I had an art history professor that insisted on being called doctor; she said she’d put in a lot of time and spent a lot of money to get that degree, and so she wanted to get her money’s worth.
No; adjunct faculty can also rightly be called professor without having achieved a doctorate. I’ve had a few professors that had BAs and MFAs (esp. since I’m not sure that there are PhD programs for fine arts).
I was being serious. She made art history–which is normally a fairly dry subject, particularly when you’re covering art before 1100CE–a really fun and engaging subject.
It’s by Milo Manara, Italian artist who does a lot of erotic illustrations. I think maybe some comics too. I love his style and the sexy stuff is just a bonus. Really like how he does hair.
Let N be the size of the population that the villain abducts from
Let X be the event that you are abducted
Let R be the outcome of the villain’s roll
Let C be the event that you have control of the real switch
If 1-5 is rolled, then the probability that you are abducted is P(X|R∈{1,2,3,4,5}) = 1/N
If 6 is rolled, then P(X|R=6) = (N-1 choose 9)/(N choose 10) = ((N-1)!/(9! * (N-10)!)) / (N!/(10! * (N-10)!)) = 10/N
The probability of getting abducted at all is P(X) = P(X|R∈{1,2,3,4,5})P(R∈{1,2,3,4,5}) + P(X|R=6)P(R=6) = (1/N)(5/6) + (10/N)(1/6)
The probability that a six was rolled given that you were abducted: P(R=6|X) = P(X|R=6)P(R=6)/P(X) = (10/N)(1/6)/((1/N)(5/6) + (10/N)*(1/6)) = 2/3
So as it turns out, the total population is irrelevant. If you get abducted, the probability that the villain rolled a 6 is 2/3, and the probability of rolling anything else is its complement, so 1/3.
Let’s say you want to maximize your chances of survival. We’ll only consider the scenario where you have control of the tracks.
If 6 is rolled, then P(X|R=6) = (N-1 choose 9)/(N choose 10)
Might as well reduce that to 10/N to make the rest of the lines easier to read.
If you don’t flip it, you have a 2/3 chance of dying.
There is also a chance that your switch is not connected and someone else has control of the real one. So there is an implicit assumption that everyone else is equally logical as you and equally selfish/altruistic as you, such that whatever logic you use to arrive at a decision, they must have arrived at the same decision.
No matter what your goal is, given the information you have, flipping the switch is always the better choice.
That is my conclusion too! I was surprised to learn though in the comment thread with @pancake that the decision may be different depending on the percentage of altruism in the population. E.g. if you are the only selfish one in an altruistic society, you’d benefit from deliberately not flipping the switch. Being a selfish one in a selfish society reduces to the prisoner’s dilemma.
There is also a chance that your switch is not connected and someone else has control of the real one. So there is an implicit assumption that everyone else is equally logical as you and equally selfish/altruistic as you, such that whatever logic you use to arrive at a decision, they must have arrived at the same decision.
Ah, yes. I forgot to account for that in my calculations. I’ll maybe rework it when I find time tomorrow.
I am always surprised how my first guess gets wrecked by Bayes rule. I would have thought that there is 5/6 chance I am on side track and 1/6 that I am on the main track.
Yep, sqrt(-1) = i. Powers of i are actually really neat imo since they form a loop: i^0 = 1
i^1 = i
i^2 = -1
i^3 (or i^2 x i or -1 x i) = -i
Now the loop starts:
i^4 = i^2 x i^2 = 1 x 1 = 1
i^5 = i^4 x i^1 = 1 x i = i
etc
Any evaluation of i to the power k boils down to i^(k%4). For example, i^726 = i^2 = -1. I know this was super useful in calc 1 or 2 and not used for any of my other math classes, it’s just a fun concept to me
Aluminum was the original spelling, adding an extra I was a British thing so aluminum can match the pronunciation of other elements like helium, lithium, beryllium, uranium, and plutonium.
Why didn’t you guys change iron to ironium? Or hydrogen to hydrogenium? Tungsten to tungstenium? Lead to leadium?
It doesn’t make any sense to change one element name when there are plenty of other elements that don’t match the naming scheme.
The original spelling wasn’t aluminum, it was alumium. Which then was proposed to be aluminium in French, and got picked up by the Royal Society. After, the guy who introduced the term to the Royal Society (Humphry Davy) started calling it aluminum but the other term had already stuck.
the English versions of element names are mostly stolen from other languages anyway. Some were isolated before the theory of elements and atoms had been solidified, so they already had names in common use. All of the examples you listed for “ium” elements were only discovered in the last few hundred years
They try to correct me here and I laugh at them, then they call me an uncivilized yank. And by they I mean my Brit partner, but he grew up in NJ so I’m not sure who he is calling uncivilised.
The new one that bugs me is saying “actually” and “genuinely” before every fuckin statement. Those (a long with “not gonna lie”) make me think I shouldn’t trust anything you say unless you clarify you’re being sincere first
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