Can Bees Count?


From the annals of clever research designs:

A wonderful study was published last week in Science by Scarlett Howard, Adrian Dyer, and their colleagues at RMIT University in Melbourne. Here’s what they wanted to know:

Do bees understand zero?

Title of this post aside, it’s actually already been demonstrated that honey bees can count. But, understanding zero as a mathematical construct is something much bigger. From the NYTimes summary:

This is a big leap. Some past civilizations had trouble with the idea of zero. And the only nonhuman animals so far to pass the kind of test bees did are primates and one bird. Not one species, one bird, the famed African gray parrot, Alex.

The problem is that bees make terrible interview subjects, and aren’t big on math class either. So here’s what the researchers did. They placed small white squares, each of which had 1-4 black shapes printed on it, on a wall. Each had a small landing platform. Bees were then released into the enclosure, and some rewarded for landing on squares with more shapes, others for landing on squares with fewer.

Once the bees were trained, the researchers introduced a blank card (zero shapes). And with a drumroll: bees who had been trained to seek fewer shapes landed on it, while bees trained to seek more shapes avoided it.

What this shows is that bees understand that zero is a mathematical construct, a number lower than one that is part of a sequence of numbers. Moreover, the bees did even better when the zero card was paired with a high number (e.g., four or five) vs. a lower one (e.g., one or two). What this suggests is that bees understood numerical distance – that is, one is bigger than zero, but five is much bigger than zero.

Moreover, the bees were even able to distinguish between two unfamiliar numbers. In a final experiment, the researchers trained bees using cards with 2-5 black shapes, and then presented them with two brand new cards at the same time: one with one black shape, and one with zero. Again, bees that had been trained to seek fewer shapes preferred zero to one – meaning that they could carry their training into a completely new setting and order two novel numbers.

This degree of mathematical ability has actually never been observed in insects, and actually places bees on a level with “animals such as the African grey parrot, nonhuman primates, and even preschool children.”


You Are Royalty, and So Is Everyone Else

Here is a statement I find surprising:

The most recent common ancestor of everyone alive today lived only about 3,400 years ago.

Here is one that is even harder to digest:

About 20% of humans living in Europe a millennium ago – in 1018 AD – have no descendants today. The remaining 80% are the ancestor of every person of European decent alive today.

Neither of these statements ring true, but they are. And this is a wonderful example of a finding that was first demonstrated mathematically, and then confirmed empirically.

Start with the math: you have two parents, four grandparents, eight great-grandparents, and so on. But, this geometric progression isn’t borne back ceaselessly into the past. If it were, by the time we get to Charlemagne’s time (750 AD), your family tree would have 137,438,943,472 individuals on it – more people than have ever been alive.

Rather than branching out forever, our family trees fold back on themselves. The same person (your great-great-great grandfather) might hold that one position several times over. So, our family trees aren’t really trees once you get beyond a few generations, but rather meshes (or maybe some sort of vine?).

One early researcher to demonstrate this was Joseph Chang, a statistician from Yale with an interest in ancestry. He constructed a model and found that, given Europe’s current population size, the lines of ascent of every family tree cross about 600 years ago. 

Other researchers have since confirmed this through ever-larger DNA sequencing studies. It turns out we’re all related – and a lot more closely and a lot more recently than most of us would guess. And this leads to a remarkable proposition:

No matter the languages we speak or the color of our skin, we share ancestors who planted rice on the banks of the Yangtze, who first domesticated horses on the steppes of the Ukraine, who hunted giant sloths in the forests of North and South America, and who labored to build the Great Pyramid of Khufu.
— Rohde, Olson, and Chang, 2004

In other words, you are of royal decent – because everyone is.

From a remarkable and very enjoyable article by Adam Rutherford in Nautilus, excerpted from his book A Brief History of Everyone Who Ever Lived.

Perfectly Reasonable Problems


I recently came across a note that strikes me as the clearest and most valuable advice a scholar might receive. The following letter, dated February 3, 1966, is part of an exchange between physicist Richard Feynman and his former student named Koichi Mano. Feynman asked Koichi what he was working on, to which Koichi responded, “studying coherence theory with some applications to the propagation of electromagnetic waves through turbulent atmosphere… a humble and down-to-earth type of problem.”

Dear Koichi,

I was very happy to hear from you, and that you have such a position in the Research Laboratories. Unfortunately your letter made me unhappy for you seem to be truly sad. It seems that the influence of your teacher has been to give you a false idea of what are worthwhile problems. The worthwhile problems are the ones you can really solve or help solve, the ones you can really contribute something to. A problem is grand in science if it lies before us unsolved and we see some way for us to make some headway into it. I would advise you to take even simpler, or as you say, humbler, problems until you find some you can really solve easily, no matter how trivial. You will get the pleasure of success, and of helping your fellow man, even if it is only to answer a question in the mind of a colleague less able than you. You must not take away from yourself these pleasures because you have some erroneous idea of what is worthwhile.

You met me at the peak of my career when I seemed to you to be concerned with problems close to the gods. But at the same time I had another Ph.D. Student (Albert Hibbs) was on how it is that the winds build up waves blowing over water in the sea. I accepted him as a student because he came to me with the problem he wanted to solve. With you I made a mistake, I gave you the problem instead of letting you find your own; and left you with a wrong idea of what is interesting or pleasant or important to work on (namely those problems you see you may do something about). I am sorry, excuse me. I hope by this letter to correct it a little.

I have worked on innumerable problems that you would call humble, but which I enjoyed and felt very good about because I sometimes could partially succeed. For example, experiments on the coefficient of friction on highly polished surfaces, to try to learn something about how friction worked (failure). Or, how elastic properties of crystals depends on the forces between the atoms in them, or how to make electroplated metal stick to plastic objects (like radio knobs). Or, how neutrons diffuse out of Uranium. Or, the reflection of electromagnetic waves from films coating glass. The development of shock waves in explosions. The design of a neutron counter. Why some elements capture electrons from the L-orbits, but not the K-orbits. General theory of how to fold paper to make a certain type of child’s toy (called flexagons). The energy levels in the light nuclei. The theory of turbulence (I have spent several years on it without success). Plus all the “grander” problems of quantum theory.

No problem is too small or too trivial if we can really do something about it.

You say you are a nameless man. You are not to your wife and to your child. You will not long remain so to your immediate colleagues if you can answer their simple questions when they come into your office. You are not nameless to me. Do not remain nameless to yourself – it is too sad a way to be. Know your place in the world and evaluate yourself fairly, not in terms of your naïve ideals of your own youth, nor in terms of what you erroneously imagine your teacher’s ideals are.

Best of luck and happiness.
Richard P. Feynman.

Thank you to the Farnam Street blog for tipping me off to the existence of the letter. It appears in the collected letters of physicist Richard Feynman, published by his daughter in 2005 as Perfectly Reasonable Deviations from the Beaten Track.

Gary Larson on the Creative Process


Constraints, even arbitrary ones, are central to the creative process. Constraints force us to consider new alternatives, discard subconscious assumptions, and think outside the box. I've written about this before, but I'll be the first to admit that I lack the gravitas that others might bring to the issue. Gary Larson, for instance, has published 23 books, drawn a cover for the New Yorker, and even has a species of lice named after him. And here's what he says about his art:

Because The Far Side is a vertical, single-panel cartoon, I've rarely had the luxury of being able to draw long things (like whales, snakes, ships, etc.) in an accommodating shape. In general, the perspective has to be from front to rear, as opposed to side to side…
In cartoon strips, you frequently see the latter approach - because the strip lends itself well to horizontal images. In The Far Side... ships come at you head on, classrooms are viewed from either the front or the back, and riding in the car is often seen from the perspective of the backseat looking forward or from the windshield looking inward. I just can't draw a '59 Cadillac in profile. 
I'm saying this because I drew The Far Side for years without truly being cognizant of why I approached it this way. I was just trying to figure out ways to cram things into a little rectangle. It was a friend of mine (also a cartoonist) who pointed out that I had inadvertently developed one or two drawing skills in the process. 
The limitation of space I fought in the beginning ended up being the best drawing instructor I ever had.

From Larson's 1989 The PreHistory of the Far Side. Published without any accompanying cartoons per the artist's wishes.