Stats, Maths, XKCD, and Nerds Otherwise Nerding

I genuinely love having my mind blown. Statistics have a way of doing this, but I am interested to here a collection of other similar examples that are simply amazing.

This is what got my juices flowing:

what else you got? @anon26814599?

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Who can give the most concise synopsis of the Hot Hand Theory?

In a room of 23 people there is a 50-50 chance that 2 people have the same birthday.

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fooey, explain yourself sir.

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he’s right, you know

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Probability has some NUTTY results. (My favorite area of math.)

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Monty Hall Problem is the GOAT. Always switch, you idiots.

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you’re assuming that the probability of any given birthday is 1/365, when in reality birthdays cluster.

Math is all about elegance and simplicity. Like Ernie Els’ golf swing.

this actually means that the number is less than 23…

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I can’t recommend the Numberphile youtube channel highly enough if you are interested in this sort of thing.

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Has anyone studied Euclid’s propositions and gone through the proofs themselves?

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his result is perhaps made more plausible by considering that the comparisons of birthday will actually be made between every possible pair of individuals = 23 × 22/2 = 253 comparisons, which is well over half the number of days in a year (183 at most), as opposed to fixing on one individual and comparing his or her birthday to everyone else’s.

I learned something today guise… bless this place.

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That every time you shuffle a deck of cards, you’re creating an order that has never been seen before.

Intuitively it makes sense, but reading this post blew my mind: https://czep.net/weblog/52cards.html

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My favorite course in grad school was combinatorics - a whole quarter of problems like this where you could make what seemed like a completely valid argument for 2 or 3 different answers.

Oh baby I have one that I bet many of you haven’t seen. It’s a result in math known as Benford’s Law.

Let’s say you have data that spans multiple orders of magnitude (this is key), perhaps something like transaction amounts in the general ledger at a bank. You could be repaying someone’s $3 atm fee, or maybe you’ve lost a lawsuit and owe $50 million (I know these wouldn’t all show up on the general ledger for a large bank, but bear with me). The first digit of these numbers is not evenly distributed. The number 1 is substantially more likely to be the first digit of ledger entries than the number two, which is more likely than the number 3 etc.

I’ll spare the details of why this happens, but it’s a very useful law. It’s been used in the past to catch people attempting to cook the books/commit fraud at financial institutions. Similar to the coin toss example up above, people’s intuition about how fake transactions should be distributed is much different than reality. Forensic accountants can identify this discrepancy and use it detect fraud.

Also fun fact, I believe it was initially discovered because some guy (I’m assuming Benford) noticed that certain pages in books containing log tables were much more worn than others. He noticed many books with this pattern and tried to figure out why it was happening, and Benford’s law is the result.

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We learned about this in my combinatorics class and you just reminded me of it.

It turns out the statement “pick a random chord in a circle” is too vague, as there are multiple sensible ways of doing it that yield very different distributions.

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This is wrinkling my brain. Why does this happen? Does it have something to do with rarity of larger numbers in data sets making the “next” order of magnitude have a higher concentration in the lower range?