Re: [boost] Re: Re: Re: Re: Physical quantities

From: Kevin Lynch (krlynch_at_[hidden])
Date: 2004-01-14 15:13:10

Andy Little wrote:
> "Kevin Lynch" <krlynch_at_[hidden]> 
>>Andy Little wrote:

>>Actually, the SI system is a really nasty  :-)  
> 
> Personally I am very grateful to those guys. 
> 

Well, I'm not UNGRATEFUL.  I've just found out by experience that the 
"rough edges" in the SI documents tend to cause all sorts of 
misunderstandings/misapprehension about dimensional analysis and the 
unit systems you can build on top of them.  SI is great as far as it 
goes, but it tries to claim more than it should....

>>The "logic" of dimensional analysis has been quite cogently described by
>>  Deane Yang.
> (Understating) I find this remark slightly odd. 

I'll let Deane respond, I guess, but I haven't seen it that way.  But 
maybe that's because I'm up on the technical jargon.

> If there is something in Deanes work I would like to see a more
> comprehensive paper, ideally written for a 'simple guy' like myself.
> (Diagrams help).
> Heres mine(needs updating):
> 
> http://www.servocomm.freeserve.co.uk/Cpp/physical_quantity/Concepts.html
> 

I'll try to take a look at it.

> 
> One observation.. when you say 2m I know exactly what you mean. 

Ahhh, but do you really?  Which m do I mean?  do I mean the current 
international standard meter defined in terms of the distance light 
travels in vacuum in a certain length of time?  Or do you mean the 
international standard platinum bar meter?  Or a fraction of the earth's 
pole-to-equator distance?

Yes, yes, I know which one you REALLY mean in this context, but my point 
is that it isn't as simple as "the meter", or any given unit.  and a 
DA+unit framework that doesn't include the flexibility to include many 
is not going to be particularly useful to the communities that need that 
flexibility.  and I suspect that those communities are the ones that 
will be most likely to use such a library.  But I could be wrong.

>>By "non-dimensionalized", I mean that you recast your equations directly
>>in terms of dimensionless ratios instead of in terms of the division of
>>two identically dimensioned quantities 
>>
>>Here's an example ... Greatly simplified, it looks something
>>like this:
>>
>>exp(-t/tau)*(1+cos(w*t))
>>

[becomes]

>>the "non-dimensionalized" equation
>>
>>exp(-T)*(1+cos(W*T))
> 
> 
> although the original ones (t/tau), (w*t) are dimensionless:
...
> Basically you are avoiding creating a unit system.... 

Actually, in a sense, what I'm doing is exactly the opposite, since I 
haven't done anything to the equations!  I've just created a unit system 
in which time is measured as a multiple of tau, so I drop the term tau, 
as it is redundant, rather than dividing by 1 tau everywhere.  Because 
the terms are being divided or multiplied by one everywhere, I just drop 
them from the equations, and use pure numbers instead.  I've 
non-dimensionalized the equation (a misnomer, I guess) since by a 
careful choice of units, I can treat time as if it has no dimension.

If we had a good, flexible DA+unit system for me, I could use it to 
define the time unit in terms of taus instead of seconds, and use the 
equation in its original form, and still get the aesthetic and technical 
benefits without teh work of non-dimensionalization.  But, doing so 
would require flexibility in the definition of unit systems.

-- 
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