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Via Tumblr, this morning I stumbled across an interesting event in the physics world, about a fellow called Weinstein with a PhD in mathematics, but who doesn’t work in the field anymore, with claim for a theory of everything that purports to explain some new fundamental ideas in particle physics. I’m am not going to pretend for a minute that I understand very much at all of what is said about this theory; I’m interested in the debate here around which knowledge is formed.

The storm, it seems, is over the way this supposedly groundbreaking knowledge was revealed: in an article in the Guardian newspaper. That set off a rather frenzied reaction, links to which can be found in the Tumblr link I posted at the start of this article.

This sort of thing – research by newspaper article – happens in historical disciplines pretty much all the time and it’s hardly ever called out, at least in public. Its often accepted uncritically, even by scientists (because they are dealing with something outside their specialisation, usually). Think every time you see a newspaper article about an archeological find dealing with Alexander something or Cleopatra just-about-anything; it’s mostly fantasy masquerading as history-by-press-release. Sometimes this stuff takes on highly disturbing nationalist overtones – at least mathematics and physics are usually spared that ignominy! In part this is because the discipline of Classics itself has a deep coupling with a range of European pretensions about what exactly a worthwhile civilisation really looks like, and a pre-scientific origin in the collections of antiquaries, rather than a truly scholarly uncovering of the past, gentlemen merely wish to stock their houses and gardens with ancient objets d’art. Thus the object’s inherent beauty being more important than what it can tell us about the past (which led in turn to the destruction of evidence that wasn’t beautiful enough to take note of). There was also sometimes a uncritical acceptance that ancient writing was necessarily true in a rather straightforward manner, that led to artefacts being assigned appellations like “The mask of Agamemnon”.

All this led me a deeper meditation on the production of knowledge and how we go about obtaining it.

In the sciences, it’s usually taken there is a straightforward path to the establishment of truth. Develop provisional theory; determine novel predictions; undertake experiments; publish results; rinse and repeat. The biggest cries of outrage about Weinstein’s ideas were not just “show us your working” (i.e. “where’s the paper?”) but rather simply that “this is not science” as the usually-reliable PZ Myers posted. But you can note the first comment on that blog post by commenter “Unity”;

“This is not how anyone does science.”

Except mathematicians.

[ ... ] This is often how mathematicians operate, on the clear understanding that what they are present is, at this stage, provisional and that publication and peer review will necessarily follow – that is, of course, unless someone spots a serious flaw during the talk and raise it during the Q&A.

Several other commenters make similar points.

That’s not dissimilar to the way things work in the humanities (at least in Classics); you try out approaches at conferences and seminars and then later publish your work, of course with fundamental caveat of the important differences as to how argumentative ‘proof’ works between the humanities and the sciences.

Still, those links led me to this interesting article by Caroline Chen about an extraordinary proof of an important mathematical conjecture by Shinichi Mochizuki just last year (don’t worry, you need a Mathematics degree to understand the article, at least).

This is fascinating because the article points to an approach that’s diametrically different from the “publish first, questions later” method that we’re given by some of the commenters on the Weinstein controversy. Here, a brilliant but reclusive mathematician has simply dumped his proof of the conjecture on the internet and refuses to come to seminars and explain what it all means to other mathematicians. The problem it seems is that the papers are long, and full of very dense and new mathematics. So mathematicians who want to understand the proof need to do a lot of work digging into this new and dense mathematics; not surprisingly, not very many of them possess both the ability and the will to do this. They want the seminar version, but the author won’t supply the seminars. Talking about Machizuki, a mathematician, Cathy O’Neil says;

“You don’t get to say you’ve proved something if you haven’t explained it,” she says. “A proof is a social construct. If the community doesn’t understand it, you haven’t done your job.”

So why the original reaction to Weinstein couched in terms of the diametrically opposite terms? I can’t say anything about the correctness of either Weinstein or Machizuki, but I think it’s an object lesson that even Mathematics, the purest of the pure sciences is still firmly rooted in human social systems. Evidently if you don’t co-operate with social standards like “don’t have your results trumpeted in the newspaper before your colleagues see them” and “don’t just dump your proof into a series of long papers on the internet” you’re not ‘doing science’. While the science itself may be mathematically rigourous, like everything else that humans have discovered or invented, it’s deeply embedded in social systems, not just mathematical ones.