I have a bit of a dilemma. What do you say to someone who says things like “I believe in ghosts because I see and have conversations with them”? (Not a hypothetical example!)
Calculus itself isn’t inherently more difficult to learn that earlier math, but it is where many math students hit a wall because it has a lot of prerequisites; if you were a mediocre student in algebra and trigonometry, there is a good chance that you will have trouble with calculus because you never completely mastered other skills that you have to use over and over again when doing calculus.
There are bootleg videos on YouTube, and if you happen to be in New York, the public library system there records all major Broadway shows and lets people watch them for free.
Reminds me of this...
Generalized Efficient Markets—if something is easy and obvious, someone else is already doing it.
You can get a lot of very tight feedback loops when playing video games, too...
Possibly Antonie van Leeuwenhoek’s study of microorganisms; he made microscopes that were much better than anyone else’s at the time, and he kept his methods secret and they weren’t properly reverse engineered until the 1950s. (Conventional lens making techniques did catch up, and people like Robert Hooke had been investigating biology on micro scales, but he was probably a generation or so ahead of everyone else.)
Looks kind of cool, but won’t you be reading and writing to disk an awful lot?
If there’s a minimum voting age, I think there should also be a maximum voting age. Sufficiently old people suffer from cognitive and physical decline, frequently to the point of dementia, and can be as vulnerable to manipulation or coercion by their caretakers as children are to their parents. It seems entirely reasonable to me that people over 80 should not be allowed to vote.
There’s a simple, very common conflict that happens all the time and frequently results in the appearance of akrasia:
A) In the future, I want X to have been done.
B) I don’t want to be doing x.
It’s like someone pointing a gun at you and threatening to kill you unless you cut yourself with a knife, or wanting to stop taking a harmful drug with extremely unpleasant withdrawal symptoms. You must “voluntarily” inflict this bad thing upon yourself, or the world will inflict something worse upon you.
There’s a “simple” fix for this. Make the computer play with the same user interface the human does: a screen, keyboard, and mouse. I don’t know if robots can control a computer mouse with superhuman precision or not, but it certainly would keep it from making moves all over the map at the same time...
Humans try to make their pets happy, usually...
Can I get a source on that “six years to recalibrate a set point” thing?
That’s a lot of math. It looks good to me and seems plausible but I haven’t combed it in detail; could one of the math experts weigh in here?
One thing, though… why overload the term “logical uncertainty” to include observer-independent statements about the actual universe as well as mathematical statements that would be true in any universe?
Incidentally, people have refuted the claim experimentally; soap bubbles fail to correctly solve larger instances of the tree problem.
I got permission from the math department at Rutgers to skip the proof-writing class… I think I must have picked up the skill elsewhere, because I didn’t feel like I had any trouble with the proof-based linear algebra and real analysis classes that would normally require the proof writing class as a prerequisite.
(The most likely places I learned the skill was from non-textbook books on mathematics and from the philosophy department’s classes on formal logic that I used to cheat on my degree’s humanities requirement.)