Tools that calibrate each other

Here's a question that puzzled me the first time I saw it: Can you have two tools, each of which is used to calibrate the other? 

More precisely: Suppose you calibrate some of your own tools in-house, instead of sending them out. And suppose that when you calibrate Tool-1, you use Tool-2. Normally there's nothing wrong with that, so long as Tool-2 itself is also correctly calibrated. But back when you calibrated Tool-2, you did it using Tool-1. Is that a problem?

The first time I saw this, it bothered me. It looked like, "I'll tell them you're an expert; and then if they want to know what gives me the standing to say so, you tell them I'm an expert. Since they already know that you're an expert (because I just said so) they should trust your judgement. Right?"

And in a static world, I might have had an argument. But I forgot about time. 

Remember that when you calibrate any tool, that measurement typically has a validity period. Maybe it's valid for one year. So let's say you calibrate Tool-1 every January, and that calibration is good from January to December. Then you calibrate Tool-2 every July, and that calibration is good from July to June.

Last month was July 2023. Time to calibrate Tool-2.

So you pull out Tool-1. Is it a valid tool to use? Check the sticker. It was calibrated in January 2023, and is good through December 2023. So it must be good to use.

But wait. Let's check the paperwork to make sure. According to the paperwork, when we calibrated it in January 2023 we used Tool-2. Hold on! Isn't that the same tool we're trying to check right now?

No. It's not.

The tool we are trying to check "right now" (meaning last month, when I've set this story) is "Tool-2-as-of-July-2023." The tool we used last winter back when we were calibrating Tool-1 was "Tool-2-as-of-January-2023." If you look at it right those should count as different tools, because tools drift over time. We all know that tools drift. That's why calibration has to be repeated. That's why there is a validity period in the first place!

Sure enough, if you keep following the paperwork back in time, you'll find the two tools leapfrogging each other. Each time you use this one to calibrate that one, the one you are using turns out to be a legitimately calibrated tool because it's only six months into its 12 month validity period. And when you trace them far enough back in time you find the day that each tool was purchased from the manufacturer, at which point it came with some kind of certification and guarantee.

It took me a while to figure it out, but I'm sure this is the answer.