Hi folks,
Let’s continue talking a bit about the magic ingredients the sorcery of mathematics uses and after telling you last week a few things about « zero » and its importance, let’s try today to make a quick and unpretentious (as we always do) overview on numbers.
When it comes to how numbers appeared in human thinking, mainstream (told you our own definition of it in our previous article) mentions the needs of telling apart « more » from « less » which inherently developed further into counting and numbering.
Out of the need, it is stated (making perfect sense, of course) to be able to perform naturally required tasks like dividing food or other resources for sharing amongst family/tribe members or evaluating the chances against enemies.
And that the complexity of the way numbers are understood and used by a culture can be a reliable means of measuring its degree of civilization.
As a proof, Australian aboriginal « primitive » tribes (read: which lived an un-disturbed life for thousands of years) still have no names for numbers even as little as 4 (four).
A BBC documentary released less than a decade ago (in 2005) titled « The Story of 1 » and presented by Terry Jones shows an aged Australian aboriginal from a tribe called the Warlpiri being asked how many grandchildren he has.
« Many« , comes the reply translated into English and he then names each of the 4 grandchildren he actually had by their own name.
« See? Many! » concludes the old man with a disarming innocent smile.
Quite spectacular and certainly convincing scene but is it really so?
An extremely well documented ethno-mathematics study published in 1987 and available on the « Australian Institute of Aboriginal and Torres Strait Islander Studies » website demonstrates the false and misleading assertions in the mainstream linguistics and anthropology literature, which proved to be « curiously persistent » assertions too.
In a nutshell, the author (John Harris) demonstrates that Australian indigenous cultures aren’t low on the scale of human development, that their counting system isn’t mathematically inadequate and that actually they simply reduce numbers’ expressing and handling to a minimum, according to the relevancy requirements of the context.
Their simple way of life doesn’t require « western » precision as a routine and any of them opting for modern education will have no difficulties in handling numbers and understanding their use in sciences.
Moreover, we « civilized » people use similar reducing-to-relevancy techniques too.
Just an example, when big numbers are involved, there is usually no need to know the exact number, the magnitude scale is enough for relevancy (like, for example, billions or trillions).
Also, if having to count a big pile of coins, we don’t count them all like successively: instead, we count them in groups of ten and in the end we count the number of groups and add the remains, if any.
The point of this short digression is (besides repeating our constant advise of always taking everything with a pinch of salt, including our own articles of course, regardless of the efforts we make for information accuracy) that our relationship with numbers might be even more mysterious and deeper than already known it is.
And humans don’t appear to be the only species dealing with numbers; animals have (or must have, given their behaviours and habits) a sense of numbers too, at least for keeping track of their offspring for instance.
« Instinct« , one might argue, but instinct -at least for now- is the name of a blackbox: we have no idea what’s inside.
But if someone will crack it open and find numbers, it surely won’t be much of a surprise.
So we can jokingly say that « numbers » are things that make us « numb« .
The material evidence we currently have on earliest numbers handling consists in animal bones clearly carved with non-trivial structured markings, such as the Lebombo bone (cca. 35,000 BCE) or the Ishango bone (between 9,000 and 6,500 BCE).
Both are Baboon fibula bones and are considered ancient mathematical artifacts although their purpose as tools is still unclear.
A major breakthrough in the history of handling numbers was replacing markings with tokens (like pebbles or little rocks).
As modest as it may seem, this modification was a huge step ahead for at least three reasons: it allowed visualizing substraction (by removing items from a group), division (changing the grouping of items) and allowed creation of imaginary shapes like triangles, rectangles and so forth.
Actually, the word « calculation » comes from the Latin « calculus » which meant « pebbles« .
This original sense of the word is still kept today in medicine: « renal calculi » are « kidney stones« .
The more complex human societies grew, the more complex the quantification systems became and along with it, spoken and written words and numerals developed.
Historical development lines among cultures are « the usual« : Sumerians, Babylonians, Egyptians in the Middle East, Greeks in Europe, Maya, Inca in Southern/Central America and Indians (Hindu) and Chinese in Asia.
With a very special mention for the Hindu: it’s the civilization that spawned the concept of « zero« and the simpler writing of numerals today known as Arabic but from which the Arabic numbers writing actually derived.
But Hindu contribution is even bigger than literally changing the world with « zero » and numerals: their religious concepts of Nirvana and eternity were highly abstract therefore requiring highly abstract tools to help describe them.
Such as extreme numbers.
Have you ever heard of « rajju« ?
Well, the « rajju » is a unit for measuring space, basically being the distance covered by a deity (a « deva« ) flying for six months.
Sounds familiar?
Of course it does, it is similar to nowadays space measuring unit we call « light-year« , except the « rajju » is lots of centuries older.
But they had other measurement units, too: the time measurement unit named « palya » is the time required to build a 10 kilometers cube out of lamb’s wool by laying one strand of wool every century.
And that’s just a mediocre unit of time if compared to the « Paramanu » (cca. 17 micro-seconds) or the « Maha-Manvantara » (311.04 trillion years).
Brahma scriptures weren’t the only religious primary cause to push maths forwards: the development of fractions’ calculation seems to have its roots in the Koran (or Qur’an) which teaches Muslims how to divide the possesions of a deceased person among its relatives.
Unlike other religions (such as Christianity of the time) women too were to inherit part of the belongings but with lesser shares, so in order to strictly comply with the religious prescriptions, fractions were a must.
Fractions reached the required high degree of sophistication in the Muslim world thanks to the Hindu numerals which the Arabs imported, developed further and perfected to also give the world algebra and algorithms besides the equally important contribution that calculating fractions is.
Later on, in the late 1600’s enters the scene of numbers the German mathematician Gottfried Leibniz whose major contributions to mathematics includes the description of the binary system, published in French as « Essai d’une nouvelle science des nombres » (« Essay On A New Science of Numbers ») to mark his election in the French Academy.
The binary system, the « 0 » and « 1 » simplest of them all, the « all or nothing » system is what makes the world go round today.
We cannot finish without mentioning « constants », quite properly named so as they reflect never changing proportions (now that’s a really impressive concept!).
Such as « Pi « , the ratio between a circle’s circumference and its diameter (if you’re obsessed by it, get ready to celebrate it soon).
But there are many others too, among which there is one crowned as « The Golden Ratio« , the number that Western thinking seems to have established as borderline between arts, sciences and religion.
All in all, we humans-as-species continue our amazing advancements towards big numbers in the Macro Universe as well as towards small numbers in the Micro Universe.
But paradoxically, either directly or indirectly everything is carried out by each of us, humans-as-individuals, whose lifes are inexorable dictated by numbers: our lifes are limited by the numbers of our financial earnings, needs and status, we’re merely a number if asked about the social security identification or the adress of our home or the license plate of our cars, we’re numbers when using our phones or, when using the internet, we’re our IP and MAC numbers.
Sorry for the deviation, folks, we just weren’t sure whether we control numbers or they control us!
But hey, we’re not in the philosophy business anyways, so let us exclusively reveal for you our internal way of quantification and measurement units:
-the « loic » – 1 « Loic » equals to Nirvana, the perfect hapiness, satisfaction, absolute fullfillment in the cult of the things well done.
This is an ideal value which can be only asymptotically tended to but never possibly (and actually) be reached.
-the « orpalis« : – 1 « Orpalis » is a measurement unit for striving.
For example: if you strived for about 1 million « orpalis » to do things right, you’ve only reached a value of 0.1 Loics.
So you didn’t strive enough.
OK, you’re forgiven. But just keep on striving.
-the « elodie » – a measurement unit for compliance with the Company.
It measures results expressed in « loics » and « orpalis » and -based on the results- it either kills you or saves you.
-the « cedric » -a realistic number value meant to connect the ORPALIS team to the real world.
The « 1 cedric » value cannot be exceeded because otherwise the « 1 Loic » value might be reached, which case, by definition, is impossible.
Quod Erat Demonstrandum.
See you next week, folks!
Bogdan