A bat and ball together cost £1.10. The bat costs £1.00 more than the ball. How much does the ball cost?I fell straight into the trap — the ball must cost 10p. I jotted it down, and waited for the next.
All roses are flowers. Some flowers fade quickly. Therefore some roses fade quickly. Is the logic right or wrong?WRONG! Just because some flowers fade quickly, it doesn't mean that roses are in that group automatically. And while some roses might fade quickly, it's not because of the reason that 'some flowers fade quickly'.
The latter I felt able to 'do': it was a syllogism, and its third part didn't follow from its first two, a logical fallacy.
The maths question niggled at me, I felt dumb, because I knew it must be a trap, but I literally couldn't think how to solve it: the ball probably cost less than 10p, but I didn't know why. Luckily Ed Vaisey MP got it wrong too, on national radio, giggling and wondering if the answer was 'zero'.
In the end I had to be put out of my misery. Of course! If the whole total is £1.10, then you have to subtract the pound, and halve whatever is left to give you a price for the ball and something to tack on to the pound. So the ball costs 5p and the bat costs £1.05. For Kahneman, I had thought too fast. Doh!
It was my daughter who stumbled on the fact that you have to halve whatever is left over after you subtract £1.00, to work out the answer. Her first answer was the same as mine, the ball must cost 10p. But her very next attempt was to say, "well, it must be less than 10p, so why don't we say 5p"? Bingo, she had the answer and the method — although she didn't realise it.
Such a stupid little thing, but I was so annoyed I couldn't 'do' it. That terrible feeling of brain going soft, just not being quite as quick as I was. There. I've said it.
I can justify my way out of it: pre-pregnancy, I still don't think I would have got the answer right immediately (I can only really do maths if I can translate it into Base Word, as opposed to Base 10). I have broccoli interruptions now. Other things on my mind. Sorting out arguments, homework, name labels, school run, playdates, birthdays, shopping, ironing, aaaaaarrgh, for example.
But it made me think about other logic problems that have got under my skin. The Cretan Liar's Paradox, for example.
Epimenides, a Cretan, said: "All Cretans are liars".As Epimenides is Cretan, this means that he is a liar too. But if he is a liar, then his statement cannot be true. Cretans must be truthtellers. Except that if they are all truthtellers, Epimenides, a Cretan, must be telling the truth by saying that they are all liars. But if Epimenides is telling the truth, and all Cretans are liars, what does that make him? A Cretan telling the lie (or the truth) that all Cretans are liars.
It's unresolvable, a paradox. A contradiction that cannot be collapsed. Pointless. Maddening. Pure theory. Is this what we waste taxpayers' money on? Etc etc. My daughter quite liked it, actually.
Proust specialized in paradoxes too: the one I have always loved, and use a lot, is:
[…] les "quoique" sont toujours des "parce que" méconnus […]from A l'ombre des jeunes filles en fleurs, the second part of A la recherche ("althoughs" are always misunderstood "becauses"). He's painting a vicious portrait of the pompous diplomat Norpois, whose professional identity depends on his being all things to all people. Thus, Norpois focuses on individuals, not despite being so busy, but because of it; he is charming not despite being so much in demand, but because he needs to be everywhere at once. We call it 'working the room'.
Proust's paradox is a linguistic laser, shining from the outside of Norpois's head to its hidden workings. Suddenly Norpois, the slightly overbearing Polonius figure, who puts down the young narrator's writing with a thoughtless remark, is skewered into place, and, uncomfortably, we dimly see ourselves at parties, circulating, hoping not to be stuck with bores, smiling, smiling, trying not to be seen looking past our interlocutor for the most important person in the room, trying to be gracious and not dismissive. Proust's paradox is like a literary version of Gunther von Hagens's macabre plastination process, making the inside visible.
I wish I understood the word "psychology". Kahneman is a psychologist who writes about decision-making and economics (by which I assume he means negotiation, trading, at whatever level — maths in the marketplace, performative maths between humans). Proust was a novelist whose insights into the workings of the mind seem to me to rival Kahneman's, but do so through linguistic description.
In my own daily life, responsible for (or just standing around watching) the psychological formation of two children, I am aware of psychology as an infinitely mutating set of relations. 'Psychology' seems to be something that exists both within an individual's mind, and between individuals, as a constantly-rippling, always contradictory and conflicted relation.
I think perhaps I wasn't so aware of the relational aspect of psychology until I had children, because I simply had no experience of durational development, of meeting minds in flux — I had only theorized about it from well beyond that stage in my own life, with other adults.
Now in a state of near-permanent bewilderment and self-estrangement, I am only intermittently internally connected as I fight to engage with the children's fleeting, fairylike or demonic projections.
My psychology is now fixed, or much harder to change, while my children's is in the process of fixing. How that happens remains a mystery to me, because I do not yet know which of my moods, rules, refusals, omissions will leave a permanent trace in their plastic neural pathways. I must constantly put up and dismantle boundaries, keep them safe from themselves, anticipate but not pre-empt where their wildness will take them, let them invade or escape without harming themselves.
Now that's a paradox.