Consider a mental inventory of your own knowledge for a moment. Picture a big pile of all the things you know: concepts, processes, ideas about the world and humanity, equations, whatever. It’s hard to quantify but I bet you’ve got a decently-sized pile. Now next to that stack up a pile of the things you don’t know: all the subjects you wished you’d had time for in college, the equations that we’ve yet to derive, the contents of the universe, and so on. You’ll find that the pile of unknowns is to the pile of knowns as planet earth is to an electron in a single atom of helium. That is to say, the amount of stuff you or I or even collective civilization knows about the world is a lot, but it pales in comparison to what we wished we knew.
All of this to say that there are plenty of things we’re confident about. We live in a world where the newest sub-atomic particles are being tested and analyzed, but we still can’t quite figure out how our brains really work. We can send men to other planets, and yet we’re sorely lacking if asked for a good reason why humans need sleep at all. Our world is huge and unfathomably complex, and yet we have somehow (and I’ll never believe this) have been able to distill at least parts our world down to math and equations.
If you throw a ball up in the air, could you give someone a qualitative description of its action? “It left my hand and shot upwards, then slowed down to a point and came back down to earth pretty quickly.” Well, this isn’t exactly a scientific description, so how about something quantitative? Not only can we determine speeds, accelerations, and distances traveled by nearly any object in motion, but we’ve learned that the variables that go into the motion of such an object are really few in number. Armed with only a starting velocity, acceleration, and stopwatch, we can accurately determine the motion of objects. In essence, consider everything that has ever left the crust of the earth and has been temporarily under the control of only the gravitational force. We can describe its motion near-perfectly. Indeed, we can use the equations to the right, each of which are essentially the same statement but re-arranged four different ways.
In my mind, the fact that we can need only 3 or 4 variables to describe motion on earth is astounding — there are few, if any, hidden variables that we don’t yet know about in many of our “knowns.” Compared to the stuff we don’t know, we have somehow culled all the things we do know about motion in the right combination such that “motion of objects” is contained in our “knowns” pile. The odds of this happening in any universe are, in my mind, astronomically low, but of course I’ve got no evidence to back up that claim.
We can measure invisible electric and magnetic fields with pinpoint mathematical accuracy and tell our friends the time to the nearest millionth of any given day (excluding leap seconds here). This is stuff we know and have tested over and over – somehow these properties of earth and the universe ended up in our teensy weensy “knowns” pile.
One more example: Say you pump some oxygen gas into a room with no ventilation. If you know the temperature and pressure of the room, you can use a very simple math equation (PV = NRT) to find out the volume of that room (and consequently the oxygen gas you pumped into it). Let’s look at that equation a little closer.
The pressure exerted by a bucket of oxygen molecules: PV = NRT (where P is a pressure, V is a volume, N and R are constants, and T is the temperature)
Scientists agree that the product of pressure and volume is numerically equal to the temperature and two constants in any given situation. Of course there are some correcting factors for advanced chemist fanatics, but even they’re not too terribly complex. In short, this equation with only 3 variables and 2 constants fully describes the behavior of nearly any gas in any size room and at any temperature.
Have we really distilled molecular behavior into such a simple formula? It’s kind of hard to believe, but this is once again in our “knowns” pile. The whole point of this post is to spark a thought in your mind: with all the stuff that we don’t know, we still have lots that we DO know, and the stuff that we do know can sometimes be the simplest principles. We can combine the very firm theory behind the laws of motion and flight to get airplanes running; we can measure the density and buoyancy of any liquid matter inside a column and then find the pressure it exerts at any depth inside the column.
Someday we’ll be able to map out the motion of atoms during nuclear fusion, or realize that the perfectly efficient engine is just a combination of the right four or five variables. There’s so much to learn and so much to know that we haven’t even begun to study, and once we’ve got it all under our belts there’s a good chance that some currently unexplained phenomenon will be accurately represented with an equation — nothing more than a few letters and an equals sign.
Your Brain on Sci 