Tuesday, July 26, 2005

Virgin Management

When I had lunch with Julian, Amy, and Tim on Saturday, the following intriguing question came up: If you were a Muslim, and you died and went to the Muslim heaven, how would you space out your enjoyment of the 72 virgins? Suppose that you actually find virginity desirable, and suppose that the virgins’ maidenheads are not magically restored periodically. If the afterlife has infinite duration, then no matter how long you wait to deflower your 72nd virgin, you’ll still be looking at an infinitely long virgin-less future thereafter. (More abstractly, the question is how to allocate your consumption of a finite non-durable good over an infinite period of time.)

To begin with, assume the existence of a discount rate, so that later periods are valued less than earlier periods (when viewed from the present). Even so, you would not choose to take them all in one night if virgins have diminishing marginal utility. You would save some virgins for the future, because the gain in value from regaining your appetite exceeds the loss in value from time-discounting. Still, under reasonable assumptions, eventually you’d use up your virgins. Your appetite for virgins presumably increases with the length of time since your most recent virgin; but unless your appetite continuously rises at a rate greater than your discount rate, you’ll eventually find it worthwhile to take the last virgin.

But does it make sense to have a discount rate when you’re dead? Discounting of the future presumably reflects our uncertainty about whether it will arrive at all. If you know your future will last forever, arguably you should weigh all periods equally. So what happens if we assume no discounting? Then we have a paradox: you might choose never to take the 72nd virgin. This will happen so long as your appetite always increases with the length of time since your most recent virgin. Even if the increase in your appetite is diminishingly small, the absence of discounting means you’ll wait any amount of time for the tiniest increase in satisfaction. To escape this conclusion, we must assume your appetite for virgins “tops out” after a certain amount of time – say, T years. In that case, there would be infinitely many optimal allocations of your virgins. One such solution would be to take one immediately, wait T years, take another, wait T years, etc., until you take the 72nd virgin after 71T years. But an equally good solution would involve waiting T + 1 years between virgins, or T + 2, etc. In fact, the intervals need not have equal length, and you could wait as long as you wanted before taking the first virgin.

Fewer solutions work if your appetite, after topping out at T years, begins to decline. In that case, you must space your virgins at intervals of exactly T to maximize your utility. How long you should wait before taking the first virgin depends on how great your appetite for virgins is when you arrive in heaven.

All of the above assumes that only the actual act of taking a virgin gives satisfaction, though the amount of satisfaction may depend on how long it’s been since your last virgin. Things change dramatically if recollection or anticipation is a significant source of one’s satisfaction. A person who enjoys looking back fondly on his experiences would rationally choose to take the virgins earlier – possibly in one fantastic orgy – so as to increase the duration of the pleasant memories. Of course, there will always be infinite time after the last virgin, so it could be countered that taking the virgins earlier will not increase the time spent recollecting. But I think it makes sense in this case to make comparisons of infinities, since one infinity begins earlier.

The real paradox of choice arises, I think, in the case where anticipation is highly important. If the joy of looking forward to taking a virgin were the primary source of your satisfaction from doing so, then your optimal plan would require always having one virgin ahead of you. Every period, you would have the choice of taking the virgin now or taking her tomorrow, and taking her tomorrow would always generate a greater sum of instantaneous utility and anticipatory utility (if we maintain the assumption of no time-discounting). But in that case, you would never actually take the last virgin – in which case your anticipation would be unjustified.

Gil said...

This is hilarious.

Maybe there's a national security issue here.

Perhaps if you spread the message widely that having 72 virgins for eternity is more problematic than it appears, you might encourage some would-be martyrs to take another crack at forging a good life on earth, instead.

Jeff Brown said...

These are interesting paradoxes. I'm wondering about two more phenomena that might be worth modeling.

Phenomenon 1: Anticipation is felt more intensely the nearer a future event becomes. That's related to but distinct from present-value discounting.

Phenomenon 2: Either or both of one's anticipation and one's at-the-moment enjoyment might (depending on the particular angel's preferences) be greater when the angel does not know when he'll enjoy his next defloweree. For instance, a probabilistic contrivance could determine the next big event.

Better yet, an enterprising angel might set up a virgin-management firm, and advertise the determination of those events in some scientific pleasure-maximizing fashion that will completely exhaust a client's virgins, when in fact the plan is to maximize the clients' happiness by holding them in anticipation forever.

If such a firm had only a finite number of angels, it would be difficult to keep up such an appearance permanently. But if the firm has an infinite population of well-behaved deceased Muslim men to draw on, it could conceivably never be found out.

Anonymous said...

Really interesting analyses. But I've been told there's no such thing as 72 virgins waiting for Muslim martyrs or promised in the Koran. Do you think they all died for nothing then?

Anonymous said...

Do sacrificial virgins have any supernatural rights? I think not. So it can't help her any to scream, "get the hell (heaven?) off (out) of me, you rapist bastard!" And there is no reason to assume that the length of the sex act is limited in paradise, except perhaps from the virgin being screwed to death. But presumable she is already in an immortal form, so she's safe. Can you conceive of any normal guy (even suicide bombers are normal in this context) voluntarily stopping intercourse to, say, eat from the heavenly cornucopia? Hunger pangs are sated in heaven. Check you Koranic verses if you don't believe me. So we can conclude from all this that for any T period she is likely going to be banged for the entire T period. Sorry, lassies, Mohammad seems not to have cared about your feelings in the afterlife. You are nothing but a slave and a plaything for murderous mongrel muslim men. The women's rights movement in eternity is sadly forever behind the times. Glen, please adapt your analysis to include this new and sadistic piece of information.

sk said...

ugh. this post seems sexist although your only intent was to poke fun at the stupid beliefs of the terrorists thinking there is a heaven with 72 virgins.

But what if the real joy is not from anticipation or the actual act of deflowering a virgin, but the satisfaction of being the first and last one to have a virgin; basically being the only one to be with the virgin being the height of satisfaction (probably not an uncommon thought of some men). Then one can be infinitely satisfied with 1 or 72 virgins.

FH said...

Is it really so difficult to read an analysis and understand that the subjects' preferences are accepted as given?
This post isn't sexist or just making fun, and no, 72 virgins or 1 virgin wouldn't provide infinite satisfaction even if deflowering were the one and only goal.

alina said...

Glen, my fondest hopes are that you "get you some".

sk said...

FH: is it so difficult for you to just read comments that express sentiments or different viewpoints without being a total asshole? how do you get by in life? just because you're anonymous, don't give me your higher than thou shit.

Sara said...

sk, I think I can speak for all of us when I say:
Stop commenting like a twit, then. If you can't take criticism, don't comment on a highly intelligent blog, the content of which you rarely seem to understand. (Sorry, Glen.)

Anonymous said...

You're not speaking for this random bloke in cyberspace. I think sk is hot, hot, hot & smart, smart, smart! I've been missing her frequent personal takes on Glen's posts. I didn't fully understand glen's "72 virgins" post either. Was it all meant to be tongue-in-cheek or was his tongue wanting to be someplace else? Come back sk, wherever you are! We love you!!

sk said...

ok sara, so you read my comments enough to be able to make the call that i rarely understand the content? i don't think so.
i can comment however i want to sara. and please don't get testy with me. i'd rather not pepper this blog with any more unecessary banter.

sk said...

ok to nip it in the bud--end any more unecessary comments hereafter (really i flatter myself), i'll just admit to the mistake of name-calling in my second comment. Maybe the word "jerk" or if that too is name calling, "jerk-like" would have sufficed. ;)

Anonymous said...

I'm reminded of a short story in which a railroadman is given a magic stopwatch by the devil, in exchange for his soul. At any time, he can stop the watch, and that moment will last forever.

Of course, he never stops the watch, always waiting for a "better" moment - just as the devil had expected. He eventually dies, and the train comes to take him to Hell. As they're careening down the track into the abyss, the devil laughs in his face and asks for the watch back.

That's when he stops it.

It's a great story.

-Tony

Anonymous said...

I'm reminded of a short story in which a railroadman is given a magic stopwatch by the devil, in exchange for his soul. At any time, he can stop the watch, and that moment will last forever.

Of course, he never stops the watch, always waiting for a "better" moment - just as the devil had expected. He eventually dies, and the train comes to take him to Hell. As they're careening down the track into the abyss, the devil laughs in his face and asks for the watch back.

That's when he stops it.

It's a great story.

-Tony

Anonymous said...

I'm reminded of a short story in which a railroadman is given a magic stopwatch by the devil, in exchange for his soul. At any time, he can stop the watch, and that moment will last forever.

Of course, he never stops the watch, always waiting for a "better" moment - just as the devil had expected. He eventually dies, and the train comes to take him to Hell. As they're careening down the track into the abyss, the devil laughs in his face and asks for the watch back.

That's when he stops it.

It's a great story.

-Tony

Anonymous said...

On the other hand, it looks like Tony has popped his watch already.

lcduplatt said...

Could you imagine the hell it would be for the 72 women who find out they have some guy they are hooked up with "forever!" LOL What a joke. I thought you may like this…found this site of NDEs that are cool. This is probably more representative of what the afterlife looks like... Near Death Experiences

Anonymous said...

My question is this:
Just what will happen to all of the women, when they are no longer virgins?? Who will take care of them? Where will they reside? HOW will all those horny men contend with the billions of women that are no longer worthy of being screwed?? If screwing virgins is the only thing that women are good for, seems to me that these men are going to have a MAJOR problem on their hands when they are all 'used up'.

Anonymous said...

interesting analysis. I think the virgins concept is more of an abstract of great rewards. I don't think terrorists kill themselves to sleep with 72 virgins. they alredy do that on earth. i like the way the analysis go, but i think the concept is in no way to be taken literally.