Chasing The Greek Foot

Chasing the Greek Foot

Somewhere along the line I was trying to find out how they properly located things on the planet, that led to geo – metrology, that lead to the fact that the Greeks and Egyptians had a measure named a ‘foot’ (pous) that is almost the same as the English foot. (Within a couple of mm 304.8 for the Engish, 304 mm for the Minoan, 308.4 for the Attic, 300 for the Egyptian and Phoenician, etc.)

This lead me to the factoid that if you take the earth’s equatorial circumference in ‘feet’ (English) as 131479724.6 (from the wiki metric number, converted) and divide it by 360 x 1000 (call it 60 minutes x 60 seconds x 100 or call it 360 degrees x 1000) you get: 365.2214573

Gee, that looks familiar, I think… Dividing by ‘tropical year days’ of 365.2422 gives 99.994% agreement. Hmmmm….

(If the English foot were 304.7828 mm, which rounds to 304.8, the agreement would be 100.0000% which is inside the error band of 304.8 so it is possible that the original English foot is exact and the metric conversion is not precise enough to capture that…)

Numerology? Or did those Ancient Greeks & British Druids know something? Is the ‘foot’ perhaps a bit more rational than mythology asserts?

One can only hope that the Met Office can achieve 99.994% accuracy and that GISS can learn what those digits after the ‘point’ are all about… (“Never let your precision exceed your accuracy”…) and maybe that we can be as good at science as they were 4000+ years ago…

(BTW, you can derive the “foot” using a bit of string, two sticks, and the night sky… but maybe you ought to work it out for yourself… Hints: 1) Make a time standard using a celestial object transiting the two sticks. 2) Make a pendulum tuned to the time standard. 3) Measure the pendulum… You now have a very scientific time standard and distance standard that can be recreated by anyone anywhere. Think about it…)

FWIW, the European / Scientific tendency to change perfectly clear units into things that honor some guy or other but hide their physical truth is just nuts. It turns more kids off to science than anything else. Why have Hz when cycles/second TELLS you what it is? Compare a “Pascal” to a “pound per square inch”. There is no clue what a “Pascal” is… which is probably why my tires have kg/cm2 on them.

So I, for one, will be happy to use feet (that have a history going back to before recorded history, being nearly identical to the Minoan foot… and having nothing to do with human feet) pounds per square inch and yes, F for decades to come. Though from time to time I will use Centigrade (a name that tells you something…) for some uses (my car, for example, is calibrated in C ).

And NOAA ought to retain F so as to retain the integrity of the data series (which seems to me to be a valid scientific reason – unless of course you want to recalibrate every single site for the change of equipment…)


About E.M.Smith

A technical managerial sort interested in things from Stonehenge to computer science. My present "hot buttons' are the mythology of Climate Change and ancient metrology; but things change...
This entry was posted in Earth Sciences, Metrology, Science Bits and tagged , . Bookmark the permalink.

17 Responses to Chasing The Greek Foot

  1. peter_dtm says:

    and remembering that it was Napoleon who ‘invented’ the metre (& got it wrong) is another good reason to go imperial !

    Nothing wrong with SI units for science & engineering – but they are pretty useless in the ‘real world’ not to mention the crippling effect all that decimal stuff has on the ability to do mental arithmetic !

    Just as long as they stop changing the damn standards – I have had to live through :
    Imperial (UK measure)
    cgs (horrible little units)
    mks (horrible BIG units)
    SI (hey I speak English – why isn’t it IS ?)

    And SI keeps changing. And there are so many exceptions to the prefix rules (small letter = divide; capital letter = multiply) as to render the System a misnomer !

  2. E.M.Smith says:

    I spent a while hunting down the history of the foot. Only a synopsis is here. I’m thinking about expanding this, or adding another (time, I need more time…) that goes into more depth.

    The “thumbnail sketch” was that I ended up mightily impressed at the ancients. They had a couple of different cubits. Why? One was used for navigation, the other for land… like our nautical mile that maps to degrees … The “land” unit had some variation depending on what latitude you were at. Why? It was used for measuring AT THAT LATITUDE and a degree covered a different distance. There were other special units for special purposes. We deride this now as crude; yet go to a metal casting shop and you may well find special rulers calibrated for the shrinkage of the cast metal. Make a “1 foot” long object and it comes out less than “1 foot”… so you build the molds with the “1 mold-foot” ruler and the product is one “cold foot” long … It is actually an elegant system that avoids repeated calculations.

    So the ancients had several “cubits” and related units each used for particular purposes – effectively they built the calculator into the ruler. And now some folks want to disparage that wisdom. Some of them are related via Pi. Some via Phi. Some are corrected for the oblateness of the planet(!) and used for north / south measure. (i.e. go so many degrees it is this many “units” including the oblateness correction! While East West have no such correction so you used a different cubit. All very systematic, very scientific, and very easy to use (especially without a calculator and planetary spec sheet in hand…)

    I came away impressed, and thus my happiness to continue to use feet, Greek, English, or otherwise…

  3. Beautiful article!. Perhaps those “revolutionaries” who sought to change everything for worse were doing it consciously: purportedly breaking the relation of man with surrounding reality in order to deprive it from its numinous character, from sacred to secular.
    It is so artificial that the geometric perfect figure the circle it was never accepted to have the 400 degrees!! they wanted us to accept.

  4. Fluffy Clouds (Tim L) says:

    from WUWT
    (Having been Director of Facilities for a hundred thousand square foot scale building, trust me, you do not want responsibility for the thermostat! You only know it’s right when the complaints are evenly split… So they want to control the thermostat: Fine. Start telling them what temperature you want and complaining about them having it set wrong… )

    I worked in a 250K sf building and it had momentum of its own. the only thing you can do is add cloths or take off a few.
    my complaint here at the 45th is that most places have the heat set at 72-74 so wearing three layers of clothing is hot to be in a building for more than 2-5 minutes(in the winter), so shopping for groceries is darn difficult!!!!
    One more particularity is that all winter the temp is set at 72-74, now it is summer they want the air set at 66-68 lmao!!!
    now I am back into two layers(thin ones) to stop from freezing!!! JUST GO FIGURE!!!

  5. Fluffy Clouds (Tim L) says:

    BTW the old people had to survive under more difficult times so I believe they were far more intelligent than us at this time. there are lots of things from 2000-4000 years ago that studying makes you shudder!!!!
    throw it all out cause were better!!!! ya right!!!
    I think the bible may have it correct when it say degrading is problematical. pride there may indeed be cocky arrogance today.
    ok off of the soap box!!

  6. E.M.Smith says:

    @Adolfo – the 360 has the wonderful property of many factors. One of the advantages of 12 inches and 360 degrees is that math with fractions works much more easily with lots of factors to work with. That was one of the things I discovered. Many of the “cubit” are very precise when Pi is a fraction of 2 integers rather than presented as a decimal value. Basically, they knew Pi as a fraction and adjusted the rulers used for circular things by that fraction. If you want to divide a circle into parts, there are far more integer factors available in 360 than in 400. On a boat, you want that when you take a ‘dividers’ to the chart… Want to divide a board into “parts”? 12 lets you do 1/2 1/3 1/4 1/6 and 1/12 where 10 lets you do 1/2 1/5 1/10 sized parts. I’ll take that greater granularity, thank you… (and I find more uses for 1/3 and 1/4 of a thing than I do for 1/5 …)

    @Fluffy Clouds:

    Yeah, my complaint too. Here, at Lat 38 or so, I have to take a coat to the theatre in summer just in case they have the AC set on “Fridge!”. I feel darned silly taking a coat in when it’s 100F outside, but I’ve needed it too many times !

    I had one corner of the building that got more sun and was too hot in the mid morning, then too cool in the afternoon when the OTHER corner was too hot in the sun. I instructed the occupants in the use of the window shade …

    Per the ancients: Yup. The more I look, the more I appreciate what 50 years of looking at a single problem with no distractions from TV, movies, the telephone, or the internet, can do for focus and depth of understanding. We spread our selves too thin, distracted way to much by junk, and expect to know more than someone who spent their whole life contemplating reality sun up to sun down and beyond.

    We get a quick flash “feel good” conclusion and run off a cliff of conclusion with it. They worked and polished an idea until every aspect was just right. They didn’t always have the tools or precision we have (such as with Pi) but their solutions tend to the highly insightful and elegant. They had time, focus, and depth of their side.

    I’ve found that more of my time is attracted into rediscovering the wisdom of the past and much less into the fads of today where someone is just trying to “make a revolution” to “make a name” rather than improve understanding.

  7. H.R. says:

    “The game is afoot, Watson!”

    It has a much nicer ring to it than, “The game is ameter, Watson!”

  8. H.R. says:

    E.M., your comments about knots and making a time standard made me think about the history of clocks with 12 hours, 60 minutes, and 60 seconds. That’s what made navigation calculations easier.

    The things you learn in grade school and forget…

    One of your more fun musings, E.M. Thanks!

  9. Julian Braggins says:

    Have you come across the Quarter Girth Tape ? used for measuring round timber, one side was feet and the other in four inch units. Length in feet, times circumference in units of four inches results in board feet (12″x12″x1″) with an allowance for conversion loss.

    From memory (last time I used one was 60 years ago) we had a book of ‘Hoppus Tables” that converted it to cubic inches, board feet and cubic feet without a lot of calculation. Very useful.

  10. E.M.Smith says:

    Had not come across that one. Neat!

    Part of the “complaint” about the older units is that there are often several different measuring tools. It was held that this is an example of local variation and inaccuracy when in fact it was often built in computation.

    An example of this survives today. There are often “mold measures” that are calibrated to the shrinkage of an object in casting. That lets you make a mold that will produce and object of the proper size without going through all the calculation of thermal expansion on each individual measurement.

    So there was, occasionally, one length unit for latitude and another for longitude. That made allowance for oblateness effects. Similarly there were units that were the hypotenuse of the triangle (useful in building).

    Basically, we found a bunch of “gauges” and assumed they were different units of length or errors of calibration. Silly us.

    Your example is a good example of the same thing. Would someone finding such a measure in the future realize it had a built in allowance for kerf losses in wood cutting if they were not themselves a wood cutter?

    One of the major features of the older systems is that they are designed to make non-mechanical calculation easier. Fractions are easy to use (and preserve very high precision) if you have a factor rich base. Thus the widespread use of 360. Also the use of measuring tools with various adjustments already built in.

    It’s much easier to do rapid ‘in you head’ calculations with fractions than with a 10 digit floating point…

  11. Verity Jones says:

    Just found this from a comment at WUWT

    Scroll down to the part about the book “Ancient Metrology”

  12. E.M.Smith says:

    @Verity Jones: Nice Catch!

    For navigation the differences induced by oblateness matter, thus the use of equatorial (tropical) and “northern” units. We still have this issue today, but deal with it by loads of calculation. When calculation is hard, you build it into the unit of measure you use… (though theoretically it could be an artifact of constructing the unit of measure based on the earth and sky at some point on the surface…)

    At any rate, once you start using fractions and not decimals AND accept that the ancients were rational in what they did, all sorts of things start to make sense.

  13. bob sykes says:

    The pressure rating on the side of your tire (kg/cm^2) is not an SI unit. It is a non-SI European engineering unit in the kg-force, kg-mass, meter, second system. It parallels our customary US engineering system of the lb-force, lb-mass, foot, second system. Both are supposed to be replaced by SI, but that hasn’t happened even in Europe, although the Euro-weenies think it has.

    By the way, in either engineering system, Newton’s second law has to be written

    F = ma/gc

    where gc is either 32.174 lbm ft/lbf sec^2 or 9.8066 kg m/N sec^2

    Modern day engineering students have to know at least six different unit systems. All because the idiotic physicists screwed up the electro-magnetic units in the 19th Century.

  14. E.M.Smith says:

    I was looking up a strange thing about Puma Punku and ran into something interesting about the English foot. Above I note that if the English foot were not 304.8 mm but was 304.7828 the agreement would be 100.000% on the tropical day value in that division of the earth equator. Turns out, it may be that value (or very close). In the wiki on the foot it is talking about the conversion of the foot to the standard foot defined in metric terms, then back-figures the PRIOR older English foot as:


    In the United States, the foot was defined as 12 inches, with the inch being defined by the Mendenhall Order of 1893 by 39.37 inches = 1 m. In Imperial units, the foot was defined as 1⁄3 yard, with the yard being realized as a physical standard (separate from the standard metre). The yard standards of the different Commonwealth countries were periodically compared with one another.[8] The value of the United Kingdom primary standard of the yard was determined in terms of the metre by the National Physical Laboratory in 1964 as 0.9143969 m,[9] implying a pre-1959 foot in the UK of 0.3047990 m.

    So at that point we’ve got agreement out to 4 decimal places (304.78 vs 304.79) and it’s looking to me like we’re getting well inside the error bands of the original data and standards used… That original ‘standard’ of the earth equator and division base 60 is looking mighty good.

    As an aside, the year length also shows up in an offset of star positions from day to day.

    OK, what lead to this? In the wiki on Tiwanaku, the reference an odd unit of measure. My attempts to find something about it using Yahoo, Google, or Bing! have yielded nothing, so I’m stumped as to what the unit is, where to find something more about it, or just what system it is from. The “luk’a”?

    Many theories for Tiwanaku’s architecture construction have been proposed. One is that they used a luk’a which is a standard measurement of about sixty centimeters. Another argument is for the Pythagorean Ratio. This idea calls for right triangles at a ratio of five to four to three used in the gateways to measure all parts. Lastly Protzen and Nair argue that Tiwanaku had a system set for individual elements dependent on context and composition. This is shown in the construction of similar gateways ranging from diminutive to monumental size proving that scaling factors did not affect proportion. With each added element, the individual pieces shifted to fit together

    What caught my eye about it is the “about 60 cm” statement. There is a kind of cubit that is ‘2 feet’. So what are two (Greek, Minoan, English) feet? Yeah, “about 60 cm”… 60.96 cm… ( The Roman foot was 29.6 cm, so depending on which way the “about” goes, it’s still 2 x somebodies foot…)

    So why were the folks in Boliva using an English or Roman foot? Hmmm?

    I would just note that it is very near (within the error band we have) of 1/10 of a 5 second pendulum.

    which would be 62,76 cm

    So take the Egyptian 5 second pendulum of 360 counts in 1/2 hour, and instead of dividing it by 12 to get the Egyptian Royal Cubit, divide it by 10 and you get the luk’a (at least, to the degree I can find anything about the proposed length of that unit…)

    This implies to me that the Bolivians were using the same ‘divide the pendulum’ method as the ‘western world’ way back before “they met” per the history we believe…. Somehow, I think “they talked”…

  15. E.M.Smith says:



    If any person shall hereafter exhibit in this manner the dimensions of the remains of the old buildings of the Babylonians and other nations, it will not be difficult to determine from thence the antient Cubits of those countries. In the mean time I shall produce one instance, which occurs, as a specimen of this calculation. Mr. Purchas (c)[3] informs us, that there is still extant between the antient Babylon and Bagdad, a vast rude structure of brick; the bricks of which his friend Mr. Allen found to be one Foot long, eight Inches broad, and six Inches thick; he means Inches of the English Foot. These proportions shew, that the bricks were regularly formed, and consequently, that in the making of them regard was had to some particular measure used by the Babylonians, which was of great use, to enable the workmen from the number of bricks to determine immediately the dimensions of the walls with respect to the length, breadth, and thickness, and vice versa to compute the number of the bricks necessary to the building of the wall agreed upon. As the Babylonians therefore measur’d their buildings by Cubits, it follows, that the bricks according to their length, breadth, and thickness conjunctly must compose the measure of the Cubit. Now two bricks according to their length, three according to their breadth, and four according to their thickness, form the same measure; and consequently the measure is that of a Cubit. A Babylonian Cubit is therefore equal to two English Feet; and the component parts intimate the division of this Cubit into six Palms, so that the dimensions of the bricks may be express’d in round numbers of Palms; the length by 3 Palms, the breadth by 2, and the thickness by 1 1/2. This Cubit may perhaps be determined hereafter with more exactness by a greater variety of observations.

    So we have the folks in ancient Bolivia using the Babylonian Cubit…

    At this point it’s getting just a bit too much to be any kind of accident.

    What is that quote from?

    A DISSERTATION upon the Sacred Cubit of the Jews and the Cubits of the several Nations; in which, from the Dimensions of the greatest Egyptian Pyramid, as taken by Mr. John Greaves, the antient Cubit of Memphis is determined.
    Translated from the Latin of Sir Isaac Newton, not yet published.

    Somehow I think Sir Isaac Newton got his sums right…

    OK, I see only a few possibles here.

    1) Parallel development / invention. Possible, but not that likely. Over several generations on several continents and it keeps coming out the same?

    2) Space Aliens or God or whatever gave the the method. Maybe, but hard to swallow.

    3) They Talked. Much more likely. There are other bits of evidence for sporadic voyages and they had ships. Not hard to imagine someone going off to school in the foreign land and coming home with info. Would the Egyptians really make a testimonial carving that “Joe from Bolivia came to study – he was an OK B+ student; for a primitive tribe.”?

    4) There was an earlier shared civilization ancestor. Either one that actually did the making, and we’ve got the dates wrong, or one that broke down yet had the know how live on to surface in different cultures. Likely, IMHO. The story of Atlantis says this (from both sides of the Atlantic ocean…) and if it was a modestly common way to make units, construction via a pendulum, one of the first things a surviving teacher would do is teach the tools to do the rest…

    That’s all I can think of, but there might be more.

    In any case, I’m going to do a more careful read of that Newton text (no sense re-doing what he’s already done) and I think we need to spend a bit more time looking for evidence of Babylonian Cubits in old monumental architecture. Perhaps that Golbeki Tepi one…

    Wonder what their proportions are in Babylonian Cubits…

    And the stuff in Persia too:

    It of course follows from the close agreement of the English Foot with 1/2 the Babylonian Cubit and near identity with the Greek and Minoan feet, that it would be a lot better to measure old structures in feet than in meters (that are guaranteed to give non-unit fractional measurements…) and watch for ‘even numbers’…

  16. P.G. Sharrow says:

    The Celtic University in Britain was the most important in the world. A small group could travel from any part of the world to Britain in 3 years, even three thousand years ago. Travel around the world did not change much until the 17th century. Knowledge travels easier then anything else.
    The Celts taught by rote memory, no written books to haul around.
    In the world of shipping the pilot or navigator was the most important person on board ship. In the construction of major projects the master builder was the most important person. Knowledge was the most important commodity. Groups, no mater how isolated were not totally separate.

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