Musings

We had a beautiful talk today by our own Eiichiro Komatsu on the latest WMAP data. A big part of the talk was devoted to the polarization data, and how this greatly helped constrain the cosmological parameters.

The fisking of the Washington Post Online’s new right-wing blogger has gotten off with a bang. P.Z. Meyers has an excellent summary of clueless Ben’s views on Evolution. He is, apparently, a knuckle-dragging creationist¹

Surely, you are thinking, Jacques can avoid the cheap thrill of piling on. Well … I almost did. But then the following passage struck my eye

Like any theory, new discoveries force scientists to reexamine their previous conclusions: as recently as last month, many scientists believed their dating of the Big Bang (another theory) to be dead-on - but new discoveries imply they were off by millions of years.

The Washington Post just hired a total innumerate as their representative of “Red” America.

The age of the universe is approximately 13.73 billion years. The uncertainty in this number, with the best current data (WMAP 3^rd year results) is a stunningly impressive 1.2%. With WMAP 1^st year results (which is what was available when clueless Ben wrote those words), the uncertainty was about twice as large.

What could Domenech have been thinking when he asserted that the scientists’ estimates of the age of the universe was “off by millions of years”? An error of “millions of years” is a hundred times smaller than the already-stated uncertainty in the age of the universe. Most cosmologists would bite off their left toe for an instant hundred-fold improvement in the accuracy of our knowledge of the cosmological parameters. But that’s what it would take for them to be only “off by millions of years”. Far from discrediting the Big Bang (“another theory”), Ben unwittingly pays it too high a compliment.

From reading the CNN story from which he got this tidbit, the only conclusion I can draw is that Domenech is confused about the difference between “millions” and “billions.” Why this doesn’t disqualify him from commenting on … well … pretty much anything of importance, in the online pages of the Washington Post, is a mystery to me.

Perhaps he was the best they could come up with (seems unlikely). Or perhaps this is yet another underhanded plot by the “liberal MSM” to discredit conservatives.

A while back, I wrote about the work of Headrick and Wiseman on numerical Ricci-flat metrics on K3. The big limitation in extending their work to complex dimension-3 (or to less-symmetrical K3s) was simply a matter of storage.They needed to store the values of the Kähler potential for each point on the grid which, while doable in real dimension-4, was prohibitive in real dimension-6. Though their numerics were very efficient, their calculations were highly storage-limited.

I bumped into Matt today, and he told me about a recent paper by Simon Donaldson which seems to alleviate the storage problem. The trick is that, if you expect the Kähler potential to be fairly smooth, you are storing a lot of redundant information by recording its value at each point of the grid. Instead, you can get a good approximation with much lower storage requirements by storing its coefficients in a basis of “harmonic functions.”

Donaldson works with a projective embedding of the manifold, and expands in a basis of harmonic functions on the ambient projective space. $$e^K = \sum_{n=1}^{\infty}\frac{h_{A\overline{B}} p^A(z)p^{\overline{B}}(\overline{z})}{\Vert z\Vert^{2n}}e^{K_0}$$ Here $z_a$ are homogeneous coordinates of the ambient projective space (sections of the hyperplane bundle), $p^A$ are a basis of homogeneous polynomials of degree $n$ in the $z_a$, $K_0$ is the fiducial Kähler potential (perhaps the one induced from the Fubini-Study metric of the ambient projective space) and $\Vert z\Vert^2= g^{a\overline{b}}z_a\overline{z}_b$ for some suitable positive-definite matrix, $g^{a\overline{b}}$. Instead of storing the values of $e^K$ at each grid point, we store the values of the constants, $h_{A\overline{B}}$. For reasonably slowly-varying functions, this is vastly more efficient.

Toby and Matt are working on combining Donaldson’s proposal for efficiently storing the Kähler potential, with their own algorithm for solving the Monge-Ampère equation. Provided that they don’t sacrifice too much speed in translating back and forth from Donaldson’s nonlocal variables, $h_{A\overline{B}}$, this should be a big step forward.

If one ever begins to forget that RSS 2.0 is a crappy, underspecified format, a controversy erupts in RSS-land to refresh one’s memory. The latest wrangle reminded me of my intention to migrate my Comment feed from RSS 2.0 to Atom 1.0, a much more robust alternative.

For the time being, the old RSS 2.0 Comment feed will remain in place, but I recommend people migrate to the new one.

Since I was in the process of housecleaning, I decided to hack away at some of the other less-useful feeds hereabout. As I warned 8 months ago, the Atom 0.3 feed has gone away. It now redirects to the Atom 1.0 feed. The RSS 0.9.1 feed has similarly bitten the dust. It redirects to the RSS 2.0 feed.

The same holds for the feeds at The String Coffee Table.

The trouble with eating your own dogfood is that, when you bite down on some gristle, there’s no one else who’s gonna fix the recipe. And so it was with the previous entry, where I discovered that itex2MML was, in utterly stupid fashion, splitting numbers at the decimal point. 2.233 was being marked up as <mn>2</mn><mo>.</mo><mn>233</mn> instead of <mn>2.233</mn>.

Grumble… Time for a new version.

WMAP has released their 2^nd and 3^rd year data.

The measurements of the CMBR anisotropy show clear signs of the 3^rd acoustic peak.

WMAP CMBR power spectrum, for multipole moments, $l=2,...,1000$.

On the subject of polarization, they find no evidence for $B$-modes and an upper limit on the scalar/tensor ratio, $r=\lesssim 0.55$, which is getting close to the predictions of simple inflationary models, $r\sim 0.3$.

The fit to the ΛCDM model has improved markedly over the first year results.

The full list of papers, doubtless contains more nuggets of information. Perhaps our cosmologist friends over at CosmicVariance will provide some insight.

Blogging about physics is a bit of a tightrope walk. On the one hand, I don’t want to say something manifestly foolish in this very-public forum. If I’m going to comment on some topic, I need to put in the (sometimes considerable) effort to make sure I’m saying something sensible. On the other hand, if I put in enough effort, the result is sometimes better-presented as a paper on the arXiv than as a blog post.

That’s the story of one half-written blog post that’s been sitting on my computer for a few weeks. I’d been somewhat confused by the recent paper of Adams, Arkani-Hamed, Dubovsky, Nicolis and Rattazzi. Finally, after a discussion with Ben Grinstein, who was visiting this past week, I think I understand the source of my confusion and, at least in some examples, how it is resolved. Together with Ira Rothstein, we’re writing up a short paper, but in the meantime, I’m going to break my usual rule and explain what’s going on in a blog post as well.

Ever since the trackback system at the arXivs was announced, it was clear that, sooner or later, a controversy would erupt. And, indeed, one has, surrounding the trackbacks of well-known 'Net personality, Peter Woit.

From the beginning, it was made clear that trackback privileges would not be open to all and sundry. The arXivs are a vehicle for communication between research scientists. Not everyone can have their papers appear on the arXivs. Similarly, not everyone would be able to have their trackbacks appear.

Woit has loudly protested the decision not to accept his trackbacks, and the discussion has spread elsewhere in the blogosphere. I have refrained, up till now, from commenting publicly because as a member of the arXiv Physics Advisory Board, I feel very constrained about what I can say publicly, either about the specifics of the case at hand, or about the internal deliberations of the Advisory Board.

But one thing became clear in the discussion over at Cosmic Variance. There’s a lot of confusion about the trackback policy. Some of that confusion was deliberately sown by people with an axe to grind; some of it was the unfortunate result of the less than transparent process under which the policy was developed.

So, what I’m going to do is try to explain the thinking that went into the policy, and then solicit your feedback.