Is Abū ʿAbd Allāh Muḥammad ibn Mūsā al-Khwārizmī Dead?
Date: 27 Jan 2007 19:46:03 -0800
Message-ID: <1169955963.472306.65720_at_j27g2000cwj.googlegroups.com>
Abū ʿAbd Allāh Muḥammad ibn Mūsā al-Khwārizmī died in 850 AD, leaving a significant contribution. He is often called the Father of Algebra. His publication in 825 of "On the Calculation with Hindu Numerals" was a significant industry milestone. Its translation into Latin in the twelveth century introduced the BTen system of numbers to the West and started a firestorm of marketing hype. This was picked up by academics and also the commercial concerns, aka "Big Math." Now this system has reached the point of being enshrined as gospel. When I began my investigation into arithmetic, I was taken in by this pairing of BTen with theory. But it's really not proven at all!
I prefer an alternative system of numbers. This system was used for centuries, with great success, by the most powerful civilization on Earth. But once al-Khwārizmī published his paper, we discarded this system simply because BTen purported to have a better theory, without examining what was good about the old system.
I am speaking of course about RN.
What is RN, you ask? Why, it is simply a system of numbers, much like BTen, but without the arbitrary constraint that each digit represent exactly ten times the digit to its right. Instead, each digit can flexibly be used to represent any quantity whatsoever. This lets us choose digits in a more natural way, akin to how we use human language.
For example, consider the quantity "one thousand." In RN, this number is written simply "M" where the same quantity would require *four* digits in BTen. Many familiar numbers can be represented in RN by a single letter, such as five, ten, one hundred, etc. (V, X, and C respectively.)
Of course, these days we have very different calculating requirements than we did in al-Khwārizmī's time. A polynomial is very, very different now from what it was more than M years ago. If nothing else, the rise of XML and the Web and their tremendous success should make us go back to first principles and consider whether it might be time to revive what was once, for centuries, the dominant numeric form. In particular, the fact that XML uses *text* tags, represents everything as character strings, and discards the straightjacket of rigid, well-defined schema should make us consider the value of a number system that represents quantities as strings of letters without any fixed base.
Now, I am not saying that BTen doesn't have its place. In fact, using a fixed base might be appropriate for some applications.
For example, the Intel corporation, while normally in bed with Big Math, actually uses a BTwo system internally in the logic of its Pentium processors. This is probably fine since end users don't have to look at it! You can have a system which builds the higher-level logic of RN on top of it. Although I can't help but remember the Pentium bug, which occurred despite the alleged superiority of fixed-base arithmetic. I looked, and could find zero empirical evidence of any RN-based CPU *ever* having a comparable failure. Perhaps this is just the sort of thing that happens with fixed-bases.
But this sort of failure is easily dismissed by those following the religion of al-Khwārizmī. They would rather not see a head to head comparison of their system with RN. When I propose to them that we should consider teaching RN to new students because it is better and more natural, they don't respond with mathematical proofs. Instead they just call me an idiot and say I don't understand the basics of arithmetic. Where is the science in that?
What I would really love to see would be a big industrial study comparing programmer productivity with long-term use of RN and BTen. I have searched for one but I haven't found anything. You would think that if BTen were as superior as it is made out to be, that sort of thing would be out there, but it's really not in the best interests of Big Math. Instead they continue to focus on indoctrinating each new generation of students in BTen, to make sure they have enough trained workers as necessary to operate their complex products. Of course, if we used RN, we probably wouldn't need so many of them!
My advice is simply this: cast off your rigid notions of what a digit can be! There's no mathematical *proof* that says we must shoehorn a limited set of numerals into each position. al-Khwārizmī is truly dead, and we can now begin the arduous task of trying to undo the damage done by the over-literal acolytes of the "Father of Algebra." Note the masculine.
Marshall Received on Sun Jan 28 2007 - 04:46:03 CET