Just realized this is the last day before the challenge so I've donated AU$25

When you say that the posterior probability is 1/3, this depends on the three combinations being equally likely, but as I said in my other comment, they are not equally likely, given your way of obtaining the information.

My posterior probability that you hold two aces should be the same either way

Yes, but the posterior probability is 1/3, not 1/5. p(two aces|AH) = 1/3 (As the possible options are, AH+AS, AH+2D, AH+2C) p(two aces|AS) = 1/3 (AS+AH, AS+2D, AS+2C)

However, if you had interpreted argument 2 as asking p(two aces|ace of hearts OR ace of spades) you would end up with 1/5, which is the same result as the prior p(two aces|have an ace). I think the fallacious reasoning here is that conditioning on the disjunction of having either ace, p(both aces|AH OR AS) = 1/5, does not provide you with any new information, as it is the same query as before. But actually selecting one ace and conditioning on that information gives you the correct result, namely that p(both aces|AH) = p(both aces|AS) = 1/3. So argument 1 is correct.

As far as I can tell, this article is pure journalistic flair. There seems to be little to almost no sufficient data for the authors of the article to make any of the assumptions they claim in the article.

Looking around Google, there seems to be at most a handful of these 'boskop' brains which were discovered at the start of the 20th century. I think the case for the existence of an entirely new 'superintelligent' species that lived tens of thousands of years ago does not seem plausible, given the lack of evidence for the boskops. There seems to be some evidence that larger-than-human brains did exist around that era, but even so, many of the authors claims regarding the properties of having bigger brains simply do not stand up to any scientific rigour. It is an absurd case of generalizing from one example.

For example, how do they determine that a brain which is 30% larger would have an average IQ of 149? IQ measures are only valid between humans, so assuming the boskops are a superintelligent-human-like species, the notion of administering it an IQ test like ours is a ludicrous proposition. Even now, with chimpanzees running around, we don't have a quantitative method of measuring their intelligence, nor can we compare it to our intelligence in a quantitative manner.

Some of the speculations the authors make are downright nonsense. They claim that 'With their perhaps astonishing insights, they may have become a species of dreamers with an internal mental life literally beyond anything we can imagine.' Where is the evidence for their rich mental life? Unfortunately, the discussion of the boskops 'better' cognitive abilities, seem to be pure speculation along the lines of 'like humans, but better'. They even posit that the boskops were able to see their own demise due to their big brains's abilities, which is simply more nonsense.

I would love to hear if anybody knows anymore about these boskop brains...

Thanks, that's helpful, but the original spreadsheet being sortable would still be very useful, because the librarything doesn't have "shelf", so you can't sort and view all math books together, for example.