151–160 of 201 posts
Earlier quoted context omitted.
>Romans after all, which likewise produced little (not none) new math. They had Archimedes of Syracuse
Archimedes was Greek, the Romans killed him. https://en.m.wikipedia.org/wiki/Archimedes
Many Greeks were part of Roman empire, what difference does it make?
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.)
The original answer that I read yesterday has since been removed by the mods for some reason.
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[-] 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.
Earlier quoted context omitted.
Have you looked at the population spread of the Roman Empire? Rome had people, the rest of the empire was predominantly to the East/South. Rome was Mediterranean, not Western European.
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”.
https://en.m.wikipedia.org/wiki/Demography_of_the_Roman_Empi...
edit terrible math on my part.
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…
> English, more than about 400 years ago is almost wholly foreign Are you suggesting this text is from the 17th century? I'm no expert but this much Germanic influence seems much older.
Earlier quoted context omitted.
A Muslim Persian, and Baghdad was the melting pot of the world at that time. It’s like saying a German physicist in Princeton, NJ, which is to say that America not Germany was the place where the work was valued and promoted. Likewise, Alkhawarizmi was educated in Baghdad (not in Persia) and wrote his book on Algebra in Arabic. He was not educated in Persia and he did not write his book in Farsi. If we put ethnicity…
No, Baghdad was located in the heart of the former Persian (Sassanian) Empire, a mere 35 km from the site of the Sassanian capital (Ctesiphon). Although the whole area gradually became Arabized, at the time it was still significantly Persian. (Frankly, I doubt we know where Al-Khwarizmi was educated. We know he was originally from what's now Uzbekistan, and that he ended up in Baghdad, but not much more than that.)
Mesopotamia was conquered by Arabs in 633. Al-Khwarizmi was born in 780. Most the Arabic lands were gained by conquest. Even modern day Yemen and Oman were not under Arabic influence if you go back far enough. The "original" arabs spread from Hijaz and Najd.
edit: from wikipedia
> The Abbasid Caliphate first centred its government in Kufa, modern-day Iraq, but in 762 the caliph Al-Mansur founded the city of Baghdad, near the ancient Sasanian capital city of Ctesiphon.
My guess is that families from the Sassanid have immigrated to the new city and as a result Al-Khwarizmi was born there.
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…
To add to your points on both flat terrain and waterways in England: in fact the current railway that runs a few blocks from my house runs along what used to be a canal dug from the Thames to enable transport. It was one of the last ones to open before the railway took over (and the operator went bankrupt and sold the land to a railway company that drained it and used the conveniently flattened land for more rails) A…
China though has its Great Canal which dates to 12 BCE and has had pound locks since the 10th century: https://en.wikipedia.org/wiki/Grand_Canal_(China)
In the US the Erie Canal opened up the West and cemented New York City as a transport, commerce, and financial hub, beginning in the 1830s.
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…
Granted, NZ's a small country, but if it was known about there pre Great War, I suspect many people knew about it elsewhere too.
It is one of those things that until very recently had been quite easy to ignore though I suppose (and many still try even now).
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…
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.
That really was my experience growing up in Western education. My understanding was that history focused on the important things and it wasn't until much later in life that I learned there was a lot happening globally after the fall of the Roman empire before the European renaissance.
After the USA was established, US history lessons completely ignore the rest of the globe until the early 20th century. I only learned yesterday that Italy wasn't a country until 1861 and I am almost 40.
Earlier quoted context omitted.
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.
His point is that most Western history lessons completely ignore everything but Western Europe during that time frame and present a view of history that nothing was happening globally of any importance. That really was my experience growing up in Western education. My understanding was that history focused on the important things and it wasn't until much later in life that I learned there was a lot happening globally…
That’s because they’re Western history lessons. I had world history as a separate class in high school.
