Cybertruck approaches infinity

Tesla has made an amazing claim for its soon-to-be-available, coyote ugly Cybertruck: the ability to pull “near infinite mass.” Here’s the text from the Tesla site:

RUGGED STRENGTH

With the ability to pull near infinite mass and a towing capability of over 14,000 pounds, Cybertruck can perform in almost any extreme situation with ease.

This could be absolutely true, for small values of infinity

Let’s define two terms used in this claim: “near” and “infinity.”

Colloquially speaking, let’s say that “near” means 80% of the way to something. So if you’re loading your truck with 100 pounds of cargo, you’re nearly there when you’ve loaded 80 pounds of stuff.

What is infinity? As a former mathematician who actually worked with infinities, I can speak to this. Infinity is not a conventional number. You can look at it as the limiting case of a set of numbers (for example, 1, 10, 100, 1000, 10,000, … is a series that approaches infinity). And if you calculate with limits, this actually makes sense (subject to certain rules). For example, it is a true statement that as x approaches infinity, 1/x approaches zero. The key is the word “approaches,” because you can never actually get to infinity in conventional arithmetic.

Infinity is also an actual “number” in the class of transfinite cardinal or ordinal numbers, but arithmetic in that class of numbers is not the same as with traditional numbers. For example, ∞ – 1 = ∞, which is a statement that is true for ∞ but not for any real number. Once you start allowing infinity to be a number, the rules of arithmetic change.

Since we want to do arithmetic with numbers like 14,000, let’s consider the first concept, that of “approaching” infinity. And for now, just for the purpose of this analysis, let’s ignore the fact that pounds are a unit of force and not mass and conflate the two concepts, causing all the actual physicists and physics students in the audience to wince.

So what number does “near infinite” mass to? If 14,000 pounds-mass is near infinite, by our 80% test, infinite mass would be 17,500 pounds, or 8.75 tons. That’s an awful lot, but it doesn’t seem anywhere near infinite.

Of course, 14,000 is just the towing capability. Perhaps the Cybertruck is able to pull more than that, if only for a few moments. Let’s give Tesla the benefit of the doubt and imagine it can pull ten times that, or 140,000 pounds (70 tons).

If that’s near-infinite, then infinite mass is 70 tons divided by 80%, or 87.5 tons.

Just for comparison, the Statue of Liberty including the copper, the framework, and the foundation weighs 27,000 tons. That’s more than 300 times the infinite mass implied by our Tesla calculation. Therefore the Statue of Liberty has (more than) infinite mass, and New York Harbor and the entire Earth are about to be pulled into a black hole.

Hmm, we must have made an error somewhere. Either we did, or Tesla did.

Infinite lies

It’s best not to use the infinite in marketing claims regarding numerical quantities. You can have infinite love, or infinite desire, but not infinite towing capacity or infinite cabinet space.

Telsa’s CEO lies all the time. I guess Tesla’s marketing department takes its cues from there.

Face it, only one car company is allowed to talk about infinity. And that, of course, is this one: