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I woke up a few hours ago, but I'm just now getting my brain booted up. Mostly that was because of waking up to an incipient migraine. I've taken all the standard precautions, and I seem to have dodged that bullet, so now I can proceed with my normal wake up routine. After that, I suppose I need to knuckle down and do some writing since this is the only free time I have for it for the remainder of the week.
Jul. 5th, 2007
Facebookisms
Jul. 5th, 2007 02:26 pmI've just got a friend request from a Siegfried in Germany. I have a very bad memory for names, but I don't think I've ever known a Siegfried. I may have met one in 1990 when I was in Germany for a few weeks, but I don't think so.
Does everyone else get this out-of-the-blue friends requests from total strangers?
Does everyone else get this out-of-the-blue friends requests from total strangers?
Category Theory.
Jul. 5th, 2007 04:49 pmI have been making another attempt to understand Category Theory. This time I've managed to get as far as figuring out that what I simply don't understand is the basic definition of a category and its properties. I've now read the first few chapters of about a dozen different books which claim to be gentle introductions to category theory from various perspectives.
The trouble is that they ALL use almost the same language in their definitions and its very clear that the words they use don't mean what I think they mean. They say 'assign' in contexts where no assignment is occurring (or possible). They say a 'diagram commutes iff X' and then give a condition for X that, depending on meanings I assigned to undefined terms earlier on, is either a tautology or a contradiction. In other words, as far as I can tell based on the definition of a category, either all diagrams commute, or no diagram commutes.
This happens time and time again as I try to figure out what the heck the author MEANS when they write their definitions and before long I have this huge tree of possible interpretations, all of which are contradicted by the examples. Its extremely frustrating.
I don't suppose anyone on my friends list has gotten further in this pursuit and would be willing to help translate this stuff into language I can follow?
The trouble is that they ALL use almost the same language in their definitions and its very clear that the words they use don't mean what I think they mean. They say 'assign' in contexts where no assignment is occurring (or possible). They say a 'diagram commutes iff X' and then give a condition for X that, depending on meanings I assigned to undefined terms earlier on, is either a tautology or a contradiction. In other words, as far as I can tell based on the definition of a category, either all diagrams commute, or no diagram commutes.
This happens time and time again as I try to figure out what the heck the author MEANS when they write their definitions and before long I have this huge tree of possible interpretations, all of which are contradicted by the examples. Its extremely frustrating.
I don't suppose anyone on my friends list has gotten further in this pursuit and would be willing to help translate this stuff into language I can follow?