the Interested Reader to the links provided above.

Euler and Diderot

From Dirk J. Struick’s A Concise History of Mathematics (1967), quoted by Shallit:

There exists a widely quoted story about Diderot and Euler according to which Euler, in a public debate in St. Petersburg, succeeded in embarrassing the freethinking Diderot by claiming to possess an algebraic demonstration of the existence of God: “Sir, (a+b^n)/n = x; hence God exists, answer please!” This is a good example of a bad historical anecdote, since the value of an anecdote about an historical person lies in its faculty to illustrate certain aspects of his character; this particular anecdote serves to obscure both the character of Diderot and of Euler, Diderot knew his mathematics and had written on involutes and probability, and no reason exists to think that the thoughtful Euler would have behaved in the asinine way indicated. The story seems to have been made up by the English mathematician De Morgan (1806-1871). See L. G. Krakeur and R. L. Krueger, Isis, Vol. 31 (1940), pp. 431-32; also Vol. 33 (1941), pp. 219-31. It is true that there was in the eighteenth century occasional talk about the probability of an algebraic demonstration of the existence of God; Maupertuis indulged in one, see Voltaire’s Diatribe, Oeuvres, Vol. 41 (1821 ed.), pp. 19, 30. See also B. Brown, Amer. Math. Monthly, Vol. 49 (1944).

Krakeur and Krueger state that his investigations into mathematics “dominated Diderot’s youthful activities and represent an important phase of his universal interests.” They speculate that a lack of mathematical background among scholars who studied the man impaired those scholars’ ability to address this part of Diderot’s life.

Cordova’s “Advanced Creation Science”

Salvador “Darwin was a flatulent puppy-killer” Cordova has decided to enslave quantum mechanics in the service of Intelligent Design, or as he calls it, “Advanced Creation Science.” It’s amazing how poorly they hide the religious agenda, isn’t it? I was a little surprised when Michael Behe admitted on national television that ID was a tool for God’s Christian Soldiers to fight back against science, but letting your medievalism all hang out is apparently a ubiquitous practice among the ID crowd.

Anyway, Sal was, like, completely floored that Fourier transforms are used in both quantum physics and electrical engineering. He says he has to take a year to blog his “Advanced Creation Science” in full detail, but I have the feeling it will all reduce to the following:

Fourier transforms are used in engineering; Fourier transforms appear in quantum physics; therefore, quantum physics must have been engineered by Jesus.

Anyway, Tyler DiPietro and I are chatting about this over at his place.

UPDATE (11 December): Mark Chu-Carroll has weighed in.

UPDATE (14 December): More from Tyler here.

Currently on the Reading Queue

The arXivotubes have delivered unto me A. James and M. J. Plank’s “On fitting power laws to ecological data” (4 December, arXiv:0712.0613).

Heavy-tailed or power-law distributions are becoming increasingly common in biological literature. A wide range of biological data has been fitted to distributions with heavy tails. Many of these studies use simple fitting methods to find the parameters in the distribution, which can give highly misleading results. The potential pitfalls that can occur when using these methods are pointed out, and a step-by-step guide to fitting power-law distributions and assessing their goodness-of-fit is offered.

The classic in this genre is Clauset, Shalizi and Newman’s “Power-law Distributions in Empirical Data,” but more correctives are always appreciated.

Vacation Memories 2: Baggage

I’m back home from my brief travels, and I returned to find the latest outbreak of quantum woo infection, followed immediately by a heap of silliness about anthropic twaddle.

“Too soon,” I thought. “I need to go back on vacation.”

So, instead of complaining at great length about things I’ve already complained about, I’ll just share one quick observation and then head out into the outside world, shopping for art supplies.

Yesterday, I flew into Boston. In my laptop I carried a hardback of Lois Lowry‘s The Giver (1993) and, to recapture a more innocent time, Feynman and Weinberg’s Elementary Particles and the Laws of Physics (1987). In between reading these two, I happened to glance at the pamphlet-type thing which the airline clerk had given me to hold my boarding passes in. Here’s the puzzling part, under the “Free Baggage Allowance” heading:

Carry-on Baggage is limited to one piece per passenger, plus a personal item such as a purse, briefcase or laptop computer. The carry-on cannot exceed 51 inches (11″ × 14″ × 26″) and must fit under the seat or in an overhead compartment.

Why are the three linear dimensions added? The frame device the airline positions at each gate for testing whether or not your carry-on will fit rejects your baggage if any dimension exceeds the threshold set. Your baggage is deemed invalid even if the total volume is less than 11″ × 14″ × 26″ = 4004 in3 (just try carrying on something long and skinny). The longest diagonal of an 11″ × 14″ × 26″ box is

[tex]\sqrt{14^2 + 26^2} \approx 29.5[/tex]

inches long. So, you can have a carry-on item the sum of whose edge lengths is, say, thirty-one inches, and which won’t fit the actual airline restrictions no matter how you try to wedge it in sideways. The sum of the height, width and depth is a meaningless number.

Give Us Original Mistakes

Zeno might appreciate this (where “appreciate” is used in the technical sense of “bang head against wall on account of”). Via Isabel comes Eric Schechter’s page of Common Errors in College Math. If you survived calculus, read through it and congratulate yourself on all the mistakes you don’t make anymore!

(See how optimistic I am?)

Schechter provides one of the most inspiring examples of getting the right answer through the wrong method that I’ve ever seen. The problem is to evaluate the following definite integral:

[tex]\int_0^{2\pi} \cos x\, dx. [/tex]

This is how our student started:

[tex]\int_0^{2\pi} \cos x\, dx = \left.\frac{\sin x}{x}\right|_0^{2\pi} = \frac{\sin 2\pi}{2\pi} – \frac{\sin 0}{0}.[/tex]

But wait, there’s more!

[tex]\frac{\sin 2\pi}{2\pi} – \frac{\sin 0}{0} = \sin – \sin = 0.[/tex]

And they say we can’t eliminate sin from the world.