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    Posted: 05-May-2008 at 03:58
Originally posted by red clay

...Considering fermentation and distillation in some form or another, were almost universally known you'll get a lot of arguments about that one.
 
Fermantation is almost universal. Destilation it isn't. Arabs named alcohol precisely for that achievement.
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Posts: 1900 		  Quote Chilbudios Quote  Post ReplyReply Direct Link To This Post Posted: 05-May-2008 at 04:17
Originally posted by Pinguin

It may be, but Newton without the branch of trigonometry developed by the Arabs, hardly would have invented Calculus. That is such simple like that.
 Do you know anything of calculus or trigonometry? Leibniz or Newton? Have you read their works or you're just spilling the usual poison against Europeans? Will you ever stop this scornful attitude against a part of the world?
 
 
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Posts: 117 		  Quote kafkas Quote  Post ReplyReply Direct Link To This Post Posted: 05-May-2008 at 04:20
Trousers
Stirrups
Cymbals
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Coffee

It's much easier to think of Europeans influences on other societies since Europe has been ahead of everyone else technologically in recent times.



Edited by kafkas - 05-May-2008 at 04:24
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Posts: 4613 		  Quote Leonidas Quote  Post ReplyReply Direct Link To This Post Posted: 05-May-2008 at 04:22
Originally posted by pinguin

Originally posted by red clay

...Considering fermentation and distillation in some form or another, were almost universally known you'll get a lot of arguments about that one.
 
Fermantation is almost universal. Destilation it isn't. Arabs named alcohol precisely for that achievement.
thats is much more specific and a somewhat different than just saying alcohol
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Posts: 1900 		  Quote Chilbudios Quote  Post ReplyReply Direct Link To This Post Posted: 05-May-2008 at 04:24
Originally posted by Pinguin

Have you studied Calculus? Have you read some Newton biography?
I have done both, and I admire Sir Isaac Newton.
Both and I even read most of Newton's works and Leibniz's. Which you obviously didn't.
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  Quote Guests Quote  Post ReplyReply Direct Link To This Post Posted: 05-May-2008 at 04:25
Originally posted by Chilbudios

Originally posted by Pinguin

It may be, but Newton without the branch of trigonometry developed by the Arabs, hardly would have invented Calculus. That is such simple like that.
 Do you know anything of calculus or trigonometry? Leibniz or Newton? Have you read their works or you're just spilling the usual poison against Europeans? Will you ever stop this scornful attitude against a part of the world?
 
Have you studied Calculus? Have you read some Newton biography?
I have done both, and I admire Sir Isaac Newton.
 
Actually, my problem is not against high IQ Europeans like Newton, Leibnitz, or Einstein. People that usually knows better than the rest of mediocre people that makes most of the population of planet earth.
Usually my poisson is addressed to the idiology that denies the importance of non-European peoples in the development of the modern world.
 
 
 


Edited by pinguin - 05-May-2008 at 04:26
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  Quote Guests Quote  Post ReplyReply Direct Link To This Post Posted: 05-May-2008 at 04:28
Originally posted by Chilbudios

.. Both and I even read most of Newton's works and Leibniz's. Which you obviously didn't.
 
So, if you know so much about Newton's work, could you tell me where he got the basic idea of calculus from? And also what was the book he bought in a street sale that made him focusing in the topic?
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  Quote Guests Quote  Post ReplyReply Direct Link To This Post Posted: 05-May-2008 at 04:31
Originally posted by kafkas

...It's much easier to think of Europeans influences on other societies since Europe has been ahead of everyone else technologically in recent times.
 
it is worth the effort of thinking on that LOL. Actually, the list of things that Europe owes to the rest is longer than people thinks 
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Posts: 1900 		  Quote Chilbudios Quote  Post ReplyReply Direct Link To This Post Posted: 05-May-2008 at 05:15
Originally posted by Pinguin

So, if you know so much about Newton's work, could you tell me where he got the basic idea of calculus from? And also what was the book he bought in a street sale that made him focusing in the topic?
In his book De Analysi (1669, but published only in 1711) he speaks of a method devised some time ago, of quantifying curbes by infinite series and he further develops the concepts of integration and derivation in a problem of quadrature. The infinite series are however something on which he worked with (his binomial calculations are part of it) and also part of his influences from earlier readings, Euclid, Descartes, and also more recent scholars like John Wallis (whose book Arithmetica Infinitorum was certainly influential and also constitutes in one pioneering work on calculus).
The story with the book is a bit different from what you present. His interest in mathematics came in college when he bought a an astrology book and he couldn't get the mathematics from it. So he bought a book of trigonometry which he couldn't understand either. So he bought Euclid. It's worth noticing that most of the trigonometry books we know Newton to had were by contemporary European authors.
 
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  Quote Guests Quote  Post ReplyReply Direct Link To This Post Posted: 05-May-2008 at 05:20
Well, you forgot Barrow, his teacher.
 
And you are right about the book in trigonometry.
 
All of this was to show you that without the Indo-Arabian branch of trigonometry (that included trigonometrical functions like sin and cos, rather than the ackward Ptolmey cords calculations) Newton wouldn't had the matematical tools to develop his work.
 
 
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Posts: 1900 		  Quote Chilbudios Quote  Post ReplyReply Direct Link To This Post Posted: 05-May-2008 at 05:56
Originally posted by Pinguin

Well, you forgot Barrow, his teacher.
I did not, you asked me about his calculus theory and about books, not about teachers.
 
 
All of this was to show you that without the Indo-Arabian branch of trigonometry (that included trigonometrical functions like sin and cos, rather than the ackward Ptolmey cords calculations) Newton wouldn't had the matematical tools to develop his work.
 
The Indians probably got from the Greeks the notion of chord and they found it's more practical to use the half-chord, making all the calculations more easier. The Indian term for half-chords was brought into Arabic as "jiba" (I don't remember now the Indian term, nor I am familiar with Sanskrit to reconstruct it myself), which due to the Arabic writing system was perceived by Latin translators as "jaib" and translated as "sinus" (sine). So basically the "Indian sine" is a half-chord, nothing more fancier than that. The "cosinus" (cosine) was then derived by Europeans for complementary "sinus" and it represents a development from Regiomontanus onwards when the these trigonometrical functions ceased to be viewed dependent on circle but on the right triangle. It was also when the trigonometrical functions became not only lengths of segments (like for Ancient Greeks and Indians) but ratios between right triangle's sides as we understand them today.
Anyway, for Newton's mathematics (if you understood a iota of what I've said) these trigonometrical functions were somehow secondary. He indeed calculated several power series (including trigonometrical functions) but the idea of infinitesimals was not at all correlated to them.


Edited by Chilbudios - 05-May-2008 at 06:09
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Posts: 7035 		  Quote gcle2003 Quote  Post ReplyReply Direct Link To This Post Posted: 05-May-2008 at 10:28
Originally posted by Maharbbal

Exams to become civil servant from China
Silk
Sugar
Cotton

 
Silk, sugar and cotton weren't 'invented' or 'discovered' by anyone in particular. They're just agricultural (in a broad sense) products that happened to grow where they did. Obviously the people where they grew learnt how to use them first, but that's just happenstance. For instance sugar from beets is a European 'discovery', and India never 'discovered' pine trees. Alcohol as an impure product arose pretty well everywhere independently, but wine was developed where grapes grew, and beer was developed where barley grew and cider developed where apples grew and mead developed where bees flew around....and so on.
 
Crediting a 'civilisation' with 'inventing' or 'discovering' the natural products that surrounded them in particular is kind of silly.
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Posts: 7035 		  Quote gcle2003 Quote  Post ReplyReply Direct Link To This Post Posted: 05-May-2008 at 10:30
Originally posted by pinguin

But remember that Isaac Newton was modest enough to recognize he was standing on the shoulders of giants. And one of those giants were the Muslim scientists and mathematicians of the Middle Ages!
 
That rather destroys your entire argument. I don't think anyone in Europe or elsewhere has ever been taught about Newton without that quotation being included.
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Posts: 7035 		  Quote gcle2003 Quote  Post ReplyReply Direct Link To This Post Posted: 05-May-2008 at 10:48
Originally posted by pinguin

It may be, but Newton without the branch of trigonometry developed by the Arabs, hardly would have invented Calculus. That is such simple like that.

I know there's no hope of your doing so, but would you mind explaining that?
It is amazing how nervous Europeans get in the denial of ancient Muslim influences.
It's amazing you keep saying that even though it is patently untrue.
 I wonder if that will be the same 100 years from now when Europe become finally a Muslim continent LOL
With any luck at all in 100 years the rest of the world will have matured like Europe into becoming a religion-irrelevant zone.
 
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Posts: 7035 		  Quote gcle2003 Quote  Post ReplyReply Direct Link To This Post Posted: 05-May-2008 at 10:55
Originally posted by pinguin

Well, you forgot Barrow, his teacher.
 
And you are right about the book in trigonometry.
 
All of this was to show you that without the Indo-Arabian branch of trigonometry (that included trigonometrical functions like sin and cos, rather than the ackward Ptolmey cords calculations) Newton wouldn't had the matematical tools to develop his work.
 
But you completely fail to show it. Just assertiong something isn't demonstrating it.
 
What you haven't explained is how trigonometry as developed by Arabs or Indians or anyone else for that matter is necessary for the development of calculus. That Newton was interested in astrology and understood trigonometry is true (IIRC he was also interested in alchemy and other occult studies), but it was not necesary to the development of the calculus - at least you've shown no reason to think so.
 
 
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Hello to you all
 
About trignometry, greek trignometry was a primitive form of todays trignometry and it simply has no similarities. The basic functions are different, the basic applications are different and the major rules and theorems that govern it weren't discovered by the greeks. Trignometry as we know it is an Islamic invention with some Indian and greek elements. A book on trignometry by Al-Tusi is not much different than modern books on the same subject except with the relative absense of calculus, derivatives were known to muslims scientists.
 
Same thing goes for Algebra, greek algebra was part of geometry and abstract ideas about Algebra, matrices, Pascal triangle, imaginary numbers, symbolism etc which are at the heart of algebra were chinese-Arab additions. So saying everything started with the greeks, which is not true, is as absurd as denying that other civilizations added to the sum of human knowledge.
 
As for how trignometry is important for calculus, well, if you know maths you will probably know that sin and cos functions are derivates of each other with changing signs. Several important trignometric relations can be proven easily through calculus than through normal logical algebraic steps. Newton's approach to the theory of calculus was through what he called "method of fluxion" (which is the name of Newton's book explaining his theory of calculus) which essentially used geometry and trignometry to prove his fundamental theory of calculus.
 
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Posts: 651 		  Quote Richard XIII Quote  Post ReplyReply Direct Link To This Post Posted: 05-May-2008 at 11:43
It's not important who discovered this or that but who made the discoveries available for the usual people, and Europe did it. 
"I want to know God's thoughts...
...the rest are details."

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Posts: 1900 		  Quote Chilbudios Quote  Post ReplyReply Direct Link To This Post Posted: 05-May-2008 at 12:43
Al Jassas,
 
Greek trigonometry bears many similarities for today trigonometry mainly because many theorems of theirs are studied in school today - Pythagora's theorem, Menelaus', Thales'. The law of cosines for instance is included in Euclid's elements (without reference to cosine, of course, but with a correct substitution nevertheless). For Islamic scholars the trigonometrical functions were lengths of half-chords in a circle of certain radius, for us they are ratios in a right triangle. Even if we're to talk about trigonometry on a circle, most modern formulas were unknown to medieval Islamic scholars, e.g. e^ix = cos(x)+i*sin(x), because simply our approach on trigonometry is much more elaborate than theirs. No one is removing their contributions from the history of trigonometry, but to say trigonometry is mainly their development it is, without doubt, an exaggeration.
 
Like you said, same thing goes for algebra. Greek algebra was not part of geometry, Diophantus in his Arithmetica was preoccupied with solving equations. Also the importance of Eastern contributions is overrated, do we actually use Pascal triangle in binomial expansions or combinatorics? Aren't the complex numbers actually those defined by Descartes, but actually discovered by Italian scholars like Bombelli (his work on algebra remarks that the square root of a negative number is neither positive, nor negative, calling it impossible number). And where is algebra today?
 
In both of your mini-histories of trigonometry and algebra you started with the Greeks (though also you may have started from Babyblonian mathematics), so why you say it is not true?
 
The theory of fluxions is the idea of infinitesimals (dx, dy). Which does not require trigonometry,  even today in schools is taught independently of it.
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Posts: 1900 		  Quote Chilbudios Quote  Post ReplyReply Direct Link To This Post Posted: 05-May-2008 at 12:48
If we're in the history of the Maths, here's one mail I got today:
 
Originally posted by My inbox

Mathematics Version 2.12


What's new in this update?


* Pi now equals exactly 3.

* e now equals exactly 2.

* Fixed problem where division by zero led to undefined results.

* Fixed spelling mistake in description of Pythagorean theorem.

* Various optimisations now mean that all problems can be solved in polynomial time.

* The term "negative number" has been deemed offensive. The term "non-positive non-zero number" is now in use.

* Various optimisations now mean that all problems can be solved in polynomial time.

* Support is no longer offered for Imaginary Number Feature (i).

* Fixed problem where 1 = .999...

* Now compatible with Microsoft products (65536 <> 65535 <> 100000).

* Fixed problem that lead to the Axiom of Choice being undecidable.

* Implemented L'Hopital's rule for non-indeterminate forms.

* Groups are now required to be abelian; former groups will now be called groupites.

* Fixed the Banach-Tarski cloning glitch.

* Removed the Proof By Contradiction exploit.

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* Basic arithmetic is now complete and consistent.

* Fractals have been smoothed out to improve rendering.

* All matrices are now invertible, former matrices are now called matrons.

* Cantor's dust has been swept from the servers.

* New valid method of proof: Proof by Example.

* All incompleteness theorems are now false. Anything can be proven or disproven.

* The halting problem is decidable.

* Anything can be written as an elementary function if we go far enough in calling something elementary.

* The Riemann Hypothesis is false.

* The Collatz Conjecture is false.

* Calculus now consists of only addition and subtraction.

* Fixed known bug where Fermat's Last Theorem failed to hold for n=1 or n=2.

* Due to customer complaints about other implementations, the natural numbers now start at -1.

* After a successful beta test in category theory, proof by diagram chasing is now applicable across all of mathematics.

* During extended server downtime, problems will now slowly solve themselves, simulating the progress you would have been making.

* Fixed bug where large cardinals failed to show up in certain models of ZFC.

* Mobius Strip fixed to have two sides.

* Infinity has been nerfed to constant value of 1,000,000.

* Negative numbers now use differently colored numbers to reduce confusion.

* All numbers above 3 are now a suffusion of yellow.

* Subtraction has been removed, however it is still available on special subtraction servers.

* New Axiom: Axiom of Clarity. If after explaining a proof to someone for 5 minutes, if they still do not understand, they may use the Axiom of Clarity to assert the existence of a proof that your proof is invalid.

* In response to demand, elegant proofs of certain theorems have been shortened that they may fit into the margins of books as commentary.

* Research has shown that random numbers along a finite distribution were unfairly biased towards the digit one over other digits. This has been fixed.

* We are proud to unveil a new kind of super-calculus, which requires twenty people to complete even the most rudimentary calculations over a period of hours of collaborative work. We feel this new math will challenge those at the higher-end of the profession.

* New, epic applications of super-calculus have been implemented as well.

* "Proof by Wikipedia" is now a valid form of proof.

* Feature: Uniform probability measure for the real line has been added. Expect support for other spaces in subsequent versions.

* For a small monthly fee, all infinite series can be summed. All users will be allowed to use that 1 + 2 + 3 + ... = -1/12 for a trial period of week.

* The math servers are going down soon to make way for the new BioWare math.

* Russell's Paradox fixed - sets can now include themselves and not include themselves at the same time.

* For usability, numbers of the form a+bi have been made less complex.

* All "maths" not involving numbers has been split off into daughter projects so that Maths 2.1.2 can now fit in one brain.

* Everyone finally understands how abbreviations and number work, and now the singular word "mathematics" is properly abbreviated "math" worldwide.
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Posts: 2810 		  Quote Styrbiorn Quote  Post ReplyReply Direct Link To This Post Posted: 05-May-2008 at 13:27
Originally posted by pinguin


Usually my poisson is addressed to the idiology that denies the importance of non-European peoples in the development of the modern world. 

That must be some South American poison then, since I haven't seen it here.
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