"But if you can't picture it..."

The other day, I was talking to a couple of friends of mine - a literary theorist and a historian/political scientist - about the (apparently) recently proved Poincaré Conjecture. The Poincaré Conjecture involves a statement about the 3-sphere - that is to say, something like the usual sphere, but one dimension bigger. In order to visualise a 3-sphere, you would need to picture it in four dimensions, just as the usual sphere (2-sphere) is usually considered to be a two-dimensional surface, embedded in three-dimensional space. The idea of four dimensions can provoke puzzlement among humanities students of a sort to startle a blasé mathematician for whom such things are second nature. My friend the student of history and politics asked, with a slightly concerned look on his face,

"Can mathematicians actually picture four dimensional space?"

"Roger Penrose says he did it - briefly - once," I said, grinning [1].

"No, but are there people out there who can actually..."

"Not that I know of."

My historian friend was relieved. My literary theorist friend was confused. "If you can't picture it," he asked, "how could you have any intuition about it? I mean, you could just say whatever you wanted about it and no-one would be able to refute you."

The first way that students of mathematics start dealing with four (or more) dimensions is fairly simple. If you're in two dimensions, you can describe any point with, say, an x co-ordinate and a y co-ordinate.


To go to three dimensions, you need a third co-ordinate in, say, the z-direction (use the previous picture but imagine the third axis coming out of the screen towards you.). To go to four dimensions, add a fourth number, and there you have a way of describing four dimensional (flat/Euclidean) space.

It gets more complicated when you start dealing with curved surfaces, but the idea is similar. If, earlier, you wondered why we consider the surface of a sphere to be two-dimensional, think of it this way. The Earth is approximately a sphere. We can describe positions on the Earth's surface with two co-ordinates: latitude and longitude. Two co-ordinates, two dimensions. Exact definitions might worry about the poles, where there is no real longitude to speak of - it could be anything - but there are fairly simple ways of getting around that which need not concern us here.

Besides the question of four dimensions, there is a broader principle raised by my friend's comment. The extent to which intuition plays any role at all in the basic system of mathematical proof is arguable. This is a fascinating topic in its own right that deserves a post of its own, so for now I shall simply promise to address it later.

[1] He says it in The Emperor's New Mind.

What I Wish I'd Said About Women And Sex...

... because "what I wish I'd said" must surely turn up on blogs everywhere.

"I've never had sex," I admitted, one drunken night several months back.

"Oh, don't worry," he said. "You're not really missing anything."

I shall pause to give you time to choke at the idiocy of this.

Now I shall perhaps provoke confusion when I admit that my reply was not "Don't be silly" or "That's absurd" - but please remember that "That's sexist and absurd" is sometimes not an easy thing to say if you want to be taken seriously. So I replied with a heartfelt

"Oh, don't say that!"

Yeah? Makes sense to me, but it ended up meaning we were having a conversation about whether women can really get anything out of sex.

"Look, we'll ask A__"

A__ (not his real name, or even his real initial, actually; just the first letter of the alphabet) sobered up visibly and thought about the issue. "I think," he said, "... certainly within the context of a loving relationship, women can definitely get something from it, yeah."

Okay, be nice. The generous way to view this is to note that A__ has a long-standing girlfriend and is therefore (hopefully) speaking from experience when providing this counter-example to the idea that women don't get much from sex.

Agreement from the guy who had been speaking to me initially; A__ waffles a bit more and then asks me:

"I dunno - I mean, what do you think, what do you feel?"

A__ is, I suspect, consciously allowing me, as a woman, to define my own experience; he is a nice liberal man who generally tries and, yes, usually succeeds; this conversation does not really show him at his best. However, it is me who fails at this point.

"I don't know," I say, and it's true, of course; how could I know, of my own knowledge? "I mean, it's not like I'm waiting for any particularly special moment - I'm just waiting until I feel comfortable." Sufficiently comfortable, anyway; not, like, comfortable comfortable.

Actually, I'd give anything for a comfortable comfortable opportunity to have sex. I just don't know when I'll get one.

But look, let's go back.

"Don't sat that!" Why? Because "you're not really missing anything" is, get this, exactly equivalent to the statement "sorry, Lynet, there is no satisfaction." It's a horrible thought - one of my worst irrational fears, actually. Apparently the man I was speaking to missed the point entirely. He probably honestly doesn't realise how it feels to be a woman in my position. I ought to have corrected his ignorance, but it's hard. It's very personal to talk about these things. Stating it here is an attempt to redress the balance; the best I can do. So let me tell you.

The worst times are when I ovulate. Seriously, at least when I'm getting my period I have a tummyache to distract me*. There have been times when I'm ovulating when I end up lying in bed, drenched in my own sweat and dissolving in my own sexual frustration, trying to masturbate though my clitoris aches 'cause I've been rubbing it too hard - I've been over once already and it's not enough - and when I shove myself up and over into orgasm I spontaneously burst into tears because even as my body shakes I feel as though it's really not doing anything, I still need sex just as badly (oh, gosh, I just burst into tears typing), and it just feels like nothing's going to help, nothing not ever.

*Ovulation and menstruation are the two times when a woman's libido is highest, in general. Most sources say the feeling is stronger on average during ovulation, but it's certainly perceptible at mestruation; sometimes I can tell when my period is arriving by the increased tendency to think about sex.

Now, I'm happy to say that this has only happened to me a couple of times - most months aren't that bad. I mean, there's no time of the month when I don't think about sex at all, and there is no time of the month when I don't want sex, but, while it's not unusual for ovulation to be a difficult time of the month, I don't always end up crying.

"You're not really missing anything"? NO! Please, please, no! Please, please, please, oh, please, no! Tell me it isn't true. Tell me it doesn't always feel this bad. Tell me one day I'll be okay in some sense of the word, I know I won't ever be free from sexual desire, but tell me that - I don't know - tell me something.

I'm crying again.

"In the context of a loving relationship"? Tell that to my cunt. The only thing I need a loving relationship for is to provide a situation in which I can have sex and still trust the person who I am having sex with to respect me. A situation which provides the latter but is not equal to the former would still be fine; I just don't like the idea of someone touching me if he thinks he is degrading me - or increasing his masculine power at my expense - in so doing. The idea makes me sick. Especially when I'm ovulating. And it would hurt me even worse than the sexual frustration that makes me cry.

But I didn't say that at the time.

It's hard to show people a part of yourself that's so very fragile.

Alphabet Meme

Alon hasn't tagged anyone - so I've just picked it up for myself.

Accent: New Zealand, overlaid by years of singing training.
Bible Book that I Like: Proverbs - except for all that stuff about believing in the Lord - and the stuff about how horrible loose women are... hmmm... maybe I should pick the Song of Solomon instead. It's cool how there's a part of the Bible that acknowledges the beauty of sex.
Chore I Don't Care For: No-one makes me do horrible chores at the moment. The worst I have to do is laundry - and that's usually a nice break from studying.
Dog or Cat: I left my cat Rosina behind when I left NZ to study in the UK. I miss her.
Essential Electronics: Laptop - what else?
Favourite Cologne: My least clued-in set of cousins gave me a set of two types of cologne once. I've had them for years, but on special occasions I'll sometimes wear one or the other. One smells of incense; the other one is more flowery.
Gold or Silver: Silver.
Handbag: Black leather, fairly small.
Insomnia: My sleeping pattern gets out of joint very, very quickly. Sometimes I'm definitely an insomniac; occasionally I manage to get back into a decent pattern.
Job Title: Student.
Kids: None, thank goodness - though I'd like to have some when I'm older, assuming I'm that lucky.
Living Arrangements: You'd call the place I live a 'dorm' in America, I suppose.
Most admirable trait: Honesty.
Naughtiest Childhood Behaviour: Throwing huge noisy tantrums. Especially when I did it in a public place.
Overnight Hospital Stays: Don't think I've ever had one.
Phobias: A slight, but manageable, fear of small spaces - but it has to be pretty small before it bothers me.
Quote: All who believe in daffodils while the snow falls about them are leading uneasily beating lives, their rhythm is the lost note that cannot or will not join the chord because although it will gain security and strength from being with the other notes it will at the same time forget the sound of itself, and therefore it stays alone in strange hollow places where there is no other music. The loneliness is the price and the reward. - Janet Frame, in her story Snowman, Snowman.
Religion: Atheist.
Siblings: Three younger sisters.
Time I Wake Up: Variable. See Insomnia.
Unusual Talent or Skill: Learning. Mwahahaha.
Vegetable I Refuse to Eat: Artichokes. Hate them.
Worst Trait: Well, I spend an awful lot of time fighting the urge to react to social insecurity by closing off from people. But I do manage to avoid that, most of the time.
X-Rays: One, when I broke my arm when I was four.
Yummy Stuff I Cook: I don't cook much, here, but I used to like cooking back home. I had a quiche recipe that always worked rather well...
Zoo Animal I Like Most: Meerkats.

The Truth

I've finally discovered the truth.

Actually, I've always had something of a love for the truth of things. My mother tells me that when I was a toddler I initially didn't believe lying was possible, and then, when I was convinced, still had trouble understanding why anyone would want to lie.

Later, when I was four or so, I vowed to myself that I would never tell lies - apart from 'polite lies' ("I like my new top, thank you Gran"). I think it was my mother who suggested the exception.

I told my first, proper, protecting-myself-from-disapproval lie when I was five. I felt guilty about it for years afterwards. My sister and I had been sneaking out the side fence (I felt so daring for sneaking about a metre into the path that led off the street to the neighbours' gate). The lie was brief. It may even have been a reply like 'nothing' to a question about what we had been doing. At any rate, my sister, who was only two, and much more inclined to tell lies in general (she cares more for love than truth, always has), seems to have been convinced that since I was doing it, it must be okay, and blithely showed our mother the gap in the fence.

Mum wasn't mad; she would have hesitated before discouraging us from exploring, in general. And if she was conscious of my having lied initially, she didn't show it, which is why I think my lie may have been imperceptible to the less idealistic adult eye. I think I almost felt more terrible because no-one but me was aware of my crime (and there was no way I was going to tell anyone).

As I got older, my notion of honesty grew. Somebody once referred to the idea of giving some real part of yourself on stage as 'honesty', and the idea took root in my head and flourished beautifully into an idea of being true to some genuine feeling when you express yourself. When I see it in other people, I actually find it the sexiest thing on Earth.

On a slightly different note, which is more truthful: a factual statement from which people might get the wrong idea, or a statement which is not strictly correct, but which is more likely to give people the right general feel? That is, is the truth of a statement in ordinary conversation best measured by its content, or by the way it will be heard?

What about poetry? I used to have trouble with Keats:

A thing of beauty is a joy for ever...

Yep, that's right, folks, when the sun has turned into a red giant and long since engulfed the Earth, those crocuses on the way to college will still be a joy.

A thing of beauty is a joy for ever
Its loveliness increases, it will never
Pass into nothingness, but still will keep
A bower quiet for us, and a sleep
Full of sweet dreams, and health, and quiet breathing.

That's the beginning of Keats' Endymion, by the way. My quiet bower is up at the top of the rhododendron tree, with the sunlight streaming through the spring leaves of the ash tree, and me, twelve years old, relinquishing pain for a while and only seeing beauty.

A poem can be 'honest' in the same way that a freely given emotion can be honest; a rich way that goes beyond what can be factually contained in a given set of literally interpreted words. This increased breadth in what can be conveyed admittedly comes at the price of complete and definable accuracy. "For ever"? No, not really. But which of us knows forever?

We are getting close to what a friend of mine (who just happens to write poetry) calls "truth of the heart" as opposed to "truth of the mind". If it conveys some truth about the way you see the world, is it okay to paint your life with metaphors? With myths, like the ancients did, personifying the power of the storm and the fertility of the crop?

Can a religious ritual act as a physical metaphor? If so, does this mean there is "truth" in it, if it embodies some genuine feeling?

When people say that religion will die, that it's just too stupid, I don't know if they are right. I do know this. The non-scientific part of us that goes into poetry isn't going to die. And there will always be people who value that way of thinking above hard objectivity, who will discard the clear evidence of their own senses in favour of "melodies unheard" (Keats again, and that line in the second verse was the part of the poem that first caught my eye; it hits me like a sharper version of deja vu).

I think it is possible to care for both ways of thinking. I suspect that we require the more objective input of our senses before the imagination could even take flight. I know we need to trust our senses in order to survive. Still, the experience of beauty, the feeling of love - these things are part of what makes survival worth it in the first place. I love science, but I have never been short on imagination.

I tend to think that the line between an imagined story and the truth or an attempt thereof should never be blurred. [EDIT: Even when I'm taking some belief as given, I almost always make a little note in the back of my mind that that's what I'm doing. Somehow that doesn't get in the way of the purpose of believing it in the first place]. Some people disagree, and always will. That doesn't make them right, but many of them are worthy people, nevertheless, who contribute to the world in other ways.

Back to Ode on a Grecian Urn:

When old age shall this generation waste,
Thou shalt remain, in midst of other woe
Than ours, a friend to man, to whom thou say’st,
“Beauty is truth, truth beauty,”—that is all
Ye know on earth, and all ye need to know.

No, no, Keats, no! Rightfully lauded poet though you are, I will never forgive you for that one!

Edited slightly for The Humanist Symposium - but all I did was cut a basically irrelevant paragraph, alter some punctuation here and there, and add the sentence above that is declared as an edit.

Why do men seem so much more eager for sex?

Being new to blogging (even though I've been hanging around for a while) means that I keep seeing fairly old posts. This one is about 1/9 of the way down the huge pile of comments on this thread:

In casual social situations of single people, if a woman suggests sexual activity to most any man there, he's willing, probably eager, and more than likely thrilled. If most any man there suggests the same to a woman, she'll say no, probably be offended, and very likely will decide that he's a shallow jerk, regardless of whatever interests and attitudes he might have.

I quote it not to refute that statement in particular, but because I have my own thoughts on this phenomenon, and I was finding it difficult to describe without sounding silly. I kept saying things like "People think women can have sex whenever they want, whereas men have to keep asking and asking", which is ridiculous, everyone knows there are plenty of sexually frustrated women out there (don't they?), and the reason men have to 'ask' is because that's the convention and women don't usually break it (my discussion below should suggest some reasons why they don't break it to anyone with sufficient imagination). Described as above, though, it at least seems to be getting at something that looks like it might have a grain of truth in it. I do think there is a(some?) genuine social phenomenon(s) here, buried under the inevitable generalisation.

Before I get to my main point, though, I wouldn't be me if I didn't nitpick:

In casual social situations of single people, if a woman suggests sexual activity to most any man there, he's willing, probably eager, and more than likely thrilled.

Ok, can I just ask something? How many men have actually been in that situation? I mean, when men say they'd be thrilled, can they point to any examples? And if so, was the man in question in fact thrilled? I'm not a man, let alone an "average man", so I don't know if the average man would be thrilled if the average woman suggested sex. I have had at least one male friend mention being propositioned with the remark "not flattering, trust me", so I know it's not always true. The question needs to be asked if it is true in general. I'm wondering if part of the reason men can say that is because they've never seen the reality, but I don't actually know if that's a reasonable suggestion.

Now that I've got the minor question out of the way, I'll get to my main thought on this matter.

As far as I can tell, in a "casual social situation between single people" it is just about impossible for a man to lose status by having sex.

There are some notable exceptions to this, the cruellest and most obvious being "unless the girl is fat", but, in the main, I think it holds.

Similarly, it is just about impossible for a woman to gain status by having sex.

Exceptions to this rule tend to be both equivocal and reliant on there being some commitment between the two people. For example, a woman might gain status by having a successful husband (personally I think such 'status' would probably annoy the heck out of me, but some might disagree). However, this is a far cry from a casual sex situation. In general, a girl having casual sex is going to have to fight to keep the status she has, let alone gain any. Sometimes I scare myself by wondering if the word 'slut' has more synonyms than the word 'good'. If it's true, I don't want to know. The idea behind the word is pervasive, and it means more than 'promiscuous', it means more than 'woman who has sex'. Mostly, the meaning which bothers me is that of woman who is used - used sexually by men. And if being perceived as being used doesn't lower your status, I don't know what does.

A woman is less likely to be perceived as being used if she makes a show of being choosy. That's a point in itself and I'll leave it there.

Another point, though, is that if a woman appears eager for sex, she might end up with less control over the situation. Unless she trusts the man, she can't be sure he won't just do whatever makes him happy with no care for what she wants. Ideally, she would have a say in these things no matter what, but there are men who would be oblivious to their own sefishness (especially if she was begging for sex in the first place), and there are women who would find it hard to protest.

Add that to the fact that the man is essentially asking her to put the way people see her on the line in a way which simply isn't true for him, and the fact that it still isn't conventional for the woman to do the asking; add the stereotype that women are less interested in sex...

... and biological determinism really has only so much explaining left to do.

EDIT: It occurs to me that I didn't really need to reference biological determinism to make my point. The stuff I've shown gives reasons why women might appear less interested in sex that do not rely on any actual difference in sexual interest between the sexes.

There may well be a difference between male/female sex drive, on average, but I think people probably overestimate it - there are just so many reasons why they would.

Things are becoming clear.

More on a similar topic, because I'm still thinking about this 'objectification' thing, and my thoughts keep being refined.

Maia at Alas! A Blog gives an insightful commentary in which she states

There are many, many different ways women are taught that for us being sexual is being desired, rather than desiring.

Desired/desiring. Object/subject, grammatically speaking, and this is part of what 'objectification' means. Of course, there is also a link between 'objectification' and treating women as objects. The extent to which women are dehumanised - treated as objects - and the extent to which the idea of a woman being desired ends up eclipsing the idea of a woman desiring are both important issues, and they are to some extent related. However, I know very well that in the past I have confused myself by mistakenly conflating the two issues. Thanks, Maia. Things are becoming clear.

"Female Chauvinist Pigs" review at The F-Word

The F-Word has a review up of Ariel Levy's Female Chauvinist Pigs. The book is strident in its views, so I was glad to see that they had viewpoints from several women, rather than simply posting one woman's view on the subject.

I particularly liked this remark from Holly Combe

“objectification” (as I understand it) is only dehumanising when it excludes all other possibilities

She goes on to say that she can see why the incredibly large amount of objectified images of women

leads some of us to say a big final “no more” to anything that could be perceived as “raunch”.

I think her original remark is spot-on, though. The biggest problem is not that there are images out there that objectify women sexually. The biggest problem is that there are not enough images out there that portray women sexually without objectifying them.

I don't think we can get rid of the former without first creating the latter.

I think trying to get rid of the former sometimes prevents us from creating the latter because we are too afraid we will mis-fire and end up back at the dreaded, demonised objectification of women. A big final "no more" can get in the way, sometimes.

But I have hope.