It's simply not the case that there are duplicates. There is just one event there are two boys who are born on a Tuesday.

<eldest boy born on Tuesday, youngest boy born on Tuesday>

There are two events where there are two boys and one is born on a Monday and the other is born on a Tuesday.

<eldest boy born on Monday, youngest boy born on Tuesday>
<eldest boy born on Tuesday, youngest boy born on Monday>

Your confusion arises from introducing a new random variable (whether you've met X or not) and enumerating over this, but only for the both-born-on-a-Tuesday event. You would need to do this for all the other events as well; this would have the effect of needlessly multiplying events but wouldn't change the relative frequencies of the original events.

You are introducing probabilities too early. We start by just counting events. This will lead in turn to frequencies and thence to probabilities.

So: there is only one event where two boys are born on Tuesday, and it is this:

<Eldest boy is born on Tuesday,
Youngest boy is born on Tuesday>

There are no other events where both boys are born on Tuesday. There are two events where there are two boys who are born on a Monday and Tuesday, and they are these:

<Eldest boy is born on Monday,
Youngest boy is born on Tuesday>
<Eldest boy is born on Tuesday,
Youngest boy is born on Monday>

That's all there is to it.

Gladly. The available outcomes are actually:

1. 1. Girl on Monday, Boy on Tuesday
2. 2. Girl on Tuesday, Boy on Tuesday
3. 3. Girl on Wednesday Boy on Tuesday
4. 4. Girl on Thursday, Boy on Tuesday
5. 5. Girl on Friday, Boy on Tuesday
6. 6. Girl on Saturday, Boy on Tuesday
7. 7. Girl on Sunday, Boy on Tuesday
8. 8. Boy on Monday, Boy on Tuesday - BB
9. 9. Boy on Tuesday, Boy on Tuesday - BB
10. 10. Boy on Wednesday Boy on Tuesday - BB
11. 11. Boy on Thursday, Boy on Tuesda - BB
12. 12. Boy on Friday, Boy on Tuesday - BB
13. 13. Boy on Saturday, Boy on Tuesday - BB
14. 14. Boy on Sunday, Boy on Tuesday - BB
15. 15. Boy on Tuesday, Boy on Monday - BB
16. 16. Boy on Tuesday, Boy on Wednesday - BB
17. 17. Boy on Tuesday, Boy on Thursday - BB
18. 18. Boy on Tuesday, Boy on Friday - BB
19. 19. Boy on Tuesday, Boy on Saturday - BB
20. 20. Boy on Tuesday, Boy on Sunday - BB
21. 21. Boy on Tuesday, Girl on Monday
22. 22. Boy on Tuesday, Girl on Tuesday
23. 23. Boy on Tuesday, Girl on Wednesday
24. 24. Boy on Tuesday, Girl on Thursday
25. 25. Boy on Tuesday, Girl on Friday
26. 26. Boy on Tuesday, Girl on Saturday
27. 27. Boy on Tuesday, Girl on Sunday

Note that there are only 27 outcomes as both boys being born on a Tuesday is only one outcome, not two. There are 13 outcomes labelled BB, so the probability of having two boys is 13/27. Hope that's clear now.

It's not part of the problem that only one of the children can be born on a Tuesday, you might be dealing with two boys of differing ages, both of whom were born on a Tuesday. In Keith Devlin's analysis (which is correct, given certain assumptions about the problem), there is only one outcome where there are two boys born on a Tuesday. This is why, once you've accounted for this by enumerating the outcomes where the elder child is a boy born on Tuesday, you can't count it again when enumerating the outcomes for the younger child.

Sadly, we're not even in a position where we can say whether it's inevitable or not. We don't know what strong AI is or how we could tell if we had it (the Turing Test isn't a good way of evaluating this). I agree that it's short-sighted to claim that we'll never develop strong AI, but you're wrong to claim that it's inevitable.

<cough>Ontologies: A Silver Bullet for Knowledge Management and Electronic Commerce</cough>

Having spent over ten years working professionally in the field, I've found this kind of thing to be all too common, especially among ambitious-but-talentless academics where grant applications are concerned, particularly where said grant applications contain the words "semantic" and "web" in close proximity - now that really is pure, undiluted snake oil. The semantic web community has received hundreds of millions of dollars/euros/pounds in funding and they've delivered nothing of any use. Zippo, zilch, zero. Compare this with enormous amounts of useful functionality delivered by the machine learning community. The difference is that machine learning is rigorous and can be really quite difficult, whereas the semantic web is based on the belief that 3-tuples are really neat.

It seems that you forgot about the use of 'sie' for the third person plural, so the GP's quote was orthographically valid.

It only seems weird if you fail to recognise that decisions that politicians have an effect on the future. Take the current banking crisis in the UK. As far as I can tell, many people who know far more about this kind of thing than I do, say that this is directly attributable to the stripping away of regulatory control of the financial sector that happened in the 80s. Now, whether or not this is true, it is clearly plausible that the current economic shitstorm is directly attributable to the economic policies of Thatcher.

You don't need to store massive amounts of electricity, just massive amounts of energy, in whatever form. That's what pumped-storage hydroelectric power stations do - they pump water uphill overnight using the cheap electricity produced by the coal and nuclear power stations that can't be turned off, and then let it fall during the day, driving the turbines.

How about the state Bush left the fucking *world* in when he left office? Asshole.