More concretely, "PA is consistent" can be as expressed "PA does not prove 1 = 2".

I must have missed when this became apparent.

The dateline on the link is Feb 6, 2013 -- so fairly recently.

BTW, your link seems much more like the coping mechanism low level employees develop when it's clear to them that their situation is absurd and complaining to their superiors won't help than anything resembling knowing fraud.

I think you're correct -- I posit that the knowing fraud was perpetrated by the superiors, who I think must have ordered the relaxation of rating standards that the employees that were quoted in the link were complaining of.

I believe the sequence of events goes like this: Shadow banks (e.g., Lehmann Bros.) wanted to lay hands on large amounts of AAA-rated securities to use as collateral for the repo that funded their day-to-day activities. That plus the lack of regulation requiring mortgage issuers to hold some proportion of mortgages on their own books (and hence skin in the game) led to slipshod or outright fraudulent mortgage screening and wholesale securitization of the resulting mortgages, inflating the housing bubble.

In detail: since security issuers pay the rating agencies to rate the resulting securities, the three big rating agencies were forced to compete for share of this new market, and one way in which they did so was by relaxing rating standards so that super-senior tranches of crappy MBSes got undeserved AAA ratings and could then be sold to satisfy the shadow banks' demand for AAA-rated securities.

I'm tapping out now.

My name is Cyan, and I am a post narcissist.

Or, in other words, comparative advantage for the win!

I freely grant that lots of people who contributed to the meltdown were incompetent. However, I don't think that's the claim you were making in the original comment. It seems to me that your original comment's implication is that mathematicians in finance were incompetent, this implication being supported by the fact that they came up with models that were later used (by the mathematicians themselves? by others?) to justify the AAA ratings. But it's now apparent that those AAA ratings were the result of knowing fraud, not incompetence, so I don't see how that can be evidence for your implied claim.

I like the quote, but I have a nitpick:

We would all like to believe that... if we lose it is because of the good luck or cheating of our opponent.

When I've lost in the first round of single-elimination tournaments, I've found myself hoping that the person who beat me would prove skilled enough to win the entire tournament. That way, my loss wouldn't mean that I totally sucked, but only that I wasn't the best. So I think the quoted observation fails to account for nuances relating to how losses inform us about our skill level.

<a typo>

Well done!

A nitpick:

you'll have to change one variable at a time and take note of the results, like any good scientist would.

In the shower control problem, this is a satisficing approach. Any good scientist, however, ought to know that changing one variable at a time is incredibly wasteful relative to fractional factorial experimental designs, which are themselves not optimal designs in general.

In fairness to the skills of mathematicians in finance, it should be noted that those ratings were evil, not stupid.