Significant figures: scientists' time machine

We live in a continuum. A continuum of time, a continuum of emotions, a continuum of ever decreasing telomere lengths...our life is always in perpetual motion. But of course, if you are able to stop time, or the construct thereof, you get a discrete snap shot of our lives. I want to argue that you as a scientist, practicer of statistics can control time.

How can we control time? Through manipulating significant figures!

I liken significant figures to be the god of time. Let me explain. Time measurements can be in the form of continuous or discrete variables. Let us quickly define these terms:

• Continuous variables: measurements within a range that is composed of infinite possibilities
• Discrete variables: measurements taken from finite number of possibilities. 

So time can be continuous in that there are infinite possible time points you can achieve even from 0 to 1 second. Conversely, time can be discrete as either 0 or 1 second for example. What dictates this difference is the number of significant figures. As you see, continuous variables contain many significant figures to capture millseconds, nanoseconds, or even picseconds such that there are infinite possibilities of measurements. And discrete values have fewer significant figures to capture a range of time measurements into a finite possibilities. So, by decreasing the number of significant figures by rounding down, you are traveling back in time or traveling into the future by rounding up. 

Surely, this is just a philosophical adventure (which mostly doesn't make any sense) into continuous and discrete variables. But every time you are measuring time, continuous or discrete, think of yourself as traveling through time. And with that, I think we have just invented time travel through research and statistics.

Variables in the Publix Marathon

In class this semester, we learned about two different types of variables. Variables may be continuous or counted. Counted variables are, perhaps obviously, things we can count. They are represented by ordinal numbers. Let’s look at these two types of variables in a real life example: the Publix marathon. The Publix marathon took place in Atlanta a few weeks ago. There were 1,378 participants. There were 909 male participants. The number of people is a counted variable. What continuous variables are there in the Publix marathon? Time is a continuous variable.

You might think time isn’t a continuous variable because you can count it. You can tell me what time it is: “It’s 12:30”. Looking at the difference between second and third place overall winners (which can be found here), minutes are specific enough to separate them. There are 13 minutes separating these two runners. Sometimes though, time needs to be more specific than just hours and minutes. The 9^th and 10^th place finishers overall, Jacob and Jeffery Law are separated by 1 second. These two, who appear to be brothers, ran the whole race together with the same pace of 6:46 per mile but in the end one of them had to finish before the other. Since time is continuous, Jacob, the older brother, gets to brag about beating his brother in a marathon.

Still, we all learned that a second is “one Mississippi” in kindergarten. We can find things that are measured in less than a second by turning away from an everyday example and back towards science. In my lab, to determine enzyme kinetics we use a rapid flow quench machine. 

This machine allows for a minimal reaction time of 2.5 milliseconds! An example of the data generated from this machine can be seen below where one student in our lab collected five data points in 0.5 seconds.

Whether you are trying to win a marathon or determine the kinetics of your favorite enzyme, the fact that time is a continuous variable is a good for you.