Circles, social circles and Pi Day

March 14 (or 3/14) is Pi Day. During this somewhat whimsical holiday, science nerds around the globe eat pies and perform needlessly complicated operations to celebrate the fact that the ratio between a circle’s circumference and diameter is 3.14152653… It may be a little confusing from the outside, but that’s sort of the point.

There are several reason behind Pi day, I think: Pi is a good symbol for science, it’s a fantastically inclusive one, and it’s the perfect thing to turn into a nerdy holiday.

Let’s start from its symbolic value. Pi is very recognizable, because most people have run into it at some point in their education. That holds also for a lot of important physical and mathematical constants. Physical constants, however, are not really absolutely constant (their value depending units of measure), plus they are often unsavorily large or very small.

Mathematical constants, instead, are just numbers, like 0 and 1. So why not celebrate excellent numbers like those? Well, Pi has more depth. Nobody knows all of Pi because it’s an infinite, ever-changing sequence of digits. Irrational numbers like Pi (or the golden ratio, e, square root of 2) are elusive and fascinating, but none makes as good a holiday as Pi.

Few (if any) of them can be as easily turned into a date. Then, none is as well-known as Pi. This number is freakin’ everywhere: from school geometry to quantum mechanics, from pendulums to number theory and probability.

Its ubiquity is a testament of how circles enter everywhere in science: whether something involves actual circles (or spheres) or trigonometry (which is just badly disguised circles), Pi is bound to pop up. Any oscillation, from a pendulum to the waves in the sea, to the wave function of quantum mechanics, calls for some trigonometry, and its Pi. Actually it shows up so much in quantum mechanics that scientists found ways to avoid having to write it.

In statistics and mathematics, Pi often comes out through calculations that involve the famous Gaussian probability distribution. This amazing function describes an unbelievable number of phenomena, from the result of rolling many many dice to the distribution of people’s height.

Students organized by height in an old experiment: they follow the characteristic bell shape of a Gaussian distribution.

The Gaussian is circles’ ninja way to come back in the picture (because of details in the math: won’t bore you with that). And one can tell they came through, you guessed it, from Pi.

So mathematician, physicists, engineers and all scientists alike are familiar with this fantastic number and use it practically every day. At the same time, Pi appears almost only in scientific contexts. As a symbol, it includes every branch of science, nothing more and nothing less.

This is also why it’s a great nerdy holiday. One of my favorite definition (-ish) of nerd comes from John Green:

What is nerdier, then, than celebrate the fact that a date looks like the ratio of a circle’s circumference to its radius? In other words, it’s not really about Pi: it’s about meeting and eating pies and finding creative new ways to calculate the ineffable number.

As Christmas is actually a day about love and family, Pi day is actually about community, nerd identity, and being unironically enthusiastic about science and math. There aren’t many such days, let’s cherish this one.

Cover photo: CC-BY Bill Ward/flickr

Advertisements

Illness ideas and evolution

We all get sick at times. When we do, there’s a certain probability we will transmit our sickness to other people, who will then transmit it over, and so on.

CC-BY Tina Franklin/flickr

The spread of illness can be described mathematically. For example, it can tell us how contagious a virus has to be if it is to become an epidemic, or what categories of people have higher probability of coming in contact with the germs. Or how the wave of sick people will sweep through the population.

Computers spread viruses as well. Someone opens some stupid attachment and their computer becomes infected. The virus replicates itself and starts barraging all contacts with emails to spread. But they also spread another type of infection: ideas.

We all see posts and news on social media. Sometimes we share what we saw with our friends, who might share it with their friends—and so on. If it spreads enough, that cute cat video you shared will become… well… viral.

Once you have a general model for how germs spread through the network of people you know, you can use it just as well on computer networks or social networks. The idea is the same.

But there’s another thing that we can disperse across our populations: our genes. Like illnesses and fake news, genes too spread (as generations pass), competing with each other for limited resources. And like genes, clickbait articles and viruses mutate and evolve, finding the fastest way to proliferate. Whatever it is.

Before the nonsense of PenPineappleApplePen, Rickrolling, and Doge—actually way before the internet—eminent biologist Richard Dawkins coined the term meme. It describes exactly what internet memes are: the “unit of cultural imitation“, a conceptual thing that replicates itself and spreads through the population, like a gene does.

Although the basic concepts of how illnesses and ideas spread are very old, the real world is—as usual—more complicated. So mathematicians and physicists are hard at work to find better, more realistic descriptions, and with them better ways to defend us from the flu—and fake news.

If you want more
  • An Italian team has recently published an example of these realistic descriptions: an efficient description of how viruses and memes spread in quite complicated populations.
  • No article on epidemics from a geeky writer is complete without mentioning Pandemic
  • A couple of years ago, CGP Grey took a deeper look at how memes evolve on the internet

Cover photo: CC0 Myriam/pixabay.com

Things numbers do, things numbers don’t

So the US presidential polls turned out… shall we say not entirely right? And it isn’t the first time this year: think of Brexit or the Colombian referendum. Something’s gone awry in the numbers.

Numbers are pretty cool because they provide objective, factual answers. In science, you ask a question, then go measure the answer, which will come in the form of a number. That number is a fact, which you can use to prove other facts.

Numbers are also tricky, because they answer without any comment on the question. Was it posed correctly? Was it stupid? Was it the right question to begin with?

If we pretend we asked something we didn’t, or try to read in the numbers something that we didn’t ask for, the whole point is moot. And that’s when statistics look arbitrary.

But that’s not the numbers’ fault. It’s about who reads them and how they read them. It’s about the question.

This reminds me of The Hitchhiker’s Guide to the Galaxy. A super-intelligent alien race builds Deep Thought, a fenomenal supercomputer tasked to find “the answer to life, the universe, and everything”. After millions of years of calculations, the answer comes (in the form of a number, no less), but—mild spoiler—it’s kind of underwhelming.

As you can see, the question was just as important as the answer, no matter how true (and my heart has no doubt that is the answer), accurate or objective. And you don’t get much more objective than an accurately measured numerical value.

Here’s, I think, the thing about polls and elections: pollsters know what they are doing. They know how to account for all possible biases and how to accurately measure something that always proved to reflect voting reults. But they cannot know whether the vote is going to go that way. That’s not the question.

So what’s wrong? We don’t know, but hordes of statisticians are surely hellbent on figuring it out.

The awesome power of numbers is to tell us exactly what we asked for or, if the answer makes no sense, show we asked it wrong. The awesome skill of scientists, their art even, is to find the right questions and the right way to ask them.

Statisticians will figure it out, and we’ll learn a cool lesson from it. Silver linings, people.

Cover photo: CC0 Andrew Martin, via pixabay

Theoretical donuts and quantum computers: the Nobel prize 2016

So it wasn’t gravitational waves after all: the Nobel prize for physics went to David Thouless, Duncan Haldane and Michael Kosterlitz. That’s the easy part. The motivation needs a little unpacking:

For theoretical discoveries of topological phase transitions and topological phases of matter.

We all know and love a few phases of matter: solid, liquid and gas (maybe plasma if you want to get kinky). Phase transitions happen when, changing temperature or other conditions, matter goes from one form to the other, like melting ice. But there are more phases and more transitions transitions, some involving electrical and magnetic properties of materials.

Thouless, Haldane and Kosterlitz

David Thouless, Duncan Haldane and Michael Kosterlitz

That’s what the newly-minted Nobel laureates where after. They studied the sudden changes in electrical conductance—the efficiency in carrying electric currents—that some cold materials (I mean -270-odd Celsius) undergo when the temperature changes slightly. This effect is impossible to deal with using quantum mechanics, because it has to do with collective behavior of electrons rather than single ones.

Instead, Thouless, Haldane and Kosterlitz used topology. Topology is the branch of math that deals with properties that stay the same when stretching, twisting and bending stuff, but not puncturing, ripping or gluing it. Topologically speaking, a donut is the same as a pipe—we can turn one into the other—but is different from a ball, because we’d have to sew its hole shut.

Topological features like the number of holes must come in integer numbers: there’s no such thing as a half-hole! So they change in jumps, like that weird conductance. So the scientists theorized that topological transformtions (though not really holes appearing), were behind it.

topology_steps

Steppy changes in topology cause sudden changes in conductance. There are no actual holes involved in the process, though! Holes appearing are just one example of topological changes. Credit: Johan Jarnestad/The Royal Swedish Academy of Sciences

The unusual part of the award is that the discoveries haven’t been applied quite yet: they are purely theoretical. However, they opened the floodgates for the research on materials that exploit these properties. For one, topological materials are an avenue towards the dream of building a quantum computer. During the press conference, Haldane explained that topology could protect the fragile signals in quantum computers from disruption due to impurities in the material itself.

Cover photo: CC0 Thomas Kelley via unsplash.com

If you want more:

Earbuds must tangle!

We’ve all been through it: we want to listen to some music, take our earbuds out of our bag only to find—THE HORROR!—an impossibly tangled mess.

Can’t anyone assuage this terrible scourge? According to physics… nope, not really.

As it turns out, earbuds tangle up because of a simple but deep reason. Namely, there are  precious few ways for a chord to register as “tidy”, but a bajillion different ones to be “tangled”. Though each is relatively unlikely to form, we don’t really care which specific sequence of knots formed, all we know is that now we need to go untangle them.

weknowmemes.com

 

When we fold the earbuds in our pocket and go about our business, the chord starts shuffling around. In a way, it’s as if it “chose” a random shape to take, among the multitude it possibly could take. As tangled shapes are overwhelmingly more than the untangled ones, the chord will almost certainly end up tangled.

In 2007, two American physicists even experimented on this problem, and rigorously verified how likely it was to form various knots (which, by the way, also has to do with how DNA knots in our cells). They found that, in general, the longer and more flexible the chord is, the more likely it is that it forms knots (they even predicted which knots were more or less likely to form).

It’s no coincidence that all lifehacks to solve the tangle basically try to limit these factors, for example make the chord shorter by spooling it around something. Keep in mind, earbud chords are the worst: long, soft, they even fork at the end, tripling* the chance of knotting.

It may look mundane, but tangled earbuds are actually a manifestation of the universal increase of entropy. Among other things, this famous principle is also known as “everything spontaneously tends to disorder” and prohibits perpetual motion. Not bad for a ten-bucks piece of wire.

CC0-Optimusius1/pixabay

CC0-Optimusius1/pixabay

Tangled earbuds are just in the annoying fringe of a bunch of effects, from why a bowl of hot soup cools down, to why our books inexorably mix up, no matter how orderly we put them, to even why we smell flowers in a meadow. All, in very different ways, expressions of the increase of entropy. And we didn’t go into the really angst-inducing stuff, like why time flows in one specific direction!

So no, we cannot solve this problem any more than we can freeze time. But at least we can go around it with a few bucks worth of gadgets… or wait for Apple to eradicate it (for a lot more).

 

Cover photo: twisty (240/365), CC-BY Tim Pierce via Flickr. Some rights reserved.

*Think about it: the chances triple, not double.

How many times can you fold a piece of paper?

Some time ago I came across a fun article. I got curious, and embarked on a journey that took me to the source of a famous internet myth and even to explore what it means to be a physicist.

But let’s not get ahead of ourselves. The article was about the myth that it’s impossible to fold a piece of paper more than 7 times, and about the nice Finnish gentleman who tested it in this popular YouTube video.

At the seventh fold, the paper collapses spectacularly under the intense mechanical stress. After just one fold, it seems we get a new sheet, half as big as the original, and twice as thick. Clearly, that is just an approximation: the folds are in fact arcs, and the paper on the outside has to go all the way around the layers in between.

Moreover, the number of layers goes up exponentially. First it’s 2, then 4, 8, 16 and so on: at fold number seven, the outermost paper has to go around over 120 layers. At that point the stress on it is unbearable.

Bigger sheets could allow more space for the folds, strain the material less and avoid the problem. Some years ago, the people at MythBusters actually took a football-field-sized piece of paper and managed to fold it 11 times.

The world record belongs to a girl that reached 12 using a huge and very thin sheet. Personally, I wasn’t satisfied: giant sheets are cheating!

In physics, however, we can ignore some rules—say, the mechanical resistence of the paper—to answer bigger questions. For example: how many times could I fold an indestructible A4 paper if I could always make folds as perfect as the first?

A back of the envelope calculation told me that, always folding along the longest available margin, I can get to… 7 (that’s where it came from!). At that point I’d be holding a cubeish piece of paper, and further folding wouldn’t change it anymore following this rule.

But we could get as high as 22 changing the rules. For example, folding always along either the initial length or width of the paper, I’d end up with an object as wide as the initial sheet was thick (and a few hundred meters thick).

Can I keep folding something that small? And if I can, what to do when it reaches the width of an atom? or of a proton? The very idea of “fold” would lose meaning.

The issue, now, becomes: what rules are reasonable to ignore?

That is the art of physics: to decide what rules are important and what can be ignored, to walk the fine line of the reasonable approximations to answer a question. Albeit only… on paper.

 

Cover picture: CC0 Counselling, via pixabay.com