Ancient Babylonians Figured Out Forerunner of Calculus (sciencemag.org)

sciencehabit writes: Tracking and recording the motion of the sun, the moon, and the planets as they paraded across the desert sky, ancient Babylonian astronomers used simple arithmetic to predict the positions of celestial bodies. Now, new evidence reveals that these astronomers, working several centuries B.C.E., also employed sophisticated geometric methods that foreshadow the development of calculus. Historians had thought such techniques did not emerge until more than 1400 years later, in 14th century Europe.

Comments

We might as well break the new management in.

[PopeRatzo]

Since today is Friday, the most important issue regarding this story will be whether or not the ancient Babylonians were white men.

For the record, Stormfront says, "Bet your ass they were". When asked for comment, Donald Trump said that if elected president, he'll make sure the US has "the classiest calculus of any country."

Re:We might as well break the new management in.

[Hognoxious]

From what I've seen of sculptures and stuff they look awfully like murzlums.

I think we should err on the side of caution and bomb them back into the bronze age, just to be sure.

Re:We might as well break the new management in.

[kbonin]

Babylonian religion predates Judaism and Islam by a long time, they worshiped lots of gods, lots of statues, a good deal of it adapted from Sumerians.
https://en.wikipedia.org/wiki/...

Re:We might as well break the new management in.

[Pseudonymous Powers]

Babylonian religion predates Judaism and Islam by a long time, they worshiped lots of gods, lots of statues, a good deal of it adapted from Sumerians.

Well, it sure didn't take long for this discovery to spark a war over priority. I guess "The Babylonians ripped off proto-calculus from the Sumerians" is the new "Leibniz was actually using calculus years before Newton."

Re:We might as well break the new management in.

[Anonymous Coward]

Well, what did the Sumerians ever do for us?

Re:We might as well break the new management in.

[Anonymous Coward]

There's a good reason that Judaism, Islam, and Christianity are called "Abrahamic" religions.

Abraham (Abram) had a son by a concubine (Hagar). That son was named Ishmael. The Arabs claim ancestry back to him. He also had a son by his wife (Sarai/Sarah). That son was named Isaac. The Jews claim ancestry back to him. Jesus (Christ) was a Jew.

Abraham was from "Ur of the Chaldeans", also known as Uruk. The name hasn't changed. That place is still called Iraq. (Say both of those names out loud if you don't "get it".) Specifically, the city of Ur was in the southern part of the Euphrates basin, right about where it curves east and runs to the Persian Gulf.

Babylon was much farther to the north and a little east, where the Euphrates and Tigris run closest to each other. You can still see where Babylon was on Google Maps. It's immediately north west of Al-Iqsandariya (Alexandria), Iraq. It's a scorch mark, basically. Nothing grows there, nothing lives there. There was a prophecy issued about that in the 800's BC. (Isaiah 13:20, specifically.) Interestingly, it holds true despite many attempts to make use of that portion of land. Make of that what you will.

Re:We might as well break the new management in.

[Hylandr]

They brought us Goezer and the StayPuft Marshmellow man.

Re:We might as well break the new management in.

[Camel Pilot]

Disinformation....

Looks pretty lush actually.

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

Re:We might as well break the new management in.

[Anonymous Coward]

Patently false. The primary functions that religions serve in most people's lives are:

1) provide a community for social interaction with friends, and a dating pool.
2) provide emotional support during times of distress.
3) facilitate the collection and distribution of charitable donations to benefit the impoverished.
4) provide adult education on various topics including history, culture, current politics, and life skills.
5) provide moral guidance when needed.

The desire for these things is quite high, and humans will build communities around these needs one way or another. The means by which some of these needs are met (especially emotional support) include ritual and symbolism, and in many cases superstition, all of which make them effective.

It is also true that the institution is abused, and used as a means of exercising considerable influence over huge numbers of people. It is an effective way to motivate people to go fight and die, as well as influence their political views, or just overtly extract money from them. So, all of this happens, but none of this is what draws people in. The practical benefits listed above are really the purpose...power-over-people is just an abuse of it.

Re: We might as well break the new management in.

[Type44Q]

You're either completely delusional, terribly ignorant of history or both.

Re:We might as well break the new management in.

[Dog-Cow]

To this day, not all Jews embrace monogamy as a religious principle, though polygamy is not practiced for practical reasons. Hagar was Sarah's slave. Why would she give Hagar to her husband as a full wife?

Yes, Muslims have a different version of that story, but theirs is much more recent, and is obviously intended as revisionist.

You don't have to believe in the historicity of either version to see this.

Re:We might as well break the new management in.

[Dog-Cow]

Actually, lying to save your life is considered OK in most cultures. Not that the story isn't weird, but he's hardly immoral for doing that.

Re:We might as well break the new management in.

[Coren22]

People who hear about Iraq from the US news mispronounce it. Those who actually deal with the country pronounce it "Urak".

People who denigrate a whole group of people because of a caricature of what they think that group is like are called Bigots. You sir are a bigot.

Archimedes had calculus

[DanDD]

Archimeded in the first century AD may have built upon Babylonian and Egyptian mathto create true calculus.

Re:Archimedes had calculus

[gstoddart]

It's like saying the Vikings discovered North America.

Wait, the Vikings discovered it and settled it.

They didn't go around telling people they'd invented it, but they sure as hell 'discovered' it and navigated back and forth.

The entire point is Europeans, after many hundreds of years rooting around in the muck like ignorant morons, rediscovered many things which had been known in antiquity ... and then proceeded to pretend like the barbarians who came before them were far too unsophisticated to have known this stuff.

And increasingly that view of history written to soothe the egos of those Europeans and their descendants is proven to be largely rubbish, which has nothing to do with reality.

And I say this as a white guy of European ancestry -- what we call history is really mostly "the history as told by white people who had no clue about what was really happening before they got their heads out of their asses".

While Europe rooted around in the muck and the filth, they forgot that things like math, navigation, and indoor plumbing had been around for a very long time. And then they pretended like they invented them.

Re:Archimedes had calculus

[known_coward_69]

there is strong evidence that the ancients had figured out Precession of the Equinoxes maybe even as far back as 10000-12000 years ago so it's not impossible that Archimedes knew the implications

Re:Archimedes had calculus

[jbeaupre]

It was more than that, and he did have an inkling of the use. But he treated it as academic. In college, we had to study his technique for integrating the area under a curve. Specifically, the area of a spiral. And he got it right. We even applied it to other geometry with success.

What made it painful was that it was done without algebra or even the symbol pi. Think long wordy descriptions involving limits and ratios and you end up with 3 pages of text for what takes half a line in modern notation. Heck, even his result takes a couple lines to write.

Re:Archimedes had calculus

[gstoddart]

Your narrative claims some form of racism but even your own example has nothing to do with race

No, my narrative hasn't got a fucking thing to do with racism.

After the Dark Ages, where the Church basically did their best to wipe out human knowledge and sanitize everything ... then the descendants of those damned people went about "discovering" everything they had long since forgotten.

The point isn't white, brown, pink or yellow skin ... it's about morons obliterating knowledge and history for their own purposes and then being too clueless to realize they'd just "discovered" things which had been known before.

Self inflicted ignorance isn't some noble thing to hold up for all to see.

Re:Archimedes had calculus

[pjt33]

If Archimedes did create calculus then it was considerably earlier than that, because he died more than 200 years before the first century AD.

Re:Archimedes had calculus

[epine]

Furthermore, SMS service was a bit spotty back then, so let's just assume that whatever Archimedes accomplished, he mostly accomplished ab initio.

Furthermore again, calculus isn't really calculus without the notion of continuous functions over an algebraic coordinate system.

Merely inscribing exterior and interior polygons around a circle and then amping up the edge count is obviously a pretty good place to start, but Newton or Leibniz it sure the heck wasn't.

Re:Archimedes had calculus

[PPH]

Cite where the church wiped out any knowledge.

Here's an example. Perhaps not intentionally. But the attitude of "Screw this science stuff. We need the parchment for a prayer book." eradicated a lot of earlier knowledge. Not until King Ferdinand of Spain figured out that all the stuff the Moors had collected in their libraries might actually be important, the Churches attitude toward knowledge was pretty much indifference.

Re:Archimedes had calculus

[Anonymous Coward]

Well, let's start early, because you seem so surprised by this.

Emperor Jovian is a guy who managed, in his 8 month reign over the Roman Empire, to reinstate Christianity as the religion, and burn down the Library of Antioch and all knowledge contained therein.

See, the thing is, it's really not "religion" that keeps doing these dirty nasty things, it's the Church, or rather the leaders who seek to abuse their power by way of religious authority, that do such things.

And please realize - this sets the stage for the following 1200 years.

Re:Archimedes had calculus

[jedidiah]

No. What the church brought was stagnation and illiteracy. Anyone caught translating the bible was burned at the stake. All knowledge was reduced to religious dogma including the mistaken ideas of the ancients.

Preserving the bad ideas of the Greeks may or may not have been a good thing. We might have been better off flushing the whole thing and starting over completely from scratch.

The real problem was not being able to challenge bogus crap for 1000 years.

Re:Archimedes had calculus

[HiThere]

Archimedes didn't discover the calculus. He didn't discover the theory of limits. He discovered what I to be a more accurate thing, the method of approximation.

As I don't believe in infinities or continuity, I consider the calculus to be a useful but false approximation of reality, just as I consider the real number line. I mean just think a minute about one of the proofs: You make two copies of all the real numbers between 1 and 0, and you paint one red and the other blue.... What does that even MEAN!!

Just because the universe is continuous to below levels that we can measure (and probably below levels that we can hope to measure...i'm thinking around 10^-33 cm here ... that doesn't imply that it's continuous below that level. Just because the space-time is continuous as far as we can see, and plausibly far beyond that, doesn't imply that it's actually unending. Just that we'll never be able to see the end. (Or it could wrap around and rejoin itself even within our visual horizon, and we'd never know because of the time variable.)

This doesn't, by the way, imply an absence of singularities. It actually implies that small singularities are everywhere, they're just usually too small to see.

And this is much more in agreement with the theories of Archimedes than with either the calculus or Cantor. But when seen from a distance you can't tell the results apart.

Re:Archimedes had calculus

[AthanasiusKircher]

What made it painful was that it was done without algebra or even the symbol pi. Think long wordy descriptions involving limits and ratios and you end up with 3 pages of text for what takes half a line in modern notation. Heck, even his result takes a couple lines to write.

But that's not the only way to do calculus with geometrical methods. And no, I'm not talking about the idea of integration with rectangles that get thinner and thinner.

Tom Apostol (author of one of the most well-known -- and abstract -- Calculus textbooks ever) highlighted the possible benefits of a geometrical approach years ago. A lot of complex problems are incredibly simple and intuitive to solve, once you get used to geometrical methods.

It's also important to remember that geometry was critical to Newton's conception of calculus too. Read his Principia, and you'll find plenty of geometrical proofs showing things that today we'd do with algebra.

Anyhow, the point is that we tend to think in algebra today because that's primarily how we're taught. There are actually intuitive and simple ways to use geometry to do calculus, and it doesn't surprise me at all if the Babylonians figured some of them out. It would surprise me if it really took a couple thousand years before anyone else did anything like that again -- my guess is that many historians who look at treatises from that period don't always realize what's going on in some historical methods, because we no longer work from a geometry-centric view of mathematics.

Re:Archimedes had calculus

[erapert]

After the Dark Ages, where the Church basically did their best to wipe out human knowledge and sanitize everything...

I was under the impression that it was rather the opposite. In reality the "dark ages" were neither literally nor figuratively dark. The name was given by Italians who were butthurt about not ruling the world anymore.

It also seems that Christianity (Catholic monks in particular) was responsible for preserving western culture, civilization, and knowledge during the "dark ages" not destroying it.

Even a gutter press site like Cracked seems to disagree with you on this matter.

Contrariwise, there's a lot of evidence that certain modern, "scientific", and atheistic governments have destroyed and censored knowledge (I've linked only a few obvious and famous examples but there are others).

Re:Archimedes had calculus

[AthanasiusKircher]

No. What the church brought was stagnation and illiteracy. Anyone caught translating the bible was burned at the stake.

Another myth. (Note -- before I go on, I'm NOT Catholic, and I have no interest in defending the Catholic Church. But I do think we have a moral duty to accurate history.)

The Catholic Church punished people who translated the Bible AND threatened heresy/schism, etc. Yes, there were some incidents in medieval Europe where translators were punished, but that was because they were associated with political movements against the church. If you wanted to translate the Bible AND lead an insurrection, sure they might kill you.

On the other hand, there are plenty of examples where portions or the entirety of the Bible were translated in the years 1000-1500, and the Church didn't do anything to the translators. It only became a significant controversy after the whole Luther thing and the Counter-Reformation.

By the way, I don't mean this to be argumentative or even that you should have known this. Errors in scholarship have a long life, and there were some influential studies done on this stuff based on incomplete evidence and erroneous interpretations of medieval documents in the early 1900s. That's why this myth endures.

But it's a myth nonetheless.

And illiteracy was just a consequence of lack of utility. Parchment was expensive -- how many animals did you have to kill and skin to make a book? So, why would literacy be common until paper became cheap in the 1400s (due to a sudden excess of scrap linen that could be pulped)?

Preserving the bad ideas of the Greeks may or may not have been a good thing. We might have been better off flushing the whole thing and starting over completely from scratch.

Well, that's all very debatable. Arguably the major medieval renaissance in knowledge was in part driven by reclaiming the knowledge of the ancients, which in turn led to what most people think of as the real "Renaissance," which in turn led to Humanistic enterprises that were no longer dominated by the Church, which led to the Scientific Revolution.

That's only one way of telling the story, of course. But there's some truth to it.

The real problem was not being able to challenge bogus crap for 1000 years.

You really have no idea what medieval Scholasticism was about, then, do you? Medieval universities were largely started by priests and monks. Debates were the norm. Empiricism and logical argument were combined into a new method. Challenging accepted facts was commonplace. In fact, some historians of science actually argue that the reason why the West had a "Scientific Revolution" and other places (e.g., China, the Arab world) didn't was because of the accepted level of scholarly debate that occurred in the West compared to other areas of the world... which didn't have the same kinds of debates.

Re:Archimedes had calculus

[erapert]

Churches attitude toward [secular] knowledge was pretty much indifference.

Just as it should have been.
Just as most scientists are indifferent to religious knowledge.

Re:Archimedes had calculus

[erapert]

What the church brought was stagnation and illiteracy.

Prove the following:
1. That any such stagnation occurred.
2. That any such stagnation was an intentional goal of the Church at the time.

Anyone caught translating the bible was burned at the stake.

[citation needed]

All knowledge was reduced to religious dogma including the mistaken ideas of the ancients.

1. [citation needed]
2. The knowledge of the ancients was pretty much already steeped in religious dogma.

Preserving the bad ideas of the Greeks may or may not have been a good thing. We might have been better off flushing the whole thing and starting over completely from scratch.

Then why are you accusing the Church of destroying knowledge as though a) it was a thing that happened on purpose and b) like it was a bad thing even though you yourself don't seem to think it was bad?

The real problem was not being able to challenge bogus crap for 1000 years.

I'll remember this next time someone shouts down another for questioning global warming-- or was it "climate change"?

Re:Archimedes had calculus

[AthanasiusKircher]

But the attitude of "Screw this science stuff. We need the parchment for a prayer book." eradicated a lot of earlier knowledge.

You do realize that early books made of parchment were from animal skin, right? So, to put a new page in your book, you had to kill a sheep?

Parchment was extremely valuable. Books required you to slaughter lots of animals. So yeah, people reused the animal skin when they could. It wasn't just reused for "prayer books" -- it was reused for community records, for legal documents, for endpapers to join the spines in new books, etc., etc., etc.

Not until King Ferdinand of Spain figured out that all the stuff the Moors had collected in their libraries might actually be important, the Churches attitude toward knowledge was pretty much indifference.

Huh? That's simply not true. The attitude was: "Here's some valuable material that has a bunch of squiggles on it I can't read. I need paper to make records of new stuff. Let's scrape and reuse."

It's not that they didn't value knowledge -- they didn't value stuff they weren't able to use. That's how life was for most of history for most people. It's only in the past few decades that we've reached a point where production to excess is so great that disposable stuff is everywhere and regular reuse of old stuff isn't necessary.

Very few people in Europe could read Greek for much of the medieval period, so a lot of old manuscripts were scraped off and reused. It's kind of like you came upon an old hard drive which was corrupted and you couldn't read it (and you didn't know what was on it), so you reformatted and started over. That's not "indifference" toward the contents of the drive -- it's just saying, "I need more space, I can't use this thing as-is, so I'll make it so I can reuse it."

On the other hand, there were plenty of books that were kept that maintained knowledge that was important to them. Prayer books were important to them, because without them you might be suffering in eternal torment forever. So, it's kinda like: "I don't have any fresh sheep to kill to make a new book, and here's this skin with squiggles on it I can't read, and if I don't make the new book, I might burn in hell forever."

That's not indifference toward knowledge. That's being practical with materials you have to live your life in a pretty bleak historical period.

Re: Archimedes had calculus

[AvitarX]

Older than your examples even. There were some germanic translations very early in the Church.

A Bishop in 3-4 hundred CE translated the old testiment.

There was also a similarly old translation of the new testiment that also updated to a germanic setting.

This was after early missionaries desired poorly using more agrressove tacticts.

  The second wave of missionaries into the germanic areas are why so much of the celebrations in the west are germanic in root.

Re:Archimedes had calculus

[belthize]

I like discovery. For instance today I discovered I needed re-calibrate how stupid I think people can be.

Re: Archimedes had calculus

[Anonymous Coward]

OK, mathematician here. The Europeans truly deserve almost all the credit for calculus. That's because real calculus is a significant advance over pre-European mathematics. Archimedes' method of exhaustion was a great idea and the true precursor as he was a genius who fully realized the power of his idea, but calculus is something else which could only appear once some other momentous ideas (also European) had been discovered, such as Cartesian geometry, and a form of exposition sufficiently precise to handle the new ideas, which itself built on two thousand years of Euclid's masterpiece.

You don't get to claim fundamental ideas like calculus for antiquity, because pre-European mathematics throughout the world was largely based on analogy and mysticism with the shining exception of the Greek tradition, which itself handled abstraction beautifully but was much too cumbersome and obtuse for the advances that have occurred in the last 400 years, to the point that it couldn't make those calculus advances without a complete retooling, which is exactly what occurred in the sixteenth and seventeenth century.

Re:Archimedes had calculus

[PPH]

if I don't make the new book, I might burn in hell forever.

And this is one of the biggest arguments about all religions. They divert energy and resources from work or study with value to wasting time worshiping imaginary sky fairies.

Very few people in Europe could read Greek for much of the medieval period,

So stop babbling to nonexistent beings and learn Greek.

Re:Archimedes had calculus

[Mr. Slippery]

It also seems that Christianity (Catholic monks in particular) was responsible for preserving western culture, civilization, and knowledge

Yes, preserving...in part by burning to death people who suggested advancing that knowledge.

Re:Archimedes had calculus

[mikael]

I don't believe the Great Flood was a myth. The "world" at that time was centered around the Euphrates river. Going by the description in some of the clay tablets, it would seem that someone upstream may have decided to destroy a natural dam out of revenge right when the mountain snow was melting in Spring (The Epic of Gilgamesh). That would have unleased a torrent of water 40x that of normal, and led to up to 11 feet of mud being deposited on the lower plains.

http://www.globalsecurity.org/...

https://newrepublic.com/articl...

The layout of some of these clay tablets looks like someone invented the spreadsheet before the computer:
http://isaw.nyu.edu/exhibition...

http://isaw.nyu.edu/exhibition...

They even invented a tablet with round corners before Apple:

https://s-media-cache-ak0.pini...

Re:Archimedes had calculus

[redlemming]

On the other hand, there are plenty of examples where portions or the entirety of the Bible were translated in the years 1000-1500, and the Church didn't do anything to the translators. It only became a significant controversy after the whole Luther thing and the Counter-Reformation.

Translation of the Bible was a significant controversy in England, more then a century before Martin Luther started the ball rolling for the Protestant Reformation in 1517.

The Wycliffe translation of 1382 would eventually become associated with the Lollard Heresy.

The Oxford Convocation of 1408 banned further translations being made without approval.

The first person burned at the stake for heresy in England was a Lollard, in 1410.

Re:Archimedes had calculus

[HiThere]

Math doesn't require infinities. Or infinitesimals. They are only there because they make calculation easier. There were a lot of arguments about this back in the early days of the calculus, and the people in favor in infinites won only for two reasons:
1) God is infinite and unbounded, and
2) It makes calculation easier.

While agree with the second point, this doesn't imply accepting it as anything other than a calculational convenience.

In a way this is sort of like boolean logic. It's a great tool, but one never knows with 100% certainty that something is either true or false. Probability theory is a more accurate statement, but harder to calculate with. And finite probability theory is, I believe, and even better model. Unfortunately, it's also harder to calculate with.

Similarly, Relativity gives more accurate orbital predictions than Newton's laws, but NASA uses Newton, because the calculation is easier. Ease of calculation is frequently the deciding factor, but the underlying model should understand the inherent uncertainty in the measurements, and acknowledge that we don't have infinite precision. (And I believe that the universe doesn't contain infinite precision, but *that* is a belief, not a fact.)

Re:Archimedes had calculus

[Kartu]

Remind me, what happened to Giordano Bruno?
Or about the wonderful relationship between Church and, cough, Galileo Galilei? Did he agree he was wrong, or did he prefer to be burnt alive?

Re:Archimedes had calculus

[tehcyder]

The layout of some of these clay tablets looks like someone invented the spreadsheet before the computer

Accountants were using ledgers and analysis paper with figures in multiple columns since the Middle Ages. The spreadsheet started off as an electronic version of a ledger page.

Re:Archimedes had calculus

[erapert]

1. I didn't say Atheism is an organized religion. 2. There have been atheistic governments-- case in point: the USSR. 3. A government isn't one person, it's many. But your same argument that one instance/person doesn't characterize the whole should also be kept in mind when demonizing the Church over certain misdeeds during the middle ages. Over the course of a thousand years every institution will err and often will err greatly. 4. Yes, actually atheism is by definition an overarching ideology. 5. I'm not saying the Church is infallible, nor that it didn't cause some problems during the middle ages. I'm just saying that a) the "dark ages" weren't the result of the Church brutally stamping out all knowledge as some would claim and b) that the "dark ages" were neither metaphorically nor literally dark.

Modern arithmetic not up to Babylonian standards?

[haruchai]

How does "several centuries BCE" plus 1400 years = 14th century??

Re:Modern arithmetic not up to Babylonian standard

[Aighearach]

Because the youngest end of their date range is less than 100 years BCE, and off-by-one is close-enough. Likely it 200 years older, but that isn't certain. 350 to 50 BCE is the range given.

ancient babylonians

[zlives]

ancient Babylonians were just poor students of calculus, which their ancient astronaut alien overlords kept trying to teach them unsuccessfully.

Lost knowledge?

[Tablizer]

And their VCR's didn't flash "12:00" all day

Re:Lost knowledge?

[slew]

And their VCR's didn't flash "12:00" all day

What is this VCR you speak of?

Re:Lost knowledge?

[Tablizer]

You flunked history, kid.

Re:Lost knowledge?

[slew]

You flunked history, kid.

whoosh ;^)

Re:Modern arithmetic not up to Babylonian standard

[buchner.johannes]

The 14th century started in 1301, so it is not off-by-one.

The concept of limit is simple

[Anonymous Coward]

Using it analytically to derive the familiar differential and integral calculus is not.

Re:The concept of limit is simple

[HiThere]

The concept of limit is not only not simple, I believe it to be false. It's a very useful theoretical concept, as is the real number line, but I do not believe that it has any actual existence in the world outside of mathematics. Just because you can't look at something close enough to see where it dissolves into pieces doesn't mean that it's actually continuous. This is why Xeno's paradoxes were so annoying. Most of them rely simplicity on the assumption of continuity, which is intuitive, but false. (Some of them have more complex failing, however. Achilles and the Tortoise also relies on the sums of infinite series being not being finite.) But Cantor's solution was not the way the universe solves the problems.

I'm Confused

[avandesande]

So if calculus is derived from this Babylonian knowledge, should we rename it threerunner?

Not surprising

[rasmusbr]

Civilizations tend to "discover" philosophy, mathematics, literature, drama and great works of music in the centuries after they invent ways of writing those things down.

What's probably going on is that these things have been cropping up intermittently for thousands of years (or tens of thousands of years), but the ideas would usually not survive for very long because it would take unreasonable amounts of human effort to remember and transmit them.

By the way, video finally made it possible to commit dancing to permanent media in the early 1900's, so future historians will probably think of the 1900's and 2000's as the centuries when great dancing was first invented.

Re:Not surprising

[grasshoppa]

How do you have "advanced" mathematics ( or perhaps a better term might be "non-trivial" ) without at least a rudimentary writing system?

Re:Not surprising

[rasmusbr]

How do you have "advanced" mathematics ( or perhaps a better term might be "non-trivial" ) without at least a rudimentary writing system?

You can't. You can do a lot of basic arithmetic and basic geometry.

But you could for example come up with the hypothesis that stars are faraway suns, just by noticing that different stars vary in brightness and guessing that the brighter ones are closer to Earth, with the Sun being much closer than all the others. You could argue that spherical objects are more efficient than other objects because they minimise both their surface area and the distance of any surface feature to the center of themselves for a given volume, then pose the hypothesis that the universe likes to be efficient about things and then conclude that the Earth is therefore probably spherical, like the Moon and the Sun.

It does take writing and some instruments to prove beyond all doubt that these things are true, but the ideas themselves could have been dreamt up by the same people who painted lions on cave walls 30,000 years ago.

Re:Not surprising

[thinkwaitfast]

Another interesting question is that if you had a culture where multiplying numbers was irrelevant, where is he impetus to invent the mathematics to do so.

Re:Not surprising

[colinrichardday]

Try to multiply XCIV * LXXII and see how you'd do in comparison.

Try using an abacus.

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

Babylonians are...

[azzy]

... our last best hope for peace.

Re:Babylonians are...

[jfdavis668]

But that all changed when the Fire Nation attacked

Re:Misleading summary

[jedidiah]

This sounds like something that seems more significant in hindsight than it was at the time. They may have been on the cusp of developing something but didn't. Or maybe they discovered it and then didn't know what to do with it.

The ancient Greeks invented the steam engine. It just didn't lead to trains or powered ocean vessels or massive factories.

It is a vanity of modern people to think that the ancients didn't know anything and never achieved or built anything of significance (in modern terms).

Re:Fixed summary

[Anonymous Coward]

Yup, because those Eastern Chinese Historians taught about how the Babylonians had this knowledge?

No, but contrary to popular belief there are many *Muslim* Historians and they have taught about babylonian mathematical knowledge.

Here's a short list of Muslim historians.

Obviously, I have not read through all the documents produced by these historians, but of what I have researched, there are many references about the historical tablets that were recovered that talk about computing the motion of Jupiter using sophisticated computations and approximation techniques, they of course don't use the word "calculus" to describe their approximation technique.

This latest development simply speculates that they specifically used a variant of the trapezoidal rule to make these computations concerning the motion of Jupiter and notes that these methods were not in general use until later in Europe. The summary apparently calls using the trapezoidal approximation rule as somehow foreshadowing calculus whatever the fuck that means.

I know you think you are being clever and making a point, but you are really making yourself to be a complete and utter ass.

Well, I apparently have your company in this respect.

FWIW, I doubt "Eastern Chinese" historians taught this...

Re:Modern arithmetic not up to Babylonian standard

[HiThere]

I bet you don't believe in the year 0 BCE either.

Is it calculus? Or extrapolation?

[140Mandak262Jamuna]

These orbits are all elliptic curves, second order curves basically. With enough observations one could construct some kind of regression, extrapolation based predictions. So what the clay tablets contain could be simple prediction tables. Can one tell the difference between extrapolation or regression prediction and trapezoidal quadrature?

Re:Modern arithmetic not up to Babylonian standard

[belthize]

On a related note how does 1st and 2nd century BC count as "Ancient Babylon". That was toward the end of the Hellenistic period of what was barely left of Babylon. Ancient Babylon by archaeological standards (to avoid conflating it with any number of other empires that just happened to share the same geographical area) had ended some 1000 years before. In fact the article suggests that the 2nd century BC tablets were actually copies handed down from as far back as actual ancient Babylonian mathematical texts in or around 1700 BC. Which is quite a bit more interesting.

So what they really mean is Persian mathematicians during the Hellenistic period in the area that was known as ancient Babylon and now modern Iraq, but I guess that doesn't have the same ring.

Well, so did the Greeks, around 500 BCE.

[hey!]

How do you think they figured out the formula for the volume of a sphere? Or proved that the area of a circle was proportional to the square of its radius when it's impossible to construct a square of the same area in a finite number of steps with ruler-and-compass methods? The same techniques were rediscovered in China around the 3rd century CE, again as a result of trying to calculate the area of a circle.

I think the basic ideas behind integral calculus are pretty much inevitable when you have mathematicians messing with geometry problems that can only be solved with successive approximations -- although inevitable only because eventually someone really smart will get bored with doing things the long way.

What's distinctive about modern calculus is it's connections to analytic geometry and algebra (algebra with good notation, I might add). This allows us to generalize problems in a way that transcends geometric resemblance, e.g., the area under the curve of any polynomial.

Re:Well, so did the Greeks, around 500 BCE.

[interval1066]

I think the basic ideas behind integral calculus are pretty much inevitable when you have mathematicians messing with geometry problems that can only be solved with successive approximations

I agree with this, and I suspect any adoption problems, if any, were with the notation. Until algebraic notation came along, I bet integration, like Greek geometry, was a serious pita for the Babylonians. I took a class that included a long division problem using Roman numerals for extra credit in one test. OMG... if the Babylonians were using cruciform numbers for their calculations, holy cow...

Re:Well, so did the Greeks, around 500 BCE.

[colinrichardday]

Proof by contradiction from constructing a triangle with one side that of the and the other of the circumference.

What contradiction occurs?

Re:Well, so did the Greeks, around 500 BCE.

[hey!]

That the area of a circle was other than such-and-so.

Area of a trapezoid

[colinrichardday]

The article mentions trapezoids. Did the Babylonians approximate curved regions with trapezoids, or did they just use trapezoids? Finding the area of a trapezoid doesn't require calculus.

Religion decelerated the advancement of humanity

[vinaychittora]

What bothers me really is after thousands of years and reading tons of history, we failed to understand the simple thing the biggest culprit was/is the Religion. Why don't we just try to get rid of it.

Re:Modern Hubris

[thinkwaitfast]

I recently read an interesting book on this subject written in the early 1900's about this exact matter: The Decline of the West by German historian and mathematician Oswald Spengler. According to him, there have been about 7 recorded civilizations prior to Western Civilization; that history is not a linear progression to some higher goal, but rather a cyclical phenomena with each going through well defined stages and an overall period of ~1000 years.

At the least, it's a new perspective about how history progresses and attempts to describe the development of the arts and mathematics based on the sole defining purpose of the culture that brings it about. The later stages are when cultures develop into civilizations at which point the defining purpose has run its course and dies. I guess at the most, it's an eerily accurate prediction and description of the world today (written 100 years ago). According to him, the defining purpose western civ is based on Norse culture's search for the infinite which it can never reach. Calculus is an example as are shared cultural myths (Arthurian legend and search for the Holy Grail).

Re:Religion decelerated the advancement of humanit

[thinkwaitfast]

Environmentalism is a religion Are you going to stop the environmentalists?

Re:Modern arithmetic not up to Babylonian standard

[Kartu]

Sorry for nitpicking, but it actually started in 1300.

Re:Modern arithmetic not up to Babylonian standard

[buchner.johannes]

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

Re:Modern arithmetic not up to Babylonian standard

[Coren22]

1. You have to actually get a technical point right before you can claim a victory, you can't just claim victory before you actually win, or you look like Buch with "Mission Accomplished" over his head when Saddam fell.

2. You couldn't make anyone eat their words, your arguments are repetitive and easily debunked. You have never actually won an argument, you just fall back on repeating the same argument over and over in hopes of getting the other person to shut up, which I refuse to do.

3. One person looking at your code is not a code review. Code reviews happen out in the open among a group of security researchers. It isn't like you have anything special in your script, it would take a few lines of shell script in Linux and Windows Powershell. Download all the other people's work, combine them, sort them and unique them. Simple shit man, stop being afraid someone will steal it from you, as there is nothing there to steal, and copyright covers you from stealing. If people steal your software from the source code, YOU CAN SUE THEM!

4. You really need to stop losing to the wet paper bag of your own arguments, it just makes you look incompetent when you keep making the same arguments, and keep supporting yourself.

5. Stalking people, and trolling everything they post is a sure way of coming off as creepy. I defend people I see you attacking, because I have been attacked by you, that doesn't make the other person my sockpuppet, and it doesn't make you automatically win an argument. If you want to have a civil conversation, have a civil conversation. Stop stalking people and posting the same shit over and over which has been proven to be inaccurate or silly.