From Oswald Veblen’s opening address to the 1950 ICM:
Mathematics is terribly individual. Any mathematical act, whether of creation or apprehension, takes place in the deepest recesses of the individual mind. Mathematical thoughts must nevertheless be communicated to other individuals and assimilated into the body of general knowledge. Otherwise they can hardly be said to exist. By the time it becomes necessary to raise one’s voice in a large hall some of the best mathematicians I know are simply horrified and remain silent…
The solution will not be to give up international mathematical meetings and organizations altogether, for there is a deep human instinct that brings them about. Every human being feels the need of belonging to some sort of a group of people with whom he has common interests. Otherwise he becomes lonely, irresolute, and ineffective. The more one is a mathematician the more one tends to be unfit or unwilling to play a part in normal social groups. In most cases that I have observed, this is a necessary, though definitely not a sufficient, condition for doing mathematics.”
This view of mathematics and mathematicians is deeply alien to me. I experience mathematics as thoroughly communal. Does this reflect a change in mathematical practice in the last 60 years, or just a difference in temperament between Ozzie and me?
I didn’t know this about Amie:
I went to college, and I was feeling very insecure about my abilities in mathematics, and I hadn’t gotten a lot of encouragement, and I wasn’t really sure this was what I wanted to do, so I didn’t apply to grad school. I came back home to Chicago, and I got a job as an actuary. I enjoyed my work, but I started to feel like there was a hole in my existence. There was something missing. I realized that suddenly my universe had become finite. Anything I had to learn for this job, I could learn eventually. I could easily see the limits of this job, and I realized that with math there were so many things I could imagine that I would never know. That’s why I wanted to go back and do math.
This was basically me, too. After college I got into the fiction writing program at Johns Hopkins, which made me think maybe I could really make it as a writer, and I deferred grad school and moved to Baltimore and wrote fiction all day every day for a year, and while I valued that experience a lot, there was not a single day of it where I didn’t kind of wish I were doing math. Having had that experience — not just suspecting but knowing how annoying it is not to be doing math — took the edge off the pain of the painful parts of grad school.
Happy to report that the UW-Madison math department has added two more terrific young faculty members, both joining us next fall: Daniel Erman in commutative algebra and algebraic geometry (seen previously on the blog counting smooth members in semiample linear systems over finite fields) and Uri Andrews in model theory.
In other awesome news, my former Ph.D. student Derek Garton will join the department at Portland State (his master’s degree alma mater!) as a tenure-track assistant professor.
Strange and kind of great new novel by Jenny Davidson (who, for full information’s sake, is someone I’ve known on and off since college) about young intellectuals who believe in the power of text more than is perhaps good for them. ”Text” here means books, as you’d expect, but also text-as-in-texting and chat windows and games. A lot of the dialogue is in an interestingly distant Delmore Schwartz register. It reads strangely at first but makes sense once you get used to it.
What I liked best is this. The book gestures at being one of those in which real life gives way to the fantastic, but ends up insisting (correctly, I think!) that when the fantastic intrudes into ordinary life, it does not replace ordinary life but rather overlays it — so that one can have the most heightened and extrawordly experience possible, and then go home, with the smell of it still on you, and check your e-mail and brush your teeth. It is a novel for the world of Google Glass, and should be read whether or not the world of Google Glass turns out to be our world.
UW-LaCrosse started it, launching an online math course, “College Readiness.” with the help of a grant from the Gates Foundation. A lot of the energy around MOOCs has centered on advanced courses: machine learning, business analytics, and so on. The kind of thing that gets funders and nerds excited. But funders and nerds are already educated! If MOOCs are to provide the educational equity they promise, they’ve got to do it at the low end — giving kids access to a better math course than their understaffed, underresourced high school can provide. Is there a demand for basic, unflashy math instruction online? Seems like it: a thousand people have signed up, twice as many as UWLC expected, including an 83-year-old and an 11-year-old. Those are much smaller numbers than Coursera gets for its sexy machine learning course, but I’ll bet the gap in number of finishers will be much narrower; this course is an “I need to,” not an “It would be cool to.”
And now UW-Madison has gotten into the act, announcing yesterday that UW would be offering four courses with Coursera, two to start this fall.
Readers: would it be a good idea, a bad idea, or some combination of both, for me to propose to teach a number theory MOOC?
Razib Khan says it is, in a post several people in my networks shared today:
[Cultural anthropology] has embraced deconstruction, critique, complexity (or more accurately anti-reductionism) and relativism to such a great extent that whereas in many disciplines social dynamics and political power struggles are an unfortunate consequence of academic life, in cultural anthropology the fixation with power dynamics and structures has resulted in its own self-cannibalization, and overwhelming preoccupation with such issues. Everyone is vulnerable to the cannon blast of critique, and the only value left sacred are particular particular ends (social justice, defined by cultural anthropologists) and axioms (white males are oppressive patriarchs, though white male cultural anthropologists may have engaged in enough self interrogation to take upon themselves the mantle of fighting for the rights of the powerless [i.e., not white males]) which all can agree upon.
(That whole barrage is two very convoluted sentences, by the way!)
What Khan objects to is stuff like this:
“It’s a profoundly damaging argument that tribal peoples are more violent than us,” said Survival’s Jonathan Mazower. “It simply isn’t true. If allowed to go unchallenged … it would do tremendous damage to the movement for tribal people’s rights. Diamond has constructed his argument using a small minority of anthropologists and using statistics in a way that is misleading and manipulative.”
But does this really support the black hole claim? I think Khan reads the quote to say “Tribal people’s rights are sacrosanct, so any claim by a scientist that, like Diamond’s, tends to undercut those rights must be factually incorrect.” But to me it reads much more like “Diamond’s claims are factually incorrect, and the reason this matters — the reason it is not only an academic dispute between scientists, and the reason people who read the newspaper should care about it — is that it has real-world consequences for tribal people.” Which seems like a fairly normal thing for a social scientist to say in the newspaper.
As for me, I have no opinion about the intellectual state of cultural anthropology, knowing nothing about it. I’m not sure I’ve ever read a book about cultural anthropology, unless Seeing Like A State is a book of cultural anthropology, in which case every book of cultural anthropology I’ve ever read is great.
Hal Pashler, a psychologist at UCSD, tweeted my post about the “end of history” study, and this led me to his interesting paper, “Is the Replicability Crisis Overblown?” (with Christine Harris.) Like all papers whose title is a rhetorical question, it comes down in favor of “no.”
Among other things, Pashler and Harris are concerned about the widespread practice of “conceptual replication,” in which rather than reproduce an existing experiment you try to find a similar effect in an adjacent domain. What happens when you don’t find anything?
Rarely, it seems to us, would the investigators themselves believe they have learned much of anything. We conjecture that the typical response of an investigator in this (not uncommon) situation is to think something like “I should have tried an experiment closer to the original procedure—my mistake.” Whereas the investigator may conclude that the underlying effect is not as robust or generalizable as had been hoped, he or she is not likely to question the veracity of the original report. As with direct replication failures, the likelihood of being able to publish a conceptual replication failure in a journal is very low. But here, the failure will likely generate no gossip—there is nothing interesting enough to talk about here. The upshot, then, is that a great many failures of conceptual replication attempts can take place without triggering any general skepticism of the phenomenon at issue.
The solutions are not very sexy but are pretty clear — create publication venues for negative results and direct replication, and give researchers real credit for them. Gary Marcus has a good roundup in his New Yorker blog of other structural changes that might lower the error rate of lab science. Marcus concludes:
In the long run, science is self-correcting. Ptolemy’s epicycles were replaced by Copernicus’s heliocentric system. The theory that stomach ulcers were caused by spicy foods has been replaced by the discovery that many ulcers are caused by a bacterium. A dogma that primates never grew new neurons held sway for forty years, based on relatively little evidence, but was finally chucked recently when new scientists addressed older questions with better methods that had newly become available.
but Pashler and Harris are not so sure:
Is there evidence that this sort of slow correction process is actually happening? Using Google Scholar we searched <“failure to replicate”, psychology> and checked the first 40 articles among the search returns that reported a nonreplication. The median time between the original target article and the replication attempt was 4 years, with only 10% of the replication attempts occurring at lags longer than 10 years (n = 4). This suggests that when replication efforts are made (which, as already discussed, happens infrequently), they generally target very recent research. We see no sign that long-lag corrections are taking place.
It cannot be doubted that there are plenty of published results in the mathematical literature that are wrong. But the ones that go uncorrected are the ones that no one cares about.
It could be that the self-correction process is most intense, and thus most effective, in areas of science which are most interesting, and most important, and have the highest stakes, even as errors are allowed to persist elsewhere. That’s the optimistic view, at any rate.
The Wall Street Journal op-ed page is always good for a full-throated demand that we distrust the experts:
The general public is not privy to the IPCC debate. But I have been speaking to somebody who understands the issues: Nic Lewis. A semiretired successful financier from Bath, England, with a strong mathematics and physics background, Mr. Lewis has made significant contributions to the subject of climate change.
…Will the lead authors of the relevant chapter of the forthcoming IPCC scientific report acknowledge that the best observational evidence no longer supports the IPCC’s existing 2°-4.5°C “likely” range for climate sensitivity? Unfortunately, this seems unlikely—given the organization’s record of replacing evidence-based policy-making with policy-based evidence-making, as well as the reluctance of academic scientists to accept that what they have been maintaining for many years is wrong.
Domain knowledge, phooey — this dude is successful!
“Distrust the experts,” as a principle, does as much harm as good. A better principle would be “Distrust people who are bad and trust people who are not bad.” Of course, it can be hard to tell the difference — but that distinction is one we have to make anyway, in all kinds of contexts, so why not this one?
I was pleased to see that this year’s Joint Mathematics Meetings in San Diego offers subsidized on-site childcare for participants in the meeting. But even after the subsidy, it isn’t exactly cheap; at $14/hour, a mathematician who wanted to attend the conference full-time would easily spend over $300 on childcare.
Can you use your NSF grant to cover this $300? Nope:
Can NSF award funds be used for travel and associated dependent-care expenses for dependents of individuals funded on an NSF award?
NSF award funds may not be used for domestic travel costs or associated dependent-care expenses for individuals traveling on NSF award funds. Travel costs associated with dependents may be allowable for International travel in accordance with Award and Administration Guide Chapter V.B.4, which contains several stipulations, including that travel must be continuous for a period of six months or more.
What about organizers of NSF-funded conferences? Can we offer to use NSF money to cover childcare costs for attending mathematicians? That’s another nope:
Can conference/workshop awards or travel funds from research awards be used to support child care at conferences and workshops?
NSF award funds may not be used to pay for travel costs or expenses related to onsite care (e.g., daycare) for dependents of participants at NSF-sponsored conferences and workshops. NSF-sponsored conferences and workshops are encouraged to consider child-care services to ease the burden on attendees, but the costs of such services are the responsibility of those that choose to utilize the accommodations.
For me to go to a conference requires me to buy a plane ticket and book a hotel room. NSF wants me to go to conferences, so they allow me to charge these unavoidable expenses to my grant. If I’m a single parent of a 1-year-old child, going to a conference requires me to have childcare available at the conference location. No childcare means I don’t go to the conference. If NSF is willing to pay two hundred bucks a night for my hotel room, why not a hundred bucks a day for childcare?