
The Birthday Paradox – On Jupiter, and Beyond (2012) - ColinWright
https://www.solipsys.co.uk/new/TheBirthdayParadox.html?sc03h
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jedberg
For those of you who read the comments before the article, this is actually
about calculating hash collisions and is pretty interesting.

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ColinWright
Thank you.

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blackholesRhot
the authors are basically rediscovering Chen-Stein’s concept of Poisson
approximation... which can be used to almost trivially approximate any
birthday problem variant. For example, how many people do you need to have a
50% Probability that at least 6 people were born on the same day on Jupiter?
Ez w/ Poisson approximation. I first learned about this in Persi Diaconis’
graduate probability class but the method is very simple

[https://projecteuclid.org/euclid.ss/1177012015](https://projecteuclid.org/euclid.ss/1177012015)

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cbsks
>Just as a reminder, we use n! to mean n(n−1)(n−2)(n−3)...3.2.1, so that means
6!=6.5.4.3.2.1=720. The exclamation mark is sometimes pronounced "pling" and
this operation is called "factorial".

I’ve never heard the factorial symbol called “pling” before, I think we
pronounced “6!” as “six factorial” in my undergraduate math classes in the US.
Is “pling” a common term that I completely overlooked? Or is it more common in
the UK?

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ColinWright
In various circles it can be called pling, bang, or shriek. These are names
for the symbol, whereas "factorial" is the name for the function.

In particular the opening line of a (U|Li)nix script is:

    
    
        #!<path>
    

and that's sometimes called the "hash bang".

From wikipedia[0]:

    
    
        In the printing world, the exclamation
        mark can be called a screamer, a gasper,
        a slammer, or a startler.
    
        In hacker culture, the exclamation mark
        is called "bang", "shriek", or, in the
        British slang known as Commonwealth
        Hackish, "pling".
    

[0]
[https://en.wikipedia.org/wiki/Exclamation_mark#Slang_and_oth...](https://en.wikipedia.org/wiki/Exclamation_mark#Slang_and_other_names_for_the_exclamation_mark)

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cbsks
Don’t forget about interrobang, aka “?!”

“Shriek” is a new one to me, however. What context is it used in?

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ColinWright
From Wikipedia[0]:

> _The name given to "!" by programmers varies according to their background.
> In the UK the term pling was popular in the earlier days of computing,
> whilst in the United States, the term shriek was used. It is claimed that
> these word usages were invented in the US and shriek is from Stanford or
> MIT; however, shriek for the ! sign is found in the Oxford English
> Dictionary dating from the 1860s._

From another web site[1]:

> _It is also called an exclamation mark or tellingly, in newspaper jargon, a
> shriek._

================

References:

[0]
[https://en.wikipedia.org/wiki/Exclamation_mark#Computers](https://en.wikipedia.org/wiki/Exclamation_mark#Computers)

[1] [https://www.thoughtco.com/multiple-exclamation-
points-169141...](https://www.thoughtco.com/multiple-exclamation-
points-1691411)

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bogomipz
I have a question. Under the section "Where did that come from?" The author
states:

>"But after a bit of futzing about I found it to be remarkably close ..."

And the number under the radicand symbol he shows "ln(4)"

What is this exactly? Why is it significant?

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ColinWright
"ln(4)" is the natural log of 4, so it's the solution to the equation e^x=4,
where e ~ 2.71828... also known as Euler's number[0].

Reading further in the post will explain where that quantity comes from, and
why it's significant, but if you have any questions you can ask them via the
comment box on the article.

[0] The constant "e" turns up in lots of places, you can read more about it
here:
[https://en.wikipedia.org/wiki/E_%28mathematical_constant%29](https://en.wikipedia.org/wiki/E_%28mathematical_constant%29)

The usual examples for how Euler's number turns up are to do with calculus and
compound interest, but there are many other.

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bogomipz
Yes of course, thank you. I am so used to seeing the word "log" written out in
things like time complexity/Big O analysis that I forgot about the natural log
- ln. Cheers.

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resource0x
Related: given a permutation of numbers 0..999, find out the position of a
given number (e.g. number 5). It may seem that on average, you need 500
iterations. In fact, you need much less:

let index = 5; while (element[index] != 5) index = element[index];

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pavel_lishin
> _In fact, you need much less_

How many iterations does that take on average? And why?

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resource0x
see [https://math.stackexchange.com/questions/1409862/average-
len...](https://math.stackexchange.com/questions/1409862/average-length-of-a-
cycle-in-a-n-permutation) Which gives you 1000/7.48, not 1000/2

