September 8, 2013

Future as a function of the past

Himanshu Kateja uploaded a status today, 
"the future is independent of the past, given the present" - Andrey Markov, 1856-1922
Food for thought - aisa sirf theory mein hota hai

This has prompted me to think about it & I have come to the realisation that the past affects are future to a varying degree depending on the time difference between the past & the future.
P. S. : present is a past for the future. So present by itself is already affecting the future as a past.

f(t) = f(t-$t)•e^(-$t) + c(t-$t)f(t-$t)

Where $ = delta (a variable time difference measured backwards from now) 
c(t-$t) is special relation function. For eg. If this the college entrance time, then the c function of t-$t = entrance exam time becomes significantly important for your present.

What I am basically trying to say is, that the dependence of any time on the past reduces with the time difference between the past & the said time, but for special events dependent entirely (or majorly) on a specific point in the past, the relation with the particular time in past may have a peak.
& $t is a variable time difference, so all previous value of function f at past times are considered.
Also the present is being determined by the past, to a certain degree, & the future is being determined by the present which is in turn affected by the past.
(considering a general event, for which c = 0) However due to the repetition of the exponential reduction, the dependence of the future on the past is much lower than either of the following two :
1. Dependence of the present now on the said past.
2. Dependence of the future on the present now.

So, my dear friend, start working in the present instead of futilely musing on the past because the effect, on future, of what you are doing right now is much higher than what you did in the past.



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