mathbabe

Last Friday I visited my high school math camp, HCSSiM, where I became a nerd. I also taught there multiple times over the years, and in 2012 I blogged my lectures.

Why the visit? You see, we loyal alums of HCSSiM have a tradition of going back every July 17th to celebrate “Yellow Pig day,” which consists of a talk where founder and director (David) Kelly talks extensively about fun facts regarding the number 17, which happens before dinner, and then after dinner we sing “yellow pig carols” and eat an enormous amount of cake in the shape of a yellow pig. You can learn more about this ridiculous and hilarious tradition here.

Anyhoo, this year we (I went with other nerds) missed the 17 talk because of traffic in Connecticut but we made it for the dinner and carols. Luckily at dinner I had the chance to talk to Kelly, and I asked him if there were any new 17 facts this year. He told me there was one, and it was slightly mysterious. This post is an attempt to explain it a bit.

The mathematical set-up is explained here. Namely, we start with something called the Ulam Spiral, which is simply a way to label the boxes of an infinite two-dimensional grid with the natural numbers. You start at some place and then spiral outwards from there. Here’s a picture:

The center of the Ulam Spiral

OK, so the first thing to say is that, when you label the plane like this, primes tend to cluster along lines. I think this is what Ulam thought was cool about his spiral:

Primes are black. This is the spiral with 200 layers.

Now comes the observation. You need to know what a triangular number is first, though. Namely, it’s a number that corresponds to counting up how many dots you need to form a triangle. We say the nth triangular number corresponds to a triangle with n rows. Here are the first few:

You can also draw these triangles so that consecutive ones fit together to form squares.

When you highlight the triangular numbers in the Ulam Spiral, instead of the primes, then you get something that looks weird:

Green dots are triangular numbers within the Ulam Spiral.

OK so if you count those spiral arms, you’ll see there are 17 of them. But does that last forever? And if so, why?

Well, the answer is going to be yes. And here’s a rough proof. Rough because it uses asymptotic limits, so technically I will not show that the above picture extends perfectly, but rather that it eventually does look like a spiral with 17 arms.

A famous story about Gauss tells us that the formula for the nth triangular number is

Also, by construction of the Ulam Spiral, the bottom right corner of each “spiral layer” is an odd square, and that if we call that number there will be boxes on the very next layer, corresponding to the 4 sides of the next layer plus the 4 corners of the next layer.

Now imagine that there’s a triangular number right on that bottom right corner. That would mean that for some

or in other words that

This is when things get asymptotic. Imagine that is very very large. That would mean that is too (everything here is a positive integer), and in particular that the term would dwarf the term above. In other words, we could approximate:

My next question is, how many triangular numbers would lie on the next layer of the spiral? Well, as we said above there are spots in the next layer, which we will approximate by  and the triangular number coming after is which is bigger than corresponding to adding one layer to a triangle with rows. We will approximate  by  again ignoring small terms.

For that matter, the next few triangular numbers after come regularly, about spots after the first. Therefore there are about triangular numbers in the next row of the Ulam spiral. That comes out to which is about 2.83.

So far we’ve figured out that, when is huge, then after meeting the th triangular number on the th row, we will see two more, and get most of the way to a third, by going one more row.

Now let’s do that 6 more times. After traveling 6 rows past a triangular number, we will meet about more triangular numbers. But

which is very close to 17. So after traveling the Ulam Spiral for 6 rows, we will just about hit 17 triangular numbers, which will be more or less evenly spaced from each other.

What this means is that we should expect to see a spiral with 17 arms, but that when the picture is enlarged to include a very large number of rows, we will see the spiral shifting very slightly to the other direction.

By the way, I didn’t figure this out immediately. First I had a most delightful time understanding when, exactly, square numbers and triangular numbers coincide. In other words, I wanted to understand when there is a and an so that:

or

I might write this up in another post, but play around with it for a while if you get bored on the subway.

The Occupy Summer School students are organizing a clever demonstration tomorrow morning to protest racial and gender inequality. From the men/women pay gap to how the police arrest black and brown people for minor nuisance crimes, the girls from the UAI have figured out thoughtful ways of raising consciousness while having fun.

The plan is to have two tables. At the first table, there will be a “bake sale” where cupcakes will be “sold” for $1 to men but 77 cents to women, to protest unequal pay. They will be handed over using a plate which details many other kinds of gender inequalities. In actuality, anybody who shows up to the protest can get a free cupcake.

At the other table, we’ll be handing out brownies with toothpick flags, which are toothpicks with facts about racial inequalities taped to them. For example one might read, “While people of color make up about ​30 percent​of the United States’ population, they account for ​60 percent​of those imprisoned.”

Everyone loves free food, of course, but given that black women like Sandra Bland get killed in this country for minor traffic infractions, there’s a deeply serious side to it as well.

If you have time, please join us. The event will take place on Cadman Plaza near Tillary, in downtown Brooklyn, tomorrow morning from 9-11am. The girls will appreciate your visit.

When I was a young idealistic mother, pregnant with my first kid, I had this crazy idea that I’d dress my kids in gender neutral clothing, like they have on Star Trek. In fact my actual goal was to get them Star Trek uniforms, but I knew that might be slightly difficult. It was 1999 and we were all worried about Y2K.

Little did I realize, until after the kiddo was born, how difficult it would be to get anything remotely gender neutral. Especially because I was rarely willing to spend lots of money on clothes I knew would be immediately outgrown, I ended up shopping at places like Toys R Us and similar, and man oh man are those clothes gendered. There’s a pink section and a royal blue and red section. Nothing in between, and no overlap.

Well, things have changed in the past 16 years, and nowadays there are clothing companies deliberately creating kids clothing that doesn’t have the awful princess/superhero dichotomy embedded into every garment. According to this Bloomberg article, there are now pink and purple clothes for boys and dinosaur, pirate, and science clothes for girls. Svaha, for example, sets itself up as a place that makes “clothes that empower your children.” Here’s an example of a girls’ shirt:

There’s also a boys’ shirt, also pink, with flowers and test tubes. That would have been great for my first son, whose favorite color was, as he described it at the time, “light red.”

A couple of things. First, these shirts are $25. That’s approximately 4 times more than these shirts that are standard issue “boy” clothes. Partly that’s just because it’s not a concept that’s really taken off, so we don’t have huge factories in Bangladesh churning out these shirts at ridiculous rates. But even so, it means that, like organic food, open-ended gender categorical clothing is firmly within the realm of the well-off parent.

Second, I don’t think it’s all that reasonable to say a shirt “empowers” a kid. Most times, when a kid is defined externally, through a shirt or a social convention or an adult’s comment, or even another kid’s comment, it’s an exercise in limiting that kid, not expanding him or her. Kids assume they can do anything until we tell them otherwise. When you say to a young girl, “You can be a scientist too, you know!” she thinks, “I never thought I couldn’t. Wait, why should I think I couldn’t?”. It’s not until they’re teenagers that they get this stuff, and can have a critical mindset about it.

In other words, I’m going back to Star Trek uniforms for everyone. The great thing about them is how utterly vapid they are of style or message. If you had to pin a message on to them, it would be an awesome (but distant) future.

Yesterday, as I was accompanying Adam Reich to the Occupy Summer School on the downtown 2 train, he pointed over my shoulder at someone reading a Metro, because the girls were on the front page:

We also were on the second page:

After I got to the UAI, the high school where we run Occupy Summer School, I found the online version of the Metro story as well, which is also exciting.

Since Occupy Summer School (OSS) is half over, I think it’s a good time to update you on what’s been happening.

• Last Monday we introduced ourselves, met the students, talked a little bit about Occupy, agreeable disagreement, and had a discussion about what they wanted to focus on using “stack.” Among the issues they came up with: inequality, Black Lives Matter, taxing the rich, how teenagers are unfairly targeted, and gender issues.
• Tuesday Ale and Mo, a high school activist, came and talked to the girls about activism. We discussed how organizing actually works, what were the props for events, like stickers, flyers, signs and banners, how to get the word out among networks via text or twitter or other social media, and so on. We ended the day by quickly planning a protest against overly lengthy standardized tests.
• Wednesday Tamir’s friends from Local 79 came and talked about unions and union organizing. The girls didn’t know much about unions, and were interested to learn how power can be created through numbers. 
• Thursday Gerald provoked a fantastic discussion on #BlackLivesMatter and related topics. This was the first time where the girls really took over the discussion and the grownups in the room were merely listening and every now and then joining the discussion.
• Friday Marni dazzled the girls with her approach to creative protests. She brought her own entourage, which ended up being how we got into the Metro. The day ended by planning a bake sale where women would be charged 78 cents and men one dollar for the same brownies, to illustrate the difference in pay.
• This Monday I spoke to the girls about “why high school is free but college is expensive,” and then about debt more generally. We ended the day by planning a protest around a $100 ticket one of the girls had gotten for “doubling up” in the subway with her cousin, who didn’t have a student Metro card. The demand was to be unlimited metro rides for high school students on all days, not just school days.
• Yesterday Adam came and talked to them about sociology, what is power (power is the opposite of dependence), and his work helping orgainze workers at Walmart. By the end of it he had two volunteers who wanted to join the cause.

I can’t wait for the rest of OSS! I’ll write another update at the end of next week when it’s over.

As you already know, Puerto Rico is in a debt crisis. It’s unsustainable – take a look at some of the numbers – and people are suffering. There’s very high prices, few jobs, and on top of that there’s a terrible drought as well. I’m trying this week to learn what some of the details are of this situation, which is incredibly complicated because Puerto Rico is a U.S. commonwealth, not a state, and has historically been ignored by the political system.

Here’s what I know. The bond markets for Puerto Rico have historically been attractive to investors because the bonds are “triple exempt,” which basically means no taxes are applicable to them. This made it too easy for Puerto Rico to borrow money and has put it in a hole, very analogous to the Greek situation. And now we have to decide how much the people should suffer for the results of the bond markets.

Yesterday I reblogged a post by Marc Joffe, who argued that the U.S. should extend Chapter 9 to Puerto Rico. Hypothetically this would allow Puerto Rico to declare bankruptcy and restructure its debts in some reasonable way. However, as Kristi Culpepper explained in this Medium piece (hat tip Tom Adams), it actually wouldn’t give Puerto Rico the relief that it needs, first of all because it would redefine Puerto Rico as a “state” but states are not eligible to declare bankruptcy, and secondly because the corporate bonds issued by Puerto Rico’s public corporations have a special status that also prevents them from restructuring.

Culpepper also notes in her piece that people who cry foul at the concept of restructuring debt after it has been issued can rest assured that there is precedent for it. Personally, I don’t even understand that complaint; surely everyone realizes that any debt might go into default, and it hardly matters exactly what that procedure looks like.

Culpepper recommends something else entirely, namely a federal financial control board. The idea is that there’s also precedent for this, in the 1990’s in Washington D.C.. However, it would essentially mean handing over control over its finances to the board. Culpepper notes that this could even happen without consent. I think the Puerto Rican people may have something to say about this. She also suggests we could provide liquidity for Puerto Rico if we wanted, although it might look something like a bailout.

The biggest problem is that, even now, no politician seems to really care about Puerto Rico, except to fight against it becoming a state.

Today I want to tell you about $heriff, an awesome new tool I learned about recently. It’s currently an add-on to the Firefox and IE browsers, but it will be compatible with Chrome soon. I mention this because I think you will want to use it, partly for the good of scientific discovery, but partly for your own good.

Because here’s what $heriff does for you. It allows you to see how prices for goods you’re interested in buying would change depending on where the request is coming from. And sometimes the answer is “a lot,” even on Staples.com or Amazon.com.

I talked to one of the creators, Nikolaos Laoutaris, who works as a computer science researcher in Barcelona. Nikos described how he came across the idea of creating $heriff. Namely, he and a friend were discussing their upcoming vacation to a town in Austria, and they were both looking into booking the same type of room at the same hotel (at the same time, since they were doing it over Skype) and they were seeing very different prices.

The way it actually works is that there’s a way to “check” prices when you come across one, and the results pop up in a separate window. Here’s a screenshot of what happened with Nikos showed me $heriff checking on the price of a fancy camera at digitalrev.com:

The list corresponds to what price showed up when a bunch of servers at academic institutions were asked to send a price request that $heriff extracted from the local webpage. To be clear, your personal request for price, coming from your browser, might depend on location as well as your cookies and referral url, among other things, but these other prices correspond to “clean browsers,” with no browsing history, and no login history, making a request from a specific location. So those price variants correspond to location changes only.

There’s also a space below for “Results from local users,” and this is where you come in. If there’s a person with a $heriff add-on in your local area, the idea would be to use the information your browser collects to allow someone to compare their price with your price. In this way we would (slowly) also learn how prices change depending on browsing history. The more people who use $heriff and donate their data to the project (third party cookies, some browsing history, and prices), the faster we will learn about how prices vary.

Among other things, this could be a way of figuring out how to intentionally set your input data so that you get the best price for a given product.

A few notes:

• Local sales tax and shipping costs are valid reasons for prices to depend on location of the buyer, but they are typically added later, after the prices are shown.
• It’s possible that tariffs come into play, but they don’t seem consistent. Also, the prices vary too much to be accounted for by tariffs.
• Nikolaos Laoutaris and his colleagues have also been doing great work looking into how people are tracked, and how such information is used to steer them into environments of “search discrimination,” which means that which products or offers they are shown changes, rather than the prices themselves.
• Also, he’s part of a cool project called the Data Transparency Lab.

Get started with $heriff or learn more about Nikos’s work, by going here.

Yesterday i had the good fortune to interview Sonja Starr, who has been researching evidence-based sentencing models and wrote this New York Times op-ed on the subject.

If you haven’t heard about them, they are “recidivism risk” models being widely used by judges – in 20 states at least – to help determine sentencing lengths. Different judges will use them differently, but think of them as one factor in deciding how long someone convicted of a crime goes to jail. Recidivism refers to the concept of returning to jail, so high recidivism risk means someone is deemed by this model to be likely to return to jail, and when a judge sees that, they typically put them in jail for longer.

Moreover, the attributes which go into recidivism models are often proxies for race and class, which means that, hidden underneath the computer code, a given judge is essentially putting someone away for longer because they are poor.

So, there are lots of issues, but one thing I asked her to talk to me about was whether recidivism is the right question in the first place. After all, when we consider recidivism we are judging someone more harshly if “people like them,” however that is defined, have recommitted crimes after being in jail. In other words, we are judging them more harshly because we suspect they might commit a crime in the future. This is Minority Report type stuff.

The other side of the argument is that judges are explicitly told to decide on sentencing based on multiple factors, and always have been. Namely:

1. Punishment for the crime that was committed (“just deserts”)
2. deterrence for others who will want to avoid prison,
3. the public good – we want to protect people from criminal acts, and
4. rehabilitation, where we prepare the prisoner to be a well-functioning member of society after they leave prison.

The third goal, that of protecting the public, is where recidivism comes in. If we have good reason to believe the person will commit yet another crime, we want to keep them away from doing so, or even better decrease their recidivism risk with various methods. A few problems, however:

• The models don’t measure the effect of prison on recidivism risk.
• In fact they don’t measure how recidivism risk changes at all.
• The recidivism risk models are probably amplifying that third factor in judges’ sentencing opinions.
• Drug offenders have higher recidivism risks than people who commit violent crime, but we really only care about the latter in terms of the public good.

After thinking this through, I’m pretty convinced that, aside from using problematic inputs in recidivism models, we need to carefully examine how we want to weight those four factors.

Occupy Summer School is going great! Hopefully today we’ll start a blog of some sort to document the goings on. And, as promised, I don’t have a lot of time.

However, I did want to share this with you, keeping in mind I have no idea how representative it is:

Quick question: how often did women of yore get leather stains on their light colored hosiery? Is that really a thing?

I’m very excited for the first day of Occupy Summer School. It will run for three weeks, every morning, in downtown Brooklyn, so I’m not sure how much blogging I’ll be doing. Hopefully I’ll find time to document some of what’s happening. We’re very excited about the line-up, and we have high hopes for the final event.

Today we introduce the kids to ourselves and Occupy, we talk about the next three weeks, we ask them to introduce themselves to us, we ask what they are planning to get out of the experience, and of course we eat donuts.

Readers!! Dear friends! Aunt Pythia is overwhelmed with happiness. She is currently sitting in the middle of the woods scribbling away inefficiently on an android tablet, doing her best to deliver a knock-out advice column for your reading pleasure. It’s absolutely nuts that she can accomplish this fear considering her environment, but that’s just how much she loves you.

Definitely not as hot as Manhattan.

Please enjoy being rustic with Aunt Pythia!

Oh, and before you leave,

ask Aunt Pythia any question at all 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 Aunt Pythia,

Do you dream of composing the perfect Aunt Pythia question, complete with awesome sign-off? I guess you don’t, but maybe you have the same issue with Dan Savage?

That’s my problem. I just can’t stop obsessing and find myself so jealous of the problems of others. Why can’t I be “an intellectual property lawyer, who is launching a big data business with a former colleague/lover, who has just given up lesbianism and decided to become a man, and who can’t quite decide on how to deal with her residual feelings of attraction for said business partner”?

Or, what about wanting to be able to write “I’m completing my junior year majoring in Clown and, while I would love to go to graduate school, just feel I don’t measure up against my classmates who are so ahead they’re already working on Advanced Buffoonery  and researching theoretical foundations integrating hijinks, pratfalls, and farce. I feel like a Paul Reubens amidst all these future Lucys. Can I make it?”

With awesome problems like those, how can my mundane life make it onto the hallowed pixels of an AP page? I’m afraid I’m going to start creating a mini-crisis in my life, just to have some entertaining material for you. Help!

Lousy Sign-off Doesn’t Trump Really Interesting Person

Dear LSDTRIP,

I just can’t believe I figured out how to copy and paste on a tablet. Very excited over here.

Great sign off by the way. I get the impression it’s accurate as well.

Here’s the thing. You don’t need complicated problems. Asking how to feel happy or even non suicidal in the midst of everyday life is already hard and interesting. And I would prefer genuine kindness over being entertained any day.

As for the question of whether I dream of asking question, no. I have always wanted to give advice more than ask it. Probably a personality defect but there it is.

Aunt Pythia

Aunt Pythia,

I have a math question. I am writing a series of short stories, based the Many-worlds theory of Quantum Mechanics. The stories postulate (in contrast to current theory, science fiction, you know) that there is a way to pass information between universes. Naturally in an infinite number of universes, some, an infinite number, use this technology, like painting, photography, writing, mosaics, film, TV, and the Internet, for porn.

My questions is, if the resolution of every quantum event creates at least two new universes, what is the cardinality of that infinity? It seems like aleph-null but it’s been a long time since my last legitimate use of infinities.

No cats were harmed in the forming of this question.

Slim Odds And Possible

Dear SOAP,

Is this the day for weird questions? I mean don’t you need to tell me what a quantum event is and how often to expect a quantum event? Does it happen every time someone passes porn between universes? Even if that is the case I would need to know there are a positive number of horny people in existence.

Unless I am being dumb, I don’t have sufficient information here.

Aunt Pythia

——

Aunt Pythia,

I think I’m in love with my best friend. She told me about a year ago that she wasn’t interested in romantic relationships because her ex-boyfriend hurt her / she hurt him / they had a bad breakup. I haven’t told her my feelings, because of a variety of reasons, including I wanted to tell her in person (we live on opposite coasts of the US), I don’t want to hurt her (she is going through some serious stuff right now, and I don’t want to add to that), I have literally zero romantic experience and I don’t want to fuck things up with her (I kind of feel like I’m going to fuck up my first few relationships), and last but not least I’m bad at talking. We’re going to college together next fall. I want to tell her at some point in the future, because of some kind of honesty idea and also it seems unfair to try and get rid of these feelings without asking her. What do you think I should do?

Having Equanimous Love Problem

Dear HELP,

First of all thanks for the perfect sign off and straight forward letter. Although not sure you are equanimous.

Next, believe me, you are in love. No need to say you think maybe you are. Babe, you got it bad.

Third, you want to tell her because love demands it of us. It has nothing to do with a sense of honesty or fairness. Love has its own logic, or illogic, and we are slaves to it. That’s OK.

Seeing as you asked, I say go for it. Make it happen my friend. Which is to say: tell her you love her in a dramatic and romantic and absolutely unmistakable way. Be that guy who really spills out his guts and lays it on the table.

You know what there isn’t enough of nowadays? I’ll tell you what. Gut spilling. We are all so careful not to offend or appear vulnerable we forget that none of that really matters. What really matters is living life fully and taking chances and going out on a limb and being the person you always wanted to be.

And here’s the thing about it. It’s not really a risk. If she says no you will be crushed, to be sure, but in fact you will be crushed if you say nothing. It will just take longer and feel less courageous. Also she’s your best friend so I imagine we can trust her not to be cruel.

Tell me how it goes, and good luck!

Aunty P

P.s. nobody has experience at your age.
P.P.s. if you’re worried about talking then write a letter of a song or a poem.
P.P.P.s. ignore her bad ex. Everyone gets over their bad exes eventually. Plus it’s been a year. Don’t ignore her current problems though. Just tell her how much you want to be there for her.

——

Aunt Pythia,

We clearly have a long way to go still for getting more girls and women into STEM careers, but there has been a lot of progress as well. For example, my department has a pretty M/F balanced group of faculty and grad students. I also notice there are various programs and events for women and minorities in mathematics, which appear to build some lasting professional relationships and you know, like,  friendships.

My gripe is that many of these programs are *exclusively* intended for women, leaving minority men, especially black men, out in the cold while universities are patting themselves on the back for publicly fulfilling their diversity initiatives. I don’t think there’s a great conspiracy behind this, just that there aren’t very man black men in STEM fields, particularly math, to let everyone know- Hey! We’re here too!!

Comparatively, women, black women, uh literally any other group you could reasonably get higher education statistics on, is doing better than we are. Most of these programs aren’t helping us, and I know of none specifically designed for us. You probably know the statistics better than I do, but according to this article [http://chronicle.com/article/Black-Man-in-the-Lab/149565/] from 1992-2012 there were only 203 black men that got math PhDs. Wait, in 20 FUCKING YEARS?? Please be a typo. One black guy per year in the ENTIRE COUNTRY has been getting a math PhD for two decades…? JESUS CHRIST ON A STICK, THAT’S SOME FUCKERY, PLAIN AND SIMPLE. No really, I have to be making some kind of error somewhere.

Of course, these are just averages; the actual count probably is trending upward and probably increasingly so from 2012-2015. JUST NO, VOICE OF STEADINESS AND REASON, TODAY YOU CAN STFU, YOUR SERVICES ARE NOT NEEDED. Why? For one, these numbers include graduates of historically black colleges and universities, which are disproportionately represented. I’m not saying that’s a bad thing, but if a sizeable chunk of the 203 PhDs are concentrated in these schools, then of course the rest have fewer than expected PhDs produced, and the baseline was already at WTF.

There’s nothing wrong with that, but as black guy interested in math, I don’t want to go to the black school I want to go to the math school; no offense to Howard, but I’m aiming for Harvard. The article then says, for all STEM degrees combined, there was an upward trend from black men making up 1% of all PhDs awarded in ’92 to 2% in ’12. If you have no soul, you can convince people of improvement by saying it doubled, but it’s still really, really fucked. So (finally) my question is: Given the obvious need, why isn’t there a program similar to Edge for men in math from underrepresented groups?

P.S. Who lets the mathematicians of the African diaspora website remain on the internet? It’s hella embarrassing.

Randomblackdude

Dear Randomblackdude,

I’m with you. Those are some outrageously low numbers. And I don’t know what resources there are out there but clearly not enough. Maybe my readers will fill us in. Also agreed about people who deliberately mislead with statistics having no soul.

Aunt Pythia

——

People, people! Aunt Pythia loves you so much. And she knows that you love her. She feels the love. She really really does.

Well, here’s your chance to spread your Aunt Pythia love to the world! Please ask her a question. She will take it seriously and answer it if she can.

Click here for a form or just do it now:

Some of you may have stumbled across the New York Times’ recent Room For Debate, addressing the pursuit of happiness. Short and insufficient summary:

1. William Davies: Once you focus on optimizing happiness, you will be asking for trouble. At the individual level, optimizing for happiness will be used against us at work. At a higher level, it will be a form of social control.
2. Bina Agarwal: We need both objective (GDP, health) indicators and subjective (happiness, satisfaction polls) to measure the progress of nations.
3. Barbara Ehrenreich: Happiness scores can be easily tampered with, and rarely gets at the concept of accomplishment of goals.
4. Sonja Lyubomirsky: Don’t measure happiness too much, but don’t forget to measure happiness, because it’s good for you.

I found the conversation frustrating. I’ve been thinking about happiness a bit lately, and it strikes me that the above conversation is entirely muddled because of its lack of precision. There are different kinds of happiness, and only the third debater, Barbara Ehrenreich, really touches on that.

So, at the very least, there’s hedonic pleasure, and then there’s eudaimonic pleasure, which basically correspond to short-term versus long-term. Hedonic joy comes when you see a naked body or you eat doritos. It can also happen when you see your child laugh or enjoy the smell of garlic. In other words, it doesn’t have to be bad for you, but it is a form of short-term sensation.

Eudaimonic joy happens when you feel the pleasure of some kind of longer-term accomplishment. Aristotle invented this concept, deeming happiness vulgar, and stressing that not all desires are worth pursuing as, even though some of them may yield pleasure, they would not produce wellness. We experience eudaimonic joy when we clean our house, when we gain understanding of something that was elusive, or when we spend “quality time” with our friends and loved ones. It’s anything that gives us pleasure and contributes to our goals.

Now that we are equipped with these terms, the above debate is easier to parse. And of course the debaters weren’t given very much space for their arguments, so I’m not suggesting they don’t know this stuff, but it’s still helpful for us readers.

Barbara Ehrenreich’s point is that hedonic pleasure, being fleeting, is also easy to manipulate; at the same time, when we are asked whether we’re happy, we often interpret it to be some combination of those two kinds of happiness, with possibly random weights assigned to each. Right after I get off a roller coaster I’m more likely to be thinking hedonic pleasure, right after I listen to a poetry reading, or take a nap, maybe I’ll be more interested in the eudaimonic kind.

William Davies, on the other hand, is mostly discussing hedonic happiness, because in terms of brain chemicals, we can measure the stimulation of the pleasure centers of our brains, and we can manipulate people based on those measurements. Davies imagines a world where our corporate masters have a perfect view into our brains and have figured out how to stimulate our pleasure centers so that we are maximally “productive.” This approach is deliberately unrelated to our eudaimonic pleasure, because it’s not focused on our long-term goals, but rather the goals of our employer.

Bina Agarwal seems to want to understand eudaimonic happiness but is making do with the random mix, and Sonja Lyubomirsky seems to confuse “trying too hard to be happy” with focusing on hedonic happiness.

We could get better data and better debates around “happiness as a thing to strive for or not” if we distinguished between short-term happiness and long-term happiness. It’s not that hard to do, and it obviously matters.

You might have heard about Sidewalk Labs, which is backed by Google and plans to repurpose phone booths all over New York City as wifi hubs. They are also planning to install large advertising screens on the sides of the phone booths to display dynamic advertising to passersby. A few comments and questions.

• When you use that wifi, they can track what you do.
• Even if you don’t use it, if you walk by with a wifi-enabled device (smart phone), the phone booth will sense your device and tag you.
• Presumably this is not charity. They will expect to make ad revenue with their screens.
• Best guess: they will tailor the advertisements depending on who is walking by and what they’re doing.
• The overall negotiation then is that we are willing to exchange free wifi for having our experience in a public space tracked by a private company. I’m not sure we are all thinking that’s a good deal.
• They plan to do it in other cities, using street lamps and bus shelters as well.
• Prepare to enter into a realm of existence one step closer to Blade Runner.

Last Sunday I had the pleasure of meeting Anna Bernasek and Dan Mongan, who came to the Alt Banking group meeting to tell us about their book All You Can Pay: How Companies Use Our Data To Empty Our Wallets.

While they were discussing their book, the topic of online advertisement naturally came up. Dan and Anna made an interesting point in that discussion which I’ve been chewing on ever since. Namely, they provocatively suggested that we should never use the word “advertising” to describe the complicated and sophisticated process of tailored and targeted offers to an individual internet browser. Instead, we should call it a “negotiation.” Let me explain their reasoning.

They started by introducing the concept of a “consumer surplus.” This is the difference between what a given consumer would be willing to pay for a product versus what the price actually is for that product. If the difference is positive, the consumer buys the product and has a theoretical bit of “extra” money in their wallet, which corresponds to the happy fact that the price was lower than their maximum price. If the difference is negative, the consumer doesn’t buy the product because it’s too expensive for them.

Does that make sense? For me it only kind of makes sense. I mean, it makes quite a bit of sense for certain situations, like when I’m buying something I don’t actually need, out of funds I consider limited but discretionary. So, for example, after my soggy experience a couple of weeks ago I threw away my faulty tent, so I’m looking at buying a new tent, but then again I’m not going camping any time soon, so the price has to be right.

Here’s an important example where it doesn’t make as much sense. If I’m poor and I need a car to go to work, and I know I have to borrow money to buy the car, then the amount of the loan is less important than the fact that I can get a loan in the first place. The “consumer surplus” is less obvious when it’s a matter of debt rather than cash, and when it’s a desperately needed purchase rather than discretionary.

Anyhoo, let’s imagine consumer surplus to be a thing that people consider useful. The point Is, big data companies are getting better and better and determining or at least approximating what a given consumer’s surplus is, and making offers accordingly.

So, if you’re on a platform where there are advertisements, the algorithms behind those offers might infer that you have a certain amount of money to spend on a car or hotel, and might offer you certain models of cars with or without leather seats, or hotels in certain neighborhoods priced in a certain range, to squeeze out your consumer surplus. Yes, there might be cheaper versions of these things that you’d be happy with, and that would save you money, but the algorithm has determined your spending power, which is all they care about.

Thus, instead of an advertisement, which sounds like something we imagine many many people see, this is a personalized negotiation, just to you personally, and crucially, you don’t see what other people are being offered. So it’s a one-sided negotiation with enormous information asymmetries.

Note this is the opposite of what we’d expect in the “free market,” where all the offers are on the table and you get to choose the one with the lowest price. Partly we ignore that vision because many of the platforms we now spend time on are more or less monopolistic in nature, and partly it’s because of the nature of the auction system of advertising: the “ad” for a more expensive hotel room, that’s still in your price range, will win an auction because it is worth more to the seller.

I think it’s a pretty good distinction, although I’m not sure “online sale negotiations” is a catchy enough phrase to replace “online ads” any time soon.

I recently had a weird and negative experience applying for a job.

I went for standard the day-long interview, and answered a bunch of questions, and met a bunch of people, maybe 9. In one of the interviews, they asked me how I would approach some of the data questions they were working on, and I gave them some spur-of-the-moment advice. In one case I exactly outlined the approach they were actually taking. All this is fine, and to be expected.  In fact I felt like the interview had gone well, and I had liked and been liked by most of the people I’d met.

Then, when I was about to leave for the day, they told me they wanted to send me “homework.” This is not something they had mentioned to me beforehand, but I was exhausted from the long day and I responded in a vague way, something like, “um, OK, well, I’ll take a look.”

When I eventually got it, the homework was very open-ended and very very hard. In fact I was guessing that it was probably an NP-complete problem, although I didn’t look it up (although I’m sure I could have, which is also weird). Moreover, it was directly relevant to the company’s business.

I felt like it was a fair question for them to have me work on if I had been hired, but it seemed too much to ask for me to work on it before then. Moreover, I was (and still am!) working very hard on my book, and I’d already given them a full day of my time. It seemed like they wanted me to give them free consulting in addition to applying for a job. I decided to write back to them and tell them I was very busy, and that I’d rather not do this homework “unless it was a dealbreaker.”

Here’s what happened next. First, the person who had sent me the homework told me it wasn’t a dealbreaker, and that I’d hear back soon. Then, nothing happened. Nothing at all. I didn’t hear from them for weeks, so I figured that was all the news I needed to know.

I finally wrote to a friend of mine who worked there just to say, hey, no hard feelings, I hope you’re well. By then I had totally given up on the job, but he was curious as to why. After telling him the story, the next day I got an email from his boss’s boss explaining that he had been waiting for me to go ahead and do the homework, and that he was disappointed I hadn’t been willing to. So it had been a dealbreaker after all.

So my question to you kind folks is this: when does an interview, and homework afterwards, become free consulting? What are the standards? Do you think I should have done the homework? Do you think it was unreasonable for them to ask of me? Or do you think it was OK for them to ask me but not OK for them to mislead me about whether it was a requirement?

I was interviewed for an article entitled No Child Left Un-Mined? Student Privacy At Risk In The Age Of Big Data by journalist Farai Chideya, who writes for The Intercept along with Glenn Greenwald and other impressive people.

Here’s the article, I think it came out pretty well and I’d be grateful for your thoughts.

Readers! Dear readers!

Today is such a wonderful day for lovers everywhere. We are celebrating love in all its forms. As part of the that celebration, Aunt Pythia has decided to knit up something appropriate:

Actually, she just loves rainbows. Always has. She finished this recently though.

Many apologies for missing last week’s column! Aunt Pythia was busy getting stung by mosquitos and dripped on by a soggy tent at the Clearwater Festival. Next time she’s definitely taking the Aunt Pythia tour bus:

Most likely waterproof.

Are you all ready?! Let’s do this thing! We’ve got some doozies this week, folks.

Oh, and before you leave,

ask Aunt Pythia any question at all 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 Aunt Pythia,

My kid is a math whiz, and we will soon be doing college tours. I would love to find a program that teaches him to use quantitative skills in an applied, team environment. Any suggestions?

Mom Asking Math Advice

Dear MAMA,

First, who wants him to be applied? Who wants him to work as part of a team? Is this something you want, or he wants? I hesitate to give advice to parents about their child’s goals when their child is embarking on adulthood. And, being a mom myself, I completely understand that you want them to go to a college that suits them, but at the same time, let’s make sure they have agency as well.

OK, now I will assume that yes, your son wants very much to find such a place. In that case, I would suggest at least looking into Worcester Polytechnic Institute. I have a friend named Suzanne Weekes who is a professor there and also directs the Center for Industrial Mathematics and Statistics. Whenever talk to her about her job she mentions various team projects on applied subjects that she has her students working on. They sound great, and fascinating, and it makes me want to go back in time and go to WPI.

And even if that isn’t the right place for your son, take a look at the kinds of things that the CIMS does. And good luck to your son!

Aunt Pythia

——

Dear Aunt Pythia,

After reading the article you referred to in your answer to PORN NOT SCORN, I am somewhat suspicious of the first item. It seems self-serving for big-name porn actresses to recommend sticking with the big labels such as those that they themselves work for. My own feelings about porn mirror yours: the vast majority of it turns me off even when I don’t think about how it was made. And I share your concern that sexuality as depicted in porn, as opposed to desire and pleasure, would drive expectations of inexperienced lovers. I have a question about a porn-related phenomenon you seem to have either missed or chosen not to comment on in your answer.

There is a huge and fast-growing “camgirl” segment of the industry, using the internet and webcams for real-time conversations and interaction between sex workers and their customers. The article you referred to actually mentions “camgirls” briefly, and some of the points about subscription websites are similar. There’s an older article in the New York Times taking an in-depth view at this phenomenon. There is also a response from the camgirl interviewed for that article and more recently an indie documentary interviewed lots of them.

As someone who strongly dislikes porn, I have been surprised that interacting with camgirls has become a significant part of my sex life. My wife and I both value how it alleviates stress in our relationship, caused by a discrepancy between how frequently she and I want sex, while avoiding some of the concerns we both have about open relationships. The interaction with these camgirls isn’t just about sex and money, though. Over time, I have gotten to know a few of them very well indeed. I could call it an extreme form of the advice about porn to “stick with performers you know”, but that misses how well they get to know me in return.

I am curious how you feel about the potential for developing a biased view of female sexuality resulting from that kind of interaction. The women choosing this work are not at all a representative sample of women, and there are strong incentives for them to try to please their customers. But they are real women, and in my experience many of them do really seem to love their jobs and to take seriously that they have an educational role in helping their customers explore female sexuality.

Curious About Masturbating Females’ Autoerotic Needs

Dear CAMFAN,

Wow, lots of thoughts, and I don’t know where to start.

As for the camgirl industry, I read the first two things, but I don’t have time for a movie, so I’m going to have a pretty narrow perspective. That said, it’s interesting, and obviously complex. I also think the articles do a good job of pushing back against the assumptions that anyone doing stuff like this must be unhappy and desperate. Obviously not true.

As for your letter, I’ll take it on in no particular order.

First, it seems a tad arbitrary to me that you and your wife are comfortable with you getting to know camgirls but are uncomfortable with an open relationship. If I read your letter correctly, it’s the intimacy between you and the camgirls that makes it feel to you like it’s not yucky, but that intimacy is the very thing I’d expect your wife to be threatened by. Is it because you feel like, due to the payer-payee nature of the relationship, this could never become serious? Do you actually think it’s true? From my experience, actual physical sex is not the threat to marriage, intimacy and feelings are.

Next, let’s talk about the act of being a camgirl. From your sign-off, I’m interpreting most of these acts as being more or less shows where girls masturbate live on camera for a single man or a crowd of men. My reaction to that set-up is, wow, what if you don’t feel like masturbating? You still need to put on a show to earn the money. It’s your job. So right away I imagine that sometimes, even in the ideal situation where a camgirl likes her job, she’s not always authentically horny, because that would be just very unlikely. That makes me unattracted to the whole business as far as the female sexuality that it exhibits.

Finally, to your question of whether it creates a biased view of female sexuality, I think I’ve kind of answered that. Imagine if a camgirl got on camera and said,

Hey guys I’m actually not horny right now, and even though I often really enjoy being an exhibitionist, and it really turns me on, tonight I’m just not in the mood. OK if we just make popcorn and watch a movie?

That’s not going to happen, because what you’re seeing isn’t reality, it’s a performance. These women don’t want to ruin their brands by admitting they aren’t horny, and why would they. It’s not a criticism of camgirls, it’s a statement of fact. But the other side of that coin is, if the men (and I assume, some women) who watch camgirls think they are interacting with the camgirls in an authentic way, they will of course have very biased views of what women and their sexualities are actually like.

Having said all that, let’s assume that you understand that not only is there a selection bias for the kinds of girls that do cam, but also that even a girl who does cam is sometimes just performing and isn’t actually genuinely turned on. That doesn’t mean you can’t learn something about what women actually like sexually. That of course will depend on how much a given camgirl explains to her audience, and of course such information might be quite biased as well, depending on what brings in more tips. After all, it’s a business!

Aunt Pythia

——

Dear Aunt Pythia,

Just curious about your thoughts on the Columbia sexual assault story involving the student carrying around the mattress (I’m not involved in it, I’m not even at Columbia). If you were Columbia (or Lee Bollinger, in particular), what would you do? Would you allow her to carry the mattress around, or at graduation? Do you think it is creating a hostile environment, especially for the accused guy? Your thoughts on the guy’s lawsuit?

And what about Kirsten Gillibrand bringing the mattress lady to the state of the union address…do you think that was a mistake on Kirsten’s part?

Lee (not really)

Dear Lee,

I haven’t followed the story closely enough to have a very nuanced opinion, but I’ll say a few related things.

1. It’s absolutely true that campuses, at least historically, have tried to put the hush-hush on sexual assault. I know this from being at Harvard in the late 1990’s. The problem is that there’s an obvious conflict of interest for campuses. They want to preserve their image, and seen that way it seems dumb that they are in control of such issues at all.
2. The reason they are in control is multi-faceted but includes the fact that towns often don’t want to pay for policing of campuses, and because campuses often don’t think town do a good enough job so they take over. Let’s focus on the second point, although the first point is sometimes important.
3. So, instead of focusing on how college students are treated after they are sexually assaulted, and how the accused is treated, I want to raise the issue of how we deal with rape and sexual assault as a society. What are the standards of proof and evidence for sexual assault and rape for the police? Why are so few rapes reported? How do we spot sexual assault? How do we protect children? How do we make this a priority for the nation? RIght now the general statistics are terrible.
4. I guess another way of saying that is when the police are good at this outside of college campuses, then we won’t need to rely on college administrators to do this. We’ve got a long way to go.

Aunt Pythia

——

Dear Aunt Pythia,

I’ll be attending a math conference this summer in Utah. According to a blurb they sent out, it says:

“Participants who request residence hall accommodations will be housed in dormitories on the University of Utah campus. The rooms are suite-style rooms where a bedroom and a bathroom will be shared. Each person is reserving one bed for one person, and will be paired with roommates within his or her gender.”

I feel this is so old-fashioned. Why do roommates have to be of the same gender? I think everyone should have their own room and have some privacy. A part of me also wants to stick up for transgendered people and make a point that there are not just two distinct genders, but that there is a continuum. What should transgendered people register as? I am biologically male, but have feminine traits both emotionally and physically (although the plumbing is male) (and btw I’m attracted to females) and much rather prefer hanging around women than men although I can’t figure out whether it’s because I’m attracted to women or because I can relate better to them on an emotional level. Since gender is a social construct, I want to register as a woman. If anyone asks or objects, I’ll say I’m confused about my gender, consider my brain to be feminine, and I am transgendered. This is going to be super awkward, but that will stir up controversy and discussion. What do you think of this?

And what about all these conferences or clubs for women (like the Harvard Women in Computer Science)? I love women, and think of myself as a woman, but am biologically unquestionably male. Are transgendered people allowed to go to these conferences/events if they self-identify as feminine? If I’m a male and show up, what are they going to do? Arrest me? Check my plumbing and then disqualify me? And if I claim my brain is feminine (which I actually kind of believe) how are they going to check that?

My main point is that for administrative purposes people introduce categories like race and gender, as if these are well-defined categories, but they are not (this idea I think is pretty well known).

(Algebro) Geometric Isomers

Dear GI,

Hey, great questions! I’ll take them in order.

First, I think you totally should tell them that you identify as a woman and want to share a room with a woman, even though biologically speaking you’re male. I know that when I was attending math conferences I would have preferred to share a suite with you than with some random person: you sound interesting! And yes, the math community should be shaken up a bit, it’s old-fashioned for sure.

Second, about the women’s groups. I think it depends. For example, Barnard College recently announced it would accept transgender women. That’s cool!

On the other hand, a given STEM group for women might – at times – be discussing the exact issues that you wouldn’t relate to directly, since you present as male. Such as being told you got into grad school because you’re a girl and standards are lower for girls, to name one. That doesn’t mean you wouldn’t be able to relate to such issues at all, nor does it imply that such groups wouldn’t want you, but I think you should understand that it’s a tricky issue, because they want a community that understands such issues and has a safe place to discuss it and create strategies.

Anyhoo, the world is changing quickly, and these issues are being discussed quite deeply right now, and I’m looking forward to all of us sorting through them. And I’m very much hoping that you will be one person who helps drag the math community into this new era. Good luck!

Aunt Pythia

——

People, people! Aunt Pythia loves you so much. And she knows that you love her. She feels the love. She really really does.

Well, here’s your chance to spread your Aunt Pythia love to the world! Please ask her a question. She will take it seriously and answer it if she can.

Click here for a form or just do it now:

Chapter I

I walk down the street.
There is a deep hole in the sidewalk.
I fall in.
I am lost… I am hopeless.
It isn’t my fault.
It takes forever to find a way out.

Chapter II

I walk down the same street.
There is a deep hole in the sidewalk.
I pretend I don’t see it.
I fall in again.
I can’t believe I am in this same place.
But it isn’t my fault.
It still takes a long time to get out.

 Chapter III

I walk down the same street.
There is a deep hole in the sidewalk.
I see it there.
I still fall in… it’s a habit… but,
my eyes are open.
I know where I am.
It is my fault.
I get out immediately.

 Chapter IV

I walk down the same street.
There is a deep hole in the sidewalk.
I walk around it.

Chapter V

I walk down another street.

– Portia Nelson

Lately you’ve seen a string of articles about how women say sorry too much. We’ve got yesterday’s New York Times opinion piece entitled Why Women Apologize and Should Stop, we’ve got Amy Schumer’s amazing-as-always skit on accomplished women apologizing for everything including existing, and even academics are weighing in.

This is not my problem. I don’t apologize as an automatic response. I learned that early on, when I got my first teaching evaluation; I had apologized exactly once to my (all female) class about not being prepared, in a summer semester where I met with them daily for 10 weeks, and at the end of the summer they all mentioned that I came to class unprepared. I had never come unprepared a second time, nor had I ever mentioned being unprepared a second time. That experience cured me of apologies more generally.

But I remain curious about how men and women perceive things differently, in terms of politeness. That’s why I play chicken with men on the street. I’ve been doing it for years, and I’ve collected a LOT of data.

It’s actually not fair to say that I do it “with men,” since I do the same thing with women. But it ends up being something that only actually comes to something with men. Let me explain.

I live in New York City, and I don’t own a car, so I’m always walking on the sidewalks. I’ve been here for 10 years, and after a couple of them, I thought I noticed a pattern. Namely, that I found myself moving out of the way for men far more often than I found myself moving out of the way for women. Now, it needs to be said that there is a certain amount of ballet-level choreography that one learns when one lives in a busy place, and it mostly happens at an unconscious level. Which is to say, most of the time you make a kind of tacit agreement with someone who is walking towards you, that you’ll move slightly to the right, and so will they, and there will be no bumping. That’s something we do so often and so thoughtlessly. We hardly notice such things.

In fact, it’s only when that unspoken agreement doesn’t happen that we notice. And it’s often unclear why the agreement failed. Did I come out of nowhere? Was the other person checking their phone? Were they lost in thoughts?

Anyhoo, after some thought, I decided to start an experiment. I would choose a moment when I am walking in broad daylight (no visibility problems) and when someone else is walking directly towards me, by all accounts looking around themselves (no distractions by cell phones or the like), and moreover where there was plenty of room to do the “silent tacit agreement” thing which we all learn to do as New Yorkers.

Once that scene was set, which actually happens multiple times every day as a New Yorker, here’s what I’d do next: I’d mimic the person coming at me. If they moved to the right, I would too, as soon as I could react to their movement. It was nearly simultaneous. I’ve become very good at reading body language and knowing when they would swerve, and swerving myself. It’s almost always like that, and those are valuable data points. Let’s call those successful games of chicken, where nobody gets bumped.

But sometimes there are unsuccessful games of chicken. This is when I am fully prepared to move out of the person’s way, but it never happens. I never see their body acknowledging mine, and getting prepared to move out of the way. And, as part of my data-collecting experiment, whereby I mimic that person, I also never move. What ends up happening is a bump. I’ve never gotten hurt, and neither have I ever hurt anyone, because that’s not the point. The point is to see who is ignoring common courtesy.

And, as you might have anticipated, it’s predominantly men. White men. Women, all women, and black and Hispanic men all get out of my way, especially Hispanic men, as do most white men for that matter. But there is a certain subcategory of white men that just don’t seem to know the rule about mutual accommodation, and the result is I’ve bumped into hundreds of white men on the streets of New York over the years. Some of them even turn around and say things like, why didn’t you get out of my way?

Just to be clear, this is similar but not the same as a phenomenon known as manslamming, whereby one refuses to move out of the way for anyone. That’s much more rude, and I don’t do it. To be clear, I move out of the way in almost all interactions.

I’ve told people about my experiment, and they are sometimes offended by it (other times they find it hilarious, or want to try it themselves). They often suggest that certain people are simply lost in their own thoughts, and shouldn’t be bumped because of that. But I think the question is, who gets to get lost in their thoughts on a busy street? Getting lost in one’s thoughts is a form of carefree behavior that only certain people have regular access to.

Also, mitigating factors: I’m a white woman. I have no idea how this experiment would play out for other people. Also, I’m a large person. I’m also not sure if small people would have the same experience. I’d love to hear from other people.