Re: [Phys-l] definitions ... purely operational, or not

[John Denker <jsd@av8n.com>]

On 11/08/2010 09:00 PM, William Robertson wrote:
> Just this last week I was discussing with a group of teachers the fact  
> that scientists consider all changes in velocity as accelerations, and  
> that using deceleration might be lay talk, but not scientifically  
> appropriate. 

Actually, if you listen to scientists, they use the term
"deceleration" all the time.

The trick is that there are two kinds of acceleration:
 -- the scalar acceleration (d/dt) |v| == (d/dt) speed
 -- the vector acceleration (d/dt)  v  == (d/dt) velocity

> One teacher said that she accepted that, but that all  
> reductions in speed were to be considered negative accelerations and  
> all increases positive accelerations. 

Note that she used the word "speed".  In that context her 
notion of acceleration and deceleration (aka positive and
negative acceleration) is formally and quantitatively correct.  

A scalar acceleration is an increase in |v|.
A deceleration is a decrease in |v|.

> In the short time we had, I  
> tried to help her understand that the world does not come with pluses  
> and minuses attached. She was the victim of previous educators who  
> deemed it "simpler" to assign increases in speed as positive and  
> decreases in speed as negative. 

It's not just simpler;  it's entirely true, so long as she is
using the word "speed".  The speed is a scalar and therefore any
change in speed is either an increase or a decrease.

You can make the point that the laws of motion are much more simply
stated in terms of velocity rather than speed ... but you can't
say that speed is "wrong", and as long as speed exists then scalar
acceleration and deceleration will exist.

For thousands of years the word "acceleration" has meant an increase
in the scalar speed, and "deceleration" has meant the opposite, from 
the Latin _celer_ = fast, swift, speedy.  Physicists have extended 
the word "acceleration" to apply to changes in the vector velocity 
... and are in no position to complain when folks use the word in 
its original sense.

> It might have suited the purposes of  
> those educators at the time, but it blocked this teacher from seeing a  
> bigger picture of how scientists analyze the physical world. That's a  
> case where educators used a technique that actually constrained this  
> teacher's understanding.

It's not that terrible.  You just need to segue from the old scalar
acceleration to the new vector acceleration.  It is not necessary or
even desirable to destroy the old notion.  You just need to insist
that it is not what we want to talk about today.  Today we want to
talk about motion in more than one dimension.  The real world is multi-
dimensional.  In one dimension there is a notion of "increase" and
"decrease" but in higher dimensions there is not.  That is to say,
quite formally, vectors are well-ordered in D=1 and not otherwise.

AFAICT her attachment to the term "deceleration" is symptomatic of 
a much deeper problem, namely an attachment to a one-dimensional 
model of kinematics.  As always, fussing over terminology is not a 
good idea.  Ideas are primary;  terminology is tertiary.  Terminology
is important only insofar as it helps us formulate and communicate 
the ideas.  Once the multi-dimensional *concepts* are there, the 
terminology will fall into place.  If the concepts are not there, 
then fussing over the terminology is 100% a waste of time.

=========

It is extremely common to find one word being used with two different
meanings.  Sometimes this is no problem, because the proper meaning
can be figured out from context ... but sometimes it is a very serious
problem, especially when people don't realize the word has more than
one viable meaning.  (This is an example where terminology hinders
rather than helps with the ideas.)

In thermodynamics, there are two inequivalent notions of "adiabatic"
and at least four inequivalent notions of "heat".

=========

I put "there's no such thing as deceleration" in the same category
as "there's no such thing as a centrifugal field".  
 -- It is entirely OK for the teacher to say we don't want to talk
  about such things in this course.
 -- It is not OK to say such things don't exist.  They are perfectly
  well-defined concepts, and they are /sometimes/ useful.