Why didn't the Romans contribute much to mathematics? • Hacker News Board

Re: Why didn't the Romans contribute much to mathematics?

#161

Post by dredmorbius » Sun, Aug 25, 2019, 1:30 PM UTC

mdemare wrote: post #114

dredmorbius wrote: post #89

Earlier quoted context omitted.

China has been a largely continuous political entity for about 8,000 years. It's been invaded at least in part a few times (Mongols, 13th c., English, 18th c., and Japanese, 20th c., most especially), but retained its overall identity and either assimilated (Mongols) or repelled (English, Japanese) the invaders, eventually. Contrast Europe which has seen vast shifts in control, and utter replacements or eradication o…

That text is over 1000 years old. This is Shakespeare, from 1599: Friends, Romans, countrymen, lend me your ears; I come to bury Caesar, not to praise him. The evil that men do lives after them; The good is oft interred with their bones; So let it be with Caesar. The noble Brutus Hath told you Caesar was ambitious: If it were so, it was a grievous fault, And grievously hath Caesar answer’d it. Hardly foreign

I'm given to understand (as I neither speak nor read Chinese) that a fairly typical high-school or college educated modern Chinese can at least read some Confucious (551-479 BCE). There is no comparable English-language case as 1) Old English didn't exist until the 5th century -- the Britons of Roman time (43 CE) were Celts and spoke Celtic, 2) The Latin alphabet hadn't been imported, and 3) literary tradition was slight -- largely oral.

Even taking the tack of following Germanic Anglo-Saxon culture buys you little -- spoken and written language would be unintelligible.

A Western college graduate of ancient languages today might understand Latin, which could get you to 240 BCE, or possibly, with a different alphabet, Greek, whose earliest writings, the Illiad and the Odyssey, date to the 6th century BCE in written form. But that's not a common skill.

Greek and Latin had been taught, as part of the high school curriculum, through the 1940s or 50s, but not generally any longer. Keep in mind that high school graduation rates in 1900 in the US were about 6%, lower than Ph.D. attainment rates today.

Re: Why didn't the Romans contribute much to mathematics?

#162

Post by dwheeler » Sun, Aug 25, 2019, 1:38 PM UTC

In general the ancient Romans were more interested in mathematical application, instead of abstraction. I think that's true for many other ancient civilizations as well. It's not true that the Romans didn't understand mathematics, they were spectacular engineers. They just focused on something different.

The Romans invented Roman numerals, and it's important to acknowledge that this was a mathematical achievement even though we don't use them as much any more. By putting smaller numbers in front of larger ones, they created a number writing system where you did not have to learn a large number of symbols yet any particular number was short and easy to write. Greek numbers had separate symbols not only for one through nine, but for each of the symbols 10 through 90, which meant you had to learn a lot more symbols for just one through 99.

It's true that doing calculations with Roman numerals is a pain, especially division, but I don't think the Romans thought this was a big deal. Calculations were typically done using an abacus anyway, so you simply needed a simple way to record results.

Re: Why didn't the Romans contribute much to mathematics?

#163

Post by edanm » Sun, Aug 25, 2019, 1:43 PM UTC

jacobolus wrote: post #30

WalterBright wrote: post #26

I suspect the roman numeral system played a bigger role in retarding roman mathematics than the reddit postings suggest. After all, it's fairly well known that the characteristics of a particular programming language have a strong influence on the way the language is used. (For instance, people don't do OOP or FP using C.)

Roman numerals are profoundly misunderstood by most people today, whose main knowledge about them is that various authority figures use them as an example of an awkward and cumbersome precursor to Hindu–Arabic numerals, backed up by a slight bit of personal experience learning to encode/decode Roman numerals, which is difficult because nobody today has any substantial amount of practice at it. Roman numerals are a re…

This is not the first time I've seen you writing about this on HN.

Do you have a good source to read more about this? Both about the distinction you're making (recording vs. calculation) and in general about historical capabilities around them? I'm very interested in learning more!

Re: Why didn't the Romans contribute much to mathematics?

#164

Post by dredmorbius » Sun, Aug 25, 2019, 2:25 PM UTC

chrisco255 wrote: post #95

dredmorbius wrote: post #89

Earlier quoted context omitted.

China has been a largely continuous political entity for about 8,000 years. It's been invaded at least in part a few times (Mongols, 13th c., English, 18th c., and Japanese, 20th c., most especially), but retained its overall identity and either assimilated (Mongols) or repelled (English, Japanese) the invaders, eventually. Contrast Europe which has seen vast shifts in control, and utter replacements or eradication o…

https://en.wikipedia.org/wiki/History_of_China#/media/File:T... Watch that graphic to see the evolution of the extent of "China" since the Zhou Dynasty in 1000 BC. It occupies a fraction of the current extent of China. So there were lots of wars, and lots of revolutions before modern Chinese borders were established. I get that Chinese have had more cultural and language cohesion, but that's at least partially becaus…

And a nearly comparable (and orchestrated!) time-lapse evolutionary map of Europe, though extending back to only 400 BCE:

https://www.invidio.us/watch?v=UY9P0QSxlnI

Note that China was under a largely single and unified set of linguistic, cultural, and political organisation throughout the entire 3,000 year period you depict. The "modern" map of Europe has changed dramatically just in the past 30 years, let alone the past 100 - 200. Entire linguistic and cultural tribes have completely vanished, save for a few pitiful relic remains. Political continuity has been nil (Greece, Macedonia, Byzantine Empire, Rome, Moorish Spain, the Gauls, Britons, Celts, and Germanic tribes, the Rus? (Swedish invaders, BTW), Holy Roman and Austro-Hungarian Empires? Soviet Bloc? Independent Baltic and Balkan states? Ireland, under English subjugation since 1601, the north to this day. Poland as the pinball kid of Prussia, Russia, and Germany.

That's Europe.

Addenda: The extreme extents of the Chinese empire varied greatly. The bulk of the population, then as now, was in the eastern coastal region, largely the Yellow and Yangze river floodplains.

Re: Why didn't the Romans contribute much to mathematics?

#165

Post by Koshkin » Sun, Aug 25, 2019, 2:30 PM UTC

jacobolus wrote: post #30

WalterBright wrote: post #26

I suspect the roman numeral system played a bigger role in retarding roman mathematics than the reddit postings suggest. After all, it's fairly well known that the characteristics of a particular programming language have a strong influence on the way the language is used. (For instance, people don't do OOP or FP using C.)

Roman numerals are profoundly misunderstood by most people today, whose main knowledge about them is that various authority figures use them as an example of an awkward and cumbersome precursor to Hindu–Arabic numerals, backed up by a slight bit of personal experience learning to encode/decode Roman numerals, which is difficult because nobody today has any substantial amount of practice at it. Roman numerals are a re…

Yes, and in fact it was a seminal discovery that one can calculate (‘calculus’ means ‘pebble’) by manipulating symbols.

Re: Why didn't the Romans contribute much to mathematics?

#166

Post by toasterlovin » Sun, Aug 25, 2019, 2:35 PM UTC

dredmorbius wrote: post #73

toasterlovin wrote: post #50

Earlier quoted context omitted.

How much of the Chinese/Japanese vs Western Europe dichotomy in term of technological development do you think is due to geography (Europe has been fractured, politically, for all of history, mostly due to geography, I think, whereas China and Japan have both been comparatively unified and stable for thousands of years). My thinking is that this has a lot to do with how European elites were not able to prevent accumu…

The general form of this question, or at least one version of it ("why did the Industrial Revolution occur in England and not in China, which had developed a vastly larger set of technologies far earlier") is known as the Needham Question , after sinologist Joseph Needham, author of Science and Civilisation in China , an epic 30+ volume work covering Chinese invention and technology, begun in 1954 and still in proces…

Thanks for that most excellent answer! It gets at the industrial revolution (and the importance of coal deposits), but the scientific revolution preceded the industrial revolution by quite some time and was not dependent on coal. Something was happening around the English Channel and what is now Germany starting in around the 1600s. Why there and not somewhere else?

Re: Why didn't the Romans contribute much to mathematics?

#167

Post by dredmorbius » Sun, Aug 25, 2019, 2:36 PM UTC

yongjik wrote: post #99

dredmorbius wrote: post #89

Earlier quoted context omitted.

China has been a largely continuous political entity for about 8,000 years. It's been invaded at least in part a few times (Mongols, 13th c., English, 18th c., and Japanese, 20th c., most especially), but retained its overall identity and either assimilated (Mongols) or repelled (English, Japanese) the invaders, eventually. Contrast Europe which has seen vast shifts in control, and utter replacements or eradication o…

> Even written language in China is still largely intelligible to moderns .... That's largely because Chinese characters themselves didn't change, even though the underlying sound and grammar changed. In your English example, imagine "ic" is written as "I", "nihte" as "night", and so on, so that every word is written as the modern spelling of its descendant word. It will be much easier to guess its meaning.

True, and an interesting contrast in properties of Western alphabets vs. Eastern logosyllabic writing.

Advantage West: a compact, typeset- and keyboard-friendly characterset with a writing style that generally allows sounding out of unknown words.

Advantage East: a pronunciation-independent mapping of ideas allowing mutually unintelligible spoken language across either space (Japan, to some extent Korea, as well as modern Chinese provinces, particularly Mandarin vs. Cantonese) or time (modern vs. ancient) to at least largely understand one another.

Much of the shift in written English parallels changes in spoken English. Chinese doens't have that problem. But it's far harder to learn and type or encode in modern computers, where it is not letterforms but encodings standing for letterforms which are stored and projected via fonts and Unicode codepoints.

Chinese, as a tonal language is so dependent on inflection that my own primitive attempts to pronounce even simple phrases are not understood based on my incorrect tonality.

Contrast with various Germanic languages (German, English, Dutch, Danish, Norwegian, Swedish), which vary greatly in pronunciation and orthography. German is spelled and spoken logically. Danish is spelled much like German but not pronounced the same. Norwegian pronunciation differs, but its spelling at least corresponds to that pronunciation. Swedish is pronounced very differently, and the spelling doesn't much conform.

All share common linguistic roots.

Each approach of writing and alphabet appears to be brittle in its own ways.

Re: Why didn't the Romans contribute much to mathematics?

#168

Post by kgwgk » Sun, Aug 25, 2019, 2:39 PM UTC

boomboomsubban wrote: post #153

kgwgk wrote: post #147

Earlier quoted context omitted.

What is your definition of “Western European” precisely? https://aaron7roberts.files.wordpress.com/2015/04/roman_empi... https://en.m.wikipedia.org/wiki/Demography_of_the_Roman_Empi... also shows larger populations in the “Latin West” than in the “Greek East”.

The first map shows roughly thirteen million people in non-Italy "Western Europe" and roughly twenty two millions in the non Western Europe parts. Wikipedia has an actual population density map[1] that highlights my point. Even in traditional "Western Europe," the population is predominantly Mediterranean. It also has a list of the most populous cities during the peak of the Empire, largely outside of Western Europe.…

So about half the roman empire (including Italy) was in Western Europe? Of course the Roman Empire extended further (and longer in other regions), but saying Middle Age's Western Europe doesn't include large regions that were previously part of the Roman Empire seems strange to me.

Re: Why didn't the Romans contribute much to mathematics?

#169

Post by torben-friis » Sun, Aug 25, 2019, 2:41 PM UTC

dredmorbius wrote: post #89

fiblye wrote: post #54

Earlier quoted context omitted.

How did geography have an effect here? I don't see what you mean. And China hasn't really had too much stability. It's always been full of revolutions, competing empires, dynastic changes, warring states, shifts in power, changes in ethnic ruling class, and so on. Go through a list of deadliest wars and revolutions and a good chunk of them are in what is today China.

China has been a largely continuous political entity for about 8,000 years. It's been invaded at least in part a few times (Mongols, 13th c., English, 18th c., and Japanese, 20th c., most especially), but retained its overall identity and either assimilated (Mongols) or repelled (English, Japanese) the invaders, eventually. Contrast Europe which has seen vast shifts in control, and utter replacements or eradication o…

> Even written language in China is still largely intelligible to moderns, from a thousand years ago or more. English, more than about 400 years ago is almost wholly foreign:

You're pretty much equating English and Europe when talking about language, which in this case is very wrong. I, as a spaniard, can read poetry from a thousand years ago perfectly fine, and we do indeed do it in school.

Re: Why didn't the Romans contribute much to mathematics?

#170

Post by empath75 » Sun, Aug 25, 2019, 2:43 PM UTC

Sag0Sag0 wrote: post #138

known wrote: post #58

The Arabic countries led by the Muslims were the most advanced scientists/engineers in the world, until they let the religious crazies take over. J https://en.wikipedia.org/wiki/Timeline_of_science_and_engine...

I just have to object. Early science throughout the world came about because of religion, not despite it. Early Muslim proto scientists like Ibn Sina and Ibn Khaldun explicitly did their science through religion and were heavily involved the religious politics of the day. This was also true also of early scientists in europe like Issac Newton. Also that statement implicitly kinda carries the idea that europeans took…

The Pythagoreans were also a religious group, as well as the platonists who followed them.