Why Modern Math base Ten?

Question

Please, do not tell the story of Humans fingers or Sheep, it was very old theory.
Tell in modern Science.
http://www.geocities.com/numerals1234

Answer 1

Most newly-discovered mathematics is done in all bases, not just base 10. Theorems of isomorphisms and fields and sets are meant to work over any consistent number system, but I don't believe that's what you're talking about when posing this question.

Modern science does little to answer why we use base 10. Modern science (applied mathematics) would tell us to use binary, with hexadecimal as a way to express numbers more easily. Why write out 1001100 when 4C will do?

No, the reason modern math is done in base 10 lies more in history than it does in science. It's easy to look back and see other bases used... the Babylonians used base 60, the Mayans and many ancient European cultures (including the Greeks) used base 20. You also have to admit that human fingers is a very good reason for using base 10, as much as you say you don't want to hear it.

Base 10 is used because it's the cash language, so to speak, of numeracy. In speaking, reading, and writing, the cash language was Greek 2000 years ago. 1700 years ago it was Latin. The argument today is that the cash language is English, which is why many Americans who speak English only don't bother learning other languages, but why many from other countries find it necessary to learn to speak English, but I digress.

2000 years ago, as I said, the cash language was Greek. Greek was read and written by anyone trying to express themselves at that time (as an example, each of the books of the New Testament were written in Greek).

As the Roman Empire and the Catholic church took over the western world, things were changed to Latin. Roman numerals (based on 10's and 5's) were very difficult to compute, though, and mathematics was not terribly important to the Romans except for taxation. To stress this, name one (just one!) Roman mathematician. You can't. They didn't study it. The closest person you can claim to have been a Roman mathematician was Boethius, but he didn't discover any new maths at all... he merely translated others' work from Greek to Latin.

The Roman Empire crashed and Europe was steeped into the Dark Ages. There was almost no new studies in mathematics for 1000 years. The only folks doing math at all were in Asia... China, India, and Arabia.

Enter Al-Khowarizmi, ca. 800CE. He was responsible for all math the way it's presented to students in grades 1-9 today. Not only did he invent a process for solving equations (algebra), but his work helped popularize the Hindu-Arabic base 10 place-value system we use today. The symbols and terminology were easy to understand. Algorithms for computation became modernized for the day, and they've improved since. By the time Europe was coming out of the Dark Ages and its scholars finally ready to again discover new mathematics, anything recently (within the past four centuries) written was all done in the base 10 system; they had to learn it or not study maths at all.

Sure, there are still other number systems used... you can look to China and Japan or to any computer geek for examples. Even so, they also learn the Hindu-Arabic numerals and the base 10 place-value system because it's the cash language of the day. It would be difficult to buy and sell things to other countries in the world if no one understood the numbers involved.

Answer 2

Sorry, but I think the basis may well be the fact that we have 10 fingers/thumbs. The common number base is pretty arbitrary, and it is unfortunate that we insist on using 10 (since it makes doing calculations with numbers like 7 or 9 almost impossible without computational power).

FYI, to those who answered saying that "It is easy to divide/multiply by 10", it is easy is BECAUSE we use a common base of 10.

Regarding binary/hex/octal (used heavily in computer science), these are number bases chosen for logical and compelling reasons:
- Binary is the first number base which allows a structured representation of a number using more than one symbol. This means that we can represent any number up to a certain point with a given number of bits. (I'll get back to this point). Binary also lends itself to representation with transistors, magnets. pits (in optical media) or electrical impulses (i.e. the basis for most of our current data storage and transfer mechanisms).

Regarding the concept of using a set number of bits to represent any number in a finite set, this is important because it allows the structure required to manage this in hardware. It is more practical to represent a number using a combination of 0's and 1's than it is to just use 1's (i.e. base 1), because the length of the number would change less often. For example:

Base 1 (don't forget, we can't pad out the number with leading zeros, because in base 1, there is no 0):
1: 1
2: 11
3: 111
4: 1111

Base 2:
1: 0001
2: 0010
3: 0011
4: 0100

Unfortunately, binary numbers are impractical for humans to read, write and memorise. This is why octal and hexadecimal are used; their number bases are exponents of the binary number base (2). Hexadecimal in particular is very good for representing binary data, because one hex-digit can represent precisely 4 bits. You can translate hexadecimal numbers to binary and back, segment by segment; this is not possible when attempting to convert decimal numbers to binary.

As for octal, I've never used it much myself; it may have been used as an alternative to hexadecimal because it only requires digits, not characters, but this is just a guess on my part.

So, to summarise, I don't think there is a good reason that we use base 10; however, it would be difficult to change (very few people even understand the implications of using a particular number base, as other answerers have illustrated here). But there are other number bases in common use today, which were chosen for good reasons.

Answer 3

cause we have ten fingures in hands. so it was easy to make a base 10. It would be very difficult to count making base 11 or 9. In some languages the base is 20

Answer 4

Computers operate in base 2 (binary system, Boolean Algebra). That's modern math, too.

Answer 5

because ten is easy to work with, mutiply by 10 get add another zero. Times it by a number just put the number there in front of the zero

Answer 6

It came from a place of convenience, i.e. fingers, toes etc., but now that it's here, it's probably no better or worse than any other base.

Answer 7

Then take off your shoes and socks. Count your toes. Substract (SIC. I'm just quoting what one of my college professors used to say for subtract) 3.