11 ms·

Why didn't the Romans contribute much to mathematics?

180 points by curtis 7y ago

riazrizvi 7y ago
> "There was once a workman who made a glass cup that was unbreakable. So he was given an audience of the Emperor with his invention; he made Caesar give it back to him and then threw it on the floor. Caesar was as frightened as could be. But the man picked up his cup from the ground: it was dented like a bronze bowl; then he took a little hammer out of his pocket and made the cup quite sound again without any trouble. After doing this he thought he had himself seated on the throne of Jupiter, especially when Caesar said to him: 'Does anyone else know how to blow glass like this?' Just see what happened. He said not, and then Caesar had him beheaded. Why? Because if his invention were generally known we should treat gold like dirt. " (Satyricon 51) This apocryphal story on economic incentives vs progressive incentives is as relevant today as it was 2000 years ago.
- ZhuanXia 7y ago
  The rise of technology was not so much the birth of new capacities, but the removal of old constraints. China, despite a much larger and more educated population, did not spark the industrial revolution. Their feedback loops were too stable, their elites too competent. From the perspective of the old power hierarchy, the industrial revolution was a disaster. The nobility floated on that great cruel ocean first charted by Malthus, an ocean which began to boil.
  - toasterlovin 7y ago
    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 accumulation of new technology and ideas, whereas Chinese and Japanese elites were (and did). And then I guess a follow up question would be: do you have an opinion on why the scientific revolution happened in Western Europe and not in the Mediterranean, which is similarly fractured, but also better situated for exchange of technology and ideas (being connected to Asia and Western Europe).
    - fiblye 7y ago
      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.
      - dredmorbius 7y ago
        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 https://www.arts.gla.ac.uk/stella/readings/OE/ROOD.HTM)
        chrisco255 7y ago
        https://en.wikipedia.org/wiki/History_of_China#/media/File:Territories_of_Dynasties_in_China.gif 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 because certain dynasties and regions won over these other regions in large swaths and history is written by the winners.
- dredmorbius 7y ago
  The resistance to technological innovations is a very well-established human practice. I've shared Bernhard J. Stern's "Resistances to the Adoption of Technological Innovations" (1935) multiple times -- it's because I find it highly illuminating and well worth reading. Original: https://archive.org/details/technologicaltre1937unitrich/page/39 https://archive.org/details/technologicaltre1937unitrich/pag... (faint copy) Re-typed / markdown: https://pastebin.com/raw/Bapu75is https://pastebin.com/raw/Bapu75is (updated and corrected from April, 2019 version.)
olooney 7y ago
Romans aren't the outlier here. Most ancient civilizations had a similar level of accomplishment; a one or two outstanding mathematicians every century, a few practical applications, some new rules of thumb. We did have a dark age, after the Romans after all, which likewise produced little (not none) new math. The question should rather be, what made the Greeks (and, later, others who adopted their deductive, axiomatic method) so exceptionally productive at mathematics? Or to paraphrase Wigner, why is Hellenistic mathematics so unreasonably effective?
- crooked-v 7y ago
  > 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 discovery of ways to solve high-order polynomial equations (approximately AD 1200 in India and China). [1]: https://slate.com/human-interest/2015/01/medieval-history-why-are-the-middle-ages-often-characterized-as-dark-or-less-civilized.html https://slate.com/human-interest/2015/01/medieval-history-wh... Edit: Fixed a location.
  - notinpersia 7y ago
    Wrong on Algebra’s origin. Often people will say Persia but it was in Ancient Greece and Baghdad. And the latter is not Persia and was certainly not under Persian occupation during the time of Alkhawarizmi (who is also credited for the invention of the algorithm or at least it was named after him.) The original title of his book that coined the term Algebra is Al Jabr wal Muqabala (casting and equation) Just Google it: where was algebra invented? https://www.google.com/search?q=who.invented+algebra&ie=UTF-8&oe=UTF-8&hl=en-us&client=safari https://www.google.com/search?q=who.invented+algebra&ie=UTF-...
    - deleted 7y ago
      [deleted]
oneepic 7y ago
O/T: One real answer, and multiple bot posts, including one about removing another real person's comment. As a person who doesn't read much Reddit, it leaves a really strange impression. Anyway, the top answer was still a cool read.
- umanwizard 7y ago
  This is typical of /r/AskHistorians , not Reddit as a whole. They have an explicit policy of removing any amateurish or unsourced answers, in order to keep quality high.
  - Judgmentality 7y ago
    Doesn't that imply that the rest of reddit which is less heavily moderated has more low quality comments?
    - umanwizard 7y ago
      Yes, and IMO it really does.
    - mdorazio 7y ago
      Yes.
  - msla 7y ago
    And they still get things drastically wrong sometimes: https://web.archive.org/web/20190825021639/https://old.reddit.com/r/badhistory/comments/2jhhje/a_psa_do_not_trust_heavily_upvoted_responses_in/ https://web.archive.org/web/20190825021639/https://old.reddi...
- scarejunba 7y ago
  It's a "serious" subreddit. Unlike HN (or many other subreddits), where you can say something completely incorrect and be upvoted by the army of uninformed people, /r/askhistorians specifically allows only well-sourced posts.
boomboomsubban 7y ago
I'm not an expert here, but wasn't the development of "zero" a rather monumental leap that was required before you could advance past Greek math? The spread into the Islamic world certainly enabled them to finally push past the Greeks.
mjfl 7y ago
They probably innovated in math, in some form of risk modeling or something, but no single fancy intellectual wrote it all down: https://priceonomics.com/how-maritime-insurance-built-ancient-rome/ https://priceonomics.com/how-maritime-insurance-built-ancien...
Gatsky 7y ago
Makes you wonder what will be said for our era in 500 years time...
- markholmes 7y ago
  Does it? We visited the moon and created the internet in the span of one generation. We are arguably in the most innovative scientific period in our history.
  - HarryHirsch 7y ago
    We are selling ads and moving money from one desk onto another instead of addressing antibiotic resistance and climate change.
    - derp_dee_derp 7y ago
      You lack serious historical context. We went fromom electricity to flight to nuclear to space flight to the internet in less than 150 years. Its been less than 100 years since antibiotics were invented, so, sorry we aren't addressing antibiotic resistance at a fast enough pace for you. Hope you don't mind all those vaccines that are keeping you healthy and providing here immunity: they've only been around for about 130 years. It's the most innovative time in human history, despite your negativity.
      - HarryHirsch 7y ago
        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.
        jbay808 7y ago
        "and in the 1970s we had supersonic flight" 1947?
w8rbt 7y ago
I was under the impression that the Romans were more applied/practical and less theoretical, but I may be wrong. I got that notion from a professor I had years ago who was fond of saying, "The Romans built roads. The Greeks talked about building roads." Has anyone else ever heard that saying?
- riffraff 7y ago
  I've heard "Greeks were mathematicians, Romans were engineers", which conveys the same concept.
WalterBright 7y ago
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.)
- saagarjha 7y ago
  > For instance, people don't do OOP or FP using C. Oh, but they do. It’s just that their syntax is awful.
  - WalterBright 7y ago
    Yes, I've seen OOP etc. done in C. As you say, it's awful, and so people don't do it. People devise their algorithms and data structures in ways that work smoothly with the language's features. I'm sure you can compute sine and cosine tables using Roman numerals, too. But it would be so awfully ugly and tedious it's hardly a surprise that few would consider attempting it.
    - jacobolus 7y ago
      > I'm sure you can compute sine and cosine tables using Roman numerals, too. But it would be so awfully ugly and tedious it's hardly a surprise that few would consider attempting it. Ptolemy’s table of chords was calculated in base 60 (inherited from Mesopotamians), by probably a Roman citizen living in Egypt and writing in Greek. It was probably done on some kind of a counting board analogous to the ones used for decimal calculations. Hellenistic mathematicians didn’t do written arithmetic either. And yes, making such tables is inherently “awfully ugly and tedious”, unless you have an electronic calculator to do it for you.
      - WalterBright 7y ago
        Yeah, I've seen that table. It was just a few entries, if I recall correctly. Few enough that one could have gotten the numbers by using drawings instead of calculation. And there were errors in it, too. > And yes, making such tables is inherently “awfully ugly and tedious”, Yup, but people did make such extensive tables long before calculators, many thousands more entries than that chord table, and far more accurately.
fortran77 7y ago
We still use their numbering system today, in prefaces and clocks!
- jackcosgrove 7y ago
  And SuperBowls.
strainer 7y ago
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 cultures achievements in different areas could owe substantially to the spectrum of mindsets which it hosts and celebrates.
- sumitviii 7y ago
  >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?
  - strainer 7y ago
    It would seem to be a well kept secret branch if so
    - sumitviii 7y ago
      By out there I don't mean in the physical world, I mean in the world of possibility.
known 7y ago
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_engineering_in_the_Islamic_world https://en.wikipedia.org/wiki/Timeline_of_science_and_engine...
- sumitviii 7y ago
  Maybe its like a going-under for them as a civilization?
- Sag0Sag0 7y ago
  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 over role of the "advancers of science" due to their tolerance and secularism. That was certainly not the case, european christianity in the 16th and 17th centuries was not in any way tolerant/moderate. Similarly even if we agree that a decline occurred there are a myriad of other factors that could potentially cause a drop in scientific output such as the various consequences of war, the policies of the Ottoman empire, a lack of the urbanisation that occurred in China and Europe etc.
  - empath75 7y ago
    The Pythagoreans were also a religious group, as well as the platonists who followed them.
williamDafoe 7y ago
I bet it's a bitch to learn addition or multiplication using Roman numerals!
- ithkuil 7y ago
  You might find this interesting: http://www.phy6.org/outreach/edu/roman.htm http://www.phy6.org/outreach/edu/roman.htm
LeonB 7y ago
Yeh, what have the Romans ever done for us? https://www.youtube.com/watch?v=Y7tvauOJMHo https://www.youtube.com/watch?v=Y7tvauOJMHo
29athrowaway 7y ago
Paper makes you productive. Romans did not have it. They had papyrus, parchments and wax tablets, none of them were as convenient or affordable as paper. The adoption of paper was what really set things in motion in Europe, the Renaissance.
- yesenadam 7y ago
  Paper - yet another Chinese invention, about 100AD, along with movable type printing, about 1000AD. With gunpowder and compass, two more Chinese inventions, Europeans navigated and conquered the world..
  - deleted 7y ago
    [deleted]
  - 29athrowaway 7y ago
    And technology and animals from the fertile crescent, efficient crops from the Americas, African slaves and significant military help from local groups. A lot of merit to share.
- Bayart 7y ago
  >They had papyrus, parchments and wax tablets, none of them were as convenient or affordable as paper. Papyrus is cheap, easy to make and affordable. It would certainly have been much cheaper than paper, which didn't become any good until substantial industrial and chemical advancements. It was used all over the place. We don't have much left from the Northern Mediterranean because it rots. Wax tablets were used until the 19th century because it's also cheap and practical. Velum didn't become mainstream until the Islamic invasion of Egypt cut the supply of papyrus. >The adoption of paper was what really set things in motion in Europe, the Renaissance. The idea that there was a Renaissance at all is dubious. Paper was certainly a step up from velum. But It would have been much better for everyone if we could just have used papyrus continuously.
  - 29athrowaway 7y ago
    Paper is thin, light, durable... you can make books from it and transport them easily. It can be manufactured from materials available in abundance in Europe. A book made of wax tablets, or velum is not as good. I don't imagine vast libraries and universities running on books made of wax tablets or velum. With respect to Papyrus, I agree. The Great Library of Alexandria was all papyrus. It can be produced at scale. But Europeans had to import it from far, far away.
dwheeler 7y ago
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.

180 points by curtis 7y ago

> "There was once a workman who made a glass cup that was unbreakable. So he was given an audience of the Emperor with his invention; he made Caesar give it back to him and then threw it on the floor. Caesar was as frightened as could be. But the man picked up his cup from the ground: it was dented like a bronze bowl; then he took a little hammer out of his pocket and made the cup quite sound again without any trouble. After doing this he thought he had himself seated on the throne of Jupiter, especially when Caesar said to him: 'Does anyone else know how to blow glass like this?' Just see what happened. He said not, and then Caesar had him beheaded. Why? Because if his invention were generally known we should treat gold like dirt. " (Satyricon 51) This apocryphal story on economic incentives vs progressive incentives is as relevant today as it was 2000 years ago.

ZhuanXia 7y ago
The rise of technology was not so much the birth of new capacities, but the removal of old constraints. China, despite a much larger and more educated population, did not spark the industrial revolution. Their feedback loops were too stable, their elites too competent. From the perspective of the old power hierarchy, the industrial revolution was a disaster. The nobility floated on that great cruel ocean first charted by Malthus, an ocean which began to boil.
- toasterlovin 7y ago
  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 accumulation of new technology and ideas, whereas Chinese and Japanese elites were (and did). And then I guess a follow up question would be: do you have an opinion on why the scientific revolution happened in Western Europe and not in the Mediterranean, which is similarly fractured, but also better situated for exchange of technology and ideas (being connected to Asia and Western Europe).
  - fiblye 7y ago
    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.
    - dredmorbius 7y ago
      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 https://www.arts.gla.ac.uk/stella/readings/OE/ROOD.HTM)
      - chrisco255 7y ago
        https://en.wikipedia.org/wiki/History_of_China#/media/File:Territories_of_Dynasties_in_China.gif 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 because certain dynasties and regions won over these other regions in large swaths and history is written by the winners.
dredmorbius 7y ago
The resistance to technological innovations is a very well-established human practice. I've shared Bernhard J. Stern's "Resistances to the Adoption of Technological Innovations" (1935) multiple times -- it's because I find it highly illuminating and well worth reading. Original: https://archive.org/details/technologicaltre1937unitrich/page/39 https://archive.org/details/technologicaltre1937unitrich/pag... (faint copy) Re-typed / markdown: https://pastebin.com/raw/Bapu75is https://pastebin.com/raw/Bapu75is (updated and corrected from April, 2019 version.)

olooney 7y ago

Romans aren't the outlier here. Most ancient civilizations had a similar level of accomplishment; a one or two outstanding mathematicians every century, a few practical applications, some new rules of thumb. We did have a dark age, after the Romans after all, which likewise produced little (not none) new math. The question should rather be, what made the Greeks (and, later, others who adopted their deductive, axiomatic method) so exceptionally productive at mathematics? Or to paraphrase Wigner, why is Hellenistic mathematics so unreasonably effective?

crooked-v 7y ago
> 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 discovery of ways to solve high-order polynomial equations (approximately AD 1200 in India and China). [1]: https://slate.com/human-interest/2015/01/medieval-history-why-are-the-middle-ages-often-characterized-as-dark-or-less-civilized.html https://slate.com/human-interest/2015/01/medieval-history-wh... Edit: Fixed a location.
- notinpersia 7y ago
  Wrong on Algebra’s origin. Often people will say Persia but it was in Ancient Greece and Baghdad. And the latter is not Persia and was certainly not under Persian occupation during the time of Alkhawarizmi (who is also credited for the invention of the algorithm or at least it was named after him.) The original title of his book that coined the term Algebra is Al Jabr wal Muqabala (casting and equation) Just Google it: where was algebra invented? https://www.google.com/search?q=who.invented+algebra&ie=UTF-8&oe=UTF-8&hl=en-us&client=safari https://www.google.com/search?q=who.invented+algebra&ie=UTF-...
  - deleted 7y ago
    [deleted]

oneepic 7y ago

O/T: One real answer, and multiple bot posts, including one about removing another real person's comment. As a person who doesn't read much Reddit, it leaves a really strange impression. Anyway, the top answer was still a cool read.

umanwizard 7y ago
This is typical of /r/AskHistorians , not Reddit as a whole. They have an explicit policy of removing any amateurish or unsourced answers, in order to keep quality high.
- Judgmentality 7y ago
  Doesn't that imply that the rest of reddit which is less heavily moderated has more low quality comments?
  - umanwizard 7y ago
    Yes, and IMO it really does.
  - mdorazio 7y ago
    Yes.
- msla 7y ago
  And they still get things drastically wrong sometimes: https://web.archive.org/web/20190825021639/https://old.reddit.com/r/badhistory/comments/2jhhje/a_psa_do_not_trust_heavily_upvoted_responses_in/ https://web.archive.org/web/20190825021639/https://old.reddi...
scarejunba 7y ago
It's a "serious" subreddit. Unlike HN (or many other subreddits), where you can say something completely incorrect and be upvoted by the army of uninformed people, /r/askhistorians specifically allows only well-sourced posts.

boomboomsubban 7y ago

I'm not an expert here, but wasn't the development of "zero" a rather monumental leap that was required before you could advance past Greek math? The spread into the Islamic world certainly enabled them to finally push past the Greeks.

mjfl 7y ago

They probably innovated in math, in some form of risk modeling or something, but no single fancy intellectual wrote it all down: https://priceonomics.com/how-maritime-insurance-built-ancient-rome/ https://priceonomics.com/how-maritime-insurance-built-ancien...

Gatsky 7y ago

Makes you wonder what will be said for our era in 500 years time...

markholmes 7y ago
Does it? We visited the moon and created the internet in the span of one generation. We are arguably in the most innovative scientific period in our history.
- HarryHirsch 7y ago
  We are selling ads and moving money from one desk onto another instead of addressing antibiotic resistance and climate change.
  - derp_dee_derp 7y ago
    You lack serious historical context. We went fromom electricity to flight to nuclear to space flight to the internet in less than 150 years. Its been less than 100 years since antibiotics were invented, so, sorry we aren't addressing antibiotic resistance at a fast enough pace for you. Hope you don't mind all those vaccines that are keeping you healthy and providing here immunity: they've only been around for about 130 years. It's the most innovative time in human history, despite your negativity.
    - HarryHirsch 7y ago
      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.
      - jbay808 7y ago
        "and in the 1970s we had supersonic flight" 1947?

w8rbt 7y ago

I was under the impression that the Romans were more applied/practical and less theoretical, but I may be wrong. I got that notion from a professor I had years ago who was fond of saying, "The Romans built roads. The Greeks talked about building roads." Has anyone else ever heard that saying?

riffraff 7y ago
I've heard "Greeks were mathematicians, Romans were engineers", which conveys the same concept.

WalterBright 7y ago

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.)

saagarjha 7y ago
> For instance, people don't do OOP or FP using C. Oh, but they do. It’s just that their syntax is awful.
- WalterBright 7y ago
  Yes, I've seen OOP etc. done in C. As you say, it's awful, and so people don't do it. People devise their algorithms and data structures in ways that work smoothly with the language's features. I'm sure you can compute sine and cosine tables using Roman numerals, too. But it would be so awfully ugly and tedious it's hardly a surprise that few would consider attempting it.
  - jacobolus 7y ago
    > I'm sure you can compute sine and cosine tables using Roman numerals, too. But it would be so awfully ugly and tedious it's hardly a surprise that few would consider attempting it. Ptolemy’s table of chords was calculated in base 60 (inherited from Mesopotamians), by probably a Roman citizen living in Egypt and writing in Greek. It was probably done on some kind of a counting board analogous to the ones used for decimal calculations. Hellenistic mathematicians didn’t do written arithmetic either. And yes, making such tables is inherently “awfully ugly and tedious”, unless you have an electronic calculator to do it for you.
    - WalterBright 7y ago
      Yeah, I've seen that table. It was just a few entries, if I recall correctly. Few enough that one could have gotten the numbers by using drawings instead of calculation. And there were errors in it, too. > And yes, making such tables is inherently “awfully ugly and tedious”, Yup, but people did make such extensive tables long before calculators, many thousands more entries than that chord table, and far more accurately.

fortran77 7y ago

We still use their numbering system today, in prefaces and clocks!

jackcosgrove 7y ago
And SuperBowls.

strainer 7y ago

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 cultures achievements in different areas could owe substantially to the spectrum of mindsets which it hosts and celebrates.

sumitviii 7y ago
>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?
- strainer 7y ago
  It would seem to be a well kept secret branch if so
  - sumitviii 7y ago
    By out there I don't mean in the physical world, I mean in the world of possibility.

known 7y ago

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_engineering_in_the_Islamic_world https://en.wikipedia.org/wiki/Timeline_of_science_and_engine...

sumitviii 7y ago
Maybe its like a going-under for them as a civilization?
Sag0Sag0 7y ago
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 over role of the "advancers of science" due to their tolerance and secularism. That was certainly not the case, european christianity in the 16th and 17th centuries was not in any way tolerant/moderate. Similarly even if we agree that a decline occurred there are a myriad of other factors that could potentially cause a drop in scientific output such as the various consequences of war, the policies of the Ottoman empire, a lack of the urbanisation that occurred in China and Europe etc.
- empath75 7y ago
  The Pythagoreans were also a religious group, as well as the platonists who followed them.

williamDafoe 7y ago

I bet it's a bitch to learn addition or multiplication using Roman numerals!

ithkuil 7y ago
You might find this interesting: http://www.phy6.org/outreach/edu/roman.htm http://www.phy6.org/outreach/edu/roman.htm

LeonB 7y ago

Yeh, what have the Romans ever done for us? https://www.youtube.com/watch?v=Y7tvauOJMHo https://www.youtube.com/watch?v=Y7tvauOJMHo

29athrowaway 7y ago

Paper makes you productive. Romans did not have it. They had papyrus, parchments and wax tablets, none of them were as convenient or affordable as paper. The adoption of paper was what really set things in motion in Europe, the Renaissance.

yesenadam 7y ago
Paper - yet another Chinese invention, about 100AD, along with movable type printing, about 1000AD. With gunpowder and compass, two more Chinese inventions, Europeans navigated and conquered the world..
- deleted 7y ago
  [deleted]
- 29athrowaway 7y ago
  And technology and animals from the fertile crescent, efficient crops from the Americas, African slaves and significant military help from local groups. A lot of merit to share.
Bayart 7y ago
>They had papyrus, parchments and wax tablets, none of them were as convenient or affordable as paper. Papyrus is cheap, easy to make and affordable. It would certainly have been much cheaper than paper, which didn't become any good until substantial industrial and chemical advancements. It was used all over the place. We don't have much left from the Northern Mediterranean because it rots. Wax tablets were used until the 19th century because it's also cheap and practical. Velum didn't become mainstream until the Islamic invasion of Egypt cut the supply of papyrus. >The adoption of paper was what really set things in motion in Europe, the Renaissance. The idea that there was a Renaissance at all is dubious. Paper was certainly a step up from velum. But It would have been much better for everyone if we could just have used papyrus continuously.
- 29athrowaway 7y ago
  Paper is thin, light, durable... you can make books from it and transport them easily. It can be manufactured from materials available in abundance in Europe. A book made of wax tablets, or velum is not as good. I don't imagine vast libraries and universities running on books made of wax tablets or velum. With respect to Papyrus, I agree. The Great Library of Alexandria was all papyrus. It can be produced at scale. But Europeans had to import it from far, far away.

dwheeler 7y ago

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.