By JC Stoner

In Fall 2002 I was enrolled in Computation and Experimentation in Physics, a three-credit science class at Kansas State University. It was a wild course full of impractical, but actually quite practical, projects and labs with a lot of math. For example, for one assignment we used Excel to create a table with the X-Y coordinates of two objects, their masses, the gravitational force between them, and starting velocities (among other things) that then calculated the objects’ placement relative to each other over time. For hundreds of thousands of rows… Once we finally graphed the table, the instructor said, “you just plotted the Earth and an asteroid’s trajectory over time. Now spend the next 30 minutes experimenting with the starting distances and velocities and masses and try and ‘catch’ the asteroid in Earth’s orbit.” Nobody ever caught an asteroid. I think I got to six complete orbits before the asteroid still got flung off outside my graph.

That assignment was my first introduction to the sheer power of Excel’s; particularly its ability to run recursive formulas and rolling calculations. Over my career I’ve thought about that assignment frequently as I continued to advance my Excel abilities and formula usage when building budgets, compiled assessment and programming data, and sometimes just for fun when making spreadsheets more complex than necessary. 

But the assignment that really stuck with me started off with an even stranger prompt.

“How many molecules are in the width of a car tire?”

Everyone in the class looked at each other like we didn’t expect those words to come out of anyone’s mouth that day. But we had the assignment and we “understood” the assignment. We all worked independently and came up with our numbers. The instructor told us to write all our individual answers on the board.

As each person wrote their answer on the board, the class collectively chuckled. All of our responses appeared to be so wildly different it was almost hysterical. I’m talking numbers ranging from 250M to 750M, if I remember correctly.

The instructor responded: “Nice job. Believe it or not, you are all correct.” 

He continued by explaining that the exact number itself didn’t matter. The order of magnitude is what mattered. 

As it turns out, being off by several hundreds of millions is inconsequential when looking at a scale of billions or even tens of billions. At any scale, differences within the same order of magnitude matters far less than differences across orders of magnitude. There is no meaningful difference between 26 and 78, provided there is also something in a different order of magnitude (i.e., 3 or 470). In other words, even wildly different estimates can still be “correct” if they fall within the same order of magnitude.

I think about this every day. Not the car tire. The lesson on magnitude and scale.

• A $100 RA program is insignificant within a $45M operational budget. But a $100 RA program means something on a $500 hall programming budget. One is 0.0002% and the other is 20%.

• In my first full-time job I had a campus-wide maximum occupancy of 400 beds. Missing my occupancy projections by 1 resident had a substantially bigger budgetary impact there than if I miss my current occupancy projections by 1 out of 6500, even with the same room rate at both campuses. 

• Replacing one closet door in a dorm room isn’t a big deal (~$300). But adding 1000 closet doors in a new build adds up quickly ($300K, or 3 orders of magnitude more). But then again, on a $150M new build project budget, it’s still only about 0.2% of the total cost.

• Logistically, there isn’t much of a difference in planning an event for 30 people and 60 people. But scaling up an order of magnitude and planning for 100+ people feels very different. The difference feels even more substantial when planning for one more order of magnitude up (1000+ people). Scale up another order of magnitude (10K+) and all of a sudden your event is actually just running a university.

• I know from my residence life days, there is a noticeable difference between directly supervising fewer than 10 RAs and 10 or more RAs. It’s nearly impossible to increase full-time direct reports more than one order of magnitude, but indirect reports can easily scale on orders of magnitude. In my previous job I had nearly 75 in my reporting umbrella. Now I’ve got ~150. The guy across the hall from me runs our in-house dining program. He has 1,500 in his reporting umbrella.

It’s certainly interesting to think about the economy of scale. It can actually be quite addictive because not only do the numbers grow, but they also accelerate. 

Thinking one order of magnitude up is also a valuable skill to develop. What would I have to expand, change, or modify in my process/procedure/system to handle the volume one order of magnitude higher? What techniques would I have to change in my management style if my staff size were to increase by one order of magnitude? What budget strategies would be effective or ineffective if my budget were to increase by one order of magnitude?

If these sound like questions you might get asked in your next job interview, they very well could be. Minimally, the answers to these questions should be imbedded into your responses in your next interview. If you want to move up, you should already be thinking about the next order of magnitude.

J.C. Stoner, Ph.D.
Director of Housing Systems & Services
University of North Texas