In the world that you can see and feel, how many dimensions can you represent? One? Two? Three? I can forgive you if you can only think of three dimensions.
It is a fact that the earth moves in space. If you don't accept it, DROP DEAD! Now suppose you were standing at the bus station waiting for your morning ride and you have a box with you. You got tired and you put the box on the ground where it looks "still". Good thing the bus isn't late and you only waited five seconds.
The simplest dimension that you can represent your box with is a 3D vector (length, width, height). However, since the earth is moving in space, you can add time as another dimension wherein you can compare the location of your box in space with every tick of the clock. It is also a fact that your box has weight (caused by the gravitational pull of the earth) and there are some boxes wherein the weights are the same but the sizes are different (e.g. S, M, L, etc.). The amount of matter that it occupies in space (relative to size) is also known as mass. Now, is it possible to append these three attributes that your box has to the vector I just introduced a while ago? The answer is affirmative and thus an ordinary box can be represented as a vector with dimensions (length, width, height, weight, mass, time). Now, that's six dimensions for crying out loud. That's 6D!!!
During interviews, I am always asked "So what was your research all about and how is it applied?" How am I going to impress my interviewer about vector spaces of dimensions 40, 42, and 44 when my interviewer's knowledge is locked up in a 3D world?
Tuesday, November 02, 2004
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