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In my opinion there are two approaches to the idea of a function

Some use it as a method to separate code into independent, concise blocks that represent a singe step in a larger algorithm. Do one thing and do it well.

The other is code reuse, if a function is not reused in other places why create it at all? That's the reason for preferring comments rather than fragmenting code into add_vertical_scrollbar() functions. It's easier to read from top to bottom instead of jumping all over the place

I like this a lot and I also use this. Comments as a narrative - you may quickly scan the function and read only 'headlines'-type of comments and if they are good, not too verbose, not too sparse, you have all the information needed. Combine it with a bit more descriptive summary at the beginning and and it's a pleasure to read and you immediately know where are the parts of interest. Reading pure code, even with the crazy enterprise style verbose function names is much harder and takes more time you need to waste on parts that in the end don't matter for the case you're looking for

Universe is tiny compared to mathematics and software, even simply RSA keys are already 2048bit.

Lots of problems suffer from 'combinatorial explosion' [1].

I recently learned about the Archimedes's cattle problem, the solution is of order 10^206544 [2]

[1] https://en.wikipedia.org/wiki/Combinatorial_explosion

[2] https://en.wikipedia.org/wiki/Archimedes%27s_cattle_problem

This argument pops out in many societal issues, not only cheating on exams.

Most people don't cheat and act in good faith but we make them suffer anyway because we will be damned if even one person cheats their way through the system, not on my watch! Make sure it's bad for everyone just because if someone exploits the system it will be bad for everyone.

In the end there is a healthy balance and those who cheat the system will either fail later from the lack of skill/knowledge or, if they don't, it means it was sort of unnecessary anyway

The difference is the 'can be misinterpreted' part. It's an oil painting

On the other hand, 'you have right' translated literally to polish is 'masz prawo' which is exactly what 'you have right' means. I think 'masz racje' -> 'you have correct' -> 'you are correct' would be a better way to show the difference.

And the longer I think about the word 'racja' the less I'm confident I'm able to explain precisely what it means using english.

I guess that's part of the fun of learning other languages, I will never understand articles in english and I made peace with it. Now I'm also learning spanish and subjuntivos drives me nuts but spanish and polish grammar are surprisingly similar (waaay closer than both are to english)

So, if I understand correctly, it's just an evolution of the cryptocurrency itself? In the sense that instead of having a token you have an unique token? And going back to the currency analogy it just means you have a banknote with an autograph?

Comparing programming languages to maths doesn't really makes sense because they serve to express vastly different things. Programming languages need to unambiguously describe how to transform input data into output data. Maths language is more like a natural language and is used to communicate. It evolves in the same way as natural languages evolve and an attempt to codify it precisely is futile because there will always be idiomatic expressions, exceptions to the rules and it depends heavily on a context. You use maths language to write a story or talk with a friend what you did last night, you use programming language to build a shed or bake a bread

It might be awful from the outsider's perspective but so is a foreign language if you never learned it. Hard to complain about it though and if you want to know what others are taking about there is no other way around but to learn it - it won't change in order to make it easier for you, it will change to make it easier for the speakers

It doesn't have anything to do with a pi though. If you had a cube-shaped earth and the same rope, you would need 80ft of additional rope (instead of 62ft for a spherical planet).

Well, of the two neighbors, one speaks Spanish and the other speaks French a bit

What do you mean? (sorry, english is not my first language).

The way I understand it is that if you have the law of excluded middle you cannot discard 'non-constructive' proofs as invalid since they follow straight from the axioms.

Constructive mathematics rejects the law of excluded middle.

In a non-constructive mathematics it is true that 'either A or not A is true' and that allows you to prove existence of objects with certain properties by disproving their non-existence (if it cannot not-exist then it has to exist, by the law of excluded middle). Constructive mathematics, on the other hand, says that that's not enough and to prove that there exist objects with some properties you have to prove their existence.

How do you get enough fuel to the asteroid to bring it back if even sending a 'measly' rover to Mars is a multi-year endeavor. Asteroids weight a lot more than a rocket and you need to change their velocity by the same amount

What a movie, I chose it randomly on an airplane, without ever hearing about it, and I think at the beginning I was thinking about switching to something else but I didn't and then I couldn't... took me by surprise how much I liked it. I don't know why, it's the first time I'm seeing it mentioned on the internet and I had to make a comment.

Don't use 'it is worse over there' as a counterargument against someone who fights (rightfully or not) for things to be better 'here'.

This touches on an interesting topic I've been thinking about for quite some time now. I have a somewhat reverse feeling about the definition of natural numbers (or for that matter, about the 'foundation of mathematics' as in ZFC set theory or whatever you want to choose) than you've presented above.

Those definitions were developed after we had something useful in order to 'codify' it and make it more precise. They are not, in my opinion, a basic blocks that the rest is built from but an added layer of abstraction on top of whathever it is you're defining.

I don't mean I don't understand set theory and the role it has, or advocating for any other system, I absolutely love it.

What I mean is, in practical things (programming languages etc.), it feels a bit counter-productive to me to reduce them to the simplest possible definitions/terms (that have to fit to the particular use case by definition), declaring that a building block and then explaining every other concept in those terms as if it was a proof that we have trully found a foundation and the rest is just a 'syntactic sugar'

edit: You all probably know this famous gif of a ballerina that can rotate to the left or to the right depending on how you think about it. After writing the above post the notion of S(S(S(S(0)))) keeps flipping in my brain between being an abstraction of and simplification of natural numbers. It's weird.

And only 30days/yr of this is from the employer's pocket, the rest is from the state which is also a good deal the other way around.

Ukraine is not in the EU and I wouldn't say the invasion there started 'decades' ago though I don't remember exactly when the war started, must have been after Maidan

No one has ever gone bankrupt by taking profit. State level actors/smoke screen/geopolitical implications all sounds great and are exciting but this might be a small group that just thought 'let's get what we can, easier to launder 100k that billions lol'

They might be, no doubt. I was mainly objecting (unrelated to the article) to the 'smallness' of the neighboring state and to the fact that if something could be considered an act of war doesn't mean it will be one. Bottomless oil well is a good counter to an unlimited war chest.

Turkey has the second largest military in NATO (after US) and by quite a margin

It's one of those theorems that still boggles my mind even though I know it for so many years now. Either complex functions are so much well behaved or complex differentiability is so much stronger condition, I can't decide which. Top it off with the uniqueness of analytic continuation and you start to wonder what causes real functions to be such a pain.

If anyone knows some nice articles about this topic I would love to read them

Anyone interested in this approach to lossless compression should visit (and try to win!) Hutter Prize website[1][2]. The goal is to compress 1GB of english wikipedia

[1] http://prize.hutter1.net/

[2] https://en.wikipedia.org/wiki/Hutter_Prize

Author is a crackpot, judging by his posts on that forum

You would see effects of tidal forces in the scenario you described, I think.

The other thing is, if it's not curved then you still need to explain Mercury's orbit precession (43 arcseconds per century is it?). This is not an easy thing to do

No it didn't and it doesn't :)

I understand what you are saying but you've asserted as truth that the author said what you said and in a pretty accusatory tone. If you use 'Imperial India' as standalone phrase it does refer to the British rule because it is the most recent and that's what most assume you mean. But when talking about Buddha it is quite a leap to think the author would use such a pointless timeframe so the context alone is enough.

Even a paragraph later the emperor Asoka is mentioned explicitly

Imperialism does but not the adjective 'imperial' which simply implies relation to an empire. Imperial Japan has nothing to do with the British and yet it is 'imperial'.

This is first incompleteness theorem. What deepsun was referring to is second incompleteness theorem - in a consistent system F the statement 'F is consistent' is in fact unprovable (in F).

These are complex issues and people are willing to discuss them but my comment was about how you straight up compared EU to a communist regime

You are alienating yourself from any reasonable discussion by making such extraordinary and baseless claims that are of no merit but are meant to elicit an emotional response

Arguments like that work in echo chambers but once you step into a discussion that is in good faith you will notice that it is counter productive and doesn't lead to anything useful