Tuesday, October 13, 2015

The Q-Test: What's Cute, and What's Not?


This post is about a survey I created on October 12th, 2015. I encourage you to make sure that you take the survey before you read any further.

It was Thanksgiving Sunday in 2015, and I was at a café with my extended family. There are some babies and toddlers in the family, so I brought up the topic of Sophie the Giraffe, a wildly popular toy designed for babies to chew on while their teeth are growing in. My aunt Andrea looked it up on her phone, and thought that the design looked terrible -- she said it was creepy, and that Sophie's lifeless black eyes reminded her of a shark. ("A cute shark, perhaps?" I suggested to no avail.)

(Above: Sophie the Giraffe. Photo courtesy of Toys R Us. Used for educational purposes)

This surprised me. I thought Sophie's designed seem rather cute and harmless. I asked some other relatives, and many of them agreed: Sophie's eyes looked disturbing, like an alien.

This puzzled me, enough that I was still thinking about it when we had finished Thanksgiving dinner. It interested me partly because I've drawn cartoons in a professional capacity (in that I have been paid at least once in my life to draw a cartoon) and partly because of my interest in psychology. You would think that cuteness would be a universally agreed upon thing. It's an emotion we feel in order to motivate us to take care of our young, isn't it? So, shouldn't we all find the same things cute?

Sophie's face uses what I thought was a universal recipe for cuteness: large pupils, eyes far apart. It's what you see in many popular emojis, cute logos, and in cute baby animals of almost any species.

(Above: A baby sloth, courtesy of your-daily-baby-sloth.tumblr.com. Used for educational purposes.)

I asked my relatives what they would do to make Sophie cuter. They showed me examples of cartoons and designs they considered to be cute, and they all had eyes closer together with smaller pupils. I don't hate that design, but done poorly, it seems kind of tacky to me. Indeed, it describes almost all of the results that come up when I look up "bad cartoon clipart" on Google Images.

(Above: The result of an actual Google Image search. If you look in the upper-right corner, you can see remnants of my research for the previous photo in this blog post.)

My theory, although I didn't dare say it out loud, was that the older family members would prefer small pupils close together, and younger family members would prefer large pupils far apart. I wasn't sure why yet, but it seemed like a reasonable prediction, especially since it seems to be the younger generation that's always using emojis and sharing photos of baby sloths on the internet. So, I performed a little survey of everyone in my family, or at least, everyone who was at Thanksgiving dinner that year. I drew two simple cartoon faces, one with tiny pupils and eyes close together, and one with big black pupils and eyes far apart, as follows:

(Above: A scan of the paper towel I quickly drew the faces on. The words "Left" and "Right" are primarily for my benefit. I've written down the names of each family member, but I trust that my crappy handwriting will help maintain their privacy. You can see my note to myself "Facebook Poll?" at the top.)

The left face got 14 votes. The right face got 12 votes. I was surprised that it was so close to a 50-50 split, especially since some of my family members were very passionate on one side or the other. I mentioned that my aunt Andrea thought the right image was creepy, and some other family members said it looked like an alien. On the other hand, a few of my cousins said that the right face was cuter by far, and that the left one looked creepy.

The participants included my first cousins once removed, Lyla (age 5) and Luca (age 3). Lyla said that the one on the right was cuter. Luca preferred the one on the left, because it reminded him of Cookie Monster.

I wasn't able to immediately figure out whether age was a factor; the factions didn't neatly divide the older generation from the younger generation.

There were some flaws in my methodology. For one thing, my strategy was to go around and ask people what they thought, while they were distracted by other things, and while other people were listening to their answers. This might have affected their answers.

In addition, when I drew the two pictures, I was really changing two variables, which is a no-no in science: I was changing both the pupil size, and the distance apart. If I wanted to get some decent findings, I would need to use four faces, not two.

So, I decided to set up an online survey.

The Survey

On the morning of October 12th, I taught myself to use Google Forms to create a survey and post the link on Facebook so my friends could see it. The survey centred around four smiling faces I drew with MS Paint. I assigned them the arbitrary numbers 1 to 4.

This forms a more complete set of possibilities than the two I drew on the paper towel. You can see that I've included large pupils far apart (1), large pupils close together (4), small pupils far apart (2), and small pupils close together (3).

Strictly speaking, it probably would have been better if I had randomized the numbering for each survey participant so that the order would not affect the overall results. But I had just learned to use Google Forms that morning, so give me a break.

In order to test my prediction, I had each participant give their age. Then, instead of asking the participants to just tell me which face was the cutest, I had them rank the faces from cutest to least cute. I did this because it gives me more information to work with than simply telling me which one they like the best, and I like having information to work with.

Plus, it gave me a chance to interpret the results in terms of voting methods. After all, each participant, in giving a ranking of the faces, was expressing their preference, and that's basically what a vote is. Traditionally, most voting we encounter in everyday life works by simple plurality, but there were two other methods I wanted to try: Instant-Runoff voting (IRV, also known as Single Transferable Vote or STV in Canada), and the Beatpath method, both of which work best when the voters give a ranking of their preferences, rather than just putting an X beside the one they like best.

This is where it gets a little boring and technical, because this section has less to do with cute faces, more to do with mathematics of social choice. I won't be offended if you skip to the next section.

For those of you who chose to read on: Given a set of rankings given by voters (also known as a preference schedule) my job was to aggregate the votes and figure out how they determine a ranking for the entire population. This is easier said than done. In fact, according to Arrow's Impossibility Theorem, it's, well, impossible to do it in a way that totally satifies a small set of reasonable criteria.

Still, even in the face of possibility, I thought it was important to do as well as I could to aggregate the results. And in fact, some vote-counting methods are superior to others. In particular, the Beatpath method is better than IRV and Plurality in almost every way. The Wikipedia article on voting systems has a nice table that explains how various voting systems fare according to different criteria, each criterion more complicated and abstract than the last. But the important facts are this:

- Both IRV and Beatpath prevent the simple Ralph Nader-style vote splitting that happens when the plurality method is used.
- In addition, unlike IRV, Beatpath is monotonic, meaning that there is no way for a "candidate" to change from winner to loser by rising in a voter's ranking. This page contains some examples which should clarify what it means to say that IRV fails to be monotonic.

I don't read many psychology papers; I'm sure I'm not the first person who's had to take a group of participants' rankings, and figure out how to summarize them. I'm not sure what most psychologists do in this situation, so I just aggregated the rankings using Plurality, IRV and Beatpath to see what it looked like. However, I ultimately place more trust in Beatpath than in the other two methods.

The Results

As of writing this blog post, my survey has had just over 100 responses. The median age is 25. I turn 24 this year, so it makes sense that most of my friends, many of whom were classmates in high school and university, would cluster near my age. The youngest participant in the Google survey was 17, and the oldest was 73.

You can see the results for three categories: General, 24 and Under, and 25 and Older. Since 25 was the median, it seemed like a natural cutoff point to separate older and younger participants.

In each of the three categories, I've used three methods of aggregating the participants' rankings, as described in the previous section. Since I trust Beatpath the most, I have put it in boldface.

For convenience, I'll reproduce the image of the four faces again here:

General voters:
Plurality: [1, 3, 2, 4]
IRV: [1, 3, 2, 4]
Beatpath: [1, 2, 3, 4]

Voters 24 and Under:

Plurality: [1, 2, 3, 4]
IRV: [1, 2, 3, 4]
Beatpath: [1, 2, 3, 4]

Voters 25 and Older:
Plurality: [3, 1, 2, 4]
IRV: [3, 1, 2, 4]
Beatpath: [3, 2, 1, 4]

A few observations immediately jump out at me:

Generally, the face with big pupils far apart (1) was the favourite of the group. This makes sense to me, since (1) is the category of puppies, baby sloths, emojis, and so on.

However, if you look at voters 24 and under vs. voters 25 and over, it becomes clear that (1) and (3) are very polarizing -- just like it was among my family at Thanksgiving dinner. Younger people think (1) is the cutest and (3) is the third cutest, whereas older people think (3) is the cutest and (1) is the third cutest. This is in line with my prediction that younger people prefer large pupils far apart while older people prefer small pupils close together.

(2) was universally considered to be second cutest, and (4) was universally considered to be least cute. This seems odd to me. You would think that if big pupils far apart (1) are cute, then big pupils close together (4) would be almost as cute. But putting big pupils close together seems to ruin the cuteness, even for the 24 and under group.

Those are the questions that I was focussed on answering, but perhaps you have others. For example, do the answers give us a way of measuring the intensity of preference for one face over another, at least for the population? What if we were to divide the group into further age subdivisions, or perhaps subdivisions by which face they thought was cutest, or second cutest, and so on? If you want to try to answer any of these questions, or questions of your own, feel free to look at the data yourself.

Crazy Speculations (a.k.a. Discussion)

What theory of cuteness would explain these results? Hell if I know. But I can still make some guesses.

For example, I still think I was essentially correct in my belief that big pupils far apart (1) is a reliable recipe for cuteness. As I've mentioned, it's the face of most baby animals.

It's not clear to me why humans should find other species' babies cute. But the fact remains that we do. The big, black pupils are a trait we're more likely to associate with other animals than with humans.

In addition, having the eyes far apart might make the face look less threatening, because it's the trait of herbivores. Herbivores usually have eyes closer to the sides of their heads, so that they can always have a good panoramic view of their surroundings to look for predators (e.g.: deer, horses, hummingbirds, baby sloths). Carnivores and omnivores, in contrast, are more likely to have their eyes on the front of their head in order to get good depth perception, which is useful for hunting (e.g. humans, spiders, cats, dogs, owls, raccoons).

This would help to explain why big pupils close together (4) was universally considered to be the least cute. Big pupils make it look more animalistic than human, and the fact that the eyes are close together makes the face look more like a predator than like prey.

However, this doesn't explain why the older crowd found small pupils close together (3) so cute. One clue towards figuring this out might be the fact that (3) looks more like a human baby than the other faces. Humans have eyes close together rather than on the sides of our heads, and we have small pupils surrounded by big white sclera. Perhaps the older group contains more parents and grandparents, who are more likely to find babies cute -- perhaps becoming a parent actually causes a person to find babies cuter than they did before. Younger people find babies less cute, as evidenced by the fact that most of the cute pictures that get shared on the internet are of animals, rather than baby humans. However, it's not clear to me why young people like myself are so indifferent towards babies.

I have another guess as to why older participants found (3) to be the cutest: perhaps they somehow learned to find it cute. My 3-year-old cousin Luca might have hit upon a profound observation when he said that the face with small pupils close together looked like Cookie Monster. Sesame Street and The Muppets have been around for over 40 years, and most of them are designed to have small pupils, close together. Looney Tunes and Disney characters also have small pupils close together, and they've been around even longer. Perhaps we're born with the capacity to experience cuteness, but what triggers that feeling is something we have to learn -- kind of like how we're all born with the capacity for language, but the specific language we learn is determined by our environment. Visual styles go in and out; perhaps big pupils far apart are simply "in" these days, and the next generation will defy us by preferring small pupils close together.

It would be a mistake to finish this discussion without mentioning the Uncanny Valley. We like abstract, simple, cute faces (e.g. emojis, baby sloths) and we like them even more when they're slightly more realistic (e.g. Disney cartoons, superhero comics). But there comes a point where a face is almost perfectly realistic, but not quite: this is called the Uncanny Valley, and contains the almost-human faces that creep us out (e.g. zombies, horror movie masks, sex robots, Michael Jackson). But if we push past the uncanny valley, towards realistic human faces, eventually we find them appealing again (e.g. Mona Lisa, Neil Patrick Harris... do I really have to list examples of people with human faces?)

I mention this because it might be useful in understanding the results of the survey. Young people liked (1) -- it's simple, with big black eyes that are far apart. It's not human enough to be even close to the Uncanny Valley, so it's just cute. Everybody, young and old, was okay with (2) -- it's slightly more human than (1), but not enough to be creepy. (4) is where it gets interesting. I think that, at least relative to the other faces in this survey, (4) represents the uncanny valley. The proportions of the face are similar to a human baby, but the eyes are too animalistic. It looks like some kind of alien baby. Finally, (3) was the face that the older group loved. (3) is the face that is most like an actual human. Perhaps for the older crowd, (3) was well past the uncanny valley, but for the younger crowd, (3) was still not quite human enough to be cute.

So, that's my analysis. Feel free to look at the data and find patterns on your own, and maybe try to convince your friends to take the survey before they see this blog post.

Sunday, October 4, 2015

Marijuana and the Infinite

Whoa. I usually try to think of government policies in economic terms, e.g. what are the costs and benefits of passing law? But it looks like my entire worldview might have been based in a lie.

Because, you see, I've been working under the assumption that the amount of positive or negative utility of any law would be finite. But if Harper is correct (and why wouldn't he be?) marijuana is, in fact, INFINITELY WORSE than tobacco. This implies that marijuana is INFINITELY bad.

National Post: 'Marijuana is infinitely worse' than tobacco, Harper says as he encourages pot debate to go up in smoke

INFINITELY. I just want to make sure that sinks in.

Let's suppose we're counting in terms of human lives. Then if one person gets killed, that's 1 unit of badness. If 10 people get killed, that's 10 units. If 7 billion people get killed, that's 7 billion units.

But marijuana? Forget about it. We're not talking about 1, 10, 7 billion, or Ackermann(G_64, G_64) here. We're talking about INFINITY.

This brings up many complex philosophical questions.

(1) Pascal's Wager states that, since an afterlife in Heaven is infinitely good, then as long as there is a small positive probability of an afterlife, it is a good idea to practice religion. But what if there's a small positive probability that the afterlife includes marijuana?

(2) Since marijuana exists in our universe, that means our universe is already infinitely bad. We can't do anything to change it, since our finite efforts would prove fruitless (negative infinity + anything = negative infinity). Doesn't this contradict Leibniz's claim that we live in the best of all possible worlds? Or does it simply mean that all worlds are equally bad, i.e. infinitely bad? If so, does this mean that all possible worlds contain marijuana, or do there exist other things that are infinitely bad?

(3) Furthermore, in spite of the existence of marijuana, we seem to live in a universe where good things exist (friendship, love, art, science, beauty). If marijuana is infinitely evil, then whence cometh goodness?

This whole revelation is really making me question what it means to be a good person.

Tuesday, August 25, 2015

Pet Philosophers (Script from 2008)

This is a mockumentary I wrote in 2008 for a Grade 12 Directing and Scriptwriting class. It takes place in a world where people keep philosophers as pets.

1: Jennifer Fontaine interview


Tell us who you are, and a little bit about yourself.

I’m Jennifer Fontaine, and I own two philosophers.  My children have gone off to college and my husband has passed on, so it’s nice to have something around to take care of.

Tell us a little bit about your philosophers.

The older one is Nietzsche… is that right?  I’ve never been able to pronounce it correctly, so we just call him Nee-Nee.  My younger one is called Sartre.  He and Nee-Nee get along fine, but you know, Nee-Nee’s getting on in years, and I think he’s had a good life, so I think it’s time to put him to sleep.

How has the “Cognitive Critters” phenomenon affected your life, postively or negatively?

It’s always nice to have around something to take care of.  Ever since my children have gone off to college and Harold passed away, I guess you could say having these little guys around has filled a part of that… void, in my life.  I know it sounds a bit silly, I’m sorry.

Now, you say that one of your philosophers is getting old and you want to put it to sleep.  What is the process for putting a philosopher to sleep?

The book is upstairs, but I’ll see if I can paraphrase it.  Basically, you feed the philosopher until it’s so full and satisfied that it’s too stuffed to care about anything.  Then, I will take Nee-Nee into a quiet spot outdoors, and shoot him.

Now that you’re putting your philosopher to sleep, how do you feel about it?

I sometimes get a bit choked up about it… you may need to excuse me a moment… but I’ve come to terms with it.  I think it’s time.  I mean, Nee-Nee’s getting old and senile.  To be honest, I don’t really understand what he says anymore.  Yes, it’s definitely time to let him go.

What do you have to say to people who think of putting a philosopher to sleep as “cruel”?

To be honest, I’m not sure it’s up to me to decide what’s right and wrong.  But the Cognitive Critters handbook says it’s okay, and let’s be honest, it’s better to be dead than to live in misery, in a senile, unwanted state.

2: Dr. Mark Hoffman Interview


Before we go on, would you please tell the audience a little bit about yourself and your business, in summary?

I’m Dr. Mark Hoffman, PhD, and I founded the company, “Cognitive Critters”.  I breed philosophers and see them adopted into loving families.

How did this whole idea start?

I’d just gotten my degree as a veterinarian, and, of course, I had to write papers, so I dealt a lot with the academics at my university.  I noticed that there were a lot of philosophers running around, unable to fend for themselves in this difficult world, and I decided that if someone wasn’t going to try to give them a home, they just wouldn’t survive.  So, I took a few into, and kept them.  Over the next few months, I’d gotten quite a few, and obviously, I couldn’t keep them all, so I got some of my friends and family members to take them off my hands.  And that’s how this whole phenomenon got started.

At what point did you know your idea was going to be a success?

I’d have to say it was my first appearance on “The Susan Show”.  You know, it’s a show that I’ve always respected for keeping with the times, while also maintaining its social messages.  I went on the show, with my book, of course, and it was at that point that I realized that the phenomenon had become a nationwide, uh, thing.

How do you respond to critics like Roger LaMarche, who describe your success as being just a passing fad?

Ah, yes, Mr. LaMarche.  I’ve read his articles.  I think it’s more than just a fad, and I think Mr. LaMarche should see the faces on the people who take the philosophers into their homes.  It’s just a beautiful thing.  You can’t put a price on that.

Do you have any advice for people thinking of getting a philosopher for themselves or a family member?

All I can say is, buy my book.  No, seriously.  It’s a good book, it tells you all you need to know about caring for a philosopher.  You know, feeding, sleeping, that sort of thing.  And you have to keep in mind, a philosopher is a living creature, so it’s important to remember that it’s a big responsibility to take care of one.

Would you show us a philosopher in his natural habitat?

Okay, well, I have two philosophers of my own.  One’s named Kant, the other’s named Hegel.  This is Kant here.  Say hello, Kant.  Okay, he’s a bit shy, isn’t he adorable?  Well, not all philosophers are alike.  Some of them don’t get along with each other.  Kant and Hegel sometimes get into little scraps, occasionally.  It’s just a matter of tearing them apart before it gets too out of hand.

Do you have any final words for the audience?

Having a philosopher around is something that can enrich your life.  It’s not just a pet.  It’s like having a friend around.

3: Roger LaMarche Interview


Before the interview, tell the audience a little bit about yourself.

Okay.  I’m Roger LaMarche, critic for the Enlightener magazine.  My job is to look at culture, and tell people exactly why it’s wrong.  I’ve been working at the magazine for fifteen years or so.

You’ve been keeping up with this fad since the beginning.  How have philosophers as pets swept the nation?

It’s your classic story. Mark Hoffman, he’s the alleged “doctor” behind Cognitive Critters.  He noticed that there were a lot of philosophers around, basically serving no purpose in nature.  But he wants to make a quick buck, so he figures he takes a few, breeds them, and sells them as pets.  Next thing you know, he’s on “Susan”.  Well, you know how it works, a guy goes onto this show, promotes his book and his business, everyone buys it even though they don’t understand it.

Although I’m sure your readers already know the answer to this question, would you mind telling the audience your opinion of the “Cognitive Critters” fad.

The “Cognitive Critters” fad?  Well, that’s all it is, just a fad.  It’ll pass, just you wait.  People will move on to the next big thing.  The “Cognitive Critters” phenomenon is a perfect example of idiotic, illogical, blind consumerism among the proletariat.

May I ask, why do you think so poorly of the fad?

Well, think about it.  People adopt these poor, dumb animals from their local Cognitive Critters center, and feed them and take care of them and whatever for a few years, no problem there.  But sooner or later, the creatures aren’t cute anymore.  People might as well just be flushing them down the toilet like baby turtles and alligators.  They either put the philosophers to sleep, or worse, just let them go and have them roaming the streets.  I don’t know about you, but I don’t want these creatures in my backyard.  It seems kinder to just kill them, put them out of their misery.

Do you have any final words for the audience?

Don’t buy into propoganda.  Don’t think that you suddenly have to take care of a philosopher just because everyone else is doing it.  They’re useless animals.  I know people don’t like to hear it, but that’s what they are, and you’re not helping anyone by trying to prove any other possibility.


Thursday, April 2, 2015

More Mathematical Cranks

(Crossposted from my Facebook page)

I am now 200 pages into Mathematical Cranks. Neat book. I have a few more comments:

(1) So far, only one woman has been mentioned. The author doesn't use the people's real names, but she was a teacher with a PhD in Mathematics who tried and failed to give a short, simple proof of Fermat's Last Theorem.

(2) Speaking of Fermat's Last Theorem: One interesting fact is that this book was published in 1992, before Andrew Wiles came up with an actual proof.

Other fun fact: Fermat's Last Theorem was, until 1993, neither a theorem nor Fermat's last anything. He wrote it early on in his career, famously saying that he had a marvelous proof that wouldn't fit in the margins of the book he was writing in. But there's good reason to believe that, whatever Fermat's proof was, it was wrong and Fermat himself knew it, because apparently there is evidence that he worked on proving the theorem for n = 4 and 5 later in life life (which would be redundant if he already had a proof for the general case).

(3) You might have heard about the Indiana Pi Bill, and how legislators allegedly tried to legally change the value of Pi. This is a misrepresentation of the story. It wasn't a story about a scientifically ignorant government trying to change reality to their liking: it was the story of one crazy guy who claimed that he had found a set of exact algebraic solutions for Pi (I think this was known to be impossible even at the time) and convinced his representative (no doubt desperate for votes) to bring a bill to the senate proposing that these solutions be made freely available to public schools.

Although, it is still pretty absurd that the bill managed to get to the senate before the other senators laughed it out of existence. It's come up again and again in the book: apparently, it's surprisingly easy to get your bad ideas noticed if you can find a politician desperate enough for your votes.

(4) Most of the stories of these cranks start with, "Person X wrote up their theory, and sent it to over 100 universities across the continent." Apparently, if you just mail your dumb theory to a random university's math department, you'll sometimes get a response.

Don't believe anyone who tells you that scientists are in an elitist conspiracy to keep out people with unconventional ideas: the responses from the mathematicians who deal with these cranks are surprisingly polite for the most part, often more polite than warranted (the cranks themselves usually take criticism personally and immediately start hurling insults at anyone who points out their errors). One guy, who claimed to have come up with a short proof of the Four Colour Theorem, got offended when a professional mathematician said that there would be room for other mathematicians to "build on" what he had done -- as if his work wasn't perfect already!

(5) One more thing: A lot of people have tried to "disprove" non-Euclidean geometry, claiming that Euclid was divinely inspired and anyone who dares question his wisdom is engaging in blasphemy.

But then they try to show that non-Euclidean geometry is invalid by trying to derive Euclid's fifth postulate from the first four. (This is known to be impossible. Euclidean Geometry starts with 5 postulates, and non-Euclidean geometry looks at what happens when you change the fifth postulate.) But if they think Euclid was so perfect, why would they think that Euclid was so stupid as to add a redundant postulate to his system if he only needed the first four?

Tuesday, March 31, 2015

Mathematical Cranks

(Crossposted from my Facebook page)

I'm reading a book called "Mathematical Cranks". It's an anthology summarizing a sample of different people, ranging from the mildly eccentric to the downright insane, who have tried to put forward their bad ideas as legitimate mathematical research.

A couple examples: A guy who claims that the number 57 is intimately linked with every major event in US history; numerous people claiming to have found fault in existing theorems; and a bunch of people who claim to have a Grand Unified Theory of Mathematics, which will change the world and will solve every problem in existence, provided that you purchase their book for 29.99. A modern example would be the Time Cube guy, or roughly half the people listed in the Wikipedia article about Usenet celebrities.

I'm about 56 pages in, and so far, all the cranks mentioned in this book have been male. Further evidence that we need to do more to remove the stigma around women entering the field of fake mathematics.

I get the sense that the author is being as generous as possible to the people he talks about, which I like -- I was worried the book would just be a series of "Hey, let's all point and laugh at this idiot for being bad at math!" but that hasn't been the case.

For example, there's a chapter on the Dozenal Society, a group of people who want everyone to switch to a Base 12 number system instead of Base 10, with the reasoning that Base 12 makes a lot of calculations easier. The author admits that these people aren't *wrong*, per se, but it's still never gonna happen. There are other cases where the crank in question has found something mildly interesting, but it's in the middle of a series of grandiose claims.

Part of the reason I was interested in reading this book is because I'm always interested in figuring out ways I hadn't considered in which my thinking could be wrong. In my last Facebook post, I mentioned that my high school math teacher made a joke about how, if I didn't keep my thinking under control, I would end up like Howard Hughes. I'd like to avoid that fate, if I can (the part where his mental illness drove him to become a paranoid recluse, not the part about being a genius billionaire playboy philanthropist).

And of course, there are a lot of mathematicians who end up losing their sanity obsessing over something or other. The best example that comes to mind is Georg Cantor, who spent his later years alternating between staying in mental hospitals and obsessing over the theory that Francis Bacon is the actual author of all the Shakespeare plays. But the subject of mathematicians and mental illness is a topic for another day.

But a recurring theme I've noticed among the cranks is that the most grandiose claims seem to come from the people who do the least actual mathematics. They spend most of their time talking about how great and powerful their theory is, how it makes all other mathematics obsolete, but then their "theory" turns out to be a couple of equations that aren't really that impressive, without elaborating on how to use these findings.

In other cases, the crank will make a grandiose claim, but fail to actually prove it formally. This is kind of a no-no in mathematics -- not that every finding always requires a formal proof, but if you don't have a proof, at least have the decency to call your finding a "conjecture" rather than a "Grand Unifying Theory that will Change the World". I can't find the quote, but I remember a mathematics blogger saying "The worst kind of mathematics is no mathematics at all" and that seems to be the case here.

Tuesday, March 24, 2015

Phil Robertson, Conformity and You

Phil Robertson (don't stop reading yet, I swear this will be interesting) said something stupid recently. It is something that I don't think anybody I know actually agrees with or takes seriously. There might be a few contrarians among my friends who are interested in taking Phil Robertson's views to their logical conclusion as a purely academic exercise (I'm a bit of a contrarian myself sometimes), but that's not the same thing as sincerely believing it.

And yet, clearly there are people who take Phil Robertson seriously. I guarantee you that swarms of people will jump to his defense, for everything stupid he's said in the past or will say in the future. I'm not talking about defending freedom of speech for views you hate (I don't think he should be arrested, I just think it's sad that he's probably going to live the rest of his life and die as a hate-filled idiot -- an entire human life wasted). I'm talking about people who actively defend his views and believe that people should agree with him.

So, my first question is, why have I never met one? With Duck Dynasty being as big an empire as it is, I would have to think that, even in a place like BC, there must be a non-trivial percentage of people who totally agree with Phil Robertson's worldview. Statistically, I must have walked past a few of them in the street at some point. These people clearly exist. I've just never had the pleasure of having a conversation with one.

I have about 300 Facebook friends. As far as I know, none of these people share Phil Robertson's worldview.

I don't know what percentage of the population of BC shares something similar to Phil Robertson's worldview -- archetypical, old-fashioned, bigoted, religious extremism. Let's say BC is 1% "Robertsonians" to make up a word (I'm just making up a number here, but as they say, if something's worth doing, it's worth doing with fake statistics. I doubt it's as high as 10% or as low as 0.1%).

Then if my friends were selected for me randomly, the odds that a randomly chosen friend is a Robertsonian is 0.01, which means that the odds they are not a Robertsonian is 0.99. Then the odds that all 300 of my friends are not Robertsonians is 0.99^300, which is close to 0.05. Not impossible, but still pretty unlikely, IF we assume that it occurred randomly.

Obviously, it didn't occur randomly. One huge factor is that I've spent the last 6 years in post-secondary education, so I've been spending my time around educated people. But it would be dishonest to ignore the possibility that, like it or not, I'm most likely to find myself gravitating towards people who, for the most part, share my values. If nothing else, I typically don't actively seek out people whose values clash with mine (look up The Parable of the Polygons to see the problem with that).

So: Consciously or unconsciously, I have excluded people from my life because they don't share my values.

On the one hand, I don't expect any of you will think less of me for not wanting to be buddies with Phil Robertson. On the other hand, when you phrase it like that ("excluding people from my life because they don't share my values") I sound like a bit of a jerk. Isn't it supposed to be a good thing to spend time with people who have different values than you have so you can be open-minded and learn from them?

In spite of people like Phil Robertson, I think the answer *might* be yes. It's just not easy to do. You know that anger you feel when someone like Phil Robertson comes along and says something you think is bigoted and ignorant? That's how it feels when you come across a person whose values ACTUALLY clash with yours.

Remember my last long post, where I made fun of people who say "I'm open-minded, but only to good ideas"? Its close cousin is "I'm tolerant of other people's values, unless I think they're going too far" -- if that's all it takes to be tolerant, then Phil Robertson is tolerant too. In fact, so is pretty much every person in the world.

You might wonder why I'm so obsessed with being open-minded to stupid ideas. I'm obsessed with it because it would be so easy to imagine a world where the roles are switched: 99% of the people in BC are the clean, decent, God-fearing Phil Roberts followers, and the other 1% are the frightening, militant, liberal secular humanists who everyone hates. In such a society, would you stick with what you know is right, or would you find yourself convinced by the Robertsonians?

Bear in mind, they have all the cool and powerful people, not to mention all their good columnists are writing thinkpieces about how secular humanists are Problematic. Plus, there are people on the internet who, upon finding a tweet you made expressing your heathen views, will do their best to report it to your employer so you lose your job. What if the people who agree with you are only 0.1% of the population, or 0.001%? What if it was just you?

And -- here's the Twilight Zone twist -- whatever mode of thinking you would apply in this alternate universe, are you applying the same mode of thinking in this universe?

(Take a moment to look up the Asch experiments on conformity if you haven't already heard of them.)

When I see someone like Phil Robertson, I don't think "Hah, what an idiot" -- not because I don't think he's an idiot, but because it's not very productive. My questions are more along the lines of "How does a human brain come to have those beliefs? Heck, how did I come to believe the things I believe? And, in some hypothetical universe where I was wrong and the Phil Robertson and Fred Phelps' of the world are right, what evidence would it take to convince me of it?"

If I have a point here, it's that Phil Robertson's brain is not fundamentally different from yours or mine, and that should terrify you, or at least motivate you to consider how much of your own thinking is in error.

Friday, March 6, 2015


I occasionally hear someone say "I'm open-minded, but only to good ideas." This implies that, as soon as they're exposed to an idea, they *immediately* know whether it's a good idea or not even without taking any time to consider it.

This is an amazing and miraculous talent to have -- the ability to instantly recognize an idea as good or bad. I, for one, usually have to *think* for at least a couple seconds before I know with any certainty whether an idea is good or not (hell, even when I *know* an idea is bad, I usually try to think out its consequences anyway just to make sure I'm not missing anything).

So, the next time I meet someone who says that, I'm going to tie them up in front of a computer screen and force them to watch a program that generates every series of English words in increasing lexicographic order. By their own claim, whenever the series of words describes a good idea, their response will be open-mindedness, which has a somatic feeling which I suspect would lend itself to being detected by an existing scan, possibly fMRI.

The principle is this: you show this person a sentence describing an idea, e.g. "Increase funding of space exploration by X dollars". If the person is open-minded to it, then it's a good idea. If not, reject it. Move on to next sentence.

I know this sounds extreme, but consider all the potential good ideas that nobody has detected yet. Cold fusion, feasible quantum computing, cures for all known diseases -- it would be an extreme act of stupidity NOT to at least try it. Think of the billions of lives that could be saved or improved, compared to the miniscule cost of this one person's freedom and wellbeing.

The human visual system can quite comfortably process visual information at 10 "frames per second" for lack of a better term. Provided we feed the person while they're staring at the screen, and allow them to sleep about a third of the time, I figure we can have them looking at ideas for about 16 hours a day, and we could probably keep the person alive for about 50 years if we had to (and we DO have to -- we can't let an opportunity like this go to waste).

So, at 10 ideas per second, 16 hours a day for 50 years, that adds up to them being exposed to about 10 billion ideas in a lifetime. One issue is the sheer number of possible English sentences. It is estimated that each letter in English represents about 0.6 to 1.2 bits of information (I'll round it to 1 bit). So, with a little cleverness, we would be guaranteed to expose this person to every 33-character English sentence if we wanted to. If we restrict it even more to get rid of obviously nonsensical phrases or restrict ourselves to vocabulary in the fields of ideas we want evaluated (e.g. medicine, engineering, economics) we could probably get even more value out of them.

I mean, unless they're lying about being open-minded, or about being open-minded only to good ideas. But I'm pretty sure nobody would do that.
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It Seemed Funny at the Time by Ben Buckley is licensed under a Creative Commons Attribution-Noncommercial 2.5 Canada License.