HN user
This oughtn't be super surprising, even the DE comment at the end - people do just have bits of maths they gel with more than others!
Even so, CT is not easy to motivate without a lot of experience in a few specific areas of maths - it's definitely a very "meta" subject (even though a lot of these blogs pretend it's super applicable to everyday engineering) and is a very different lens from the maths taught up to that point.
I'm surprised to see no mention of topos theory in this page? The sense in which category theory is a generalisation of set theory is pretty weak imo until you bring in concepts like subobject classifiers. This isn't the only thing topoi generalise, but is a pretty significant one
I know it varies by topic, but my experience asking ChatGPT about things I already know about (eg a smattering of topics in algebra) was bad. Like, bad bad. It got the intuition completely wrong, and asking for more explanation just got you complete garbage that ignored everything except the most trivial cases. Just be careful for anything outside of a 101 class!
Not commenting on whether it's good/bad, but I think it's completely different to your examples. Both of those say "here is context of my past achievements; this is an indication that what follows may be of high absolute quality"
As opposed to the "I am N years old", which is saying "here is context, which doesn't by itself indicate achievement, which may be an indication that what follows is of high relative quality"
Last I checked this was opt-in on Android; it's been default on iOS since I think 2017ish?
I remember using this site for checking my work in a number fields course years ago; I never realised it had so much more
Very weird seeing this on the front page
That's not the best way to view it. You can prove it by showing that for an n-dimensional disc, there is no contraction to its boundary; which I think is a bit more illustrative of what this FPT is doing
Cool! I love collections like this :) A 10-min format and sort (alphabetical or chronological) would make this so much more scanable though
Absolutely. In cities which are equipped for it, the small self-driving vehicles make so much more sense, for this reason.
Starship (https://www.starship.xyz/) have been running in a big way regularly in Milton Keynes (UK) for years now; the little robots driving around are a regular feature. Seems to be expanding to Cambridge (UK) too.
I imagine US suburb design makes this less feasible (I think I read that Starship started on college campuses in the states), and that's why we don't hear so much excitement about this approach? It seems to make way more sense to me than drones, mostly for the weather issue
If anyone is yet to see it, Tantacrul (on youtube) is now deeply involved with MuseScore (UX lead or similar?); he put out an awesome vid on the design of MS4 at the beginning of the year: https://youtu.be/Qct6LKbneKQ
His video on how Sibelius' UX is a pile of shit remains one of my favourite vids on yt: https://youtu.be/dKx1wnXClcI
I honestly don't know. This might be a skill issue on my part (very much not an educator), but I think of it as a language for thinking about structural abstraction, so to me the question is akin to "is there a real-life problem that German relates to?"; I can certainly think of lots of problems that would be made much much easier by understanding the language (e.g., getting around Germany, i.e. noticing abstractions), but it's tough to point to anything for this explicit question other than "conversing with someone in German".
I guess to try and mirror your calculus example, I'd try and motivate why someone should care about abstraction itself, perhaps with examples like 'calculating my taxes each year is exactly the same problem, except the raw numbers have changed'.
Alternatively it might go over better to say something like: "Imagine you have a map with a bunch of points, and paths which you can walk between them. CT is the study of the paths themselves, the impact of walking down them in various routes: for mathematicians, this means looking at things like turning sentences such as 'think of a number, add 4 to it then divide by 2 then add 6 then subtract 1' into 'think of a number and add 7'. Once you've spotted this shortcut on this silly toy map, you'll recognise the same paths and the same shortcut when you see on your tax form 'take your income, add £400 to it, divide by 2, add £600 and subtract £100"
This is my field :)
Category theory is about connecting the dots between different areas of maths. The "general application" is to allow you to reason over the structure of a problem you're interested in, while throwing away all the superfluous details. It arose when geometers and topologists realised they were working on the same problems, dressed up in different ways. I think the utility for technical people, from this perspective, is pretty clear.
As for the general working person? I think it's just an exercise in learning to do abstractions correctly, which is valuable in any line of work.
There are actually people who advocate that we should base maths education on category theory much earlier (much as New Math was interested in teaching set theory early on, as a foundational topic). CT is an unreasonably effective tool in a large section of pure maths, so this doesn't sound unreasonable to me; it wouldn't be nearly so scary if it were introduced gently much earlier on (in the same way we start to learn about things like induction in the UK in secondary school, long before formalities like ordinals are introduced at uni). Currently only a very specific, highly-specialised section of the population learn CT, but if something like this were to happen, I'm sure we'd see lots of benefits which are hard to identify at the moment.
This makes the same mistake being called out in the comment you're replying to. The point isn't about the mechanics of solving a differential equation, it's about gathering the intuition about a way of approaching problems.
(Also, while it might not be the tools needed for the average homeowner, there are plenty of optimisation problems similar to "how much fence do I need" which are most easily solved by solving the Euler-Lagrange equations)
Not a solution but FWIW, in my time working at Apple, they encouraged you to log in to work devices with your personal ID (with the expectation you don't allow files to sync). There were some people who kept them apart, but the overwhelming majority just used their personal with no issues. Personally I made a new one, but at the time it was my first Apple device so wasn't really a decision.
And Exponential Idle!!
Honestly I just think the concept of Son/Radarr doesn't translate well to music, I find Lidarr fiddly in general.
In particular I'd add to your list that the overnight scans to update cover art are an absolute mess. It's not so big a deal on my libraries in Sonarr and Radarr, but for Lidarr? Jesus Christ. I have reasonably sized music library (~400/500 gig), and every night Lidarr starts phoning out to check, for every single album and artist, whether the associated cover art or artist image has changed. This takes hours, and is completely unnecessary, and cannot be turned off. I've resorted to just blocking the addresses it does this on, but this breaks things when I try and use it to add new music.
I'm don't think this dichotomy is at all fair. Just because someone makes a piece of software public does not mean they want it freely copied, and I think that can be a completely reasonable stance to have. I'm struggling to make sense of your argument unless you believe either:
- Code is not intellectual property; I don't see this as easily defensible. It takes time, effort, and in some cases seriously heavy resources to come up with some of the tech companies rely on. Should all private companies rescind copyright on literally everything their staff write?
- Intellectual property is a nonsense concept altogether; in this case, I don't think you're ever going to get your way in the court of public opinion.
The point here is that this isn't some example from a textbook or even stack overflow, but licensed pieces of work with all the legal complications that come with that. This is about the potential use of this code in proprietary code (or code otherwise incompatible with the original licenses), and I really don't think anyone would say it is "accepted best practice" to copy out someone else's work you find online, licenses be damned, in a professional setting.
Even from this page there appears to be a fair bit missing. E.g. one of the biggest UK gov orgs is @alphagov (~1.6k repos), which I can't seem to see on your dash?
Today's developers didn't learn binary before learning Python, why should you learn how to code without the most modern tools?
This phrasing makes me wary. There's a difference between being self-taught, and not even bothering to teach yourself the absolute fundamentals of computing, like binary...
I genuinely think this is a UK/US thing (limiting to those countries because that's the limited experience I have); in the UK this is absolutely true. There is a definite cultural thing going on where people play down how much effort they put in to things. It's definitely 'uncool', throughout school, higher education and in the workplace, to be super keen.
Contrast to the US: American colleagues I've had have all agreed that it's kind of the reverse on that side of the pond. I've heard people brag about the hours they've put in to work; that would be a complete embarrassment over here, especially if the work turns out not to be top-tier.
Well this is wildly wrong. Scales, arpeggios, etc. are taught not just for the theoretical understanding they help with but because they occur VERY frequently in actual pieces
Sure, but they also take an extraordinary amount of money from taxpayers. Also, there are issues over whether they own everything they make money from (e.g., properties, and recently a large number of official state gifts). I'd say they're doing rather well off of us ;P
The Gruanidad has been running a series on this (especially nice to see in the run up to the coronation) https://www.theguardian.com/uk-news/series/cost-of-the-crown
In particular, from here, https://www.theguardian.com/uk-news/2023/apr/07/british-roya...
Elizabeth II and Charles III have extracted cash payments worth more than £1.2bn from two hereditary estates that pay no tax, in addition to the millions they receive in public funding for their official duties. In 2022, they received £21m each from the duchies of Lancaster and Cornwall respectively, despite a centuries-old debate over whether the two estates in fact belong to the British nation.
I absolutely love Xmonad, and I'm very impressed by how easy its architecture makes it to get complex changes to your environment off the ground. It's a godsend in terms of interfacing with the box, mostly because its configuration is so good, I just wish it had some prettier GUI building blocks to use --- the included packages like TreeSelect and GridSelect are absolutely hideous. I've always assumed their problem could be that no one who can really do UI is interested in an X WM focused on functionality over style, but it's a shame.
Huh? This isn't making a lot of sense to me. Why do you say the rationals aren't much better then floats? In situations like this surely we absolutely want to be working in the rationals, and they're a very easy way to do these calculations correctly without having to worry about tolerance bounds for arbitrary-precision float calculations
I would avoid flash cards. A few tangible steps you could take:
- Play and read lots of sheet music. Especially by sight. It will come, I promise :)
- Complete Ear Trainer is hands down the best aural training aid out there. Be warned, it is difficult (I got it while studying for my later instrumental grades and it was initially very tough) but I’ve never come across a tool as good. Think of it as being a bit like aural flash cards with harmonic context
- Transcription is a good idea. I’ll also suggest transposition; my main instrument is horn, and for grades (at least in the UK) you had to do sight transposition as well as sight reading. Once you’re comfortable sight reading, try doing the same thing but playing it up a fourth, or down a third, etc.
So I come at this from a mathematical background --- graduate student in categorical algebra --- but I've done a couple years of SWE work, so I'm not unsympathetic to this point of view. The way I see it, when you want to reason about things like data processing (which is what a massive chunk of writing software is, moving data from form A to form B), category theory provides what is in some sense the "correct" language/framework in which to think. It's not just an abstraction circle-jerk, it's a genuinely useful perspective, particularly for guiding your mind to spot non-obvious connections between pieces of code.
The problem as I view it is that CT is first and foremost a discipline of maths. It was developed to help mathematicians, is very sophisticated, and very specialised; learning CT for SWE is taking a sledgehammer to a nut. I can't honestly recommend it as a field of study to someone who isn't interested in the problems it was developed to solve. If you don't have a solid grounding in set theory, logic, algebra, topology, etc., it's a very tough field to motivate. The vast majority of CT is of little to no relevance for SWE work. Adjunctions, for example, are absolutely fundamental to all of maths, but in truth are not really relevant for SWEs. As a result, you see people trying to teach concepts like monads without reference to them; this is slightly insane from where I'm standing...
Your question about whether there are things CT does that other branches didn't already do; one of the fundamental utilities of CT in pure mathematics is "making trivial things trivially trivial". That is to say, it makes it very clear which parts of your problem are local to your specific situation, and which are purely "structural" from the categorical constraints. The SWE analogy would be separating business logic from other layers. So at least for mathematicians, it absolutely does have novel utility, and has drawn links between a huge number of disparate studies that were not well-understood previously.
So if you _do_ care about posets and groups and cohomology theories, CT will genuinely open your eyes, and (albeit, this coming from someone with less working experience than yourself) it could give you a deeper, or at least different understanding of the code you're writing. Otherwise, I'm not sure it's worth putting yourself through it, tbqh.
(If you do decide to give it another go, please use a better resource than the linked post; after a quick scan it looks pretty weak)
There was discussion of this a while back on reddit: https://www.reddit.com/r/BrilliantLightPower/comments/ffnnxw...
Sounds like the arxiv author may be greatly exaggerating or misunderstanding, but I'm not up to speed enough on the math to say for myself