ZERO IN: The number zero developed in fits and starts over thousands of years.
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The number zero as we know it arrived in the West circa 1200, most famously delivered by Italian mathematician Fibonacci (aka Leonardo of Pisa), who brought it, along with the rest of the Arabic numerals, back from his travels to north Africa. But the history of zero, both as a concept and a number, stretches far deeper into history—so deep, in fact, that its provenance is difficult to nail down.
"There are at least two discoveries, or inventions, of zero," says Charles Seife, author of Zero: The Biography of a Dangerous Idea (Viking, 2000). "The one that we got the zero from came from the Fertile Crescent." It first came to be between 400 and 300 B.C. in Babylon, Seife says, before developing in India, wending its way through northern Africa and, in Fibonacci's hands, crossing into Europe via Italy.
Initially, zero functioned as a mere placeholder—a way to tell 1 from 10 from 100, to give an example using Arabic numerals. "That's not a full zero," Seife says. "A full zero is a number on its own; it's the average of –1 and 1."
It began to take shape as a number, rather than a punctuation mark between numbers, in India in the fifth century A.D., says Robert Kaplan, author of The Nothing That Is: A Natural History of Zero (Oxford University Press, 2000). "It isn't until then, and not even fully then, that zero gets full citizenship in the republic of numbers," Kaplan says. Some cultures were slow to accept the idea of zero, which for many carried darkly magical connotations.
The second appearance of zero occurred independently in the New World, in Mayan culture, likely in the first few centuries A.D. "That, I suppose, is the most striking example of the zero being devised wholly from scratch," Kaplan says.
Kaplan pinpoints an even earlier emergence of a placeholder zero, a pair of angled wedges used by the Sumerians to denote an empty number column some 4,000 to 5,000 years ago.
But Seife is not certain that even a placeholder zero was in use so early in history. "I'm not entirely convinced," he says, "but it just shows it's not a clear-cut answer." He notes that the history of zero is too nebulous to clearly identify a lone progenitor. "In all the references I've read, there's always kind of an assumption that zero is already there," Seife says. "They're delving into it a little bit and maybe explaining the properties of this number, but they never claim to say, 'This is a concept that I'm bringing forth.'"
Kaplan's exploration of zero's genesis turned up a similarly blurred web of discovery and improvement. "I think there's no question that one can't claim it had a single origin," Kaplan says. "Wherever you're going to get placeholder notation, it's inevitable that you're going to need some way to denote absence of a number."
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36 Comments
Add Commentthis article doesn't do justice to the concept. I read the first book (no I am not a math nerd, but I like history) and for something we absolutely take for granted, it is amazing the path the world has taken in accepting it as a concept. How this notion's final acceptance developed into things like calculus and the motions of the planets is fascinating.
Reply | Report Abuse | Link to thisZero has played quite a role in making of numerals or at least modern numerals. The modern numerals were based on the Arabic numeric system as indicated by this article. Al-Khwrizm+ laid foundation to modern numerics in Arabic format of course. Not to forget he is the same guy who laid foundation of Algebra and Algorithms to name a a few.
Reply | Report Abuse | Link to thisAn italian book ("La rivoluzione dimenticata - The forgotten revolution" Russo, 2003, Feltrinelli by Lucio Russo) makes a fairly strong case for the use of zero by Ellenistic Mathematicians, including Archimedes, which would have himself defined a decimal notation system equivalent to the Indo-Arabic one.
Reply | Report Abuse | Link to thisI am not sure if it has been translated in English, but the author is a well known Mathematician and Classicist and he marshalls several interesting facts about the advance of Greek Ellenic maths, far beyond of what is commonly held today. For example, the concept of infinity, geometric algebra, mechanics, the use of perspective for mapping and drawing, etc.
It may be interesting to think how the same concept might have arise in very different contexts: religious -astrological in Maya, indian and Sumerian, Scientific - Rationalistic for Greeks and Arabs. The first two "traditional" societies; the latter in the context of a Urban, commerce based society.
Perhaps zero is a number in addition to being a placeholder, as in the progression: -2, -1, 0, 1, 2. Unlike any other number, we are told not to divide by zero. I assume any number divided by zero except zero would give infinity as a result. Perhaps the origin of infinity as a "number" would be an interesting topic. The Greeks proved by straightforward method that there were an infinite number of prime numbers, but they found the concept of infinity scary.
Reply | Report Abuse | Link to thisWhere and when "zero" appeared is one question, but its appearance is one of histories most important as is its meaning; I have no food to feed my child; I have no arrows in my quilt....iniatially the zephr did not denote a number base between -1 and +1, it means nothing at all, a valid perceptual concept, unlike the number 1 which has no meaning in nature; that is, there is not 1 of anything in Universe, ergo does not exist in the structure of Universe.
Reply | Report Abuse | Link to thisFrom the begining there was absolute zero,and from everything thing else arose from what we see know,Zero came first.
Reply | Report Abuse | Link to thisThere is a phamphlet that nicely describes the importance of zero, although fiction, describing two marooned mathmaticians who discover and translate a mathmatical "rosetta stone". It begins: On day zero God created nothing. Then God asks, "I have here one empty set." And following that, all numbers rational and irrtional tumble out. If anyone remembers the title, help!!
Reply | Report Abuse | Link to thisZero was used by Aryabhatta in 490 AD. The soft copy of English translation of written by him known as Arbhartiya is on scribd . The arabian had learnt the present number system from Indians.
Reply | Report Abuse | Link to thisIn Michael Welland's book Sand he suggests zero may have come from the imprint left in the sand after a pebble is removed.
Reply | Report Abuse | Link to thisIt is unfortunate that time and again Westerns want to give the credit to somebody who has not invented/discovered it. Both Zero and decimal systems were invented by Indians and just because Arabs used to do sea trade, it has been taken by them and propagated that. That is why these are called Indo-Arab Numerals. Spectacular inventions and discoveries have been made by Indians Saints. Just search for Vedic (Veda means Knowledge) Mathematics, everybody will be filled with joy of knowledge. If practiced properly, even the dumbest in Maths will be very confident.
Reply | Report Abuse | Link to thisHistory is being misinterpreted and after sometime, this becomes the correct thing. At least from onwards try to do the search correctly and report without any prejudice.
Regards
Ravi Kumar Tenneti
Its more than just a number or a place holder,
Reply | Report Abuse | Link to thisA/0=/A (A divided by Zero equals NOT A) where NOT A is a numberset unrelated to A except at superposition.
The act of dividing anything by zero is not a division of value, it is a disengagement from that which is being interacted with.
I thought Al Gore invented zero.
Reply | Report Abuse | Link to thisI thought Al Gore invented zero.
Reply | Report Abuse | Link to thisI fully agree with Ravi Kumar.
Reply | Report Abuse | Link to thisDevendra Tibrewal
In math we define the result of a/b : the number c for b*c = a. But if b = 0 then 0*c is always 0 and not "infinity" !
Reply | Report Abuse | Link to thisThe concept of zero, as in void, was
Reply | Report Abuse | Link to thisknown in India during the Buddha's
time, circa 500 - 600 BC. Early
Buddhist literature [the Suttas of
the Theravada Buddhist tradition
who's provenance can be traced back
to Buddha's lifetime] is replete
with references to Sunnata, the
concept "void of 'self'". Reading
the descriptions of this in the
early Buddhist discourses [the
Suttas] it becomes clear that the
concept of voidness was well-known;
the Buddha applied this concept to
deny the notion of a "self".
Incidentally, the concept of
infinity [ananta - without end, and
appamana - infinite in quantity]
also appear in these discourses.
Zero as a number was introduced by Mahavira, an Indian mathematician in the 9th century.
Reply | Report Abuse | Link to thisThe decimal system was perhaps the most revolutionary and greatest scientific achievement in the ancient world in mathematics. The numbers in the decimal system were called Arabic numerals by the Europeans, but surprisingly the Arab scholars called them Hindu numerals. Were they really Arabic or Hindu? In this connection it may be mentioned that the languages Urdu, Persian and Arabic are written from right to left but if you ask any speaker of these languages to write any number e.g. 257 he will write the number from left to right. This shows that these numbers were taken from a language which was written from left to right and not from right to left.
Reply | Report Abuse | Link to thisThe number 1,00,000 is called a lakh in the Indian numeral system. 100 lacs is called one crore, 100 crores is called one arab, 100 arabs is called one kharab, 100 kharabs is called one neel, 100 neels is called one padma, 100 padmas is called one shankh, 100 shankh is called one mahashankh, etc. Thus one mahashankh will be the number 1 followed by 19 zeros (for further details you may see V.S. Apte's Sanskrit English Dictionary on the internet by using Google). On the other hand the ancient Romans could not express any number larger than one thousand except by repeating M and the other numerals again and again.
Ref. : http://www.outlookindia.com/article.aspx?262393
Mukul Ojha
As we all know, ancient Rome was a great civilization, the civilization of Caesar and Augustus, but if one would have asked an ancient Roman to write the number one million he would have almost gone crazy because to write one million he would have to write the letter M which stands for millennium (or one thousand) one thousand times. In the Roman numerals there is no single number greater than M, which stands for one thousand. To write 2000 we have to write MM, to write 3000 we have to write MMM, and to write one million one has to write M one thousand times.
Reply | Report Abuse | Link to thisOn the other hand, under our system to express one million we have just to write the number one followed by six zeros.
In the Roman numerals there is no zero. Zero was an invention of ancient India and progress was not possible without this invention.
I Agree 100 with comments from Ravi Kumar.
Reply | Report Abuse | Link to thisI Agree 100% to comments from Mr Ravi Kumar.
Reply | Report Abuse | Link to thisZero is not even a magnitude, much less a number.
Reply | Report Abuse | Link to thishttp://thenewcalculus.weebly.com
You are absolutely correct Ravi Kumar Tenneti. The chronoogy that the West uses for India, has no connection to reality. It is a fictitious chronology originated by Max Mueller . He himself says that no power on earth can determine the age of the Veda, implying he was wrong when he said that the Rg was composed around 1200 BCE. The English historians of India deliberately pushed every date into the AD era, since that would prevent Indians from convincing the world of our higher antiquity. Please read my publications available in Amazon and my latest book on the origins of astronomy, the Calender, and time, that wild shortly be available in Amazon
Reply | Report Abuse | Link to thisIt is not very convincing that zero was being used only in the fifth century. Human history goes quite back. Even if that is the case it is controversial to say it came from a country. The countries and regions existed then was differnt from the modern days. Significant part of Indus valley civilization was in areas other than what we call India now. Great univertsities such as Nalanda was in Afghan area. So is what is these days called vedic math. In case Arya Bhatta, no one cleary knows where was he really born. Aryana was Afghanistan's other name - may be he came from there too.
Reply | Report Abuse | Link to thisYet they named them Arabic Numerals hmmm
Reply | Report Abuse | Link to thisThis is a fascinating article! I don't have much mathematical experience, beyond 30 years as an engineer, but I do know the Japanese flew Zero's in the Second World War.
Reply | Report Abuse | Link to thisIt's why they lost.
Mikrobi was saying:
Reply | Report Abuse | Link to this" In math we define the result of a/b : the number c for b*c = a. But if b = 0 then 0*c is always 0 and not "infinity" ! "
If b=0, that is indeed true for b*c=a ... c=0
but if b=0 in your initial a/b=c ... then c=infinite
So it depends on the choice of which one of the two equations you want to calculate first.
(Just bear with me for now)
So what if both are correct - compare this to sub-atomic entities, they can be measured to be waves or particles depending on what and where and how you are intending to measure.
Let me develop my point a bit further, let's say that 'infinite' stands for all the manifestations of form that can, will, and did exist - an infinite number of forms, and that zero stands for emptiness, that nicely underscores the point I was making that if b is 0 that both
b*c=a ... c=0
a/b=c ... c=infinite
are correct.
This simultaneity ties in with what one of our Indian friends here was alluding to: the form and emptiness problem.
Even before, say Mahavira, one Vedic sage - Avalokiteshvara from the Heart Sutra - tried to come to grips with this, and he discovered that "form is emptiness AND emptiness is form". He is the one who also is credited with discovering the five aggregates: solid, liquid, plasma, vapor, ether (for lack of a better word) and who discovered named the five senses. (It's all in the Heart Sutra.)
There is quite a bit of misguided philosophy based on a misunderstanding of his form <=> emptiness discovery and a misinterpretation of the difference between the notions of senses and sensuality. But let's not go there... If you are interested I did some analysis work on this Sutra (I used a rather surprising and uncommon way to make my his conclusions clear - have fun with it)
http://www.freebynature.org/2007/05/form-is-emptiness-emptiness-is-form.html
Hi Ravi, not sure if you are still actively following this thread. In comment 27 I made a connection to the Heart Sutra which deals with void... actually "form <=> emptiness"
Reply | Report Abuse | Link to thisOn my website I have analyzed "the Heart Sutra" - you might find it interesting
http://www.freebynature.org/2007/05/form-is-emptiness-emptiness-is-form.html
Hi mikrobi, not sure if you are still actively following this thread. Please read my comment 27... It also ties in with some remarks by readers here with an Indian background.
Reply | Report Abuse | Link to thistest
Reply | Report Abuse | Link to thisplease disregard messages 27, 28, and 29
Reply | Report Abuse | Link to thisthis is new to me and i am going to try it out
Reply | Report Abuse | Link to thissurreal numbers by donald E knuth
Reply | Report Abuse | Link to thisIT SUITS THE EGO AND PERSONAL PRIDE TO TRY AND TAKE CREDIT FOR ZERO. AS MUCH AS I WOULD LOVE TO ASSOCIATE IT WITH MY HERITAGE (MUSLIM, AFRICAN, ETC.) THE REALITY IS THAT HISTORICALLY THE PRACTICAL USE OF ZERO DATES BACK TO ANYONE WHOEVER MEASURED ANYTHING. JUDEO/CHRISTIAN ACCOUNTS SHOW MOSES MEASURING TO BUILD AN ARCH. MANY INVENTIONS WERE FOUND DUE TO NECESSITY AND IT WOULD SEEM THAT "ZERO" WAS ALSO ONE OF THOSE ITEMS THAT APPEARED SIMULTANEOUSLY THROUGHOUT HISTORY DUE TO NECESSITY. SOME ACQUIRED IT FROM OTHERS AND OTHERS WHO WERE DELVED IN THOUGHT AND/OR PURPOSE USED THEIR GOD GIVEN MINDS TO GIVE LIFE TO A NECESSARY AND REVOLUTIONARY CONCEPT. BUT, INFORMATION SHOWS THAT NO SINGULAR SOCIETY HAS THE SOLE CLAIM ON "INVENTING" ZERO.
Reply | Report Abuse | Link to thisONLY ALLAH INVENTED THE ZERO.
The origin of 0 in India was to symbolize God. An infinite potential, that is why its round and hollow... When Fibonacci (100 years before Leonardo De Vinci who adopted his ideas of Golden ratio) brought it to Rome, the Vatican opposed its introduction claiming its a foreign idol concept of God. Only by the pressure of Vatican court mathematicians who saw the advantage of it that was allowed.
Reply | Report Abuse | Link to this0 is in perfect balance. a potential. If you put it before 1 (which is a unified concept of human/god, that is you/me), it stays a potential and you stay you. But, if you put it after the 1, it increases your value ten folds and so on...All numbers and letters are symbols originated from philosophical ideas accompanying humanity from prehistory time. Al.
We treat numbers, letters and words with standard everyday approach, not knowing that they all took thousands of years of human believes and experiences to be formed as symbols for philosophical ideas and experiences descriptions.
Reply | Report Abuse | Link to thisI personally believe, that the zero symbolizes god, the total infinite space and potential, to be realized when focusing on the breath which goes round and around....hence, 0...happy breathing to all.