Tuesday, October 7, 2008

Spin the yarn

The following is result of a heated argument, a train journey and ample amount of leisure.


Mathematical truth, I think is the innate pattern embedded in whatever math we have discovered and would discover in future. What is required is to acknowledge the fact that, that math is so much more than just numbers, additions and calculus. There is a reason why we have primes just like there is a reason that there is a pattern found among them, or rather lack of it.
I have always found differential equations the most fascinating of all. If one notices, they are extremely powerful. They circumscribe a whole lot of things about a system in the most precise form.
Now, thats elegant. Morever, they are "complete", they describe the system for all boundary conditions and intermediate states between them. If ever, the equation for the universe is found, I am biased enough to believe that it would be in the form of a differential equation ( :D ).
I wonder, what would be the differential equation of emotions like love ? Or would they appear as just boundary conditions ? Temporary constructs of time-bounded variable ranges, stagnating a system to a certain state. If that is the case, there isnt much hope, you see ! One cannot be in love forever.
Maybe the differential equation is such that, towards the end of a life span, it just settles itself, from transient state to a stable state and the boundar conditions dont really matter in the end.
What if one wants to attain this state of "equilibrium" prematurely ? Is there an external way or more importantly is it worth it ? Maybe an equation's "purpose" is only fulfilled if it experiences all the bounday conditions. In that case, the extreme states that it experiences are justified. Is it possible to be ambivalent, while experiencing a powerful emotion ? Or maybe getting swepty away in it, is a part of the plan ?
That raises the question, that what is this darned "plan" anyways ? Is it conceitous to think that i play some part in the whole fabric of the universe ? Or am I an independent unit, which just experiences its sets of boundary conditions and then perishes ? But then if the tool that describes me is same as the tool that describes the universe, then a huge power is vested in each of us. Somehow, each of our differential equations somehow fit in infinitismely into the equation of the universe, maybe it justifies the phenomenon of butterfly effect.
Now with this insight, what is the purpose of each "differential equation" ? And why is that the knowledge of this purpose is not known to us ? Or is it ? present but not known. Thats tricky ! Its like a new math to describe the existing one.

There has to be a pattern in how we think and the things we devise to describe what/how we think. How many times have we felt that there is something huge, incomprehensible and somehow everything is related in some unknown way ? Is finding that relation our purpose ? But not everyone can learn or choose to learn advanced math, and its stupid to establish math as the only tool.
Considering only the group of lunatics who hold that mathematical truth as the only truth, one can hypothesize that purpose is to find the relation between my "equation" and the "equation" of the universe. But what if I dont want to actively pursue the so called "purpose" ? What if i deal in math, but dont neccessarily think that there is such relation or even if there is, dont neccessarily care what it is ? Does it make me "purposeless" ? Or is there a function estimator, that infinitismely defines the purpose, defining just a small step at a time, something like slowly zooming out and in the end viewing the complete picture. In way, there is a purpose hidden in even being "purposeless".
I am grade A lunatic.

Statuory Warning : Curosity and leisure are a dangerous combination.

6 comments:

UserDeleted said...

Extremely thought-provoking post and well written too...

"What if one wants to attain this state of "equilibrium" prematurely?"

I was talking to (though in laymen's language :) ) a good friend about relationships among people in general and I too had this very same question, of whether it is possible to sweep aside the transients in a flash. I don't know if it is.. but i think its highly unlikely. With this mathematical model, I think I can atleast conjecture that time is a factor in the transient terms of the equation.

Mathematics is beautiful isn't it? :)

Juggernaut said...

It is only in the mysterious equations of LOVE that any logic or reason CANNOT be found [:p]

('misquoting' John Nash in A Beautiful Mind)

Jyotika said...

@Rooju : Thats a very keen observation. Time is a very important factor in the equation, after its the fourth dimension of the universe ;)
Mathematics is beautiful, no doubt !

@Juggernaut :
Oracle: He doesn't understand them, he can't. To him they are variables and equations. One at a time each must be solved and counted. That's his purpose: to balance the equation.

Neo: What's your purpose?

Oracle: To unbalance it.

Oracle could easily represent "Love" ;)

UserDeleted said...

Also, I think the equations should have some variables of a Boolean nature.. that may explain the event-driven action-reaction sequences that exist, boolean terms that describe If-then-else structures. I wonder if there are differential equations on boolean variables. Its likely though, because derivatives are defined in boolean algebra.

Jyotika said...

@Rooju:
Umm, I beg to differ here. It can't have boolean variables, because uncertainity is ingrained in the universe even at the sub-atomic level. Though your point on why the boolean variables should be used is correct, as you said the event-driven if-then-else sequences.
Imagine all these transitions between the states but within a certain probabilistic framework. "If" transits to "then" ,but not with a boolean value 0 or 1, but with a certain probability. Machine Learning already has at least two models i know of which already uses this technique, HSM and MDP's.

UserDeleted said...

Ok.. I think I need to learn ML for better insights into this. :)

And I forgot to add in my previous comment, I also believe entropy S should factor in the equation, don't you think?