When Errorbars Hit Mainstream News

It’s interesting to me how science has come into conflict with the news in the past week. First we had the deflategate, where footballs mysteriously deflated during a playoff game, and then we had an over hyped blizzard.

The NFL recently hired physicists at Columbia to help make the case for science with the football fiasco, but I think that’s unnecessary: a few good experiments with temperature and friction and lots of measurements by lots of different pressure gauges will empirically demonstrate how much of a range we might expect from such things. In other words, understanding errorbars.

As for the blizzard, this article nicely articulates the science of weather forecasting and what went wrong. But what is interesting is that, in general, models have gotten much better, and in particular are good at predicting how powerful a storm is going to get. In this case the model got that right, but then the error came in figuring out exactly where the storm would travel and when.

Again, it’s a case of errorbars, and the public seems not to understand it. Or maybe they just don’t want to.

In fact, I heard quite a few people call in to ESPN radio over the past week trying to explain to the sports radio hosts what might be going on scientifically, only to be hung up on. The truth is, it’s not as interesting a story to think about it just happening outside our control. It messes with our sense of omnipotence and control.

This is bad news for society, as more and more things become “datafied” and as we assume that will translate into perfect information.

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Dartmouth Math Colloquium & All Souls Panel on Mega-Foundations

This Thursday I’m heading up to the Dartmouth Math department to give a colloquium on the subject of data science. They made the following poster for my talk:


Also, next month I’m excited to be the moderator of a panel at the All Souls Unitarian Church on the east side of Manhattan, with some amazing panelists. There’s also a poster for that event:


I hope I see you there!

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The exciting news today (besides tonight’s blizzard!) is the Greek elections. Yesterday an anti-austeristy party called Syriza won the plurality of the votes, and is on the very verge of winning a majority as well.

This is huge because the leader of the party, Alexis Tsipras, has basically promised the Greek people that, if elected, he would refuse to pay off any more of Greece’s debt.

How did this happen? Well, From the perspective of the Greek people, the negotiations around their economic problems have been taken on by their last two governments since 2008 with a bunch of European technocrats behind closed doors and in an intensely undemocratic process. Well, this is when democracy fought back.

Possible ramifications: If Greece indeed defaults, and it might leave or get booted out of the Eurozone (this is called “Grexit”), which may or may not be a good thing for Greece long term, but in any case is very interesting. Short term, the black market in Greece is said to be highly developed, so the average person isn’t entirely dependent on functioning banks anyway.

Also, I’m sure Greece has been looking at Argentina recently to see how their (accidental) default has been going, namely not as bad as everyone predicted. The world will be watching Greece to see what happens and to see how smaller countries can and will deal with stifling debt in the future.

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Aunt Pythia’s advice

Time passes quickly, my friends. It seems like only yesterday that Aunt Pythia was answering really long questions, and today her questions seem to be extra short. Last week it was cold outside – freezing! – but this week it is warm and snowy (but not for long!). Last week she was knitting a cowl, this week a colorful scarf. Crazy changes, in other words.

Indeed the only thing that hasn’t changed is an absolute willingness, on the part of Aunt Pythia, to offer up irrelevant and terrible advice to you earnest people. Many apologies, you definitely deserve better, but this is just something Aunt Pythia was born with, there’s nothing for it.

My suggestion for you is to just turn away and stop reading. I mean, how many obscene images must one be subjected to??

This is a liqueur filled sperm-shaped bottle. I know it really exists because I bought one in San Antonio last week, no shit. I haven't opened it yet.

This is a liqueur filled sperm-shaped bottle. I know it really exists because I bought one at a liquor store in San Antonio a couple of weeks ago, no shit. No, I haven’t opened it yet.

Wait, you’re still here? Really? Well, in that case, come on in, enjoy the warmth, get under a hand-knitted blanket, and don’t forget to:

ask Aunt Pythia a question at the bottom of the page!

By the way, if you don’t know what the hell Aunt Pythia is talking about, go here for past advice columns and here for an explanation of the name Pythia.


Dear AP,

is it worth saving, or should we just burn it all down and start again?

Sick of Bull Systems

Dear Sick,

I’m going to assume you’re talking about the financial system. I’m tempted to say “burn it” but there would actually be severe short-term problems caused by there being no financial system. Moreover, it isn’t clear that a new one would be built better than the existing one. I know that sounds disappointingly unrevolutionary, but there it is.

If you are feeling desperate, may I suggest ignoring it and starting a new one. If I had time I would be more active in the public bank movement in this country, which seems like a better alternative to ours and can exist in parallel.

Aunt Pythia


Dear Aunt Pythia,

Have you seen the Celtic Oracle designs? I made a deck but would like additional divination material.

Oracular Designs

Dear Oracular,

Nice! And flattering to oracles such as myself! Can I make a wee request? More naked people, especially men? Thanks.

Aunt Pythia


Dear Aunt Pythia,

I would like to start watching Dr. Who but I’m intimidated by 50+ years of shows. How do you get started?

Dr. Who Ignoramus

Dear DWI,

Common problem, I sympathize. The truth is, it doesn’t matter much. Let me give you a cheat sheet which should be more than adequate:

  1. Dr. Who is always a man who talks fast and is incredible smug, although usually in a lovable way.
  2. He sometimes has a dog named K-9 with him. If he does, you’re watching an earlier show.
  3. He almost always has a “companion” with him, who is almost always female, mostly young, and sometimes a love interest, although not in earlier shows.
  4. Sometimes his companion has other companions, who are often there as comedic relief.

That’s about it! Oh, and they travel through time solving problems on earth and on alien planets. So there, now you have no excuse not to watch.

Aunt Pythia


Hello Aunt Pythia,

Not a question, but a thank you for your answer to my previous question. It was helpful, and you are right! College towns are still towns, and as such the occupants must take the usual precautions when going out. I knew this, from personal experience walking home many a late night during grad school. But somehow the father in me did not want to admit it.

After I first wrote, a talk with my daughter segued into a talk about college, academics, academic pressure, and campus safety, and I was once again surprised by how grown up my daughter is. She and her friends are well aware of the risks, and do watch out for each other. And now that she has been accepted at Cornell (we found out last night), we’ll no doubt have these talks again, at which time I will mention Aunt Pythia’s advice.

Thank you once again,

Worried In Academia

Dear Worried,

Wow, wonderful! I almost never know if my advice actually helps, so this is amazing feedback, thank you for giving it to me!

Aunt Pythia


Dear Aunt Pythia,

I’m in my first year in a Phd program in math. I’ve always been academically successful, especially in math, and this semester is no exception. Although I know it will be difficult and take a lot of hard work, I’m moderately confident that I have the ability to get through my qualifying exams. After all, my aptitude for high stakes testing is what’s gotten me this far.

It’s what comes next that concerns me. Specifically, I’m not at all confident that I have what it takes to actually do research in math. I generally have a good memory (especially in the short term); I’m good at reproducing proofs I’ve seen before and at applying techniques in ways I’m familiar with, but I worry that I’m not an especially creative thinker and also that I coast by via collaborating with others. (I realize that the second concern can be irrational, at least from a coursework perspective, since I do comparably well on exams as on homework, but it’s still in the back of my head.)

(It’s probably also be pertinent to mention that I’m male, and haven’t ever felt invalidated either institutionally or on an individual level with respect to my ability–these concerns are entirely my own.)

I’ve had only two research experiences up until this point. The first I don’t put much weight on, since it was in another field that I quickly realized I was not that interested in (which contributed to my decision a few years ago to focus more on math). The second was a project I worked on with a faculty advisor throughout my last year and a half of undergrad. It was in an area that I was interested in and my advisor was great. However, I often would become consumed with anxiety and overwhelmed to the point that I was unable to get anything done.

Part of it was adjusting to working independently and in an unstructured environment, but even when I was given a list of moderately specific things to do it didn’t necessarily help. Despite having plenty of time available to devote to the project, I would put off working persistently, often getting to the point where I would stay up later and later the hour before my next meeting, becoming more and more panicked but for some reason still incapable of working. By the time I’d snap out of it, it would be so late that I would be too exhausted to really do my best work, and it definitely showed. It was stressful for me, frustrating for my advisor, and (clearly) not really productive mathematically. And yet I couldn’t bring myself to change, week after week!

I felt especially bad for being a disappointment for someone who has done a lot for me and who inspired me to seriously pursue math in the first place. Especially, since to anyone not in my head this all came across as purely poor work habits/laziness–my advisor told me shortly before graduation that I have everything it takes to succeed in grad school, as long as I work hard enough, which was simultaneously affirming and distressing. Part of me also thinks that this was all just garden variety laziness and that if I just had worked harder and focused better it wouldn’t have been an issue.

So I guess my question is, where do I go from here? What can I do to keep this from happening in the future? Do I really have a problem, or is it just a combination of laziness and lack of self-confidence?

Uneasy New Scholar, Upbraiding or Reassurance Essential


First off, amazing sign off. Much appreciated.

Next, thank you so much for asking this question. And, given that you are a highly successful and encouraged male, the issue is nicely isolated: how does doing well on highly structured undergrad work and standardized tests relate to being a good researcher?

The answer is unclear, actually, in general. I mean, I don’t want to panic you, because I actually think math research is a skill you can pick up if you are smart and work hard, but on the other hand, it might not be that easy, especially for you.

Let me put it this way. Theoretically, we want to attract to math research a bunch of people who:

  1. love math,
  2. work hard and don’t mind being wrong and can live with not knowing whether they are, and
  3. are “good at math”, where I’m going to ignore what exactly that means, partly because I don’t want to get drawn into the genius myth discussion and partly because I actually think the first two qualifications are dominant.

But here’s the thing. Instead, we attract to math research, via our post-college applications selection method, people who:

  1. may love math but may just have been told they’re “good at math” and may not know the difference,
  2. know how to master a well-defined skill where they get continuous feedback from tests and other people that they are making progress, and
  3. are probably plenty “good at math.”

So you see, there is likely a mismatch between the first two points.

I’m going to hope, for your sake, that you love math. Because you’ll need it, believe me.

Assuming you do, then you’ll need to spend time on #2, which means you (ironically) need to stop caring about outside measures of progress so you can lose yourself in your work and make progress. Get it? It’s confusing when you first encounter it, and unintuitive, and it might be extra hard for someone who is addicted to external evaluations and encouragement, which honestly it sounds like you are to some extent. Just as an example, you don’t owe your advisor anything except your gratitude. You are doing math for yourself from here on in.

The good news is, it often sucks at first, so don’t think you’ve already failed. You just need to develop new skills. It’s kind of like a muscle you didn’t know you had that you need to make super strong.

I suggest trying it out in short bursts. Find yourself a few hours of time, where you are not urgently needed by some classwork or something, and lose yourself in thought around some mathematical object, with no specific need of a milestone. Play with the math, see what you find, and don’t feel like you’ve wasted your time at the end, even if you feel like you have. It was your time to waste, after all.

Anyhoo, that’s the muscle you will need to develop. Once you get good at it, you can lose yourself for days or weeks at a time and then every now and then stumble on actual progress. You can do it! Start small!

At least that’s how it has always worked for me. Other mathematicians, feel free to chime in if you disagree.

Good luck!

Aunt Pythia


Well, you’ve wasted yet another Saturday morning with Aunt Pythia! I hope you’re satisfied! If you could, please ask me a question. And don’t forget to make an amazing sign-off, they make me very very happy.

Click here for a form or just do it now:

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Intentional discrimination versus disparate impact

I’m paying lots of attention to the Supreme Court’s coming decision on The Fair Housing Act. A New York Times editorial of this morning does a good job explaining the issues, including the concern that Chief Justice Roberts seems to think we’ve moved past racial discrimination in this country.

The burning question is whether housing developments and the like are responsible only for intentionally discriminating against individuals, or whether they are responsible in a more general, statistical sense, of having disparate impact on groups of people. The New York Times, like me, hopes for a broader reading, consistent with the 11 courts of appeals decisions over the last 40 years. From the Times:

The ability to show discriminatory effect has only become more important as intentional discrimination has become harder to prove. To take one prominent example, the Justice Department relied on it to negotiate the largest-ever fair-lending settlement — $335 million — with Bank of America in 2011. The bank’s mortgage unit, Countrywide Financial, had charged higher average fees and interest rates to black and Latino borrowers than to whites with the same credit risk, a practice that former assistant attorney general Thomas Perez called “discrimination with a smile.”

This case is focused on housing, but of course it could generalize to all sorts of other systems, including job applications and credit applications among others.

If we stick to the “intentional discrimination” only, we are opening up a door to (even more) widespread use of algorithmic decision-making that produces unfair and discriminatory results. And as it turns out, it’s easy to produce a model that effectively discriminates.

And if you are not in charge of your own system, then who is?

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Two articles on feminism

I’m neck deep in writing nowadays, but I wanted to share two extremely interesting and provocative pieces around women which come at feminism with from very different angles.

First, this essay, entitled If we liberate men’s sexuality, the war against women can end (hat tip Susan Webber), was written by a professional dominatrix, which is always an eye-opening perspective. She suggests that if we promote a new kind of feminism which she calls intersectional feminism, rather than depending on the old-school moralistic feminism, then we have a better chance to reach men, especially the men who might otherwise join the extremist misogynistic “men’s right’s” movement or become part of the vile pickup artist movement.

I think she has a bunch of interesting points. It is clearly true that men are boxed in in terms of their sexuality just as women are, and for men that don’t fit the standard mold it amounts to a kind of torture; the answer then is to promote a kind of sexual license for all people, not just women. Also, I think she’s absolutely correct to focus on sexual frustration as a major cause of all sorts of bad things. It’s not just about competing for jobs with women, it’s also about not getting laid.

Second, this Science Friday piece (hat tip Thessy) on the perceived requirement of innate genius as an obstacle for women in various fields. I wrote about this issue recently.

In particular a caller named Emily tells the guests how she was a straight A student at NYU, who graduated summa cum laude, and was passionate about philosophy, but was told by her advisor that she “just didn’t have what it takes” to go on to graduate school.

I cannot tell you how many people I know who have gone through something similar. And, I might add, such stories, which are generally completely unreported, flies in the face of ridiculous claims such as those made in this recent New York Times opinion piece that sexist mistreatment in science is minor and anecdotal.

Last thing: it’s cool and interesting how many conversations are being conducted around these important issues. I see it as progress just to be able to assume that other people I run into are sufficiently aware of the issues to talk about them, including my teenage sons.

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Peter Woit: The NSA, NIST and the AMS

This was crossposted from Not Even Wrong and written by Peter Woit.

Last summer I wrote here about an article in the AMS Notices which appeared to make misleading claims about the NSA’s involvement in putting a backdoor in an NIST cryptography standard known as DUAL_EC_DRBG. The article by Richard George, a mathematician who worked at the NSA, addressed the issue of the NSA doing this kind of thing by discussing an example of past history when they were accused of doing this, but were really actually strengthening the standard. He then went on to claim that:

I have never heard of any proven weakness in a cryptographic algorithm that’s linked to NSA; just innuendo.

This appears to be a denial of an NSA backdoor in the standard, while not saying so explicitly. If there is a backdoor, as most experts believe and the Snowden documents indicate, this was a fairly outrageous use of the AMS to mislead the math community and the public. At the time I argued with some at the AMS that they should insist that George address explicitly the question of the existence of the backdoor, but didn’t get anywhere with that. One of their arguments was that George was speaking for himself, not the NSA.

The question of fact here is a very simple and straightforward mathematical one: how was the choice used in the standard of points P and Q on an elliptic curve made? There is a known way to do this that provides a backdoor. Did the NSA use this method, or some other one for which no backdoor is known? The NSA refused to cooperate with the NIST investigation into this question. The only record of what happened when the NIST asked about how P and Q were chosen early on in the development of the standard is this, which indicates that people were told by the NSA that they were not allowed to publicly discuss the question.

Remarkably, the latest AMS Notices has a new article with an extensive discussion of the DUAL_EC_DRBG issue, written by mathematician Michael Wertheimer, the NSA Director of Research. At first glance, Wertheimer appears to claim that the NSA was unaware of the possibility of a backdoor:

With hindsight, NSA should have ceased supporting the dual EC_DRBG algorithm immediately after security researchers discovered the potential for a trapdoor. In truth, I can think of no better way to describe our failure to drop support for the Dual_EC_DRBG algorithm as anything other than regrettable.

On close reading though, one realizes that Wertheimer does not address at all the basic question: how were P and Q chosen? His language does not contain any actual denial that P and Q have a backdoor.

For a careful examination of the Wertheimer piece by an expert, see this from Matthew Green. Green concludes that

… it troubles me to see such confusing statements in a publication of the AMS. As a record of history, Dr. Wertheimer’s letter leaves much to be desired, and could easily lead people to the wrong understanding.

In a recent podcast on the subject Green states

I think it’s still going on… I think that the NSA has really adopted a policy of tampering with cryptographic products and they’re not going to give that up. I don’t think that this is a time that they want to go out admitting what they did in this particular case as a result of that.

Given that this is now the only official NSA statement about the DUAL_EC_DRBG issue, the Notices article has drawn a lot of attention, see for instance here. The Register summarizes the story with the headline NSA: So sorry we backed that borked crypto even after you spotted the backdoor.

The publication of the George and Wertheimer pieces by the AMS has created a situation where there are just two possibilities:

  • Despite what experts believe and Snowden documents indicate, the NSA chose P and Q by a method that did not introduce a backdoor. For some reason though they are unwilling to state publicly that this is the case.
  • P and Q were chosen with a backdoor, and the AMS has been now repeatedly been used to try and mislead the mathematics community about this issue.

I’ve contacted someone at the AMS to try and find out whether the question of a backdoor in P and Q was addressed in the refereeing process of the article, but been told that they won’t discuss this. I think this is an issue that now needs to be addressed by the AMS leadership, specifically by demanding assurances from Wertheimer that the NSA did not choose a backdoored P and Q. If this is the case I can see no reason why such assurances cannot be provided. If the NSA and Wertheimer won’t provide this, I think the AMS needs to immediately cut off its cooperative programs with the agency. There may be different opinions about the advisability of such programs, but I don’t think there can be any argument about the significance of the AMS being used by the NSA to mislead the mathematics community.

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