[FRIAM] Comparing negative numbers

[Nicholas Thompson]

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?).

So there it is.

Yeah.  I know.


Nick
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