L’infini vu par Noémie July 17, 2009Posted by Alexandre Borovik in Uncategorized.
Les galaxies,Les rimes en* I*,
le pipi,Et puis………
Ne fait pas la comédie
Mais c’est joli l’infini…
Et puis c’est pas fini!!
(18 Mai 2000)
From Mathieu Marion July 17, 2009Posted by Alexandre Borovik in Uncategorized.
I do not know if this is of interest to you or not but here is a thought-experiment of mine, probably around the age of 7-8, for sure after 6 and before 10.
I started thinking about death and wanted to convince myself I would never die, instead of thinking about life after death… So I started thinking about an infinity in this way: first, I assumed that my entire life was only one dream in one night in another life where I am still the same person but could not fully realize that a full life goes on in each dream (an interesting point about personal identity, I guess). Now, that other life would be finite and have only a finite number of nights. So, I thought further that in each night there must be a finite number of dreams, encapsulating a finite number of lives. This was still short of infinity, so I started thinking that in each of these finitely many dreams of the finitely many nights, I would live a life that would in turn contain finitely many nights, which would contain finitely many dreams, and so on. I was not so sure that I was safe that way (i.e. that I would go on living forever), but I convinced myself that these were enough lives to live, so that even if the process would end, I would still have lived enough, and stopped thinking about it.
Two Streams in Hatfield July 6, 2009Posted by dcorfield in Uncategorized.
Brendan Larvor and I ran a conference – Two Streams in the Philosophy of Mathematics from 1-3 July. I thought I’d put up a post here for post-conference discussion.
In accordance with one stream’s policy of encouraging dialogue with real mathematicians, we invited Yehuda Rav (Paris-Sud), Michael Harris (Jussieu) and this blog’s very own Alexandre Borovik. For me two of the most interesting issues to emerge during the conference was Borovik’s ‘phantoms’ and Harris’s ‘avatars’. The first of these may occur when there is a question as to whether a certain entity exists. Even if it does not, it may transpire that some counterpart of this nonexistent entity exists elsewhere. The setting of finite simple groups is a rich environment for this phenomenon.
In the case of avatars, on the other hand, they all exist, but they indicate the existence of a not yet expressible universal object. Grothendieck’s theory of motives is the classic example, and indeed it was here that he coined the term ‘avatar’ to describe an instantiation of a motive in a particular cohomological setting.
What I’d like to know is what can be said about these phenomena. What is the right language to formulate them? Do we have earlier cases of avatars or phantoms which we now know how to express? Might it be possible to understand both phenomena in the same framwork? I.e., perhaps there may be avatars which happen not to exist, but for which existing fellow avatars act as phantoms.
So that’s a small taste of two of the talks. There were fourteen others. Personally, I was very pleased to hear Ivor Grattan-Guinness speak about ‘notions’, such as symmetry, convexity, and linearity, continually reappearing in mathematics. My own talk focused on duality, but I gave it a Cassirerian gloss as a ‘principle’.
If anyone would like to share their thoughts on the conference, please feel free.