Mathematics

12:45 AM

we're running the air conditioner for the first time this year.

trying to get the second floor below 80.

I love almost integer stuff. It's interesting that there are lots of examples involving $e$, the most famous ones coming from the Heegner numbers. en.wikipedia.org/wiki/Almost_integer It's pretty easy to make quadratic ones, using Pell's equation.

Also, I hear the 4th root of (9^2 + 19^2/22) is pi.

leslie townes

oh, that's evil.

even by xkcd standards.

PM 2Ring

One of the pi guys (Borwein ?) did a similar thing involving cosh, IIRC. I should be able to find the anecdote on MO...

leslie townes

oh yeah, i've read that anecdote. it was one of the borweins.

PM 2Ring

1:05 AM

John Baez has an article about that stuff: Patterns That Eventually Fail

Ted Shifrin

@leslietownes It's not that bad here.

leslie townes

it's muggy here.

Ted Shifrin

Well, it's because munchkin is so full of hot air.

leslie townes

SD always has better weather. it's the best weather on earth.

PM 2Ring

I think the Borwein example involved the integral of a product of sinc terms, not cosh. More examples here: mathoverflow.net/questions/15444/…

leslie townes

1:15 AM

we have a coastal pine tree nearby that reminds me of SD.

PM 2Ring

We've had a couple of days with no rain (or little rain), but they've been very rare for months. At least the weather is starting to get cooler, so it's merely humid, not muggy.

Found it!

17

A: Integral of the Sinc product

Borwein integrals As Eckhard wrote in comments B[n] is the n-th Borwein integral. (The letter B was not accidental :) ) This funny properties of Borwein integrals is related to the Fourier transform of Sinc function FourierTransform[Sinc[x], x, k] 1/2 Sqrt[Pi/2] (Sign[1 - k] + Sign[1 + k])...

As a prank, Jonathan Borwein reported this to Maple, claiming there was a bug in the software. Maple computer scientist Jacques Carette spent 3 days trying to figure out the problem. Then he realized: There was no bug! That's what these integrals really equal!

leslie townes

that's the anecdote. you found it.

sadistic.

PM 2Ring

Perhaps. I like to think of it as an "interesting" teaching technique. ;)

Ted Shifrin

1:38 AM

"Interesting," huh?

PM 2Ring

I'm trying to write a program to calculate the time of sunrise & sunset. Some of the equations I'm using come from this paper from 1989. doi.org/10.1093/mnras/238.4.1529 Unfortunately, their equation for sidereal time has a sign error. It took me a few days to fix that. :( But now I'm wondering if there are other errors in smaller terms that are harder to notice. I can check my results against results from JPL, but that doesn't really help much with the smaller terms.

@TedShifrin Well, I bet Jacques Carette now knows a lot more about those integrals than he otherwise would. :)

robjohn

2:03 AM

@PM2Ring Back in the late 80s or early 90s, I wrote a program that would print out the sky including moon and planets. It was pretty accurate, but the moon position was a bit off since I used the Earth as a sphere.

I had about 880 stars, hand input from the Nautical Almanac and Astronomical Ephemeris.

I was wrong, it was written for the PET, so it was in the early 80s, maybe late 70s

copper.hat

loved the pet

was supposed to go to healdsburg winetasting with friends, but i met another friend yesterday who just texted that he tested +ve, so i had to cancel my end of the trip :-(

robjohn

I got an extra graphics board that had 32K of RAM to use and 2 PROM sockets that I could use for some 3-D graphics software I'd written.

copper.hat

cool!

PM 2Ring

Nice work! This site has some amazing algorithms. neoprogrammics.com/index.html Accurately compensating for the effects of the Moon isn't easy. Here's the IAU2000 stuff for computing the effects of nutation on longitude & the obliquity of the ecliptic: neoprogrammics.com/nutations/nutations_1980_2000b I'm definitely not putting that stuff in my program!

robjohn

@copper.hat It was that software, I think, that got me the job at Apple.

copper.hat

2:11 AM

@robjohn I can see why.

PM 2Ring

Lunar theory has improved significantly, especially in the last 20 years, thanks to refinements in Lunar Laser Ranging.

copper.hat

plus the 6502 was used in the II

robjohn

@PM2Ring Yeah, I'm not real interested in trying to resurrect and improve that program. It lies on cassette tapes and printed on paper.

copper.hat

in Basic?

robjohn

@copper.hat Yeah, I'd also written an assembler for the 68000 and upgraded to 68030+MMU

copper.hat

2:13 AM

i know its clunky by today's standards, but it was a great leaning vehicle

wow,

robjohn

@copper.hat The PET software was in BASIC

PM 2Ring

JPL uses a fairly sophisticated model for the Moon's interior, but they also fit their ephemeris calculations to a lot of actual data.

robjohn

@PM2Ring I'll leave that to them ;-)

copper.hat

the discovery that you could peek & poke opened up a whole world of exploration for me. we had no documentation at all, and coming across such stuff was practically impossible. byte magasine had some good stuff from time to time

PM 2Ring

It's still fun to compute orbits, but there's no way to compete with JPL. They integrate the equations of motion to the level where they model all the major bodies of the Solar system down to the top 340 asteroids as individual bodies, plus they have access to a huge amount of terrestrial & spacecraft observations for data fitting.

robjohn

2:18 AM

@copper.hat That is how I wrote the 3-D software on the PET 6502 code POKEd in a BASIC program.

@copper.hat Loved BYTE

@PM2Ring If it were anyone but JPL, I'd say "get a life"

PM 2Ring

The best lunar theory from a couple of decades ago, ELP didn't bother trying to model actual observations directly, they took all their data from the then-current JPL ephemerides.

copper.hat

i wrote a little plot program that managed 'double resolution' plots. the pet had 16 characters with each quadrant on/off.

not terribly exciting, but i was so proud of that little routine

all sorts of things suddenly became interesting, scatter plots least squares, etc

PM 2Ring

I thought the PET was wonderful. I never owned one, but I played with them in the shop. A bit later, I had an Osborne

Osborne 1

The Osborne 1 is the first commercially successful portable computer, released on April 3, 1981 by Osborne Computer Corporation. It weighs 24.5 lb (11.1 kg), cost US$1,795, and runs the CP/M 2.2 operating system. It is powered from a wall socket, as it has no on-board battery, but it is still classed as a portable device since it can be hand-carried when the keyboard is closed. The computer shipped with a large bundle of software that was almost equivalent in value to the machine itself, a practice adopted by other CP/M computer vendors. Competitors quickly appeared, such as the Kaypro II. ��2...

A few years later, I got an Amiga 2000. In fact, I still own one (not my original), which I use as a monitor stand. It might still work, (assuming its electolytics haven't dried up), but I no longer have an analog monitor for it. I guess I could get an adapter...

leslie townes

this is the best one.

Sphinx (home automation system)

The Sphinx (Russian: СФИНКС, romanized: SFINKS) was an experimental Soviet project for a home automation system, commissioned by the State Committee for Science and Technology and designed by Dmitry Azrikan, in collaboration with A. Kolotushkin and V. Goessen, in 1987. Sphinx, an acronym for Super Functional Integrated Communication System (Russian: Суперфункциональная интегрированная коммуникативная система), was intended to be an ensemble of modules that would allow consumers to easily interact with information systems. The home environment, as described in a 1987 issue of Soviet magazine Technical...

PM 2Ring

@copper.hat You could do a similar double res trick on the Osborne.

anak

2:37 AM

Alessandro was the set theory fellow, right?

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$Mathematics$ Mathematics