Tuesday is going to be a killer paper. Linear Algebra. In linear algebra, we deal with the concept of a "vector space" (which I don't really understand that well myself). We deal with supspaces of vector spaces, namely, Euclidean N-space, column spaces, rowspaces, nullspaces, eigenspaces, what have you. In his introductory lecture on Classical Physics, the Stanford lecturer Leonard Susskind made a reference to, "an abstract space in which there is are only two laws of physics" (pretty interesting but I am unable to elaborate further, due largely to my lack of understanding for such abstraction).... 

Through it all, I realised one thing... That I have no inkling of what exactly a space is. 

So I wiki-ed it and I realised that the concept of space has been a rather hotly debated topic since the 1600s, maybe even earlier. Two giants of their time who argued as to what a space actually is, were Newton and Leibniz. Newton argued that space was absolute and independent of matter (meaning that there is a universal reference frame, see Newton's bucket experiment, which is pretty convincing). Leibniz on the other hand, regarded space as relational (meaning that the reference frame must always be pegged onto a particular object from which we want to take reference from).

According to wiki, Immanuel Kant's believed that the nature of space was "synthetic" (his working definition of the word "synthetic" still puzzles me, but I now it does not simply mean "man-made" as in the conventional sense). But Kant rejected both the Newtonian and Leibniz(ian?) view of space, concluding that space was not an objective feature of the world, but rather, an unavoidable systematic framework in which people organise their sensory experiences.

Well, I can see the sense in all their views, but these discuss the nature of a space. Not what a space is. After having a discussion with Jason, I guess we've come away with the working definition "for now" that a space is a kind of set. Like a bag that holds things. However (very intuitively), a space is a set that has certain rules, in which the things it holds must be a vector (which means spatially extended). Whether or not the bag has anything in it, it still exists (where in the event it is empty, it is known as a "zero space" or a null set"). Hence, wouldn't the word "general vector space" be slightly redundant? Because the word space itself says that the space contains vectors. 

It's not the best definition, and people may be inclined to disagree, but please, do share your thoughts. 

This is touching the more philosophical aspect of physics/mathematics already. Physics sure isn't easy. But it's definitely not uninteresting....