Preamble:
Most of us (atleast most engineers and scientists!) know that a vector needs two points and a direction. Attributing time to be a unidirectional entity, we can assign vectors to represent a change. So, in principle (anybody have enough enthusiasm to take up this problem?), all that has happened between any two given time line can be expressed by a finite (or infinite) set of vectors.
In other words, the world is a state machine (i dont know if its finite or infinite) which moves from one state to the other as the time progresses. Interestingly, this state machine is self contained. Also, this state machine does not have unreachable states (have u seen the warning "unreachable code" in your programs?). Given sufficient time, it can move to any state.
With the above arguments, we can define the following Theorem:
Theorem: Change, which is axiomatically understood to be a continuous phenomenon is nothing more than a bunch of vectors in an infinite dimensional vector space!
Motivation:
Betterment is the drive that all creatures strive for, all through their lives. Change has always been with us since the absolute zero occured (say, big-bang!). Identifying change happens only by comparision. And to compare, we need atleast two comparable things!
CRUX:
The next question is, what does all this have to do with history?
A precise answer would be that, history provides a finite set approximation to the possible infinte spaces that the world assumed at some earlier point in time (possibly hundreds of years ago!). Historians are those able people who can aggregate and infer from the traces that the world leaves as it progresses in time.
We know the current space in which the world lives (this is still an ideal assumption!), knowing history helps us define vectors that can tell us where the whole world is leading to in general. It could help us define our roles better thus give a nobler purpose for life.
Subscribe to:
Post Comments (Atom)
2 comments:
Hmm.. After our coffee table discussions, i am now in a position to understand your post. First of all, let me disagree with you in placing change as the fundamental parameter of interest. The universe can be represented as a vector in an infinite dimensional vector space (technically, it has to be Hilbert space). The vector changes with time and the tip of the vector as a function of time gives the state trajectory which describes the "history" of universe. The usual way to address time is to consider it as a real parameter. Whether time is continous or discrete is not understood yet. Assuming time to be continuous, we see that at each instant the universe is in one state space (infinite dim ofcourse). The space itself changes at each instant. This is similar to completely erase and re paint the screen (You are in better shape to understand this analogy:-)).
While your theorem about change is true i don't see any way as to how it would help in understanding universe. Ofcourse, you would monitor the state (of which we do not have complete information) at each instant and try to infer what might have been the state previously, under certain restricted conditions.
When you say historians approximate the infinite dimensional space by a finite dimensional space it doesn't sound nice to my ears. There is no approximations involved. What the historian does is only hypothesise based on certain data. His hypothesis has nothing to do with the dimensions and other technical stuff :-). In a sense, you are trying to compare oranges with apples.
Let's see what you will follow it up with.
Interesting ideas, but what is the guarantee that
(a) Time is linear and
(b) Time exists - it could be a concept that seems to exist due to our limited capacity at understanding the true nature of the universe...
Post a Comment