Re: [FRIAM] Comparing negative numbers

[Nicholas Thompson]

Hi, everybody (anybody),

 

Many thanks to Russ, Frank, Stephen, and Steve S and others who got in touch 
with me off line. I try not to bother you guys unless I am pretty desperate, so 
I guess I was pretty desperate. 

 

A little history: I have been a weather-nerd ever since my early teens when the 
Worcester Tornado and two substantial hurricanes tracked through Massachusetts 
in  the early  I am also a gardener, so during the 80's I wrote The 
Weather-Wise Gardener 

 . Most of my knowledge comes from obsessive reading of forecaster discussions 
and recently I began to notice terminology creeping in that I did not 
understand and I began to wonder if I might update the book.  So I began 
reading weather texts and the numerous wonderful publications of NOAA and the 
AWS, and sat down to read Mid-latitude Atmospheric Dynamics with a friend from 
LANL. 

 

I have learned two lessons from this review, one happy, one sad.  The happy one 
is that my book holds up remarkably well, given its author and its longevity. 
It not only lays out the basic theory of the time pretty faithfully, but 
anticipates some ideas that weren’t all that current at the time.  I only 
detected a few colossal blunders, eg., a failure to honor the difference 
between centrifugal and Coriolis forces.   

The sad discovery was that meteorology is a cesspit of counter intuitive 
relations.  As altitude goes up, pressure goes down, temperature goes down, 
potential temperature goes up, potential vorticity (mostly) goes up. As 
temperatures go down, stability goes down, and clouds go up.  The more moist 
air is, the lighter air is, but precipitation releases latent heatand makes air 
lighter.  Both sun angle and daylength contribute to heating but in the winter 
hemisphere those es work together where as in the summer they work against one 
another. 

 

Most weather people when dealing with the public obfuscate these problems 
hideously.  For instance, a TV forecaster will speak about warm air advection 
aloft.   The air that is advecting is usually pretty cold by human standards, 
but its potential temperature is warm by the standards of that altitude.  75 
degree air in Santa Fe would be 110 degree air in Houston!  Santa Fe air, when 
it floats out over the plains, produces the temporary capping inversions that 
allow thunderstorm explosions during Oklahoma afternoons.  In the summer, one 
can see little pockets of Santa Fe air aloft almost anywhere in the country, 
and where they occur over pockets of cooler, moister air, the normal venting of 
diurnal heating to the upper atmosphere is temporarily inhibited with 
potentially explosive results. 

 

If I do rewrite this book, I will have to explain all of this to the layish 
(layer?) reader, and this is how I got thinking about my poor cats, Dee and 
Ess.  What words do I use to explain these dynamics when the signs are going 
every which way.  I suspect that you-guys learned something crucial while I was 
engaged in a fruitless struggle to become interested in Chaucer, something 
about how to make words and numbers work together, something that perhaps one 
cannot learn in one’s 80’s.  

 

Ah Well, 

  Frank and Russ, thanks for working through basic 5th grade 
mathematics with me and reminding my that if I want to compare two numbers, 
subtraction is the way and that the order of the subtraction can be manipulated 
to get any result like, positive or negative.  (Duh!) That’s how desperate I 
was.  

 

Thanks to Stephen and Steve for honoring  my childlike wonder and my faith that 
with enough help, even I can learn it.

 

NIck 

 

 

 

 

 

On Fri, Apr 12, 2024 at 12:00 PM Nicholas Thompson mailto:thompnicks...@gmail.com> > 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 

Re: [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  
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 StandishPhone 0425 253119 (mobile)
>Principal, High Performance Coders hpco...@hpcoders.com.au
>  http://www.hpcoders.com.au
>
>
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Re: [FRIAM] Comparing negative numbers

[Steve Smith]

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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Re: [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.



-- 


Dr Russell StandishPhone 0425 253119 (mobile)
Principal, High Performance Coders hpco...@hpcoders.com.au
  http://www.hpcoders.com.au


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[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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