Re: [FRIAM] Comparing negative numbers
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 > > >-. --- - / ...- .- .-.. .. -.. / -- --- .-. ... . / -.-. --- -.. . >FRIAM Applied Complexity Group listserv >Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom >https://bit.ly/virtualfriam >to (un)subscribe http://redfish.com/mailman/listinfo/friam_redfish.com >FRIAM-COMIC http://friam-comic.blogspot.com/ >archives: 5/2017 thru present https://redfish.com/pipermail/friam_redfish.com/ > 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/ -. --- - / ...- .- .-.. .. -.. / -- --- .-. ... . / -.-. --- -.. . FRIAM Applied Complexity Group listserv Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom https://bit.ly/virtualfriam to (un)subscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ archives: 5/2017 thru present https://redfish.com/pipermail/friam_redfish.com/ 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/
Re: [FRIAM] Comparing negative numbers
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. -. --- - / ...- .- .-.. .. -.. / -- --- .-. ... . / -.-. --- -.. . FRIAM Applied Complexity Group listserv Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom https://bit.ly/virtualfriam to (un)subscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ archives: 5/2017 thru present https://redfish.com/pipermail/friam_redfish.com/ 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/
Re: [FRIAM] Comparing negative numbers
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 -. --- - / ...- .- .-.. .. -.. / -- --- .-. ... . / -.-. --- -.. . FRIAM Applied Complexity Group listserv Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom https://bit.ly/virtualfriam to (un)subscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ archives: 5/2017 thru present https://redfish.com/pipermail/friam_redfish.com/ 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/
[FRIAM] Comparing negative numbers
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 -. --- - / ...- .- .-.. .. -.. / -- --- .-. ... . / -.-. --- -.. . FRIAM Applied Complexity Group listserv Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom https://bit.ly/virtualfriam to (un)subscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ archives: 5/2017 thru present https://redfish.com/pipermail/friam_redfish.com/ 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/
