[FRIAM] Comparing negative numbers

[Russell Standish]

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.



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Dr Russell Standish                    Phone 0425 253119 (mobile)
Principal, High Performance Coders     hpcoder at hpcoders.com.au
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