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Why didn't the Romans contribute much to mathematics?

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

#81

Post by usrusr »

asveikau wrote: post #70
BalinKing wrote: post #34

Earlier quoted context omitted.

> If we put ethnicity ahead of national origin America can’t claim anything to its name. Period. It's silly to put ethnicity ahead of national origin, though, since one of America's biggest qualities it that it is a melting pot. This feels like saying "If we put learning curve ahead of type safety Haskell can't claim anything to its name. Period." It's true, but kinda vacuous.

But that particular super-famous German who lived in Princeton, NJ is also recognized as a German physicist. To say he was already quite accomplished when he left Europe would be an understatement. Personally, I think if an immigrant of descendant of immigrants invents something prominent, it is fair for both countries to be proud of the accomplishment, and share that enthusiasm. It doesn't, or shouldn't hurt anyone.…

> it is fair for both countries to be proud of the accomplishment

Depending on the reasons for emigration, it might be fair to replace most of that pride with "dann, could have been 'ours'".

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

#82

Post by mlyle »

jacobolus wrote: post #72
ghayes wrote: post #69

Earlier quoted context omitted.

Wouldn’t a slide-rule be a similar modern day approach?

An (analog) slide rule is a whole lot faster than doing digital arithmetic. But it’s approximate, yielding about 3 digits of precision, or maybe 4 digits on a large slide rule. With an abacus or with written numbers, you can get 10 digits of precision (or 50) if you are willing to put the work in.

You can iterate slide rule calculations to get more precision, too... You're not restricted to the width of your abacus nor the number of sigfigs you can get in a single slide rule calc..

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

#83

Post by sumitviii »

strainer wrote: post #49

Consider the title of this famous Great work wrote later : "The Compendious Book on Calculation by Completion and Balancing" It has a graceful theme which is perhaps not accidental for mathematical inspiration. The same symbolic methods, being symbolic could have been painted as "domination and sacrificing" but that might not temper a mindset as mathematically conducive as notions of "completion and balancing". A cul…

>but that might not temper a mindset as mathematically conducive as notions of "completion and balancing".

Or maybe what would be considered a mathematically conducive mindset is determined by whose mathematical tradition we are following? Maybe there exists a mathematical mindset out there where "domination and sacrificing" are the requirement for conductivity of ideas?

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

#84

Post by novacole »

steve19 wrote: post #16
crooked-v wrote: post #9

Earlier quoted context omitted.

> We did have a dark age, after the Romans after all, which likewise produced little (not none) new math. Use of the term "dark age" is both dramatically inaccurate in many ways [1] and totally elides everything that happened outside of Europe, such as the establishment of algebra as an independent field of mathematical study (AD 800 in Baghdad), the creation of algebraic geometry (AD 1070 in Persia), and the discove…

Yes but the Dark Age specifically refers to Western Europe, in much the same way the disastrous impact of the Mongol Empire on Islamic scholarship, for example the burning of libraries during or after the Siege of Baghdad, barely touched Western Europe. Chances are the Mongols destroyed some advanced mathematics that took centuries to rediscover.

Yes, but Rome isn’t Western Europe. So western Europe’s entire history is a “dark age” before the Age of Enlightenment.

(Edit: incorrectly said renaissance instead of Age of Enlightenment... the renaissance wasn’t Western European either)

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

#85

Post by cbHXBY1D »

juanbyrge wrote: post #77
cbHXBY1D wrote: post #57

Earlier quoted context omitted.

If I had to bet, western society will be judged for creating an industrialized world while knowingly ignoring the effect of greenhouse gases.

To be fair I think the severity of climate change has only come into mainstream focus in the past 5-10 years. Just as one data point, when I was shopping for a car in 2012, I did not even consider CO2 emissions. Now, climate change is top of mind for me. I now own an electric car, stopped eating beef, mostly eliminated travel, etc... I'm not saying this will make a difference overall, but I imagine others feel simila…

We've known for a while:

https://en.wikipedia.org/wiki/History_of_climate_change_scie...

https://www.nytimes.com/interactive/2018/08/01/magazine/clim...

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

#86

Post by sumitviii »

jcranmer wrote: post #68
HarryHirsch wrote: post #56

Earlier quoted context omitted.

The first powered aircraft flew in the 1900s, and by the 1940s we had jet aircraft. The Boeing 747 was introduced in the 1960s, and in the 1970s we had supersonic flight. The pace of innovation has stalled since.

We sculpt rocks to dimensions that are most easily measured in terms of layers of atoms for the price of mere dollars per rock.

And might soon be able to design life! Present FTW!!!

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

#87

Post by sumitviii »

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...

Maybe its like a going-under for them as a civilization?

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

#88

Post by atroche »

breck wrote: post #78
Chathamization wrote: post #55

Earlier quoted context omitted.

I mean, there definitely seems to have been a large decline in population, economic output, political cohesion, urbanization, record keeping, trade, etc., in much of the former Roman world following the fifth/sixth century. I suppose it's a value judgement on whether one considers that a "bad time."

Curious if you have any sources? I've never seen a data driven case that such a thing as the "dark ages" ever happened.

This is an excellent read: https://slatestarcodex.com/2017/10/15/were-there-dark-ages/

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

#89

Post by dredmorbius »

fiblye wrote: post #54
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…

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 of local culture or tribes multiple times, going to prehistoric times, to the present (past century certainly, past few decades quite arguably). There have been very few constant borders or identities, certainly not on the scale of China.

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:

Hwæt,ic swefna cyst secgan wylle, hwæt me gemætte to midre nihte siþþan reordberend reste wunedon.

("Behold, I wish to tell the best of dreams which I dreamt at the middle of the night, after speakers remained in rest." https://www.arts.gla.ac.uk/stella/readings/OE/ROOD.HTM)

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

#90

Post by dredmorbius »

riazrizvi wrote: post #80
dredmorbius wrote: post #73

Earlier quoted context omitted.

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…

Clearly by the 13th Century China could be considered a technological forerunner, but then the Mongols took over. I suspect the cultural tendencies of the Chinese civil service that drove innovation just couldn’t weather the merging of cultures and the scholarly edge of Chinese culture was collateral damage.

I'm still very weak on my Chinese history, but it was the turning-inward of the Ming dynasty (15th century), not the Mongol invasions, which precipitated the halt.

Also (as already mentioned in this thread), the asset-sheltering tendency of established power groups, halting the emergence of potential rivals, as Bernhard Stern documents in other (non-Chinese) instances.

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