@nateberkopec That's why at my day job we are decommissioning some of the microservices (especially in places where latency is important to the customers). Not all the way to something I'd quite call a monolith, but in that direction.

@kangmeister Ooh nice. That's my excuse to go read https://en.wikipedia.org/wiki/Ramsey's_theorem especially the table in the "Known values" section. It shows that R(3,k) is known for k from 1 to 9 and that (at least as of 2023), k=10 is the first place where the value is only known within some bounds, not exactly.

Just yesterday, I was musing to a (younger) research visitor, "I hope that within my lifetime we will still see another breakthrough on the bounds for R(3,k)"...

https://arxiv.org/abs/2505.13371

I am excited to see what developments follow on from here!

(Also that old adage: just as soon as you publish a survey (https://arxiv.org/abs/2501.03379) it is out of date.)

#math #mathematics #combinatorics #ExtremalCombinatorics #graphtheory #probability

How do we compute a function f : (ℕ → ℕ) → ℕ abstractly?

This question goes back to Brouwer in the early 20th century, and was investigated by many people, including Kleene.

Think of the input α : ℕ → ℕ of the function f as a sequence of natural numbers.

So out of a sequence of natural numbers, we want to get a natural number.

How is the sequence α given?

In our set-up, we can only query α at inputs i : ℕ to know what αᵢ is.

So you can imagine a computation of f α as a finite sequence of queries to α until we are satisfied and finally can answer a natural number f α : ℕ.

You can picture this as a tree.

The leaves of the tree are answers.

The internal nodes are questions. We ask "what is α i?". There are countably many answers to this question. It can be 0,1,2,⋯,n,⋯. So a question has countably many subtrees.

So we inductively define a type 𝕋 of trees by constructors

η : ℕ → 𝕋
β : (ℕ → T) → ℕ → 𝕋

The idea is that, when such trees are interpreted computationally:

* The leaf "η n" gives the answer n and completes the computation.

* The branching tree "β ϕ i", where ϕ : ℕ → 𝕋 is a forest of countably many trees, asks the question "what is α i?" and then proceeds to the subtree "ϕ n" if the answer to the question is n.

2/

@jeffkibuule My threshold is closer to an hour a day than an hour every three months but I totally admire the general attitude you are espousing here.

@testobsessed I mean I should probably take that question as rhetorical but "because six hours is not a trivial amount" and "because I feared it would be 60 or 600 hours" are valid answers (I do notice your other answer to this thread which makes it sound a lot less deliberate than that, which also seems pretty relatable).

@Patricia @balpha OK, when faced with something like this I often think "maybe Martin Fowler can cut through the noise and think clearly about this topic". And he did try: https://martinfowler.com/bliki/TeamTopologies.html . (I'm just as bad as anyone else in terms of skimming or not even really trying to finish a book, so I'll just quip that Fowler must have written "Team Topologies: the good parts" without being able to particularly evaluate that claim).

@balpha @Patricia The first dozen or two posts were good. I couldn't decide whether to buy the book just to see whether it really says all the things the thread claims it does, or run away screaming for all the reasons in the thread.

@LaurensHof You'd know better than I what people in general are thinking about. But the number one question in my mind is what happens when/if Bluesky PBC is no longer able to run infrastructure on the scale they are now (presumably, in the scenario that revenue does not materialize).

@mattmcirvin @richardelwes @mavu I don't know which way the causation ran, but agreed 18 and 36 bit computers tended to use base 8 in contexts like dumping memory ("octal dump") whereas 16 and 32 bit computers tend to use base 16 ("hex dump").

@ggwash I used to park at a BART park and ride overnight or even for a weekend but they don't allow that any more (driven by fuller parking lots maybe? I'm not really sure). For various reasons, I don't have a current situation where I'd do this if I could, but if park and ride is a good idea (a big topic itself) I don't see why you'd exclude the overnight case.

@mattmcirvin @mavu Ok yes this is very cool! The biggest constructible odd-sided polygon is the product of the known Fermat primes:

3 . 5 . 17 . 257 . 65537

which is 2^32 - 1

which is the largest integer expressible in computational systems which allow integers to have length up 32 bits.

@kingtor @wayword I was vaguely aware of those questions into the origin of the term, but reading the summary on that webpage makes it sound like this may go a bit deeper than "etymology is not destiny" style debates (tied to how this term has been somewhat common–although hardly everyday–in software development circles), into things like how society reacts to.... uh ... I think I'd have to do more reading/listening to really complete that sentence.

@kingtor @wayword LOL, and it gets worse. I have been using it enough that I just instinctively go to "well, of COURSE you just mouse over it or click on it to figure out which [at]wayword it is." Which, if I remember the terminology of user interface design correctly, is called "Stockholm Syndrome".

@tallyroom Really nice description of various electoral systems with a particular focus on preferential voting systems with one or several candidates elected per district. As for whether 3 or 5 is better, one of the things that surprised me when I learned the Ireland system is that they compromise! Depending on the district, it elects 3, 4, or 5 parliamentarians.

The San Bruno BART train station seems to have (at some point in the past) declared war on pigeons. The pigeons are winning. (Present but not pictured: lots more pigeons)

@bodhipaksa @jeridansky I probably will regret prolonging this thread but what are the alternatives for dental floss? A handle with some non plastic material? (Don't remember if I've seen those) Using the dental floss wrapped around fingers technique? (this means half a meter or so per use, which also seems like it probably isn't great for the wildlife)

@HelenBranswell This is actually good news compared with the delays and moving goal posts I had expected. I won't try to go too deep in a short message like this, but approval is for everyone 65+ years old and "people aged 12 to 64 who have at least one medical condition that puts them at higher risk of severe illness if they contract Covid".

@kingtor A Way with Words is now at @wayword so you'll want to update wherever you got that old address.