On 1/25/2022 6:27 PM, Aditya Mahajan via ntg-context wrote:

Some of the units, particularly for measurement of land area, are still in use as they are effectively codified in the land records. Wikipedia has some summary of the ancient and medieval systems in India. https://en.wikipedia.org/wiki/Indian_units_of_measurement

the same in nl ... for instance farmers still use old measures (e.g. when selling or buying land), also because for instance lots are defined that way

But it got more complicated than that (particularly for time). See, for example: https://sites.google.com/site/mathematicsmiscellany/time-measurement-in-anci...

There is also this fascinating book which covers the non-European history of mathematics (a lot of which in ancient times was to do with units and measurements but more importantly, calculations):

https://press.princeton.edu/books/paperback/9780691135267/the-crest-of-the-p... also nice ... all gets figured out independent and multiple times over time

https://www.youtube.com/watch?v=KIEJHNoSWF4&t=10381s ----------------------------------------------------------------- Hans Hagen | PRAGMA ADE Ridderstraat 27 | 8061 GH Hasselt | The Netherlands tel: 038 477 53 69 | www.pragma-ade.nl | www.pragma-pod.nl -----------------------------------------------------------------

On 1/25/2022 8:41 PM, Henning Hraban Ramm via ntg-context wrote:

Am 25.01.22 um 18:45 schrieb Hans Hagen via ntg-context:

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On 1/25/2022 6:27 PM, Aditya Mahajan via ntg-context wrote:

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Some of the units, particularly for measurement of land area, are still in use as they are effectively codified in the land records. Wikipedia has some summary of the ancient and medieval systems in India. https://en.wikipedia.org/wiki/Indian_units_of_measurement

the same in nl ... for instance farmers still use old measures (e.g. when selling or buying land), also because for instance lots are defined that way

I don’t think that farmers (in Germany) still use them, but “Morgen” (morning) and “Tagwerk” (a day’s work) were usual measures for areas, depending on the region and the type of work (farming, viniculture, fresco painting...) a 'bunder' land is one still used and a 'mud' potatoes

(taking a 'sip' of water now ... and i bet that this is not the same wverywhere) ----------------------------------------------------------------- Hans Hagen | PRAGMA ADE Ridderstraat 27 | 8061 GH Hasselt | The Netherlands tel: 038 477 53 69 | www.pragma-ade.nl | www.pragma-pod.nl -----------------------------------------------------------------

As you know, there were very variable measurement systems in Europe after the fall of the Roman Empire, depending on the region within the same country. It is difficult to say precisely why political unity, when there was one in a given country, did not make it possible to systematize the use of the same standard of measurement throughout the country, because it is quite astonishing to see that the cubit, the foot, the pound etc. vary from one region to another during the medieval period. The answer to this question on the variability and versatility of measures is undoubtedly due to the fact that the birth of modern nations has been accompanied by the emergence of a rational State which has increasingly taken the place of a rational administration (legal) of social relationship. The French Revolution of 1789 carried out the efforts at rationalization that we had seen develop with the appearance of a strong State from the end of the wars of religion and the reign of Louis XIV in France: the metric system (based on a segment of the Greenwich meridian) in base 10, makes it possible to obtain measurements of surfaces, distances and volumes which are the same everywhere and which do not vary according to whether one is in Normandy, Lorraine or Provence. For those interested in the point Didot (the printing point under the French monarchy), its value was 1/72 of a foot (of the king's foot)... which king's foot could not be a foot of English king, nor a symbolic value as guinea was ! see here : https://en.wikipedia.org/wiki/Units_of_measurement_in_France and here : https://en.wikipedia.org/wiki/Units_of_measurement_in_France_before_the_Fren... Le 25/01/2022 à 20:28, Henning Hraban Ramm via ntg-context a écrit :

Am 25.01.22 um 18:27 schrieb Aditya Mahajan:

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On Tue, 25 Jan 2022, Henning Hraban Ramm via ntg-context wrote:

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why didn’t "we" stick to the Roman system?

All you need to do is look at the definitions of roman imperial units to understand why we didn't stick to that:

An inch was the width of the base of the thumb, a foot, well length of a foot, a fathom was the width of outstretched arms, yard was the length of the man's belt, mile was 1000 paces of marching roman soldiers, and so on.

Ah, of course. So “normalization” to some ruler’s shoe size was already progress.

...

In India, from what I am aware, the pre-imperial units of measurements had similar origins as imperial. Length was based on width of fingers, cubit (also used in other civilizations of the time), person-height and so on. As with the imperial units, these definitions were not uniform and went through a uniformization process in the middle ages. However, India moved to imperial units with colonization, and adopted metric system after Independence.

Some of the units, particularly for measurement of land area, are still in use as they are effectively codified in the land records.

Interesting.

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Wikipedia has some summary of the ancient and medieval systems in India. https://en.wikipedia.org/wiki/Indian_units_of_measurement

But it got more complicated than that (particularly for time). See, for example: https://sites.google.com/site/mathematicsmiscellany/time-measurement-in-anci...

Oh, that is nice!

...

There is also this fascinating book which covers the non-European history of mathematics (a lot of which in ancient times was to do with units and measurements but more importantly, calculations): https://press.princeton.edu/books/paperback/9780691135267/the-crest-of-the-p...

Yes, that’s probably worth reading.

Thank you! Hraban ___________________________________________________________________________________

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-- Jean-Pierre Delange Ancients&Moderns Professeur Agrégé de Philosophie (HC)

On 26 Jan 2022, at 00:17, Hans Hagen via ntg-context wrote: […] times (clocks) were definitely different per city

Regarding the issue of the absolute necessity of defining a standard time the book by Peter Galison « Einstein’s Clocks, Poincaré’s Maps » gives some interesting insight. In particular, since after the mid 19th century trains were developed while the time was not standardized, many accidents happened with hundreds of people killed. This led Henri Poincaré, Lorentz and Einstein (among other mathematcians and physicists) to th enotion of relativity… Regarding the measure of the distance, area, volumes and weight indeed each region of the world had its own units because the trade and exchange of products were essentially local. With the progressive extension of the exchanges between regions and countries the need for a standardization appeared more and more. For example the problem of measuring grains is a quite difficult one: if one measures the weight, depending on how much humidity the grains contain, one has different amount of the real stuff. If one measures the volume of the grains, then according how compressed they are, the amount of the grains may be different… (at some point there was a law which stated that when a unit vessel of grains was to be sold, the seller should struck the bottom of the vessel on a table three times and then refill again sthe vessel for it to be full). The measure of the distances on roads in the Persian empire had one unit and one subunit: « parasang » and « mil ». Parasang, which means « big stone » in Persian, was the average distance which a fantassin could walk in a certain amount of time, and was marked by a large piece of stone on the road (this is also reported by Herodotus). Each parasang was divided into three « mil », which means « iron bar » in Persian, and was marked by planting an iron bar on the road side. A parasang is between 5400 and 6000 meters, and thus a « mil » is something about 1800 and 2000 meters. These units were used in many areas outside the Persian empire, and are still used, in particular the parasang, in Iran and Afghanistan (in Iran a parasang is 6 kilometers now). (Personnaly I think the Roman mile has its origin in the Persian « mil »: I think the etymology of the word mile based on the word « mille », a thousand, cannot be correct since it does not correspond to one thousand of any other unit of length used in the Roman empire). Best regards: Otared

In line with what Otared writes about the measurement of distances in the context of Persia and ancient Rome, I am always very surprised to see the precision of the measurements in the evaluation of the circumference of the earth by Eratosthenes of Cyrene. What intrigues me is not really the geometry calculations involved, but the calculation of the distance between Aswan and Alexandria. There is little information on the taking of this measurement: is it Egyptian surveyors (bematists: https://en.wikipedia.org/wiki/Bematist) or the use of an instrument equivalent to a pedometer? see here: https://en.wikipedia.org/wiki/Eratosthenes Le 26/01/2022 à 09:41, Otared Kavian via ntg-context a écrit :

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On 26 Jan 2022, at 00:17, Hans Hagen via ntg-context wrote: […] times (clocks) were definitely different per city Regarding the issue of the absolute necessity of defining a standard time the book by Peter Galison « Einstein’s Clocks, Poincaré’s Maps » gives some interesting insight. In particular, since after the mid 19th century trains were developed while the time was not standardized, many accidents happened with hundreds of people killed. This led Henri Poincaré, Lorentz and Einstein (among other mathematcians and physicists) to th enotion of relativity…

Regarding the measure of the distance, area, volumes and weight indeed each region of the world had its own units because the trade and exchange of products were essentially local. With the progressive extension of the exchanges between regions and countries the need for a standardization appeared more and more. For example the problem of measuring grains is a quite difficult one: if one measures the weight, depending on how much humidity the grains contain, one has different amount of the real stuff. If one measures the volume of the grains, then according how compressed they are, the amount of the grains may be different… (at some point there was a law which stated that when a unit vessel of grains was to be sold, the seller should struck the bottom of the vessel on a table three times and then refill again sthe vessel for it to be full).

The measure of the distances on roads in the Persian empire had one unit and one subunit: « parasang » and « mil ». Parasang, which means « big stone » in Persian, was the average distance which a fantassin could walk in a certain amount of time, and was marked by a large piece of stone on the road (this is also reported by Herodotus). Each parasang was divided into three « mil », which means « iron bar » in Persian, and was marked by planting an iron bar on the road side. A parasang is between 5400 and 6000 meters, and thus a « mil » is something about 1800 and 2000 meters. These units were used in many areas outside the Persian empire, and are still used, in particular the parasang, in Iran and Afghanistan (in Iran a parasang is 6 kilometers now). (Personnaly I think the Roman mile has its origin in the Persian « mil »: I think the etymology of the word mile based on the word « mille », a thousand, cannot be correct since it does not correspond to one thousand of any other unit of length used in the Roman empire).

Best regards: Otared

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-- Jean-Pierre Delange Ancients&Moderns Professeur Agrégé de Philosophie (HC)

Just be careful, though (writing as a native English speaker), because the word 'polymath' for English speaker is not a reference to mathematicians at all. (Greek/mathē/ means 'learning' not mathematics). Translators are well aware of the danger of homonyms, and if you go for a title like Manual for Polymathematicians, then the word is being wrongly used. There is a word 'polymath' in English, but not 'polymathematician', unless of course you make it clear that it is merely a play on words. But personally, I'd avoid that. Julian On 26/1/22 20:36, Hans Hagen via ntg-context wrote:

On 1/26/2022 10:23 AM, Jean-Pierre Delange via ntg-context wrote:

...

In line with what Otared writes about the measurement of distances in the context of Persia and ancient Rome, I am always very surprised to see the precision of the measurements in the evaluation of the circumference of the earth by Eratosthenes of Cyrene. What intrigues me is not really the geometry calculations involved, but the calculation of the distance between Aswan and Alexandria. There is little information on the taking of this measurement: is it Egyptian surveyors (bematists: https://en.wikipedia.org/wiki/Bematist) or the use of an instrument equivalent to a pedometer? see here: https://en.wikipedia.org/wiki/Eratosthenes    Eratosthenes of Cyrene was a Greek polymath ...

Ah ... that makes a great subtitle for Mikaels upcoming math manual: "A manual for polymathematicians"

   A polymath (Greek: πολυμαθής, polymathēs, "having learned much";

and then we can talk 'polymathematical typesetting' and such (I'm sure that Arthur can come up with a reflective historical tex-talk.)

Hans

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Den ons 26 jan. 2022 09:44Otared Kavian via ntg-context skrev:

...

On 26 Jan 2022, at 00:17, Hans Hagen via ntg-context wrote: […] times (clocks) were definitely different per city

Regarding the issue of the absolute necessity of defining a standard time the book by Peter Galison « Einstein’s Clocks, Poincaré’s Maps » gives some interesting insight. In particular, since after the mid 19th century trains were developed while the time was not standardized, many accidents happened with hundreds of people killed. This led Henri Poincaré, Lorentz and Einstein (among other mathematcians and physicists) to th enotion of relativity…

Regarding the measure of the distance, area, volumes and weight indeed each region of the world had its own units because the trade and exchange of products were essentially local. With the progressive extension of the exchanges between regions and countries the need for a standardization appeared more and more. For example the problem of measuring grains is a quite difficult one: if one measures the weight, depending on how much humidity the grains contain, one has different amount of the real stuff. If one measures the volume of the grains, then according how compressed they are, the amount of the grains may be different… (at some point there was a law which stated that when a unit vessel of grains was to be sold, the seller should struck the bottom of the vessel on a table three times and then refill again sthe vessel for it to be full).

The measure of the distances on roads in the Persian empire had one unit and one subunit: « parasang » and « mil ». Parasang, which means « big stone » in Persian, was the average distance which a fantassin could walk in a certain amount of time, and was marked by a large piece of stone on the road (this is also reported by Herodotus). Each parasang was divided into three « mil », which means « iron bar » in Persian, and was marked by planting an iron bar on the road side. A parasang is between 5400 and 6000 meters, and thus a « mil » is something about 1800 and 2000 meters. These units were used in many areas outside the Persian empire, and are still used, in particular the parasang, in Iran and Afghanistan (in Iran a parasang is 6 kilometers now).

(Personnaly I think the Roman mile has its origin in the Persian « mil »: I

think the etymology of the word mile based on the word « mille », a thousand, cannot be correct since it does not correspond to one thousand of any other unit of length used in the Roman empire).

The unit of which the Roman mile was a thousand was a pace, which was otherwise not commonly used as a measurement. The full Latin term is _milia passum_, literally 'a thousand of steps', i.e. of a military unit on march. I wonder if _mil_ as a Persian unit of measurement isn't spurious, or in fact a Greek (or e.g. Phrygian) word since Old Persian did not have any /l/ sound. At least in the OP script PIE _*l_ has merged totally with _*r_. In Middle Persian OP _rd_ became _l_. Possibly that happened early in the spoken language. /Benct

Best regards: Otared

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