So, there’s a joke going around BirdSite about how scientists said “the internet will revolutionize the sharing of information and eliminate barriers to communication”, and what we got is viral tweets asking for the solution to “4 + 8 x 3 – 7, no calculators!!”
Nobody has answered “24x – 3”.
(Grandpa Stacey voice) I am disappointed.
To the extent that academic peer review is good for anything, it is optimized to catch honest mistakes. It is weaker against deliberate fraud and stubborn denial. Science has a presumption of fair play, a sense that the natural world isn’t a cheater. If you want to explain how a “psychic” operates, you’re better off asking a magician than a physicist.
Nearly two decades ago now, there was a dust-up when a couple French TV personalities got a clutch of physics and mathematics papers published, and even received PhD’s, and their “work” turned out to be nonsense. (The Wikipedia article on l’affaire Bogdanov is currently not terrible, and it contains more pointers to details than almost anyone could honestly desire.) The news stories about the incident really played up the “even the physicists can’t tell if the papers are nonsense or not” angle. That rather oversells the case, though. I read the Bogdanovs’ “Topological field theory of the initial singularity of spacetime” when I was a first-year grad student, and I could see through it. If you know what a Lagrangian is, and the fog doesn’t intimidate you, then you can tell something is wrong. If you don’t know what a Lagrangian is, you’re probably not reading theoretical physics papers yet.
So, what went wrong?
Continue reading What’s Wrong with this Sting Operation?
Not infrequently, crackpot physics papers attain a level of wrongness where trying to point to specific mistakes is useless, and a critique of the specifics collapses down to “just take a physics class” — true, but unhelpful to the curious bystander. The physicist, trying to say anything substantive, ends up picking out psychological “tells”, like the suspiciously convenient mention of too many famous big problems all in a row. There are no solid particulars of physics to discuss, so we end up talking psychology and sociology. I find the psychological questions that arise quite fascinating. Why, for example, is the population of pseudophysics perpetrators so heavily skewed to the male? But, in general, it is difficult to take physics and mathematics crankery and find interesting comments to say about it. All these years later, and the circle still refuses to square.
I’m reminded of self-proclaimed mega-genius Christopher Langan, whose “Cognitive Theoretic Model of the Universe” mixed incoherence, impenetrability and arrogance. As one of my fellow science bloggers put it back in the day:
I have no idea what he means by “replacing set-theoretic objects with syntactic operators” – but I do know that what he wrote makes no sense – it’s sort of like saying “I’m going to fix the sink in my bathroom by replacing the leaky washer with the color blue”, or “I’m going to fly to the moon by correctly spelling my left leg.”
My personal favorite might be the parenthetical clarification, “conspansion consists of two alternative phases accounting for the wave and particle properties of matter and affording a logical explanation for accelerating cosmic expansion”. Words words words words, words words!
A kind of “security by obscurity” sometimes operates in cases like these, where the total lack of solid material to criticize leads to indifference and silence from established scientists. This “why bother?” response then becomes fodder for the pseudophysicist to claim that the academy is too stuffy to understand his work, or even actively censoring it. The truth is less dramatic, though not without its own interest to old-fashioned students of human nature.
This is what I get for skimming an entertainment website for a momentary diversion.
So, everybody’s seen the cool new video, “‘Cantina Theme’ played by a pencil and a girl with too much time on her hands,” right?
And we’ve heard the claim, via Mashable and thence The AV Club, that the formula “can actually be used to determine the speed of light,” yes?
It’s a joke. The “proof” is words thrown into a box and filled with numbers so that nobody reads it too carefully. The algebra isn’t even right — hell, it does FOIL wrong — but that’s just a detail. I tried to think of a way to use it as a hook to explain some real science, as I’ve tried before upon occasion, but there just wasn’t any there there. The whole thing is goofing off.
Obvious goofing off, I would have thought. Somewhere south of a Star Trek Voyager technobabble speech. But no, never underestimate the ability of numbers to make a brain shut down.
An image burbled up in my social-media feed the other day, purporting to be a list of “17 Equations that Changed the World.” It’s actually been circulating for a while (since early 2014), and purports to summarize the book by that name written by Ian Stewart. This list is typo-ridden, historically inaccurate and generally indicative of a lousy knowledge-distribution process that lets us down at every stage, from background research to fact-checking to copy-editing.
Continue reading 17 Equations that Clogged My Social-Media Timeline
Or, “Oh, Wikipedia, How I Love Thee. Let me count the ways: one, two, phi…”
From Wikipedia’s page on Duchamp’s Nude Descending a Staircase, No. 2 (today’s version):
It has been noted disquisitively [link] that the number 1001 of Duchamp’s entry at the 1912 Indépendants catalogue also happens to represent an integer based number of the Golden ratio base, related to the golden section, something of much interest to the Duchamps and others of the Puteaux Group. Representing integers as golden ratio base numbers, one obtains the final result 1000.1001φ. This, of course, was by chance—and it is not known whether Duchamp was familiar enough with the mathematics of the golden ratio to have made such a connection—as it was by chance too the relation to Arabic Manuscript of The Thousand and One Nights dating back to the 1300s.
Euhhhhh, non.
As best I can tell, all this is saying is that the catalogue number of Duchamp’s painting contains only 0s and 1s.
Continue reading Today in Incoherent Numerology
Every once in a while, a bit of esoteric mathematics drifts into more popular view and leaves poor souls like me wondering, “Why?”
Why is this piece of gee-whizzery being waved about, when the popularized “explanation” of it is so warped as to be misleading? Is the goal of “popularizing mathematics” just to inflate the reader’s ego—the intended result being, “Look what I understand!,” or, worse, “Look at what those [snort] professional mathematicians are saying, and how obviously wrong it is.”
Today’s instalment (noticed by my friend Dr. SkySkull): the glib assertion going around that
$$ 1 + 2 + 3 + 4 + 5 + \cdots = -\frac{1}{12}. $$
Sigh.
It’s like an Upbuzzdomeworthy headline: These scientists added together all the counting numbers. You’ll never guess what happened next!
“This crazy calculation is actually used in physics,” we are solemnly assured.
Sigh.
The physics side of the story is, roughly, “Sometimes you’re doing a calculation and it looks like you’ll have to add up $$1+2+3+4+\cdots$$ and so on forever. Then you look more carefully and realize that you shouldn’t—something you neglected matters. It turns out that you can swap in $$-1/12$$ for the corrected calculation and get a good first stab at the answer. More specifically, swapping in $$-1/12$$ tells you the part of the answer which doesn’t depend on the particular details of the extra effect you originally neglected.”
For an example of this being done, see David Tong’s notes on quantum field theory, chapter 2, page 27. For the story as explained by a mathematician, see Terry Tao’s “The Euler-Maclaurin formula, Bernoulli numbers, the zeta function, and real-variable analytic continuation.” As that title might hint, these do presume a certain level of background knowledge, but that’s kind of the point. This is an instance where the result itself requires at least moderate expertise to understand, unlike, say, the four-colour theorem, where the premise and the result are pretty easy to set out, and it’s the stuff in between which is much harder to follow.
ADDENDUM (19 January 2014): I’ve heard the argument in favour of this gee-whizzery that it “gets people excited about mathematics.” So what? A large number of people are misinformed; a tiny fraction of that population goes on to learn more and realize that they were, essentially, lied to. Getting people interested in mathematics is a laudable goal, but you need to pick your teaser-trailer examples more carefully.
And I see Terry Tao has weighed in himself with a clear note and some charming terminology.
Prompted by this review of Colin McGinn’s Basic Structures of Reality (2011), I read a chapter, courtesy the uni library. It was endumbening. To the extent that he ever has a point, he says in many words what others have said more clearly in few. He confuses the pedagogy of a particular introductory book with the mature understanding of a subject, displays total ignorance of deeper treatments of his chosen topic, blunders into fallacies, and generally leaves one with the impression that he has never done a calculation in all the time he spent “studying physics”. Truly an amazing achievement.
A few years ago, I might have blogged my way through the whole darn book. I must be getting old (“REALLY? NO WAY!” declares my weak knee). But is it a healthy and mature sense of priorities, or a senescent academic crustiness? Have I become one of those people, concerned with my vita to the exclusion of all else? Dark thoughts for this cold autumn evening, dark as our current season of superhero movies—Fimbulwinter 3: Flame of Despair….
Now that 2.2 metric Ages of Internet Time have passed since Andrew Hacker’s ill-advised “math is hard!!” ramble, I figure it’s a good day to propose my own way of improving high-school mathematics education. Be advised: this is a suggestion about the curriculum, not about how to train teachers, buy books and all that un-TED-friendly stuff which reformers happily gloss over. And I’ll be talking about changes late in the game, which won’t address problems at the “why can’t Johnny add?” level.
When I was in high school—at a pretty well-supported public school, out in the ‘burbs at the comparatively unimpoverished end of town—I took a “precalculus” class my eleventh-grade year. Most of the advanced-track students I knew did the same thing. (If you’d gotten yourself on the even-more-advanced track back in eigth grade, you took precalculus in tenth.) This was supposed to prepare us for taking the AP Calculus class our senior year, which would allow us to get college credit. Instead, it was a thoroughgoing waste of time. The content was a repeat of Algebra II/Trigonometry, which we’d taken the year before, with two exceptions thrown in. The first, probability, was a topic our teacher didn’t know how to teach. In fact, she admitted as much: “I don’t know how to teach probability, so you’re all going to read the book today.” The second, limits, served no purpose. I’ll explain why in a moment.
I suggest the following: scrap “precalculus” and replace it with a year-long statistics course. This plan has several advantages:
Continue reading Precalculus -> Statistics
“This room smells of mathematics!
Go out and fetch a disinfectant spray!”
—A.H. Trelawney Ross, Alan Turing’s form master
It’s been a while since I’ve felt riled enough to blog. But now, the spirit moves within me once more.
First, I encourage you to read Andrew Hacker’s op-ed in The New York Times, “Is Algebra Necessary?” Then, sample a few reactions:
Continue reading “Is Algebra Necessary?” Are You High?
For your convenience:
The following is a list of debunkings of Stephen C. Meyer’s Signature in the Cell, arranged more or less in chronological order. I have not included every blog post I’ve seen on the topic; as I did for Behe’s The Edge of Evolution, I’ve focused on the most substantive remarks, rather than keeping track of every time somebody just quoted somebody else. (I’ve also probably overlooked, forgotten, mistakenly thought I’d already included or never been made aware of some worthwhile essays.) In some cases, additional relevant posts can be found by following links within the essays I have listed.
Continue reading Signature in the Cell (Repost)
Copied from my old ScienceBlogs site to test out the mathcache JavaScript tool.
Ah, complex networks: manufacturing centre for the textbook cardboard of tomorrow!
When you work in the corner of science where I do, you hear a lot of “sales talk” — claims that, thanks to the innovative research of so-and-so, the paradigms are shifting under the feet of the orthodox. It’s sort of a genre convention. To stay sane, it helps to have an antidote at hand (“The paradigm works fast, Dr. Jones!”).
For example, everybody loves “scale-free networks”: collections of nodes and links in which the probability that a node has $k$ connections falls off as a power-law function of $k$. In the jargon, the “degree” of a node is the number of links it has, so a “scale-free” network has a power-law degree distribution.
Continue reading How Not to be a Network-Theory n00b
Today, everything from international finance to teenage sexuality flows on a global computer network which depends upon semiconductor technology which, in turn, could not have been developed without knowledge of the quantum principles of solid-state physics. Today, we are damaging our environment in ways which require all our fortitude and ingenuity just to comprehend, let alone resolve. More and more people are becoming convinced that our civilization requires wisdom in order to survive, the sort of wisdom which can only come from scientific literacy; thus, an increasing number of observers are trying to figure out why science has been taught so poorly and how to fix that state of affairs. Charles Simonyi draws a distinction between those who merely “popularize” a science and those who promote the public understanding of it. We might more generously speak of bad popularizers and good ones, but the distinction between superficiality and depth is a real one, and we would do well to consider what criteria separate the two.
Opinions on how to communicate science are as diverse as the communicators. In this Network age, anyone with a Web browser and a little free time can join the conversation and become part of the problem — or part of the solution, if you take an optimistic view of these newfangled media. Certain themes recur, and tend to drive people into one or another loose camp of like-minded fellows: what do you do when scientific discoveries clash with someone’s religious beliefs? Why do news stories sensationalize or distort scientific findings, and what can we do about it? What can we do when the truth, as best we can discern it, is simply not politic?
Rather than trying to find a new and juicy angle on these oft-repeated questions, this essay will attempt to explore another direction, one which I believe has received insufficient attention. We might grandiosely call this a foray into the philosophy of science popularization. The topic I wish to explore is the role mathematics plays in understanding and doing science, and how we disable ourselves if our “explanations” of science do not include mathematics. The fact that too many people don’t know statistics has already been mourned, but the problem runs deeper than that. To make my point clear, I’d like to focus on a specific example, one drawn from classical physics. Once we’ve explored the idea in question, extensions to other fields of inquiry will be easier to make. To make life as easy as possible, we’re going to step back a few centuries and look at a development which occurred when the modern approach to natural science was in its infancy.
Our thesis will be the following: that if one does not understand or refuses to deal with mathematics, one has fatally impaired one’s ability to follow the physics, because not only are the ideas of the physics expressed in mathematical form, but also the relationships among those ideas are established with mathematical reasoning.
This is a strong assertion, and a rather pessimistic one, so we turn to a concrete example to investigate what it means. Our example comes from the study of planetary motion and begins with Kepler’s Three Laws.
KEPLER’S THREE LAWS
Johannes Kepler (1571–1630) discovered three rules which described the motions of the planets. He distilled them from the years’ worth of data collected by his contemporary, the Danish astronomer Tycho Brahe (1546–1601). The story of their professional relationship is one of clashing personalities, set against a backdrop of aristocracy, ruin and war. From that drama, we boil away the biography and extract some items of geometry:
Continue reading The Necessity of Mathematics
I was prepared to enjoy Susan Jacoby‘s Op-Ed in the New York Times, “Best Is the New Worst” (30 May 2008). Yes, the title “Best Is The New Worst” is a snowclone, the sort of trite phrasal template with plug-and-play slots which is the refuge of lazy writing. In fact, “X is the new Y” is a classic of the genre. (Is this headline choice an example of such, or a clever meta-reference intended to mock declining standards? Discuss.) However, this bit was more troubling, and made me look askance:
Another peculiar new use of “elitist†(often coupled with “Ludditeâ€) is its application to any caveats about the Internet as a source of knowledge. After listening to one of my lectures, a college student told me that it was elitist to express alarm that one in four Americans, according to the National Constitution Center, cannot name any First Amendment rights or that 62 percent cannot name the three branches of government. “You don’t need to have that in your head,†the student said, “because you can just look it up on the Web.â€
Ahem. Laziness in a student may well be a cause for alarm, but uncritically accepting the spin which innumerate and agenda-driven reportage has placed upon a survey is, I dare to suggest, even worse. I’m going to go out on a limb here and say that these numbers, intimidating though they may be, are in fact completely worthless. They don’t measure what they’re claimed to measure. The reason goes back to the First Amendment itself:
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the government for a redress of grievances.
This breaks down to six different rights. The first half of the religion bit — the Establishment Clause — covers a different territory than the second half, the Free Exercise Clause. It’s possible to have the right to follow your personal religion even in a country which has an established church (hint, hint: the United Kingdom has Muslims). Speech and the press get one “freedom” each, but the people have a “right” to assemble and another “right” to petition.
The National Constitution Center website features a 1997 survey which speaks of “four rights” in the First Amendment, and lists them as “speech,” “religion,” “press” and “assembly.” Now, I’d argue that this obscures the constitutional status of religion, reflecting or enforcing an oversimplified view of the matter, but more importantly, the right to petition vanished down a memory hole.
If it were universally acknowledged that, say, petitioning and assembly were two faces of the same freedom, then I wouldn’t mind so much. However, a 2006 survey by the McCormick Tribune Freedom Museum asked respondents to name their First Amendment rights, and their “correct” answers were the freedoms of religion, speech, press, petition and assembly. When two different love-the-Constitution groups can’t even be consistent on how many freedoms exist, can the results be considered reliable? What, exactly, are we citizens supposed to know, and will we lose credit for knowing the wrong “right” answer? Suppose that the NCC called you one September morning in 1997, and you said that the First Amendment covered speech, religion, press and peaceable assembly. You would be a sterling citizen in 1997, but nine years later, the Freedom Museum would stamp you defective.
Both surveys share another flaw. As was pointed out back in 2006,
several “freedoms” which are likely to be uppermost in an American’s mind are found in other, later amendments: bearing arms, avoiding self-incrimination, avoiding unreasonable search and seizure, not being enslaved (took a while for that one) and so forth. What happens if you remember a whole list of these rights, but can’t recall which amendment they go under?
Continue reading Statistics: Tool of an Elitist Bastard
Megan Garber writes the following in the Columbia Journalism Review‘s daily blog:
We currently find ourselves in, to put it mildly, a lull in the 2008 campaign’s primary season. The delegate tallies are in limbo. Parsing them seems to require a postgraduate degree in calculus.
I call mathification! The analogue of linguification, this term refers to statements which, as Isabel Lugo puts it, “clearly intend to get across a true point about the real world by making a false point about mathematics.”
Continue reading Mathification
An interesting development has unfolded in the math-blogging world. Sal Cordova, famous for calling Charles Darwin a puppy-killer, has attempted to show that he, Cordova, is not a stupefied ignoramus on the subject of quantum mechanics. Naturally, such ignorance would not be a crime, except that Cordova is hell-bent on using quantum physics to prop up his “Advanced Creation Science.” See here, here, here, here and here if you’ve been suffering a lack of reading material. If, on the other hand, you’re a busy citizen of the high-speed modern world, let us summarize:
If I post a comment in which I fail to address the criticisms leveled at me on a long-dead blog discussion thread and, two days later, crow about it before a sycophantic audience while intentionally mangling my critic’s name, not only will I demonstrate my intellectual superiority over the filthy Darwinists, but also, Jesus will bring me 72 virgins in Heaven.
Oh, by the way, an integral sign is not the same thing as an upper-case S.