When math works itself into political debates at the national level, it generally takes the form of a cudgel.

To whit, the president wields a large number as the reason he needs to take away a fundamental right: the right to a trial.

Articles like this one argue about the ethics, legality, and moral soundness of what the president is trying to do. But what we don’t see in typical discourse is a sanity check on the fundamental assertion: would it really take 200 years to process hundreds of thousands of deportation cases? Does that math hold up? [Spoiler: no.]

FERMI PROBLEMS
The mental reckoning of estimating with large numbers and imperfect information was popularized by the physicist Enrico Fermi. According to legend, he did a quick mental calculation before the first atom bomb was tested, concluded that the radiation wouldn’t hurt him (or his eyes), and was the only one to watch the blast outside of the lead bunkers.

He was known for quickly finding uncannily close answers to problems such as “How many piano tuners are there in Chicago?” These “Fermi problems” can be fun exercises in the classroom. One of my favorites is due to Randall Munroe, of xkcd.com, who answered the question, “If you went outside and lay down on your back with your mouth open, how long would you have to wait until a bird pooped in it?”

But now we have a lot resting on a Fermi problem. So, let’s not be cowed by a big number! Would it really take 200 years to give everyone a trial? Let’s find out!

A SANITY CHECK

First off, how many trials are we talking about here? He says hundreds of thousands.
Let’s say 400,000.

Now, how many days does a judge work a year? There are 365 days in a year. Take away weekends and you have about 260 days. Holidays, etc., … let’s round it down to an even 200.

Two hundred days a year for 200 years is 200 × 200 = 40,000 days. That means if you could try 10 deportation cases a day, it would take 200 years to do them all.

Hmmm… 10 cases a day doesn’t seem like very many for the entire country to handle. Ten cases a day seems like what a single judge could handle. So I guess if there were only one judge working on this in the whole country, maybe it would take 200 years.

But that’s ridiculous! We must have more than one judge working on this, right?

A MORE REASONABLE ESTIMATE
With some hand-wavy estimates (they don’t have to be perfect) and googling, here are a couple of assumptions of numbers for a basic estimate:
Number of immigration judges who might work in this area: 400
Number of cases a judge might handle a day: 5
Working days a year: 200

Total cases processed in a year: 400,000.

So… maybe it would take a year to work through the backlog?

And to be clear, we might be off by a factor of 2 or more. Maybe it would take 2 years. Maybe 6 months. But we have a sense of scale here. And if the president said, “We cannot give everyone a trial because to do so would take, no exaggeration, 1 year,” it just rings different.

THE MORAL
This is all to say that it’s easy to get caught by a number wielded like a club. Whenever you hear someone make a point by tossing around a big number, you should run it through your own filter of what makes sense. Sometimes issues are more complicated, and require more expertise; sometimes not. Common sense can catch a lot of this “big numbers as rhetorical cudgel” BS, and make us smarter consumers of news, and debaters.

POST SCRIPT

I have unfortunately limited bandwidth to write blog posts these days, and even as math is showing up in politics in all kinds of guises, it takes me longer to write a blog post than it takes the news to make the reflection irrelevant. Here’s where I gave up and just posted about what I had hoped to write up in more detail.

Trying to write a blog post about the bad math modeling underlying the tariffs. In the time since I started it, the tariffs on China went from 20% to 54% to 104% to 125% to 145%, and tariffs on other countries paused and went down to 10%.

— Dan Finkel (@mathforlove.bsky.social) 2025-04-10T17:42:34.507Z