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Count Those Numbers
First, I’ll start by describing our currently used decimal system and move on to other basics that might be more efficient and easier for us to use. The ancient or fairly recent origins of each of them will be briefly explained and in which areas of development you can meet them today. Here are some examples of the particular types of challenges that a core system change would face and in which situations you might apply them. Finally, why thinking about issues like this can help you?
The decimal base (10) is widely believed to have been created due to humans counting with the fingers of both hands. The first people estimated to have used the decimal base are either the Elamites (3500 – 2500 BC) in today’s Iran, or the Egyptians (c. 3000 BC). The way we write the decimal base today is naturally called Arabic numerals, but without getting too bored with the origins, it’s time to focus on its limits. First of all, ten (10) is divisible by four numbers, 1, 2, 5, and 10. And of these four divisors, none work really well when dividing or multiplying consistently. Let me explain this better after introducing the following basic system.
The octal base (8) does not contain the digits 8 or 9, but after 7 comes 10. This system has the same number of divisors, which are 1, 2, 4 and 8, but they make more sense in calculation. Here is the expected example, divide the number 10 consecutively by 2. This gives the following sequence: 10, 4, 2, 1, 0.4, 0.2, 0.1 and so on, always cutting the previous amount A half. Now do the same on a decimal basis: 10, 5, 2.5, 1.25, 0.625, 0.3125… and you get the picture. Dividing and multiplying by 4 using octal radix naturally works just as easily. So it has the same number of divisors with a lower base and is easier to calculate. What else is there?
The base duodecimal/dozen (12) is quite intriguing. It has six divisors (1, 2, 3, 4, 6 and 12). By simply adding two digits to the base, you lose the 5, but you gain the 3, 4 and 6. You can find dozens of companies in the US and UK who want to change the world for this number system more applies. However, deciding what the two extra numbers should look like is undecided, A and B, X and E, * and # (as on a telephone) or backwards 2 and 3.
The hexadecimal base (16) is the most widely used in today’s computing world. It stands for color scale and is used in different forms of computer programming. Even music software like trackers use hexadecimal systems and additional numbers are usually displayed from A to F. Naturally, the binary radix is still more familiar to computer people, and musicians also enter different numeric radix with less effort. Ok, the following basic system is the last one I will present.
The sexagesimal base (60) comes to the point that you can discuss whether it is a base or just a multiple of another base. What is particularly remarkable about the sexagesimal system is its age and the way it is still used today. The ancient Sumerians, who can be considered the first people to develop a civilization, originally used base 60 and the Babylonians later adopted it. The base 60 system has a whopping twelve divisors (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60), which leads to an adequate explanation why it is still used today. today to measure the time. We are able to divide the seconds of a minute and the minutes of an hour in so many ways that it explains why the way we measure time has stood the test of time. Pushed further, this base was multiplied by 6 by the Persians to create a calendar of the days of a year. The applicability of the number 360 is still used today to measure the degrees of a circle.
Undoubtedly, there are better bases than the decimal base. The real resistance, of course, lies in adaptation. There was already more than enough media coverage of the supposedly difficult transfer from national currencies to the euro. Then imagine the time and effort required to transform humanity into an octal or dozenal system. The decimal base is so deeply ingrained in today’s technology and in people’s thinking that it might take a generation – to push forward those who are truly stubborn and/or ancient. However, it is not necessary to go so far when we still have our imagination and creativity to use all this information if only to come up with some fun thoughts.
Imagine that you are reporting a financial statement with an octal system. Now, I am in no way suggesting that one should break the law, but consider this. How long would it take for someone to notice that there are no eights or nines? How easily would you notice such a thing? Ok, if you feel legitimately offended by this example, consider pranking someone using this approach. What different ways can you shoot someone’s leg and still mathematically prove that what you did is totally okay? You just calculate differently from others.
Here is another example. I let you decide if this one is more or less practical than the previous one. Imagine that we are contacted by another form of intelligent life. Suppose also that we can communicate with them and they tell us that their population is 100 million. Sure, that seems like a small amount compared to us, but what if they use a quadrovigesimal (base 24) number system? Well, their population in decimal terms is just over 110 billion. So much for that ego boost.
Consider that we’re moving to an octal base and also redefining the seconds and minutes to 100 instead of 60. In decimal that would mean 64 seconds and 64 minutes, so the chronological impact wouldn’t be that noticeable. But then think how difficult it is for 100-meter shooters to beat the 10-second mark again. Would they still cover the same distances? Now you could really grasp what a digital baseline change would bring. All the results and all the data that humanity has stored for so long would then have to be redefined. How’s that for a day job?
Going to an octal or dozen base wouldn’t have to change the way we measure time and degrees or anything else. As stated before, we can always count up to 60 minutes even if the basis is different. This just causes the decimal base number 60 to appear in a different way, still meaning the same amount while retaining its excellent dividing ability.
In conclusion, it seems we are too far down the wrong road to turn around and make a difference. But, as an individual, you can find many creative and intuitive ways to effectively use different number bases for anything you want to accomplish – intentionally creative and productive of course. I hope to hear from you about your efforts. At least we can agree on a certain notion that would have made life easier today if it had been understood in ancient times. The thumb is not a finger.
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