Reader survey: do you know your credit card number by heart?

I don’t know mine.  I have to look at my card whenever I purchase something online.  Why?  It seems to me that I type or say my credit card number as much as I type or say my phone number, and I would consider it totally weird not to have my own phone number committed to memory.

On the other hand, my youth was spent in an environment where you had to recall your own phone number all the time, because it wasn’t programmed into your phone and you had to dial it every time you wanted to use it.  So the followup question for those readers who grew up in the cellphone era is:  do you know your own phone number by heart?

 

Reader survey: have you ever clicked on a Facebook ad?

Apparently Facebook is said by some to be valued at $75 billion.  Facebook’s revenue, just under $2b last year, derives mostly from online ads.

I visit Facebook most days and was only dimly aware that it had ads.  I just looked, and yes, they’re there:  not on the main newsfeed page, but on my profile page.  I’m trying to get my head around the fact that buying Facebook ad space is a good investment.

Question:  have you ever clicked on a Facebook ad?  Have you ever clicked through and then purchased?

Secondary (or maybe really prior) question:  Does it matter to advertisers whether Facebook users click?  Or is the point just to put the name of the product in the corner of people’s eyes, for brand awareness?

Anticipated objections:  1.  Yes, I know the readers of this blog are not a good sample of FB users.  2.  No, I don’t think “businesses wouldn’t buy ads if they weren’t effective” is obviously correct, though it does carry some force.

Update:  Reader Rod Carvalho points out that the same question applies to Google — so feel free to answer that too!

Reader survey: how seriously do you take expected utility?

Slate reposted an old piece of mine about the lottery, on the occasion of tonight’s big Mega Millions drawing.  This prompted an interesting question on Math Overflow:

I have often seen discussions of what actions to take in the context of rare events in terms of expected value. For example, if a lottery has a 1 in 100 million chance of winning, and delivers a positive expected profit, then one “should” buy that lottery ticket. Or, in a an asteroid has a 1 in 1 billion chance of hitting the Earth and thereby extinguishing all human life, then one “should” take the trouble to destroy that asteroid.

This type of reasoning troubles me.

Typically, the justification for considering expected value is based on the Law of Large Numbers, namely, if one repeatedly experiences events of this type, then with high probability the average profit will be close to the expected profit. Hence expected profit would be a good criterion for decisions about common events. However, for rare events, this type of reasoning is not valid. For example, the number of lottery tickets I will buy in my lifetime is far below the asymptotic regime of the law of large numbers.

Is there any justification for using expected value alone as a criterion in these types of rare events?

This, to me, is a hard question.  Should one always, as the rationality gang at Less Wrong likes to say, “shut up and multiply?” Or does multiplying very small probabilities by very large values inevitably yield confused and arbitrary results?

Update:  Cosma Shalizi’s take on lotteries and utilities, winningly skeptical as usual.

Reader survey: how many non-drivers in Madison?

Without looking it up:  what percent of households in Madison don’t own a car?  What percent of commuters don’t drive to work?  What percent bike?

My guesses were pretty far off.

The answers, along with similar data for other cities (drawn from the 2000 census) are here.

In which John Tierney continues to annoy me: featuring reader survey!

John Tierney has annoyed me before on the subject of women in science.  And now he’s back, this time recapping the conventional wisdom that math departments like mine are 90% male because of the inborn boyish math power we men possess.  He styles this as “daring.”  The chutzpah!

Anyway, this time around he presses some perfectly respectable social science into service.  Here’s a fact:  more boys than girls get perfect scores on the math SAT.  And a recent study by Jonathan Wai, et al found that that among students who scored over 700 on the math SAT in 7th grade — just 1/10,000 of their sample — boys outnumbered girls by about 13 to 1 in the 1980s, a figure which dropped to 4:1 by the early 1990s and has stayed roughly constant since.

Now here’s how the standard — oops, sorry, I mean “daring” — argument goes:  mathematicians surely possess a math aptitude among the top 1 in 10,000 of the population.  That segment of the population is mostly men, as proven by science.  Ergo, most mathematicians should be men.

A mistake here, or at least a potential mistake, is thinking of success in mathematics as something driven by a variable called “aptitude”, which can be measured on a scale — as if getting tenured at Harvard were something like getting a 10 million on the math SAT.  Wai et al find that girls make up a substantial majority of extremely high 7th grade scorers in the English and writing sections of the exam.  Should one conclude on aptitudinal grounds women should be a majority among English professors?  It’s easy to mistake your operationalizations for reality, as when Wai et al write:

Giving the SAT-M in the 7th grade allows individual differences in the extreme right tail of the distribution (i.e., the top 1% which includes over one third of the ability range) to be captured adequately

I can think of lots of things they might mean by “one third of the ability range” but none which have any content.

Not that I’m saying it’s meaningless to ace the SAT before getting your driver’s license.  It’s a vanishingly small proportion of people who get a 700 on the math SAT at 13.  But I’d think it would be a very small proportion of mathematicians too!  If 10% of mathematicians were extreme child math prodigies, and those extreme child math prodigies are 80% boys, one hasn’t gone far towards explaining why US math research faculties are overwhelmingly male.

There’s actually an empirical question here which I know nothing about.  So let’s contribute to my know-nothingness by undertaking a brutally unscientific survey.  If you’re a working mathematician — say, a Ph.D. student in good standing or a faculty member at a university — did you score above 700M on the SAT when you were 13 or younger?  Since I think it’s a fairly small proportion of the world that takes the exam that early, let’s ask a more widely applicable question as well:  if you took the SAT as a senior in high school, did you get 800 on the math section?  (If you answer this, you might mention whether you took the exam before or after the 1995 recentering.)

Reader survey: what open question would you ask Dick Gross?

I’m speaking on an “open problems” panel in honor of Dick Gross’s 60th birthday.  I’ve got 10 minutes.  I think I know what I’m going to say, but I was just informed that the panel is to be allowed to run late if audience interest demands it.  So I thought it would be good to stock up a little more material.  And it occurred to me this might be a good opportunity to blogsource!  So, readers:  if you were going to promote an open problem in front of Dick Gross and his wellwishers, what would it be?

Reader survey: what are the unwritten laws of hiring in math?

My post about a recent hiring controversy has generated the longest-ever comment thread on this blog, beating out the “Do you wear a watch?” survey.  One thing I learned from the comment thread is that people have quite divergent ideas about what the implicit ethical rules of hiring actually are!  There’s a lot to be said for tacit, organic systems of moral agreements as against formal laws.  But for such a thing to work requires some kind of general consensus.  Do we have it?

I thought it would be interesting to address this question directly.  I’ll start with a few things I think of as rules, both for candidates and for departments.

Candidates:

• If you accept a job, you need to show up there the following fall unless you are explicitly released from your commitment.  This commitment lasts one academic year
• Don’t apply for a job that you wouldn’t accept if it were the only job you got.

Departments:

• You can’t ask a candidate how likely they would be to accept an offer before you make the offer.  I think it’s OK, though slightly awkward, to ask after the offer is made.
• You can’t ask a candidate if they’re married.  (This is actually a written law, at least in the US — but it is widely violated.)
• If you give a candidate a deadline, you are not allowed to subsequently move the deadline earlier.  (I know of at least one such case this year!)

Are these actually rules?  What are the other rules?  Go to.

Reader survey: do you double-space after a period?

I do, just like they taught me in 10th grade typing class.  But a quick sample of my incoming e-mail suggests I’m the only one, apart from Mrs. Q and my mom.  Mrs. Q informs me the APA styleguide demands one space after a period: she uses the double space in e-mail but not in papers.  LaTeX splits the difference, using an intersentence space about half again as large as the space between words.  The iPhone automatically drops in a period when you double-space after a word, which seems designed to suit habitual double-spacers like me; on the other hand, the text it actually produces has just one post-period space.

So I’m confused — has this tradition really fallen out of use and no one told me?  Or was it never a tradition at all, outside my high-school typing class?

Reader survey: do you follow the arXiv?

For about a year now I’ve been following the math.AG and math.NT postings to the arXiv through Google Reader.  The good side of this is that you find out very quickly about papers in areas of special interest to you.  The downside, I guess, is that it can be sort of distracting; you sit down to work, you flip through the latest listings, maybe there’s one paper that’s interesting enough to read through the introduction and think about a bit, and before you know it the morning’s gone.

On balance, I like following the arXiv and intend to keep doing it.  But I have no sense of whether this is a standard practice, the way it used to be a standard practice (and maybe still is!) to go down to the library and flip through the latest issues of your favorite journals.

So:  do you follow the arXiv?  If so, what do you get out of it?

Reader survey: which of your beliefs will your descendants vehemently reject?

The other day the New York Times ran a selection of 1968 poll data on the op/ed page.  In April of that year, 31% of Americans agreed that “Martin Luther King, Jr. brought his assassination on himself.”

This makes me wonder which beliefs, currently held by 30% or more of the U.S. population, will be universally considered absurd or even despicable by Americans of 2048.  So, readers — nominate such beliefs in the comments.  But to make it interesting, the belief has to be one which you presently hold.

Here’s mine:  “People should strive to keep the details of their personal lives from becoming publicly available.”

(For more antique polling nuggets, see my previous post on Public Opinion 1935-1946.)