Orbis non sufficit
Wednesday, August 10, 2005
Mathematics
Theoretically, Maths is the most logical science around. Everything in it is based on strict rules, there is no room for "theories", only "theorems". Things are either true or they aren't, its not like in physics or something where you can have a great theory that seems to always work only to have it fall apart when some new situation or data comes along. We still use theorems developed thousands of years ago and any new ones that are developed will surely last just as long.
Still, solving mathematical problems is something of an art. While there is a logical process to it, certain problems require 'intuition', that spontaneous, almost creative response in your brain that clues you in to what must be done. Especially problems in which you have to make some crazy substitution or whatnot so that the problem is transformed into something more solvable. I suppose a lot of the more common ones get ingrained into your brain such that they are easy to recognise, but really it just means your spontanteous recognition of what must be done comes more quickly.
Now that I think about it, I would say that a lot of logic problems are like that. Maybe even logic itself is something of a creative art. How many problems do you sit about staring at, making no progress whatsoever for ages, when all of a sudden the correct method or sometimes simply the answer just appears in your head? Perhaps it's a tribute to the somewhat fantastic way in which our minds work, or the order that can suddenly come from the utter chaos that makes up our conscious and subconscious thoughts. A computer can get the answers simply by following a strict routine, some process that will slowly yet surely converge upon the answer. Perhaps on some level we do this too (I'm talking about problems complex enough that you obviously can't do this consciously), and if we don't, how do we actually arrive at some of the sudden conclusions that we do? If they are right they can be logically justified without much trouble afterwards -and I'm not saying they are always right-, but the way the mind leaps to the answer is somewhat mysterious.
There are a lot of mysterious things in our universe though, even benign things most people take for granted, like the workings of the basic forces that hold the universe together (The nuclear forces and the electrostatic and magnetic). The way two like poles of a magnet repel each other is pretty much friggerty magic, despite all that we know about the behaviour of such things. Though matter itself is held together by even more magical forces that we know far less about. The universe is really a pretty damn crazy place, for all the order that seems to have emerged from it on the large scale. I doubt that we as humans will ever really be able to comprehend the universe on its most basic levels. Manipulate and bend to our own ends, sure, but comprehend? No. Kind of scary.
-Addendum - I just discovered this interesting little thing on the web:
BlogShares
It's an online "stock market" simulation game where you 'buy' shares in real blogs, with the value of the blog being based on how many incoming links it has. It seems more complicated than that but it looks like it might be amusing. I might have a more serious look later on. I happpened by it when I was searching for "chilledfruit" on google to see if I could find my header picture anywhere and instead found the page in that game that has stock market info on my blog :p.
My blog is currently valued at B$4,491.33 apparently.
Also, just added Scotty's blog to my list for your navigating pleasure. Well, mostly for mine, but I'm generous and will also allow you to use my links if you so desire.
Theoretically, Maths is the most logical science around. Everything in it is based on strict rules, there is no room for "theories", only "theorems". Things are either true or they aren't, its not like in physics or something where you can have a great theory that seems to always work only to have it fall apart when some new situation or data comes along. We still use theorems developed thousands of years ago and any new ones that are developed will surely last just as long.
Still, solving mathematical problems is something of an art. While there is a logical process to it, certain problems require 'intuition', that spontaneous, almost creative response in your brain that clues you in to what must be done. Especially problems in which you have to make some crazy substitution or whatnot so that the problem is transformed into something more solvable. I suppose a lot of the more common ones get ingrained into your brain such that they are easy to recognise, but really it just means your spontanteous recognition of what must be done comes more quickly.
Now that I think about it, I would say that a lot of logic problems are like that. Maybe even logic itself is something of a creative art. How many problems do you sit about staring at, making no progress whatsoever for ages, when all of a sudden the correct method or sometimes simply the answer just appears in your head? Perhaps it's a tribute to the somewhat fantastic way in which our minds work, or the order that can suddenly come from the utter chaos that makes up our conscious and subconscious thoughts. A computer can get the answers simply by following a strict routine, some process that will slowly yet surely converge upon the answer. Perhaps on some level we do this too (I'm talking about problems complex enough that you obviously can't do this consciously), and if we don't, how do we actually arrive at some of the sudden conclusions that we do? If they are right they can be logically justified without much trouble afterwards -and I'm not saying they are always right-, but the way the mind leaps to the answer is somewhat mysterious.
There are a lot of mysterious things in our universe though, even benign things most people take for granted, like the workings of the basic forces that hold the universe together (The nuclear forces and the electrostatic and magnetic). The way two like poles of a magnet repel each other is pretty much friggerty magic, despite all that we know about the behaviour of such things. Though matter itself is held together by even more magical forces that we know far less about. The universe is really a pretty damn crazy place, for all the order that seems to have emerged from it on the large scale. I doubt that we as humans will ever really be able to comprehend the universe on its most basic levels. Manipulate and bend to our own ends, sure, but comprehend? No. Kind of scary.
-Addendum - I just discovered this interesting little thing on the web:
BlogShares
It's an online "stock market" simulation game where you 'buy' shares in real blogs, with the value of the blog being based on how many incoming links it has. It seems more complicated than that but it looks like it might be amusing. I might have a more serious look later on. I happpened by it when I was searching for "chilledfruit" on google to see if I could find my header picture anywhere and instead found the page in that game that has stock market info on my blog :p.
My blog is currently valued at B$4,491.33 apparently.
Also, just added Scotty's blog to my list for your navigating pleasure. Well, mostly for mine, but I'm generous and will also allow you to use my links if you so desire.
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