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 hpco...@hpcoders.com.au
http://www.hpcoders.com.au
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