At least, it's got to be the biggest one that I ever saw, in purely quantitative terms. Today's NYT Science Section has an article by Dennis Overbye ("Laws of Nature, Source Unknown") that mentions
"...string theory, the alleged theory of everything, which apparently has 10500 solutions..."
This is a reference to the so-called string theory "landscape", which is said to have about 10500 solutions. Presumably Overbye wrote the number correctly, and it was typeset wrong, at least in the online version. And 10500 is such a big number that it's hard to explain how big a typo this is.
If memory serves, the number of elementary particles in the known universe is believed to be about 1080. So if every elementary particle contained its own individual universe of 1080 particles, and every particle in every one of those sub-universes contained its own sub-sub-universe of the same size, there would be 1080x1080x1080=10240 particles in this three-level hierarachy of meta-universes. If every one of the elementary particles in this baroque construction met every single one of the others, that would be 10240x10240=10480 pairings (minus 10240 self-pairings, but never mind). And if every one of these possible pairs of particles went out a quadrillion times, that would be 10495 interactions. And if the participants posted 10,500 pictures of each of these events on Facebook, there would be about 10500 pictures in all.
[There are, of course, much bigger numbers out there. I discussed some of them earlier this year, in a post on MIT's Independent Activities Period ("Charm School (and battling logicians)", 2/3/2007). There's a somewhat more serious discussion here.
But the current competition is for the (quantitatively) largest typographical error in a serious publication. I won't be surprised to learn that Dennis Overbye can be bested in this competition. Pending documentation of a bigger mistake, though, this is the largest goof that I know about.]
[Update -- Andrew Greene writes:
I was just reading that article in my dead-tree edition of the Times, and the 500 was properly superscripted there. I've noticed before that when they convert articles to HTML the Times often fails to convert superscripts and subscripts to the appropriate tags.
[Update #2 -- though I didn't notice it at the time, there's actually a typo of exactly the same sort, but much larger consequence, in a story that I linked to in my post on the Large Number Competition at MIT last January. The article in The Tech ("Professors Duke It Out in Big Number Duel", 1/31/2007) describes the winning effort as follows:
Near the end of the duel, Rayo furiously scribbled on the whiteboard: "The smallest number bigger than any number that can be named by an expression in the language of first order set-theory with less than a googol (10100) symbols."
Although this definition took a bit of tweaking, including what Rayo described as his "second order logic trick," it soon won him the duel.
In this description, the numerical representation of a googol should of course be 10100 rather than 10100. No doubt the author was bitten by the same online production bug that lowered the superscript 500 in the case of Dennis Overbye's article.
The award might still be contested, since The Tech's error is in parentheses next to a written-out form of the number...]
[Update #3 -- Brett Altschul writes:
As both a theoretical particle physicist and a former news and production editor at The Tech, I thought I could provide a little more information about how typesetting errors with exponents occur on the Web.
First, when I read the Times article this morning, it was certainly not the first time I've seen the 10500 number for the number of flux compactification vacua in string theory mangled as 10500. A search of the Times archive comes up with two other articles on string theory with the same mistake. It's sufficiently common in online information about strings that I barely even notice it now.
As to how it happens, I can tell you exactly how it occurs at The Tech's Web site. The Tech uses custom-written scripts to convert the article files into HTML with as little human interaction as possible. The scripts have evolved and gotten much more sophisticated over the years, but the part that creates the HTML from the article copy was basically unchanged from 1994 (when The Tech launched the Web's very first news site) to 2005 (when I lasted checked on it), and it probably is the same to this day. The script works by extracting the meta-tags in the article file and creating the corresponding HTML tags.
There are a number of quirks to the process though. First of all, every type style that we wanted to be able to convert had to be put into the script by hand. While boldface and italic are supported, most other styles are not, because they were not deemed useful for journalistic prose. That included superscripts, which do come up occasionally (and more often in The Tech that in most papers, I would think), but not very often. The software also doesn't know how to handle odd typefaces. In my obituary for Prof. Henry Kendall, I was talking about his and other scientists' work on quarks. I mentioned the Omega^- particle, using the Symbol font and a superscript. The Web version renders this as W- (which is a different particle altogether). Another problem was that the style sheets used by the Quark Publishing System software that produced the print pages could do things with its style sheets that just couldn't be done in HTML. The title (e.g. "NEWS EDITOR") in the bylines is supposed to be all capitals and italicized. Both those functions can be implemented by the style sheets, but there's no way to specify all caps in HTML. So we were supposed to type our titles in all caps, so it would appear correctly in the online version, but not everybody did, and this is reflected in the online versions of some articles.
I assume that the problem with the Times' algorithm is exactly the same as The Tech's. While it's possible to implement superscripts in HTML, nobody bothered to do it.
]Posted by Mark Liberman at December 18, 2007 07:37 AM