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
> 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.
> Play and read lots of sheet music. Especially by sight. It will come, I promise :)
Grabbing an old hymnal works wonders for this, even if you're not religious. Most of the pieces are short and simple enough to use as exercises for sight reading and learning theory.
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)
I think this is a good perspective - it follows the general approach in software engineering that if you're going to introduce something with a massively different approach, learning curve, and cost of adoption, it needs to come with the associated real-world benefits.
For most software stuff it would be very hard the benefit of introducing this stuff vs. what the standard paradigms that everyone already knows
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.