@mjd@mathstodon.xyz
@mjd@mathstodon.xyz avatar

mjd

@mjd@mathstodon.xyz

I am an amateur mathematician, but not the angle-trisecting kind.

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mjd, to random
@mjd@mathstodon.xyz avatar

Take a look at this email and let me know what you think.

http://plover.com/~mjd/misc/Ask%20me%20anything.txt

I have gotten a lot of incoherent and bizarre email over the years, but never anything quite like this.

mjd, to random
@mjd@mathstodon.xyz avatar

For the first time, the complete connectome of an insect brain (drosophila larva) has been mapped.

https://www.science.org/doi/10.1126/science.add9330

It has 3016 neurons and 548,000 synapses. For comparison, c. elegans has 302 / 6702.

fanf, to random
@fanf@mendeddrum.org avatar

had a fun conversation in the pub this evening about practical chemistry

TIL conical flasks are safety equipment!

when a reaction gets too energetic, a conical flask will blow its bottom out and drop the mess on the bench or the floor

instead of exploding in all directions

ie not towards the experimenter’s face and eyes

clever design!

mjd,
@mjd@mathstodon.xyz avatar

@fanf I didn't know that, I thought it was just because they are hard to tip over

jonmsterling, to random
@jonmsterling@mathstodon.xyz avatar

Ultimately we have to ask ourselves if it was overall a good thing that computer science as a discipline ceased to be part of mathematics — rather than broadening the horizons of mathematics and bridging the gap between mathematics and social science. I am not speaking purely rhetorically, as there are legitimate arguments to be made on both sides.

mjd,
@mjd@mathstodon.xyz avatar

@boarders @antoinechambertloir @jonmsterling Just yesterday I was pondering his remark that “The establishment of a truly operational semantics of algorithms is perhaps the most important problem in computer science.”

I love Girard.

christianp, to random
@christianp@mathstodon.xyz avatar

Happy 175th birthday to Felix Klein, and happy 12th birthday to @aperiodical!
For our very first post, a youthful-looking @standupmaths and @stecks shared their top N facts about the Klein bottle: https://aperiodical.com/2012/04/top-n-facts-about-the-klein-bottle/

mjd,
@mjd@mathstodon.xyz avatar

@christianp @aperiodical @standupmaths @stecks Now I am curious to learn the bottom N facts about the Klein bottle.

mjd, to random
@mjd@mathstodon.xyz avatar

New logic post on my blog: “Well, I guess I believe everything now! ”

https://blog.plover.com/math/logic/k2.html

mjd, to random
@mjd@mathstodon.xyz avatar

But today's baffling Math SE question is similarly difficult: “A bag contains 5 balls of unknown colors. A ball is drawn and replaced twice. In each occasion it is found to be red. Again two balls are drawn at a time. The probability of both the balls red is?”

https://math.stackexchange.com/q/4903525/25554

mjd, to random
@mjd@mathstodon.xyz avatar

The hardest math problem I've ever seen on Math SE is this: Four marbles are drawn from a bag. What is the probability that two of them are white?

b0rk, to random
@b0rk@jvns.ca avatar

I've been criticizing git nonstop for months on here but I really do love it. I've been using it for probably 13 years, I'm used to all of the warts that I run into regularly, and I don't think I've had a major problem with it anytime in the last 7 years or so.

not to minimize all of the very real problems that people have with git but I really do believe that it's possible to use git successfully

mjd,
@mjd@mathstodon.xyz avatar

@b0rk I feel pretty much the same way, but all the same I'm eagerly hoping that whatever replaces it will be better.

fanf, to random
@fanf@mendeddrum.org avatar

surely this version of the joke should go,

concurrency is two of the hardest problems in computer science

https://buttondown.email/hillelwayne/archive/what-makes-concurrency-so-hard/

mjd,
@mjd@mathstodon.xyz avatar

@fanf

“Ask me what's the hardest thing about concurrent programming.”

“Okay, what's the hardest th—”

“TIMING!”

mjd, to random
@mjd@mathstodon.xyz avatar

What's a good way to draw a diagram of a not-necessarily transitive partial order? Hasse diagrams really want the order to be transitive.

((The orders I want to draw are: the nodes are permutations of ({1,2,\ldots n}) and (P\prec Q) whenver (\sum_{Q(i)<P(i)} i < \sum_{P(i)<Q(i)} i).))

mjd, to random
@mjd@mathstodon.xyz avatar

“Instead of exploding in rage, [Murderbot] decides it's going to half-ass its job and watch entertainment media instead.… Humans making that choice is probably one of the reasons we still exist as a species.”

( https://marthawells.dreamwidth.org/649804.html , via @katenepveu )

mjd, to random
@mjd@mathstodon.xyz avatar

Someone in Math SE wants to know how many ways there are to 3-color the vertices of an icosahedron and although I'm not sure what their difficulty is I feel sure that it is not mathematical.

mjd, to random
@mjd@mathstodon.xyz avatar

We don't consider 1 to be a prime number, but it wasn't always so. The convention has been different in different times and places.

“But then the statements of all your theorems would have to exempt 1,” you cry. Not so. Many would. Some would not.

On some other planet there is a culture of mathematicians who don't consider 2 a prime. When they meet us, they are surprised. “But then the statements of all your theorems will have to exempt 2,” they will cry. Our answer will be the same: many do. Some do not.

(Bonus trivia: the Treviso Arithmetic of 1478, perhapsthe earliest-known European arithmetic textbook, says unequivocally that the numbers begin with 2 and that 1 is not a number.)

mjd,
@mjd@mathstodon.xyz avatar

@christianp a friend once told me he heard his father, after half an hour of silence in the next room, loudly pronounce “ONE”.

He went into the next room to ask what was going on.

“I'm counting my belly button.”

mjd, to random
@mjd@mathstodon.xyz avatar

In early Medieval account books, the numbers 7, 8, 12, 13 were written in roman numerals as 'vij', 'viij', 'xij', 'xiij'. The trailing 'j' helped prevent a person from changing a 7 to an 8, or a 12 into a 13. (Or similarly, from misreading a 13 as a 12, etc.)

I thought that similarly numeral 6 was written as 'vj' and not as 'vi' but I haven't been able to find an example either way. Can anyone help me?

gregeganSF, to random
@gregeganSF@mathstodon.xyz avatar

It’s 30 years this month since PERMUTATION CITY was first published. But of course, all the same letters had been present in other books for centuries before, they just hadn’t been read in that order.

Excerpt at:

https://www.gregegan.net/PERMUTATION/Excerpt/PermutationExcerpt.html

mjd,
@mjd@mathstodon.xyz avatar

@gregeganSF Did you generate the random-appearing permutations on the cover? And if so, did you use the immediate output of the random number generator, or did you tweak it afterward?

mjd,
@mjd@mathstodon.xyz avatar

@gregeganSF thank you!

mjd, to random
@mjd@mathstodon.xyz avatar

This is such a weird menu. No choices more than a week, unless you want “forever”. In my case I wanted “until I forget about this loser” = 6–12 months.

(The user I was muting was not @svat, it was someone else.)

mjd,
@mjd@mathstodon.xyz avatar

@christianp Is that something you can do?

b0rk, to random
@b0rk@jvns.ca avatar

i've been hearing a lot from folks on here who are frustrated with git (for many good reasons!)

but I'm curious about the opposite perspective: if you've worked with more than one version control system over the years and you prefer git, I'd love to know:

a) what other systems have you worked with? (hg? svn? p4?)
b) why do you prefer git?

notes:

  • please no replies about why you think git is worse
  • interested in answers other than "because I have no choice"
mjd,
@mjd@mathstodon.xyz avatar

@b0rk I have worked with CVS (which I no longer remember) and SVN. I despise SVN with a white-hot fury, because one day I decided I would make a topic branch, I made the branch, which is a little weird in SVN because version numbers are sequential. I got the work done on the topic branch, and then I couldn't find the merge command.

I asked around. There isn't one. I said “How do I merge?” I was told “Oh, when you started you should have (done some asinine thing I no longer remember involving some sort of manual checkpointing of diffs).” I said “What do I do now?” They said “You'll have to incorporate the changes by hand.” I said “What is the point of a branch feature if you can't merge afterward?” Apparently it's so you can maintain different versions of the software in parallel and apply changes manually to each parallel version.

mjd, to random
@mjd@mathstodon.xyz avatar

Just now I was writing tests and for one of the properties I thought “wow, there's really no good way to test this, I guess I'll just skip it.”

I thought a little more and came up with a crappy way to test it and thought “This crappy test will be false-negative too much of the time, it probably is not even worth writing.”

Then I wrote the poor test anyway.

Then the poor test failed and revealed that my code had a bug.

b0rk, (edited ) to random
@b0rk@jvns.ca avatar

poll: how confident do you feel that you know what a "ref" or "reference" is in git? (“ref” and “reference” are the same thing)

for example in this error message (from git push)

error: failed to push some refs to 'github.com:jvns/int-exposed'

or this one: (from git switch mybranch)

fatal: invalid reference: mybranch

mjd,
@mjd@mathstodon.xyz avatar

@b0rk I think it's a symbolic name for a git object, effectively an abbreviation for a SHA. The object is almost always a commit, but in very rare cases it needn't be.

b0rk, to random
@b0rk@jvns.ca avatar

i uh spend a lot of time thinking about whether various surprising software design choices are

a) intrinsic to the problem domain ("it turns out it DOES make sense!”)
b) made sense historically ("this made sense in 1992, but it didn't age well”)
c) just a typo/mistake (the "Referer" header)
d) related to budget/time constraints (“well, prototyping with shell scripts is fast!”)
e) cultural/organizational (“well, Google is the main funder for this project, and…”)
f) something else

mjd,
@mjd@mathstodon.xyz avatar

@b0rk hey, I thought of one that might be (b) but might be different: it was designed to work under resource constraints that made sense historically but that no longer apply (and may be forgotten).

Examples:

  1. Horrible sendmail.cf syntax was designed to be parsred very quickly on slow 1970's hardware with not-fully-developed-yet 1970's parsing technology.

  2. C90 standard requires that externally-visible identifiers (e.g. library functions like printf and malloc) must have nanes that are all unique in the first 6 characters, for compatibility with then-existing linkers that ran in highly memory-constrained environments.

johncarlosbaez, (edited ) to random
@johncarlosbaez@mathstodon.xyz avatar

Hindustani music has lots of ragas, but they're often organized into the 32 kinds shown here, of which only 10 are very commonly used. These kinds are called "thaats".

Each thaat is a 7-note scale. I'll explain them in a western way, not an Indian way. This will make it clear how 𝑢𝑛𝑠𝑢𝑟𝑝𝑟𝑖𝑠𝑖𝑛𝑔 the ideas are to anyone who has studied western music theory.

Let's imagine our thaat starts with the note C. Then:

• it must contain C
• it must contain D or D♭, but not both
• it must contain E or E♭, but not both
• it must contain F or F♯, but not both
• it must contain G
• it must contain A or A♭, but not both
• it must contain B or B♭, but not both.

So, we get 2⁵ = 32 thaats. It's really unsurprising that C and G are locked in place, while the other 5 notes are flexible - after all, C and G are the 'tonic' and 'dominant', also called the 1 and 5, the most important notes in a scale.

A lot of thaats match familiar western modes, but later I'll show you some that may not. Maybe some expert on jazz can say if they've seen them.

Thaats are just the start of the story, since we can get extra ragas by leaving out some notes in a thaat... and as a result, different ragas can come from the same thaat.

But there's a more urgent issue: what are all the letters in this chart? The notes in the thaat are called

sa re ga ma pa dha ni

or for short

S R G M P D N

These are a lot like the western "do re mi fa so la ti".

But as I've said, we get a binary choice only for 5 of these notes, namely R G M D N, since the other 2 are locked in place. That's what the chart shows. It's a binary tree with 32 leaves, namely the thaats.

(1/n)

mjd,
@mjd@mathstodon.xyz avatar

@johncarlosbaez It's interesting that it starts at M in the middle and follows the circle of fifths downwards. A Western version would most likely have gone in the reverse order.

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