Your random joy of the day

Combining high amounts of sleep deprivation and THC over the last few days, always a cool mixture.
 
which green hallucinogenic nectar of mathematics would this be?

+1 - curious as well.

The course is on category theory, but we'll be emphasizing abelian categories and introducing (n,k)-categories and (∞,1)-categories early on. (Category theory is notable for many things, including being called 'general, abstract nonsense' by other pure mathematicians and even many of its own practitioners.)

The subject is very new - category theory was first developed in a 1945 paper and developed heavily, mainly by algebraic geometers and algebraic topologists, over the next couple of decades. At some point one geometer (Grothendieck) came up with a sufficiently general redefinition of *practically everything* that another pair of mathematicians (Lawvere and Tierney, who seemed to be algebro-topologically minded but with mathematical logic training) generalized further into a concept that can encode just about everything we would expect a 'universe' to have.

For a quick summary of just how absurdly powerful (and scary) the language can be... algebraic geometry began as the study of the simplest possible invariants (relatively simple algebraic quantities) of the simplest possible curves and surfaces (those defined by polynomial equations - the circle, for example, which is cut out by x^2+y^2=1 in the plane), and Grothendieck turned it into a monster that seems bent on (and capable of) taking over almost all other mathematics by force. He threw out the curves and surfaces themselves, replacing them with purely algebraic devices representing them (ideals of a ring, which can be thought of as 'generalized numbers' or 'generalized functions') and then generalizing even that viewpoint by considering an individual object in terms of *every mapping from any other object into it*. (If this does not sound insane, you might just be a potential algebraic geometer. Run.) In order to handle the new invariants that were now within easy reach, he also had to replace the usual notion of a space with what is now called a Grothendieck topos, and these were the first examples of what are called elementary topoi - things that have enough structure and depth to act as universes in which mathematics can be done. From what I understand, Grothendieck is now living in a small hut in the Pyrenees, where he alternates between sanity and coming up with ideas like 'eating nothing but dandelion soup' (fortunately prevented by the villagers near him) and selling his own... erm, fertilizer.

Jeff
 
The course is on category theory, but we'll be emphasizing abelian categories and introducing (n,k)-categories and (∞,1)-categories early on. (Category theory is notable for many things, including being called 'general, abstract nonsense' by other pure mathematicians and even many of its own practitioners.)

The subject is very new - category theory was first developed in a 1945 paper and developed heavily, mainly by algebraic geometers and algebraic topologists, over the next couple of decades. At some point one geometer (Grothendieck) came up with a sufficiently general redefinition of *practically everything* that another pair of mathematicians (Lawvere and Tierney, who seemed to be algebro-topologically minded but with mathematical logic training) generalized further into a concept that can encode just about everything we would expect a 'universe' to have.

For a quick summary of just how absurdly powerful (and scary) the language can be... algebraic geometry began as the study of the simplest possible invariants (relatively simple algebraic quantities) of the simplest possible curves and surfaces (those defined by polynomial equations - the circle, for example, which is cut out by x^2+y^2=1 in the plane), and Grothendieck turned it into a monster that seems bent on (and capable of) taking over almost all other mathematics by force. He threw out the curves and surfaces themselves, replacing them with purely algebraic devices representing them (ideals of a ring, which can be thought of as 'generalized numbers' or 'generalized functions') and then generalizing even that viewpoint by considering an individual object in terms of *every mapping from any other object into it*. (If this does not sound insane, you might just be a potential algebraic geometer. Run.) In order to handle the new invariants that were now within easy reach, he also had to replace the usual notion of a space with what is now called a Grothendieck topos, and these were the first examples of what are called elementary topoi - things that have enough structure and depth to act as universes in which mathematics can be done. From what I understand, Grothendieck is now living in a small hut in the Pyrenees, where he alternates between sanity and coming up with ideas like 'eating nothing but dandelion soup' (fortunately prevented by the villagers near him) and selling his own... erm, fertilizer.

Jeff

And people say learning is boring. Psssh...I loves me some knowledge:headbang:
 
Ordered a meal for one deal thing from a local curry place, got the meal for two for the cost of the meal for one.

No complaints, I haven't eaten enough lately.
 
The course is on category theory, but we'll be emphasizing abelian categories and introducing (n,k)-categories and (∞,1)-categories early on. (Category theory is notable for many things, including being called 'general, abstract nonsense' by other pure mathematicians and even many of its own practitioners.)

The subject is very new - category theory was first developed in a 1945 paper and developed heavily, mainly by algebraic geometers and algebraic topologists, over the next couple of decades. At some point one geometer (Grothendieck) came up with a sufficiently general redefinition of *practically everything* that another pair of mathematicians (Lawvere and Tierney, who seemed to be algebro-topologically minded but with mathematical logic training) generalized further into a concept that can encode just about everything we would expect a 'universe' to have.

For a quick summary of just how absurdly powerful (and scary) the language can be... algebraic geometry began as the study of the simplest possible invariants (relatively simple algebraic quantities) of the simplest possible curves and surfaces (those defined by polynomial equations - the circle, for example, which is cut out by x^2+y^2=1 in the plane), and Grothendieck turned it into a monster that seems bent on (and capable of) taking over almost all other mathematics by force. He threw out the curves and surfaces themselves, replacing them with purely algebraic devices representing them (ideals of a ring, which can be thought of as 'generalized numbers' or 'generalized functions') and then generalizing even that viewpoint by considering an individual object in terms of *every mapping from any other object into it*. (If this does not sound insane, you might just be a potential algebraic geometer. Run.) In order to handle the new invariants that were now within easy reach, he also had to replace the usual notion of a space with what is now called a Grothendieck topos, and these were the first examples of what are called elementary topoi - things that have enough structure and depth to act as universes in which mathematics can be done. From what I understand, Grothendieck is now living in a small hut in the Pyrenees, where he alternates between sanity and coming up with ideas like 'eating nothing but dandelion soup' (fortunately prevented by the villagers near him) and selling his own... erm, fertilizer.

Jeff

My brain just leaked out of my ear.

:lol:

Math is fascinating to me, yet I know *NOTHING* about it. It's an entire language of numbers and equasions - pretty cool man!
 
Not smoking weed for a while. Needed a change. Forgot what it was like to be completely sober! While I still love weed, and will smoke it on occasion, I no longer wish to smoke it day-in and day-out. It's nice thinking super clearly and actually being able to explain things the way I want to and in a coherent, organized manner. Not 'grabbing' odd, or the wrong words in an attempt to make my point (which projects an "I'm stoopid!" image, which I am not, I have had a great education thanks to my employer). Things actually make sense to others when I'm talking with people about science, religion, psychology and philosophy now, and not just to myself because I'm trying to find the words and phrases I need to explain something cogently. haha. I never really noticed how much my thought processes were hindered by good ol' MJ. Not in a super-retarded way, but it made me very quiet and difficult to express my thoughts.

While I did take a single toke from my vaporizer the other night before bed, I was still able to think clearly and not 'retracing' my steps. The inhibiting effects it has on my thinking must have been 'stacking up' over the last 7 years of smoking 3-4 times a day. I wonder how I'll feel in another week. Fuck.

Lately, I've watch many of my friends all in denial, trying to rationalize on how MJ affects them, while I clearly see the effects it has on them (they smoke ALL DAY LONG). They compartmentalize these observations and totally deny it has anything to do with MJ (with an "OH SHIT" look on their face). Best excuse I've heard was "Oh, I'm just dehydrated and tired." Every day? The other day I watched a friend look like a complete retard at work rearranging his desk, and trying to talk to his supervisor. Moving the same objects 100 times, and taking 3 times as long to do a simple menial task. Watching him attempt to multitask was pretty funny as well. I totally feel like an ASS now for many of the things I've said and done (more like how I've said and done them, really). While I have always been able to function stoned, engaging in conversation, I realize, has always been my downfall while stoned.

Oh, I finally completely destroyed this creationist at work with his own (il)logical arguments because of this simple omission from my daily routine. He was fucking livid, because he thought I was wrong for the last year of our discussions, and he now realizes he has no basis for his ridiculous belief system (LDS). heh. I'm not hating on anyone's MJ use here at all, I'm aware MJ affects different people in different ways, and now how it affects me.
 
My random joy of the day would have to be enjoying real coffee from a real coffee machine at home, none of that instant stuff.
It tastes better and perks you up heaps better than instant coffee.
 
It's nice thinking super clearly and actually being able to explain things the way I want to and in a coherent, organized manner. Not 'grabbing' odd, or the wrong words in an attempt to make my point (which projects an "I'm stoopid!" image, which I am not, I have had a great education thanks to my employer). Things actually make sense to others when I'm talking with people about science, religion, psychology and philosophy now, and not just to myself because I'm trying to find the words and phrases I need to explain something cogently.

Great, now you have me wondering how many people think I smoke all the time... that's what I probably sound like sober.

Jeff
 
This topic is totally worth a bump.

New flat, new broadband, no more countryside speeds.

800mb file in 8 minutes as opposed to 12 hours. 20x as fast! woohoo!