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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?

#41

Post by WalterBright »

School-Cotton wrote: post #31
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.)

I'm not convinced. The filesystem layer on Linux and FreeBSD (and probably other OSs too, though I don't have knowledge) is totally object-oriented and written in C. Gnome/GTK also encourage an object-oriented style in C, via GLib and GObject. Also, Greek numerals were just as unwieldy as Roman ones (if not worse), and at any rate the Greeks did not use numbers in their mathematics. There's an enormous amount of math…

I've seen OOP code written in Fortran-10. It blew my mind at the time (I didn't even know it was called OOP until years later).

But only once. And probably by someone who had learned OOP in another language that was built around OOP.

I was in the C business before, during, and after the OOP revolution. I never saw any OOP attempts in C before C++ came along and popularized OOP. Many C programmers didn't want to move to C++, and were determined to make it work in C. It did work, but the result was kinda hideous and terribly fragile (had to throw type safety out the window with all the necessary casting).

> I don't know of anyone else who has written a working C++ compiler almost by themselves

Neither do I :-) Thanks for the kind words.

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

#42

Post by WalterBright »

jacobolus wrote: post #40
WalterBright wrote: post #37

Earlier quoted context omitted.

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.

> 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 de…

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.

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

#43

Post by dkersten »

fortran77 wrote: post #38
markholmes wrote: post #14

Earlier quoted context omitted.

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.

Probably the discovery of solid state devices and the invention of the digital computer is more important than the "Internet"

We will be remembered for our most important achievement: bringing high speed access to cat pictures to the masses.

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

#44

Post by yjftsjthsd-h »

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…

That's genuinely interesting, but doesn't really change that it's a terrible system for abstract calculations.

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

#45

Post by WalterBright »

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…

> Romans did calculations using pebbles or other counters on a counting board.

I think you just made my point :-)

Have fun doing long division that way.

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

#46

Post by WalterBright »

saagarjha wrote: post #27
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.)

> For instance, people don't do OOP or FP using C. Oh, but they do . It’s just that their syntax is awful.

> It’s just that their syntax is awful.

I want to expand a bit on that. In the evolution of D, I have a front row seat on how people use it. It's hard to downplay how relatively minor syntactical changes can have a heavy influence on the programming paradigms people select. It's startling.

People will often say "but I can do that, too, in my favorite language X", and they are correct. But they don't actually do it in X because it's inconvenient.

For example, D has a built-in syntax for unittests. That gets pooh-poohed a lot as being pointless. But it's hard to argue with how transformational that has been for D programs. People expect unittests when writing D code. They didn't before. Unittests often occupy more lines of code than what they tested. The addition of a very minor bit of syntactic sugar changed the whole way people write D code.

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

#47

Post by jacobolus »

WalterBright wrote: post #42
jacobolus wrote: post #40

Earlier quoted context omitted.

> 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 de…

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 accurate…

Ptolemy’s table has the chords for every possible angle in ½° increments (360 table entries in all), to 3 sexagesimal digits of precision, or about 5.5 decimal digits of precision. It also had an additional column showing the derivative of the chord function at each ½° at 5 sexagesimal digits of precision, for use interpolating at arbitrary angles in between the listed ½° increments. https://en.wikipedia.org/wiki/Ptolemy%27s_table_of_chords

You might be thinking of Hipparchus’s table (from a few centuries earlier) which only had multiples of 7½°.

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

#48

Post by abdullahkhalids »

dkersten wrote: post #43
fortran77 wrote: post #38

Earlier quoted context omitted.

Probably the discovery of solid state devices and the invention of the digital computer is more important than the "Internet"

We will be remembered for our most important achievement: bringing high speed access to cat pictures to the masses.

Nope. Our most important achievement has been to create a system where smart people spend their life trying to get people to click on ads, using morally dubious dark-patterns.

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

#49

Post by strainer »

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.

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

#50

Post by toasterlovin »

ZhuanXia wrote: post #39
riazrizvi wrote: post #33

> "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 troubl…

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 charte…

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).

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