Re: [Phys-l] backwards units : entrenched usage

[Hugh Haskell <haskellh@verizon.net>]

At 10:25 -0500 05/28/2010, John Clement wrote:
> Then when students do math they are told that a ball is dropped from a
> bridge and accelerates downward.  The formula for the distance traveled in
> meters is y=4.9x when x is measured in seconds.  How far has the ball
> traveled after 2 seconds.  But often the problem is expressed without any
> reference to units.  Notice how the problem associates the units with the
> variables rather than with the constant.  So the problem is reinforced in HS
> math.
First, I hope that the formula you quote here is really y = 4.9x^2, 
but that's not what I'm writing about.

I note that this way of expressing formulas is common in engineering 
use as well, especially in those cases where the formula is 
complicated, and is written for the use of technicians rather than 
other engineers (although it is used in this context as well). Just 
as was done in the math exercise quoted above, the formula will be 
written with dimensionless numbers in place of the constants and the 
units associated with all the variables will be specified. What this 
means is that if the numbers entered in the formula are always in the 
specified units, then the answer will also end up in the correct 
units.

I can see the practical value in this when the use is intended for a 
technician on site who needs a number and really doesn't have the 
time to spend on making sure the units are correct, but the method 
inevitably seeps into and contaminates the laboratory as well. It has 
been many years since I was a reader of any of the IEEE journals, but 
I recall that most of the formulas there, even in basic research 
papers were written in this fashion. It used to drive me nuts as I 
tried to figure out what actually went into the nameless numerical 
constants that appeared in the published formulas.

From personal experience, I can testify that this practice, no matter 
how useful if may be for the technician in the field, is a formidable 
barrier to understanding, and the adoption of this practice by 
mathematics teachers makes out job a science teacher many times more 
difficult.

I can even understand why the mathematicians do this, since their 
primary interest is in the relationships and not the real-world 
application of it, but I do wish that they would understand the 
real-world implications down the line of their narrow focus at the 
beginning.

Unfortunately, even top-rated math teachers who understand the way 
that math is the underpinning of all science and engineering fail to 
appreciate the importance of getting students used to using units 
with their numbers (of course, unitless numbers exist, but compared 
to the numbers requiring units, they are far less common). The grief 
this causes later is significant, as was earlier noted in the case of 
the lost Mars lander. I even recall an incident in 
fiction--specifically in Ernest Gann's novel "Point of No Return," in 
which the navigator on a trans-Pacific flight misses a critical 
position in the flight because he forgot to convert a distance in 
statute miles to one in nautical miles.

As the life sciences become ever more mathematical, I'm sure that 
this problem is only going to get worse. The only solution I can see 
if for the math teachers and the science teachers to spend a lot more 
time talking to each other, but given the walls of isolation built 
around our various disciplines, I don't see this happening in 
anywhere near the required amount in the foreseeable future.

Hugh
--
Hugh Haskell
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mailto:haskellh@verizon.net

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