This week we are going to tell you a few words about the history and importance of… nothing.
Well, not quite of “nothing” really… more like about the notion of “zero” actually.
But we’ve allowed this introductory half-joke because it’s the nothingness the concept of “zero” expresses that stopped it from entering the Western civilization for many centuries.
Mainstream has it that the notion of “zero“, although having some (as of today, still) unclear roots eversince Sumerians then Babylonians (as usual…) and then Maya some time later, it was actually clearly defined and used as we do it today by the Hindu.
You know what mainstream is… it’s the voice imposing the general current of opinion proclaiming the absolute truth until the next absolute truth comes up to replace it but hey, let’s stick with it yet still keep in mind its evanescence for now.
So the idea here is that “zero” can be both a punctuation mark as well as a number in its own rights and that Sumerians/Babylonians and the Maya seem to have used it just as a punctuation mark, not as a number.
In other words, they only used some kind of “zero” sign as a symbol, to easier tell apart like one (1) from ten (10) from one hundred (100) similar to, for instance the today’s quite popular way of designating thousands by the letter “k” (for example, write 175,000 as 175k).
But the real deal was crowning “zero” as a Number and this idea proved to be, at least during early ages, a rather philosophic matter and an almost impossible one to digest too.
And digestion it is all about, as numerals served to express the amount of existing objects, especially the digestable ones like one having 5 sheep or a dozen of units of grain.
And those having no sheep or no grains expressed the absence of these items as a notion associated with the items, not by of using a concept meaning “nothingness” or “emptiness” or “void“.
The problem of expressing “nothing” as “something” wasn’t an easy to solve puzzle for humans, even for the brightest ones such as Aristotle, who believed that zero was -like infinity- a concept related to numbers but by no means an actual number itself.
Because basically, thought the genious from Stagira, you can obtain any number by means of dividing a bigger number.
But not “zero“: if one takes any number, as small as wanted and divide it by any number as big as wanted and keep doing this on and on, at the end of all eternities, what one will get will still be a number which is not zero.
Not exactly the most constructive approach but really nice touch though, Ari!
So here we are in India in year 628 of our common era, where the Hindu astronomer and mathematician named Brahmagupta, among other important contributions to mathematics (algebra, arithmetics geometry and trigonometry) and astronomy, wrote a book titled “Correctly Established Doctrine of Brahma” (“Brahmasputha Siddhanta” in Sanskrit).
Such a fair title to such a crucial book, which correctly established the concept of “zero“, of negative and positive numbers along with rules to manipulate them, rules to determine square roots , methods of solving linear and quadratic equations as well as many other important contributions.
Well folks, in our article about our MICR engine demo release we’ve told you that modern bank checks originate from both an etymological and a functional point of view from the Arabs, which thanks to it were able to easily practice commerce at intercontinental scale.
One of their most important routes was of course India, land of spices and other goodies but it is their merit to also have imported works of Brahmagupta besides the more tangible, exotic items, without being bothered by religious formalities, like the name of “doctrines of Brahma“.
Instead, their mathematicians based their numbers on the Indian system and further developed it to such extend that very soon, a mathematician from Baghdad named Muhammad ibn Musa al-Khwarizmi was the first to work on equations that equaled zero, in a treatise titled “Kitab al-Jabr w’al-Muqabala” (“Rules of Reintegration and Reduction“).
The “al-Jabr” part of the title gave its name to the entire domain of mathematics which we nowadays know as “algebra“.
And, as the genious scholar had also developed quick methods for multiplying and dividing numbers, they got to be known as “algorithms“, deriving from his own name, al-Khwarizmi.
It is also a Muslim merit that all this precious knowledge (along with the Arabic notation of numbers, to begin with) reached Europe thanks to the major civilizing influence of the Moor conquest and ruling over the Iberian peninsula.
This is how an Italian mathematician named Leonardo of Pisa (better known today as Fibonacci) got to learn about the arithmetics based on Hindu-Arabic numerals and, understanding its importance he went on traveling across the Mediterranean to deepen his studies under the guidance of the leading Arab mathematicians of the time.
After getting back to Italy he synthesized everything he had learned in a book (as of 1202) titled “Liber Abaci” (an approximative translation would be “The Book Of Calculation“, as the “abacus” was a tool used for calculations).
The book also explained the practical advantages of the Arab numerals system over the Roman numerals that were in use at the time and had a profound impact on European thought over time.
Not really a surprise, bankers were among the firsts enthusiasts due to the ease of calculating interests, currency conversions and bookkeeping.
But don’t make the mistake of jumping to the conclusion that adoption of this system was some kind of instant success.
The Catholic Church as well as governments of the time were dark-minded so, given the Muslim provenance of this knowledge, they simply prohibited it by law.
Despite this, due to its obvious practical advantages, the Hindu-Arab system continued to be used clandestinely which explains why the Arab word “sifr” (meaning “zero“) from which today’s word “zero” originates, is also the origin of the word “cypher” via the French “chiffre” which even to our times designates both numerals and encryption.
Later on, the objective advantages prevailed and this is why the Western world still uses to our days the Roman letters for writing words but the Arab numeration digits for writing numbers.
And in time the Catholic Church opened its minds too, so nowadays Jose Gabriel Funes (we’ve mentioned him in our first article about calendars) the jesuit director of the Vatican Observatory expressed the official position of the Vatican regarding alien life admitting the possibility of existence of extra-terrestrial intelligence.
The next important mathematician to use “zero” was the French scholar René Descartes, inventor (among others) of the Cartesian (‘Descartes‘ in Latin is ‘Cartesius‘) system of coordinates whose origin point is where x=0 and y=0 (and z=o too, in the spatial 3D model).
Finally, in the 1600’s, Newton and Leibniz independently developed the modern calculus (the mathematics of change) in which the concept of “zero” and its understanding are crucial.
The importance of modern calculus (and therefore of “zero“) is tremendous; just as a mere example physics, engineering, modern economics and finance wouldn’t exist without it.
Mathematics is the real universal language, it is present everywhere and with it comes “zero” as one of the fundaments of human thought, despite the humble “nothingness” it expresses.
Even the simple reading of this article would be impossible without the concept of “zero“; the binary system is a matter of zeroes and ones (“0″s and “1”s, to put it the Arabic way).
But “zero” is important for yet another reason: it designates the exact amount of money you, folks, have to pay for PaperScan Free Edition, PDF Reducer Free, Virtual Barcode Reader , DICOM Viewer and the MICR engine demo.
Or for a completely functional 30 days evaluation of GdPicture.NET SDK or of the PaperScan Home or Pro for that matter.
Niente! Rien du tout! Zero! Nada!
See you next week, folks!