We miss the slide rule. It isn’t so much that we liked getting an inexact answer using a physical moving object. But to successfully use a slide rule, you need to be able to roughly estimate the order of magnitude of your result. The slide rule’s computation of 2.2 divided by 8 is the same as it is for 22/8 or 220/0.08. You have to interpret the answer based on your sense of where the true answer lies. If you’ve ever had some kid at a fast food place enter the wrong numbers into a register and then hand you a ridiculous amount of change, you know what we mean.

Recent press reports highlighted a paper from Nvidia that claimed a data center consuming a gigawatt of power could require half a million tons of copper. If you aren’t an expert on datacenter power distribution and copper, you could take that number at face value. But as [Adam Button] reports, you should probably be suspicious of this number. It is almost certainly a typo. We wouldn’t be surprised if you click on the link and find it fixed, but it caused a big news splash before anyone noticed.

Thought Process

Best estimates of the total copper on the entire planet are about 6.3 billion metric tons. We’ve actually only found a fraction of that and mined even less. Of the 700 million metric tons of copper we actually have in circulation, there is a demand for about 28 million tons a year (some of which is met with recycling, so even less new copper is produced annually).

Simple math tells us that a single data center could, in a year, consume 1.7% of the global copper output. While that could be true, it seems suspicious on its face.

Digging further in, you’ll find the paper mentions 200kg per megawatt. So a gigawatt should be 200,000kg, which is, actually, only 200 metric tons. That’s a far cry from 500,000 tons. We suspect they were rounding up from the 440,000 pounds in 200 metric tons to “up to a half a million pounds,” and then flipped pounds to tons.

Glass Houses

We get it. We are infamous for making typos. It is inevitable with any sort of writing at scale and on a tight schedule. After all, the Lincoln Memorial has a typo set in stone, and Webster’s dictionary misprinted an editor’s note that “D or d” could stand for density, and coined a new word: dord.

So we aren’t here to shame Nvidia. People in glass houses, and all that. But it is amazing that so much of the press took the numbers without any critical thinking about whether they made sense.

Innumeracy

We’ve noticed many people glaze over numbers and take them at face value. The same goes for charts. We once saw a chart that was basically a straight line except for one point, which was way out of line. No one bothered to ask for a long time. Finally, someone spoke up and asked. Turns out it was a major issue, but no one wanted to be the one to ask “the dumb question.”

You don’t have to look far to find examples of innumeracy: a phrase coined by  [Douglas Hofstadter] and made famous by [John Allen Paulos]. One of our favorites is when a hamburger chain rolled out a “1/3 pound hamburger,” which flopped because customers thought that since three is less than four, they were getting more meat with a “1/4 pound hamburger” at the competitor’s restaurant.

This is all part of the same issue. If you are an electronics or computer person, you probably have a good command of math. You may just not realize how much better your math is than the average person’s.

Gimli Glider

Even so, people who should know better still make mistakes with units and scale. NASA has had at least one famous case of unit issues losing an unmanned probe. In another famous incident, an Air Canada flight ran out of fuel in 1983. Why?

The plane’s fuel sensors were inoperative, so the ground crew manually checked the fuel load with a dipstick. The dipstick read in centimeters. The navigation computer expected fuel to be in kg. Unfortunately, the fuel’s datasheet posted density in pounds/liter. This incorrect conversion happened twice.

Unsurprisingly, the plane was out of fuel and had to glide to an emergency landing on a racetrack that had once been a Royal Canadian Air Force training base. Luckily, Captain Pearson was an experienced glider pilot. With reduced control and few instruments, the Captain brought the 767 down as if it were a huge glider with 61 people onboard. Although the landing gear collapsed and caused some damage, no one on the plane or the ground were seriously hurt.

What’s the Answer?

Sadly, math answers are much easier to get than social answers. Kids routinely complain that they’ll never need math once they leave school. (OK, not kids like we were, but normal kids.) But we all know that is simply not true. Even if your job doesn’t directly involve math, understanding your own finances, making decisions about purchases, or even evaluating political positions often requires that you can see through math nonsense, both intentional and unintentional.

[Antoine de Saint-Exupéry] was a French author, and his 1948 book Citadelle has an interesting passage that may hold part of the answer. If you translate the French directly, it is a bit wordy, but the quote is commonly paraphrased: “If you want to build a ship, don’t herd people together to collect wood and don’t assign them tasks and work, but rather teach them to long for the endless immensity of the sea.”

We learned math because we understood it was the key to building radios, or rockets, or computer games, or whatever it was that you longed to build. We need to teach kids math in a way that makes them anxious to learn the math that will enable their dreams.

How do we do that? We don’t know. Great teachers help. Inspiring technology like moon landings helps. What do you think? Tell us in the comments. Now with 285% more comment goodness. Honest.

We still think slide rules made you better at math. Just like not having GPS made you better at navigation.