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

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Top 5 stories in (and around) physics of 2016

Maybe 2016 hasn’t been a great year in general, but at least for science it has. A year full of discoveries: expected, missed, surprising. From Solar System exploration to the frontiers of artificial intelligence, from the atomically small to the immensely big, it has been a busy year!

Here’s my personal top 5 news of this year. Sit back. Enjoy.

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Every snowflake is unique

No Christmas landscape is complete without snow. Lots of snow. And every little snowflake is unique, everyone knows that! How come, tho?

Snow is nothing else than teeny tiny ice crystals that form in the clouds and stay solid all the way down to the ground. Water crystallizes around microscopic imperfections, like dust particles floating in the clouds. Once the initial nucleus is formed, the microscopic droplets gather around it very rapidly.

Even though all snowflakes are somewhat hexagonal (due to the geometry of water molecules), each of them grows in slightly different conditions. Some had more water droplets close by, some other was in a portion of space a fraction of a degree warmer. Each and every factor counts: the final shape of the crystal is sensitive to exactly everything.

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Snowflake Sculpture 3, CC-BY-NC Julie Falk, via Flickr.

So the shape of each snowflake is random, it’s like rolling a die with infinitely many faces. You never know what will come out and all outcomes are different. If you want to put it in more physics-pompous terms, the formation of snowflakes is a stochastic process.

In the end, each snowflake is a picture of the exact conditions in which it formed. And since it’s impossible to reproduce the exact same conditions twice, each of them paints a slightly different picture.

Like pictures, snowflakes too come out better if the scene doesn’t move too much. Indeed, if conditions don’t stay relatively constant around the budding crystals, anything can happen. Most of the times, several crystals aggregate in one big snowflake, sort of a little snowball, which look a lot more like each other.

Regardless of the conditions, it’s really hard to tell them apart anyway.

Happy holidays from amorefisico!

Cover photo: Snow leopards playing in the snow, CC-BY-ND Tambako The Jaguar, via Flickr. Some rights reserved.