RS#36: Why should we care about teaching the humanities?

Episode #36 of the Rationally Speaking podcast is out, and this one’s a lively debate between me and Massimo about the value of humanities departments in universities. While I don’t deny the huge amount of enjoyment we get from arts and literature, I express skepticism about many of the typical justifications for requiring humanities courses. Those justifications strike me as either (1) overly vague and subjective (“the humanities make you a complete person”) or (2) making contrived claims about the practical benefits of studying the arts (“the humanities build critical thinking skills”) to which I usually want to reply, “If that’s your goal, there are much more direct ways to pursue it than studying literature.”

Rationally Speaking #36: Why should we care about teaching the humanities?

“Stand back everyone, I’ve been trained for situations like this…”

Last night my friends and I ended up talking about real-life situations in which our math skills serendipitously came in handy. And I got to reminisce about my one exciting “Thank goodness I paid attention in math class!” moment:

I was a high school kid, working as a summer intern at the Corcoran Gallery of Art (this was back in my “I want to be a museum curator” phase). In the sales office one Friday afternoon, I overheard a conversation between my two bosses:

Boss 1: “The new ticket collector didn’t keep track of child and adult ticket sales separately this week. All she sent us is the total number of tickets and total revenue. 953 tickets, $9,050 revenue. But the accountant wants us to record child and adult sales separately.”

Boss 2: “Sigh. All right, I guess we’ll have to go get the pile of ticket stubs and sort them all. What a pain in the ass…”

Me (gasps, runs over): “Wait! We don’t need to sort ticket stubs! We already have all the information we need to solve this!”

Boss 1: “We do? How?”

Me: “We need to set up a system of equations! Okay, let’s call A the number of adult tickets and C the number of child tickets. How much does each one cost?”

Boss 1: “Adult tickets are $10, child tickets are $6.”

Me: “Okay! So we know that the total number of tickets is 953 so we can write A + C = 953. And we know the total revenue is $9050 so we can write $10A + $6C = $9050. So we have two equations,  two variables:

A + C = 953
10A + 6C = 9050

And now we just solve:
10 (953 – C) + 6C = 9050
4C = 480
C = 120. Therefore A = 953 – 120 = 833.
So that’s the answer — we sold 120 child tickets, and 833 adult tickets.”

My bosses were delighted with the “cool trick” I had used. And I like to think my 7th-grade math teacher would have been tickled pink if she’d seen that go down. How often do you get to actually apply your word-problem skills in real life?

Nothing quite that math-textbook perfect has happened since. Though I keep hoping that someday I’ll overhear someone saying, “My friend and I wanted to meet up for lunch tomorrow, so we agreed to each leave our apartments at noon and walk towards each other’s place until we met. He walks at a rate of 4 mph and I walk at a rate of 3 mph. If only there was some way to figure out where and when we would meet so that I could make a lunch reservation…”

A. J. Ayer to the rescue!

A. J. Ayer is known for writing "Language, Truth, and Logic." Lesser known is his sequel, "Language, Truth, and Being a Friggin' Badass."

Couldn’t resist this anecdote from the biography of one of my favorite philosophers, logical positivist A. J. Ayer:

“Ayer was now standing near the entrance to the great white living-room of Sanchez’s West 57th Street apartment, chatting to a group of young models and designers, when a woman rushed in saying that a friend was being assaulted in a bedroom. Ayer went to investigate and found Mike Tyson forcing himself on a young south London model called Naomi Campbell, then just beginning her career. Ayer warned Tyson to desist. Tyson: ‘Do you know who the fuck I am? I’m the heavyweight champion of the world.’ Ayer stood his ground: ‘And I am the former Wykeham Professor of Logic. We are both pre-eminent in our field; I suggest that we talk about this like rational men.’ Ayer and Tyson began to talk. Naomi Campbell slipped out.”

A. J. Ayer: A Life, by Ben Rogers

An economist’s tips for dining and cooking

Just finished Tyler Cowen’s latest book, Discover Your Inner Economist, which is full of tips for applying the principles of economic reasoning to your everyday life. One of my favorite things about Tyler is that he’s even more obsessed with food than I am — check out this Washington Post article about his twin passions for food + economics. (And if you live in the DC metropolitan area, you should read his detailed and insightful “Ethnic Dining Guide” to the area.)

Tyler also shares my passion for maximizing utility in clever ways. So my favorite part of the book, unsurprisingly, was his section on how to get as much enjoyment as possible from dining out and cooking. Below, I’ve culled a few of Tyler’s best tips:

Tip #1: Pay attention to relative rents. Want to eat out in your city? Your best bet is to look for restaurants in low-rent neighborhoods that are near high-rent neighborhoods. Their costs are lower, but they’re close enough to where foodies live that they’ll be catering to foodie standards. There are better restaurants on 9th avenue (on the West side of Manhattan) or 1st avenue (on the East side of Manhattan) than there are on 5th avenue.

Even turning the corner can make a difference. In Manhattan, the avenues are generally busier than the cross-streets, and have correspondingly higher rents, so if you look for restaurants on cross-streets you’re likely to find a better deal. You’re also likely to find better food. Restaurants in high-traffic areas can thrive just by attracting a lot of first-time customers who happened to be passing by, so they have less of a need to make their food good enough to attract repeat customers.

Tip #2: Avoid “ingredient-intensive” dishes at ethnic restaurants. Eating at an ethnic restaurant in the US? Avoid simple dishes that succeed or fail on the quality of their raw ingredients, like a steak at a Peruvian restaurant. Because raw ingredients are mass-produced in the US, they’re generally inferior to their counterparts in the home country, so those dishes are at a comparative disadvantage when you order them in the US. Look instead for dishes that rely on a skillful preparation with lots of different ingredients and complex sauces and flavorings. (Or as Tyler puts it: look for dishes that are “composition-intensive,” rather than “ingredient-intensive.”)

Tip #3: Don’t trust pretty dishes. This is one that I came up with on my own, and I was both gratified and kind of bummed to read it in Cowen’s book: When you’re dining at a nice restaurant, go for the dish that sounds the least appetizing. Why? Because dishes that sound delicious can retain their place on the menu just by attracting a lot of first-time orderers. Even if most people who order that dish are disappointed with its taste, there’ll always be a steady stream of new people who want to try it because it sounds good. Same for dishes that sound familiar (think “roast chicken”). Because there are a lot of people who aren’t adventurous eaters, those dishes will always have an audience even if they’re not very tasty. If you’re an adventurous eater whose main priority is tastiness, you should look instead for the dishes that have to be tasty in order to stick around.

(My original formulation of this principle was with regards to desserts: I don’t trust pretty desserts. Those adorable petit-fours in the display case, all decorated with pastel-colored flowers? They’re likely to be dry and bland. But they stick around because so many people order them for the first time thinking “That looks so good!” Meanwhile, the homely pan of lumpy brown bread pudding or cobbler isn’t going to catch as many people’s eyes, so if it’s still on the menu, it must taste divine.

Tip #4: High inequality is the foodie’s friend. If you’re planning a “food tourism” trip, aim for countries with high inequality. It’s sad, but true: to support an amazing cuisine, it helps to have a wealthy upperclass willing to pay for it, and a poor underclass willing to work for relatively low wages preparing and serving the food. Cowen recommends both Mexico and Haiti as exemplars of haute cuisine in the Western hemisphere. By contrast, France has been gradually slipping from its spot at the top of the fine dining hierarchy, because the high wages and strict labor laws there have pushed up the costs of running a restaurant.

Tip #5: Read cookbooks with a grain of salt.  Every home cook has some rough, implicit exchange rate between the cost she’s willing to pay (in terms of money, time, calories, etc.) for a given level of deliciousness of the dish. But the recipes in your cookbook might not be calibrated to your preferred exchange rate. In fact, there are a number of ways in which the implicit exchange rate assumed by your cookbook is likely to systematically diverge from your own.

For example, older cookbooks were written during an era when the value of the cook’s time was low. Meals were prepared either by professional cooks or by wives, both of whom were pretty much expected to be cooking all day long. So if there was a modification to a recipe that would cost you an additional 2 hours of time and improve the dish only slightly, an old recipe might well recommend that you do it. By contrast, you probably value your time a lot more highly than the cooks of previous generations, so that tradeoff might not be worth it to you.

Relatedly, cookbooks published by famous chefs are likely to recommend high levels of elaborateness that pay off only in small improvements in taste. That’s because the goal of a famous chef in publishing a cookbook isn’t solely to help you make delicious food, it’s to bolster that chef’s reputation as a virtuoso. So he has an incentive to recommend recipes that are more time-consuming, difficult, and involve more ingredients than absolutely necessary for maximizing the deliciousness of the final dish. In other words, don’t be afraid to take shortcuts — just because some step is recommended in a recipe, that doesn’t mean it’s a “good deal,” in terms of the ultimate taste of the meal.

Does it make sense to play the lottery?

A very smart friend of mine told me yesterday that he buys a lottery ticket every week. I’ve encountered other smart people who do the same, and it always confused me. If you’re aware (as these people all are) that the odds are stacked against you, then why do you play?

I raised this question on Facebook recently and got some insightful replies. One economist pointed out that money is different from utility (i.e., happiness, or well-being), and that it’s perfectly legitimate to get disproportionately more utility out of a jackpot win than you lose from buying a ticket.

So for example, let’s say a ticket costs $1 and gives you a 1 in 10 million chance of winning $8 million. Then the expected monetary value of the ticket equals $8 million/ 10 million – $1 = negative $0.20. But what if you get 15 million units of utility (utils) from $8 million, and you only sacrifice one util from losing $1? In that case, the expected utility value of the ticket equals 15 million utils / 10 million – 1 util = 0.5 utils. Which means buying the ticket is a smart move, because it’ll increase your utility.

I’m sympathetic to that argument in theory — it’s true that we shouldn’t assume that there’s a one-to-one relationship between utility and money, and that someone could hypothetically have a utility curve that makes it a good deal for them to play the lottery. But in practice, the relationship between money and utility tends to be disproportionate in the opposite direction from the example above, in that the more dollars you have, the less utility you get out of each additional dollar. So the $8 million you would gain if you won the lottery will probably give you less than 8 million times as much utility as the $1 that you’re considering spending on the ticket. Which would make the ticket a bad purchase even in terms of expected utility, not just in terms of expected money.

Setting that theoretical argument aside, the most common actual response I get from smart people who play the lottery is that they’re buying a fantasy aid. Purchasing the ticket allows them to daydream about what it would be like to win $8 million, and the experience of daydreaming itself gives them enough utility to make up for the expected monetary loss. “Why can’t you just daydream without paying the $1?” I always ask. “Because it’s not as satisfying if I know that I have no chance of winning,” they reply.  Essentially, they don’t care how small their chance of winning is, they just need to know that they have some non-zero chance at the jackpot in order to be able to daydream about it.

I used to accept that argument. But in talking with my friend yesterday, it occurred to me that it’s not true that your chances of winning a fortune are zero without a lottery ticket. For example, you could suddenly discover that you have a long-lost wealthy aunt who died and bequeathed her mansion to you. Or you could find a diamond ring in the gutter. Or, for that matter, you could find a winning lottery ticket in the gutter. The probability of any of these events happening isn’t very high, of course, but it is non-zero.

So you simply can’t say that the lottery ticket is worth the money because it increases your chances of becoming rich from zero to non-zero. All it’s really doing is increasing your chances of becoming rich from extremely tiny to very tiny. And if all you need to enable your Scrooge McDuck daydreams is the knowledge that they have a non-zero chance of coming true, then you can keep those daydreams and your ticket money too.

How to argue on the internet

At least a dozen people have sent this XKCD cartoon to me over the years.

It’s plenty hard enough to get someone to listen to your arguments in a debate, given how attached people are naturally to their own ideas and ways of thinking. But it becomes even harder when you trigger someone’s emotional side, by making them feel like you’re attacking them and putting them automatically into “defend myself” mode (or worse, “lash out” mode), rather than “listen reasonably” mode.

Unfortunately, online debates are full of emotional tripwires, partly because tone isn’t always easy to detect in the written word, and even comments intended neutrally can come off as snide or snippy… and also because not having to say something to someone’s face seems to bring out the immature child inside grown adults.

But on the plus side, debating online at least has the benefit that you can take the time to think about your wording before you comment or email someone. Below, I walk you through my process of revising my wording to reduce the risk of making someone angry and defensive, and increase my chances that they’ll genuinely consider what I have to say.

DRAFT 1 (My first impulse is to say): “You idiot, you’re ignoring…”

Duh. Get rid of the insult.

DRAFT 2: “You’re ignoring…”

I should make it clear I’m attacking an idea, not a person.

DRAFT 3: “Your argument is ignoring…”

This can still be depersonalized. By using the word “your,” I’m encouraging the person to identify the argument with himself, which can still trigger a defensive reaction when I attack the argument. That’s the exact opposite of what I want to do.

DRAFT 4: “That argument is ignoring…”

Almost perfect. The only remaining room for improvement is the word “ignoring,” which implies an intentional disregard, and sounds like an accusation. Better to use something neutral instead:

DRAFT 5: “That argument isn’t taking into account…”

Done.  Of course, chances are I still won’t persuade them, but at least I’ve given myself the best chance possible… and done my part to help keep the Internet civilized. Or at least a tiny bit less savage! 

Oh Sidney, you wag

A linguistics professor lecturing at Oxford explained that although there are many languages in which a double negative implies a positive, there is no language in which a double positive implies a negative.

He was interrupted by legendary philosopher Sidney Morgenbesser, who piped up dismissively from the audience, “Yeah, yeah.”

Thinking in greyscale

Have you ever converted an image from greyscale into black and white? Basically, your graphics program rounds all of the lighter shades of grey down to “white,” and all of the darker shades of grey up to “black.” The result is a visual mess – same rough shape as the original, but unrecognizable.

Something similar happens to our mental picture of the world whenever we talk about how we “believe” or “don’t believe” an idea. Belief isn’t binary. Or at least, it shouldn’t be. In reality, while we can be more confident in the truth of some claims than others, we can’t be absolutely certain of anything. So it’s more accurate to talk about how much we believe a claim, rather than whether or not we believe it. For example, I’m at least 99% sure that the moon landing was real. My confidence that mice have the capacity to suffer is high, but not quite as high. Maybe 85%. Ask me about a less-developed animal, like a shrimp, and my confidence would fall to near-uncertainty, around 60%.

Obviously there’s no rigorous, precise way to assign a number to how confident you are about something. But it’s still valuable to get in the habit, at least, of qualifying your statements of belief with words like “probably,” or “somewhat,” or “very.” It just helps keep you thinking in greyscale, and reminds you that different amounts of evidence should yield different degrees of belief. Why lose all that resolution unnecessarily by switching to black and white?

More importantly, the reason you shouldn’t ever have 0% or 100% confidence in any empirical claim is because that implies that there is no conceivable evidence that could ever make you change your mind. You can prove this formally with Bayes’ theorem, which is a simple rule of probability that also serves as a way of describing how an ideal reasoner would update his belief in some hypothesis “H” after encountering some evidence “E.” Bayes’ theorem can be written like this:

… in other words, it’s a rule for how to take your prior probability of a hypothesis, P[H], and update it based on new evidence [E] to get the probability of H given that evidence: P[H | E].

So what happens if you think there’s zero chance of some hypothesis H being true? Well, just plug in zero for “P[H],” all the way on the right, and you’ll realize that the entire equation becomes zero (because zero times anything is zero). So you don’t have to know any of the other terms to conclude that P[H | E] = 0. That means that if you start out with zero belief in a hypothesis, you’ll always have zero belief in that hypothesis no matter what evidence comes your way.

And what if you start out convinced, beyond a shadow of a doubt, that some hypothesis is true? That’s akin to saying that P[H] = 1. That also implies you must put zero probability on all the other possible hypotheses. So plug in 1 for P[H] and 0 for P[not H] in the equation above. With just a bit of arithmetic you’ll find that P[H | E] = 1. Which means that no matter what evidence you come across, if your belief in a hypothesis is 100% before seeing some evidence (that is, P[H] = 1) then your belief in that hypothesis will still be 100% after seeing that evidence (that is, P[H | E] = 1).

As much as I’m in favor of thinking in greyscale, however, I will admit that it can be really difficult to figure out how to feel when you haven’t committed yourself wholeheartedly to one way of viewing the world. For example, if you hear that someone has been accused of rape, your estimation of the likelihood of his guilt should be somewhere between 0 and 100%, depending on the circumstances. But we want, instinctively, to know how we should feel about the suspect. And the two possible states of the world (he’s guilty/he’s innocent) have such radically different emotional attitudes associated with them (“That monster!”/”That poor man!”). So how do you translate your estimated probability of his guilt into an emotional reaction? How should you feel about him if you’re, say, 80% confident he’s guilty and 20% confident he’s innocent? Somehow, finding a weighted average of outrage and empathy doesn’t seem like the right response — and even if it were, I have no idea what that would feel like.

RS #35: What is philosophy of science good for?

In episode #35 of the Rationally Speaking podcast, Massimo and I explore philosophy of science: What is it about, and should it matter to scientists? We also discuss some of the most important questions in philosophy of science now, and some historical debates between leading philosophers of science, like Thomas Kuhn and Karl Popper, over how science should or does work.

So is philosophy of science, as Richard Feynman famously quipped, “as useful to scientists as ornithology is to birds?” Or was philosopher Daniel Dennett closer to the truth when he said, “There is no such thing as philosophy-free science, only science whose philosophical baggage is taken on-board unexamined?”

http://www.rationallyspeakingpodcast.org/show/rs35-what-is-philosophy-of-science-good-for.html

Does “socially responsible” investing do any good?

In this video, I’m discussing “socially responsible” investing with the mathematician from http://askamathematician.com. If you limit your investments to companies that uphold ethical principles you care about — for example, environmental protection, human rights, diversity, etc. — how much of an impact does your investment decision have?