How many do you have to generate before a collision becomes a remote possibility?

If you have n bits, your collision probability is 0.5 at generating 2^(n/2) values.

Or put differently: a 128bit uuid gives you a "good enough" 64bit distributed autoincrement.

- Rule 1: Be Funny

- Rule 2: Writing a spec is like writing code for a brain to execute

- Rule 3: Write as simply as possible

- Rule 4: Review and reread several times

The author isn't quite as adept at integrating the humor as seemlessly as Joel, yet it's interesting to see how effective the style is, even for someone still learning it. I commend them for making the topic more accessible. It was probably fun to write and was definitely fun to read!

https://www.joelonsoftware.com/2000/10/15/painless-functiona...

https://en.wikipedia.org/wiki/Stirling's_approximation#Speed...

You can build on that to build good, composable approximations of any the standard combinatorial functions, in log-space (and recover the approximations you want by simply exponentiating back). For example, if you've implemented an approximate ln-fac(n) ~ ln(fac(n)), you immediately get ln-choose, the logarithm of (n!)/(k!(n-k)!), as simply ln-fac(n) - ln-fac(k) - ln-fac(n-k). Fully composable: if ln-fac() is a numerically good approximation, then is so any reasonable sum or difference.

Or: the log of the binomial distribution PDF is simply ln-choose(n,k) + k*ln(p) + (n-k)*ln(1-p).

How does one write something like this?

I get the interest, and the review process. What I mean is, is this a hobby where someone is passionate about soothing, or does some employers allow people to work on side projects?

I feel my life is mostly about direct value, and I don't really understand where I went wrong in the path for meaningful knowledge.

Any philosophical help will be very welcome, as you correctly guest I'm a bit lost.