Sunday, October 25, 2009

A4 vs US Letter Papersizes .

A4 vs US Letter Papersizes .

Andre Willers

Written : 28 June 2007

Edited and Published 25 Oct 2009

An old note I did not bother to publish then .

Sources : for standards . “Prodigy” series for brain mechanisms that count . for any related queries .


The paper size routinely used by a civilization determines the stimulation of specific brain-nodes concerning counting and mathematical ability . Because of close neurological connections , language and musical talents are also affected .

Discussion :


Quote: from

“Note: The Lichtenberg Ratio – used by the standard paper format series – is occasionally confused with the Golden Ratio (which Euclid referred to as the “extreme and mean ratio”).

The Lichtenberg Ratio is defined by the equation a/b = 2b/a = sqrt(2), whereas the Golden Ratio is defined by a/b = (a+b)/a = b/(a−b) = (1 + sqrt(5))/2. While aesthetically pleasing properties have been attributed to both, the Lichtenberg Ratio has the advantage of preserving the aspect ratio when cutting a page into two. The Golden Ratio, on the other hand, preserves the aspect ratio when cutting a maximal square from the paper, a property that seems not particularly useful for office applications. The Golden Ratio was for a while a more fashionable topic in the antique and renaissance arts literature and it has a close connection to the Fibonacci sequence in mathematics. “

Two fundamental constants :

The Golden Ratio(phi)= 1.618034… (found especially in growth of finite elements)

Euclids constant (e)= 2.71828… (found especially in growth of infinitesimal small elements)

Both give rise to internally consistent counting (arithmetic) systems , with corresponding neuron clumps in the brain . Usage makes these complexes develop .

By the definitions above , stimulation of the Golden Ratio Center means a better capability of handling finite (ie digital ) elements .

By the definitions above , stimulation of the Euclid Center means a better capability of handling infinite (ie smooth ) elements . Calculus .

The two centers are evolutionary separate and not mutually exclusive .

But cultural stimulation can have disproportionate effects .

Note that (e / phi) ~1.68 ~ (1 + 2/3 )

See the importance of the 1/3 ratio in "New Tools : Reserves"

The square root of (e / phi) ~ 1.3 . Refer to Lichtenberg ratio above .

Compare paper sizes in mm:

ISO A4 US Letter

210x297 216x279


297/210=1.414 279/216=1.3

Note that the ISO A4 ratio of Length/Breath is always = the square root of 2 by definition .

The US letter ratio of Length/Breadth is = the square root of (e/phi) ~ 1.3

This means that somebody continually handling and looking at US Letter paper sizes from baby upwards has a relatively better developed integer counting brain center .

Both counting centers are stimulated from babyhood .

Hence the US superiority in digital software and (to a certain extent) , money .

Remember , it does not take much of an initial advantage to build up into huge gap over a few centuries , especially a culturally wide influence like this .

A historical note :

Where did they get this ratio (1.3) from ?

Every US town until the end of the 1800’s had at least four or five newspapers. They continually experimented with book-formats , as well as their bread-and-butter stationery publications . The publishers also belonged to some semi-secret society like the Moose , the Elks , etc . These were heavily influenced (from Benjamin Franklin’s day ) by half-baked ideas in numerology , mysticism , etc . The ratio 1.3 is simply the geometric mean of two of the most fundamental growth constants known . So it is no surprise that the fittest should triumph out of this evolutionary stew .

What will be interesting is to see which format wins .

The Future.

Without the realization of how important this is , the ISO format would have won . Otherwise , the US format is clearly superior .

Artificial Stimulation of Counting Centers

The proven influence of two dimensional aspect ratio’s on the retina opens the way to some powerful interventions .

ITARIN can be easily adapted to different aspect ratios . So can TV’s and computer screens .

Scrolls vs Pages.

The concept of pages is essential to the development of printing . Note that the Sumerians and subsequent civilizations had a well-developed art of printing . Press-seals and roll-on seals were routinely used to validate routine items . Fixed-type impressments (prints) like these would have been essential for Imperial laws over the Empire . This type of printing survived over the centuries until the Mongols . (Playing cards)

Printing .

Every Empire used printing .

Chinese paper money .

Notice the Book of Kells in Ireland .

It has all the hallmarks of a mature technology .

This was produced by refugees from the turmoil of societal collapse in Europe . Yet a page format was retained . The printing (by woodcuts or stencils) is still crisp after about 1500 years . The fancy bits were done by hand .

It was not exactly a mass produced article .

Still , it would be a coup to find some of the original wood-cuts in some forgotten bog-peat hole . This is possible , even probable . The Church elders would have ordered the destruction of the original woodcuts and stencils, but humans being humans they probably ended up wrapped in suitably treated rags (peat embalming had been known for thousands of years) and stored in peat bog in a retrievable site .

Then the Vikings happened .

A nice little treasure hunt .

Moveable type is a different story .

Moveable type has been re-invented time after time . The concept has been around since Sumerian times . The metallurgy is simple (cast lead , one of humanities earliest workable metals because of the low melting point.) The ink is simple .

But the paper , the paper .

You need a strong , fine fibre .

For a mass media , you also need a lot of paper . Also , mechanical ways of preparing it . Roman ways simply were too low volume . Reeds like papyrus ? Forget it . Too coarse and expensive . Ink smears .

Why do you need a moveable type? If you are printing Imperial edicts or the bible , no change is needed .

Many monasteries printed things like complines long before Gutenberg . But the need for novation was small

You need novation for News . Something new . In other words a newspaper . And to make money at it , you need cheap paper . This is the single ineluctable fact that has not changed in the last 10 000 years .

The paper was originally supplied by the flax fields of Belgium and the Netherlands .

So why did this not drive the change earlier ?
Answer : the flax was primarily used for clothing . In a rising population , a newspaper would have to compete with clothing . It was not a paying proposition in a cold climate .

But then the Black Death , wars and the Little Ice Age happened .

Suddenly a lot of old clothes and unused flax-capability was available . To be fair , the Little Ice Age probably contributed the most . Agricultural areas that previously could grow food crops , now could only support a crop like flax, valuable for it’s stem fibres , not food . (Notice the ironic resonance with the American South and Cotton , when greed drove them to destruction.)

The result was a huge drop in the price of rags and flax .

Quality paper became cheap . Newspapers got above the threshold of profitability , then took off as the political implications were realized .

Of course , they were not called newspapers at the time . The media-moguls had not yet evolved to tell us what we think . They were called pamphlets . The cost was low enough that anyone could afford his own pamphlet . The result was very like the present Internet/Blog explosion .

Very few of these pamphlets survived (and if you have one , you can flog it for a lot )

Even kings weighed in .

Like King James the First's pamphlet blast against tobacco . One of the first anti-smoking Nazi's .

Then mass Spectacles .

See "The most influential human in the last 1000 years : Salvino Armolo D'Armati ."

Small print is not just the purview of lawyers . Publishers thrive on it . And for small print you need good paper , ink and mass spectacles so the middle-aged people with money can read it . Look at some books printed in centuries 1600 – 1900 . The print is very small . Really small . Even juveniles have difficulty in reading it . Glasses were essential . Those small jobbies you can buy in the pharmacy , then and now .

But small spectacles means that the whole page cannot be seen . So we have an expected decline in numeracy and increase in Literature , till about mid 20th century , when large glasses became cheap and large print became less expensive .. The same effect can be seen in Asian countries .

Literacy :

Funnily enough , not a major requirement . The very development of the alphabetic system stems from Egyptian mercenaries from the Middle East , Anatolia and Southern Russia using the easily learned phonetic part of the Egyptian hieroglyphic system to write home . Surviving messages from the mines in Sinai and outposts in Southern Egypt (scratched on rock as first attempts before putting them on precious papyrus – think telegraph rates) .

Not jewels of literature . But , even troopies learned very quickly to write . From nothing . How hard can it be , once you know it can be done ? More significant is that they expected that there would be somebody at the home-end to read it . Travelling scribes .

These messages home is a recurring theme in all ordinary surviving messages in the last 8 000 years .

Widespread ability and expectancy to be able to communicate via writing .

The village noticeboard was universal . Kingly decrees and news , interpreted by scribes (for a tiny fee , of course) .

It is amusing to speculate that the center stone pylons in Zimbabwe fulfilled this role . A noticeboard . Like the Greek Agora or Roman Forum , only on a more modest scale.

Obesity .

The effects on obesity has been discussed in "Escalators make you fat" 1 Oct 2009 .


So the next time the printer or photocopier jams , you can say with suitable vehemence :

"By the root of two or e over phi , get thee hence , thou gremlin .In the name of Euler and Euclid ."

The local shamans will applaud your perspicacity and learnedness .

And maybe the machine will unjam just as the horse starts singing .

Andre .

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