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Paper sizes

royvanrijn.com

320 pointswillvarfar202 comments

I really wish we'd switch to the ISO-216 sizes. A4 to A3 is so much more enjoyable and painless than Letter to Tabloid. This kind of thing came up often while making posters for campus because it was cheaper to NOT print out all of the posters on Tabloid. Rather, using a mix of Tabloid (for the important poster posting spots) and Letter (for unimportant spots and as flyers for handout). Always ended up having to spend more time to make two layouts because of it. And A4 to A5 for booklets without having to re-layout the document is a huge plus too! And for books, I like to use B4* to fold in half. (B5 pages are nicer than A5 pages for the kind of books I tend to read.) The proportions are all the same, so it just works! One layout, many paper size (of the same proportion) possibilities!

Edit: Additional note with regard to the book publication (depending on printing and binding method used)... Sometimes/often this is printed on something like A3 size for bleeding and with crop marks. The A3 paper is then folded and cut, so that the pages become B5 size. (Signatures essentially composed of folded B4 as a consequence of the cropping. There is of course difference between the outermost sheet and the innermost sheet in each paper signature, which is why it's all cropped at the end.)

Is there are reason that B5 sized paper sheets are only available as imports from Japan in Europe?

The strict interpretation of the B series as a packaging format for the A series only seems somewhat archaic.

Lack of demand in the States for ISO 216 sizes in general makes it so that relatively/comparatively few stock such paper in the U.S. When wanting to print to the edges (full bleed), publishers will often print on B sized paper sheets with crop marks for A size (and then crop the paper to A size) or similarly print on A and crop to B.

B5 paper sheets don't seem to be easily available in the UK.

B5 books are the most common size though, most of my school exercise books were B5 or B4 — that allowed me to glue in a sheet of A-sized paper, possibly folded in half.

Why do you prefer B5 to A4 for paper?

To answer your question about my preference... For non-fiction books, A4 pages seem too big for me, A5 pages seem little too small to me, and B5 pages seem just right. Again, this is just for non-fiction books. Fiction books I prefer more A5-sized. Just my own personal, subjective preference. That's all.

The A size formats are based around A0 being 1m² in area, the B size formats are based around the short edge of B0 being 1m long. The aspect ratio of both A & B sizes are √2.

WARNING: Japanese B-series paper is not the same as ISO B-series paper!

http://en.wikipedia.org/wiki/Paper_size#Japanese_B-series_va...

Additional note: Yes, I realize 17"x22" (ANSI C) is a thing. But, that paper wasn't readily available in the specific scenario given. The point is that if all common-use paper has the same proportion, then availability of needing "this or that certain proportion" is less of an issue... or rather becomes a non-issue. When all commonly used paper has the same proportion, then the possibility for the inconsistent proportion problem occurring in every-day life essentially goes away.

Not every European is/was happy with the A series of paper formats. Jan Tschichold (1902—1974), arguably one of the most influential typographers of all time, strived against it, arguing it was unpleasant for office use (comments by jgrahamc and johnchristopher go into this direction) and downright unsuitable for book use.

I can't seem to find an English-language version of his A series rant (found in Erfreuliche Drucksachen, p. 111), but for anyone interested in traditional book layout, this (English-language) essay is a goldmine: http://www.arts.ucsb.edu/faculty/reese/classes/artistsbooks/... (pp. 39 f. touch on the A series).

I've lived in the US and also in a country that used the A-series extensively. While I've always appreciated the beauty and math of the A-series, I find the aspect-ratio of the US Letter paper to be much more appealing. A4 tends to be too long and too narrow.

From the article:

> US Letter: 216 mm x 279 mm

> A4: 210 mm × 297 mm

so it's 18mm longer while being 6mm narrower. At that small a difference, I would assume that a preference of one over the other is similar to that of metric vs. imperial - the one you were raised on just seems right.

Which one did you grow up with?

I grew up with the A sizes of paper and agree with the parent comment. When I moved to the US I was pleasantly surprised by the size/shape of US Letter sized paper.

But it is both 18mm and 6mm narrower, so it goes from 1.414 to 1.29 in terms of ratio.

In other words A4 seems 10% narrower in terms of shape, which isn't insignificant.

Having said that, I'd rather keep A4 given the useful properties described in the article.

For what it's worth: I am a European, still living in Europe and surrounded by A4 and I envy American's US Letter format.

I almost always have the feeling that A4 is too big.

That's a 9.5% difference in the aspect ratio. I don't think that's small.

It's just that you can resize everything while still keeping the same portions with the A* paper while with the US formats you just have to redesign everything.

I used to publish a magazine (in Japan) that was A4. Because of all the ads were sized to fractions of the page it was a big job to change the page size, so we just left it, for years. When I finally had the chance to make a new magazine I went for letter size -- it's a prettier proportion. As the other posters have said, A4 is too tall.

>As the other posters have said, A4 is too tall.

Is it my imagination or are magazines often taller than A4?

I've lived in both, and... of all the differences, and problems with various formats and standards and things, this one is so far down the list that I've never even really thought about it.

The aspect ratio of 1:sqrt(2) is absolutely critical to the format. You can't cut a sheet in half and end up with the same aspect ratio without it.

If you really want an aesthetically appealing aspect ratio, wouldn't it be 1:(sqrt(5)+1)/2, which is even longer and narrower?

But then I dig deeper, and find this: http://en.wikipedia.org/wiki/Canons_of_page_construction , which seems to indicate that the ideal book page proportions are 2:3, which is again longer and narrower than 1:sqrt(2).

Personally, I find that US Letter is too wide for comfortable reading without using multiple columns of text, and printed manuals using the format are too floppy to be used without a stiff cover page or a binder. And that's just in print. I can't stand it when someone makes a PDF e-book with US Letter sized pages, because it doesn't fit onto any screen that I have without scaling or scrolling. My e-ink screen is 2:3. Most of my computers are 16:9. None of my 5:4 screens rotate to vertical, and that's as close as I can get to 7:9.

How does US Letter even have any fans at all?

Also, in my opinion, B8 seems ideal for playing cards. It is very close to the ID-1 standard, as well. B7 is the same size as ID-3, used for passports.

> But what do you end up with folding the US Letter? Let’s see:

> 216 mm x 279 mm ratio: 1.291

> 139 mm x 216 mm ratio: 1.554 <- What?

> 108 mm x 139 mm ratio: 1.287 <- Ah..

> 69 mm x 108 mm ratio: 1.565 <- HUH!?

> 54 mm x 69 mm ratio: 1.278

> 34 mm x 54 mm ratio: 1.588

> 27 mm x 34 mm ratio: 1.259 <- Oh god...

These ratios, in fact, just go back and forth between two values (because when you cut a piece of paper into fourths, it has the same aspect ratio as the original). The other differences are just rounding errors.

He notes rounding errors earlier in the post, so I'm not sure why they get called out in this example with "HUH!?" and the other comments.

Agreed. The article writer really failed in that section. It's just rounding error. Based on his written reactions there, I honestly don't think he realized it was oscillating at the time he wrote that part. It seems like he just didn't want to bother to correct himself after the fact or is just intentionally being stupid.

full disclosure. I actually didn't notice the oscillations myself.

However, I was just very absentmindedly skimming, It's a little more unbelievable for the author, the one doing the calculations, to miss this.

While we're at it, couldn't we also wish for the US to adopt the ISO standard date format, YYYY-MM-DD That would be great. Thank you.

Anecdote: the office management/finance/HR people in the european office where I work really, really hate US Letter formats, because they don't really fit in "normal" binders.

They're the ones who really suffer from this, because they're the only people who deal with paper format documents these days, I guess.

I can feel their pain: I have two binders from school in Germany that don't fit on the shelf with my other (US-sized) binders. They're destined to be lying down for the rest of their days.

Also the fact that the US punches 3 holes instead of 2 or 4

US Letter is shorter than A4, so it seems like they should fit fine? I guess it's 6mm wider but that is not much.

Never underestimate the level of OCD in good finance/office management people. :)

For some important documents that you want to preserve and/or don't want to pierce there is a solution: store it in a plastic sleeve like this one:

http://i01.i.aliimg.com/wsphoto/v0/1777660007/100-X-A4-CLEAR...

If you happen to receive US letter sized paper, it won't fit because of the width, that is too much for these, and they get crumpled.

It's worse over here in the US. At least in Europe the paper doesn't require a different shelf height when dealing with printed materials from 'across the pond'.

I would find it ever so sensible if we would just let imperial measures die over here so we could end the pain of international business.

As a European, I would also like to point that the U.S. doesn't use the Letter format exclusively. Bills, in particular, come in all sorts of weird formats. Things like electricity bills sometimes come in long, narrow formats that don't fit in any kind of binder!

A comical yet accurate take on why A4 is the best paper size : https://www.youtube.com/watch?v=Mb9EsAD2jGQ. You'll enjoy this. The tone is great as well.

Today I learned something new. And I was entertained. Tip of the hat.

Yeah, funny how this video was on Reddit's frontpage a few days ago, and this dude just happens to write a blog post about it without even mentioning the video.

His table at the end purporting to show a plethora of strange aspect ratios is just his rounding errors.

When repeatedly folding paper, the aspect ratio alternates between two numbers. (Consider after two foldings, each side is half the original. Same aspect ratio.) Unless of course you have soulless A series paper, then they are all the same.

I enjoy working with paper. My favorite notebooks are ISO A4 size because they give me a bit more vertical room and still fit well in my backpacks.

The issues that come up with regard to US Letter size paper seem to be:

1) It's not metric -- yes that's true, but A4 is 210mm x 297mm. These numbers seem completely arbitrary and don't take advantage of the metric system. I wish the US was on the metric system, but it's not so 8.5 in by 11 inches at least has the advantage that it is measured in simple numbers with respect to standard measures in the US.

2) It's easier to store and work with A4 because it is one half of an A3 sheet -- however, US Letter is one half of the US Tabloid/Ledger size. The ANSI (American National Standards Institute) paper sizes in inches are A (8.5 x 11), B (11 x 17), C (17 x 22), D (22 x 34), etc. and share this advantage with the ISO standard.

3) The aspect ratio is is approximately sqrt(2)/2 for all paper in the A series, the B series, and the C series. But why is having but one shape of paper an advantage? Sometimes it's useful to have choices depending on the content to be printed on the paper. Furthermore, the ANSI paper sizes simply have two aspect ratios alternating as one increases paper size.

It is argued that printing posters with corresponding flyers is easier with ISO paper sizes. But this is true with ANSI paper sizes: one would have to jump up two sizes from letter (ANSI A, 8.5 x 11 inches) to ANSI C (17 x 22 inches). So, for the case where one would like to print at ANSI B, the aspect ratio of the page is a bit different. Here we have, what appears to me, to be the first real advantage of ISO over ANSI paper, where we need to print a flyer at A4 and A5 (but not A6). However, this hasn't been a problem for me personally. I'm usually working with pages that have additional constraints. For example space for bindings or differences in margins between recto and verso sides of two sided printing. Whenever there are bindings involved the aspect ratio advantage goes out the window.

4) Every country uses ISO sizes, why not the US (and Canada and Mexico) -- well, this is oversimplifying things a bit. Take a look at the Wikipedia page for paper sizes. There are Japanese variants, German extensions, and Swedish extensions listed that deviate from the ISO standards. There are also Architectural sizes listed that are designed to have simple ratios for their aspect ratios.

The idea that we would somehow be better off with fewer choices (just one) really for aspect ratio really strikes me as wrong. I like all the variety available in paper.

1) A0 is 1m^2

Which also lets you caclulate the weight of a document (say for shipping):

Standard printer paper is 80g/m2: A1 = 40g, A2 = 20g, A3=10g and A4=5g.

Or, alternatively, crumple up A4 sheets for quick 5g weights.

U.S. Letter size predates the European standard. The U.S. Letter size apparently originates with vellum sizes and was originally intended for handwriting not typography[1].

However, there are some good ways to use 8.5 x 11 [2] that might look odd on narrower and taller paper.

[1] http://marginalrevolution.com/marginalrevolution/2012/09/why...

[2] http://retinart.net/graphic-design/secret-law-of-page-harmon...

You write that the A4 numbers "seem completely arbitrary".

While they might seem to be arbitrary, they are obviously not the least bit arbitrary.

The base size A0 has an area of exactly 1 square meter. Each subsequent size is constructed by taking half of the previous, so for A4 it's 1/16th of a square meter, or 0.0625 sqare meters, 625 square centimeters, which is 21.0 cm x 27.9 cm (approximately).

In order to have both the halving property and the self-similarity the aspect ratio has to be sqrt(2), and therefore you can't have nice little round numbers for the sides.

If I have to choose between self-similarity and nice round numbers, I'll take self-similarity, thank you.

> The base size A0 has an area of exactly 1 square meter.

Which is still arbitrary :)

No, its the basis of paper weights too, which are measured in grams/m^2

Ok, that's revelation of the day! (sometimes you fail to connect the simplest things). Now I can eyeball the weight of a stack of paper :-)

Another thing that the US fails miserably at. 80# cover, 110# index, 24# bond … it’s all meaningless.

Those numbers aren't meaningless. They're the weight of a ream (500 sheets) of that paper at 17x22.

> 3) [...] the ANSI paper sizes simply have two aspect ratios alternating as one increases paper size.

In relatively big jumps (of the same proportion), though. Not enough in-between sizes (of the same proportion).

So for example you'd be happy if there were a 6"x7.75" and 12"x15.5"?

Yes and no.

Yes, additional sizes address the desire for satisfying the missing in-between sizes.

No, because I'd like to keep it simple and avoid having to do that or even think about it at all.

Basically, with the ANSI sizes you want to satisfy TWO proportions with gradual size changes instead of just ONE proportion with gradual size changes as seen in ISO 216. This is where the discussion cycles back to the utility of 1:√2.

In most offices in the U.S. that I've been in (I say this in a fast and loose fashion), they carry three sizes (with the following typical uses):

(1) ANSI A (US Letter) for standard letters (uses full portrait page) and leaflets (uses one-third landscape page) or booklets (uses half landscape page).

(2) US Legal because there are plenty of legal documents are out there that use US Legal (uses full portrait page). And perhaps as a bonus, but not as frequently seen, US Legal can be folded into small booklets (uses half landscape page). Although, I don't see this happen as much as ANSI A being used for booklets.

(3) ANSI B (Ledger/Tabloid) because it can be great for spreadsheets and folded to US Letter sized pages. Either for collapsing the spreadsheet or for making booklets with US Letter sized pages (uses half landscape page).

Now, yes, I did not mention all uses. I merely mentioned what I have frequently seen used based on my experience. But one of the key take-away points for the "common-use/general-purpose" ANSI A and ANSI B paper sheets is the notion of folding the paper in half to form a booklet.

You don't see many offices carrying ANSI C (17"x22"), which is the next step up from ANSI A maintaining the same proportion. (So availability of this is considered unlikely in this context.)

Of the three, perhaps US Legal can stand alone because it offers a significantly relevant special situation proportion. So, we'll set US Legal aside for now.

And so, you get usage of Half US Letter (1.5454…), Full US Letter (1.2941…), Half Tabloid (which is just US Letter, 1.2941…), Full Tabloid (1.5454…). So, you'll get an oscillation of two distinct proportions with paper that doesn't use 1:√2, and in the case of ANSI A through ANSI E, you get the 1.5454… and 1.2941… oscillation.

Now, if you had ISO 216 sized paper, all of the proportions would be the same no matter what, and it becomes very easy to choose between paper and half-paper sizes because they all work alike with regard to their proportions.

However, with the oscillating ratios, you have to choose which one you're targeting and be sure of it, because the next larger (or next smaller) size is significantly different.

Now, more in-between sizes could solve this, but that also means you'd probably end up carrying around yet another paper size because of it. If you simplify things by getting rid of the dual-proportions and have a unified proportion instead, then the added frustration from the differing layout proportions go away instead of trying to address that with another paper size for something in-between.

So, to parallel the Half US Letter (feels like an oddball that is basically super small Tabloid, 1.5454…), Full US Letter (1.2941…), Half Tabloid (is just Letter, 1.2941…), Full Tabloid (1.5454…):

Half A4 (is just A5, 1.4142…), Full A4 (1.4142…), Half A3 (is just A4, 1.4142…), and Full A3 (1.4142…).

With the layout for Half US Letter, your next proportional step-up is Full Tabloid. (Huge jump!) Or from Tabloid, your next proportional step-down is Half US Letter (Really small!) You could have an in-between size to satisfy it, but it seems excessive when you could have just had used the 1:√2 proportion to begin with and not worry about any of those additional considerations.

---------------------------------------------------------

Saying it another way...

Where, ½·x signifies folding a sheet for purpose as a booklet, and the paper that satisfies that requirement is mentioned inside the cell.

Dealing with only our "letter" size (1) and "tabloid" size (2) sheets that we have in our office, we get the following:

    ANSI    | ½·1 | 1·1 | ½·2 | 1·2 |
            +—————+—————+—————+—————+
    1.2941… | :(  |  A  |  B  | :(  |
            |—————|—————|—————|—————|
    1.5454… |  A  | :(  | :(  |  B  |
            |_____|_____|_____|_____|


    ISO 216 | ½·1 | 1·1 | ½·2 | 1·2 |
            +—————+—————+—————+—————+
    1.4142… | A4  | A4  | A3  | A3  |
            |_____|_____|_____|_____|

With ANSI:

    We don’t have a “half size” booklet with 1.2941… proportions.
    We don’t have a “full size” sheet with 1.5454… proportions.
    We don’t have a “full size” booklet with 1.5454… proportions.
    We don’t have a “double size” sheet with 1.2941… proportions.

With ISO 216:

    We have our “half size” booklet in all our proportions.
    We have our “full size” sheet in all our proportions.
    We have our “full size” booklet in all our proportions. 
    We have our “double size” sheet in all our proportions. 
    (Because we only have one proportion to deal with, 
    there’s no bothering to deal with dual proportions.)

That's four frowning faces (missing solutions for that proportion) on the ANSI side.

---------------------------------------------------------

If we were to expand on this beyond the "two typical sizes found in the office" scenario, we get the following:

    ANSI    | ½·1 | 1·1 | ½·2 | 1·2 | ½·4 | 1·4 | ½·8 | 1·8 | ½·16 | 1·16 |
            +—————+—————+—————+—————+—————+—————+—————+—————+——————+——————|
    1.2941… | :(  |  A  |  B  | :(  | :(  |  C  |  D  | :(  |  :(  |  E   |
            |—————|—————|—————|—————|—————|—————|—————|—————+——————+——————|
    1.5454… |  A  | :(  | :(  |  B  |  C  | :(  | :(  |  D  |  E   |  :(  |
            |_____|_____|_____|_____|_____|_____|_____|_____|______|______|


    ISO 216 | ½·1 | 1·1 | ½·2 | 1·2 | ½·4 | 1·4 | ½·8 | 1·8 | ½·16 | 1·16 |
            +—————+—————+—————+—————+—————+—————+—————+—————+——————+——————|
    1.4142… | A4  | A4  | A3  | A3  | A2  | A2  | A1  | A1  | A0   | A0   |
            |_____|_____|_____|_____|_____|_____|_____|_____|______|______|

That's 10 frowning faces on the ANSI side, and no frowns on the ISO side. The ISO side inherently avoids the frowning face scenario.

Yes, you could add on another set of sizes to address the missing proportions on the ANSI side. But, that's inelegant and unnecessary if you just went with the ISO way instead.

Next step: metric measurement units everywhere. I've been waiting for that for decades. If "dozens" would die as well, even better.

But I don't want my eggs in boxes of 5.

Counting in base 12 is much better than base 10. 12 has prime factors {2,2,3}, so you get 2,3,4 and 6 as integer divisors, not just 2 and 5. That's why dozens stuck as a counting unit on so many things, namely time (all the way back from Egyptians).

You can even count using your fingers. Just count using your thumb pointing at each of the finger joints and the finger tip (you have two joints and one tip per finger and four fingers excluding the thumb). Actually, that's how Egyptians counted and that's why you get 12 hours in the realm of day and 12 hours in the realm of night.

The only drawback is multiplication tables. If I tend to forget the multiplication table for 7 and 8, memorizing tables for 11 and 12 would be nightmarish :-)

P.S. This is obviously tongue-in-cheek. While it may be marginally better, switching costs mean the optimal course of action is to stay at the local maximum and avoid switching.

I've done some extensive analysis of number systems (almost enough to write a book on the subject) and come to the conclusion that the best are senary (6) and quaternary (4). Six has all the benefits of twelve, save the extra divisor of 2 (and thus 4), but that is easily remedied by use of the square (36) when required. Quaternary may seem an odd choice, but the square is 16, so one naturally learns hexadecimal without doing hardly any extra work --you just pair up the digits.

If your curious, duodecimal and octal come in after these and decimal falls to fifth place, which is fitting since its main advantage is divisibility by 5. :-)

Since you haven't written your book yet, are there any others you can recommend on this topic?

Interesting. I always thought base 16 was the only suitable number system. Base 2 is the only justifiable one, since base 1 is not much fun. Squaring base 2 twice to get a fair amount of information in a single column seems to just make sense. What are the downsides of 16?

Balanced ternary is superior to them all.

http://web.williams.edu/Mathematics/sjmiller/public_html/105...

I haven't heard many arguments against dozens. In fact, there are some groups that specifically argue for duodecimal systems. I'd be interested to hear your position in more detail.

http://en.wikipedia.org/wiki/Duodecimal#Advocacy_and_.22doze...

My main problem is that it's longer than "tens". And I have 10 fingers. And I use base-10 for everything, including counting the dozens. It's just more logical (and I say that without reading through the wiki page, so sorry if whatever I say doesn't make any sense with that in mind. I'm not good with words).

It's only logical because that's what overwhelmingly likely what you grew up using. There are duodecimal finger counting systems. (Counting to 12 isn't even all that impressive, considering counting each finger as a binary digit results in 1024.)

Also, "9 dozen" is the same in either base. "10 dozen" would become "ᘔ dozen", "11 dozen" to "3 dozen", and "12 dozen" to "10 dozen".

Finally, a dozen dozen is a gross and a dozen gross is a great gross, which at 1728 would be a likely replacement for "ton".

This is one of those things that seems technically correct (the best kind of correct) but practically ... meh. The benefit exists but is barely enough to get anyone entrenched to actually change. Much like the common usage of the US Customary units, nothing is going to actually change.

It has other useful effects: it makes it easier to standardise containers for the sheets, as well as their division, amongst other things. And all this from the simple use of a ratio.

There's just a threshold of utility that has to be passed in order for a new standard to take hold. How much would the US really benefit from switching? How much would switching cost?

The efficiency gained wouldn't come near to the efficiency lost during the switch, and nobody really cares all that much about paper size.

I'm not making the argument that the US should switch (though I wish they would), I'm just stating that the advantages are deeper than they appear at first blush.

Except, you know, everywhere that isn't the US.

Odd how every single country in the world has adopted it, except for the US and Canada. They all changed.

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

But they didn't change from a widely used system to another widely used system. They changed from no standardized system to ISO.

North America already as system in place. Switching from one to the other confers very little, if any, benefit.

Ah, so America is special again? No, many countries had standard sizes before ISO/DIN.

Britain changed from "Imperial" sizes: http://www.papersizes.org/old-imperial-sizes.htm

France had these before 1967: http://www.paper-sizes.com/uncommon-paper-sizes/old-european...

America is special in that it is large enough to use their own standard.

It is the reason why the EU can create their own standards that nobody else follows. Like Rohs, the reason your electronics fail at a higher rate than previous electronics. Smaller economies suffer when they can't use/make their neighbors goods.

The North America a huge economy. We can efficiently have our own standard.

Uk and France aren't big enough to dictate their own paper size.

The USA and the EU are currently negotiating a free trade agreement [0]. I would say call your representative to get it on the list. Not to get too political here, but that would be much more beneficial than much of the other stuff that is already on it, where usually the lower standard succeeds magically.

[0]: http://en.wikipedia.org/wiki/Transatlantic_Trade_and_Investm...

When someone claims uncritically that the ratio of any two integers is √2, I get a little edgy. I'm also having a hard time following this simplification:

    A / √A = A × A / A = A

Huh? This only holds if √A = A = 1. I haven't checked the rest, but this doesn't give me much confidence.

Of course, knowing those Europeans, these sizes do probably make tons of sense on paper (see what I did there?), even if this isn't the best explanation of it.

There's nothing crazy here. It just means that if the length of the long side is √2 times the size of short side. That has the nice property that you can bisect the sheet and get two smaller sheets where the ratio between the long and short edges is maintained, which makes it standardising a whole bunch of other things much more straightforward.

I believe that gp's point is that this is impossible, what with √2 being an irrational number. It is pretty close (4 significant digits), but of course not exact.

It's not that big a deal: once you have a basic page size that's close enough, it's just a matter of slicing it in two. In practice, any error is too small to matter.

The article's not claiming that the ratio of any two integers is √2, he's claiming that when the ratio of the lengths of the sides (the aspect ratio) is √2 that it's easy to keep that ratio with smaller pages by cutting the longer dimension in half.

As for your equation above, A/√A != A x A / A, but I'm not seeing where in the article you got this either.

> The size is 210 mm × 297 mm and has a ratio of √2 (math!).

That looks like a claim that the ratio of two integers is sqrt(2), but it's fairly obvious that he really means that it's very close.

I don't think anyone would attempt to assert that any measurement (or ratio of measurements) made with our current technology could ever be precisely √2 or even π (that's pi)

He's written A / √A = A × A / A = A, but what he means is A / √A = √A × √A / √A = √A, which is actually true and is what he uses below

another way of writing the same thing is

    A / A^(1/2) = A^1 * A^(-1/2) = A^(1 + (-1/2)) = A^(1/2)

Of course 297/210 isn't (and can't be) exactly sqrt(2). But it's very close (4 s.f.), and the important property works: 420/297 is again not exactly 297/210, but it's well within the tolerance for most use cases.

(I can't load the page to check what it's doing with this simplification).

There is a very simple rule for the size of the A series pages. Markus Kuhn covers it here: http://www.cl.cam.ac.uk/~mgk25/iso-paper.html

Basically, in metres the An page dimensions are pow(2, (plus or minus)1/4 - n/2) and always round down to the nearest mm.

Everyone who supports the A* sizes of paper (start with a square meter because it's nice and clean, then just declare that all other paper uses that humankind might ever need should be specific fractions of that square meter and no other sizes are ever needed) should also support Swatch time.

http://en.wikipedia.org/wiki/Swatch_Internet_Time

Alternately, if Swatch time seems dumb to you, then you might also accept that paper should be sized to fit a usage, not just a "clean" measurement scheme.

Does this hold true for other things as well? Should all cell phone screens be sized to be a specific fraction of a square meter, just because it's "cleaner"? Or should they be sized to fit, you know, people's hands and pockets?

And for that matter, the math isn't even right! Because SQRT(2) is not rational, you'll get noticeably different sizes if you actually started with 4A0 and sliced it in halves until you got to A10 versus directly cutting an A10 piece. That should drive you math-obsessives crazy.

I agree that fanaticism over an arbitrary paper standard seems silly, but I don't buy your analogy. The reason Swatch time probably feels dumb is that the notion of changing the time format used by essentially the whole globe is itself dumb. The transaction costs are almost certainly higher than any benefits.

Why did Americans simplify and streamline the English Language, but they didn't bother with all of the systems of measurement?

Now you know how hard it is to replace a legacy system. :)

Actually, we're going the wrong way. The last highway sign I saw in metric was on I-95 northbound. They replaced it a couple of years ago (too old - the reflective material was worn out), and the new one only has miles on it.

There's a short highway in Arizona (I-19) that is only signed in kilometers (it runs to the Mexican border), and there are calls to replace them all with distances in miles.

Americans didn't simplify and streamline the English language, certainly not intentionally. If you're talking about the spelling thing, there were no standard spellings at the time when the US broke away from Britain; standards were independently created at a later date.

Early American dictionaries deliberately set out to simplify spellings (and later editions made more aggressive simplifications that didn't catch on).

English is far from being streamlined.

In fact it's the only language I know that requires you to learn how to pronounce EACH word.

Most languages only require learning how each letter sounds, and maybe a few dozen di/trigraphs, the rest is regular. Not so in English.

You have to learn to pronounce each word with Chinese too.

To a point, but there are clues:

马 is mǎ, meaning horse. It's a picture of a horse, with 3000 years of adaptation.

女 means woman / female. It's a picture of a woman.

Put them together and 妈 means "the female thing that sounds like mǎ", which is mā (a different tone), meaning mother.

(I'm very much a beginner, but my teacher claims ~70% of characters follow this pattern.)

Yup, so in Mandarin you have a vague hint as to how to pronounce each word, based on writing. Same goes for English.

For most words you can "sound it out" in English. There are just a lot of exceptions.

Yes, but these are based on how the words were pronounced when the character was created which means there is significant variation in the sounds the same radical is indicating.

I'm guessing that the people who decided that those characters bore any resemblance to a horse or a woman are the same people responsible for naming the constellations.

That's because you're seeing them after literally thousands of years of evolution and simplification.

马, for example, is the simplified form of 馬, which is traceable back through the millenia to a pretty recognizable picture of a horse back around 1300 BCE or so. (http://en.wiktionary.org/wiki/%E9%A6%AC#Etymology)

Same with 女, which originally was a drawing of a stick-figure woman with breasts. (http://en.wiktionary.org/wiki/%E5%A5%B3#Etymology)

Quite the opposite. Once you have engraved in your brain the shape of these characters they become the very representative shapes of the things they draw. It is not a matter of resemblance, just as most caricatures do not resemble the model, but the model is still immediately recognized. Another analogy is the sign indicating lifts in airports: it do not resemble any kind of real life lifts, but everyone still understand it, without even having a sound for it. So are Chinese characters. If you don't believe me I'll pardon you: a long familiarity with them is required here.

No, you don't.

You only need to learn separate spelling and pronunciation rules for each of the languages English has evolved or stolen from.

The tough spellings usually come from Germanic roots via Old English and Middle English, whereas the French-Norman spellings are less difficult.

Greek-Latin spellings are markedly less confusing when you learn the transliterations of the Greek alphabet. Of course Philadephia is pronounced with fricative 'f' sounds instead of plosive 'p' sounds, because the Greek letter for that sound is 'phi'. Because of that, I dislike it when people pronounce the feathered dinosaur archaeopterix as [ar-key-OP-tur-iks] rather than [ar-KAY-o-(p)TEAR-iks]. It isn't incorrect either way, because in English, correct is whatever other people will understand. (Suck it, French.)

This is why I get sick of people complaining about "monolingual" English-speakers. The language has been glued together from Dutch-Germanic, North-Germanic, French-Norman, Greek, Latin, and centuries of absorbing and assimilating immigrant populations from all over the world.

You really only need to learn rules derived from four dissimilar languages to spell and pronounce almost everything in English without having a word-specific association. The remaining ten percent of words are correct when spelled and pronounced as in the native language or as anglicized renormalizations, even using the rules specific to unrelated languages. That is why the plural of octopus can be either octopodes or octopuses. Octopi is colloquially correct, but it is then acceptable to deliver a short lecture on Latinized Greek words. Similarly, the acceptable plurals of cactus are cactuses, cacti, or (los) cactus (pronounced as in Spanish). As Spanish has an increasingly large influence on American English, I have found it useful to know that it only has five vowel sounds, and knowing how to pronounce burrito and enchilada correctly gives you all five.

Despite what your elementary school teachers may have said to you, you are only incorrect in English if other people cannot understand what you are trying to communicate. Nevertheless, failure to be incorrect does not imply correctness, which is why grammar nazis exist.

>You really only need to learn rules derived from four dissimilar languages to spell and pronounce almost everything in English without having a word-specific association.

Don't you also need to learn the language from which every word is derived from?

Absolutely not. You just teach kids the very obvious rules ("silent 'e'", "two vowels go walking, the first does the talking", "just memorize that sometimes 'gh' sounds like 'f'", ''i' before 'e' except after 'c' ... excepting obvious exceptions like 'science'", ...). With just a handful of heuristics and a modicum of rote memorization, children can figure out most English words with 0 background in any other languages. Besides this, pattern recognition is strong & easy -- tons of cognates and near-cognates, and most of the homophones & homonyms are common enough words that you'll learn them quickly regardless.

>With just a handful of heuristics and a modicum of rote memorization, children can figure out most English words with 0 background in any other languages.

Most doesn't equal all.

>Besides this, pattern recognition is strong & easy -- tons of cognates and near-cognates, and most of the homophones & homonyms are common enough words that you'll learn them quickly regardless.

It's very difficult compared to a language system where the pronunciation can be directly inferred from the letters.

No. The rules come from different languages, but once the word is considered an English word, only the orthography matters. If you make a new word by combining skip and hop into "skiphop", someone may mistakenly pronounce it [ski-fope] rather than [skip-hop], despite the fact that neither "ski" nor "phop" are identifiable as Greek roots, because phi makes an 'f' sound, and that makes the subsequent 'o' vowel pronounced as the 'o' in 'phobia'.

Knowing the etymology helps, but is not necessary. When linguistic researchers create nonce words for their experiments--words with no etymology at all, like "gluff" or "splim"--they find that people still generally pronounce them in the same ways.

They also find that people impute meanings to the nonce based on structures found in the word. For instance, when given the nonce words "plorkish" and "erildophate", and told that they are synonyms, subjects may claim that the latter is more sophisticated or scientifically precise. Or perhaps they are told to match the word to the person who spoke it, and a significant fraction of subjects match the words to the pictures the same way.

You can do the test yourself. Print out photos of Bill Nye and Kanye West. Write out "plorkish" and "erildophate" on index cards. Tell people the words are synonyms, and ask them to match the word to the photo of the person who said it. If they don't swing at least 60% in favor of West=plorkish and Nye=erildophate, and pronounce the words the same way, I will eat a tiny portion of my least favorite hat.

I claim bonus points if they also use them in a sentence or identify the part of speech as adjectives. Perhaps ask your subjects to also guess the sentence their chosen person spoke when using the word.

People do actually get paid to test this. This might be a good Science Fair project, actually.

>Knowing the etymology helps, but is not necessary.

Well, often it's necessary to either memorize a pronunciation or know the etymology, because often people pronounce English incorrectly.

A lot of other languages borrowed words too. Some even more than English.

Polish is half Latin, 10% German, Italian, French and Russian, and now it becomes a lot like English too.

But it has consistent rules and after a word is used enough it becomes polonized: computer becomes komputer, and we don't ever have to wonder how to pronounce "c".

I don't want to sound pedantic, but the correct pronunciation of "archaeopterix" is [ar-keh-o-pteh-riks]. Apparently the English Wikipedia page for it has the English-tainted pronounciation.

I spent 5 good minutes trying to find a way to transcribe in a way that an Anglosaxon would pronounce correctly, as Greek-Latin vowels have a unique sound while in English their sound depend on the letters before or after them and often are pronounced as diphtongs.

In Greek-Latin AE = E, always, and sounds like the "e" in "men".

Anyway, I'm no linguist.

Of course that's correct. But the other pronunciation is not incorrect; it's just less correct, because it elides over the root boundary between the archaeo- for "ancient" and -pteryx for "winged one".

I recall hearing or seeing the less-correct pronunciation near the relevant fossil or fossil reproduction at the Chicago Field Museum of Natural History, but I can't remember if it was actually printed on the display card or not. I did have to explain to my kids why the correct pronunciation of root-combining words is important for effective communication. The exaggerated roll of the eyeballs means you're teaching it effectively! (Or at least that's what I keep telling myself.)

American English wore off some of English's bumpy bits because there was no Queen's English or aristocracy to claim social authority for the status quo or sufficient influence to dictate a conservative rate of change. The Norman Invasion set the tone for a millennium of language as an explicit social standing in the British Isles.

Throw in massive immigration and indigenous languages within and along its borders rather than overseas and American English simply adapted to more varied use.

The language thing was basically one dedicated guy (Webster).

Because the Imperial system of measurement is simplified, whether it's dividing an 8 foot wall into thirds or the ratio of flour to milk to make a bechemel sauce.

Because of inertia. We have a lot of things we need to do and running up a huge bill to change something as fundamental as unit of measure is just not an economical idea.

If we were going to do something as big as change UoM, why not go with the engineering estimate of 1 ft is now the time light takes to travel 1 nanosecond in a vacuum (about 11.8 inches)? It is sure better than "the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second". We could even base the new units of volume and weight off of the new cubic foot instead of 1/10 the unit of length. While we are at it, a national standard that all units of memory will be sold in base 2 would be a nice touch.

// apply sarcasm as needed

I know that there is a continuing fight between US measurements (inch, ...) and European measurements (Metric system) -- but I really was shocked, when a printer wanted to have "US letter" pages. The advantage of the A-System is so big over the US letter system, that I don't understand that there are still countries that don't want to adopt it. Just ask your photo copier manufacturer!

It also can't be reasoned, that so many cars or traffic signs have to be changed ...

HN effect killed the article, can't read it, have to estimate based on existing comments. Assuming they actually read it, of course.

Paperless office, checking in here. Our printer is only used for people screwing around doing non-work related projects, printing school essays for themselves or their kids, real estate MLS records, car insurance forms, stuff like that.

I think I'd be okay with A4 if it were a bit smaller. Pegging A0 to a sq. meter is the problem. That's just arbitrary.

Let's work on a demand for a metric standard instead of this..

My personal rant is that I want a global setting on every printer to override differences in requested page size.

For example, being in the UK, I print to A4, and that is the only size of paper I have available for my printer. If I print stuff from browsers, or documents from US people which are set to page size Letter, I DO NOT WANT TO HAVE TO GO TO THE PRINTER AND PRESS A BUTTON TO PRINT ON THE ONLY PAPER AVAILABLE (A4). Just print everything on A4 please - ignoring page size requests (or at least let me choose the option to do this override).

This is such a pain, and occurs very frequently. Am I alone? I rather assume the inverse applies for US people.

It could be a setting on the printer queue, but then you are at the risk of every operating system or indeed application such as browser getting it wrong... Printer manufacturers please just add a setting to your options - pretty please...

Haven't had that happen for ages...

I went into a Fedex/Kinko's in the US, to try to print something on A3.

They looked at me as if I had just asked them to sell me a unicorn. They then offered to custom cut a piece of paper for what I'd approximate as several tens of thousands of percent markup.

And what about US legal? Or Architectural Sizes?

Nevermind folios (and quartos and ovtavos).

It's a big diverse world with room for all sorts of paper applications.

[Architectural Sizes]: https://en.wikipedia.org/wiki/Paper_size#Architectural_sizes

[folios]: https://en.wikipedia.org/wiki/Folio_%28printing%29#Size

[big diverse world]: https://en.wikipedia.org/wiki/Paper_size#Other_sizes

It is a big, diverse world. And various, special use-cases are best addressed with different aspect ratios. But, to me, the point of ISO 216 adoption in place of US Letter (and other common sizes) is about having a general-purpose/common-use aspect ratio with inherent properties that help simplify things across the board for a lot of people. If it wasn't already used so much elsewhere, I'd be a "harder sell" (even to myself). But, it is used elsewhere... a lot... and has beneficial properties too. Trying to clean up the mess and simplify the chaos. Remove the unnecessary extra baggage associated with other systems.

Aside: If I was king of Sun III (previously known as Earth), my replacement for "US Legal" sized paper would be 210mm × 340mm. This maintains the width of A4, but gives it a length similar to that of US Legal. Moreover, it achieves this using the Golden Ratio. Calling it φA4 for the time being.

    US Legal..:  8.5”  × 14” (Before mm conversion.)
    US Legal..:  216mm × 356mm —> approx. 1.647:1 ratio

    A4........:  210mm × 297mm —> approx. 1.414:1 ratio
    φA4.......:  210mm × 340mm —> approx. 1.619:1 ratio

See http://i.imgur.com/S0rrRnP.png for an example.

Aside: Apparently the 210mm × 340mm size is used for some folded paper towels and some pastry bags already. Also, Mexico's "Government-Legal" is 216 mm × 340 mm — same height as my proposal but with a 6mm width difference. (Theirs matches US Letter/Legal width of 216mm instead of the A4 width of 210mm.)

Are you volunteering to transition Sun III's physical files cabinets, storage boxes, warehouse shelving? To reconfigure their printers, rewrite their report software etc.?

There's a lot of friction and it all takes place on the ground, unlike translating Python 2 programs to handle Unicode, there's no cloud service model that facilitates the transition.

The wonderful thing about standards is that there are so many of them to choose from. -- Grace "disputed attribution" Hopper

As King of Sun III, yes I am forcefully "volunteering" my subjects to do the work. Archives can remain as-is. Everything new shall use the new system. Doing otherwise incurs penalty. If you don't use the new system, you will get pain treatments and possible death. /humour

I have to note that A4 (what goes in a standard printer) is just a shitty format for documents. There is no way to get a proper layout done, you basically need two columns to use a reasonable amount of space with regards to font size and text body layout, which leads to other problems.

There is a very good reason you don't see any A4 books. A5 works OK for book layouts but still is too wide actually...

A5 booklet printed: http://mr.gy/blogopy/max/3589981109.html

The point is: An A5 booklet on A4 is the same as A4 booklet on A3, etc.

No its not. In fact its completely unrelated because when making book you should care for aspects like font size and text body layout which follow an ergonomic perspective.

E.g. the same booklet layout on a3 wouldn't work at all because the font would be huge. Keep the font size small and you have really long lines...

I regularly print out A4 documents two-to-a-page side-by-side on my office printer. It saves paper, its easier to carry around, and it works just fine. No distortion.

If your docs are US Letter, how well do they print out scaled down two-to-a-page side-by-side?

I do this a lot for printing out (research) articles, and the answer is that the text gets shrunk much more, and the margins increased to account for the difference. (This actually turns out to be useful in practice, since there's much more whitespace to take notes in.)

You are misunderstanding him. He's not saying that you can't shrink A4 down to A3. He's saying that aesthetically you can't do this without (of course) changing the font size. But if you want to retain readability, you may need to keep the font size larger, thus requiring a complete reformatting of the text. That is, you're talking about math and he's talking about the realities in dealing with humans as readers.

Makes it easy for the "large print" edition for people with eyesight issues.

> There is no way to get a proper layout done

This is puzzling - how do you explain the abundance of people who seem to have no problem with this whatsoever?

Finally: I have seen lots and lots of A4 books, but they're simply not as common. It probably does help to live in Europe in that regard.

Are you a bookmaker? The are the ones with the problems. ;)

> I have seen lots and lots of A4 books

And they all have suboptimal layouts.

> And they all have suboptimal layouts.

(my emphasis)

My question would be - would you be willing to ascribe that to taste?

No. Try to layout a document on A4 while maintaining at least basic standard rules (e.g. lines of 8-12 words, a pretty text body layout, e.g. a "nice ratio" like 3/4 or 1/2, with standard margins, that is 1 on top, left and right and 2 on bottom). Since your font size will either be 11 or 12 pt on A4 because otherwise you use less than half of the paper or your font is really huge, you're not left with many options.

All of this is voodoo that you learned working with your preferred aspect ratio and size. None of these rules have any kind of objective basis.

I wouldn't be so hasty to dismiss hundreds, perhaps thousands of years of aesthetic tweaking by experts as voodoo simply to defend a page size and proportion whose primary advantage is not aesthetic but function.

None of that makes much sense to me, to be honest.

I find it curious that you just say:

> standard margins, that is 1 on top, left and right and 2 on bottom

No units, which makes me assume you're talking inches... Perhaps your problem is that you also need to switch to metric? ;-)

No units because its all about proportions. E.g. the bottom margin is "double" so it can accommodate page numbers and set the text body on the "horizon".

I suspect the explanation is similar to the explanation of the abundance of people who seem to have no problem with US paper standards whatsoever, namely, that it's just paper, and most people don't have particularly strict usage constraints, so they just use what they have and it works fine.

Books come in absolutely random factors.

The book "advanced engineering mathematics (8th edition on my desk)" is just as wide as A4, but less tall for some reason.

I regularly print documents in A4, and full-width text is absolutely ok if you consider the required margins for binding.

Y'know, you can just make the margins wider.

Although I don't agree with the width statement, I just wanted to note that I personally find the B sizes nicer than the A sizes for non-fiction books. I find A5 pages a tad small for textbooks, but B5 seems just right. (So, effectively "B4 folded", which is usually printed on A3 to begin with, then folded into signatures, bound, and then ultimately cropped.) And since it's all the same proportion, it makes it easy.

This is what the B series is for. It maintains the geometric properties of the A series but has a 1.420 contrast ratio. B5 is what you want for a typical book.

It's also the geometric mean between A4 and A5, which is pretty cool!

As someone who printed every high-school and university essay on A4 paper, I can say it's a fine size for documents. You're right that it's a rubbish size for books, but that's a different question.

Another fun fact:

An A0 piece of paper has an area of exactly 1 square meter.

It says that right in the article.

One could just imagine Letter to be 11" x 7.7781" (preserving the sq. root ratio) but with a 0.7219" side margin for bindings. Feel better now?

I have been keeping all of my notes on B5, while living in the US, for the past ten years for this exact reason. 8.5 x 11 is simply not an attractive shape.

I personally want Japanese B5 notepads -- they are the perfect dimensions. I ran out a long time ago, and they are hard to come by in the US.

They're cheap at Muji. http://www.muji.us/store/stationery/notebooks/recycled-paper...

If you really want to have it, you can order directly from Japan. You can use a reshipping service like http://honto.jp/ and have the company you buy from ship to them if they don't ship internationally. They also help you order things if you don't know the language.

Then it just comes down to the import rules of the US (seems like you're fine with anything below 200$ of value, but I'm not sure [1]).

Yes, it's a bit cumbersome, but in this glorious age of the internet there should be nothing (legal) that cannot be procured.

[1] https://help.cbp.gov/app/answers/detail/a_id/501/kw/post/sno...

thanks! Just ordered a few of those from jetpens. Size/quality looks very promising

As another poster said, Muji has very affordable ones in a variety of styles (gridded, lined, plain, record). They're very thin and cheap, but I love them and have been using them for years. Alternatively if you're near a Kinokuniya (they have a couple US locations) they have a stationery section with other common brands (e.g. Campus).

The post seems to be inspired by a hot question on Math StackExchange http://math.stackexchange.com/questions/1143132/is-there-a-s... . Probably the author should also acknowledge it?

As a young european the printer message "Please insert letter", or something similar, always confused the hell out of me when printing certain PDFs. Letter? What letter?

Yay math. But we're not changing. Were you around for us trying out the metric system?

If you really want to start, let's begin with QWERTY keyboards

And let's not even get started on standard(?) photo sizes! Who came up with that mess?

Is this the place to bring "inches vs cm" on the table ? :p

Totally orthogonal argument. It's the ratio that matters.

It's not the place, but not that you've brought it, as an American I say imperial units can go die in a fire.

Is A4 sized paper hard to get hold of in the US?

I tend to buy two reams A4 for each ten reams Letter, but each time availability and pricing varies. OfficeMax used to have Boise A4 paper around $8 a ream, but now they are selling a Hammermill paper for $11. Never in the stores of course.

Practically, the number of people who need to ever use a paper size other than letter/A4 is minimal. So any elegance is pretty much lost.

Hmmm... I'm not sure that's true.

Looking around my desk (in London, UK) I have

- a few flyers (A5) - much more convenient for people to hand me in the street, big enough to get information across on, not to big to big cumbersome for me and (presumably) cheaper than A4 to print in bulk

- a postcard (A6) from a colleague who went on a lengthy vacation

- business cards - some (but admittedly not all) of which are A8

- and lots of A4 - it's what I print out when I need a hardcopy.

I don't currently have any A3 on my desk, but I've used it in the past when I have complicated diagrams to analyze and want to get it all on one sheet.

I often print out documents as 2 (or sometimes even 4) pages to one A4 sheet to make it easier (and more tree-friendly) to read away from my computer - this works OK because the aspect ratio remains the same.

Not true, at least outside the US where using other sizes is easy. It all "just works", so it's used all the time.

Age 5, my school work book is B4 size. I can glue the a A4 sheet (or two A5 sheets) the teacher hands out.

A little later, and the work books are B5 sized. A4 sheets fit in if folded.

I want to make a poster at home. I set the document size to A2, design it, press print, and four A4 sheets are printed, exactly the right size. I can change it to any other A-size very easily.

I want to photocopy / print some A4 documents, but save paper. Two (or four) sheets fix neatly on one page. Or, I can enlarge it to A3 — most photocopiers in most offices have A3 paper in one of the drawers for this. There's an A3 laser printer in my office, it's useful.

From my desk, I can see things laser-printed by me in A4 and A3; things produced in A5 and A6; and notebooks in B5. If I need a poster in A1 or A2 size there's a printer upstairs.

A4 and A5 are used very often, for example for notebooks in school.

I've tried in the past to explain how awesome the sqrt(2) ratio used as the basis of DIN/ISO page sizes is, but there are some very dumb people on HN: https://news.ycombinator.com/item?id=7821947

Haha that thread is great... good old metric system.

It was like talking to a brick wall. A very dumb brick wall that couldn't get it through their head that the units didn't matter, and that what mattered was the ratio.

The A0 being 1m^2 is important too, if you're ordering paper by area?

Yeah, but that's really a different argument. Once you get the ratio argument, you get the utility of the system.

The A0 being 1m^2 is important because paper weight is given in gsm - grams per square metre.

Thus when calculating postage weight by counting the number of sheets you can calculate that, for example, the weight of one A4 sheet is 1/16 the gsm of the paper - 1/(2^4).

Oppose the totally insane system used along with U.S. paper sizes:

http://en.wikipedia.org/wiki/Paper_density#Basis_weight

In order to figure out the actual mass of a sheet of U.S. paper from the reported basis weight, you must know how many sheets of paper were in the "basis ream" and what dimensions they were. The basis ream sheet dimensions may have nothing to do with your final sheet of paper, and the number of sheets varies too.

> It was like talking to a brick wall.

I know those types of conversations. They stay with you for months and sometimes years, never ceasing to irritate.

Sometimes the irritating part is when you realize that you're the brick wall.

Exactly! Furthermore: In that case, it gets more vexing the longer it takes you to arrive at that conclusion.

When it's the other way round, you can find peace at some point (even if it takes months or years). But if you were the brick wall, it first takes months or years and THEN, when you finally do realize the reality of the situation, it takes even longer to settle. shudders

I feel your pain. The tough part is realising how pointless those "someone is wrong on the internet"[1] discussions are. I get embarrassed looking back at situations like that, and think "why did I even care if this random person didn't get what I was saying about <thing-we-were-arguing-about>?"

[1] http://xkcd.com/386/

Oh, I agree. I was as dumb as him for participating in it. If I'd any sense, I'd never have engaged with him after it became clear that he was fixated on something completely separate from the actual point.

Well if its any consolation I'm as guilty as you are, and you made plenty of sense to me.

Thank! I really have no idea how I could've explained it better in context, which is the most frustrating thing.

Correct me if I'm wrong, but the point of the guy you were arguing with in that thread was that the Ax standard was defined in terms of SI units as the US imperial units are?

And I was trying to get across to him that the units used really didn't matter at all, but he didn't seem to get that point.

If you read the parent (by somebody else, not Turing_Machine), it said that the ISO/DIN page sizes are part of the metric system. I corrected him saying that they were only based on it (in that the sizes were defined in terms of metric units) and not part of it, but that what really mattered was the ratio between the long and short edges of the sheets being √2.

Then Turing_Machine came in with this total non sequitur:

> How are factors of 2 and sqrt(2) "based on metric"?

And then things went completely off the rails.

Edit: s/same/came/

Instead of blaming others for being dumb, you might want to take the following brief blog post to heart:

http://blog.codinghorror.com/but-you-did-not-persuade-me/

No, in this case, he was being dumb. He started out with a complete non sequitur, and then got fixated on that.

Clarification: the guy was being dumb, but I was dumb for engaging with him in the first place. I'm in no way 'blaming' somebody for being dumb.

raldi didn't say that anyone was or wasn't being dumb. He said that "instead of BLAMING OTHERS for [x], YOU might want to [y]".

Blaming others is a poor lifestyle adaptation. Whether or not the other guy was actually dumb or not isn't relevant.

Who was blaming anybody?

You are. I can paraphrase your original comment like so:

"I have tried in the past to explain how awesome the ratio is, but it didn't go well because of dumb people."

You are correct that you're not blaming anyone for being dumb, but you are blaming others for the explanation not going well.

No, I'm not, and you're putting words in my mouth.

This:

> I have tried in the past to explain how awesome the ratio is, but it didn't go well because of dumb people.

Does not mean the same thing as this:

> I've tried in the past to explain how awesome the sqrt(2) ratio used as the basis of DIN/ISO page sizes is, but there are some very dumb people on HN.

I believe you that that's not what you intended to say. I certainly don't intend to put words into your mouth! But I think you're wrong; I suspect the vast majority on HN read your comment the way I do.

The word 'tried' implies an attempt that failed. And in the phrase "I've tried... but...", the part after the but almost always implies causality.

2^4 x 21 mm x 29.7 mm ~ 1 m^2

Yup, he was being dumb.

They are more or less agreeing with you that convenient scaling is a feature. They just use a bad analogy, and you talk past each other a lot.

(I agree that they miss the point that you aren't promoting metric)

Yes. talideon wrote two unrelated sentences next to each other, Turing_Machine thought they were related, and the two of them started talking about different things. (This is my impression, at least. I can't seem to bring myself to properly read the whole thread, it's too frustrating.)

talideon, you do not come across well from that exchange. You may or may not have been talking to a brick wall, but you weren't listening to one. I more-or-less agree with raldi: instead of fixating loudly on what Turing_Machine did wrong in that thread, think about how you could do better next time.

Look, I repeated told him that the units didn't matter, and that it was the ratio that mattered. Other than disengaging sooner (which I would've done if I'd any cop-on myself), what could I have said differently? I'm truly at a loss. I straight-up wrote this:

> _The units are irrelevant._ That's what you're not getting. What is relevant is that the same page width/height ratio is maintained between the different page sizes.

When I was younger, I would've had more patience with this kind of thing; but as I get older, it becomes less and less worth my time and energy.

You shouldn't have said "You appear not to understand the actual utility behind the page width/height ratio used in ISO/DIN page sizes." Turing_Machine wasn't talking about utility at that point. Ve had misunderstood something confusing that you had said, and you basically straight up said "you're dumb".

That was only after he came up with the fluid measurement analogy, which made _no_ sense at all. I'd written this:

> The 1:sqrt(2) ratio used is extremely convenient as it scales up and down nicely

Then he wrote this:

> How are factors of 2 and sqrt(2) "based on metric"? At some level you could say that the U.S. measurements are "based on metric" since almost all of them are defined in terms of metric units. You just have to apply the proper factor (which is a decimal, but a terminating one --- unlike the sqrt(2) business).

(Emphasis mine.)

That is where the "You appear not to understand the actual utility behind the page width/height ratio used in ISO/DIN page sizes." comment came from. I wasn't calling him dumb. I hadn't flipped the bozo bit on him at that point, though I had by the time I wrote "Ok. I'll be super explicit about this." later on.

No, you'd written this:

> They're not part of the metric system, simply based on it. The 1:sqrt(2) ratio used is extremely convenient as it scales up and down nicely

TM thought those two sentences were related. Ve thought you were saying that the factor of sqrt(2) was what made it metric. Ve was correcting something that you hadn't actually said, but which would have been wrong if you had said it.

And then your reply to ver made the same mistake, and you do not get to feel superior about this.

("You appear to not understand" isn't literally calling someone dumb, but that's pretty much what it boils down to.)

I'm not going to make another of the same mistakes you did: I'm tapping out here.

I get your point, and I don't feel superior about it.

My emphasis didn't appear to get through. This is what I'd meant to emphasise.

> You just have to apply the proper factor (which is a decimal, but a terminating one --- unlike the sqrt(2) business).

That's where the "You appear to not understand" comment came from, because they didn't understand it.

I literally have no idea how I could've phrased that better.

I'm also tapping out: I'm in work, and didn't expect to spend so much time at this.

You say that "same page width/height ratio is maintained between the different page sizes" is the important thing, but it's the result of using that particular ratio that is important, when you take a page of 1/2 the area by cutting across the long dimension, the aspect ratio is maintained.

If you aren't worried about maintaining the aspect ratio for 1/2 pages, you can maintain any arbitrary aspect ratio as you scale up and down (but you don't get the 'easy' scaling to half or double areas).

That's where the imperial fluid analogy comes in, there is convenience derived from having it be base 2.

The fluid measurements analogy doesn't work though because volumes don't behave the same way as areas with fixed aspect ratios. Moreover, the reason why √2 is such a useful ratio is because it maintains the same aspect ratio when the sheet is doubled or halved. That's why his argument was nonsensical.

I repeated attempted to explain to him that the units didn't matter. He ignored that.

Nooo... Dunder mifflin will be out of business!

A lot of US "standards" (only US uses them) should be banned.

There is nothing weird about national standards. Everyone does it. Germany has DIN, for instance. Even tiny Belgium has the NBN.

Usually, these standards are either equivalent to international standards or are only relevant in the home country of the organization.

Please ban letter size, ever been at the printer realsing nothing printed and facing PC Load letter message? Ever been in a foreign country trying to find your home countries legal size of paper in a local store?

I think we should switch to metric, a4 paper and right hand driving.

All of the countries using US Letter already drive on the right hand side...

I think the sentiment was "standardize on the majority", not "everything the US does is wrong".

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