Did they do the same with pigs before football was discovered?
I think it was one-anotherâs heads. I think it mostly still is on a Saturday night.
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As if there isnât enough misery in the World, now the news that thereâs one-and-a-half Bonos -
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Great video! Thanks for sharing. I found this interesting:
We had a band at the restaurant last night. I didnât think anyone could make a U2 track sound worse than BonoâŚ
To be fair, the rest of the time he made a pretty decent fist of things, and the rest of the band were very good.
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Au contraire
Of course thatâs all irrelevant if the hackers get plaintext passwords
If hackers are getting plaintext passwords, a lot of people need firing. All passwords should be stored hashed, all the time.
Its not that rare, and even hashed passwords arenât that secure if theyâre not salted properly.
And most of us re-use passwords to some extent
Mmmm, salted hashâŚ
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My brain is toasted. Fascinating. Iâve forgot more than i knew on math.
I hate probabilities. The monty hall problem does my tree in.
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He has thrown me through a loop. - Fuck you loop.
It is a nice example, this one. It shows that mathematics neednât be just a matter of grinding through algebra and equations. It can be about solving a problem by using a seemingly unrelated idea. The ability to recognise that an intractable problem can be transformed into a tractable one by using insight is a lesson that doesnât get taught early enough IMHO.
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They all still get executed though, yes?
Yes the prison is in Texas
69% of the time.
One of the really striking things is how little that fraction varies with the number of prisoners in the problem. The video points out that if you go from 100 prisoners to 1000 it hardly changes at all - itâs tending towards a limit for large N and by N=100 itâs pretty much got there.
I tried reducing N. As you go down from 100 the fraction of times that they all end up dead rises slightly. Then it starts to fall again. The eventual fall is what youâd expect. If you reduced N to 1 then the single prisoner would go into the room and find just one box. Itâd have his number (1) both on the outside and on the bit of paper inside and he would always go free* - the chances of his being executed would be 0%. But with 2 prisoners following the strategy then the chance of them both getting executed would already be 50% and it rises as N increases above 2.
*Strictly speaking the problem breaks down for N=1. The rule says you can only open half the boxes which is tough if thereâs just one box. But you donât need to open it. You can be certain whatâs in it.
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If it makes you feel better, a lot of maths professors got very confused by it too. When Marilyn vos Savant wrote an article about it in the early nineties, a lot of them wrote to the magazine to complain she was talking shit. Unfortunately for them, she wasnât. Itâs slightly disturbing that even with it only containing a very small number of permutations, none of them drew up whatâs called a truth table (basically a way of plotting and calculating every permutation).
The key to understanding it is to change how you view the boxes. You pick one box, with odds of 1/3rd. You then need to effectively view the remaining two boxes as a single entity with odds of 2/3rds. Then it makes sense. The corollary that still completely bakes my noodle is that if someone were to walk into the studio after the goat has been revealed and gets the choice to pick, they are still on a 50:50 split, whilst you as the contestant still have a 1:2 split. That part I donât get.
The other fun one is how many people do you need in a group to get a 50% chance of two of them sharing a birthday (just day in the year, not matching years). Itâs a remarkably low number, something like 28 off the top of my head. To get certainty, you need 366 of course (1 + days in the year (inc leap years). But the 50% threshold is much lower. Again, the key is to think about it slightly differently, and look at the number of combinations of birthdays. Imagine putting everyone in a ring, and drawing a line from each person to every other person. Thatâs actually the number of combinations of birthdays you have, and itâs a much higher number (x!, where x is the number of people in the group).
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