The n-Category Café

Is any work by, say, Café hosts Tom Leinster and Simon Willerton to be included in their respective departments’ impact narratives?

No one’s asked me, but I’d be surprised if anything I’ve done here counts as impact. This blog is largely about academics communicating with other academics, and although there’s a sizeable minority of readers who don’t have formal academic positions, it’s a bit like the situation you mention with the public lectures. I don’t have any evidence of any non-mathematical change I’ve brought about as a result of this blog.

Given that our own school contains statisticians of a quite applied variety, and some quite applied applied mathematicians, I guess we’ll be leaning on them for our “impact”. I can see that a department of philosophy is going to be in a more difficult position.

These requirements truly are narrow-minded and pernicious. Aristotle, I imagine, could claim his work on logic would eventually impact the design and operation of automated reasoning systems in software systems such as those controlling nuclear power plants, but the 2300 years his work has taken to achieve these impacts is outside the REF’s allowed timescale.

Simon, Tom, obviously your activity here at the cafe and as a Catster attracts an audience well beyond academics, so that seems to be a clear case of impact; e.g. many computer scientists in private companies are very keen on category theory - you may have to include the term “popularizing”.

I think the biggest external impact of the nCafé/nLab/nForum has been as a large example of effectively using MathML and to a lesser extent SVG in everyday communication. The n-sites are much further developed along these lines than Wikipedia and are often used as an exemplar of how MathML is not too undeveloped, buggy, complex, etc. for everyday infrastructure.

The subject matter - higher category theory - probably doesn’t have any impact other than on categorically inclined mathematicians which doesn’t seem to fall under the REF technical definition of ‘impact’.

I am reminded of a situation years ago when I was sent as an observer by a government agency to a ‘system deployment’. When I got back I wrote up a 6 page report of my opinions of how well things went and how well the systems actually addressed their purposes. The content of my report was ignored (as is usual). However I was called in to explain how I was able to write, format, print, and turn in such a gorgeous looking report in the 2 days following my return. The ‘impact’ of my report was the agency getting new hardware and software for word processing.

I think one should try to look how science and scientists are perceived among economists and politicians. Perhaps as data-delivering servants (and, when needed, punching bags)? Both servants and scientists share in the public view the values “reliability” and “objectivity”, a distinctive slang and a stress on reputability.The difference between them is that servants define by operative usefullness, science by understanding, insight, knowledge. The described focus on “impact” is precisely about challenging that difference. A few years ago, a mathematician wrote a parody on how MBA-thinking confuses those things, to his surprize, no-one noticed the satiric meaning and it became awarded as the years most influential management books. An other idea is that maybe the “idea of science” itself gets forgotten, in a kind of “platonic amnesia”.

Many of the comments so far have been non-combative, let me suggest an attack on the impact factor, bean-pushers, so-called social scientists, etc. If someone mentions to you the lack of impact of maths or philosophy, ask them to forgo for one week all use of computers, mobile phones, DVDs, the internet in any form, no use of scanners, nor MSRI scans for saving lives, etc. i.e. to forgo use of the entire basis of the modern culture that the combination of mathematics and engineering, building on earlier philosophical work on logic, has given us.

I used to work in Cork and taught one or two lecture courses in rooms in the old college building where G. Boole used to lecture. Boole was a mathematician, not a sociologist, nor a psychologist, nor a historian. His work built on earlier philosophical work (going right the way back to the Greeks). (What is the impact of Aristotle!) Without Boole no computers!

I often visited the mathematics department of the university of Manchester. This is now housed in the Alan Turing building. Turing, a mathematician, and his impact….? What about Max Newman also at Manchester, who proved fundamental results on formal languages. Their work at Bletchley Park was of ultimate importance in the second world war. (I will stop here as David’s original question related to the UK only so I won’t mention Coding theory etc., but you get the picture.)

Where is the problem? It is simple. The impact being measured in the REF is short term and often very fleeting. We work for the long term and permanence. We cannot predict where the applications will arise if they are more than a year or two ahead. (Hardly surprising given the long history of both philosophy and mathematics. The short term impact stuff was likely to be exhausted before the word `sociology’ had been thought of.) Perhaps the basis for the next big technological revolution is being laid down now and in this café, but we cannot tell. It may possibly be due to musings here and elsewhere on the potential for modelling biological phenomena using n-categorical ideas, but who knows.

Don’t let the bean-counters get away with the short term rubbish they push out and note that Korea, China and India are all spending a lot of effort on mathematical prowess in schools and in honing up the reasoning powers of their young engineers and scientists.

If we want to navel gaze, think about what areas of the n-cat scene could be improved to have more immediate impact. I have two thoughts on this. Basic categories involve lots of analogues of relationships, and comparisons. Multiple categories involve higher order relations between relations. can that be exploited in some non-trivial way, e.g. in artificial intelligence, that has not been considered yet.

The second thought is that within an $\infty$-groupoid, it should be feasible to add in some probabilistic composition. For instance, in a Kan complex we know that all horns have fillers, but are they all equally likely to happen!!!! developing that idea sounds fun and should be useful in modelling situations where there are numerous interacting effects with probability distributions governing the actual outcome.