Nick -
If your model is that the the instability of the cat-cat-food situation
is positively (and nominally linearly) correlated with the distance
between them (more likely inversely, but that is a separate issue) then
the absolute value is a very reasonable way of removing any implied
issues with your chosen units.
Why do you consider the steps to be -1...-8... rather than 1...8...?
is the food at 0? is the significance that D must pass E to get to F?
It seems to me that the (in)stability goes to infinity when E and D are
on the same step (divide by zero)?
Can you articulate in natural language (as talking to George who is full
of shit) your more full model of what this (in)stability between cats
involving steps and food (and yourself?)? Assume a 1-D arrangement
(up/down stairs) like physicists assume spherical cows?
- Steve
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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