Why Statistics?

Science is one way people make sense of the world around us.  We look very closely at Nature, and try to describe precisely what happens--without extra, unnecessary aspects--and without missing necessary aspects.

In order to look very closely at how the Universe behaves, we look at very small particles, waves, and phenomena.  Indeed, we must look at things that are so small, they seem to have very little in common with the way we see our macroscopic world unfolding.  Our real life experiences, in the macroscopic world, are made up of incomprehensibly tiny activities on the microscopic scale.  Statistics allows us to unify these two perspectives, which is incredibly powerful (as well as profound!).

An example of this is a volume of gas particles.  For simplicity, we will consider a gas at low pressure, so that the particles effectively never collide (these days, this is routine to achieve in the lab--I do it every day).  Every particle in the system will be in a slightly different state--maybe this one's rotating this way, that one's vibrating that way, this one's going really fast in that direction, etc.  In a macroscopic system, there are simply too many individual particles and possible states to keep track of.  With statistics, we can describe them in spite of this baffling complexity!

Let's look at the speeds of argon atoms (argon makes up about 1% of the air we breathe).  In our example below, a system of 56 argon atoms is organized by color/speed and position.  Moving from left to right, and from red to purple, atom speed is increasing (the labels have units of meters per second).  Most atoms are in the middle (yellow), and have relatively moderate speed.  There are also statistical outliers that have very slow speeds (red), and very fast speeds (purple).  The beauty and power of statistics is that it doesn't matter if we have 56 atoms or 56x(10^23) atoms-- arranging them this way will always approach the shape of the curve with almost perfect precision.  The size of the system doesn't affect its behavior, and time doesn't either!  If we look at a single particle at different times, it's speed distribution will also follow that line (speeding up and slowing down as it bumps into neighbors who had been going faster and slower, respectively).  [Note that in our example, we've greatly reduced the pressure, so these energy-exchanging collisions are so rare that colors/speeds are effectively constant in time.]

This demonstrates that although we can't actually arrange atoms into neat little rows and count their speed distributions, we can do this in our minds, and it's a valuable trick we can use to understand our world, and sometimes even control it!

[download this free software if the demo doesn't load]


Details and Warnings:
The example is for argon at room temperature (300 K) and a pressure of 5x(10^-10) atm, and our box has edges of ~17 micrometers.  In order to see things happen, we have to slow time by a factor of 10^8 (so 1 demo second = 10^-8 nature seconds), and blow up the atoms to ~3,600 times their real size.  The balls are just over-sized place-markers, so when they appear to pass through one another without colliding, it's because the atoms are actually much smaller, and so have plenty of room to fly by without colliding.  Also, real atoms don't bounce off walls the way basketballs bounce on flat surfaces.  In reality, they bounce off walls the way a basketball would bounce off a bunch of packed together basketballs.  (After all, the walls are just more atoms!)