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.
Good textbooks have gone through expert reviews and multiple iterations of improvement. That can't be said of an LLM answering your personalized questions or the book problem
> 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.
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.
By that logic the US shouldn’t get involved in any other foreign entanglement or global police action because of unintended consequences. Tell me, who from the international community will seize Russian shadow fleet oil tankers evading sanctions!
Wait! Crap!
We can’t sanction Russia - if we do it might destabilize the Russian dictator and if he goes out a worse authoritarian regime might come to power!
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.
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.”
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).
Car dealerships often sit on prime retail locations. So that vast inventory will often sit in a location close to but not conveniently adjacent to the actual dealer.
> 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)
