Having actually been around a cat in a bag, the only thing that would have given it away after it settled down was the purring.

How often does it pay off?

This paper indicates 1) that in Lightstone notation, the real number .999... would be written as the hyperreal number .999...;...999 (with a caret over the last 9). And secondly, that that number wouldn't actually be the same number as .999...

http://www.math.umt.edu/tmme/vol7no1/TMME_vol7no1_2010_article1_pp.3_30.pdf

Finally, you still have not shown any flaw in the original (or any other) proof, as far as I've seen.

So where is the flaw in TFA's proof?

When do all the apps save their state to disk so they can be recovered like that?

In theory, it was originally designed to encourage invention, and ensure that inventions got publicized. Protection for inventors is the means, not the end. I'm not even sure there was such a thing as big companies when US patent law was created.

I saw some of those bikes last weekend. Guess what? They were RED!!

Nominally, meaning in name only.

No, not all possible algorithms, but specifically the Dvorak one would surely be near the top of the list. I'm not saying it won't help, I'm just saying if it's something important you should make sure it's a strong password regardless. That way you don't have to worry about whether the obscurity is working.

Fair enough. My point is that plenty of security systems rely on secrets, but not on security through obscurity.