While you can certainly argue that some texts have more substance to them than these literary works, you cannot deny that most texts have worse prose than the books.
> abusive language/notation basically everywhere in math
In most cases it is not as much abusing notation as overloading it. If you think of the context of a formula (say, adjacent paragraphs) as its implicit arguments (think lambda captures in c++), then it is natural that curly braces can denote both a set and a sequence, depending on this implicit input.
Such context dependent use of symbols is actually rather convenient with a little practice.
"it is natural that curly braces can denote both a set and a sequence, depending on this implicit input."
?
I don't even know where to begin. Overloading symbols in mathematics occurs all over the place. There's nothing wrong with that. The difference between overloading a symbol and abusing it is whether there is an agreed upon definition/convention regarding its use and to what extent its use conforms to that definition/convention. What I'm saying in my original post is that the statement "{x_n} is a sequence" disagrees with the formal idea of what a sequence is and that most writers don't bother to explain their own notational use.
If you wish to re-define the curly braces to have a context-dependent meaning, knock yourself out. But, I would imagine that that practice would confuse a lot of people. Math is a human activity. It's not a programming language.
In the context of double precision the article says
> the largest integer value that can be represented exactly is 2^53
— I am confused as to why it not 2^52, given that there are 52 bits of mantissa, so relative accuracy is 2^-52, which translates to absolute accuracy larger than 1 after 2^52. Compare this to the table there saying "Next value after 1 = 1 + 2^-52".
While the idea — of shuffling a societal system a little bit to prevent it from going stale — sounds important, I'm not convinced. Random shuffling leads to good results only when it is combined with a good fitness estimate (see: natural selection). And establishing a fitness test for a societal order seems to be a much harder issue than than that of an organized randomization.
Speaking of random shuffling, I think it should be made much easier to conduct RCTs on citizens to try out systems of governance/social programs/etc. to see what works best.
Basically test stuff instead of guessing and voting.
I think citizens are equal enough if they have equal chance to get to the treatment group.
Not necessarily—in 3d there are uncountably many non-lattice packings. They all have the same density as the FCC lattice though. To construct these packings, shift horizontal layers of FCC horizontally with respect to each other.
It is conjectured that in higher dimensions, the densest packing is always non-lattice. The rationale being that there is just not enough symmetry in such spaces.
Well these new results (denser packings than before) are regular lattices which might suggest that the optimal packing could be a lattice. (Until the record is broken again by a irregular packing ;-)
That's true — time is a big place, and a lot of things are lost in it. I for one am rather more pained over disappearing of physical objects — genomes, books, art.
Plus, it is all the more exciting to think about what caused some languages to exist and thrive for so long, and the information about the past they retained.
If you like this kind of language archeology, check out David Anthony's The Horse, the Wheel, and Language — for how the people that spoke the Proto Indo-European language were located in time and space.
And it has a maybe 3-5% accuracy rate on actually being “unreasonably” effective! There are a lot of surprising things about transformer LLMs but they were literally designed to translate human languages, so being effective at translating programming languages seems natural.
At least the “X Considered Harmful” clones describe something which is plausibly harmful.
I think that is rather different. The traditional meaning of "proofs without words" is that the picture is the proof, or at least, if you believe that a proof can only be in words, that the picture should convey the idea so transparently that anyone with reasonable mathematical skill can routinely translate it into words.
I have found Beyond Compare to be very good on Linux, even on large files/directories.