CS Column 4: Numbers

Small scales, huge numbers

I’ve recently been reading a bit about nanotechnology, and I realized the contradiction that thinking of such insanely small scales brings. You’ll always end up dealing with huge numbers.
In order to try to grasp something as tiny as a nanometer, we try to convert it to the next best thing – the smallest tangible, imaginable distance, the smallest scale on your average rule: a millimeter. This conversion forces us to use hard to imagine scales: a billion nanometers are supposed to fit in between one of the ten tiny lines on your ruler which divide a centimeter. One billion, in such a tiny space? To me, it’s impossible to even imagine such a number. Let alone to mentally chop up this centimeter-space on a ruler in a billion bits. How do I know – other than ‘very tiny’ – how big a nanometer is?
One example I recently came across stuck with me. Supposedly, during the time it takes us to pronounce the word ‘nanometer’, our hair grows ten! This fact impressed me. But, this hair example is not a stranger when it comes to imagining small scales. There are a few often-used examples of making nanometers or other small scales imaginable, one of them being to use the width of a human hair to illustrate the nano-scale.
But how helpful is that? According to one source, the average width of a human hair can vary from around 17 to 181 µm (that’s micrometer: a millionth of a meter. Huge compared to a nanometer). That means a human hair can vary from 17.000 to 181.000 nanometers. Let’s take a look back at our hair growth example. While your hair grows ten nanometers in one direction (in the time it takes you to pronounce the word ‘nanometer’), the other direction can be up to 181.000 nanometers long. That puts this impressive fact into perspective.
In the end, a nanometer is an abstract unit of measure we cannot use it in everyday life. And why would we? We can’t use it for ‘real-life’ measurement. We either use it when downscaling from bigger scales, and consequently end up with huge numbers. Or we use it when we deal with the totally abstract world of molecules and atoms, and then we end up in the even harder to imagine abstract world. Any attempt to make the scale tangible deals with intangible smallness. We’re always stuck with the contradiction of using huge numbers to imagine tiny scales.
Read my 3rd column for the Cool Science class:
» The case of my disappearing socks

Read my 2nd column for the Cool Science class:
» Mobb Deep’s Vision on Evolution Theory

Read my 1st column for the Cool Science class:
» Emerging Chaos – The Rules of Vietnamese Traffic

CS Column 3: Uncertainty

The case of my disappearing socks

I keep losing stuff. Even though I live on a surface of seven square meters I manage to misplace and lose all kinds of stuff. More than once pairs of my socks get separated, resulting in me having to wear two different socks. This leaves me wondering: did I lose these socks, or do they magically disappear by themselves? More often than not, the latter seems more likely to me.

Like a religious man clinging on to old stories to explain the inexplicable, I arm myself with science. “It’s not my fault” I tell my girlfriend, “it’s because my socks are wavy.” “… it has to do with quantum mechanics!” I bluff. This intimidating set of scientific principles can be my best friend when I’m blamed for losing stuff.

It works from inside the socks. Let’s take a closer look at my socks. Zoom in all the way, until the separate fibers that make up the sock’s fabric are exposed. Now keep on zooming, until eventually the structure of these fibers will show itself in the molecular scale. Keep on zooming still until you reach the atom-level, previously thought to be the smallest elements in our universe. Now we’re close: keep on zooming, until finally these elements break down into their subatomic parts – electrons and atomic nuclei, made up out of protons and neutrons. This is where the magic happens. This is what makes my sock disappear.

The problem lies in the behavior of the tiny particles that make up the atoms. Take electrons for example: we imagine electrons as tiny balls that fly never-ending circles around the atomic nuclei. But they’re not. Electrons are not simply miniscule balls flying around, they don’t behave like particles in a fixed trajectory. At least, sometimes they do. But at other times, they behave like a wave.

Now this wavy behavior is interesting: since a wave is never on one location at any given time, but rather on multiple locations ‘spread out through space’, it is impossible to know or measure the exact position of an electron at a specific moment in time. This means an electron has a multitude of possible locations at any moment.

So if the things in atoms behave like wavy things – wavy things with multiple possible positions, of which we can’t pinpoint the exact one – doesn’t that mean this also goes for the atoms they constitute, and for the molecules the atoms add up to, and consequently for the fibers of the fabric that make the sock? Wouldn’t it mean that if all atoms ‘wave’ their way to some other place, my sock would ride along in this atomic wave, and change its position?

So the key question is: are my socks really wavy!? Unfortunately, the answer is no. It’s not as simple as I’d like it to be: upscaling the weirdness of the microscopic world to the real world just doesn’t work. The reason a subatomic particle can show wavy behavior is not because of its scale, but because of its isolation. A single, isolated particle behaves like it does because it is isolated. Only if a subatomic particle is completely isolated, it behaves like a weird wavy thing. More surprisingly, this also implies that even to this day, science has failed to demystify the underlying mechanism of my disappearing socks. I can still bluff my way through, though. Quantum mechanics are to blame!

Read my 2nd column for the Cool Science class:
» Mobb Deep’s Vision on Evolution Theory

Read my 1st column for the Cool Science class:
» Emerging Chaos – The Rules of Vietnamese Traffic

CS Column 1: Emergence

Emerging chaos: The rules of Vietnamese traffic

When I took this picture in Ho Chi Minh City, Vietnam, I was awe-struck by the chaotic traffic. Dozens of “motobikes” buzz down the streets, seemingly not paying any attention to traffic lanes and rules, oncoming traffic or anything in their vicinity. Cars move through the thick clouds of bikes, and some brave souls even pedal their bicycles straight through it.

For an outsider such as myself, it initially looked like a totally random and chaotic event. Did these people just hope for the best when they were driving through their city? It was obvious all of this chaos would have to work out one way or another. Eventually – I assumed – everyone got where they were going. But how?

Soon I learned there is in fact a systematic at play, and there are plenty of unwritten rules involved in the apparent chaos. You learn this with the one confrontation you cannot avoid: crossing a road on foot (a very intimidating undertaking at first). The basic rule is simple: keep on moving – as long as you do, people manage to anticipate your path and will make sure not crash into you. The next step is that of total immersion: hop on a bike and jump right into traffic.

Once you participate, you realize how simple it actually works. It felt like I was part of a flock – all neighboring motomen adjusted and maintained their speed based on mine and that of the other drivers directly around us. This was not at all obvious when I was observing the traffic from the sidewalk. Eventually I didn’t even worry about horrible fatal accidents anymore, a theme predominantly on my mind when I was only watching the traffic…

Even if it looks simple when you’re in traffic, there is still speeding and overtaking, not everyone is heading to the same destination, so people are constantly moving in and out of the flock. The same principle however applies: when you take a turn, all is fine as long as your movement is fluid. It’s not the turn signals that will save you here: clear and predictable movement will.

What at first seemed totally unnatural to me started feeling more natural, and eventually made sense to me. But it only started to make real sense once I was back home and started reading about swarm intelligence and flocking behavior. The same three rules flocking behavior dictates seem to apply in Vietnamese traffic: separation (avoiding neighbors), alignment (keeping roughly the same direction) and cohesion (sticking together). These simple rules are all you need to create a realistic computer model of a flock of birds, and indeed it’s also all you need to create what seems to be ordered chaos on the roads of a Vietnamese city – I followed the same rules when driving through Ho Chi Minh City on my rental motobike.

As a matter of fact, when I came back home I had to re-adjust to the way traffic works in Holland. Traffic lights, zebra crossings, and the rules of the road were deciding for me where I was going. The Vietnamese traffic which at first seemed unnatural, chaotic and most of all very scary, eventually felt natural, ordered and elegant in its simplicity.