778 karma · joined January 1, 2023
Once upon a time, developers had to pore over manpages, paper textbooks, or memorize it. Then came google. Next, stackexchange. And now GPT-4 - which is kind of a search engine plus rudimentary synthesis.
But let's be clear. This is low-hanging fruit. It's a poor substitute for actual thought. And surely we are safe.
DE theory is still useful for designing frameworks within which numerical methods can operate.
At least, that's my understanding.
Ah so this is the purpose of UML!
If we define mathematics as, e.g. counting, it is much older.
(It's interesting that mathematics is commonly thought of today by most people as to do with numbers, yet Elements is geometry.)
I used to *enjoy* doing physics. Why did I enjoy it? I used to *play* with it. I used to do whatever I felt like doing - it didn't have to do with whether it was important for the development of nuclear physics, but whether it was interesting and amusing for me to play with.
https://www.asc.ohio-state.edu/kilcup.1/262/feynman.htmlIf anything is going to be based on how good the tech is, it's this.
My super power is a terrible memory. So I have to understand things in order to remember them (aka a cognitive compression). I can't just learn things like normal people.
OTOH there seems to be a developmental window for some specific skills, e.g. phoneme acquisition 6-12 months; (human) language acquisition < 7 years.
But who is anyone, anyway? How do you know? Is the old advice is profound or meaningless:
Temet Nosce jq -n '{"a": 1, "b": {"c": 2, "d": 3}, "e": 4} | pick(.a, .b.c, .x)
wouldn't a more jq-y syntax be: | {a, b.c, x}
(which fails on the 'b.c' term)I'm surprised TFA implies spreadsheets aren't still dominant.
But whether a person does use them, and for what, is entirely due to the person themselves.
When our first ancestor stood upright, a right angle was formed with the ground.
A hand axe, a knapped stone lashed at right angles to a branch.
Some say fire or dogs are humanity's first and greatest inventions - but we only domesticated those.
I say weaving: an extraordinary crossing of threads at right angles that magically support each other, clothing that is the biblical coming-or-age of human-kind, fabric that drapes organically (and is still used today, even as threads become artificial), rope, leaves for shelter, even decorating hair.
And it directly lead to the single greatest invention of our time, that binds all things together: gaffer tape.
Because it's a puzzle, it will be in the form sqrt(x^2), so the answer will be x.
The only perfect square I know for this level that could match is (a+b)^2 = a^2 + 2ab + b. With b=1, the first term needs to be in the form a^2 + 2a or a(a+2).
I had no intutition for what this could be, then noticed it needs to be close to a perfect square itself, and this closest to this would be the two inner factors times the two outer factors (for it to work out neatly). Writing as binomils for ease of calculation:
((1000+0)(1000+3)) ((1000+1)(1000+2))
(1,000,000 + 3000) (1,000,000 + 3000 + 2)
This is the form sought! (with a=1,000,000 + 3000). It works because 0+3=1+2. So we have sqrt( (1,000,000 + 3000) + 1)^2 ) = 1,000,000+3000+1 = 1,003,001 sqrt( (1000)(1001)(1002)(1003) +1 )
It's been an engaging way to refresh the basics, and practice them. It's also a nicely paced drip-feed, and has answers for when I get stuck.Like high-school math problems, they are manufactured puzzles (i.e. with a neat solution), which narrows the search space and tells you if you are on the right track. But unlike those, these have 2-3 tricks, so you get no feedback after the first step. It seems a bit like NP-complexity: hard to find the method; easy to check.
I'm sure there are many math olympians here on HN (and winners), who would find these unchallenging. Speaking for myself, I can do most in my head, and most of the remainder on paper - when I need their answer is when I learn the most.
A maybe-criticism: the answers are very clear, but they don't say why those steps were chosen. To me, the channel is more like a slightly-cleverer peer, rather than a super-genius master. Sometimes I find a better method, and it becomes a springboard for related ideas. And all that might well be better for learning.
At the same time, laws have been codified (i.e. the case law rewritten coherently, combining all the patches combined), such as the Uniform Commercial Code.