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Comment by samwillis | Hacker News Reader

The article sadly misses the root of the An sizes. A0 has an area of 1m^2, setting its dimensions and defining the rest of the sizes. Quite genius!

The B sizes start at B0 with a length on the short side of 1m, then follow the same pattern. The C sizes, often used for envelopes, are defined as the geometric mean between the equivalent A and B size.

As a child of an architect, when I was a kid my dad would bring old A0 drawings home as paper we could draw and paint on the back of. Loved it.

- Edit: it does mention it, I skimmed it too fast…

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I grew up in Europe and I did love the A-n system for its mathematical elegance. But having moved to the US where they use a different size without the halving property I found that I don't really miss it at all in practice and the only benefit I really derived from it was a bit of smug intellectual superiority. I find that a lot of the value of these size systems comes from network effects of many other things in the environment being compatible, such as printers, paper cutters, rulers, etc. With Letter I like that the dimensions are almost whole imperial values (8.5 x 11), while TBH I always found it annoying that A4 had so many significant digits. It has a very technocratic vibe to it - user is not as important as having nice mathematical properties, damnit! :-)

You don't miss it in practice because US society isn't built around it in practice.

There's something great about being able to print something at home on A4, see how it looks, and know that it's going to be exactly the same (no stretching or cutting required) when you go to a print shop for an A1 or A0 print.

And yes there is a lot of legacy network effects around Letter size, which is why the switching costs are very high to make switching impractical.

A move _away_ from paper, to government signed crypto certs and witness logs is the answer.

Then we just need to standardize on A5 as a standard for bills mailed out, since it'll fit inside of everyone's filing cabinets already. A5 for taxes would also be nicer too.

Then get school supplies made in A5 size (easier for kids to carry), and finally after a silent transition period where there's less and less in the US Letter size, we can relegate PC Load Letter to the Office Space movie.

What are witness logs?

A record of transactions (log) witnessed by another party. Like website cert transparency logs. The third party might be a government (in the case of banks they probably already witness this anyway, it's just making it official), banks auditing each other's books, etc.

I too moved from Europe to the US and the paper sizes are the worst - have you tried folding it? It doesn’t work.

> almost a whole value

But not a whole value.

That's the thing, though, the folding was never helpful to me even while in Europe; it was a Nice Thing but I never used it in practice. Maybe if I was there now I could take advantage of it for proofing large format prints, like one of the sibling comments pointed out. But even the envelope thing was not helpful - the only envelopes we had were the blue communist ones, the international ones, and you ended up folding the letters at the edges to make it fit.

> But not a whole value.

Right, I said that because one of the dimensions is a half. However in practice those values behave as nice round numbers as well, because in the imperial measure context most things are sized to powers of two, i.e. 1/2, 1/4, 1/8 etc.

I feel like you don’t get to criticise the value of the system if you grow up in a communist country that lacked access to the different sizes of paper and envelopes that make the system useful. Clearly you missed out! Making an A5 booklet from A4 and mailing it is something any print shop I grew up near would do.

No idea what the advantage of a whole unit is supposed to be; nobody is sat around with a ruler measuring A4 cuts. The tolerances for paper manufacturing need to be specified in tiny fractions of a mm either way. As for actual typographers, they don’t use metric units, the size of the paper is not of great concern.

Heh, that's probably a fair point.

I added some more thoughts on the value of whole units in a sibling post. Like I mentioned it's mostly subjective, and has some utility to me when working with paper and measuring cuts. So yes indeed with a ruler, measuring cuts. :-)

I would have expected a communist (i.e. poor) country to have more use for some properties of the paper system:

1. You can easily calculate the weight of that letter without a scale, and stick exactly to the 20g limit (or whatever) for the cheapest postage rate. (I remember doing this in the 1990s for air mail letters to relatives.)

2. You can crush 2, 4 or even 8 normal A4 pages onto a single sheet while photocopying, and save paper/money. Although maybe by the time photocopiers were available in your country, the cost of paper was no longer an issue. (I would press the 2-on-1 or even 4-on-1 button when printing at university, to halve the cost at essentially no inconvenience.)

a specific functional benefit, besides the network effects of standardization, is foldability

you can fold A(n) paper in half to make a brochure or booklet of size A(n+1), for example. it will fit perfectly into any envelope or folder sized to fit A(n+1) pages.

Why would anyone care about "almost whole imperial values"?

Less the "imperial" part and more the "almost whole"---it would work just as well if the pages were say 20cm by 30cm---but it is very convenient when doing layout (both electronic and physical) that both the content and the margin are "nice round numbers", and the natural divisions are also nice round numbers that you can easily measure with a standard ruler. 1/2" margins all round? Then the area is 7½ by 10. Printing a 2-up booklet? Each page is 5½ by 8½, exactly. If I had to design the size from scratch to optimise this property I'd probably go with 8"×12" (or 20cm×30cm!) but I assume there's some older printshop standard we're inheriting from here.

Not saying A4's not good. Just acknowledging that "nice round numbers" are convenient sometimes. Standards that use US-traditional measurements seem to do better at that for some reason.

This doesn't work at all, let alone just as well.

Half a 20x30 sheet is 15x20, so the ratio has changed from 2:3 to 3:4.

1:sqrt(2) is used to maintain the ratio. The round number is at the start, with the area of A0 being 1m².

Yes, I get how the A-series paper sizes work, and that they prioritise having all sizes be the same aspect ratio. That has literally nothing to do with what I'm talking about in my post. It turns out that paper "works" for things other than resizing other sheets of paper.

> Half a 20x30 sheet is 15x20, so the ratio has changed from 2:3 to 3:4.

So what? The only thing I ever try to print multiple to a sheet is slides, and those are a different shape entirely.

Yeah I’m struggling to understand the value of that too.

The US still uses imperial measurements.

The US does not use imperial units. Imperial units are those defined in the British Weights and Measures Act of 1824. What the US uses is the US customary system, where units have the same name as the Imperial ones, but not the same values. Now, the US customary units are defined in terms of SI units anyway, just with annoying, non-integer conversion factors.

EVEN BETTER

(where "better" is actually "really annoying")

Actually, no. The US gallon (3.785L) is not the same as the imperial gallon (4.546L), a point which made me see red when Canadian opponents to metrication argued that we must keep the gallon because the US is our biggest trading partner.

The real reason Canadians and Brits should have opposed metrification: the transition wasn't ever 100% completed leading to horrifying Frankensystems where Brits buy meat by the kilo but measure their own weight in stone. Or Canadians still measuring train rail distances in miles.

Then just push for full adoption of the system and over time youll get there. Can be slow and sometimes painful but so are a lot of things; "no pain no gain" as they say

You have it backwards. Metrication in Canada stopped halfway because the opponents created such a stink that the government of the time decided to back off, and nobody since has had the courage to seize the nettle. Perhaps in a generation today's schoolkids, educated in metric, will try again.

To rephrase te question: why would somebody be annoyed with the fractional metric size of A-n sizes ?

The answer is probably quite subjective. In my case, when I deal with materials such as wood, cardboard or paper I enjoy immensely to have dimensions that snap to a certain grid. Call it a mental defect if you will. To illustrate further, let me propose a strawman: would you have no preference between the A4 size being: (1) 210.32 x 297.912 or (2) 210x297? Does it not bug you that 210.25 was rounded down to 210?

It mentions A0, the 1sqm area, then goes into paper weights. You might have accidentally skipped that section.

It's pretty handy that 1 A4 sheet at 80gsm weighs 5 grams

(A4 sheet area: 1/(2^4) = 1/16 of a square metre) * (standard paper weight of 80 grams per square metre) = (5 grams per A4 80gsm sheet).

Would have been useful for calculating postage.

A few weeks ago my sister told me of a proposal for some contract that she’d been working on, and it ended up being 1600 pages, mostly double-sided A4, and printed in quadruplicate, and I rapidly worked out in my head, purely from the memory that A0 is 1m², that each subsequent paper size halves the area, and that 80g/m² is a common weight: that that was going to be something like 16kg of dead tree that was probably just going to clog up filing cabinets somewhere and mostly never actually be referred to. If I did this more often I’d remember 5g per sheet, but the mere fact that all this stuff is simple ratios and unit calculations means you can calculate it all from first principles quite easily. It’s really handy.

I'm a teaching assistant, and I use this calculation every time I have to organize a written exam

"so every students needs 11 sheets of paper... times 234 students... times 5 grams... OK I need help to bring everything to the exam building"

Also, when it comes to envelopes:

"This means that C4 is slightly larger than A4, and slightly smaller than B4. The practical usage of this is that a letter written on A4 paper fits inside a C4 envelope, and both A4 paper and C4 envelope fits inside a B4 envelope."

https://en.wikipedia.org/wiki/Paper_size#C_series

To fit A4 into a C4 envelope, do you fold in in half or thirds or fourths?

You don't. If you fold it in half you can fit it into a C5 envelope.

Within this entire system, its all about succesive halvings. So folding into thirds (which is horribly difficult to do) is never needed.

That's not true, the most common envelope at least in Germany is DL for DIN Long [1], which requires folding A4 in thirds and there is a corresponding DIN norm on how to print fold marks to aid the folding in thirds [2]

[1] https://de.m.wikipedia.org/wiki/DIN_lang

[2] https://de.m.wikipedia.org/wiki/Falzmarke

Not only difficult, but prone to being sliced when using a paper opener. Paper folded in four should be placed in the envelope with the fold at the bottom so that it doesn't get cut when slicing the paper at the top of the envelope.

Unfolded

> As a child of an architect, when I was a kid my dad would bring old A0 drawings home as paper we could draw and paint on the back of. Loved it.

You brought me memories of being a very small kid drawing on A0 roll scraps bigger than me on the floor of my parents' studio :)

Those cardboard tubes the A0 drawings where stored in were brilliant for building stuff with, and even more fun as a later teenager having parties - stick one end in a fire pit and they become fire cannons, a good 4-5ft of flame out the top…

Your point about childhood really struck a warm note with me. I feel one of the most important and loving things my parents did for me as a child was ensuring a limitless supply of stationery.

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