Re: [Phys-L] one variable at a time ... or not

[Larry Smith <Larry.Smith@snow.edu>]

On Jun 6, 2016, at 1:39 PM, John Denker <jsd@AV8N.COM> wrote:
> Therefore I find it quite strange to find statements in favor of
> changing only one variable at a time.
>
>   The OVaaT approach is favored by non-experts, especially in
>   situations where the data is plentiful and cheap.  It may be
>   that the mental effort required to conduct a complex multi-
>   factor analysis exceeds the cost of obtaining extra data, in
>   which case OVaaT might make sense.
>
>   OVaaT might make sense as a pedagogical /starting point/ but
>   never as an ending point.

I’m aware that changing one variable at a time is not an optimal strategy for finding extremal values of a function in a multi-dimensional space.  But isn’t that a different situation than the beginning physics student who is given a couple of simple harmonic oscillators and asked to determine which variables matter (and how)?  For a simple pendulum I have my beginning students vary the mass, length, and amplitude, one at a time; make graphs of the dependence of the period on these; and, along with dimensional analysis, try to deduce the formula for the period.  I can’t see this experiment being as instructive if they changed all the variables at once.  Each graph they make is a 2-D slice of the multidimensional function.  This seems pretty instructive at a couple of levels.

In the spirit of John’s comment above, I suppose I could add a comment at the end that there are many applications where changing just one variable at a time is not the best approach, so that OVaaT is not the ending point.

Larry