Most basic equation: Heart rate is in units of bpm. What are the units of "b"?

Question

This is the most simple question in the world, but it is surprisingly difficult to explain to a student. The heart rate is measured in bpm, beats per minute. Minutes are a true unit. Beats are not a true unit. However, we are using beats as if it where a unit. I'm not sure how to explain this to a student, and I'm confusing myself. Please help.

Answer 1

BPM means "beats per minute" but that doesn't mean that "beats" is a "unit." Otherwise we could have an infinite number of "units" based on counting other things.

For instance: How many red two-door cars with sagging taillights and broken headlights with expired license plates pass by a point on this road in a minute? Oh, $7$, you say? Well I suppose the rate is 7 RTDCSTBHELPPM."

So now "RTDCSTBHELP" is a "unit"?!?!

Insane.

Answer 2

@Stork led me to the answer, but he didn't quite get there. A "beat" is a "counting unit". This is the term I've been looking for! A "dozen" is also a counting unit. If you google "counting unit", you will find it is a fairly common term. So, if a "beat" is a counting unit, then what kind of unit is a "second". A "second" is a "measuring unit". This implies that counting and measuring should be treated as distinct activities, which makes sense. I had never really stopped to realize that counting and measuring are distinct.

I do apologize for dwelling on this, but I think this terminology will clarify matters for students.

ps. This ancient paper appears to discuss the distinctions.