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-wh...

Edit: Fixed a location.

Wrong! If you mean times between 500 and 1200: how about arabs, iranians, indians, chinese? Algebra, Negative numbers, 0123456789 system of writing?

They had Archimedes of Syracuse

Maybe the peoples of the future will only consider one particular mathematician as the relevant one? Maybe like Turing, because most likely computers will become a greater part of the world at large? Maybe we see programmers the way people used to see scribes some time back?

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.

Original: https://archive.org/details/technologicaltre1937unitrich/pag... (faint copy)

Re-typed / markdown: https://pastebin.com/raw/Bapu75is (updated and corrected from April, 2019 version.)

Roman numerals are a recording tool, not a calculating tool. Romans did calculations using pebbles or other counters on a counting board. Roman numerals are just a way of recording the state of a counting board before/after performing some algorithm. The goal of them is to be as direct and faithful a record of the counting board state as possible.

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 you can do without arithmetic and algebra.

(Edit: Saw your username after I posted this and I want to say that I respect you deeply -- I don't know of anyone else who has written a working C++ compiler almost by themselves. And I like D a lot, though have only had a very limited chance to use it professionally.)

Oh, but they do. It’s just that their syntax is awful.

The original answer that I read yesterday has since been removed by the mods for some reason.

---

[-] ImOuttaThyme66 points 16 hours ago

[Their number system.](http://storyofmathematics.com/roman.html)

Mathematician in studying here with a side hobby of history. Sources are included throughout.

You may recall from elementary school or personal perusing of Roman history books that they had their own numeral system with letters instead of their own numerals, excerpts of the Latin Alphabet. I is 1, C is 100, and so on.

The Romans did decent with their numeral system. They could add, subtract, multiply and divide with their numbers. However, it was missing two very important principles, if that's the right word, that today's Arabic numbers have.

The first is the idea of zero in mathematics. They knew the concept of nothing yes but they had no numeral for the number "zero." So essentially, try doing your own math homework without using the number zero in the one's place, the ten's place, and so on. Now, zero itself didn't come with Arabic numbers but they did come from an ancestor. [Origins of Zero](https://www.smithsonianmag.com/history/origin-number-zero-18...)

Which led to the second problem with Roman numerals. Their numbers do not work on a positional system. Today's Arabic numbers, 0-9 work on a positional system. That is, we have the one's place, go left one digit, ten's place, left again, hundred's place, and so on. Each digit in a number is the base raised to a certain power. And this is what makes addition, subtraction, multiplication and division so easy to do with Arabic numbers, especially with the concept of zero, a placeholder to place in a certain space when a number has no "tens" or "hundreds" or "ones". Like 109. It has 9 ones, and 1 hundred, but no tens. Without zero, we couldn't be able to write it out like this.

A little sidenote here, technically, the Romans did have a positional system. That is, the greater numerals were on the left and the lesser ones were on the right unless they were using two numerals to communicate numbers. So, it's not an explicit positional system like we do today, in which each digit means a certain number, they did order their numbers around based on size.

Now, in fairness, the Romans simplified their numeral system a little over the years by adding two principles, subtraction and multiplication. What the Romans did was that whenever they placed a smaller number before a bigger number, those two numbers communicated a new number entirely by subtracting the smaller from the bigger. So for example, 109, CIX, the IX becomes worth 9 because X (10) - I (1) is IX (9).

Multiplication, to indicate 1000's, they would put a line over the symbol, and that would be the same as multiplying it by a 1000.

Let's do a little Roman math.

For Roman numerals, 109 would be written out as CIX. Great, we get the amount communicated. Let's say we want to add 32 to this number in Roman numerals. 32 in Roman is XXXII.

CIX + XXXII

Immediately, there's a problem. We have to separate the various numbers. So CIX becomes C IX and XXXII becomes XXX II. Now we can add them together by going "Okay, IX plus I makes X, there's an I remaining, X joins the three other Xs so we now get CXXXXI." aka 141 in today's numbers.

Let's imagine as if we did that with our numbers. Let's add 109 and 32 again. Only, we're adding 100 and 9 and 30 and 2. We know 9 + 2 makes 10 and 1. We know 10 and 30 makes 40. We have 1 and 100 remaining, there's nothing else to add them together so they stay like that. The resulting number becomes 100 and 40 and 1. Exhausting.

So, addition is possible. Subtraction is also possible. You have to go through the entire grouping of bases to do it but it is possible. Multiplication is somewhat possible but very iffy, having to do all those grouping of bases manually.

Division. Division was the hell of the Roman numeral system. The Romans did not have decimals. They had fractions but they did it in duodecimal form, that is, 12ths. They did not have a 1/10th. There was no talking about that explicitly, they preferred to do everything in 12ths. Now, this makes sense, 12 has many factors compared to 10. You can divide 12 by 1, 2, 3, 4, 6 and 12 itself whereas you can only divide 10 into 1, 2, 5, and 10. There are plenty of people who believe we should move to a duodecimal system. Then again, the French attempted installing a decimal system for time during the French Revolution. Maybe not all ideas are popular.

Either way, Romans did not have very explicit fractions. They had the base fractions 1/12 through 12/12, then they continued on from there by dividing them further. Like 1/144 (1/12 * 1/12) or 1/8 (3/12 * 6/12). More information on Roman fractions can be found [here](http://dmaher.org/Publications/romanarithmetic.pdf). Another side fact of their fractions was that they always named them as fractions of something, such as 1/12 of as, which was a currency. Never 1/12 by itself.

So, now that we've gone through the clusterfuck that is Roman numerology, we can pretty much understand why they didn't advance the mathematics field too much. It was functional for their time. The Romans still did many grand engineering feats that were no doubt developed from this number system. However, when it came to further mathematics such as calculus, which would finally be found by Newton and Leibniz independent of each other in the mid 17th century, you can't get any further when you don't have a positional system that makes adding/subtracting a lot easier, no numeral for the number 0, and your dividing tactics do not allow you to do decimals very well, especially when your numerals are 1, 5, and then powers of 10. Decimals could be made possible with these numerals yes but it would be insanely difficult to understand and is made so much easier when you assign every basic integer, like zero through nine for instance, their own numeral.

And that's probably why the Romans didn't do very well in mathematical advancement.

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?

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.

Answers must be accurate, researched, supported, and factual. Generally, "scholarly". It's not uncommon to find posts with a thousand or more votes, and 100s of comments, all removed. The mods are looking for good answers. As are most of the readers.

The result may be frustrating for commenters, but that's really not the point.

I actually had an opportunity to answer on a subject which I've some familiarity last week, and got mention in the weekly wrap-up for it, which was kind of nice. A bit more than I deserved, really.

(I was talking trash ... but at least that was the topic.)

They have an explicit policy of removing any amateurish or unsourced answers, in order to keep quality high.

http://www.phy6.org/outreach/edu/roman.htm

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.