[FRIAM] Comparing negative numbers

[glen]

It seems like the relative stability argues for a translation from Ess space to the origin (0). So regardless of sign, you want to translate from absolute space (step number) to Ess space, which, in some cases, results in Russ' math. But would extend to negative steps as well.

On April 12, 2024 2:48:00 PM PDT, Russell Standish <lists at hpcoders.com.au> wrote:
>On Fri, Apr 12, 2024 at 12:00:06PM -0600, Nicholas Thompson wrote:
>> 
>> 
>> My Dear Phellow Phriammers, 
>> 
>> Over the years I have asked you some doozies.  Still, I am pretty sure this the
>> stupidest question I have ever asked this forum, so I am at your mercy.
>> 
>> I am in one of those situations where language and mathematics are rubbing
>> together and driving crazy. 
>> 
>> Let say that my patio is ten steps down from my back door.  I have two cats,  
>> Dee and Ess, and  Dee is dominant to Ess.  So, if I go out to let them in, and
>> I find  Ess on step -2   and  Dee on step -8,  I know I have an unstable
>> situation. I fear that I will have a cat fight as Dee rushes past Ess to claim
>> his rightful position by the preferred cat bowl.  Intuitively, I would  rate
>> the degree of instability as a positive 6.  How would I compare the two numbers
>> mathematically to get +6?
>> 
>> But let’s say that for theoretical reasons I now want to conceive of the
>> situation as a degree of stability, with negative stability corresponding  to
>> instability.   Now, according  to my index, the situation is a minus 6.  How
>> would I compare the two numbers mathematically to get  a -6?
>> 
>> The situation I am trying to model here is the origin of the notion of static
>> stability in meteorology.  Static Stability has a lot to do with differential
>> lapse rates, the degree to which temperature declines with increasing altitude.
>>   Lapse rates are minus numbers.  So a parcel is unstable if it has a lower
>> lapse rate (a less minus lapse rate?) than surrounding parcels, and the greater
>> the absolute value the difference between them, the greater the instability.
>> 
>> I asked “George” (GPT) to help me with this, but he (?) suggested I just take
>> absolute values and give them whatever sign I want.  However, somebody told me,
>> way back when, that taking absolute values was not kosher in mathematics.  (Why
>> else would the variance be the mean SQUARED deviation about  the mean?).  
>
>I don't know about kosher, but abs is not differentiable at zero,
>which may or may not be an issue.
>
>In terms of what you're looking for, -8-(-2) = -6.
>
>Take their difference - it accords with your intuition. George speaks shit.
>
>
>
>-- 
>
>----------------------------------------------------------------------------
>Dr Russell Standish                    Phone 0425 253119 (mobile)
>Principal, High Performance Coders     hpcoder at hpcoders.com.au
>                      http://www.hpcoders.com.au
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