Can you explain concretely why it matters in daily life that I can cut the paper posters are printed on in half several times to wind up with paper of the size that letters are printed on, and that these have the same aspect ratio? Why would I ever want to do that / why should I care that it's possible?

I'm not trying to be combative; I genuinely don't know.

Not the paper, the stuff on the paper scales the same. Want a large poster and then also handbills to give out? They're identical. Got 15 full size sheets of colour information but now want to turn it into a pocket handout ? No problem, it's the same thing but smaller.

This feels obvious - of course it works like that, until your paper sizes aren't using this ratio (which the US ones don't) and then the frustration is apparent.

Isn't the important part here just using a consistent aspect ratio?

Like the fact that the aspect ratio chosen allows manufacturers to just use one base sheet and then subdivide it into smaller page sizes is convenient for manufacturers, but it's not a necessary property for scaling the contents of the page.

Having the halving property for each step means you can easily create booklets by getting paper one size larger and pinning it together in the middle. That’s pretty useful.

Sort of. For scaling something to different paper sizes, the constant aspect ratio is the important part. But the subdivision property is also important for a few reasons. Take booklet printing as an example. You need a paper size that's twice as wide as the normal paper size to print that on (so Ledger/Tabloid for booklet printing Letter pages). But ideally you'd want this larger paper size to have the same aspect ratio, so you could scale up something like a poster to it. The only aspect ratio that works for is 1:√2.

Same for printing two copies per page (2-up). With a 1:√2 ratio, you can perfectly fit two copies of something side-by-side on the same paper size. This was incredibly common back when I was at school, where A4 worksheets were printed 2-up on A4 paper so that each individual one was A5 in size (half the area, √2/2 the length). With A4, you then just chop the printed pages in half and the worksheet fits perfectly. With any other aspect ratio, either there'd be wasted space due to the different aspect ratio of the chopped-in-half paper to the original, or you'd have to print 4-up on larger paper and chop it into quarters. The 1:√2 aspect ratio of ISO paper sizes means you can just chop a page in half and get the same aspect ratio, and that's useful to people doing printing, not just manufacturers.

Here in the US we just print posters at whatever size we want. We don’t have to rely on someone to have standardized the sizes of posters. Large–format printers often go up to eight feet wide, so you can print something as big as a wall if you want (and as long as you like, because they print on a _roll_ of paper instead of a sheet). Computers have made elegant ratios irrelevant.

But if you really think it’s important, then you can consider a series of sizes like tabloid, letter, and memo to be equivalent to A3, A4, and A5. Each is exactly half the area of the previous, and can be had by dividing the larger size in half along the longer side.

> But if you really think it’s important, then you can consider a series of sizes like tabloid, letter, and memo to be equivalent to A3, A4, and A5.

This seems like you entirely missed the thread? The whole point is that this actually works for the A-series and in your made up US series it can't work because the ratio is wrong.

These are not made up sizes. They are standard paper sizes available in any store. Most ordinary househole printers won’t actually print on tabloid, and some won’t print on memo, but all copiers (and multifunction scanner/printers) can copy two letter pages and print them side by side, scaled down to memo size, on a single sheet letter of paper. It’s just a button you press, or maybe a checkbox you check, or whatever. It’s not magic.

The sizes aren't what I said you'd made up. The series is, because of course this doesn't work properly with your scheme:

Let's try, start with 216 x 279 Letter and we'll scale that so we can fit two on the 279 long side, so they're just under 140mm wide now, memo size, but um, when we do that the scaled down pages are only 180mm high, even though they've got 216mm - there's a huge amount of empty white space wasted (at the top, or the bottom, or both) and that's because this ratio does not work.

But nobody cares, they do it anyway. Or they did when making paper copies was more common. In practice we just read a PDF on a screen.

Plus the copiers are a bit more clever than you give them credit for. Instead of scaling the whole page down they put a bounding box around the actual content on the pages, to exclude the margins, and then scale that down to fit. The size of the margins changes slightly but not enough that anybody cares. This is especially true when you’re copying a bound book because there’s a really big margin in the middle to accommodate the binding. You don’t need that any more once you’ve printed the pages on a single sheet of paper.