30Oct

The History of Counting

From a very young age, children are able to distinguish between there being none of something, one of something, two of someting, and most times three of something. But when we grow older, we need to count higher than three- in fact, we are almost always using numbers in our daily lives, from balancing our checkbook to checking the time. But what about those “numbers”, as we call them? Where did we get them?

The first counting systems

When we are children, we oftentimes use our fingers to help us figure out what addition and subtraction problems solve to, or to keep tallytrack of something. (As we shall see, having ten fingers makes a profound impact on our numbers today.). Of course, if you need to keep track of something very important, like say, how many deer your hunter-gatherer had killed, you don’t want to perpetually hold out three fingers for your three deer (Plus, how can you hunt like that?). So people invented the “Tally System”, which is still in common use today. In this system, you make a small vertical line for one unit, then another next to it for the second, and so on until you reach the fifth- which crosses the other four. You then start a bit over on the next set of five. This turns out to be a great system for keeping track of a small number of objects over time when you may need to add another at any time. Of course, as any of you that have used the tally system in grade school will know, it quickly becomes unwieldy to repeatedly count several thousand tallies.

Count like an Egyptian

As a very early and successful culture, it makes sense the Egyptians would have one of the first written numeral systems. Starting in about 3000 BC (Over 5000 years ago!), Egyptian Scribes started using a modification of the Tally system- you would write one line for one, but ten (ten fingers, so ^ means ten) was represented by a “^”. This was a large improvement, especially after the Egyptians added more signs for larger numbers. Hence, you could easily write “lll^^” to mean “23″, much easier than writing 23 tallies! Of course, like the tally system, it can get very unwieldy quite fast, and its hard to do multiplication or other operations on it.

Babylonian Base 60

We use a “base ten system” in our modern Arabic Numeral system- meaning that after 10 we count another place value and start over, so you count …8,9,10, and then 11,12 and so on. Now the Babylonians had a different system- the base 60 system! Imagine, instead of having to learn one sign for each of 10 numbers (0,1,2,3,4,5,6,7,8,9), you would have to learn 60! different symbols! Of course, that’s a quite unwieldy number of signs to learn. The Base-60 system still survives today, however- Ever wonder why there are 60 seconds in a minute and sixty minutes in an hour? It’s because of the Base-60 System!

Early counting in the Americas

While the Egyptians were developing Base-10 and the Babylonians experimenting with the odd Base-60, the Maya and Inca in the newmaya counting world were working on their counting. The Maya had a odd base 20 system, with dots “.” representing one and dashes “-” representing five, with another sign for 20 and so on. If you compare it to the Egyptian system, its much similar, with different signs for different symbols and simply stringing the sum together to make a number.

The Inca, however, were using the almost certainly strangest counting system ever, the Quipu. The Quipu was a string of rope, with smaller strings hanging down from it. The number was encoded on the Quipu by knots in the string- and different types of knots meant different digits, with there place on the string representing their place value! A very strange system, for sure, and one that has just recently been decoded.Imagine if YOU had to submit all your test problems as stacks of rope with knots in them!

The Arabic (Decimal) System

Interestingly enough, the system that most of us use today and have come to know and love is in fact the Arabic system. The Arabic system made fantastic strides over ALL previous number systems (and at least one that was yet to even come about), by using ten arabic counting historydigits- 0,1,2,3,4,5,6,7,8,9- in order from left to right with their position denoting place value. With this system, its insanely easy to write large numbers- Just string together “102″, whereas with the early Egyptian method that’d be the unwieldy “ii^^^^^^^^^^”! Imagine if you were a pharo trying to count your goats- Try writing 30,000 like an egyptian! Not fun!

In addition, the Arabic/Decimal system offers another great advantage- it is very easy to do math with it. Try just figuring out how to go about doing a multiplication problem with the Egyptian method compared to our simply Arabic system. The Arabic system was invented around 300 BC and quickly spread outwards.

The Roman System- Obsolete from the Beginning

Many of us have seen “Roman Numerals” before, like on a coin or dollar bill (Look at the bottom of the pyramid on the back of an American $1 bill!). You’ll notice that they use letters, such as I, V, X, L, D, C, and M to denote their numbers. Weird, huh? Now, take into account that the Roman system was invented in 300 AD- over 600 years after the Arabic system. Considering that the Arabic system is superior in all regards, why would anyone use this horrible roman version? Mainly because the Arabic system hadn’t gotten to Rome yet. In its basic form, the Roman system used letters to denote numbers (I for 1, V for 5, X for 10, L for 50, C for 100, D for 500, and M for 100). The letters were arranged in order, with the largest first, then adding together like in the Egyptian System. So 2001 would be MMI, and 2002 would be MMII, etc. But for numbers close to a few less than the number before it, you’d put the smaller one beforehand, meaning subtraction. Hence, 1,2,3,4 would be I, II, III, and then IV- IV meaning five minus 1, or four.

Look at that dollar bill again, see the numerals? It reads MDCCLXXVI- or 1776, the year America was formed. Now, you decide, what’s easier to write- 1776, or MDCCLXXVI?

Modern Systems

Now days, as you’ll surely have noticed, the Arabic system has beaten out the Roman Numerals to reign the supreme number system- or has it? Sure, we use the Arabic system for most of our daily life, but the Computer that we use everyday for almost everything uses a different system- the Binary System.

Binary

The Binary system, unlike our Arabic system, is base 2- there are only two digits, 0 and 1. It is used all the time for computer programming. In fact, this webpage you are reading is stored as binary, sent across a wire as electronic signals, and then turned into a page by your computer.

The Binary system works from right to left, starting with 20 as the first digit, then to the right 21, 22, and so on. A 1 in any spot denotes that you count the place it is in, a 0 means it does not. So “10″ means 2- the 1 means you add 21, or 2, but you do not add the 20. Hence, the number 13 would be written as 1101- or 8 (23)+4(22)+0+1(20). So even though we use the Arabic system in real life, our computers are only thinking in 0′s and 1′s!

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