For a long time, I was tricked by cell diagrams. Cell diagrams (such as the one above, written in ASCII, or the more spectacular multicolored diagrams that cover an entire page that you see in biology textbooks) are very interesting to look at, communicating the many different features of a cell, but also showing the neat interlocking way that the internal organelles communitcate with each other and the extracellular area through the clean process of proteins working through electrostatic, "key-in-the-lock" forces.

When I thought about it more, and really compared the size of a cell to the speed of the material inside, I saw that any attempt to compare the workings of the cell to the well worn metaphor of a billiard ball table was projecting a macroscopic model onto something it really wasn't appropriate for.

First, let's look at the size of a cell. A cell in a multicellular organism is usually between 10 and 100 micrometers. I will take 10 micrometers as my sample cell size. The atoms inside of this cell are around 0.1 nanometers, while a small molecule, such as water, sugar or an amino acid is about 1 nanometer. Proteins can go up to 10 nanometers. Which means that using linear measurements, the parts of the cell are from 1/100,000th to 1/1,000th the size of the cell. Of course, cells exist in three dimensions, so if we cube (more properly, we would use the formula for sphere volume, since they are roughly spherical, but cubes will do well enough for our estimate here) these size differences work out to a cell being a billion times larger in volume than its proteins, and some quintillion times larger in volume than the individual atoms contained there.

Personally, I find it hard to wrap my mind around numbers such as these. Translating these numbers into measurements that we may be familiar with will provide some sense of scale, although perhaps not much. If we were to take one of our atoms, at a tenth of a nanometer, and blow it up 100 million times its size, to a centimeter (roughly the size of the d10 I have in my hands right now), a sugar molecule or lipid would be about ten centimeters, the size of a tennis ball, and proteins would be 100 centimeters, or the size of a beach ball. Increasing the volume of the cell 100 million times would make it a kilometer on each side. So to put a cell in context, it would be like an orb a kilometer in diameter, full of objects ranging from the size of marbles to the size of beach balls, all moving around inside.

Even this image isn't all that hard to understand, since it can be roughly approximated by imagining one of those Chuck E. Cheese rooms full of balls, and then just imagining your favorite sports stadium filled in a similiar fashion (a very nice thought!). However, an additional factor to take into consideration is the tremendous speed of the particles inside the cell. It took me a while to realize this, but the normal brownian motion of atoms and small particles, also known as heat, is actually around the speed of sound. After all, when we shout, we aren't accelerating the air to the speed of sound, we are just creating waves in a medium that is already traveling at that speed. The speed of sound is roughly 1000 kilometers an hour, or about 300 meters a second. Which means that the normal atoms inside your body are moving at a speed that roughly translates to 3 trillion times the size of their body, every second.

So, what would happen if we were to increase the speed of our atoms as much as we were increasing their size in our analogy? If an atoms travels 3 trillion times the size of its body every second, what would that look like if it was a centimeter in diameter, instead of a tenth of a nanometer? Three trillion centimeters is 300 billion meters, or 300 million kilometers, which is a little more than the distance from Mars to the Sun. Thus, if an atom was a centimeter across, it would be moving at a velocity of 300 million kilometers a second, or roughly a thousand times faster than the speed of light.

Thus, if we were to visualize a cell as being an orb a kilometer wide, it would be full of around quintillion particles, all moving at a thousand times the speed of light. This, of course, doesn't bring into question the issues of resonance and electrical and ionic forces. But, put at this level, I have to admit that at least personally, I can't really understand the inner workings of a cell. And it is for this reason that whenever people shoot down alternative medicine theories based upon the a priori assumption that a cell can be analyzed in the same way as a "game of billiards" or some other macroscopic mechanical metaphor, I tend to think that perhaps they have misplaced their skepticism.