This will not be a long post; I have a simple question to ask: if you wanted to educate yourself to graduate level in mathematics, but didn't actually want to go to university, what would you do? I would ask for text-book recommendations, but I don't want to limit your responses (however, bear in mind that the wikipedia articles on, say, cardinality or well-ordering go over my head – they may skim my hairline, but over they go). Also bear in mind that while I personally have A-levels (British qualifications) in both Maths and Further Maths (which is to say, I know some calculus at least), there are probably plenty of people on lesswrong who don't and who desire the same information – so assume as much ignorance as you feel necessary (it's a shame, actually, that there isn't a sequence here on lesswrong for maths). What do you advise (if you think the query ill-defined, I would like to know that as well)?

This thought-experiment has been on my mind for a couple of days, and no doubt it's a special case of a more general problem identified somewhere by some philosopher that I haven't heard of yet. It goes like this:

You are blindfolded, and then scanned, and ninety-nine atom-for-atom copies of you are made, each blindfolded, meaning a hundred in all. To each one is explained (and for the sake of the thought experiment, you can take this explanation as true (p is approx. 1)) that earlier, a fair-coin was flipped. If it came down heads, ninety-nine out of a hundred small rooms were painted red, and the remaining one was painted blue. If it came down tails, ninety-nine out of a hundred small rooms were painted blue, and the remaining one was painted red. Now, put yourself in the shoes of just one of these copies. When asked what the probability is that the coin came down tails, you of course answer “.5”. It is now explained to you that each of the hundred copies is to be inserted into one of the hundred rooms, and will then be allowed to remove their blindfolds. You feel yourself being moved, and then hear a voice telling you you can take your blindfold off. The room you are in is blue. The voice then asks you for your revised probability estimate that the coin came down tails.

It seems at first (or maybe at second, depending on how your mind works) that the answer ought to be .99 – ninety-nine out of the hundred copies will, if they follow the rule “if red, then heads, if blue then tails”, get the answer right.

However, it also seems like the answer ought to be .5, because you have no new information to update on. You already knew that at least one copy of you would, at this time, remove their blindfold and find themselves in a blue room. What have you discovered that should allow you to revise your probability of .5 to .99?

And the answer, of course, cannot be both .5 and .99. Something has to give.

Is there something basically quite obvious that I'm missing that will resolve this problem, or is it really the mean sonofabitch it appears to be? As it goes, I'm inclined to say the probability is .5 – I'm just not quite sure why. Thoughts?

It has been the case since I had opinions on these things that I have struggled to identify my “favourite writer of all time”. I've thought perhaps it was Shakespeare, as everyone does – who composed over thirty plays in his lifetime, from any of which a single line would be so far beyond my ability as to make me laughable. Other times I've thought it may be Saul Bellow, who seems to understand human nature in an intuitive way I can't quite reach, but which always touches me when I read his books. And more often than not I've thought it was Raymond Chandler, who in each of his seven novels broke my heart and refused to apologise – because he knew what kind of universe we live in. But since perhaps the year 2007, I have, or should I say had, not been in the slightest doubt as to who my favourite living writer was – Christopher Eric Hitchens.

This post is not about how much I admired him. It's not about how surprisingly upset I was about his death (I have since said that I didn't know him except through his writing – a proposition something like “I didn't have sex with her except through her vagina”) - although I must say that even now thinking about this subject is having rather more of an effect on me than I would like. This post is about a rather strange change that has come over me since his death on the 15^th of December. Before that time I was a staunch defender of the proposition that the removal of Saddam Hussein from power in Iraq was an obvious boon to the human race, and that the war in Iraq was therefore a wise and moral undertaking. Since then, however, I have found my opinion softening on the subject – I have found myself far more open to cost/ benefit analyses that have come down on the side of non-intervention, and much less indignant when others disagreed. It still seems to me that there are obvious benefits that have arisen from the war in Iraq – by no means am I willing to admit that it was an utter catastrophe, as so many seem convinced it was – but I have found my opinion shifting toward the non-committal middle ground of “I dunno”.

Well, Mrs. Mason didn't raise all that many fools. It could be that what's happening here is I'm identifying closely with the Ron Paul campaign, and that since I agree with Paul on many things but not on American foreign policy (and, as it happens, I'm British – but consider myself internationalist enough that American arguments significantly influence my views), and so am shifting towards his point of view. But I think it's rather more likely – embarrassing as this is to admit – that the sheer fact that the Hitch could no longer possibly be my friend – could no longer congratulate me on my enlightened point of view, or go into coalition with me against the forces of irrationality – has freed up my opinions on the Iraq war, and I have dropped into the centre-ground of “Not enough information”. This, as I said, is embarrassing – whether or not the best writer in the world approves of your opinion is no basis for sticking to it. But this is the position I find myself in: weak; fragile; irrational – at least as far as politics go.

So here is my half-way solution: extreme and not perfect, by any means, but I think, given the unearthing of this appalling weakness, necessary: from this point onwards, until January 1^st 2013 (yes, an arbitrary point in the future), I am not allowed to settle on a political or moral opinion (ethics – the question of what constitutes the good life - I consider comparatively easy, and so exempt). Even when presented with apparently knock-down arguments, I am forbidden from professing allegiance from any moral or political position for the rest of the year. Yes, it is going to be hard to prevent myself from deciding on moral questions, or on political questions – but I am hoping that if I can at least prevent myself from defending any position for the rest of the year, I will, at the end of it, no longer be emotionally attached to any particular ideology, and be able to assess the difference at least semi-rationally. I don't want to believe anything just because Hitchens believed it. I don't want to be motivated by perceived-but-illusory friendship. I want the right answer. And I'm hoping that depriving my brain of the reinforcement that becoming part of a team – no matter how small – gives, I will be able to consider the matter rationally.

Until 2013, then, this is it for me. No longer are Marxism, fascism, anarcho-syndicalism etc. incorrect. They're interesting ideas, and I'd like to hear more about them. This is my slightly-less-than-a-year off from ideology. Let's hope that it works.