"TomS" <TomS_member@newsguy.com> wrote in message
news:dfc7ti0klb@drn.newsguy.com...

"On Sat, 03 Sep 2005 08:48:42 -0400, in article
<NY6dnQ7VjO83BoTeRVn-iA@comcast.com>, Rick Merrill stated..."

maff wrote:

Christians and Muslims share a journey
http://www.guardian.co.uk/comment/story/0,3604,1561962,00.html

David Self
Saturday September 3, 2005
The Guardian


At some point during the Middle Ages, the western world adopted
so-called Arabic numerals. They had probably originated in India; had
been used throughout Muslim civilisation for some 500 years and finally
reached Europe through Spain - then under Muslim rule. Since Arabic is
read from right to left, we still work traditional addition and
subtraction sums, set out vertically, by reading them from right to
left. Until we copied the Arabic method, we were innumerate. I mean
(and quickly now) what is MDCCLX minus XLVI?

What you have described is the discovery of PLACE VALUE.

Place value also lets us use different Base Arithmetic (binary, etc)

But also, note that when we do arithmetic, we do it from right
to left. That is an inheritance from Arabic. We first add the 1's
column, then the 10's, and so on.

I'm not sure this is correct. Roman numerals, and ancient Greek numerals,
also were written with higher powers of 10 on the left to lower numbers on
the right (this was complicated, where Roman numerals were concerned, by the
convention of writing, e.g. "4" as "IV" or "900" as "CM"). Adding these
numbers was a pain, but I suspect it was typically done from right to left
(with more cursing).

TomS wrote:

"On Sat, 03 Sep 2005 08:48:42 -0400, in article
<NY6dnQ7VjO83BoTeRVn-iA@comcast.com>, Rick Merrill stated..."

maff wrote:

Christians and Muslims share a journey
http://www.guardian.co.uk/comment/story/0,3604,1561962,00.html

David Self
Saturday September 3, 2005
The Guardian


At some point during the Middle Ages, the western world adopted
so-called Arabic numerals. They had probably originated in India; had
been used throughout Muslim civilisation for some 500 years and finally
reached Europe through Spain - then under Muslim rule. Since Arabic is
read from right to left, we still work traditional addition and
subtraction sums, set out vertically, by reading them from right to
left. Until we copied the Arabic method, we were innumerate. I mean
(and quickly now) what is MDCCLX minus XLVI?

What you have described is the discovery of PLACE VALUE.

Place value also lets us use different Base Arithmetic (binary, etc)

But also, note that when we do arithmetic, we do it from right
to left. That is an inheritance from Arabic. We first add the 1's
column, then the 10's, and so on.

We add Right to Left because it's easy to carry the overflow into the
next place. We read the number from Left to Right because the bigger
numbers are on the left and, well, they're bigger ;-)

TomS wrote:

"On Sat, 03 Sep 2005 08:48:42 -0400, in article
<NY6dnQ7VjO83BoTeRVn-iA@comcast.com>, Rick Merrill stated..."

maff wrote:

Christians and Muslims share a journey
http://www.guardian.co.uk/comment/story/0,3604,1561962,00.html

David Self
Saturday September 3, 2005
The Guardian


At some point during the Middle Ages, the western world adopted
so-called Arabic numerals. They had probably originated in India; had
been used throughout Muslim civilisation for some 500 years and finally
reached Europe through Spain - then under Muslim rule. Since Arabic is
read from right to left, we still work traditional addition and
subtraction sums, set out vertically, by reading them from right to
left. Until we copied the Arabic method, we were innumerate. I mean
(and quickly now) what is MDCCLX minus XLVI?

What you have described is the discovery of PLACE VALUE.

Place value also lets us use different Base Arithmetic (binary, etc)

But also, note that when we do arithmetic, we do it from right
to left. That is an inheritance from Arabic. We first add the 1's
column, then the 10's, and so on.

We add Right to Left because it's easy to carry the overflow into the
next place. We read the number from Left to Right because the bigger
numbers are on the left and, well, they're bigger ;-)

in article dfc7ti0klb@drn.newsguy.com, TomS at

"On Sat, 03 Sep 2005 08:48:42 -0400, in article
<NY6dnQ7VjO83BoTeRVn-iA@comcast.com>, Rick Merrill stated..."

maff wrote:

Christians and Muslims share a journey
http://www.guardian.co.uk/comment/story/0,3604,1561962,00.html

David Self
Saturday September 3, 2005
The Guardian


At some point during the Middle Ages, the western world adopted
so-called Arabic numerals. They had probably originated in India; had
been used throughout Muslim civilisation for some 500 years and finally
reached Europe through Spain - then under Muslim rule. Since Arabic is
read from right to left, we still work traditional addition and
subtraction sums, set out vertically, by reading them from right to
left. Until we copied the Arabic method, we were innumerate. I mean
(and quickly now) what is MDCCLX minus XLVI?

What you have described is the discovery of PLACE VALUE.

Place value also lets us use different Base Arithmetic (binary, etc)

But also, note that when we do arithmetic, we do it from right
to left. That is an inheritance from Arabic. We first add the 1's
column, then the 10's, and so on.

It isn't an inheritance from reading in Arabic. It is the consequence of
reading and writing numbers from left to right, in terms of greatest value
to least value.

Our number system is tied to place value. We use digits, symbol references
to values less than the base, to tell how many of a particular group size we
are taking. And with a true zero, we can say that we are taking none of a
particular group size.

But the idea of "base" indicates a grouping principle. One always groups
smaller items into groups of larger items. This worked for every number
system, and is implicit in the idea of an abacus, a universally used tool.

If we are going to combine smaller groups into larger groups, we must start
where the smaller groups are -- in this case, at the right because of how we
write our numbers. More than ten of a smaller group gets recombined, and so
5 + 8 = 1 ten and 3 ones. We are pushed by the recombination to the left. If
there were no recombination, we could move from right to left quite easily.
Or, if we were content to recombine later, as in a two step method, we could
also move from right to left, but we would still have a leftward push by
recombination.

in article dfc7ti0klb@drn.newsguy.com, TomS at

"On Sat, 03 Sep 2005 08:48:42 -0400, in article
<NY6dnQ7VjO83BoTeRVn-iA@comcast.com>, Rick Merrill stated..."

maff wrote:

Christians and Muslims share a journey
http://www.guardian.co.uk/comment/story/0,3604,1561962,00.html

David Self
Saturday September 3, 2005
The Guardian


At some point during the Middle Ages, the western world adopted
so-called Arabic numerals. They had probably originated in India; had
been used throughout Muslim civilisation for some 500 years and finally
reached Europe through Spain - then under Muslim rule. Since Arabic is
read from right to left, we still work traditional addition and
subtraction sums, set out vertically, by reading them from right to
left. Until we copied the Arabic method, we were innumerate. I mean
(and quickly now) what is MDCCLX minus XLVI?

What you have described is the discovery of PLACE VALUE.

Place value also lets us use different Base Arithmetic (binary, etc)

But also, note that when we do arithmetic, we do it from right
to left. That is an inheritance from Arabic. We first add the 1's
column, then the 10's, and so on.

It isn't an inheritance from reading in Arabic. It is the consequence of
reading and writing numbers from left to right, in terms of greatest value
to least value.

Our number system is tied to place value. We use digits, symbol references
to values less than the base, to tell how many of a particular group size we
are taking. And with a true zero, we can say that we are taking none of a
particular group size.

But the idea of "base" indicates a grouping principle. One always groups
smaller items into groups of larger items. This worked for every number
system, and is implicit in the idea of an abacus, a universally used tool.

If we are going to combine smaller groups into larger groups, we must start
where the smaller groups are -- in this case, at the right because of how we
write our numbers. More than ten of a smaller group gets recombined, and so
5 + 8 = 1 ten and 3 ones. We are pushed by the recombination to the left. If
there were no recombination, we could move from right to left quite easily.
Or, if we were content to recombine later, as in a two step method, we could
also move from right to left, but we would still have a leftward push by
recombination.

The same logic is implicit in subtraction since we generally "borrow" to
make up a deficit found when attempting to take away a larger quantity of
items from a smaller quantity. Borrowing would be inefficient if we worked
from right to left -- at least in the algorithm most used in the United
States schools. There is another algorithm which *could* do a right-to-left
subtraction quite easily.

But it would be a mistake to say that the civilized world was innumerate
before the advent of the Hindu-Arabic system. Really now, the ancient world
was quite inventive. They may not have understood numbers as we do, but they
used what they had and quite well. The Egyptians, Babylonians, Greeks, and
Romans all did remarkable work with angles. Roman numerals were the easiest
of all the ancient numbering systems to read (Greek was bad, but Hebrew was
a nightmare). The Roman system allowed more extensive engineering
applications because using the numbers was easier.

Now understand, for a non-digit based system, Roman numerals were a work of
genius. While they did not use digits (and none of the peoples in this area
did), they used symbols which were tied directly to language. Thus M was
tied to "mille" which means "thousand". Contrast that to the Egyptian lotus
flower, and you have a marked improvement both in readability and
writeability. While the Romans did not use place value, per se, they used
the next best thing. They placed the largest and most significant number
group first, followed by the next most significant, and so on.

The introduction of intermediate symbols (V for 5, L for 50, and D for 500),
as well as the multiplication bar to indicate thousands was inventive and
effective. It made the number much more readable. VIII was infinitely
preferable to IIIIIIII. And the subtractive principle which made IX mean
10-1=9 and XL = 40 and CD = 400, etc. also added to the readability.

Really. Think of it. IV = 4 and IIII = 4. Which takes more work for your
brain to see? You have to *count* the ones on the right, even if you don't
realize you are doing it.

I is easy. II is just as easy. Even III can be easily looked at. But more
than three and the brain begins to split groups apart. IIII is looked at by
the brain as II II or I III or III I. It simply has to work harder. The
Romans understood that IV was an easier way to see it, and they
pragmatically adopted it. They worked smarter than most.

Addition, subtraction, multiplication, and division were generally done on
an abacus, of course. But it could be done symbolically with but only
slightly more difficulty than we have today. General principles for carrying
and borrowing would apply.

The biggest problem with Roman numerals was that they could not be easily
adapted to fractional notation. And once people started using the
hindu-arabic numerals, calculations became quicker. Place value helped a
lot, as well as the single digit for each place (but there were more symbols
to learn!). Even so, it took over a hundred years for the hindu-arabic
numerals to replace the Roman numerals, and a veritable war was waged
between abacists and algorists (algorists used the new numbers). People
distrusted the new numbers, even though with experience they were easier to
use. And calculations could be easily checked.

But you still see Roman numerals today. They are still readable. You don't
see Babylonian or Egyptian numbers around, even for decoration.

Regards,

Raymond E. Griffith