There are no new gags

Free idea for my philosopher friends:  put out a call for papers for a volume about baseball and philosophy, called “What Is It Like To Be At Bat?”

Amazon tells me that somebody has already produced a book of articles on baseball and philosophy, but hasn’t used this gag.

But Google tells me that the gag has already appeared several times:  in a blog post, in an article by John Haugelund, and, somewhat memorably, in the last stanza of a poem by Michael Robbins that appeared in the Awl:

I never promised you a unicorn.
But still. What is it like to be at bat?
Just having T.M.I. tattooed on my balls.
The heavy lice that hang from them
run in blood down palace walls.

There are no new gags.  I think Robbins’s poems are interested in the contemporary fact of there being no new gags.

What is it like to be a vampire and/or parent?

Andrew Gelman contemplates a blog post of L.A. Paul and Kieran Healy (based on a preprint of Paul) which asks:  it is possible to make rational decisions about whether to have children?

Paul and Healy’s argument is that, given the widely accepted claim that childbearing is a transformational event whose nature it’s impossible to convey to those who haven’t done it, it may be impossible for people to use the usual “what would it be like to to X?” method of deciding whether to have a kid.

Gelman says:

…even though you can’t know how it will feel after you have the baby, you can generalize from others’ experiences. People are similar to each other in many ways, and you can learn a lot about future outcomes by observing older people (or by reading research such as that popularized by Kahneman, regarding predicted vs. actual future happiness). Thus, I think it’s perfectly rational to aim to have (or not have) a child, with the decision a more-or-less rational calculation based on extrapolation from the experiences of older people, similar to oneself, who’ve faced the same decision earlier in their lives.

Here’s how I’d defend Paul and Healy from this objection.

Suppose you had a lot of friends who’d been bitten by vampires and transformed into immortal soulless monsters.  And when you meet up with these guys they’re always going on and on about how awesome it is being a vampire:  ”I’m totally glad I became undead, I’d never go back to being human, are you kidding me?  Now I’m superstrong, I’m immortal, I have this great group of vampires I run with, I feel like I really know what it’s all about now in a way I didn’t get before.  Life has meaning, life has purpose.  I can’t really explain it, you just gotta do it.”  And you know, you sort of wish they’d be a little less rah-rah about it, like, do you have to post a picture on Facebook of every person you kill and eat?  You’re a vampire, that’s what you do, I get it!  But at the same time you can’t help starting to wonder whether they’re on to something.

AND YET:

I don’t think it’s actually good decision-making to say:  people similar to me became vampires and prefer that to their former lives as humans, so I should become a vampire too.  Because the vampire is not the same being as the human who used to occupy that body.  Who cares whether vampires like being vampires better than they like being human?  What matters is what I prefer, not what the vampiric version of me would prefer.  And I, a human, prefer not to be a vampire.

As for me, I’m a parent, and I don’t think that my identity underwent a radical transformation.  I’m the same person I was, but with two kids.   So when I tell friends it’s my experience that having kids is pretty worthwhile, I’m not saying that from across an unbridgable perceptual divide — I’m saying that I am still similar to you, and I like having kids, so you might too.  Paul and Healy’s argument doesn’t refer to my case at all:  they’re just saying that if parents are about as different from non-parents as vampires are from humans, then there’s a real difficulty in deciding whether to have children based on parents’ testimonies, however sincere.

(Remark:  Invasion of the Body Snatchers is sort of about the question Paul and Healy raise.  Many have understood the original movie as referring to Communism, but it might be interesting to go back and watch it as a movie about childbearing.  It is, after all, about gross slimy little creatures that grow in the dark and sustain themselves on your body.  And then the new being known as “you” goes around trying to convince others that the experience is really worth it!)

Update:  Kieran points out that the reference to “body-snatching” is already present in their original post — I must have read this, forgotten it, then thought I’d come up with it as an apposite example myself….

Guest post: Stephanie Tai on deference to experts

My colleague Steph Tai at the law school wrote a long, amazing Facebook message to me about the question Cathy and I have been pawing at:  when and in what spirit should we be listening to experts?  It was too good to be limited to Facebook, so, with her permission, I’m reprinting it below.

Steph deals with these issues because her academic specialty is the legal status of scientific knowledge and scientific evidence.  So yes:  in a discussion on whether we should listen to experts I am asking you to listen to the opinions of an expert on expertise.

Also, Steph very modestly doesn’t link to her own paper on this stuff until the very bottom of this post.  I know you guys don’t always read to the bottom, so I’ve got your link to “Comparing Approaches Toward Governing Scientific Advisory Bodies on Food Safety in the United States and the European Union” right here!

And now, Steph:

*****

Some quick thoughts on this very interesting exchange. What might be helpful, to take everyone out of our own political contexts, perhaps, is to contrast this discussion you’re both having regarding experts and financial models with discussions about experts and climate models, where, it seems, the political dynamics are fairly opposite. There, you have people on the far right making similar claims to Cathy: that climate scientists are to be distrusted because they’re just coming up with scare models because these allegedly biased models are useful to those climate scientists–i.e., to bring money to left-wing causes, to generate grants for more research, etc.

 

So when you apply the claim that Cathy makes at the end of her post–”If you see someone using a model to make predictions that directly benefit them or lose them money – like a day trader, or a chess player, or someone who literally places a bet on an outcome (unless they place another hidden bet on the opposite outcome) – then you can be sure they are optimizing their model for accuracy as best they can. . . . But if you are witnessing someone creating a model which predicts outcomes that are irrelevant to their immediate bottom-line, then you might want to look into the model yourself.”–I’m not sure you can totally put climate scientists in that former category (of those that directly benefit from the accuracy of their predictions). This is due to the nature of most climate work: most researchers in the area only contribute to one tiny part of the models, rather than produce the entire model themselves (thus, the incentives to avoid inaccuracies are diffuse rather than direct); the “test time” for the models are often relatively far into the future (again, making the incentives more indirect); and the sorts of diffuse reputational gains that an individual climate scientist gets from being part of a team that might partly contribute to an accurate climate model is far less direct than the examples given of day traders and chess players or “someone who literally places a bet on an outcome.”

 

What that in turn seems to mean is that under Cathy’s approach, climate scientists would be viewed as in the latter category—those creating models that “predict outcomes that are irrelevant to their immediate bottom-line,” and thus deserve people looking “into the model [themselves].” But at least from what I’ve seen, there is *so* much out there in terms of inaccurate and misleading information about climate models (by folks with stakes in the *perception* of those models) that chances are, a lay person’s inquiry into climate models has high chance to being shaped by similar forces with which Cathy is (in my view appropriately) concerned. Which in turn makes me concerned about applying this approach.
Disclaimer: I used to fall under this larger umbrella of climate scientists, though I didn’t work on the climate models themselves, just one small input to them—the global warming potentials of chlorofluorocarbon substitutes. So this contrast is not entirely unemotional for me. That said, now that I’m an academic who studies the *use* of science in legal decisionmaking (and no longer really an academic who studies the impact of chlorofluorocarbon substitutes on climate), I don’t want to be driven by these past personal ties, but they’re still there, so I feel like I should lay them out.

 

So what’s to be done? I absolutely agree with Cathy’s statement that “when independent people like myself step up to denounce a given statement or theory, it’s not clear to the public who is the expert and who isn’t.” It would seem, from what she says at the end of her essay, that her answer to this “expertise ambiguity” is to get people to look into the model when expertise is unclear.[*] But that in turn raises a whole bunch of questions:

 

(1) What does it take to “look into the model yourself”? That is, how much understanding does it take? Some sociologists of science suggest that translational “experts”–that is, “experts” who aren’t necessarily producing new information and research, but instead are “expert” enough to communicate stuff to those not trained in the area–can help bridge this divide without requiring everyone to become “experts” themselves. But that can also raise the question of whether these translational experts have hidden agendas in some way. Moreover, one can also raise questions of whether a partial understanding of the model might in some instances be more misleading than not looking into the model at all–examples of that could be the various challenges to evolution based on fairly minor examples that when fully contextualized seem minor but may pop out to someone who is doing a less systematic inquiry.

 

(2) How does a layperson avoid, in attempting to understand the underlying model, the same manipulations by those with financial stakes in the matter–the same stakes that Cathy recognizes might shape the model itself? Because that happens as well, so that even if one were to try to look into a model themselves, the educational materials it would take to look into that model can be also argued to be developed by those with stakes in the matter. (I think Cathy sort of raises this in a subsequent post about how entire subfields can be regarded as “captured” by particular interests.)

 

(3) (and to me this is one of the most important questions) Given the high degree of training it takes to understand any of these individual areas of expertise, and given that we encounter so many areas in which this sort of deeper understanding is needed to resolve policy questions, how can any individual actually apply that initial exhortation–to look into the model yourself–in every instance where expertise ambiguity is raised? To me that’s one of the most compelling arguments in favor of deferring to experts to some extent–that lay people (as citizens, as judges, as whatever) simply don’t have time to do the kind of thing that Cathy suggests in every situation where she argues it’s called for. Expert reliance isn’t perfect, sure–but it’s a potentially pragmatic response to an imperfect world with limited time and resources.

 

Do my thoughts on (3) mean that I think we should blindly defer to experts? Absolutely not. I’m just pointing it out as something that weighs in favor of listening to experts a little more. But that also doesn’t mean that the concerns Cathy raises are unwarranted. My friend Wendy Wagner writes about this in her papers on the production of FDA reports and toxic materials testing, and I find her inquiries quite compelling. P.s. I should also plug a work of hers that seems especially relevant to this conversation. It suggests that the part of Nate Silver’s book that might raise the most concerns (I dunno, because I haven’t read it) is its potential contribution to the vision of models as “truth machines,” rather than understanding that models are just one tool to aid in making decisions, and a tool which must be contextualized (for bias, for meaningfulness, for uncertainty) at that.

 

So how to address this balance between skepticism and lack of time to do full inquiries into everything? I totally don’t have the answers, though the kind of stuff I explore are procedural ways to address these issues, at least when legal decisions are raised–for example,
* public participation processes (with questions as to both the timing and scope of those processes, the ability and likelihood that these processes are even used, the accessibility of these processes, the susceptibility of “abuse,” the weight of those processes in ultimate decisionmaking)
* scientific ombudsman mechanisms (which questions of how ombudsman are to be selected, the resources they can use to work with citizen groups, the training of such ombudsmen)
* the formation of independent advisory committees (with questions of the selection of committee members, conflict of interest provisions, the authority accorded to such committees)
* legal case law requiring certain decisionmaking heuristics in the face of scientific uncertainty to avoid too much susceptibility to data manipulation (with questions of the incentives those heuristics create for actual potential funders of scientific research, the ability of judges to apply such heuristics in a consistent manner)
–as well as legal requirements that exacerbate these problems. Anyway, thanks for an interesting back and forth!

 

[*] I’m not getting into the question of “what makes someone an expert?” here, and instead focus on “how do we make decisions given the ambiguousness of who should be considered experts?” because that’s more relevant to what I study, although I should also point out that philosophers and sociologists of science have been studying this in what’s starting to be called the “third wave” of science, technology, and society studies. There’s a lot of debate about this, and I have a teensy summary of it here (since Jordan says it’s okay for me to plug myself :) (Note: the EFSA advisory committee structure, if anyone cares, has changed since I published this article so that the article characterizations are no longer accurate.)

 

 

 

Stephen Landsburg is right about numbers

I’ve often disagreed with Steve Landsburg, sometimes on this blog and sometimes in Slate.  So it seems worth mentioning that I’m totally on board with his take on the reality of numbers and other mathematical objects.  (Scroll down — and down, and down, and down — to item 9 for the part I’m talking about.)

To me, by far the most satisfying solution is a full-fledged Platonic acknowledgement that numbers are indeed just “out there” and that they are directly accessible to our intuitions. I embrace this view for (at least) three reasons: A. After a lifetime of thinking about numbers, it feels right to me. B. Pretty much every one else who spends his/her life thinking about numbers has come to the same conclusion. C. It seems enormouosly more plausible to me that numbes are “just out there” than that physical objects are “just out there”, partly because there is in fact a unique system of (standard) natural numbers, whereas the properties of the physical universe appear to be far more contingent and therefore unnecessary.

Right on!  The view that mountains, clouds, and frogs are not real things can’t really be refuted, but it’s universally judged to be a boring view that’s not worth holding, right?  So in order to decide to deem numbers “out there” we don’t have to defend the claim that they’re real, but only that they are at least as real as mountains, clouds, and frogs.  This last, weaker claim seems to me obviously correct.

You don’t have to outrun the bear!

 

 

I thought the truth was apt to be simple

but Cosma says I’ve got another think coming!  He’s blogging the Ockham’s razor conference I mentioned in the previous post, and starts out today’s entry with the following bombshell:

The theme of the morning was that Ockham’s razor is not a useful principle because the truth is inherently simple, or because the truth is apt to be simple, or because simplicity is more plausible, or even because simple models predict better. Rather, the Razor helps us get to the truth faster than if we multiplied complexities without necessity, even when the truth is actually rather complex.

I have always thought of the utility of parsimony as derving from a tendency of true things to be simple.  But am I fooling myself?  I tend to think that mathematical truths are apt to be simple — for instance, that when I have truly understood a difficult mathematical argument I see that the main idea is simple and elegant, while the visible complications are somehow inessential.  But you could argue that this is just prejudice on my part, and I denigrate the complicated part as inessential just because it is complicated.

And certainly I don’t think the truth about big biological or social systems is apt to be simple.  In fact, because I know people are prejudiced to believe in simple explanations, I find myself leaning against them;  the fact that a simple explanation is widely believed by people I trust is less compelling as evidence than it would be, if the explanation in question were prickly or technical or otherwise unpleasant to believe.

 

 

Ockham’s Razor Conference

What does it mean to say “All things being equal, believe the simplest theory?”  It sure sounds like good advice, but in practice it can be vexingly hard to understand which theories Ockham’s razor is lopping off and which are to be left behind.  So I’m happy to see this announcement of a conference at CMU this weekend on the topic, where philosophers, statisticians, and machine learning types will get together and hash it out. Speakers include my collaborator Elliott Sober and blog favorite Cosma Shalizi.

More on probability aggregation and De Finetti

A few months ago I posted a puzzle about aggregating probability estimates from different sources, and in particular how to aggregate opinions about the independence of two events.

I think I now understand the story slightly better.  I am essentially going to agree with what Terry T. said in the comments to the first post (this is my surprised face) but at the same time try to dissolve my initial resistance to talking about second-order probabilities (statements of the form “the probability that the probability is p is q….”)

To save you a click, the question amounts to:  if half of your advisors tell you that X and Y are independent coins with probability .9 of landing heads, and the other half of your advisors agree the coins are independent but say that the probability of heads is .1 for each, what should your degree of belief in X, Y, and X&Y be?  And should you believe that X and Y are independent events, a fact about which your advisors are unanimous?

The answer depends, at least in part, on what you mean by “probability” and “independence.”

On one account, probability is a number between 0 and 1 that represents your degree of belief in a hypothesis, and independence of X and Y means that Pr(X&Y) = Pr(X)Pr(Y).  Both are assertions about your mental state.  So there’s no reason that the unanimity of your advisors about the independence of X and Y should make you believe that X and Y are independent; why should this aspect of their mental state automatically be taken to be a guide to yours?  Relevant comparison:  what if each advisor said “I am really sure my belief about the coin is correct.”  Since all your advisors agree that the nature of the coin is very strongly certain, should you agree about that too?  No — given that half your advisors think the coin is very likely to fall heads and half that it is very likely to fall heads, you are reasonably pretty unsure about the nature of the coin.  Moreover, if X falls heads, you should rationally increase your degree of belief that Y will fall heads too, because X falling heads is evidence that the 0.9 gang is correct in their beliefs.  So (for you, even if not for your advisors) the two events are not independent.

There is another account, in which the probability is an intrinsic property of the coin.  On this account, it makes sense to talk about second-order probabilities:  to say, for instance, that the probability that “the probability that the coin falls heads is .9″ is 1/2.  On this account, we can talk (as Terry does) about conditional independence; we say that there is an unknown parameter p which measures the propensity of the coin to fall heads, and that the condition Pr(X&Y) = P(X)P(Y) for independence only makes sense once P(X) and P(Y) are known.

In fact, I’ve come to favor the second view, at least as regards coins.  Because here’s the thing.  Let’s say I start with the first view.  I have in mind a degree of belief that the first coin will fall heads, and I call this P(X).  Given the evidence I have, probably P(X) should be 0.5.  But once I’m forming degrees of belief, I must also have a degree of belief that a sequence of k tosses of the coin will all fall heads.  And this should be  the average of (0.9)^k and (0.1)^k, not (0.5)^k!

Having in mind the probability distributions on “number of heads in k tosses” for all k is, by De Finetti’s theorem, more or less the same as having in mind a probability distribution on the propensity of the coin to fall heads.  That is, if a binary event is one we can imagine repeating, then our subjective degrees of belief about the event automatically have the structure of a second-order probability distribution on (Bernoulli) probability distributions.  In fact, I think this was why De Finetti proved De Finetti’s theorem.  In this context, independence is an intrinsic fact about the coins, not about our knowledge, and we should agree with our advisors that the coins are independent.

I’m less sure this story applies to uncertain events which are, by their nature, unrepeatable.  What do we mean when we talk about the probability that Ankylosaurus had feathers?  Is it meaningful in this context to say “I think there’s a 50% chance that there’s a 90% chance Ankylosaurus had feathers, and a 50% chance that there’s only a 10% chance” or is this exactly the same as saying you think there’s a 50% chance?

Math linkdump Nov 11

• Tim Gowers destroys and rebuilds mathematical publishing.
• Mosteller and Youtz randomize Mozart.
• The Open Graph Archive is trying to generate a community-built, openly accessible library of graphs.
• Eugenia Cheng on what mathematicians are talking about when they use the word “morally.”
• Philipp Habegger just proved that the field F obtained by adjoining to Q all torsion points of an elliptic curve E/Q  has the Bogomolov property; the logarithmic height of a non-torsion element of F^* is bounded away from 0.  About a year ago I was going around asking a lot of people whether this was true, and no one knew; at some point I’ll write a longer blog entry explaining why I wanted to know.

Subjective probabilities: point/counterpoint

• Adam Elga:  “Subjective Probabilities Should Be Sharp” — at least for rational agents, who are vulnerable to a kind of Dutch Book attack if they insist that there are observable hypotheses whose probability can not be specified as a real number.
• Cosma Shalizi:  “On the certainty of the Bayesian Fortune-Teller” — People shouldn’t call themselves Bayesians unless they’re committed to the view that all observable hypotheses have sharp probabilities — even if they present their views in some hierarchical way “the probability that the probability is p is f(p)” you can obtain whatever expected value you want by integrating over the distribution.  On the other hand, if you reject this view, you are not really a Bayesian and you are probably vulnerable to Dutch Book as in Elga, but Shalizi is at ease with both of these outcomes.

Holden Karnovsky on the perils of expected utility

I asked a while back how seriously we should take expected utility computations that rely on multiplying very large utilities by very small probabilities.  This kind of computation makes me anxious.  Holden Karnovsky of GiveWell agrees, arguing that we are constrained by some kind of informal Bayesianness not to place too much weight on such computations, especially when the probability computation is one that can’t really be quantitatively well-grounded.  Should you give fifty bucks to an NGO that does malaria prevention in Africa?  Or should you donate it to a group that’s working on ways to deflect asteroids on a collision course with the Earth?  The former donation has a substantial probability of helping a single person or family in a reasonably serious way (medium probability of medium utility.)  The latter donation is attached to the very, very large utility of saving the human race from being wiped out; on the other hand, the probability of achieving this utility is some combination of the chance that a humanity-killing asteroid will be on course to strike the earth in the near term, and the chance that the people asking for your money actually have some prospect of success.  You can make your best guess as to the extent to which your fifty dollars decreases the chance of global extinction; and you might find, on this ground, that the expected value of the asteroid contribution is greater than that of the malaria contribution.  Karnovsky says you should still go with malaria.  I’m inclined to think he’s right.  One reason:  a strong commitment to expected utility makes you vulnerable to Pascal’s Mugging.