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.
Glad they are thoroughly prepared, it seems?
Also looks like this wont be toooo big an eruption regardless.
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.
I want this to be true… is it?
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?