Fondazione Musica per Roma presenta
La matematica dei giocolieri
Conferenza-spettacolo di Allen Knutson
un evento di Festival della Matematica 2008, 15 marzo 2008
 
Introduce Giulio Giorello  

La passione per l’algebra lineare ha portato Allen Knutson a laurearsi per la seconda volta alla Università di Princeton – aveva conseguito la prima laurea alla University of California di Santa Cruz – presentando una tesi di geometria simplettica grazie agli studi fatti sulla congettura di Horn. Si laureerà una terza volta presso il Massachusetts Institute of Technology. Da universitario aveva frequentato il  Caltech, la New York University, e il Budapest Semesters in Mathematics Program. Dopo il post dottorato della National Science Foundation presso la Brandeis University con Gerald Schwarz, nel 1999 Knutson si è trasferito alla University of California di Berkeley dove attualmente è professore associato. Ha ricevuto una borsa di studio estiva presso la Clay University e una borsa di studio della Sloan. È stato il detentore del record del mondo della International Jugglers’ Association dal 1990 al 1995 nella specialità delpassing con palline (il suo record era di 12 palline), nonché il prestigioso Levi L. Conant Prize assegnatogli nel 2005.
Il record man del Juggling, il matematico Allen Knutson si esibirà per il pubblico del festival della matematica accompagnato dalle suggestioni di Giulio Giorello. Il Juggling é una pratica millenaria, ma è soltanto in questo secolo che esso ha affascinato ed interessato scienziati e matematici. Durante gli ultimi decenni numerosi sistemi di notazione numerica sono stati sviluppati per semplificare e spiegare tricks ai giocolieri di tutto il mondo. Il sistema che ha riscosso maggior successo e diffusione è stato il siteswap, elaborato nel 1985, quasi contemporaneamente, e a conferma dell'interesse scientifico diffuso per il juggling.
“Per spiegare veramente uno schema di juggling, l’ideale sarebbe quello di riuscire a descrivere la posizione di ogni muscolo del corpo del giocoliere in ciascuna frazione di secondo, compresa quella in cui pronuncia la sua battuta. Poiché sarebbe troppo lungo da scrivere, dobbiamo semplificare le cose optando per: descrivere solo alcuni schemi, non tutti; commentare alcuni aspetti di uno schema. Il primo punto è un po’ infelice, fortunatamente riguarderà soltanto il vanilla siteswap; il secondo invece presenta meno problemi perché se abbiamo la sensazione di aver trascurato qualche aspetto importante dello schema potremo semplicemente aggiungere qualche trucco, senza dare nell’occhio. L’idea che sta dietro il siteswap è quella di seguire la traccia dell’ordine in cui le palle vengono lanciate e prese. Poiché in qualsiasi tipo di juggling, quello che si fa è lanciare e prendere le palline in un certo ordine, ci sarà sempre un qualche siteswap che potrà descriverlo. È pur vero però che se quello che ti interessa di più è da dove a dove le palline vengono lanciate (come nel Mills’ Mess), allora questa sarà una descrizione parziale non molto soddisfacente. Finora abbiamo parlato di come prendere uno schema e cercare di descriverlo. Un altro obiettivo può essere quello di prendere una descrizione e cercare di giocolare in quel preciso modo. Poiché abbiamo stabilito che è impossibile tenere traccia di tutti i movimenti di uno schema, allo stesso modo è probabile che non esista un’unica maniera per mettere in pratica la suddetta descrizione. A quanto pare nel siteswap esiste uno standard; purtroppo, è ormai invalsa l’abitudine di definire siteswap solo gli schemi che rispondono a questo standard. Così, la gente dice Ecco, questi sono siteswap e quegli altri no, perché non rispecchiano lo standard. Sarebbe meglio dire: Quel lancio è talmente unico che definirlo siteswap equivarrebbe a darne una descrizione riduttiva…” Allen Knutson      


Intervista ad Allen Knutson a cura di Anthony Trahair  

How did all this siteswap business start?  
It started many times that many people have independently discovered it, and then often found out that it was already known and that it was siteswap. It's very simple in that sense it's sort of the minimal solution to the question of how you'd mathematically model juggling. There were two groups of people in California who came up with it and they were vaguely related, in that they'd had some conversations on it, but that was completely independent from the people in England that came up with it at the same time in 1985. I wouldn't be at all surprised if there were other people that knew about it many years before and didn't get publicised enough and there names have been lost in History. The numbers of jugglers has been increasing so vastly since the mid seventies that perhaps only by 1985 was there a critical mass that it could take hold and remain known.  

What was the reaction of the juggling population to siteswaps in 1985?  
This answer is actually different depending on the continent. I was already giving workshops on siteswaps in juggling conventions in the late 80's and what I found was often a rather hostile reaction in the US of people that would say "I wanted to juggle so I didn't have to think about mathematics..." or "you're taking all the fun out of juggling..." and such. I definitely got a more friendly reaction in Europe where I didn't meet such a seriously entrenched anti-intellectualism. Initially it was "who is this strange beast and what are the weird things that he's doing. And then for many years it was "yeah, well I've heard of it but never really understood it". And now for some years it "yeah, I understand that but I don't really specialize in it, I can do a few of the basic ones but I haven't really worked on them". There are of course there are many more people that are really very good at them, much better than myself.  

Do you think that people just switch-off and say this is mathematical I don't understand it, or do you really think that it's difficult to understand?  
I think it's the first but very often you and get through there defences by showing them a fairly simple one and saying "now isn't this a lovely little pattern?" I could spend half an hour describing it to you in English or I could just say that it's 52512 or 661515 that one in particular I did see a full page explanation in Juggle magazine, 661515, from the early 80's where they say it's very hard to explain these things... there were 8 pictures and in fact they were in the wrong order, it was just that difficult to convey them before siteswap.

How would you say that siteswaps influenced juggling in general after the initial aversion?  
If we talk about juggling that the public sees that is on the stage I have started to see in the last 10 years people performing things that I think of as "that's a siteswap" rather than just a trick that's something that somebody found out on paper first. What I think siteswap is most useful for and where it's really difficult for humans to do without the mathematical training first, that is just for siteswap, is transitions. Of saying I'm in this pattern and I want to go to that pattern without having to catch everything or without having to do some boring pauses in between. It's really here that siteswaps have a great use.

For example from cascade to shower?  
For example, right. I've collected talking to a number of jugglers transitions from 5 ball cascade(5's) to shower(9's) and there's 678(9)'s or 7892(9) or there's this really beautiful one 77929192(9) very special things clearly siteswap influenced.  

Do you have anything else you'd like to say, about what you're going to talk about this evening...  
I'm extremely excited because at the end of the talk I shall be giving a little bit on recent mathematical developments that are juggling related. I'm more of a mathematician than a juggler, one might say that I'm a better juggler than mathematician but one of them earns me money and the other doesn't. It's been really exciting for me to see things in mathematics that I can understand with difficulty and with work and then say oh actually that is an aspect of juggling patterns that I studied years ago when I was first learning about siteswaps and I'll be talking about that near the end of my talk tonight.