"Mindless!"
Something that has bugged me slightly forever is the bit in "Four to Doomsday" where Adric and Nyssa are bitching at each other about mathematics. Tegan is irked about having to wait to get home. Adric suggests that, in the meantime, she reads Alfred North Whitehead and Bertrand Russell's Principia Mathematica. Tegan is less than keen. Adric, with astonishing venom, responds: "That's the trouble with women. Mindless, impatient, and bossy. " Nyssa, who's reading Russell's book, retaliates: "You mean this? Mindless!"
I thought of Nyssa's harsh dismissal of the Principia when I was reading Douglas Hofstadter's I Am A Strange Loop. Obviously she's partly just repeating Adric's words back at him, and partly unimpressed with what, to an alien from an advanced civilisation, must seem like a pretty basic text. I'm not an alien from an advanced civilisation, but luckily Hofstadter had explained it in Gödel, Escher, Bach: An Eternal Golden Braid, which I read many years ago. Very simply put, Russell and Whitehead were trying to lay out the formal logic that underpins all of mathematics, and Russell discovered what Hofstadter punningly calls "a terrible loophole".
Russell had been using set theory to explain maths. You might imagine "the set of all even numbers" or "the set of all pink elephants" (an "empty set"). But what happens if you define "the set of all sets that don't contain themselves"? If that set contains itself, then it doesn't belong to the set of sets that don't contain themselves, but if it doesn't contain itself, then the set is not the set of all sets that don't contain themselves. If it gives you a headache, imagine what it did to Russell. (The paradox which the Doctor gives BOSS in The Green Death is similar: "If I were to tell you that the next thing I say will be true, but that the last thing I said was a lie, would you believe me?")
Russell "solved" this by banning paradoxes, self-references, or loops, whatever you want to call them, from maths. But Hofstadter challenges this in many ways (he might like the sentence "This sentence was not posted on Livejournal"), and more to the point here, he talks about self-reference as being the basis of consciousness. IIUC, we are literally self-aware. He says that a mosquito probably doesn't know it has a head, that a dog probably has a pretty good idea of "that's my tail", "that's my paw", and that human beings know they have brains and minds. That's why the book's called "I Am A Strange Loop".
If self-reference is what makes a mind, and the Principia Mathematica excludes self-reference, then it is literally "mindless". :)
... good gods, I hope this makes some sort of sense to someone else.
I thought of Nyssa's harsh dismissal of the Principia when I was reading Douglas Hofstadter's I Am A Strange Loop. Obviously she's partly just repeating Adric's words back at him, and partly unimpressed with what, to an alien from an advanced civilisation, must seem like a pretty basic text. I'm not an alien from an advanced civilisation, but luckily Hofstadter had explained it in Gödel, Escher, Bach: An Eternal Golden Braid, which I read many years ago. Very simply put, Russell and Whitehead were trying to lay out the formal logic that underpins all of mathematics, and Russell discovered what Hofstadter punningly calls "a terrible loophole".
Russell had been using set theory to explain maths. You might imagine "the set of all even numbers" or "the set of all pink elephants" (an "empty set"). But what happens if you define "the set of all sets that don't contain themselves"? If that set contains itself, then it doesn't belong to the set of sets that don't contain themselves, but if it doesn't contain itself, then the set is not the set of all sets that don't contain themselves. If it gives you a headache, imagine what it did to Russell. (The paradox which the Doctor gives BOSS in The Green Death is similar: "If I were to tell you that the next thing I say will be true, but that the last thing I said was a lie, would you believe me?")
Russell "solved" this by banning paradoxes, self-references, or loops, whatever you want to call them, from maths. But Hofstadter challenges this in many ways (he might like the sentence "This sentence was not posted on Livejournal"), and more to the point here, he talks about self-reference as being the basis of consciousness. IIUC, we are literally self-aware. He says that a mosquito probably doesn't know it has a head, that a dog probably has a pretty good idea of "that's my tail", "that's my paw", and that human beings know they have brains and minds. That's why the book's called "I Am A Strange Loop".
If self-reference is what makes a mind, and the Principia Mathematica excludes self-reference, then it is literally "mindless". :)
... good gods, I hope this makes some sort of sense to someone else.