Aww yes, the days are rapidly growing cooler and shorter here at DarkSyde Manor. The winter solstice approaches, that important day of reversal celebrated around the world and through all time for as long as humans have been keeping calendars. And like most of you, 'round this time of year, in these here parts we start thinking about turkey and gravy, eggnog and homemade pie, and breaking out the obligatory fat pants that inevitably goes with them.
Of course, no Thanksgiving would be complete thinking about what we're actually thankful for. Normally I'd mumble some platitudes while thinking to myself I'm thankful as hell I don't live back when this American custom originated.
But if truth be told, outside the health and happiness of those of I love, mostly I'm thankful for technology. It is that technology that brings us together at the Daily Kos; binds us as an Internet tribe; huddles us virtually with the monitor playing the campfire; keeps us swapping stories around the ancient circle of humankind. And strangely, none of that would be possible, if not for thinking about nothing.
One of the more pleasant jobs I've had in my life is that of math and science teacher. And whenever I had a chance, I'd try to get the students mentally 'into' the topic, preferably before they've been sold on the idea that math is useless or 'hard work'. Math is abstract of course, and a great way to demonstrate it is to ask the students to show you a
number, say number three for example. Of course they write one, but that's not a number, that's a
numeral, a symbol for three. And we can designate any symbol we want, but there is only 'one' number three. They might try to show you three of something, or define it as a sum, some of the more advanced ones even point to it on a number line. All good answers, but it's a trick question designed to stimulate the burgeoning young mind: There is no number three, except in our heads
Pretty quick they get the idea: Numbers are abstract things. You can't see them, taste them, hear them, or feel them; and yet they 'exist'; they exist in the abstract. We could after all pick any symbol, any squiggle or combos of squiggles, to stand for three. In times and places in the past, numbers have been represented by specific knots in string or beads on wires, and probably a lot of other inventive ways we have no record of.
The reason we teach kids about numbers and arithmetic, and the whole field of mathematics, isn't because we adults are sadists, but because it's useful as hell. But of course, some symbols and ways of arranging them, called notation in mathematise, work better than others. Using the symbol "X" for !!!!!!!!!! is more convenient and using the symbol "M" for a thousand such marks is better still! That's what the Romans did, and most other early mathematics worked the same way.
Each and every number had its own symbol, or it was a combination of existing symbols, lots of them. Romans wrote the number three as, simply, "III", but the number four was IV where V stands for five. Thirty was XXX but forty was written XL where L is fifty. C was one-hundred, D was five-hundred, and M was one-thousand. And if a bar is placed over the top of the numeral it means to multiply the underlying symbol by one thousand.
The problem with that type of system is that if you want to add or subtract, multiply or divide, it becomes a big hairy mess! It is so complicated that specialized professionals had to be trained to do it. That means they had to memorize huge arrays of sums and products and quotients. Because, unlike the numbers we use today, Roman numerals have no columns. It's hard to imagine, because we're so immersed in our numeral system, but think about it:
If you want to add 18 and 19, we write it as:
18
+ 19 and we then add the 8 + 9, get 17, write the 7 down, carry the 1 ... to get
37.
No problem, right? Well, in Roman numerals that same sum becomes:
XVIII + XIX
It doesn't do any good to arrange them on top of each other because there are no columns to add up. You just basically have to know, that is memorize, that XVIII + XIX = XXXVII. If you have a sum you don't have memorized, there is a long convoluted way to go about it in Roman Numerals, it's almost faster to take two sets of rocks, count out each sum, put them together, and count them up.
If you think addition is time-consuming or ugly, multiplication and division are a nightmare in Roman numerals. And when it comes to fractions, the Roman numeral notation was pretty useless. They just used a word for the fraction, two-sevenths was "duae septimae" and three-eighths was "tres octavae." So arithmetic in fractions was another time consuming, dull chore.
What that all meant was that Roman clerks had to memorize huge tables of sums, differences, products, and quotients, and they had to have the ability to work them out for combos they didn't have memorized-- a chore to say the least. You begin to see why the priesthood in these early cultures was about more than simply religion. Between memorizing all the symbols, the rules, the tables, and the methods, it was the mathematics and written language think-tank of the time!
That's all well and good for priests who have the luxury of time to set around and learn this stuff, but the shopkeepers and ordinary citizens in the marketplace are busy making a living, or making war, or being repressed (Help! Help! I'm being repressed!). It would be nice to have a quicker way to keep track of whether or not you're being cheated in a transaction; one doesn't have time to whip out an expensive papyrus scroll every time one is buying olives or wine and cipher for an hour or two. Lets see here ... XIV baskets of olives, VIX jugs of oil, and III and una septimae barrels of wine, all for the low low price of septimae aureus, tres denarius and octa serstius ... is that a deal or a rip off?
That just wasn't going to work. So among the 'commoners' all kinds of shorthand mathematical notation developed, usually shunned by the priest class as being unfit for their lofty intellects, but awfully useful to the illiterates, the children, the dimwitted, or the unschooled. And one of those shorthand, ad hoc systems stumbled onto two key abstract properties both of which are absolutely essential to almost every application of modern technology today.
First, in that system there were names for every number, one for each of the first ten natural numbers, and after that they just repeated over and over in different combos all the way to the grim end of infinity. And sooner or later symbols were standardized for the new notation which may have first looked something like this:
They're called Arabic Numerals because they drifted into the West by way of Persia and Arabia; modern day Iran and Iraq. Despite the name Arabic, they seem to have originated in India as best historians can discern, perhaps as early as 500 BC.
The second advance came almost a thousand years later and it seems obvious to us, but the idea eluded mankind for a long time. That of course is the symbol for zero. Why would anyone even need a symbol for nothing? Nothing isn't worth anything, nothing doesn't have to be priced, nothing doesn't have to be taxed or bought or sold, there is no important dates or anniversaries on Day Nothing; so it may seem obvious to us, but really, it's not like the need for a zero was shouting out in the market place or hampering the priests keeping track of dates or tribute for the Rulers.
But of course the zero makes the whole Arabic Numeral system work, it allows us to hold the place, making the symbol for eleven and one-hundred one, different. More importantly, the placeholder system takes a tremendous burden off our shoulders in all kinds of arithmetic, it does a lot of the work for us. It breaks down every arithmetic problem into a series of one digit operations by column, and once we memorize those, we can add, subtract, multiply, or divide, any set of numbers no matter how large they are! It's as big or bigger an improvement as the phonetic alphabet is over pictoglyphs.
Even more amazingly, the Arabic system gave us both fractions and decimals which work by the same set of arithmetic rules as the whole numbers, and that lets us calculate all kinds of hairy problems that would have taken an ancient priest hours, if they could have done it at all. Without that advantage, advances in every branch of physical science throughout the Renaissance wouldn't have been possible, or would have been greatly retarded. The discoveries of Da Vinci, the Galilean Laws of Motion, the work of Kepler, all of it and much, much more, would probably not have happened when it did. My guess is we'd be struggling with these questions right through to this very day without the arabic numeral system and the zero.
And as if all that isn't useful enough, we get scientific notation on top of it all, which also operates by the same or closely related arithmetic rules, and gives every child the power to work with the most infinitesimal and infinite magnitudes of nature.
The real value of this numeral system came to play in England around the year 1666. There in the countryside, an eccentric, brooding supergenuis would never have been able to develop the "Theory of Fluxions" without being able to manipulate quantities approaching zero or infinity, if not for the existence of the Arabic Numeral system and the all important zero. In that case, Isaac newton could never have developed The Calculus when he did.
Today, in our modern world, almost every engineering application you can think of relies fundamentally on calculus for solving design and production issues, finding optimal points, reducing risk, raising safety and reliability, you name it. Aeronautics, rocketry, chemistry, thermodynamics, as well as finance, geology, medicine, and biology, all use calculus at one time or another, because they all use numerical data at one time or another involving related rates. OTOH the same could be said for ballistics, design of gun and cannon, bomber aircraft, explosives, fission and fusion bombs, etc.
And of course without the arabic numeral system and the zero, and the calculus it allows, the study of magnetism would never have progressed so rapidly. Just finding the charge on the electron, The Millikan Oil Drop Experiment, involves some mighty precise averaging of some very tiny fractions. No Theory of Electromagnetism which means no electronics, no solid state devices, and no integrated circuits. And that means no vaccuum tubes, no transisters, no flip-flop logic circuits and binary machines; no computers, no Internet: No Daily Kos.
Which is why this year I'm thankful for the zero, without which I probably wouldn't be alive and I certainly wouldn't be able to post this article here. So to those nameless Indian shopkeepers or whomever thought it up, thanks for the Arabic Numeral system. And most importantly of all, thanks for nothing!