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I got the job application in, finally: here's the revised (or rather, totally re-written) research proposal, and here's the summary for laymen. You will notice the point where I thought "Speculative? Ha! I'll show you speculative!" I'd really appreciate feedback, especially on the one-page summary: the two or three formulae in there should be helpful to some, but can safely be ignored if they make your eyes glaze over. The proposal got mailed off at about 5am on Wednesday morning: I then went to bed for a couple of hours before getting up to catch the bus down to Sheffield at 9.15. We missed the bus, but we were only round the block from the railway station, so we caught the train as far as Edinburgh and joined our bus there. The train journey gave me time to write most of the one-page summary: just as well, really, as I found it impossible to type on the bus.
So, to Sheffield, for the USLES (University of Sheffield Light Entertainment Society) pantomime, Jack and the Beanstalk. I was extremely impressed. They'd hired what Harry claimed was the smallest theatre in Sheffield, but at 270 seats it was something of a step up from most Light Entertainment productions: OULES usually use the badminton court in Wadham College. Nevertheless, the theatre didn't feel empty: they'd pre-sold nearly 80 tickets, and obviously sold a lot more on the door - I didn't see many empty seats. The play was a bit long, at nearly two hours, but worth it. There were some excellent performances, with the fairy godfather, Jack, and the comic particularly notable. The slosh scene was genius: they did especially well, considering that there were three or four former dames scattered throughout the audience reciting the lines along with them! Overall, I enjoyed the show a lot more than the full-budget professional panto we'd been to see in Glasgow the week before. My only criticism (and I know this is something I go on about a lot) is that some of the USLEs need to learn to project their voices: I was sitting in the second row, and I found some of the lines hard to make out. God knows what it must have been like at the back of the room. It's not hard, guys: take deep breaths, speak from your diaphragms, enunciate every word more than you think you ought to, and don't shout. But it needs practice.
Then USLES kindly allowed us old lags to crash their cast party, which was a thoroughly enjoyable affair: not least for me because of the presence of![[livejournal.com profile]](https://www.dreamwidth.org/img/external/lj-userinfo.gif)
buffalo_gill, short1sandwich, dreamstothesky and Rosie, who were up for the evening from Cambridge, and Tom "Morpheus" Wooley and Dan "El Presidente" Browne, up from, er, wherever it is they live. But many new people were met too: the USLEs turned out to be a very friendly bunch (one kindly took the time to teach wormwood_pearl how to play some stuff on her new ukulele). I shall observe their future careers with considerable interest :-)
The next morning, we all went for the now-traditional slap-up brunch at Wetherspoon's: then it was time to meet up with the Catsters, aka Eugenia Cheng and Simon Willerton. I blogged about Eugenia's latest paper a while back, but it turns out that I'd only got as far as the first cool result (of at least three), so it was great to get the full story from the horse's mouth. OK. We can consider monad objects in any 2-category C: let the collection of monads in C be Mnd(C). We can define notions of morphisms and transformations of monads that makes Mnd(C) into a 2-category. So we can iterate this construction, and consider Mnd(Mnd(C)), Mnd(Mnd(Mnd(C))), etc. It turns out (the first cool result) that an object of Mndn(C) is an object c of C together with n monads, T1,...Tn on c, plus the extra data needed to make their composite T1.T2...Tn into a monad on c. The second cool result is that this data's a lot simpler than you might have thought. Given two monads S and T, the data you need to make ST into a monad is something called a "distributive law of S over T": this can be expressed in various forms, but the simplest is as a natural transformation TS → ST satisfying some axioms. Another way would be as a lifting of S to a monad on the Kleisli category of T: I think the Haskell notion of "monad transformers" must be somehow related to this. Anyway, to get a monad structure on the composite of three monads, R, S and T, you need three distributive laws (R over S, R over T, and S over T), and they must satisfy something called the Yang-Baxter equation (which is well-known from the mathematics of knots and braids - there's a way of representing monads using "string diagrams" which makes the connection obvious, and I should really learn about this stuff). Now, I'm feeling especially gutted, because I thought about this stuff about a year ago, didn't recognise the Yang-Baxter equation, and gave up, thinking that it would only get messier; but actually, almost all the work has been done! To compose n monads on an object c, you just need distributive laws between each pair of monads, and each set of three distributive laws must satisfy the Yang-Baxter equation - no new equations arise! And it's coherent: if you compose them a few at a time (say R with S, then RS and T) you get the same composite monad as if you do them all at once.
OK, now here's the really cool bit. The operation Mnd(-) is in fact a functor from 2-Cat to itself. Better than that, it's a monad! And actually, it's an ordinary 1-monad, not a 2-monad or 3-monad or semi-weak 8-monad or something. Like any monad, we get a simplicial resolution:
The rest of the paper, as far as I can tell, is an application of this to the construction of the "free strict n-category" monad on the category of globular sets: this monad can be decomposed into "freely add composites of 1-cells", "freely add composites of 2-cells" etc, and all these intermediate monads can be composed in the way described in the rest of the paper.
Thenwormwood_pearl and I got on our respective trains, she back to Glasgow and I on to Oxford, to see our respective families for Christmas. Christmas chez Vlak has been pretty good, though marred by the need to put up endless amounts of flat-pack furniture: my Dad is building a new workshop, and needs cupboards and drawers and so on to put his stuff in. Now, I'm no great craftsman, but I'm not a complete incompetent: but these units have been a total nightmare. The instructions are unclear and barely-legible, everything's bizarrely sized so measurement is that little bit harder (the door handles are 12.8 cm from centre-hole to centre-hole - or 5 and a sixteenth inches, if you prefer), I'm 99% certain they've replaced a small but crucial bit with a new design that invalidates the bundled instructions, and no matter how paranoid I am, no matter how careful I am to measure everything three times and clamp everything as tightly as I can and drill everything as straight as I can, nothing ever fits right the first time. A single drawer unit took us nearly three hours to assemble the other day.
Other than that, Christmas has been pretty good. It's always nice to see my family, and I managed to meet up withmrkgnao and necaris the other day. My last-minute Christmas presents to the parents* seem to have been appreciated (as were theirs to me - yay for books, head-torches and Hustle on DVD!). And now wormwood_pearl has arrived down South, so we can spend New Year together :-)
In entirely unrelated, but sad news, Oscar Peterson, arguably the greatest jazz pianist of all time - screw that, arguably the greatest pianist of any kind of all time - died a few days ago, at the age of 82. If you don't know his work, you really owe it to yourself to check it out. Start with his recording of Porgy and Bess, which completely transformed my understanding of the piece, but frankly it's all good.
* Literally last-minute: they were about to close Blackwell's on Christmas Eve as I bought them. Fortunately, they were also marking everything down to half-price rather than £2 or £3 off :-)
So, to Sheffield, for the USLES (University of Sheffield Light Entertainment Society) pantomime, Jack and the Beanstalk. I was extremely impressed. They'd hired what Harry claimed was the smallest theatre in Sheffield, but at 270 seats it was something of a step up from most Light Entertainment productions: OULES usually use the badminton court in Wadham College. Nevertheless, the theatre didn't feel empty: they'd pre-sold nearly 80 tickets, and obviously sold a lot more on the door - I didn't see many empty seats. The play was a bit long, at nearly two hours, but worth it. There were some excellent performances, with the fairy godfather, Jack, and the comic particularly notable. The slosh scene was genius: they did especially well, considering that there were three or four former dames scattered throughout the audience reciting the lines along with them! Overall, I enjoyed the show a lot more than the full-budget professional panto we'd been to see in Glasgow the week before. My only criticism (and I know this is something I go on about a lot) is that some of the USLEs need to learn to project their voices: I was sitting in the second row, and I found some of the lines hard to make out. God knows what it must have been like at the back of the room. It's not hard, guys: take deep breaths, speak from your diaphragms, enunciate every word more than you think you ought to, and don't shout. But it needs practice.
Then USLES kindly allowed us old lags to crash their cast party, which was a thoroughly enjoyable affair: not least for me because of the presence of
buffalo_gill, short1sandwich, dreamstothesky and Rosie, who were up for the evening from Cambridge, and Tom "Morpheus" Wooley and Dan "El Presidente" Browne, up from, er, wherever it is they live. But many new people were met too: the USLEs turned out to be a very friendly bunch (one kindly took the time to teach wormwood_pearl how to play some stuff on her new ukulele). I shall observe their future careers with considerable interest :-)The next morning, we all went for the now-traditional slap-up brunch at Wetherspoon's: then it was time to meet up with the Catsters, aka Eugenia Cheng and Simon Willerton. I blogged about Eugenia's latest paper a while back, but it turns out that I'd only got as far as the first cool result (of at least three), so it was great to get the full story from the horse's mouth. OK. We can consider monad objects in any 2-category C: let the collection of monads in C be Mnd(C). We can define notions of morphisms and transformations of monads that makes Mnd(C) into a 2-category. So we can iterate this construction, and consider Mnd(Mnd(C)), Mnd(Mnd(Mnd(C))), etc. It turns out (the first cool result) that an object of Mndn(C) is an object c of C together with n monads, T1,...Tn on c, plus the extra data needed to make their composite T1.T2...Tn into a monad on c. The second cool result is that this data's a lot simpler than you might have thought. Given two monads S and T, the data you need to make ST into a monad is something called a "distributive law of S over T": this can be expressed in various forms, but the simplest is as a natural transformation TS → ST satisfying some axioms. Another way would be as a lifting of S to a monad on the Kleisli category of T: I think the Haskell notion of "monad transformers" must be somehow related to this. Anyway, to get a monad structure on the composite of three monads, R, S and T, you need three distributive laws (R over S, R over T, and S over T), and they must satisfy something called the Yang-Baxter equation (which is well-known from the mathematics of knots and braids - there's a way of representing monads using "string diagrams" which makes the connection obvious, and I should really learn about this stuff). Now, I'm feeling especially gutted, because I thought about this stuff about a year ago, didn't recognise the Yang-Baxter equation, and gave up, thinking that it would only get messier; but actually, almost all the work has been done! To compose n monads on an object c, you just need distributive laws between each pair of monads, and each set of three distributive laws must satisfy the Yang-Baxter equation - no new equations arise! And it's coherent: if you compose them a few at a time (say R with S, then RS and T) you get the same composite monad as if you do them all at once.
OK, now here's the really cool bit. The operation Mnd(-) is in fact a functor from 2-Cat to itself. Better than that, it's a monad! And actually, it's an ordinary 1-monad, not a 2-monad or 3-monad or semi-weak 8-monad or something. Like any monad, we get a simplicial resolution:
, where all the rightwards arrows are some form of μ and all the leftwards arrows are some form of η (that's "join" and "return" to the Haskellers). The equations given by the simplicial resolution ensure that all the composed monads you get agree, and (in some sense that I don't fully understand) the fact that Mnd(-) is only a 1-monad ensures that you don't need any higher equations after you try to compose three monads.
The rest of the paper, as far as I can tell, is an application of this to the construction of the "free strict n-category" monad on the category of globular sets: this monad can be decomposed into "freely add composites of 1-cells", "freely add composites of 2-cells" etc, and all these intermediate monads can be composed in the way described in the rest of the paper.
Then
wormwood_pearl and I got on our respective trains, she back to Glasgow and I on to Oxford, to see our respective families for Christmas. Christmas chez Vlak has been pretty good, though marred by the need to put up endless amounts of flat-pack furniture: my Dad is building a new workshop, and needs cupboards and drawers and so on to put his stuff in. Now, I'm no great craftsman, but I'm not a complete incompetent: but these units have been a total nightmare. The instructions are unclear and barely-legible, everything's bizarrely sized so measurement is that little bit harder (the door handles are 12.8 cm from centre-hole to centre-hole - or 5 and a sixteenth inches, if you prefer), I'm 99% certain they've replaced a small but crucial bit with a new design that invalidates the bundled instructions, and no matter how paranoid I am, no matter how careful I am to measure everything three times and clamp everything as tightly as I can and drill everything as straight as I can, nothing ever fits right the first time. A single drawer unit took us nearly three hours to assemble the other day.Other than that, Christmas has been pretty good. It's always nice to see my family, and I managed to meet up with
mrkgnao and necaris the other day. My last-minute Christmas presents to the parents* seem to have been appreciated (as were theirs to me - yay for books, head-torches and Hustle on DVD!). And now wormwood_pearl has arrived down South, so we can spend New Year together :-)In entirely unrelated, but sad news, Oscar Peterson, arguably the greatest jazz pianist of all time - screw that, arguably the greatest pianist of any kind of all time - died a few days ago, at the age of 82. If you don't know his work, you really owe it to yourself to check it out. Start with his recording of Porgy and Bess, which completely transformed my understanding of the piece, but frankly it's all good.
* Literally last-minute: they were about to close Blackwell's on Christmas Eve as I bought them. Fortunately, they were also marking everything down to half-price rather than £2 or £3 off :-)
Tags:
Pantos
I went off to an SF convention a while back, and the guy who played Sinclair in "Babylon 5" did one session. I was impressed by how he started: there was a bit of fiddling around with a microphone, then he just put it aside, saying "I don't need this, I am theatre trained!" And he did do a great job of projecting his voice.
As for pantos in general, one thing that surprised me recently were all the posters for "Dick Whittington" (the big Croydon pantomime). They've got Lucy Benjamin as the main star; apparently she was in "Eastenders", although I remember her from programs like "Press Gang". Anyway, I assumed that she'd be playing principal boy (or whatever the term is), i.e. putting on the tights as Dick Whittington himself. However, she's apparently playing Alice Fitzwarren (who?), and it's only some of the posters which even mention the guy playing Dick (some local DJ). Looking at other adverts I've seen (e.g. in Oxford), I think the Croydon panto is unusual in this respect, but have you seen other places moving in this direction?
Re: Pantos
Re: Pantos
Not that I endorse casting "celebrities" in pantomimes to sell them though.
Re: Pantos
As for the celebrity aspect, my experience is a bit skewed here because that was always the case when I went to pantos as a kid; I remember that Christopher Biggins would go dashing through the seats (in character) but stop to sign autographs on the way. I was quite surprised when my old flatmate told me that most pantos don't do that.
Re: Pantos
no subject
I wonder whether there's a paper waiting to be written that picks up the Haskellite monad transformers and ... I dunno ... simplifies it using the Yang-Baxter viewpoint. It seems like it should be doable.
It also seems like if we could do this properly, introducing all the necessary changes into Haskell' or something, monad transforming should be possible to do a lot better, easier and more obvious than it is done now.
no subject
Research
As for the main paper, I got a bit lost when you started talking about monoids in the first paragraph, so I didn't read through the rest (sorry).
Re: Research
In some sense, when you're dealing with objects of a category, all you really care about is whether things are isomorphic: equality is asking too much, and irrelevant anyway.
no subject
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