Re:Interview with Terence Tao
by graycat on Monday September 29, 2014 @11:48AM
(#8383430)
For the thinking about SATs, there's a standard situation
not commonly discussed:
Get a lot of multi-dimensional, empirical data and find some
pattern, maybe an equation, that fits.
Okay.
But does this equation have to work in practice?
Not really: The empirical data may not have
actually represented all the possible dynamics
of the real system. So, when apply the equation,
might not have maintained some crucial conditions
that held when found and fit the data.
Or, e.g., looking at academic performance data
and SAT scores, etc., have a lot of multidimensional
data and might find a fit. But the data collected
might have been done with some unstated, unclear conditions and not have included all cases that could occur. So, this fit might
not hold when those conditions don't hold.
So, applying the fit in reality where the
conditions are free to change might
make the fit poor.
Or, if someone pulls too hard on the
electric power cord of their vacuum
cleaner, then they will have a broken
vacuum cleaner. Well, that would be true
for women like the mother of a girlfriend
I once had! But not for me! I just
did a little work with a screwdriver and
pocket knife and fixed the problem. Maybe
I impressed the mother of the girl!
I was 14, the girl 12, and the prettiest
human female I ever saw in person or
otherwise. Maybe it was good I
impressed the mother!
So, a condition of the good fit was that
I was that the user of the vacuum
cleaner didn't know how to
repair some broken electric power wiring;
that condition held for the mother
but not when she had a drop dead gorgeous,
sweet daughter with a boyfriend whose
father had long since been teaching
him about basic work with hand tools.
For the SAT scores, early on might argue
that so far in practice they really
did capture real, pure
academic ability. Even if that was true,
that need not mean that SAT scores really
have anything very important to do with
real, pure academic ability and that
some students, maybe most students,
could, with some additional conditions,
do well on the SATs and not have the
coveted ability.
Standard, old problem in multidimensional
data analysis!
Get a lot of multi-dimensional, empirical data and find some pattern, maybe an equation, that fits. Okay.
But does this equation have to work in practice? Not really: The empirical data may not have actually represented all the possible dynamics of the real system. So, when apply the equation, might not have maintained some crucial conditions that held when found and fit the data.
Or, e.g., looking at academic performance data and SAT scores, etc., have a lot of multidimensional data and might find a fit. But the data collected might have been done with some unstated, unclear conditions and not have included all cases that could occur. So, this fit might not hold when those conditions don't hold. So, applying the fit in reality where the conditions are free to change might make the fit poor.
Or, if someone pulls too hard on the electric power cord of their vacuum cleaner, then they will have a broken vacuum cleaner. Well, that would be true for women like the mother of a girlfriend I once had! But not for me! I just did a little work with a screwdriver and pocket knife and fixed the problem. Maybe I impressed the mother of the girl! I was 14, the girl 12, and the prettiest human female I ever saw in person or otherwise. Maybe it was good I impressed the mother!
So, a condition of the good fit was that I was that the user of the vacuum cleaner didn't know how to repair some broken electric power wiring; that condition held for the mother but not when she had a drop dead gorgeous, sweet daughter with a boyfriend whose father had long since been teaching him about basic work with hand tools.
For the SAT scores, early on might argue that so far in practice they really did capture real, pure academic ability. Even if that was true, that need not mean that SAT scores really have anything very important to do with real, pure academic ability and that some students, maybe most students, could, with some additional conditions, do well on the SATs and not have the coveted ability.
Standard, old problem in multidimensional data analysis!