Bravo for bringing the notes. On a first glance, some of these feel like they require subjectivity (like, do we really believe the political spectrum is 1d?), but I agree I could run the computation myself from this.
Bravo for bringing the notes. On a first glance, some of these feel like they require subjectivity (like, do we really believe the political spectrum is 1d?), but I agree I could run the computation myself from this.
For the record - this is the argument against democracy. And it’s not so bad!
Democracy can do horrific things! It is prone to mistakes with things that can be fear-mongered, where there’s a lot of money invested in grifting, and when the real reasons are sufficiently complicated that they don’t fit on signs (or nobody is interested in doing the work to put them on signs).
depending on how much want to do, I have seen kits for ~$30. Pretty sure I’ve seen some small kits taken for camping, so they can’t be too pricy. And if you can’t afford it, just start bringing it up around town! Maybe somebody will get excited and do it for you.
Fortunately containers can get bigger =)
While we aren’t all the same, there’s a difference between things that require holding 8 complicated things in mind at once, and things that require a little language learning and the intelligence to solve a crossword. This is closer to the latter - like doing a crossword in Spanish. You need to know a bunch of little things, but learning them is basically all tedium and not brilliant insights. (Taking these puzzles, creating a dozen new variants, and solving all of those probably does require managing a lot of complexity. But to understand the work of others, is not so bad)
If it’s any consolation, you are almost certainly within ~3 years of understanding the solution and a dozen variants. It’s not a super deep area. Probably doesn’t really require calculus (you need continuous as in ‘the lion doesn’t teleport; that’s cheating’, but I think not much more).
I’m a little sad nobody with the relevant mathematics background has jumped in. These puzzles are considered; a simple version is the lion-hunting-man where both have the same speed and infinite turning speed (eg, this paper, where the arena they play in varies).
It’s likely in some cultural groups - and has been true for a friend or two of mine. A particular example was someone going to a Psych ward, where their phone was kept in a vault. Obviously you know more context than me. But the probability is nonzero.
They’ve suddenly landed in a really controlling environment (be it a partner, parents, or a government), and wish to hide your relationship/keep you out of the crosshairs.
But I think blaming children for the fact that all people are unbearable is… idk, you’ve mistaken a symptom for a problem? Working on the general misanthropy is probably a better start?
It’s very weird to me that you’re only listing loud things children do… Like, have you ever been around a sleeping child? Do they bother you? What about in a classroom, watching a movie, or running in the distance (out of earshot)?
Average volume of a child is higher than adults, but only by a factor of 2 or so. And their noises are interpretable, you can definitely figure out what they mean, unlike the adult noises.
Ah, so it’s the probability you win by playing randomly. Gotcha. That makes sense, it becomes a choice between 2 doors
Why do you have a P(x1) = 1/2 at the start? I’m not sure what x1 means if we don’t specify a strategy.
Oh that’s cool - I had heard one or two examples only. Is there some popular writeup of the story from Savant’s view?
An arithmetic miracle:
Let’s define a sequence. We will start with 1 and 1.
To get the next number, square the last, add 1, and divide by the second to last. a(n+1) = ( a(n)^2 +1 )/ a(n-1) So the fourth number is (2*2+1)/1 =5, while the next is (25+1)/2 = 13. The sequence is thus:
1, 1, 2, 5, 13, 34, …
If you keep computing (the numbers get large) you’ll see that every time we get an integer. But every step involves a division! Usually dividing things gives fractions.
This last is called the somos sequence, and it shows up in fairly deep algebra.
I now recall there was a numberphile with exactly that visualisation! It’s a clever visual
For the uninitiated, the monty Hall problem is a good one.
Start with 3 closed doors, and an announcer who knows what’s behind each. The announcer says that behind 2 of the doors is a goat, and behind the third door is a car student debt relief, but doesn’t tell you which door leads to which. They then let you pick a door, and you will get what’s behind the door. Before you open it, they open a different door than your choice and reveal a goat. Then the announcer says you are allowed to change your choice.
So should you switch?
The answer turns out to be yes. 2/3rds of the time you are better off switching. But even famous mathematicians didn’t believe it at first.
Note you’ll need the regions to be connected (or allow yourself to color things differently if they are the same ‘country’ but disconnected). I forget if this causes problems for any world map.
Would you then be posting your conclusions? Like, if you’re gonna do that work on some of these posts anyway… may as well share.