marshall

Abū ʿAbd All�h Muḥammad ibn Mūs� al-Khw�rizmī 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-Khw�rizmī 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,


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-Khw�rizmī'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-Khw�rizmī. 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-Khw�rizmī 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

bruce c. baker

<snip>

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!
<snip>

Well, the computers on which to run the study already exist:

http://en.wikipedia.org/wiki/MIX

(Marshall, you are /so/ bad! :-D )

masterdam

http://groups.google.nl/group/comp.d...db3a5f481be92a

bob badour

I prefer normalized RN, and I suggest the proper spelling is: MLX. Or is
that too much of a rigid straightjacket?

[snip]

walt

Marshall wrote: [snip]


I prefer normalized RN, and I suggest the proper spelling is: MLX. Or is
that too much of a rigid straightjacket?

[snip]

walt

I suggest the alternative spelling: MXL. This has the added benefit of
making an homage to form MLX of the (US) IRS. A paragon of structure and
simplicity, to be sure. But did you know that, if you add up the value of
the letters in the phrase "Internal Revenue Service" according to as certain
sercet code, the sum comes to the same as MCLXVI. That's apocalyptic, to
be sure.

bob badour

Now that you mention it, I suppose XML could be semi-normalized. In
which case, the fully normalized version would be MXL and not MLX.

What's the proper protocol for resolving this? Entrails of a donkey,
perhaps?