Chris Purcell @ccppurcell@mathstodon.xyz

Switched to my winter jacket today. Found an old surgical mask in the pocket, and got that deja vu feeling, like finding a five pound note in last years jacket. Then I realised, it's not just deja vu, this is the second time that's happened, as this is the third winter of covid. Will it be the last?

I omitted a detail in the previous toot for clarity. The definition of each of the above also gives the numeral representation. The number "one" has some additional technical definitions like "(number theory) the first positive natural number", but the main definition has no dots, does not refer to two, and actually seems to define one as the numeral 1...
2/2

I wanted to know the etymology of the word "eleven" so looked it up on wiktionary. It seems to be something like "one left", but that's not as interesting as the definition: "the number after ten and before twelve"...!

The numbers down to five have a similar definition, although annoyingly not standardised, there seems to be a change in wording after ten.

Weirdly, three and four additionally represent the value with dots, and two *only* has the dots and doesn't mention one.
1/2

Inspired by this toot: https://weirder.earth/@eldang/106268287486978878

(is there a way to "quote toot" in a reply to another toot?)

If 13 is a baker's dozen, can we call 3.142 a baker's pi?

Does anyone else have a strange aversion to including a space in a password?

I thought of a variation on the old "is a hotdog a sandwich" question. Is a pair of slices of bread a) an open faced sandwich with a bread topping or b) a normal sandwich with the empty filling?

I learn from Lance Fortnow on twitter that today is the 50th anniversary of Cook's STOC talk introducing P vs NP.

I wonder (and google isn't much help) what sort of problems would have been considered important or central to theoretical computer science before P vs NP? Any ideas?

I've got an algorithm that is polynomial time, naive analysis involves a multiplicative constant of 2^{45} but a short argument brings it down to 2^{15} (I can probably go a little further but not much). Is there a nice visualisation of this modest improvement?

Theorem: every planar graph has a four colouring
non-proof: name a counterexample!

Theorem: everything has a name
proof?: name a counterexample!

Had a rough couple of days: two paper rejections and then found a couple of papers that make a large chunk of my current project obsolete. Ah well.

Don't ask me how I got to it but the wikipedia page for the BCG vaccine uses a square root symbol instead of a tick https://en.wikipedia.org/wiki/BCG_vaccine#Europe

I noticed some weird behaviour on whatsapp (android). I just sent three messages with respectively 20, 30, 40 words to the same contact. The message boxes had different widths but multiple lines. When I go away and come back, they are all fixed width, but when I then scroll up and back down, the sizes are different again.

I know this is pretty trivial, but initially I just noticed the different sizes and wondered if there was in interesting reason. Now I'm very confused. Any ideas?

One idea I had: if you take a cycle and add a path between two of its vertices, you get a graph with three cycles. If you repeat, you either get six or seven depending on the choice of vertices. That means you can only achieve four or five cycles by gluing two graphs at a vertex, which I used to figure out a₄ and a₅.

Here's a sequence that doesn't appear to be in the oeis (unless I erred). Let aₙ be the size of the smallest graph with exactly n cycles. The first few terms are: 3,5,4,6...
a₅ is pretty hard to figure out by hand (I think the answer is 8) but it's easy to check that a₆=5 a₇=4.
A trivial upper bound on aₙ is 2n+1. I think there should be a not too difficult upper bound of O(√n).
Anyone know anything else?

My office mate and I failed, in quick succession, to correctly divide 60 by 5. Time to go home I guess.

Nowadays every mathematics article goes online somewhere, and I would guess that the vast majority of article-reading is done on a screen of some kind. But the format stays the same, i.e. a long linear pdf of results, even if the dependencies between sections, lemmas, theorems etc are more like a tree. Has anyone done something like a mini wiki for an article, or in place of an article?

Not even "did you mean"

I wonder which has been written/typed more in human history: "(" or ")". Obviously parentheses are accidentally left open, but on the other hand it's quite common for Russians (and presumably others) to type "))))))))" as a form of emoticon. Do these balance out? Are there other times that one gets used without the other?

Update: source
https://xkcd.com/2286/