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ISO paper sizes, rational or irrational? And date formats as well.

The aspect ratio or height-to-width ratio of all ISO paper sizes is the square root of 2, an irrational number.

Is this rational?

The rest of the ISO paper geometry seems too clever by half, but maybe some kind of order is helpful. And then what about trim size?

This says that "Inconsistent use of SI units and international paper sizes remain today a primary cause for U.S. businesses failing to meet the expectations of the global economy." What does that mean? Is this a reification error: how does the economy expect?

-- Edward Tufte

Response to ISO paper sizes, rational or irrational?

I am reminded of 2001 (the book) in which the star child muses how *necessary* the ratio of 1:4:9 in the monolith is, as the squares of the first 3 primes. Of course, Clarke never divulges just why it is necessary aside from the artistry of an arbitray base 10 system. In this sense your reification question may be valid. However, far be it from me to scoff at introducing mathematical elegance into mundane objects, since Fibonacci series were an intellectual toy until they were found useful for arranging satellite tracking receivers.

The ISO page you reference gives the raison d'etre as convenience in copying. The day I have two perfectly matched originals that I can precisely copy without multiple recourses to the sizing controls, I will also win the lottery. 11x17 also gives the same results when using 8.5 x 11 sheets. Area rather than length x height seems an odd reference point. If A0 is 1 meter square, they also need to specify the other dimensions anyway to standardize plotter output. Maybe publishers like the idea of being able to slice paper in a mathematically predictable way to maximize paper usage?

European fax machines have long been able to convert US to A4 dimensions, but with email and electronic authorization looming I can't think of anyone except (perhaps) the E&S insurance industry still clinging to paper documentation. If, on the other hand, this is intended to phase out the undeniably archaic legal size of 8.5 x 14, more power to them.

-- Gordon Fuller (email)

Response to ISO paper sizes, rational or irrational?

One advantage of the ISO proportions is that the page can be cut in half and each half has the same aspect ratio. This is helpful when printing.

In the architectural world, drawings are often produced on large sheets (a0). The contractors use the large sheets, but most other people (the client, engineers, consultants) use reduced-size sheets for convenience. You can print an a0 sheet on a3 paper at 25% size without any leftover space. That doesn't work in Imperial paper sizes.

If the paper must be trimmed (such as for full-bleed work), you can start with RA or SRA sizes.

Folding is another issue. There is even an ISO standard for folding an A0 piece of paper to fit in a A4-sized ringed binder, while making sure the drawing title is not obscured, and also allowing the drawing to be unfolded without removing it from the rings. ( The small unlabeled rectangle in the lower right corner of the sheet (both illustrations) is the ISO standard location and size for title block information, such as the drawing title, revision number, date, etc.

One thing for sure: The ISO paper size standard is thought through to much more detail than the Imperial system.

-- David Person (email)

Response to ISO paper sizes, rational or irrational?

Being in a metric country, which isn't hard as the US and Myanmar (Burma) are the only two non-metric states on the planet, ISO paper sizes are pretty much only used for business documents. Newspapers are still the old broadsheet and tabloid sizes. Books come in whatever size the publisher/author desires. The world would be a pretty boring place if all books in your library were the same size.

Maybe if Thomas Jefferson had put a bit more pressure on the First Congress the US would be metric today.

-- Andrew Nicholls (email)

Response to ISO paper sizes, rational or irrational?

You are correct Edward - the global economy cannot be said to possess expectations. The ISO paper should instead begin:

Globalization starts with getting the details right. Maximizing the efficiency of the international economy through globalization requires consistent use of SI units and international standard paper sizes by all countries.

Your statement "...but maybe some kind of order is helpful" in regard to paper sizes is interesting - has the U.S. become so affluent that the attainment of further gains in economic efficiency (through the adoption of international standards) holds little interest?

Another standard we should all adopt is the ISO 8601 International Standard Date and Time Notation. See: The non-ambiguous nature of this standard is in contrast to the ridiculous month/day/year date format favoured in the U.S. This format leads to continous confusion around the world. I recently dated an American woman who had gotten into some trouble with the authorities in Australia over her travel visa. The visa had expired, unknown to her because of her interpretation of 11/06/03 (dd/mm/yy) as 06/11/03 (dd/mm/yy). The use of ISO 8601 on her official papers would have made the situation clear to her - the visa was due to expire 2003-06-11. ISO 8601 maximizes rationality by formatting dates in the general manner in which we format times - by ordering the units largest to smallest.

-- Andrew Leonard (email)

Response to ISO paper sizes, rational or irrational?

Ordering units from largest to smallest (or most significant to least significant) is known as "little-endian" notation, and its opposite is big-endian. Some computers are built with one standard, some with the other, and the resulting differences in byte-order frequently cause problems transferring data from one machine to the other, whether on disk or over a network connection. There are efficiencies to be gained by using only one byte order versus another. The act of transforming from one notation to the other is so commonplace it has its own term, byte-marshaling.

People perform similar marshaling operations on all sorts of data, including dates, metric to "standard" measures, even paper sizes. If people no longer had to perform these tasks, how much time, money, and effort (and lost Mars-bound spacecraft!) we would save as a society!

-- Scott Zetlan (email)

Tangent: ISO dates

Andrew Leonard wrote, "Another standard we should all adopt is the ISO 8601 International Standard Date and Time Notation. [snip] The non-ambiguous nature of this standard..."

I disagree that this standard is unambiguous. As long as both months and days of the month are written as digits, there is ambiguity (unless the day of the month is the 13th or later). A non-ambiguous method of writing dates is simply to spell out the month in letters, and write the year with 4 digits. This method is advocated in Strunk & White's classic Elements of Style.

-- Zen Faulkes (email)

Response to ISO paper sizes, rational or irrational?

To follow up some tangents in this thread

The numbers 1, 4, and 9 are the first three perfect squares in ANY base, not just base 10.

Regardless of how the computer stores multibyte numbers (big- or little-endian), strings are virtually always sorted using the first byte as the most significant. So a string representation of a sortable quantity has an advantage when its components are ordered from most to least significant.

The ISO standard is unambiguous in the sense that there is no locale in which the date is written YYYY-DD-MM (AFAIK). In any locale, if the date is written YYYY-xx-zz, then xx is the month number and zz is the day number. So establishing that format as a universal convention will not contradict any existing meaning of a YYYY-xx-zz format. This format is advantageous in data files because it requires no localization and is very easy to sort chronologically.

-- rob mayoff (email)

ISO 8601

As the web page i reference states, ISO 8601 describes numeric-only date and time formats; it is a language independant standard. Have those favouring representations of dates that include words considered those who do not speak English? The method of presenting dates as advocated by the Strunk & White manual may once have been valid for some; in the globalized economy it is not.

Any numeric-only format can only be considered ambiguous if there are no conventions or written standards to guide the reader, or when the clash of these conventions is itself the source of the ambiguity, as is the case with alternative date formats (and 12h time formats). It is not reasonable to wonder if a date presented as 4digits-2digits-2digitis might have the format yyyy-dd-mm since this is not a format used by anyone, nor is it part of a written standard.

For more on this subject;

-- Andrew Leonard (email)

First, on paper sizes: although there's nothing fundamentally wrong with US sizes, the ISO ones are convenient for resizing because the ratio of length to width remains constant (sorry, 11x17 is not the same ratio as 8.5x11 as one poster suggests). It also makes it easy to calculate an approximate weight for a piece when you know that A0 is one square metre and paper is specified in grams per square metre (anyone here understand the US "basis weight" system for paper?!). And because there are parallel envelope series you know you can just buy a C4 envelope to put your unfolded A4 or folded-in-half A3 sheets in.

As for dates: sorry, I'm with Strunk & White on this. Spell the months out. Although the language issue is a real one, simply do it in the language(s) of the document. You know when you don't understand a language. The M/D/Y vs D/M/Y is a real trap because it appears to be absolutely clear to anyone who speaks English - but it's not. Any other numeric "standard" like the ISO one relies on a narrow audience who understands it - it's potentially baffling to an ordinary reader. I believe in communication that's unambiguous to the greatest possible number of people.

-- David Glover (email)

Maybe I am biased, living in a metric country, but I love the ISO paper sizes. I can print my documents 2 or 4 to a page with no distortion and no waste of paper. Being able to accurately copy two pages onto one with no distortion or waste is also a boon when using a photo copier. Also, when I was producing a newsletter for a computer user group years ago, I could print the newsletter on A4 paper, then simply copy the pages onto A3 and fold the A3 pages - no waste, no fuss.

Like the metric system, it is really simple to use and get used to, but people who have grown up with imperial measurement systems sometimes take a lot of convincing that "the way we always do it" is not always "the best way".

-- Amos Bannister

On date and time conventions, Andrew Leonard says:

"ISO 8601 maximizes rationality by formatting dates in the general manner in which we format times - by ordering the units largest to smallest."

That's not really true. Most people I know think of the date or day of the week most often, then the month, then the year. How many times do people give you a date without the year? For example, "I'll see you Tuesday", "Let's have lunch on the 19th of next month", etc.

More "typical" usage is smallest to largest, for example, "the 21st of January, 2005" or 21 January 2005.

-- Len Gilbert (email)

Regarding "ISO 8601 maximizes rationality by formatting dates in the general manner in which we format times - by ordering the units largest to smallest":

I think the point is that it is times of day we format from largest to smallest (hh:mm:ss) and that this is "rational." I think the rationality is arguable, but it also seems to me that if the first of this month had been written as 2003.11.01 there would be less ambiguity than 01.11.2003 or 11/01/2003.

I seem to remember from first-semester Japanese that the Japanese write year-month-day. Is that common in non-European languages?

-- Erik Schwab (email)

As an immigrant to Canada from the UK, I can personally testify to the confusion caused by the American versus UK date format. I frequently ask myself "is this date May 4 or April 5?" type questions. At least in the USA the month day, year format is used consistently; Canadians use it as often as the day month year format. The ISO date format is much better particularly on computers for sorting and ordering though if everyone wrote the month out in full it would be a tremendous help to us poor immigrants.

-- Ian Entecott (email)

As an American, I too am often unsure if "4/5" means "4 May" or "April 5". In natural history museums, with large collections of biological and other specimens, dates are often recorded on specimen labels in the format "Arabic day. Roman month. Arabic year"; thus, for example "4.v.2003" is 4 May and "5.iv.2003" is 5 April. The convention of using Roman numerals for the months means that even if you change the order, you know which is the month.

-- Gregory Mayer (email)

It seems to me that there is dependancy on a significant time size and a default value for the larger, less changing values. The numerical representations are often versions of verbal habits.

So for example, if someone told you that the meeting was on the 20th, you'd assume that it was this month (unless the 20th had passed and in that case, they were not talking past tense). The same can be said if someone said they were leaving at "half-past" - often here the default hour value is not the current one, but a previously mentioned one or an inferred one. "The show starts at 8pm so we'll be getting there at half-past" is ambiguous though as it will depend on the type of show as to whether the speaker means 7 or 8.

Significance could be something that influences the fact that times are specified larger to smaller and dates smaller to larger. For example, if you read the time ss:mm:hh you get the traditionally humanly useful information later (it depends on the situation as to whether this will be minutes or hours). In terms of the date, if you are told then, in human awareness you get the significance last, again. The year and month are less significant as, in human terms, they are relatively long lived.

Minutes and hours and day and month are often interchangeable as we have reasonably short-lived tasks (time), and long-term plans. At least in modern times, at any rate.

The different US and rest of world (or merely European?) methods of writing the date are both logical in that they are numerical representations of differing verbal constructs: "it happens on July 4th", "it happens on the 5th of November" respectively.

The only way to reduce ambiguity is to use a standard method, and the ISO one is a good way in this age of computers as it aids chronological sorting - even if it goes against verbal habits and significance - humans can easily translate it. I also like the fact that it is neither of the other two (competing) conventions.

Finally, another example of potential ambiguity is in the German method of saying the time. Their phrase meaning "half-four" actually means 3:30 as it is either a shortening of "half an hour before four" of "half of the hour of four" - I think more likely the former. The English "half-four" is "half past four" short for "half an hour past four". This ambiguity does not translate into numerical formats, thankfully.

-- Adam

Some asked about where the U.S. customary (not Imperial) sizes for paper comes from. First, it depends on the kind of paper (printing, card stock, etc.) which determines the basic large sheet size (from which the "basis weight" is derived.. the weight of a ream (500 sheets). Then, the various sheet sizes are developed by successively folding the sheets in half.. i.e. start with 8.5x11, 11x17, 17x22, 22x34, etc. Engineering drawings are sized A,B,C,D,E, etc. according to this system (although they have margins). This is similar to the folio, quarto, octavo, etc. system. It gets a bit trickier, because it all derives from the printing industry, and when they print the pages on full sized sheets, then they fold them, then trim the folded sheets, ready to be bound as a "signature". The process of arranging all the pages on the sheet in the right order and orientation so that when folded and trimmed it comes out right is called "imposition". All of this is probably 200 or more years old.

The ISO system was developed much later, after photocopying was becoming common, and the idea of having all sizes have the same aspect ratio was quite useful. Scaling by area ratio of two makes sense, because a 70.7% reduction or 141% enlargement is a convenient range (50% or 200% is often too big a jump). Using nth root of a base for sizes is well established (musical notes, wire gauges, resistor values, etc.). Using square root of two is also handy for photographic purposes (enlarging/reducing), since the exposure will go as whole f/stops, making the "plate making" and "process camera" folks happier.

On basis weights.. it depends on whether you are buying bond paper or card stock, or cardboard, or.... all have different standard sheet sizes (somewhere in my files I have a printer's handbook that covers all this, and I'm sure one could google for it)

-- Jim Lux (email)

Basis Weights and ISO Paper sizes

Jim Lux: On basis weights.. it depends on whether you are buying bond paper or card stock, or cardboard, or.... all have different standard sheet sizes (somewhere in my files I have a printer's handbook that covers all this, and I'm sure one could google for it)

Indeed, google bond basis-weight hits pay dirt: International Paper has the charts and conversions from their classic pocket printing and paper guide.

For yet more history, see Museum of Printing. (Full disclosure -- I was their original webmaster, and still field a little email for their collections committee.)

The ISO root-2 ratio may be too clever by half, but it does provide order, and has the advantages Lux notes. The sensible only alternative that might be more aesthetic would be the golden mean.


-- William Ricker (email)

ISO paper sizes before 1975

Jim Lux: The ISO system was developed much later, after photocopying was becoming common, and the idea of having all sizes have the same aspect ratio was quite useful.

On Markus Kuhn's website on International Standard Paper Sizes which E.T. referred to there is a short history of ISO paper formats and I quote:

The practical and aesthetic advantages of the sqrt(2) aspect ratio for paper sizes were probably first noted by the physics professor Georg Christoph Lichtenberg (University of Gottingen, Germany, 1742-1799) in a letter that he wrote 1786-10-25 to Johann Beckmann. After introducing the meter measurement, the French government published 1794-11-03 the "Loi sur le timbre" (no. 2136), a law on the taxation of paper that defined several formats that already correspond exactly to the modern ISO paper sizes: "Grand registre" = ISO A2, "grand papier" = ISO B3, "moyen papier" = ISO A3, "petit papier" = ISO B4, "demi feuille" = ISO B5, "effets de commerce" = ISO 1/2 B5.

The French format series never became widely known and was quickly forgotten again. The A, B, and C series paper formats, which are based on the exact same design principles, were completely independently reinvented over a hundred years after the "Loi sur le timbre" in Germany by Dr. Walter Porstmann. They were adopted as the German standard DIN 476 in 1922 as a replacement for the vast variety of other paper formats that had been used before, in order to make paper stocking and document reproduction cheaper and more efficient. (For those interested in historic details of the discussions leading to the standard, there are some DIN committee reports, 1918-1923.)

The DIN paper formats were soon also introduced in many other countries, for example Belgium (1924), Netherlands (1925), Norway (1926), Switzerland (1929), Sweden (1930), Soviet Union (1934), Hungary (1938), Italy (1939), Uruguay (1942), Argentina and Brazil (1943), Spain (1947), Austria (1948), Romania (1949), Japan (1951), Denmark and Czechoslovakia (1953), Israel and Portugal (1954), Yugoslavia (1956), India and Poland (1957), United Kingdom (1959), Venezuela (1962), New Zealand (1963), Iceland (1964), Mexico (1965), South Africa (1966), France/Peru/ Turkey (1967), Chile (1968), Greece/Simbabwe/Singapur (1970), Bangladesh (1972), Thailand and Barbados (1973), Australia and Ecuador (1974), Columbia and Kuwait (1975). Porstmann's DIN paper format system finally became both an international standard (ISO 216) as well as the official United Nations document format in 1975 and it is today used in almost all countries on this planet.

So maybe the ISO standard was invented after photocopying became widely used, but the foundations had been laid well before that.

-- Kees Huyser (email)

Although both systems for paper size are a bit arbitrary, it is quite obvious that the reason for keeping the less functional US system in place is tradition, and perhaps some politics. The American Forest and Paper Assoc. explains the origin of the US system: "Back in the late 1600's, the Dutch invented the two-sheet mold. The average maximum stretch of an experienced vatman's arms was 44". Many molds at that time were around 17" front to back because the laid lines and watermarks had to run from left to right. To maximize the efficiency of paper making, a sheet this big was made, and then quartered, forming four 8.5" x 11" pieces.

A couple centuries later when machines dominated the trade (although many hand made paper makers still existed), and the United States decided on a standard paper size, they stuck with the same size so as to keep the hand made paper makers in business.

Oddly enough, the United States used two different sizes - the 8" x 10.5" and the 8.5" x 11". Separate committees came up with separate standards, the 8" x 10.5" for the government and the 8.5" x 11" for the rest of us. Once these committees found out about each other a couple years later, they agreed to disagree until the early 1980's when Reagan finally proclaimed that the 8.5" x 11" was the official standard sized paper."

In other words, the US is sticking with a Dutch system that is four centuries old, and is based on "The average maximum stretch of an experienced vatman's arms".

There is no doubt in my mind that switching to the metric system, including ISO paper sizes, would make life very hard for the vatmen and some patriots for a few years, but will help Americans workl better and connect with the world.

-- Ehud Tal (email)

Regarding paper sizes and printing (with Ed Tufte's recommendation of taking A3 size paper and folding it in half for distribution to an audience during a live presentation), there is a relatively new wide format printer from Epson available that is also relatively affordable (I just purchased one to try it out, its the Workforce WF-7520, and there is a similar printer with only one paper tray, the WF-7510). The paper sizes that these new wide format printers support has quite a range and is user definable from 3.5" to 44" in length. Its maximum resolution is 9600 x 960 dpi interpolated. I've been waiting quite a while for an affordable wide format printer, and I hope to use this one for making great presentations with handouts for my audience!

-- Eddie (email)

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