Musings

A small update to itex2MML. This one covers ellipses.

\ldots,\dots

horizontal ellipsis, … ($\dots$)

\cdots

centered horizontal ellipsis, ⋯ ($\cdots$)

\ddots

descending diagonal ellipsis, ⋱ ($\ddots$)

\udots

ascending diagonal ellipsis, ⋰ ($\udots$)

\vdots

vertical ellipsis, ⋮ ($\vdots$)

As always, a MacOSX binary is included in my source distribution. Thanks to Abiola and James, updated Windows and Linux binaries are also available.

One of my favourite young physicists, Nima Arkani-Hamed, was in town today. He gave two talks.

One was about his work on spontaneously-broken diffeomorphism invariance. Specifically, consider a theory in which spatial diffeomorphisms are preserved, but time-translations are spontaneously-broken. There’s a scalar field which, in a really horrible pun, they call the ghostino, whose expectation value satisfies $\langle\dot\phi\rangle=M^2$ Expanding the field about its VEV,

under an infinitesimal diffeomorphism,

so $\pi$ transforms as a scalar under spatial diffeomorphisms, but transforms inhomogeneously under temporal ones, as befits a Goldstone boson. We also impose a shift symmetry under $phi\to \phi +\text{const}$. The naive time-translation symmetry of a static spacetime is broken in this background, but the combination

is unbroken.

If you write out a general symmetry-breaking effective Lagrangian for $\phi$ (compatible with the shift symmetry and, for simplicity, with $\phi\to-\phi$), and expand it about a minimum, you find something like (after rescaling $\pi$ to give it a canonically-normalized kinetic energy)

The dispersion relation is a nonrelativistic one (unsurprising, since the symmetry-breaking has picked out a preferred Lorentz frame) and power-counting is a bit unconventional. $t$ should have mass dimension $-1$, $x$ should have mass dimension $-1/2$ and $\pi$ should have mass dimension $1/4$. The leading interaction term is

and is irrelevant in the infrared, so there’s a good perturbative effective field theory description.

Anyway, if you take $M\sim 10^{-3}$eV, the coupling of this theory to gravity modifies gravity at cosmological distance scales, with interesting ramifications for cosmology.

There’s a bit of a swindle here, since the theory just described breaks down above the scale $M$, and requires some ultraviolet completion there. However, if $\phi$ couples only gravitationally, they argue that it doesn’t really matter what the ultraviolet completion is. While there remains a challenge to embed this in a “real” theory, their effective Lagrangian analysis indicates that it’s not completely crazy to try to do so. You might not have expected it, but the long-distance physics makes sense.

Nima’s other talk was about “high energy” supersymmetry, some as yet unpublished work of his with Savas Dimopoulos, in which supersymmetry is broken at a relatively high scale and, of the superpartners, only the gauginos are light.

I’ll talk about that in more detail some other time…

Say you want to tag some text on a web page as being in a language other than the main language of the page (English, in the case of this blog). In HTML 4, you would slap a <span lang=".."></span> around it. In XHTML 1.1, the lang attribute is gone, and you’d write

<span xml:lang="fr">ma vie en rose</span>

instead.

And therein lies a small problem. No matter how you set your Sanitize Spec in the blog preferences, MovableType will strip out the xml:lang attribute from any sanitized text like, say, the comments on your blog. It can’t handle attributes with colons in them.

Fortunately, the fix for this is easy.

--- lib/MT/Sanitize.pm.orig     Fri Apr 23 08:40:27 2004
+++ lib/MT/Sanitize.pm  Fri Apr 23 08:41:42 2004
@@ -98,7 +98,7 @@
                 (exists $tag_attr->{$name} && $tag_attr->{$name} eq '/')) {
                 if ($inside) {
                     my @attrs;
-                    while ($inside =~ m/(\w+)\s*=\s*(['"])(.*?)\2/gs) {
+                    while ($inside =~ m/([:\w]+)\s*=\s*(['"])(.*?)\2/gs) {
                         my $att = lc($1);
                         if ($ok_tags->{'*'}{$att} ||
                            (ref $ok_tags->{$name} && $ok_tags->{$name}{$att})) 
{

That takes care of easy languages, like French. But say you want to comment in Hebrew. Hebrew’s a Right-to-Left language. If you want to use a phrase in Hebrew in the midst of an English paragraph, you’d paste the Hebrew text into a <bdo dir="rtl" xml:lang="he"></bdo>.

“<bdo>” stands for “BiDirectional Override”, which temporarily reverses the direction of the text. If you want an entire paragraph in Hebrew, you’d paste the text into a <p dir="rtl" xml:lang="he"></p>.

[Update (5/11/2004): According to the W3C Draft on Handling Bi-Directional Text, you can mostly get away without using the <bdo> element, thanks to the Unicode Bi-Directional Algorithm and the super-secret character entities, ‏ (Right-to-Left Mark) and ‎ (Left-to-Right Mark), which let you control how neutral characters, like punctuation marks are treated. E.g. compare 1705 רחוב בן יהודה. (typed straight) with “‏1705 רחוב בן יהודה.‏” (uses some astutely-placed ‏s). Note: Safari screws this stuff up pretty badly; there are serious bugs in WebCore’s bidi implementation. There are also useful documents on Specifying the Language of Content and the ever-popular subject of Character Encodings (via Phil). ]

All these tags and attributes are allowed in the comments on this blog. The only bad news is with respect to Charsets. This blog uses ISO-8859-1. That handles Western Europeen languages just fine, but doesn’t know anything about non-Europeen languages. So if you enter

<span dir="rtl" xml:lang="he">הבנתי</span>

into the Comment Form and click “PREVIEW”, your browser will convert the text to numeric entities

<span dir="rtl" xml:lang="he">&#1492;&#1489;&#1504;&#1514;&#1497;</span>

which will display correctly, but which is not exactly the easiest thing to edit.

If I converted to UTF-8, presumably, this problem would be solved. Unfortunately, the last time I tried it, the interaction between UTF-8 and MT’s Comment Form was such a horror story that I’m loath to try it again.

It transpires that Bill Tozier (Erdős #4) is auctioning on eBay the opportunity co-author a paper with him, and thereby secure the successful bidder an Erdős number of 5. John Quiggin quickly jumped in to offer willing co-authors a free Erdős number of 4.

This got me to thinking. What’s my Erdős number? Can I profit from the opportunities currently flying about the 'net?

After checking the Erdős Number Project, I now know that I have an Erdős number of 4, thanks to three co-authors (Greene, Hubsch and Vafa) I have in common with Shing-Tung Yau (Erdős #2).

No help to be had from Tozier and Quiggin. If I am to improve my Erdős number, I’ll have to do it the old-fashioned way.

Tomorrow is Yom Hashoah, Holocaust Remembrance Day.

I wish I could say that the events of 60 years ago have little relevance today. But the bloody history of the intervening decade shows that the ability of Man to turn, savagely annihilationist, on his fellows is hardly diminished. As we learned in Bosnia, a little over a decade ago (to pick but one example) the veneer of civilization can sometimes be astonishingly thin.

My father survived the war by dint of luck, and good engineering skills. On this day, it’s worth taking some time to listen to his story. Maybe, thus inspired, we can someday make “Never Again!” more than a slogan.

String Theory, it has been pointed out, does not have any adjustable coupling constants. In Field Theory (say, the Standard Model), one must do a certain number of experiments, merely to pin down the values of the couplings in the theory, before one can start extracting predictions. These coupling constants are inputs, and not predictable within the context of QFT.

String Theory does not have any adjustable couplings, so one might hope to do better. It does, however, have a huge number of vacua. With enough supersymmetry, these vacua come in continuous families. But with less (or no) supersymmetry, they are typically discrete.

I say “typically”, because in the approximations in which we can compute reliably, there invariably components of the moduli space in which some or all of the flat directions are not lifted. In some cases, that’s simply a result of our inability to reliably compute the effects which lift the degeneracy. In others, there may be stringy reasons for the flat direction.

But let us, for the sake of discussion, assume what we expect “generically” is, in fact true, and the vacua of “interest” are discrete. We’ve gone from having a continuous infinity of such vacua, to having a finite number. But this number is, at first blush, frighteningly large, $10^N$ where $N$ is some moderately large number itself. (Proponents of the landscape try to outdo each other in making larger and larger estimates for $N$, just as a previous generation of string theorist tried to outdo each other in counting the number of Calabi-Yau manifolds.)

I say “frighteningly,” because these large numbers lead to two distinct, but often conflated anxieties about what it means to do physics in such a situation.

The first anxiety is what I would like to call the “Empirical” question. Which vacuum describes our world? I don’t like to think of myself as being a small fluctuation about the vacuum, but many questions — essentially all of particle physics — can be addressed by studying the physics of small fluctuations about the vacuum.

Rather than doing experiments to determine the values of the coupling constants, we need to do experiments to determine which vacuum to expand about. With a huge number of vacua at our disposal, you might worry that there will still be a large number which are compatible with current observations.

If there are only a small number of such vacua, we might even have predictions for currently-measured quantities. The 19 or so parameters of the Standard Model might not be independently adjustable. Once you pin down some of them, the rest would be determined.

But, if there are enough vacua compatible with current observations, you might worry that we could fit all current observations, and yet have differing predictions for stuff we haven’t measured yet — the mass of the Higgs, the spectrum of superpartners, …

It would be rather depressing if the LHC, and future generations of particle accelerators were simply devoted to pinning down more closely which vacuum we live in, rather than testing predictions.

Fortunately, I don’t think there is a case for the existence of a large number of vacua fitting current observations. Let me pick just two criteria: proton decay and flavour-changing neutral currents. The generic vacuum with approximate $N=1$ supersymmetry (eg, flux vacua in Type IIB orientifold models — the favourite among proponents of the Landscape) have dimension-4 baryon number-violating operators. Indeed, any theory in which extra coloured junk survives below the GUT scale will generically have baryon number-violating interactions whose magnitudes are too large to be compatible with the observed proton lifetime ($\gt 10^{32}$ years).

With low-energy supersymmetry, the only way to save the day is to find a discrete symmetry (R-parity, or something similar) and impose it on the theory. Most Calabi-Yau moduli spaces do not have such a discrete symmetry, and those which do only have it on some very high codimension subspace of the moduli space. Pick such a Calabi-Yau. Most of the fluxes you might turn on do not respect the discrete symmetry, so you have to set them to zero (thus cutting down hugely the exponent “$N$” in the above estimate) and — even if we restrict ourselves to symmetric fluxes, we need to further restrict ourselves to minima of the resulting superpotential which also respect the symmetry (remember that, just because the scalar potential has a symmetry, its set of minima need not).

If you think avoiding too-fast proton decay is easy (“Hey, we have zillions of vacua to work with!”), then you don’t remember the history of attempts to do String Phenomenology in the late '80s. Back then, people worked in the approximation of vanishing superpotential for the moduli, and simply wished to find a locus on the moduli space of some Calabi-Yau which would yield the correct physics. They allowed themselves to fantasize that nonperturbative effects would later lift the degeneracy and land them precisely where they wanted to be. But, even working with a continuous infinity of vacua (rather than the discretium), finding acceptable solution proved too hard.

I could repeat similar words about FCNC’s, but you get the idea. Finding vacua which fit our current observations is extremely hard. The worry is not that we have too many, but rather that we have too few (i.e. none).

The other anxiety has to do with what I call the “Historical” question. Given that there exists some appropriate vacuum, how did we end up here, as opposed to one of the zillions of other, inappropriate ones? One possibility is just initial conditions: they were just such that we ended up where we ended up. Given that there’s only one (observable) universe, there’s no sense in which we could reasonably ask whether this was “likely” or “unlikely.” We can’t do statistics with a sample of 1.

On the other hand, in scenarios like Chaotic Inflation, different part of the Universe may sample different initial conditions. Some will inflate, and produce an observable Universe that looks like our own. Others may look very different. Even if “most” such universes don’t look anything like ours, one might try to use anthropic arguments to say that it doesn’t matter what the “typical” universe looks like. It only matters what the typical universe capable of sustaining life looks like. In other words, we should study contingent probabilities.

Weinberg argued, for instance, that the cosmological constant could be explained by such reasoning. If it were too large, galaxies would never form, there would be no supernovæ to produce heavy elements, and we wouldn’t be here. The “expected” value of the cosmological constant turns out to be right in the ballpark of what’s observed.

Unfortunately, Banks, Dine & Gorbatov have extended this sort of analysis to other quantities. Consider again, proton decay. The anthropic bound on the proton lifetime is something like $10^{12}$ years (otherwise, you and I would glow), twenty orders of magnitude smaller than observations. There’s no anthropic bound on FCNC’s, no anthropic bound on the electron-muon mass ratio, etc.

So, merely demanding the existence of life does not explain the universe that we see.

It’s possible that, once you put in the anthropic bound — say, on proton decay — there might not be enough vacua left over to do Bayesian statistics. We might just have ended up a vacuum which exceeds the anthropic bound on the proton lifetime by 20 orders of magnitude for the silly reason that there is a dearth of vacua which satisfy the bound at all. Alternatively, if there are enough vacua, we might try to get further mileage by including other facts that we know about about our universe (aside from the fact that it supports life) in our conditional probabilities. Demanding, say, the absence of FCNC’s might yield “generalized anthropic” predictions about other quantities. At some point, the game breaks down — not enough vacua to do statistics — but it’s perfectly possible that we might be able to say something beyond Weinberg’s statement about the cosmological constant.

Overall, I’m agnostic about the “Historical” question. If some “anthropic” argument bears fruit, that’s great. If not, well that’s too bad, but I don’t think it impacts our ability to do physics. There are many things in physics which turn out to have no deeper explanation than that they are the result of initial conditions. The choice of vacuum in String Theory might be one of them.

Probably the top usability complaint with the comment system on this blog is that if you copy and paste some text into your comment, the smart quotes in the pasted text get turned into garbage characters.

This is, alas, a problem common to just about anyone who doesn’t use Windows-1252 encoding as the Charset of their website (does anyone really do that?). The only difference is that my software won’t let you post a comment with those illegal characters in it.

Since this is such a common problem, I long ago wrote a plugin to filter out these garbage characters from Trackbacks, RSS feeds I syndicate, my Technorati Cosmos, etc. I took a pretty brutal approach. The plugin defined a new global tag attribute, strip_controlchars. Adding the attribute to any MT variable substitution tag,

<$MTEntryBody strip_controlchars="1"$>

simply drops characters 0x80 to 0x9F from the content.

Inspired by Sam Ruby’s excellent Survival Guide, I recently decided that a more sophisticated approach was desirable. In the new version of the MTStripControlChars plugin,

<$MTEntryBody strip_controlchars="1"$>

works as before, but

<$MTEntryBody strip_controlchars="2"$>

translates the (would-be) Windows-1252 characters into the corresponding Unicode numeric entities.

Incorporating this filter into my Comment Preview template, we now automagically fix those mangled smart quotes.

Hopefully, this will lead to a more pleasant user experience.

Update (6/23/2004): See this comment for information on using this plugin with UTF-8 encoded blogs. If your blog uses UTF-8 encoding, then Trackbacks (or legacy data in your database) which contain these (now strictly illegal) characters are still a problem. Unfortunately, UTF-8 is a multi-byte encoding scheme, so fixing the problem is not as simple as stripping-out these “bad” bytes.

Update (7/1/2004): As Sam Ruby points out, there are other “illegal” characters in addition to the above. I’ve updated the plugin to strip those out too. Again,the plugin is currently really only useful if your blog charset is ISO-8859-1.

Hmm. Well that’s just peachy.

My old elementary school was firebombed this week¹. No one was hurt, but the school library was totally destroyed.

Library of the UTT Elementary School in Montréal, after Monday’s attack

A note left at the scene said that the firebombing was in response to the Israeli assassination of Sheik Ahmed Yassin, the leader of Hamas:

Our goal was only to sound the alarm without causing deaths … but this is just a beginning. If your crimes continue in the Middle East, our attacks will continue.

The French-language note was signed by a previously unknown group, “the Brigades of Sheik Ahmed Yassin.”

Let’s be quite clear. This had nothing to do with Hamas. When Hamas exacts their revenge, as they surely will, it will be far, far bloodier, and it will be directed at Israelis, rather than Canadian schoolchildren. These were amateurs — loathsome, hate-mongering anti-Semitic amateurs, but amateurs nonetheless.

Strangely, though, knowing that this a hobby rather than a vocation for them, does not make me more sanguine.

Update (4/15/2004): With tight security in place, classes re-opened on schedule. And, yes, they are accepting donations to rebuild the library.

The newly-formed sci.physics.strings newsgroup is finally available via Google Groups. Since UT’s NewsServer still does not carry it, this was my first opportunity to check it out. Having long-ago abandoned USENET as a hopeless cesspit, it was pleasant to find real intellectual content, with interesting posts by actual physicists. I keep shaking my head in disbelief; I wonder what it will be like when it’s carried by more that a handful of NewsServers in the world.

Right now, there’s an interesting thread on the “Landscape”. Lubos Motl, Wolfgang Lerche, Shamit Kachru and Joe Polchinski have all weighed in on this contentious subject. Alas, I see from my sidebar that Peter Woit has joined the party, so presumably, USENET will soon return to normal.

In the meantime, I’ve created an RSS feed for the new group¹, and syndicated it on my sidebar. Right now, the newsgroup itself is coming from an obscure open-for-reading NewsServer in Poland. Since my NewsServer (and, presumably, yours) doesn’t carry the group yet, I’ve set the links to open in Google Groups. This has an odd side-effect: there’s a few hours delay between when articles are posted and when they appear of Google Groups, which means that the most-recent links will invariably be broken, whereas the older ones will work.

No, it wasn’t that sort of Seder. Children under the age of nine outnumbered the adults. There were חד גדיא colour-in placemats, ping-pong balls rained down during the recounting of the plague of hail, key participants kept slipping away from the table to chase each other around the living room … You get the picture.

Still, I was impressed by my 3-year old’s elementary, but incisive grasp of the essentials of the affair:

Pharoah was a bad king. He said, “No, no, no! I will not let them go!”

Longtime readers of this blog may be curious about one other aspect of the evening. After last year’s near-fiasco, this year I spent an extra amount of time at Central Market’s horseradish root counter, pondering my options, before selecting, at last, a hefty club-like item. This year’s batch, I am pleased to say, was a … religious experience.

So, is Condi Rice really Frau Farbissina?

Nobody told me, but MathPlayer 2.0 is out of beta and has been officially released. Now, IE/Win users, even those unaccountably reluctant to install a beta plugin for use with their browser, can enjoy full MathML support¹. And, yes, with the plugin installed, their browser won’t choke and spit when it encounters a web page sent out as application/xhtml+xml.

One can hope that, now that 90% (or whatever the number is supposed to be) of the world’s web surfers can potentially read XHTML+MathML documents, we’ll see a flurry of activity, bringing MathML support to various CMS platforms.

One of the platforms I’ve been looking at is Moodle, the only CourseWare package I’ve seen that doesn’t totally suck. There’s been a flurry of activity to bring math-capability to Moodle, but, so far, the result is pretty much of a muddle. There are 3 or 4 different ways of introducing math into Moodle pages, each with its own idiosyncrasies. You’d think you know what the obvious choice is; but, alas

And as Martin explained, MathML will not display in Moodle pages under Mozilla, because Moodle currently does not produce xhtml compliant pages.