Friday, May 18, 2007

Curiouser and Curiouser

(Continued from yesterday's post.)

Oh, how fun it was. My library talk on The Curious Incident of the Dog in the Night-time was every bit as enjoyable as I had expected. The audience was well-read and responsive, the autism expert was far more willing to pull strings on Bub’s behalf than I had ever dared hope, and there was even a generous gift certificate for the campus bookstore to add a bit of frosting to the cake.

As promised, I’ll provide an additional excerpt from my talk.

The focus of my argument was on the reader’s problematic relationship to Christopher, and I began by cataloguing my own responses: I like Christopher, I feel protective of him (sometimes overwhelmingly so), and I laugh, often and affectionately, at jokes he is not at all conscious of making. All of these responses are generous and kindly meant, but there is a certain hierarchical superiority implicit in them. That hierarchy is disrupted, however, by Christopher’s savantism: in addition to liking, pitying, and laughing at him, I am also not infrequently intimidated by him. He labels his chapters using prime numbers, and while I puzzle over why the number 1 isn’t counted as a prime number, he performs dazzling feats of mathematical brilliance. It is disconcerting, again and again, to find myself noticing that this autistic boy, towards whom I feel so protective, is actually much smarter than I am.

My uncertainty only gets worse when Christopher introduces what is known as "the Monty Hall problem." You’re given a choice of three doors: two have goats behind them, one has a car, and you’ll win whatever is behind the door you choose. Once you’ve made your selection, the host opens one of the two remaining doors, revealing a goat. The dilemma is: Do you stick with the door you chose at the beginning, or do you switch?

The purpose of this exercise is to show the superiority of logic over intuition: to show, in fact, that Sherlock Holmes is a better detective than Miss Marple. Intuition tells us that there’s a 50-50 chance the car could be behind either door – and intuition is wrong. Christopher is able to demonstrate that the car is twice as likely to be behind door #2 (the door you didn’t choose initially). This solution is counter-intuitive but demonstrably correct.

What Christopher’s solution overlooks, however, is the psychological aspect of the problem. When I consider this dilemma, I am not merely trying to figure out where the car is – I’m also trying to protect myself from the disappointment that will ensue if I make the wrong decision. Assuming that the car is equally likely to be behind either door, I feel a strong impulsion to stick with my original choice. Partly that’s based on superstition (it seems like it would be bad luck to switch), but mostly it’s based on my anticipation of how I will feel if I end up with a goat instead of a car. If I stick with my original choice and win the goat, I’ll be disappointed, of course … but if I switch, and then discover that the car was behind my original door all along – well, then I’ll really be kicking myself.

As Christopher demonstrates, our intuition isn’t especially good at figuring out probabilities. But what about the emotional and psychological side? Apparently our intuition is wrong there, too: in Stumbling on Happiness, Gilbert suggests that my instinct to stick with my original choice is not at all unusual. He cites a study based on switching investments: Which feels worse – to lose money after switching to a new investment, or to lose money after forgoing the chance to switch? Nine out of 10 people assume that they will feel worse if they make a mistake (like switching doors or switching investments) than if they stick with the status quo and face the same consequences.

[The tenth person is, apparently, my husband. When I explained this part of my talk to him, he was incredulous. Why would you react differently to losing the car depending upon which door you chose? All I can say is that a roomful of vigorously nodding spectators seemed to know exactly what I meant.]

This is an aspect of the problem that Christopher never even considers: he doesn’t have the ability to imagine situations and determine how he will feel in them. For him, the Monty Hall problem is purely about mathematics and logic. One might think, then, that we are better equipped than he is to protect ourselves from the feelings of regret that would ensue from making the wrong choice. Maybe we don’t understand probabilities as well as Christopher – but at least we know ourselves, we know our feelings.

Not so much. According to Gilbert, our strongest regrets are for the opportunities we miss, not for the mistakes we make. When we take a risk and it backfires, we’re usually pretty good at rationalizing our decision. We say, "Well, that didn’t pan out, but I had good reasons to do as I did." We’re not nearly as good at rationalizing inaction, and so we kick ourselves hardest when we sit back and do nothing, letting opportunity pass us by.

[This rings true for me. The thing in my life that I should most obviously regret is my first marriage. But I can’t say I spend a lot of time beating myself up about it. Based on what I knew and how I felt at the time, I understand why I did what I did. And it didn’t turn out so badly after all. Being married to the wrong man kept me off the market until the right man reached the age of dateability. (The age gap between us was vast when I was midway through my M.A. and he was graduating from high school. A few years later it had narrowed considerably.) On the other hand, I’ve kicked myself black and blue in recent years for failing to dot my i’s and cross my t’s during my maternity leave after Bub was born, an apparently minor administrative omission which ended up resulting in a significant loss of job security.]

As much as we might like to think that our psychological intuition redeems our lack of rigorous logic, we may not be right. Christopher’s (often misplaced) confidence in his own rationality can – and should – shake our confidence in the reliability of the faculties we rely on as well.

In last week’s session, we looked at Ian McEwen’s Saturday and I commented that there is a degree of intimidation in most people’s relationship to the protagonist of that novel (a neurosurgeon). Brain surgery has become a euphemism we use for "stuff that’s really, really hard." If something is easy enough to be accessible to ordinary people, we say, "It’s not brain surgery" – or, alternatively, "It’s not rocket science." It’s no coincidence that Christopher wants to be an astronaut – that is, a rocket scientist. Math, like neurosurgery, has that intimidation factor: for those of us who are not neurosurgeons or rocket scientists, math ability tends to generate that kind of awe.

(Snip. Omitted section on the novel’s double ending, which balances readers’ emotional needs against Christopher’s esoteric interests, appealing to our protective instincts in one breath and then intimidating us in the next. Skip to the conclusion.)

Christopher’s mathematical brilliance is not a parlour trick, something he could use to win big money in Vegas – instead it functions as a key element of the relationship between narrator and reader. It keeps us off-balance, and it enables Haddon to use Christopher’s flawed perspective as a standpoint from which to make us more critically aware of our own.


I thought about asking what your biggest regret is. But that's not actually as fun a question as it initially sounds, so I'll broaden out. Do you kick yourself hardest over the things you do, or the things you leave undone?


Beck said...

The things that I regret generally are not the things that superficially should be the things I regret - not getting a degree, for one, has led me somewhat precariously to my current happy life, so I really do NOT regret it. I regret my student loans though, beause they suck.
I am frequently intimidated by YOU, buddy. You are smart.

Luisa Perkins said...

In my experience, mathematicians can be divided into two categories: those that consider 1 to be a prime number, and those who do not.

I kick myself more over the things I overtly get wrong. I turn into Homer Simpson: Doh! With things I haven't done, I guess I feel there is still potential there to make it happen at some point.

Andrea said...

Good question. That one might turn into a post--I've been thinking about it lately. For obvious reasons.

What I do and wish I hadn't, or what I don't do and wish I had--I'm with you, I think. It's what I have the opportunity to do and leave undone, that kills me.

cinnamon gurl said...

In general, I regret inaction over stupid actions, and use that as motivation to act sometimes. But I can't think of any actual regrets I have... I think I can be quite philosophical about regret, and try to use it to learn from, then shed its negativity. I'm big into self-acceptance... of course I do say Doh! a lot but regret for me is reserved for bigger stuff.

Karen said...

When I read detective fiction, I am always surprised that "what didn't happen" is the important clue, but in my own life "what didn't happen" is much more noticeable and those are the things I regret the most, the chances I didn't take, the things I didn't manage to pull off because they didn't seem worth the effort or sacrifice at the time. It's hard to look back and know I was wrong. My older, wiser self knows better, but there's nothing to be done about it now.

Karen said...

Also, maybe, for me when I make a mistake there are often ways to correct, mitigate, or make right even if not completely - but moments that passed by with chances lost, well, that's the end of the story, the lack of redemptive ending bugs the hell out of me and the words "it's all for the best" are not easily dragged out of me.

Gwen said...

To give an uncharacteristically short answer: I think the things I didn't do are the ones I have regrets about. It does seem easier to fix a mistake. But you don't often get re-do's on lost opportunities.

Robbin said...

Undone. Absolutely.

I regret amazingly few decisions in my life - in fact, a sum total of one.

But I almost always regret the things I did not do. But - that may be the quality of the unknown. If we could magically run the permutations in our head at each of our past decision points, it is entirely possibly that we would regret less the road not taken.

Susanne said...

I have the most regret for things I did. I have this feeling that I'll always get around to do the things I haven't yet in the future (of course I'll live to an astounding age in perfect mental and physical health).

No, no regretting of missed opportunities. Which is slightly odd because I have more than my fair share of missed opportunities especially professionally.

Bon said...

i think i regret the things that i feel embarrassment or shame about...the things i do that have a longterm impact on how i am perceived, even by myself. given my perfectionism, that's often i-dotting and t-crossing stuff that i fail to get right, and which then creates a perceived failed opportunity - luckily, not career-impacting so far, though i live in fear of the kind of situation you describe after Bub was born, but simply "damn, i could have gotten a decent tax refund if i'd only known about x or y". or whatever. or simply "i could have spent so much less time and heartache trying to sort out x problem if i'd only known y."

so not knowing about the probability of the doors/goats situation would lead me to much bitter self-recrimination about my ignorance, and thus my goat. :)

gspontak said...

Wow. Quite the question. I would say my biggest regrets are the opportunities I failed to follow through with. The ones I willingly let pass, I had a reason at the time and I can rationalize that just as easily as the poorly-resulting action. It's the ones that I now see I should have put more effort into that I wonder "what if?" And have spent years since wondering whether you really can't go back and do things over again. (Hmm, maybe that thought alone should tell me to just let it go.)

On a completely different note, I'm curious about the Monty Hall problem. I get that the two scenarios (3 choices vs. 2) are not unrelated, since Monty will always select a non-winning door to reveal, but I can't see how that makes the odds of the remaining choices any different from each other.

Suz said...

You ARE smart.

One of the things that I've learned, with adulthood, is to mistrust my intution in certain areas. I've learned that following it when dealing with certain types of people can just lead to disaster, so I try to be more logical and step away from myself.

I think the things I regret the most are usually the foolish mistakes that I've made, rather than the things that I fail to do.

niobe said...

I have a great deal of trouble distinguishing actions from omissions. And I regret pretty much everything.

Jenifer said...

Undone all the way. In my mind if you have tried and failed at least there are the million reasons why you at least tried. What is left undone is untainted and whether it would have worked out or not is irrelevant since you will never know. That makes me kick myself.

When you talked about brain surgery and rocket science being equated with all things hard it reminded me of something I recently read. How it is fine for someone to, "not get math" or not be a "numbers person"; there is little stigma associated with these and if someone can't work out the tip in a restaurant it is laughed at. Reading or writing however, never get the same kind of leniency.

Loved these posts, you lead an interesting life!

Becky said...

Today's new thing, from the Prime Number entry on Wikipedia (because I'm a math nerd, and I didn't know the answer): "Until the 19th century most mathematicians considered the number 1 a prime, and there is still a large body of mathematical work that is valid despite labelling 1 a prime, such as the work of Stern and Zeisel. Henri Lebesgue is said to be the last professional mathematician to call 1 prime. The change in label occurred so that it can be said 'each number has a unique factorization into primes."


And my answer is probably "undone"... but I really don't know. I don't have any real regrets. I think there are a few things that I've done that I ought to regret, but I'm like you - I rationalize that I made the best decision I could have made with the information I had. I'm also not a fan of beating myself up, so I stubbornly don't let myself have regrets.

Mimi said...

The things I leave undone. For sure. Because I am inherently and helplessly lazy. Stuff whooshes by me that I might easily have grasped: books to read, friends to make, ideas to explore. I could do so much more. But I don't. I rarely fail at things I do; I fail myself much more frequently by neglecting to attempt things I ought to.

nomotherearth said...

I always regret the things that I DON'T do. The things that I DO do are generally well thought out - even if they turn out to be a mistake.

Jennifer (ponderosa) said...

I don't think about regret much, so I guess I don't have any active ones -- nothing weighs on my mind. But if I pause for awhile to ponder, what comes to mind are ways I mistreated people. I regret the way I behaved w/ my most significant boyfriend (not counting the one I married); I regret the way I behaved with a guy in college who could have become significant.

So -- I regret things done, not things undone.

Lawyer Mama said...

The things I leave undone. Like you said, I'm usually able to rationalize the things that I've done, if only out of some sort of self-preservation. But, the thing I regret most is something I did. Go figure.

And now I must go off and find out exactly *why* it is that the car is twice as likely to be behind door #2.

Mad Hatter said...

The things I leave undone. I regret I never took up the Au Pair position in Frnace when I graduated high school. I have no regret that I left my PhD unfinished.

Mostly though, I don't feel too much regret in life. Life is what life is and all you can really do is move forward.

I love your reading of the book in terms of Christopher's relationship to the reader. It humbles the role of the reader in a way that I am not accustomed to. I spent too much time in the phenomenological camp in my grad school days, elevating the reader beyond all reason. Now I chuckle (with regret?) at my single-mindedness.

It's a funny thing academia. It privleges the single-minded scholar: he/she who can mine the depths of a topic to the point of seeming absent-minded to the outside world. And yet, the best academics are lateral thinkers. Complex lateral thinkers but lateral thinkers nonetheless.

slouching mom said...

I regret the things undone. And sadly there are a lot of them.

bubandpie said...

gspontak - Hee hee. That's what makes it such a great problem - it just doesn't seem like the solution can be right. If you Google "Monty Hall problem," you'll find a great Wikipedia article with the full explanation (including graphs). The short version is that, basically, we're comparing the probability that the car is behind the door I picked vs. the probability that it is behind EITHER of the other two doors.

Even after I looked at the graph and understood the explanation, it still SEEMED wrong - but now that I've had a day or two to think about it my mind has switched tracks and now it seems obvious.

Diana said...

B&P and/or lawyer mama: please say more about the 2x greater likelihood of the prize being veiled behind door #2. I'm intrigued, but want to be spoon fed on this one (did any of you B&P readers get through that part of the post with an understanding of the reasoning behind the solution's demonstrable correctness? If yes, nicely done! If no, I'm right there with ya.)

Hands down, without a doubt, no question--I deeply regret missed opportunity of a personal nature. In two cases, I neglected to maintain contact with friends, both of whom affected the course of my life in profoundly meaningful ways. These people are now deceased. I learned of their respective deaths after the fact (in one case, days later; the other, weeks later).

I don't know that my example has anything to do with the relationship between logic and intuition or your exposition on the topic; but there's a fairly evident link between my inaction (the thing undone) and my reaction (regret).

kittenpie said...

Definitely undone. Daniel Gilbert is right again.

Diana said...

(Just have to say that the post I deposited a few moments ago is my first ever on any blog anywhere. This seemed a lovely place to start. Thanks for the provocative, lovely forum. Me likey.)

gspontak said...

bubandpie, yes, I got impatient and looked up that Wiki article. And the explanation that works best for me is that it really doesn't matter whether the host opens a door, after your first choice the possibilities are set. The other logical fallacy I kept trying to follow was that it boiled down to choosing between a goat and a car - which is not the situation at all. Good mind game!

And I've been greatly enjoying your blog, so Thanks!

bubandpie said...

Diana - I didn't actually include the explanation, so no worries if you didn't get it. (I figured the logic geeks would check it out for themselves.) I'll try the explanation again:

I pick door #1. There's a 1/3 chance that the car is behind that door.

Doors #2 and #3 remain. There is a 2/3 chance that the car is behind one of those two doors.

Monty Hall WILL open a door with a goat behind it, so there is a 2/3 chance that the car is behind the door he did NOT open, and still only a 1/3 chance that the car is behind the door I chose originally.

(If you want to see the graph, go to Wikipedia. The graph helps.)

ewe are here said...

A very interesting post. I have to admit, I started the book once but didn't get very far. I just couldn't get into it. But the goat vs car doors discussion... that is an interesting discussion about probabilities. Fascinating, really.

And my husband I suspect is like yours - I believe his response would be almost identical to the situation.

Diana said...

Aha! The Monty Hall Problem at Wikipedia. Most excellent. I read it before seeing your most recent note, B&P. Door #4 (the entry to my underused statistics brain) has been blown off its rusty hinges! btw, I love the Host Behaviors discussion in the Variants section. All in all, a fun diversion this afternoon.

Terri B. said...

I don't spend much time in regret mode since I find it terribly unproductive. But ... I do regret the things that I have the opportunity to do and then don't do out of fear of failure.

mcewen said...

I recall being particularly frustrated with the part of the book, because it was so patently apt.
Best wishes

Her Bad Mother said...

Things left undone, FOR SURE. Things done - they're done, and they've led me to where I am. (I suppose that the things left undone could be said to have played as much a role in getting me to where I am - had I gone to AADA in New York at 19, I wouldn't have follwed the path that led me here, but still. Road not taken and all that.)

Catherine said...

Great summary of how you respond to Christopher - exactly as I felt. And I've been scratching my head over that Monty Hall problem ever since. I feel like I want to poke the kid next to me and whisper "I don't get it" instead of actually raising my hand and asking the teacher. I mean, I GET it. But, I don't get it...

Sandra said...

I am enjoying getting caugth up on all this.

For me .. it is DEFINITELY things left undone. Without question. I have a list of top five burnt into my brain.

Julie Pippert said...

I adore that book. I'm sorry I missed until so late your two posts about it. It's been a while since I read it, and I find myself thinking about it sometimes still. I want to go back to it, but alas it is still packed up, waiting for us to not just finish but actually start the bedroom renovation.

Thanks for throwing in the logic problem. :)

What do I regret?

I regret the empathic failures-emotionally stunted times.

I know, you'd think there was an F in my INTJ wouldn't you---but that's the point, yes? There isn't an F.

And I regret that because well, it means sometimes I leave a trail of Not Fans of Julie behind me.

I don't regret things I have done or things I have not done.

I regret the times I missed what was right in front of me: a person I cared about or should have cared about and who I hurt.

c4cara said...

The things I leave undone. Absolutely. As you said, if I have a go and it turns out differently than I anticipated, such is life and often there are gifts in the alternate ending that I'd never have got to otherwise. (First marriage = clearer idea of who I was and realising there were certain things about me I couldn't change).
Things I give up on, or never start - those are my regrets. I have a stern dose of 'bewareness' in my psyche, so I am often fearful when new oppotunities arise. Many times I have backed away and/or given in at the first hint of resistance.
My experience has been that the more I have a go at - despite my nervousness - the more I get back.

TrudyJ said...

I definitely experience more regret over things left undone, than things done.

I also would like to know if the Monty Hall problem makes any accommodation for people who would actually rather have a goat, than a car. Surely there must be some tree-hugging, back-to-the-land environmentalist who has a two out of three chance of getting what they want in this game?

atypical said...

I tend to regret more the things I have done than not done. I think that might be for a combination of reasons. First, I tend to give myself a little latitude for inaction when there are extenuating circumstances (or when I realize that hindsight is 20/20). Also, sometimes my actions have resulted in something NOT happening; therefore, the action is really an inaction.

My math geeky side says that the Monty Hall problem is using improper reasoning. In probability problems, if there are three possible choices, and you eliminate one, there are now only two possible choices. So, while your odds of having a car may have started as 1/3, once one of the choices is eliminated, the odds of having a goat are 1/2, and the odds of having a car are 1/2 (example: you put 6 buttons in a bag, two are red, four are black. Your chances of pulling out a red one are 2/6. If you do not return that red one to the bag after pulling it out, your chances of pulling out a red one on the next draw are 1/5).

It's kinda like the algebra problem my son keeps showing me that seems to prove that 1=2.

Anyway, I adored that book, and I would have loved to have been there for the talk.


Jaelithe said...

I kick myself about every mistake, all the time, whether it was the mistake I made by sticking to my guns or the mistake I made by changing my mind.

But of course, I suppose you can spend a lot more time imagining the missed opportunities, since the possibilities of what might have happened are nigh infinite in that case.

bubandpie said...

Atypical - Thanks for prompting a stimulating breakfast-table conversation with my math-geek husband! The crux of the matter appears to be the host's knowledge: if he is randomly selecting a door that just happens to be a goat, then it's a 50/50 chance, but if he is required to reveal a goat once you've made your choice, you're better off to switch. I think. Maybe.

PunditMom said...

Wonderful discussion. Answer to the question -- definitely things undone.

I constantly beat myself up about the cleaning and organizing that doesn't get done, the book project I have hard time getting started, the dinner parties I dream of, but never organize. But even tho' there are certain things I might have done differently in retrospect, I don't regret having sone them (except my first marriage, tho' i, like you, try to believe that if my life had followed a different path, I would not have found Mr. PunditMom and we would not be the parents of PunditGirl).

theflyingmum said...

the things left undone, because: you can go back and make apologies, rationalize, etc. the mistakes you make, but you can't fix what didn't happen. does that make sense? like, if i hadn't had ben - by the time my siblings were having grandkids - it would be too late for me to pony up and start my own family - and then i'd have this lingering regret.

Lucy said...

Fascinating discussion. I lurk her occasionally and really enjoy your writing (I can't remember if I've commented before).

I have no opinion about the Monty Hall thing. Way over my head.

As to regrets, I agree with the commentor who said she regrets everything! I'm that way, too! I wish I had the confidence of some of the other posters. I have things that nag at me from years ago, both opportunity-wise and relationship-wise. I have regrets every single day, both about things I did and things I didn't do. I especially regret the things I did that I thought through really well, because it shows that my thinking was flawed somehow. Like buying our current house. Hubs and I kick ourselves all the time, but we can't afford to move. We got too good a deal on the house and it would take too much money to get it ready to sell. We can't really afford to live here, either. We're stuck.

I regret that I didn't finish college. I regret that I didn't do a semester abroad. But I really regret things that have happened in relationships and people that I've hurt by being dense and people I've lost touch with because I'm lazy and lose track of time.

Very thought provoking post. Thanks!

Gunfighter said...

I almost never kick myself about anything.

Having that much confidence can really be a good thing.... or really, REALLLLY bad.

Gunfighter said...

Oh... the only thing I really regret in life was my first marriage.

atypical said...

In my opinion, it wouldn't matter whether the host picked randomly or not. Either way, one variable is removed. I am imagining a theoretical mathematician would propose a disagreeing theory (which is pretty much what happened in the book - LOL).

Of course, we probably can't take my word for fact because, other than homeschooling the kids, I haven't had much exposure to math for a FEW years now.