Vibe coding is cursed gold from the first 'Pirates of the Caribbean' movie.
> "For too long I've been parched of thirst and unable to quench it. Too long I've been starving to death and haven't died. I feel nothing. Not the wind on my face nor the spray of the sea. Nor the warmth of a woman's flesh."
[steps into moonlight becoming a skeleton]
It was sarcasm, no one uses anything like that outside of the US. Using football fields as a measure of distance is as "stupid american" meme around the world.
Most of the rest of the world assumes a soccer pitch when an American says a football field. They are basically the same length, so what exactly is your problem with using them as a marker for distance?
We Brits have our own markers, e.g. the area of Wales or the volume of a double decker bus. They don't translate that easily either.
Interestingly the area of a football pitch has a pretty huge degree of tolerance - between 45-90m wide and 90-120m long - and iirc while they can be nearly square, they aren't allowed to be exactly square (i.e. you can't have a 90x90m pitch, but 90x91m is ok ... if a little unusual).
At some point I believe the home team would adjust the width/length according to opponents' preferred tactics, but idk if that happens anymore.
There probably aren't many regulation football pitches that narrow ... but it is absolutely permitted. You can get this information plenty of places but since you raised FIFA, it's in their PDF containing the Laws Of The Game (determined by IFAB) https://digitalhub.fifa.com/m/1cf301829f1cf996/original/ifab... - see pages 36 and page 37
Note that they do impose some additional restrictions for internationals. And yes UEFA also have restrictions on the dimensions of the pitches that can be used for their competitions (Europa League, Champions League, Conference League) much like they have restrictions on stadia at various levels in those competitions. But according to the laws of the game, those are the dimensions. It wasn't always this way - Rangers narrowed their pitch by "a couple of yards" to mess with Dynamo Kiev in the European Cup back in the late 80s (it worked, they beat them and advanced).
We both know that a 45x120m pitch would look certainly look weird, but if we are talking about what is allowed in football the standard are the IFAB laws, not what UEFA stipulate for their elite competitions. If you're watching the English Premiership then you won't see such pitches - these clubs will believe they can compete in such competitions and will want to do host home games at their own stadia. If you're watching or playing in 2nd tier or lower (a number of clubs and pitches vastly outnumbering those at the very top) in any country you very well might encounter them.
> if we are talking about what is allowed in football the standard are the IFAB laws, not what UEFA stipulate for their elite competitions.
To be pedantic though, EUFA defines grassroots football as anything that is non-professional and non-elite, and since 2017 IFAB says that national FAs are free to make their own rules on pitch dimensions for grassroots football. So there is no contradiction - IFAB, EUFA and your FA are all in agreement :)
How would I know? But it doesn't matter: If your local youth club decides to host an officially sanctioned international tournament, they might go ask IFAB about what size to make the pitches. IFAB is going to tell them that if they meet the national FA guidelines, then they meet the IFAB guidelines. (Look at page 25 of the IFAB law book)
Good point about IFAB, I have only been referring to orgs like UEFA and the FA.
In England all organised football, even amateur, is regulated by the FA, so we can say there is no regulation pitch here in England that is less than 60m wide
But you're right, elsewhere it could be all sorts. Pitches can be hemmed in by rocks, trees, water, dwellings, whatever so people will just play on what they have.
I believe the FA actually
use the looser dimensions (meaning 45 metre width is ok), but you're right few clubs at the upper end of the pyramid will really push the boundaries so to speak. Might make for some fun cup encounters though :)
In Italy we definitely often use "campo da calcio" as a quick measurement unit for areas. I'm guessing that's due to the fact that for most people using squared meters is really limited to measuring housing areas and other few use cases, so reverting to something that everybody knows well (a football field) is much more effective. For distances, everybody is very comfortable using all powers of 10 of the meter for all kind of purposes so there's no need to use references to real world measurements.
> Just like it is in many parts of the world today.
It's not true, despite population increase number of people dying of starvation goes down https://sites.tufts.edu/wpf/famine/ the reason of starvation in modern times is political, not production shortage.
So in all the thousand years mankind has been around we had to wait for the 1800 to be rescued from all famine waves, yet 3 centuries, a large portion of countries still hasn't managed to have been saved from such trends.
How many farming fields and insects have been destroyed with chemicals and genetic modifications from that wonderfull revolution?
Just next door to Poland, in Germany, it's already $15 per ticket. And at least with adults or teenagers it's very easy to spend another $10 per person on snacks and something to drink, which already pushes you to $100 for four people.
At my local theater in California, an adult ticket to see A Man Called Otto at 7:30 pm is $11.75 and a child is $8.50. So a family of four would be spending $40 - $50 to see the film.
Avatar: The Way of Water at 6:30 has the same pricing.
A package of candy from a local store will be $1.50 - $3. (Each.) There's no way you're getting up to $100. (You could spend more by buying food inside the theater, but you'd have to be stupid to go for that.)
Another hyperbolic geometry game and previous discussion here [1]. The different areas in the game help with a grasp of different interesting properties of the non-euclidean geometry.
"We will assume no background knowledge on behalf of the student, starting from scratch on both the programming and mathematics."
This is a fantastic "side effect" of the fact that category theory isn't built on any other mathematical knowledge. You don't even need even any arithmetics for that.
At a meta level, Category Theory requires some comfort with abstraction, which really only comes with a mathematical education. So while it may stand apart from much math, it relies on your strong mathematical foundations.
That's a really great analogy, actually. You can't tell a brand-new cook "salt to taste," but you can tell a cook with an intermediate level of experience "salt to taste" even if it's a recipe they've never made before. You can't impart the experience in words, pictures, or symbols. You can't add a chapter zero that gets them there. But the right kind of experience will get you there pretty quickly.
I admit it's kind of frustrating that it can't be boiled down to a list of discrete things you need to know, but if I had to explain the difference between me before I had "sufficient mathematical maturity" and me after, I would explain it in terms of habit and confidence and other squishy things that aren't mathematical at all.
Giving a precise value for this doesn't work in any case. "Salt to taste" is inherently qualitative.
Most pizza dough recipes quote around 5g of salt for 250g flour. Personally I prefer double that amount, and this is the case with many recipes.
Perhaps specifically with salt there is an insane amount of paranoia about blood pressure. In many ways it feels as irrational as Korean worries about fan death.
On the other hand, giving a "5g of salt" value is a good starting point, to avoid undersalting due to paranoia or oversalting due to inexperience.
What they really need is someone to tell them to add less than they probably need, then taste, add more, taste, add more, and expect to over-season and under-season some dishes as they get experience. Salt quantities in recipes have to be short, sometimes way short, so you're stuck learning the process with or without the quantities. I've never seen this explained in a cookbook, at least not in a way that made an impression on me.
Edit: A piece of advice that has stuck with me for a long time, long after I forgot where it came from, is it's a mistake to look for the state in between "not salty enough" and "too salty." That state doesn't really exist, especially when you're feeling nervous! Instead you should look for the overlap where you can perceive the dish as alternately "not salty enough" and "too salty," like that ambiguous drawing that your brain can resolve to either an old woman or a young woman[0]. That advice really works for me, but my wife, who seasons like a pro, thinks it's nonsense, which I think illustrates how subjective the process is and how it isn't information you can impart but rather experience you have to guide someone toward.
Which is kind of ironic, because students take classes exactly because they feel 'immature' with respect to that subject.. Honestly, most of my smoothest educational experiences with hard topics assumed some immaturity on my part, and that that was OK
People don’t generally take category theory because they don’t really understand how proofs work or how to read definitions. The maturity required is about being able to cope with proving things and following proofs based on definitions which will probably seem somewhat bizarre at first and unmotivated at first. The immaturity you seem to talk about is people taking category theory because they don’t know category theory but that’s different and not what is meant by mathematical maturity.
That said, a background in mathematics helps with category theory. Things like group theory, topology (particularly algebraic topology), Galois theory and set theory can be useful in motivating a lot of category theory. I’m yet to see much of a strong motivation from programming (where is there a functor that isn’t an endofunctor?)
When I first went from CT as an implementation detail of typed FP to studying CT on its own, I was very aggravated by this point: "where is there a functor that isn’t an endofunctor?"
Over time it has fallen away in two directions.
In one direction is that though you are always stuck in a category with types as objects and functions as arrows, that doesn't stop you from subdividing. This became more intuitive to me as I encountered more and more categories that are basically just Set with extra structure (just as the one we program in is basically Set with bottom). If you start putting extra structure on your arrows (that is something that carries around a function along with some extra proof-relevant structures, like say a way to show that some zero element in the domain under the function equals the zero element in the codomain and that multiplication is preserved under the function, now you have monoid-homomorphisms) then you end up in the general case with something that looks a lot like a binatural transformation of profunctors, which pretty cleanly encodes "exo"-functors between different sub-categories of the category with all types as objects and functions as arrows.
In the other direction is realizing that even imprecisely, there's quantifiable value in observing functors to and from the category of types and functions, say one between whiteboard diagrams and code, or between a specific problem domain and code, etc etc. If you have some other space with composable relationships that you want to preserve when you write code to correspond to it, or you have some other representation you want to produce based off some given codebase while preserving the structure of the code taken as input, you can gain a ton of conceptual leverage out of identifying a functor.
Isn’t an endofunctor a morphism from/to the same category? So a functor would be any morphine from/to different categories, and that wouldn’t be an endofunctor?
More or less. "Morphism" is defined by the category it lives in, so a functor is a morphism between categories in the category of (small) categories. (Insert technicalities about size concerns and Russell's paradox.)
In particular, a map between categories that does not preserve composition is not a functor. It is important that F(f;g) = F(f);F(g).
In the typical functional programmers view of category theory, there is only one category of interest so all functors are endofunctors. My main issue is that category theory the thing being studied is categories plural and so I feel like the language of category theory is being used to only ever talk about a single category.
It feels like doing “group theory” entirely with the symmetric group of the integers. While it’s true that the group is very general and has interesting properties, the focus of group theory isn’t single groups but rather the relationships between groups.
Compare this to something like algebraic topology or Galois theory where you have a Galois correspondence (a functor) between objects you’re interested in and groups.
I think I got more appreciation of abstraction from physics and programming than what mathematical education I had; I'm weak at maths -- experimental physics doesn't need much :-/ -- but I do understand that weakness, and am quite comfortable with abstraction.
This is almost every upper division undergrad math class. It was always fun watching people squirm when they pulled out some useful fact from their past 14 years of math education and then got told they had to prove it before they could use it.
If only it were limited to facts learned from math education. For example, there’s the Jordan curve theorem (https://en.wikipedia.org/wiki/Jordan_curve_theorem), which I guess most four-year olds ‘know to be true’ from their experience with coloring books.
> It is easy to establish this result for polygons, but the problem came in generalizing it to all kinds of badly behaved curves, which include nowhere differentiable curves, such as the Koch snowflake and other fractal curves, or even a Jordan curve of positive area constructed by Osgood (1903).
So to some extent, the reason why such an "obvious" statement requires a complicated proof is because our everyday notions of what a "closed curve" is are much more restricted than what we consider in mathematics. This is kind of common in maths, especially in fields with a lot of visual intuition.
Except this isn’t really true in the common sense meaning (schoolchildren do arithmetic fine without knowing about category theory) or in the formal sense you’re trying to get at (there are formal axiomatic foundations which arithmetic can be based on which do not need category theory. A simple proof is by causality: arithmetic was successfully formalised before category theory was invented)
Not universally. In Germany, there is only a federal decree guaranteeing 56kbit/s modem speed, and this is not a human right but merely an obligation to the state telco.
I have made a funny Sierpinski carpet clicker recently, it's only 30 lines of code in react and unfortunately not one div, but it's still quite performant (safe to open, even on low-tier phones)
> "For too long I've been parched of thirst and unable to quench it. Too long I've been starving to death and haven't died. I feel nothing. Not the wind on my face nor the spray of the sea. Nor the warmth of a woman's flesh." [steps into moonlight becoming a skeleton]