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

The sound of silence

Think about the most quiet place you’ve ever been to. Now imagine something even quieter. What does that sound like? If you can’t figure it out, physics can help: let’s start by looking at how sound works.

Loudspeakers, vocal folds and instruments all function by the same principle: rhythmically push and pull on air. The air molecules, in turn, push and pull on their neighbors, that push on their neighbors, and so on. Air thus stretches in some points, compresses in others, creating a wave of pressure. A sound wave is born.

translational_motion

Molecules of air “staying put” actually do a lot of moving. CC-BY-SA Greg L, via Commons

But what if there is nothing to move air and produce sound: what does silence sound like? Does it have one at all or is it like questioning the color of an invisible thing?

Air molecules bump into each other and vibrate all the time. Just by being there and having a temperature, air is bound to create microscopic changes in pressure here and there. Even the most barren, isolated, still place has a sound: the sound of silence.

Molecular collisions like these are pretty much random and independent. Their sound—silence—is then white noise, the stuff some people use to relax or focus.

The loudness of silence kind of depends on what frequency range you look at: the narrower the window, the fewer kinds of bumps you will find, and the quieter silence will appear.

According to some calculations, in the band of maximal sensitivity of humans (around the pitch of speech), air sitting there is about -20 decibels. That’s silent. Too much for us: it’s just audible for an owl, a super-specialized stealth predator with ears literally the sound of its face.

That big circle around an owl's face funnels sound: it's basically a giant ear. CC-BY-NC-ND Brian Scott/flickr

The owl’s face circle funnels sound from the environment: it’s basically a giant ear. CC-BY-NC-ND Brian Scott/flickr

However, in the full range of human hearing, silence is considerably louder: about 0 decibels, which is also about the faintest thing we can hear.

That means our hearing can handle anything barely louder than total silence just as well as a conversation—a thousand times louder. Sounds good enough.

If you want more
  • How is 60dB a thousand times more than 0? Decibels are weird: here’s a summary of this and other peculiarities.
  • What does it mean “white noise”? Can it be other colors too?
  • Some say total silence drives you crazy. Scientists don’t work on hear-say. They try.

 

Cover photo: CC0 Sam Halstead, via pixabay.

What the eff is an fMRI?

Some parts of the brain “light up” when we feel certain feelings, or listen to music, or tackle math problems. Certainly you’ve stumbled upon such news, given how frequently they end up in mainstream media. The technique used for these studies (and many others in neurosciences) is called functional Magnetic Resonance Imaging (or fMRI), which is an amazing thing, but also seems to have a few issues. I think we’ll be hearing about it in the near future, so it’s worth knowing what it’s all about.

An MRI machine. CC-BY-NC Penn State, via Flickr.

Let’s start from the beginning. The magnetic resonance imaging—MRI, the stuff sportspeople get done to assess injuries—uses magnetism and resonance (you don’t say!), or the unusual reaction of an object or material to stimuli of a specific frequency.

If, for example, we push someone on a swing every time they arrive all the way back, we’ll make them go higher than if we just pushed at random times. Simplifying (a lot), the MRI uses radio waves to push hydrogen atoms, of which there’s plenty in tissues rich in fat and water, like the brain.

Their nuclei have spin, a property that makes them react to magnetic fields somewhat like a compass would. The MRI machine applies a strong magnetic field, which aligns all the spins, then it hits them hits the atoms with a pulse of radio waves. If its frequency is just right (called resonance frequency), the wave will flip a few spins (not their atoms!) opposite to the magnetic field.

As soon as the pulse stops, it’s all back to normal, and atoms that flipped release a little energy. Recording these emissions with an antenna it is possible to distinguish tissues with different water contents, for example, different parts and layers of the brain, and build an image.

Simplified sketch of an MRI. The atoms (red balls) align along the green magnetic field until the magenta wave flips some of them. As soon as they can, atoms fall back to their original state, emitting energy recorded by the blue antenna. Credit: howequipmentworks.com

fMRI works by rapidly taking a lot of MRI pictures. Analyzing them we can understand what parts of the brain were more active at various time, because oxygenated blood rushes to these areas, producin a slightly different signal from that of “used” blood being flushed out.

The idea is simply genius. However, some recent studies urge caution and intense scrutiny on the statistical analysis used to process the images. In one of these studies, for example, a dead salmon seemed to react to pictures of humans.

That does not mean that the technique is rubbish, it just means we need to be careful. These studies are fundamental for research, because they let us identify issues. Only this way can we know what we’re doing and that we’re making the fullest and rightest use of the amazing results of spectacular techniques like fMRI.