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Doesn't "orthogonal" convey that meaning more crisply and precisely?

Hear, hear. "Complex" makes it sound difficult, when the original idea was that they were a complex--as in compound--of two numbers. Complex analysis turns out to be almost trivial, thus taking an orthogonal journey, compared to the gnarliness of real analysis.

That should have been the gate all along. Not "You didn't write it, so why should I read it?" [0] but "You didn't even read it, so why should I?"

[0] https://news.ycombinator.com/item?id=49794330

Glad you outed Terry as the bad guy that jealous Salieri was in the film.

I was misled into thinking that his "all academics feel for the Salieri character" comment could've been--in the dimmest of possibilities--paraphrasing Grothendieck that he felt outclassed by his peers:

“Since then I’ve had the chance in the world of mathematics that bid me welcome, to meet quite a number of people, both among my ‘elders’ and among young people in my general age group who were more brilliant, much more ‘gifted’ than I was.” (Récoltes et Semailles)

Perish the thought.

> the Sierpinski triangle is a counterexample

How so? It's bounded by the large initial triangle. The line containing any two of the vertices doesn't intersect any other point.

Find one that bridges only two points, no more. Unless ofc you're given a configuration that's obviously impossible: all of them in a line.

Maybe this'll help: Every bunch of points on a plane has a lonely bridge. A lonely bridge is a line connecting only two points, no more.

Obvious caveat: The points can't all lie in the same line (the collinear condition).

Not-so-obvious caveat: There can't be an infinite number of points.

You can ask the LLM to write a prompt for you. Example: "Explore prompts that would have circumvented all the previous misunderstanding."

LLM to the rescue. Feed in a problem and ask it to explain it to a layperson. Also feed in sentences that remain obscure and ask to unpack.

> If you are skipping a step in the procedure, aren't you also possibly going to skip writing a step down?

Exactly, so when she reviewed the notebook, she caught the error.

Even if she made a slip in the notebook, merely reviewing it helps jog the memory to revisit and replay what she did in the lab. It's the power of touchstones.

> What if you have to do several steps rather quickly? Say adding a particular chemical, then waiting for ten seconds and adding, another chemical? Do you have time to write it down?

The notebook doesn't always have to operate as a log. It can also operate as a plan of action.

Wouldn't attention to getenv() calls yield more benefit? Such calls are where input typically isn't parsed--because parsing is "hard"--becoming targets for exploit.

The present fix is to sanitize user input. Does it cover all cases?

EWD 1036: On the cruelty of really teaching computing science (1988)

“My point today is that, if we wish to count lines of code, we should not regard them as ‘lines produced’ but as ‘lines spent’: the current conventional wisdom is so foolish as to book that count on the wrong side of the ledger.”

For even better measure here's a slice of HN reactions to EWD1094:

https://news.ycombinator.com/item?id=46085897

> Good textbooks have gone through expert reviews and multiple iterations of improvement.

That's an assumption increasingly false, unfortunately. The spirit of collegiality has been beaten back.

Far better to hone logical skills that sift between fact and error than to rely on social reputation. Ironically we're discussing a text designed to do exactly that.

The savvy LLM user already knows to be on the lookout for falsehood, if not bad pedagogy. That's a benefit, not a drawback of LLMs.

The logical skills to evaluate the output of a LLM are the same skills brought to bear reading any book. What makes you trust this textbook then? Textbooks are not infallible.

re: Chapter 15.8 on the so-called pigeonhole principle

Following Dijkstra’s EWD1094, here’s a way to solve the hairs-on-heads problem eschewing the language of pigeonholes and employing the fact that the mean is at most the maximum of a non-empty bag of numbers.

We are given that Boston has 500,000 non-bald people. The human head has at most 200,000 hairs. Show that there must be at least 3 people in Boston who have the same number of hairs on their head.

Each non-bald Bostonian must have a hair count between 1 and 200,000. The average number of such people per hair count is 500,000 / 200,000 = 2.5. The maximum is at least that; moreover, it must be a round number. So the maximum >= 3. QED.

Such problems are a cakewalk for LLMs, you realize? Lots of didactic activities you could do with LLMs.

Which nation did Maduro invade again? Did you confuse Venezuela with Russia?

> By that logic the US shouldn’t get involved in any other foreign entanglement or global police action because of unintended consequences.

Strawman. No-one is claiming that.

Are you arguing two wrongs make a right? This most recent wrong would likely gestate an even worse authoritarian regime than the earlier wrong.

Where is the right you're seeing?

A grid with 19 columns is enough. Every column at worst has all 3 colors, one of them used twice. Once we fix that one color, there are C(4,2)=6 ways of filling out the rest of the entries. Since there are 3 colors, there are exactly 6*3=18 worst possible columns. With 19 columns a repetition is guaranteed, yielding the desired rectangle.

For fun, try strengthening the result to a square.

M&Ms much? There is no finite field with six elements.

I'm game. Email's in the profile. Aside from HN, do you have other plans on gathering up the numbers?

No, I actually mean what I wrote: Not everything that counts can be counted. Take the happiness produced by a piece of software. Can we put a number on it?

Contrast Lord Kelvin: “When you can measure what you are speaking about, and express it in numbers, you know something about it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarely, in your thoughts advanced to the stage of science.”

And also this doozy writ large in our lives: “If you can’t measure it, you can’t manage it.”

Worth filing under: Gaming the System, in this case: image compression benchmarks.

Not everything that counts can be counted.

Spitballing here: more land in the US means lower cost to stock cars in dealerships. Also makes it easier to do an impulse purchase with all the easy financing available, compared to the European scenario of waiting for delivery (and possibly changing one's mind).

> The fear of a legacy (or your ancestors or your lineage) being forgotten is very, very real.

Temple Grandin, decorated autist and celibate, once yearned wistfully about how to pass on the knowledge she has gained over her lifetime.

And who can forget:

“I've seen things you people wouldn't believe. Attack ships on fire off the shoulder of Orion. I watched C-beams glitter in the dark near the Tannhäuser Gate. All those moments will be lost in time, like tears in rain. Time to die.” - Roy, Blade Runner (1982)

To answer obliquely: I observe some men to rage for vengeance at being cuckolded. Subsequently, in an episode of repeat impotence, the bullets rebound on the shooters.

Example: the father may take drugs to relieve the pain. Said father may invite the child to join him, setting up the child for life.

Don't have a dog in this race, but doesn't that certain vegetarian-leaning religion also prohibit violence against human beings? How do the terrorists square such contradictions in their mind? And is that one of the many mysteries driving the narrative in GP's novel forward?

Apparently, the research literature calls this feature Sheet-Defined Functions (SDF). Doesn't it use this result from Microsoft Research UK that was just recently published in ICFP 2020:

Elastic Sheet-Defined Functions: Generalising Spreadsheet Functions to Variable-Size Input Arrays

https://icfp20.sigplan.org/details/icfp-2020-papers/46/Elast...

Fastest beeline from research lab to the end-user I've ever seen.

> I have a topic I’d like to write about. However, I’m getting lost In the weeds and failing to structure my content in an easy to consume way.

Ricocheting from your consumption metaphor, could it be that your topic has enough meat in it that it deserves to be sliced and served over the course of several meals?

The attention economy being the way it is today, articles that succeed in being read observe the rule of thumb of one idea, one message, one piece of writing.