Collectively, our class recorded positions and times of a bowling ball. This sounds like a funny thing to say unless you were there to witness it. The bowling ball got rolled down a long hallway, and groups were able to synchronize their timing devices and associate a time with a given position of the bowling ball as it passed by. After a few different trials of this, we collected back into the room to share data. After all, the data are all only interesting once we see them all together. That’s an important point of the exercise.
We didn’t have time to compile all of our data from all four trials of the bowling ball rolling, so I left it as “an exercise for the reader,” as they say. (Sometimes in physics it seems like this is what we call the really hard problems, as though the textbook author or teacher doesn’t actually know how to finish the problem. I’m guessing that sometimes there’s some truth to that.) So, we set up a place where everyone could contribute their data online, and as those points were entered in a graph was created to display what the data look like. Right now, as I’m writing this, students are contributing their data points, and, so far, here’s what a graph looks like:
Almost everyone has put in their contributions, but two of our research groups haven’t yet submitted their data. (Don’t worry, it wasn’t due yet and I was getting ahead of myself.) You can see these points in their default positions on the left side. I’d just entered false numbers in for these at first, so the points show up, but not in the right place.
But we know where they’re going to go, don’t we? There’s a pattern here that the rest of the data is describing for us really clearly. If graphs could talk, this one would be screaming at us about the trend that’s taking place. If those last two data points come in and are not fitting into the line that’s inferred from the rest of the collection, we’re going to be really surprised and we’d probably even question what went wrong.
In fact, not only do we know about where these next two points are supposed to go, but we know an infinite amount of information from this graph already. The bowling ball was in all of the places in between all of these data points, all of the positions and times represented in this pattern. But we didn’t need to get an infinite number of stopwatches and recorders of the bowling ball. By knowing about only ten points in time and space, we could construct all of the information about all of the travel of this bowling ball. This is incredibly powerful. When was the last time you figured out an infinite amount of information and were able to represent it in one picture? In science, this is just what we do.
Why is this important?
First, this exercise — the collection and organization of data, the analysis and pattern-finding via the graph — tells us about patterns and how we use them to make sense of data. No single point of data was important. And, really, even though the collection of the data was essential, it wasn’t this assembly of ten points that was important. It was the overall trend that the collection showed to us. It shows us clearly what would happen in between all of our recorded observations; and it also shows us what happened even before we were collecting data. (Look closely: Can you describe where the bowling ball was when the time was at “zero?” What does that mean?)
Second, it tells us that Nature plays fair. Nature is understandable, predictable, and consistent. If it didn’t play fair and play by the same predictable rules all the time, we couldn’t do science. In fact, we couldn’t have even imagined the existence of anything scientific. Never would we have even thought to invent science if we didn’t have a universe that is operating in a consistent way. We probably can’t even imagine a universe that wouldn’t behave that way. We take it for granted that it plays fair because we’ve never known a universe that does not. (Okay, once in a while “life isn’t fair,” but that generally has more to do with the whims of people, and they’re really complicated bundles of nature, making it hard to get all of the right data to predict what they might do, not to mention why.) If Nature did not play fair and consistently, we would now have only ten or twelve bits of information that have no connection to anything bigger. Instead, we know everything.
Finally, that pattern and the interpolation of what nature is doing tells us something very specific. This is a bowling ball rolling down a hallway — to be sure, a questionable practice, but one that pays scientific dividends. That ratio of how far (position change) to how long (time change) is constant. We see this by virtue of the fact that the slope is always the same. What’s remarkable is that no one is doing anything to the bowling ball except for making sure it doesn’t run into anyone. And yet, it keeps going in exactly the same way throughout the trip. This is remarkable and miraculous, at least to my common sensibilities. How does the ball know to keep going, and especially to keep moving at exactly the same pace? Also, to be clear about our amazement, we don’t know why this is. It just happens. It’s not something that we could logic for ourselves without having rolled the bowling ball or some other object — maybe a hockey puck on ice or a craft through space, for example. We trace this kind of finding and this kind of data collection back to Galileo in the early 1600s; and, Newton used this to build the same physics that we use to run NASA’s space programs. We call this particular rule, “Newton’s 1st law,” but it’s more appropriate to say it’s the wonderful nature of motion. Motion is natural and consistent, not because we are doing anything to make it so, but because we are not doing anything to the bowling ball while it’s rolling. We’ll be trying to make sense of this.