*Logging in this email exchange with my Uncle Dave. *

* Davo graduated with a BS in Math from Rice University in Houston, worked on aircraft carrier restraining cables for Chance-Vought in Dallas and then joined the Apollo Moon Mission team in back in Houston. When the moon landings were over he relocated to Seattle working on IT systems for the VA.*

*He had been playing string instruments all his life. The first I recall was the ukelele (“My Dog has Fleas”). In Seattle and later in further retirement on vachon Island he continued a performing on the fiddle, specializing in Cajun and other country music*

*He is still an active researcher and is involved with various near-space experiments, the nitty-gritty of which I don’t understand.*

*What a lucky guy I am to have this lucid relationship with Dad’s little brother. *

*

Davo,

OK, we know that the relationship between Fahrenheit and celsius can be put as °F = (°C * 9/5) +32, or inversely °C = (°F – 32) * 5/9

Minus forty (-40) is the point where the two systems cross. But where are they palindromic? That is, the numbers are “flat” and simply represent themselves, with no content, as inverted?

That is, where does °F (xy) = °C (yx), except that x and y are not being multiplied rather represent concrete numbers without being in any additive or subtractive relationship with each other? 34 / 43, 92 / 29, etc.

How does one put that mathematically?

I know the actual answer, BTW, experientially. Just curious what the formula would look like, if mathematics has a way to represent numbers without value.

Otherwise, all is as well as can be. Nancy is coming for a week and we and th

Hi George,

Always good to hear from you.

Thanks for the interesting, if random, query.

I see two linear-functions (straight lines) both passing through the common point (-40,-40) on a graph of “C-vs-F” but nothing else of curiosity.

I am wrestling with the “palindromic” property you refer to….not sure I’m understanding this attribute. Might you provide what such numerics would look like.

Davo,

PS: as related to your field of linguistics lately I ave been reading a bit about American Sign Language … fascinating

**On Oct 11, 2020, at 12:50 PM, George Lang <xerxeslang@gmail.com> wrote:**

What I discovered the other day is that 82 F and 28 C coincide for at least part of their respective ranges (given the fact that their scales are not equal by a factor of 5/9 or 9/5).

I can see that “palindromic” is misleading, since 28 and 82 are not strictly the same if read in each direction, like the name A-N-N-A or MOM or level:

https://en.m.wikipedia.org/wiki/PalindromeBut they mean the same thing when they refer to temperature in each system.

Numbers can be palindromic, for ex., 4554. But that is not the same thing as 28 and 82. So my bad.

But still I wonder how, if I didn’t already know that they were the same physical temperature, I could derive that common point in two systems, mathematically I mean, like we can for C/F -40.

The problem is that math depends on intrinsic values for numbers but the sought-after formula in question would have to deal with the relative position of numbers in the formula itself.

2+ 3 = 5 is the tautological equivalent of 3 + 2 = 5.

I never formally studied calculus but suspect there is some way to use functions to solve the problem.

O well, just whiling away time in the middle of a pandemic, one which is proving itself to bevmore of a syndemic than we think

https://en.m.wikipedia.org/wiki/Syndemic.

Davo,

Thanks for humoring me with this exercise. As you can tell, I was trained to think in linguistic / literary terms, never having taken a math class since high school, where the terminological framework was not important. Hence my “palindromic” and “tautological” as opposed to “commutative” etc.

I think I followed your thoughts pretty well.

Am I right to conclude that if one didn’t know that 82F = approximately 28C, the most likely way of finding any pairs of inverted numbers (e.g. 28 and 82) which are equal in the C and F scales would be an iterative algorithm which would test each number in F and in C and stop when it ran into a number which could be rounded off to a whole number? I gather that is how computers tally up prime numbers. Or something like that.

There would have to be some kind of directions to the machine that would allow for rounding up or down, or if not then a human eye intruding into the process.

Is -40 the only point in which the F = C would obtain whole numbers? Apart from 32F / 0C and 212F and 100C?

Anyway, this is a gas, for me. When I was a kid, I used to do sums in my head late at night in bed, before I discovered masturbation, that is 😉

I think I mentioned to you once that after four years of solely humanistic studies for the BA I still scored better on the GREs in math skills than in language skills. If only I hadn’t had that horrible 11th grade solid geometry teacher ….

Nancy will be here tomorrow and we’ll have a good ole time.

Best, George

George,

This was a fun ‘lil thought adventure. It certainly got me thinking as I had not ever realized that there was a thermal state for which both scales rendered the same temperature value (albeit the Rankin and Kelvin scales both render the temperature as “zero” for the “absolute zero” thermal state – but that seemed contrived by definition).

You’re quite right about how a computer algorithm would search for those palindromic type number occurrences. Actually, the detection of such occurrences could easily be detected, by indexing through, say, the Fahrenheit scale values using just integer number temperatures (51, 52, 53, …ad infinitum), and for each F temp, calculating the corresponding centigrade temperature; for example, if the F temp being tested is 58 deg, then if the corresponding Centigrade temp is within X% of 85 deg, then declare a “palindrome candidate”; if no candidate, then just move on to the next F temp value and try it.

Of course, to expedite the search you would first use a “rough-hit” criteria (relatively large X%). If you get a rough hit, then you can reduce X% to see just how close to 85 the Centigrade value actually is.

Of course, the issue here is the size of the discriminator x%; how small a value should it be? What does it mean. If one is searching-out such occurrence under the suspicion that “something numerically interesting is going on”, then your search could be tailored accordingly to help your quest. IF an exact match is sought, then a candidate C value can be tested exactly (example in Fortran “If(Candidate .EQ. Palinvalue) then” “declare a hit” (note: per above example, Palinvalue would have been set to 85). You could easily write this code using a simple user-friendly language like “Basic”, etc, on your desktop.

BTW, I’m not sure if -40 is the only place where the F-C interaction yields yields strictly integer value-pairs.

Regarding night-time pastimes, I think would prefer your latter discovery 🙂

Give our love to Nancy! Say hi to Nasrin for us,

Davo

Davo,

OK, we know that the relationship between Fahrenheit and celsius can be put as °F = (°C * 9/5) +32, or inversely °C = (°F – 32) * 5/9

Minus forty (-40) is the point where the two systems cross. But where are they palindromic? That is, the numbers are “flat” and simply represent themselves, with no content, as inverted?

That is, where does °F (xy) = °C (yx), except that x and y are not being multiplied rather represent concrete numbers without being in any additive or subtractive relationship with each other? 34 / 43, 92 / 29, etc.

How does one put that mathematically?

I know the actual answer, BTW, experientially. Just curious what the formula would look like, if mathematics has a way to represent numbers without value.

Otherwise, all is as well as can be. Nancy is coming for a week and we and the Dogs will have a Face Tme session with her then.

Hope Jane is doing well. And yu too.

Best, George

*

George,

This was a fun ‘lil thought adventure. It certainly got me thinking as I had not ever realized that there was a thermal state for which both scales rendered the same temperature value (albeit the Rankin and Kelvin scales both render the temperature as “zero” for the “absolute zero” thermal state – but that seemed contrived by definition).

You’re quite right about how a computer algorithm would search for those palindromic type number occurrences. Actually, the detection of such occurrences could easily be detected, by indexing through, say, the Fahrenheit scale values using just integer number temperatures (51, 52, 53, …ad infinitum), and for each F temp, calculating the corresponding centigrade temperature; for example, if the F temp being tested is 58 deg, then if the corresponding Centigrade temp is within X% of 85 deg, then declare a “palindrome candidate”; if no candidate, then just move on to the next F temp value and try it.

Of course, to expedite the search you would first use a “rough-hit” criteria (relatively large X%). If you get a rough hit, then you can reduce X% to see just how close to 85 the Centigrade value actually is.

Of course, the issue here is the size of the discriminator x%; how small a value should it be? What does it mean. If one is searching-out such occurrence under the suspicion that “something numerically interesting is going on”, then your search could be tailored accordingly to help your quest. IF an exact match is sought, then a candidate C value can be tested exactly (example in Fortran “If(Candidate .EQ. Palinvalue) then” “declare a hit” (note: per above example, Palinvalue would have been set to 85). You could easily write this code using a simple user-friendly language like “Basic”, etc, on your desktop.

BTW, I’m not sure if -40 is the only place where the F-C interaction yields yields strictly integer value-pairs.

Regarding night-time pastimes, I think would prefer your latter discovery 🙂

Give our love to Nancy! Say hi to Nasrin for us,

Davo

Davo,

Thanks for humoring me with this exercise. As you can tell, I was trained to think in linguistic / literary terms, never having taken a math class since high school, where the terminological framework was not important. Hence my “palindromic” and “tautological” as opposed to “commutative” etc.

I think I followed your thoughts pretty well.

Am I right to conclude that if one didn’t know that 82F = approximately 28C, the most likely way of finding any pairs of inverted numbers (e.g. 28 and 82) which are equal in the C and F scales would be an iterative algorithm which would test each number in F and in C and stop when it ran into a number which could be rounded off to a whole number? I gather that is how computers tally up prime numbers. Or something like that.

There would have to be some kind of directions to the machine that would allow for rounding up or down, or if not then a human eye intruding into the process.

Is -40 the only point in which the F = C would obtain whole numbers? Apart from 32F / 0C and 212F and 100C?

Anyway, this is a gas, for me. When I was a kid, I used to do sums in my head late at night in bed, before I discovered masturbation, that is 😉

I think I mentioned to you once that after four years of solely humanistic studies for the BA I still scored better on the GREs in math skills than in language skills. If only I hadn’t had that horrible 11th grade solid geometry teacher ….

Nancy will be here tomorrow and we’ll have a good ole time.

Best, George

Hi George,

It’s inquisitive minds that discover shit, so count yourself fortunate 🙂

BTW, regarding our palindromic diversion, 82 (F) = 27.7777777 (C) 🙂

You may have intuitively suspicioned that there must a temperature state (ie. -40) that would yield identical temperature values in both scales since the transformation relationships were linear graphs (straight-lines of dissimilar slope, thus (by the tenants of plane geometry) bound to cross somewhere.

The whole conversion issue is fairly straight forwardly handled by the basic algebra, to wit; given the facts that the two scales exhibit the following properties:

On designates the Freezing point to be 32 deg, the other 0 deg

On designates the Boiling point to be 212 deg, the other 100 deg

Given that the actual thermal aspects of these two states are invariant across measuring protocol, it is evident that the unit of temperature is different between the to scales, and there is also a reference bias (ie. the baseline for “zero”) difference between the two scales. Since neither scheme alludes to unit non-linearity (ie. the unit of temperature invariant with temperature itself, “a deg is a deg is a deg”), the transformation between the two would expressible as a simple linear function, ie

F = aC + b (where a and b as constants TBD).

Applying the above to the two thermal states will yield the two simultaneous linear equations needed to solve for a and b.

212 = 100 a + b

32 = 0 a + b

The last equation conveniently yields b = 32, which can be plugged into the first equation to find “a”.

212 = 100 a + 32

or a = (212 – 32)/100 = 1.8 (9/5)

Hence: F = 1.8 C + 32

or: C = (5/9) [F – 32]

….this equation is then solved for C as a function of F to yield the inverse relationship.

So if one ponders whether there is a thermal state for which C = F, simply start with either equation and set C = F, to wit,

F = 1.8 F + 32

becomes

F = 1.8 F + 32

that yields

F = – 40

Now to confirm all is well, plug -40 (C) into the equation that yields an C values, given an F value

C = (5/9) [F – 32]

C = (5/9) [C – 32]

C = (5/9) C – 17.7777777

(1 -5/9) C = – 17.7777777

4/9 C = – 17.7777777

C = – 40

QED

BTW, strictly speaking 2 + 3 = 3 + 2 is not a tautology, but rather a pivotal axiom (of the real number arithmetic system) that establishes the “commutative property” of summation, to wit:

If A is a number, and B is a number, then there is a one number called the “Sum of A and B”

denoted by A + B. The sum of A and B is identical to the sum of B and A (ie. A + B = B + A)

Just a nit-pick, but possibly of pedagogical value 🙂

Sorry to start off your Monday like this 🙂

Davo

What I discovered the other day is that 82 F and 28 C coincide for at least part of their respective ranges (given the fact that their scales are not equal by a factor of 5/9 or 9/5).

I can see that “palindromic” is misleading, since 28 and 82 are not strictly the same if read in each direction, like the name A-N-N-A or MOM or level:

https://en.m.wikipedia.org/wiki/PalindromeBut they mean the same thing when they refer to temperature in each system.

Numbers can be palindromic, for ex., 4554. But that is not the same thing as 28 and 82. So my bad.

But still I wonder how, if I didn’t already know that they were the same physical temperature, I could derive that common point in two systems, mathematically I mean, like we can for C/F -40.

The problem is that math depends on intrinsic values for numbers but the sought-after formula in question would have to deal with the relative position of numbers in the formula itself.

2+ 3 = 5 is the tautological equivalent of 3 + 2 = 5.

I never formally studied calculus but suspect there is some way to use functions to solve the problem.

O well, just whiling away time in the middle of a pandemic, one which is proving itself to bevmore of a syndemic than we think

https://en.m.wikipedia.org/wiki/Syndemic.

Hi George,

Always good to hear from you.

Thanks for the interesting, if random, query.

I see two linear-functions (straight lines) both passing through the common point (-40,-40) on a graph of “C-vs-F” but nothing else of curiosity.

I am wrestling with the “palindromic” property you refer to….not sure I’m understanding this attribute. Might you provide what such numerics would look like.

Davo

PS. as related to your field of linguistics, lately I have been reading a bit about American Sign Language….fascinating.

Davo,

OK, we know that the relationship between Fahrenheit and celsius can be put as °F = (°C * 9/5) +32, or inversely °C = (°F – 32) * 5/9

Minus forty (-40) is the point where the two systems cross. But where are they palindromic? That is, the numbers are “flat” and simply represent themselves, with no content, as inverted?

That is, where does °F (xy) = °C (yx), except that x and y are not being multiplied rather represent concrete numbers without being in any additive or subtractive relationship with each other? 34 / 43, 92 / 29, etc.

How does one put that mathematically?

I know the actual answer, BTW, experientially. Just curious what the formula would look like, if mathematics has a way to represent numbers without value.

Otherwise, all is as well as can be. Nancy is coming for a week and we and the Dogs will have a Face Tme session with her then.

Hope Jane is doing well. And yu too.

Best, George