Scientific Method- Part 4

KISLAY WROTE:

Writing this after reading both your mails.

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Can you not describe your motion at every single instant of time?
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In what terms will I know it? In what terms will I describe it? Other than probably Saying "I'm moving damn fast!!!!!" which doesn't mean anything.That's what I mean when I say that understanding presupposes a
mode of expression.

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what do I do if I want to know its motion both in space domain and time domain simultaneously?
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Suppose you want to tell what an elephant looks like from front and behind.Can you say it using a single language construct? You will have to say it in 2 different statements.
Man you can know it but HOW WILL YOU SAY/EXPRESS IT? All external symbols and formulae are means to conveying that to-fro motion of the pendulum. You are falling into Capra's "map for territory".
Trap - thinking that symbols mean something independently of the phenomena they are attached to. They do not. They are a map using which you have to visualise the territory.

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Another point with the usage of mathematics for this approximation. Science in its attempt to make a discrete event as continuous as possible, introduces the concept of "dt" or 'delta t'. Science has not given a
scientific, mathematical definition of 'delta t'. The definition is of intuitive nature and to make it mathematical, have introduced the idea of limits. (tending to zero but not equal to zero. Is it not a proof enough of the inadequacy of science to explain phenomena?
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"Delta t" is a way of saying that however small a change is, maths can track it. Observe that the Final deliverables of maths, i.e., equations, don't have deltas in them.
V = u + at ---------- 1
may be derived using delta but as an 'end-user', you are free to enter any random time instant/interval in this equation. Delta T is way of modelling an arbitrary precision time interval.

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Can you not describe your motion at every single instant of time? When you are doing a scientific analysis, are you not taking snapshots at discrete intervals and then trying to construct a continuous picture out of it?
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Yes I am. And I can tell you that I am successful because now you can enter any value of t in Equation 1 and the answer would be correct. I would consider that damning evidence in favour of the scientific method!!!

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We both know that y(t)= A sin(w*t) is different from y(t) = A'cos(w'*t). When I say understanding it,I mean I should be able to able to identify that there is some difference between these two, without constructing their
equations.
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Without showing me the equation, what will you say? How would you convey to me the difference between the two?

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Can we define acceleration as something more than dv/dt?
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Well we definitely can!!!! All bike/car enthusiasts define it as 0 to 100 kmph in x seconds. Even here you see that all these guys need this figure to express how fast a bike is, and looking at this figure( the analog for physics equations), a bike enthusiast will know how slow or fast a bike is.