This should be a month with quite a bit of experimental news, including
- Latest Higgs news from the LHC experiments here on Wednesday.
- Release of data from AMS-02 was advertised as “two to three weeks away” back on February 17.
- Planck data release on March 21.
A couple weeks ago, Arianna Borrelli of the Epistemology of the LHC project gave a talk at CERN (slides here). It includes some interesting data from surveys of HEP physicists in September 2011 and September 2012.
The Simons Foundation website keeps having some of the best writing on math and physics around. Natalie Wolchover has an excellent story about a complex subject, that of the role of computers in proof. The also have an essay by Barry Mazur about another complicated related subject, the nature of evidence in mathematics.
Finally, if you want to watch a very good introduction to D-modules, see video from David Ben-Zvi at MSRI here and here.
Update: Edward Witten will be speaking here in New York this evening (Monday March 4) at Hunter College, for more information see here. Unfortunately I have other plans and will have to miss this.
What happened with Moriond? they dont put the slides
The new results from LHC, Planck and AMS are important but there will not be any surprise, only confirmations of previous experiments and reduction of uncertainties
jihn,
Their website says slides will be posted only after the session is over (next Saturday), presumably here
https://indico.in2p3.fr/conferenceOtherViews.py?view=standard&confId=7411
The findings quoted below by Borrelli’s group look very consistent with Lakatos’s “Methodology of Scientific Research Programs.” You have the “hard core” theoretical preconceptions that are not tested (e.g. SUSY), the “protective belt” of disposable models that mediate between the data and the hard core, and the use of overall judgments about the expanding or contracting nature of what the scientific research program can satisfyingly explain to decide amongst them.
“these results do not support the traditional pictures of physicists comparing and
preferring models/theories according to some criteria
– models are rather regarded as exploratory tools for research than as serious
candidates to a theory of new physics. Yet the general approaches (SUSY, extra
dimensions…) are taken seriously (“theoretical cores” Borrelli 2012)
– LHC results did not change much the pattern of (rather feeble) abstract
preferences, but seem to have further eroded the belief in individual models –
yet interestingly SUSY is somehow slightly, relatively better off (Sept. 2012!)”
The article about using computers for proving theorems (and possibly for sniffing out or discovering theorems) is indeed interesting.
Still, after 30 years of discussion there is still existential Angst about the usefulness or the fruitfulness of using symbolic manipulation by machine to break through problems … damn!
After all, we know that proving theorems is not exactly in P (so the program needs to be very astute to make progress unaided) and that Hilbert’s program is unattainable as such so there will always be fine-tuning and possibly unprovable theorems to make life interesting (though for some reason, one encounters these very rarely in practice). Humans won’t be out of a job! At least until full AI that is demonstrably not unhinged has been mastered.
Doubts about a proof done by machine (“by steam”, if one so will), though it may never go away, can ultimately be brought down to an adequate level. I am sure most people will take “three independent programs have found proofs that are, unfortunately, too large or obscure to be checked by brain – let’s start from there” over “no proof exists”. And even then, the search of possibly nonexistent but elegant (“highly compressible”?) proofs can go on.
Conversely, are there any proofs that were found to be wrong long after they had become “common knowledge”?
Physicists seem to go for it instead of wallow in doubt here. Does this come with the territory?
Recommended reading:
The Four-Color Problem and its Philosophical Significance – Thomas Tymoczko, Journal of Philosophy, Feb. 1979 (not sure whether that link is legit though)
and
The Four-Color Theorem Solved, Again – Casey M. Rufener, July 2011
For quantum field theory the interesting aspect of the “univalent foundations” mentioned in Wolchover’s article is that it has the *gauge principle* built right into the foundations of mathematics. Moreover, a good chunk of Lagrangian, local (pre-)quantum field theory has a natural and fairly immediate axiomatization in univalent foundations: http://ncatlab.org/schreiber/files/QFTinCohesiveHoTT.pdf .
Peter, you can call him Ed.
“Conversely, are there any proofs that were found to be wrong long after they had become ‘common knowledge’?”
One item of common knowledge that comes to mind would be the status of the classification of finite simple groups. My copy of Dummit & Foote from 2004 states, “The classification of finite simple groups…. was completed in 1980…” In fact it was completed in 2004. See for example Wikipedia for discussion.
I’m not sure I would count the classification of finite simple groups as a “proof” exactly. More of a framework I would say, which of course involves many proofs. In any case it’s not like it was wrong in 1980 exactly, it just wasn’t quite finished. Off the top of my head and assuming “long” means long, I can’t think of anything really. There are plenty of published proofs which are later discovered to be wrong, but usually it’s pretty quick. In my field there was a “result” of McKean showing that eigenvalues of the Laplacian on Riemann surfaces are >= 1/4, but Randol came up with counterexamples 2 years later. There are plenty of other things like that around.
It looks like the big announcements and data releases from Planck might end up clashing with the announcement of the new Pope, which will probably divert public attention. I wonder if positive media coverage is important enough for them to reschedule?
Read this about how the erroneous solution of the Malfatti problem survived for more than a century.
http://www.cut-the-knot.org/Curriculum/Geometry/Malfatti.shtml
Ironically, the paper “The Four-Colour Theorem Solved, Again” linked to above does not reference the paper where the four-colour theorem was solved again.
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