But the photo serves to tell my story from the 9th Congress on Logic Methodology and Philosophy of Science that happened in Uppsala, Sweden in 1991. I had just finished my PhD and submitted a short abstract about the thesis, actually about a development of the thesis, the work with Martin Hyland on Full Intuitionistic Linear Logic (FILL). I presented my abstract thoroughly convinced that both Linear Logic and Category Theory were the best things in the world, since sliced bread, and that everyone in the audience would know it and agree with it. When I finished, a Swedish (I assumed) professor asked me: So this is all very well, I can see that the mathematics is neat, but if this is logic, how do you explain what your "par" is to a man in the street?
Well, I didn't know to reply to him then. And I didn't know this was Professor Martin-Loef. And in some ways, I still do not know the best answer for his hard question. (I had thought he would like FILL, given FILL's commitment to intuitionistic linearity).
Later on, when he visited Brazil, we took a long walk, chatting about logic, the universe and everything in Jardim Botanico. Prof Martin-Loef really appreciated our Botanical Gardens and would go there everyday before doing any work at the University. I really wish that I had had more time to ask more questions, but I had young kids to look after and I have never been very good at grabbing the right opportunities.
I am hoping to use some of 2022 to think and write about the answers I have, so far. It is all about games, after all!
In the human world a game might be a safe learning experience, in maths it's usually a bounded and logical simplification of competition : by enforcing fixed rules and appealing to fixed symmetries or assuming logical behaviours - a game boils down to filtrations about updating expectations .. I think they're very different meanings of the same word. It sounds like this man doubted their own ability and asked you about 'par' either as a reflection or a plea for help or antagonistically. In my life I find that hard topics tend not to have cute "man in street" analogies .. so instead I bore my mother with technical details - she says "yes dear I'm glad you're happy" .. but trying to explain something does seem to activate a different type of thinking.
ReplyDeleteDid you come across Eugenia Cheng's X+Y and Congressive approach?
Hi, sorry for the delay in replying. Yes, I do know about Eugenia's approach. But no, I don't think his question was antagonistic or that he doubted his own abilities. I think it was a genuine question and one that is important in life. but as I said in the post, more about this will be forthcoming later one! thanks for engaging.
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