My comment was within the context of the first post by Arya where the proposal was for simulation as opposed to experimentation. I concur with negi's point that to replace experimentation with simulation is to miss the importance of experimentation (a basic failing in the education system, IMHO- it is driven too much by theory).shaardula wrote:this is also correct. but to make this point you reduce the value of simulation. i used to be a TA for courses in controls, probability and stochastics.The core idea behind an experiment is to let nature teach you. Using a program in lieu of an experiment is akin to reading about something rather than doing it.

I agree that there is a need and place for simulation, I've done a lot of them (note that the simulation you talk about- stochastic modeling, is quite different from the simulations Arya referred to) but within the context of Indian school education, I think experiments should be emphasized a lot more. And the experiments dont have to be complex, there is a lot one can learn with very simple things like rolling a cylinder down an inclined plane and trying to calculate the velocity (one has to account for rotational dynamics, friction and, hey, statistical differences in the experiment, to come up with explanations), or how high a ball will bounce the second time (depends on height and other factors such as material, shape of ball etc. all neatly rolled into co-eff of restitution eh?)

True, but if you pose a simple model for a practical problem and find that your answer does not match the experiment, you will go looking for the source of the difference in solution...and that will tell you something about the system that you did not know before. That is the learning that comes from an experiment, which will never come from textbook reading. You also learn how to trouble-shoot unknown systems- the most important lesson from an experiment, IMHO.well that way textbook problems are also simulations.

The point you bring up (x=2, y=3 vs. using a series), I see that as a matter of the level of accuracy needed from a theoretical solution. As an example, if one wants understand projectile motion i.e. where will a projectile of mass 'm' and velocity 'v' land- one can write a set of equations of increasing complexity, starting with simplest ones first and checking the level of error between theory and experiment. If the error band is large, you try to go beyond just mass, initial velocity and acceleration due to gravity and incorporate more and more of the real-world physics like wind speed, direction, temperature, projectile shape- (some may be second-order effects and some not ). Taking each of these into account progressively complicates the models and decreases the error, but you are learning from nature. How accurate is accurate enough is a judgment that the student can always make during the experiment.in real life there are no well posed problems. there are no problems like x =2, y =3 find z = x + y. you go around normal life without ever formulating the problems you have as a geometric series. and yet solving z = x + y is rewarding.