I don't have any particular insight on this issue, but I'm glad you called my attention to it. Thanks, man.

This is not a language issue. The problem statement is simple and correct. People are imagining twists in the problem because they can't fathom how such a simple problem has such a strange answer.

Tboy boy
boy Tboy
Tboy girl
girl Tboy
each 1/4 prob

They aren't each 1/4, you ninny.

The best advice I can give anyone is to try hard to suppress their sense of certainty, especially when they're disagreeing.

Read this closely.

Four mothers:
Elaine has B B
Peggy has B G
Millie has G B
Dawn has G G

If I had 100x as many mothers, the proportions would be roughly the same.

Elaine, Peggy, and Millie tell you they have a boy. Only one of the three have two boys. This proportion holds for 100x as many mothers.

I consider this a test of my faith in other people. Is this helping your intuition? Or do I have to resign myself to the idea that most people can't change once they've latched onto an idea?

You're straight up wrong.

In the scenario where someone says, "I have two children and one of them is a boy," the odds of there being two boys is 33.3%. B-G, G-B, B-B

Run some simulations if you doubt the math. Also, read up on the Monty Hall Problem.

In the scenario where someone says, "I have two children and the youngest of them is a boy," the odds of there being two boys is 50%. B-G, B-B

The magic comes from B-G and G-B being two different events, and the fact that the former scenario specifies no particular child.

The "Tuesday" constraint is a funny case where the scenario sort of does specify a particular child, but not absolutely. It's a very gratifying thing to understand.

I think a lot of people are missing what's actually going on, here.

First off, there's no "only one child/boy was born on Tuesday" constraint.

If someone says, "I have two children. One of them is a boy." The odds of the other one being a boy is 1/3.

If someone says, "This is little John. I have another child." The odds of the other one being a boy is 1/2.

Saying, "One of my children is a boy born on Tuesday," is a lot like saying, "This is John," except the possibility that there's another boy born on Tuesday slightly skews the odds away from 1/2. "Boy born on Tuesday" almost, but not completely, identifies the child.

You're right, it's 1/4. It's weird that the parent got the right answer anyways.

I think I got it right here:
http://science.slashdot.org/comments.pl?sid=1701394&cid=32728606

The fundamental thing is that if your selection criteria is biased against boys (We only support realities where a boy is born on a Tuesday), then more boy-boy pairs survive.

Oops.

P(X|boyboy) = 1/7*1/7 + 1/7*6/7 + 1/7*6/7 = 13/49
P(X|boygirl) = 1/7
P(X|girlboy) = 1/7
P(X|girlgirl) = 0
P(boyboy) = P(boygirl) = P(girlboy) = P(girlgirl) = 1/4
P(X) = (13/49 + 1/7 + 1/7 + 0) * 1/4 = 27/196
Reverend Bayes:
P(boyboy|X) = P(X|boyboy)*P(boyboy)/P(X) = 13/49 * 1/4 * 196/27 = 13/27
=0.481

Our calculations differ on one point.

P(X|boyboy) = 1/7*1/7 + 1/7*6/7 + 1/7*6/7 = 13/49
P(X|boygirl) = 1/7
P(X|girlboy) = 1/7
P(boyboy) = P(boygirl) = P(girlboy) = 1/3
P(X) = (13/49 + 1/7 * + 1/7) * 1/3 = 9/49
Reverend Bayes:
P(boyboy|X) = P(X|boyboy)*P(boyboy)/P(X) = 13/49 * 1/4 * 49/9 = 13/36
=0.361111

P(boyboy) with no conditions is 1/4, not 1/3, right?

And the other bit, using thick client stuff like Flash allows you to code your entire web application service as a meaningful API that can be used by your website just as easily as by an iPhone app or by a third-party web application. No more web-specific spaghetti controllers on the server. It's just kind of a better way to program. Thick-client JS frameworks are still evolving, with GWT at the front, although it's still easy to write GWT server hooks in a non-service-oriented way.

The Flash ecosystem has a couple things going for it that aren't widely known.

Adobe Illustrator now exports to FXG. FXG is an XML format which is a declarative refactoring of Flex graphics objects and controls.

In this workflow, the Flex developer still has to do a bit of work to turn the FXG objects into useful controls, but Adobe has gone a step further and created tools that allow the designer to designate the basic operation of controls, even to the point of creating fully functional mockups.

It's a great way to design sites and web applications, and it takes a lot of the fundamentals out of the hands of developers and into the hands of designers, without screwing over the developers in the process.

I wish Adobe had pushed this out four years ago. If FXG and the scripting thereof cannot be brought into the standards process, then I at least hope similar tools with be available for HTML5 and Canvas soon. Adobe's probably the best contender for making such tools. It's hard to love GWT when there are so many good things about Flex development.

"Religion is fine, as long as it makes no testable statements about reality and does not shape expectations about human behavior." That's an apologist's justification for a religion that, for all practical purposes, does not exist.

It's not about the crank ideas... I'll acknowledge that I've utterly failed to make my case and leave it at that.

Oh, you are saying the people on the "other side" are out of touch with reality?

Nope, not saying that. But I would suggest that your desire to assign equal rooting in ideology to liberals is ungrounded and stems from a misguided desire to assert parity among actors.

I don't think that's really a fair dichotomy. The space in which ideas are argued strictly on their merits rather than in contrast to some ideological rubric, has been fully disowned by people calling themselves conservatives. That's a pretty damning asymmetry.