Roman Numerals
Dr. Derek R. Oliver
Dear all,
I am after a bit of information regarding the "roman" numbering system. As
I understand it, the system of strokes that yield what we describe as
roman numerals evolved from the hand signs to tally marks on tablets of
various types, as well as the later inscriptions on monuments and (much
later) printing in european manuscripts.
Is there a "standard" reference that documents this history?
Specifically, how/when did the practice of "subtraction" become common -
and were "rules" laid down governing when/where this is used. - e.g. IX
instead of VIIII and so on. As I understand it, initially the numbers were
written in the long form - with no subtraction. From the brief reading
that I have done, "subtraction" was common in the Germanic formalisms of
Roman Numerals (circa 16th century AD), and may (I'm not sure here) have
been used in the latter stages of the Roman Empire. I have sources which
contain evidence for subtraction not being in use in the 1st century AD.
Why the interest? Trying to answer the question of how to write "1999"
correctly. With "subtraction" MIM appears sensible. The standard useage
in the media is something like MCMXCIX. However, I am not comfortable with
this - it assumes that each pair of symbols converts into a decimalized
numbering system ( M=1x1000, CM =900, XC=90, IX=1) which is (of course)
derived from the arabic/indian notation that was adopted by Europeans
in/around the 16th Centry AD.
Any posts/email most welcom - thanks in advance,
Derek
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Dr. Derek R. Oliver <de...@rsc.anu.edu.au>
Post-Doctoral Research Fellow, Laser & Optical Spectroscopy Group,
Research School of Chemistry, The Australian National University,
CANBERRA ACT 0200, Australia.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Paul Hoover
>
>... Why the interest? Trying to answer the question of how to write
>"1999" correctly. With "subtraction" MIM appears sensible. The
>standard useage in the media is something like MCMXCIX.
>However, I am not comfortable with this - it assumes that each pair
>of symbols converts into a decimalized numbering system
>
>Derek
Call me a liar if the Roman Numeral System is not precisely that: a
decimalized numbering system; which works well enough, IMO, once you
get the hang of it.
Paul
Dr. Derek R. Oliver
<hoo...@erols.com> wrote:
The lack of a zero in the roman notation means that there is no
decimalization - other than that "imposed" by later concerns/cultures (in
the case of MCMXCIX and similar useage: the movie/television industry).
The Romans originally did not use subtraction (hence no need to worry
about zeroes - and thus didn't decimalize).
I have no (personal) problem with writing MDCCCCLXXXXVIIII for 1999, in
fact I have good evidence that this is how a "roman" would have done so. I
am trying to ascertain WHEN various degrees of "subtraction" were
introduced - a significant change in accountancy and other trade-related
activity would have been required had the notation scheme changed. More to
the point,I am trying to work out if a principal reason for the useage of
"subtraction" (as "taught" in many primary schools) was in fact the advent
of the printing press (fewer characters implies fewer pages) and the
conversion to the current numerical notation (as used today).
David Kolodney
when the roman notation is more efficient than the arabic, i.e.., in how many
characters it takes to write the year.
Catiline
Any computer programmer can point out that the distiguishing feature of
all radical systems of counting (such as our "decimal" system) is the
use of position in the line to indicate some power of the radix. The
range of values for any position in a stream of digits is known in
advance. Thus, digits in the rightmost position (the "least significant
digit" excluding decimal fractions -- those digits to the right of the
period) represent multiples of the zeroth power of the radix, always 1.
In the position to the immediate left of that, digits represent
multiples of the radix to the first power, i.e. the radix itself. To
the left of that comes the square of the radix, then the cube, and so
on. Thus, in the decimal system
101
represents "one hundred one." In the binary system (radix 2), it
represents "five." In the octal system (radix 8) it represents
"sixty-five." In the hexadecimal system (radix 16), it represents "two
hundred fifty-seven."
In Roman numerals,
LXVIII
represents "sixty-eight." The last four positions in the stream of
digits represent various multiples of one, additively. The fifth and
sixth positions represent multiples of ten, again additively. On the
other hand
LX
represents "sixty." In this case, the last two positions represent
multiples of ten, not multiples of one as in the earlier example. The
range of values of the "least significant digit" in a stream of Roman
numerals cannot be known in advance; indeed, one cannot predict in
advance the range of values to be represented at any given position in
the stream of digits, and thus the system of Roman numerals fails the
primary test for positional (read "radical") counting systems. And it
cannot then be "decimal."
Paul Hoover
the value of its symbols? If a system is based on a quantity of
ten, such as the Roman Numeral System is (X; C; M are 10^1, 10^2,
10^3), then it's a DECIMAL system. (A simple dictionary states,
"decimal: adj. of or based on the number 10; progressing by tens")
If it were an octal system, the "X" having a value of 8, then the
"C" would be 64, etc.
Paul
Catiline wrote in message <36A73115...@ipa.net>...
>It is certainly the case that Roman numerals are NOT a decimal
system.
>Any computer programmer can point out that the distiguishing
feature of
>all radical systems of counting (such as our "decimal" system) is
the
>use of position in the line to indicate some power of the radix.
The
>range of values for any position in a stream of digits is known in
>advance. Thus, digits in the rightmost position (the "least
significant
>digit" excluding decimal fractions -- those digits to the right of
the
>period) represent multiples of the zeroth power of the radix,
always 1.
>In the position to the immediate left of that, digits represent
>multiples of the radix to the first power, i.e. the radix itself.
To
>the left of that comes the square of the radix, then the cube, and
so
>on. Thus, in the decimal system
>
>... <snip>
Dr. Axel Bergmann
try http://www.deadline.demon.co.uk/roman/front.htm
Best wishes,
Axel
=================================================
Dr. Derek R. Oliver wrote:
> Dear all,
>
> I am after a bit of information regarding the "roman" numbering system. As
> I understand it, the system of strokes that yield what we describe as
> roman numerals evolved from the hand signs to tally marks on tablets of
> various types, as well as the later inscriptions on monuments and (much
> later) printing in european manuscripts.
>
> Is there a "standard" reference that documents this history?
>
> Specifically, how/when did the practice of "subtraction" become common -
> and were "rules" laid down governing when/where this is used. - e.g. IX
> instead of VIIII and so on. As I understand it, initially the numbers were
> written in the long form - with no subtraction. From the brief reading
> that I have done, "subtraction" was common in the Germanic formalisms of
> Roman Numerals (circa 16th century AD), and may (I'm not sure here) have
> been used in the latter stages of the Roman Empire. I have sources which
> contain evidence for subtraction not being in use in the 1st century AD.
>
> Why the interest? Trying to answer the question of how to write "1999"
> correctly. With "subtraction" MIM appears sensible. The standard useage
> in the media is something like MCMXCIX. However, I am not comfortable with
> this - it assumes that each pair of symbols converts into a decimalized
> numbering system ( M=1x1000, CM =900, XC=90, IX=1) which is (of course)
> derived from the arabic/indian notation that was adopted by Europeans
> in/around the 16th Centry AD.
>
> Any posts/email most welcom - thanks in advance,
>
Ken Moore
Oliver" <de...@rsc.anu.edu.au> writes
>I have no (personal) problem with writing MDCCCCLXXXXVIIII for 1999, in
>fact I have good evidence that this is how a "roman" would have done so. I
>am trying to ascertain WHEN various degrees of "subtraction" were
>introduced - a significant change in accountancy and other trade-related
>activity would have been required had the notation scheme changed. More to
>the point,I am trying to work out if a principal reason for the useage of
>"subtraction" (as "taught" in many primary schools) was in fact the advent
>of the printing press (fewer characters implies fewer pages) and the
>conversion to the current numerical notation (as used today).
A piece of evidence, not sufficient on its own, but of some relevance,
is that some dial clocks still use IIII for four, never IV. The first
mechanical clocks in Europe date from just before 1300, so the
indication is that the change to IV was certainly not complete by then
and probably happened later.
--
Ken Moore
k...@hpsl.demon.co.uk
Mike Dana
>
> Isn't it true that the name of the numbering system is determined by
> the value of its symbols? If a system is based on a quantity of
> ten, such as the Roman Numeral System is (X; C; M are 10^1, 10^2,
> 10^3), then it's a DECIMAL system. (A simple dictionary states,
> "decimal: adj. of or based on the number 10; progressing by tens")
The problem with *that* is that the Roman system is *not* base 10. If I
may invent a term here; it's a "binary base 5" (or perhaps a "half base
10"?) system. V = 5*I; X = (2)V; L = X*V; C = (2)L; D = C*V; M = (2)D.
It's actually a very "human-based" system: your hand has five fingers,
and you have two hands... everything is extrapolated from there. So,
instead of being "based on the number 10 and progressing by tens", as
Paul stated; it's 5, doubled, times 5, doubled, etc.
--Mike (posting from soc.history)
Catiline
matter). If it were, then the "I"s in
III
would have to be multiplied by 25, 5 and 1 respectively in order to
arrive at the value for the sequence.
The fact is that the values of the symbols are somewhat random. "I" is
1, but "III" is 3. To represent 5 you use "V" and not "IIIII" and 10 is
neither "IIIIIIIIII" nor "VV" but "X." They are manifestly not
predictable multiples of any number other than the trivial case of 1,
and not even that for low values. Simply being able to represent 1, 10,
100 and 1000 with single characters does not make for a decimal system.
The Greek system is actually more orderly. I'd much rather have to
multiply
PKA (121)
by
TMB (342)
than
CXXI
by
CCCXLII
Dr. Derek R. Oliver
<k...@hpsl.demon.co.uk> wrote:
> A piece of evidence, not sufficient on its own, but of some relevance,
> is that some dial clocks still use IIII for four, never IV. The first
> mechanical clocks in Europe date from just before 1300, so the
> indication is that the change to IV was certainly not complete by then
> and probably happened later.
Many thanks Ken. A further piece of evidence is to be found in the 1514
reproduction of Köbel's "Rechenbüchlein" (short book of arithmetic) in
which an array of computations are shown including the numbers VIIII and
IIII.
This, and other evidence that I have seen so far is lending more weight to
my assertion that the advent of "subtraction" within the notation (as
opposed to the mathematics) was hurried by the growing use of the
arabic/indian notation (that we now use) because a column-based system is
more efficient in terms of space, and therefore preferable for accountants
and printers......
Derek
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Dr. Derek R. Oliver <de...@rsc.anu.edu.au>
Medievalist
means of using roman numerals. The use of roman numerals to
dignify film production dates was instituted because producers
believed that most viewers would find them incomprehensible -
thus making it easier to pass off a film a couple of years old as
a new release. (It worked, incidentally).
If you start checking the roman numbers used in films you will
find a great number of errors - occasionally not simply of
notation, but actual dating errors. This has been documented but
I am afraid I cannot supply sources - it's been a long time since
I looked into it.
--Charlie
Dr. Derek R. Oliver wrote:
>
> Dear all,
>
> I am after a bit of information regarding the "roman" numbering system. As
> I understand it, the system of strokes that yield what we describe as
> roman numerals evolved from the hand signs to tally marks on tablets of
> various types, as well as the later inscriptions on monuments and (much
> later) printing in european manuscripts.
>
> Is there a "standard" reference that documents this history?
>
> Specifically, how/when did the practice of "subtraction" become common -
> and were "rules" laid down governing when/where this is used. - e.g. IX
> instead of VIIII and so on. As I understand it, initially the numbers were
> written in the long form - with no subtraction. From the brief reading
> that I have done, "subtraction" was common in the Germanic formalisms of
> Roman Numerals (circa 16th century AD), and may (I'm not sure here) have
> been used in the latter stages of the Roman Empire. I have sources which
> contain evidence for subtraction not being in use in the 1st century AD.
>
> Why the interest? Trying to answer the question of how to write "1999"
> correctly. With "subtraction" MIM appears sensible. The standard useage
> in the media is something like MCMXCIX. However, I am not comfortable with
> this - it assumes that each pair of symbols converts into a decimalized
> numbering system ( M=1x1000, CM =900, XC=90, IX=1) which is (of course)
> derived from the arabic/indian notation that was adopted by Europeans
> in/around the 16th Centry AD.
>
> Any posts/email most welcom - thanks in advance,
>
Dr. Derek R. Oliver
<berg...@Mailer.Uni-Marburg.DE> wrote:
> Dear Derek,
>
> try http://www.deadline.demon.co.uk/roman/front.htm
>
> Best wishes,
> Axel
Thankyou Axel,
For others interested, this website asserts MCMXCIX because the origin of
the representation is in the abacus (which is inherently columnized).
Accepted - but the earlier origins are tallysticks/hand signals (the
latter were still in use in the medaevil times - see "The Venerable Bede"
- so I query the completeness of the argument (i.e. this is THE way to do
it).
Dr. Derek R. Oliver
In article <36A7CD1C...@MyCompany.Com>, Medievalist
<MyN...@MyCompany.Com> wrote:
> To clarify a trivial point - the media do not have a standard
> means of using roman numerals. The use of roman numerals to
> dignify film production dates was instituted because producers
> believed that most viewers would find them incomprehensible -
> thus making it easier to pass off a film a couple of years old as
> a new release. (It worked, incidentally).
Yes - this was mentioned on the BBC World Service recently, apparently
most movie industry types are a little touchy about admitting it!
William C Waterhouse
de...@rsc.anu.edu.au (Dr. Derek R. Oliver) writes:
>...
> Specifically, how/when did the practice of "subtraction" become common -
> and were "rules" laid down governing when/where this is used.
> contain evidence for subtraction not being in use in the 1st century AD.
Certainly the basic subtractive forms were in use by the 1st century AD,
though I think the choice between those and the additive forms was
quite free. A good example is an inscription from 5/4 BC recording
an aqueduct repair by Augustus in Rome (CIL 6.1244, #29 in A. E. Gordon's
_Illustrated Introduction to Latin Epigraphy_); it uses both XIX and
XIIII.
For those interested, here is the text, with abbreviations
expanded:
IMP(erator) CAESAR DIVI IULI F(ilius) AUGUSTUS
PONTIFEX MAXIMUS CO(n)S(ul) XII TRIBUNIC(ia)
POTESTAT(e) XIX IMP(erator) XIIII RIVOS AQUARUM
OMNIUM REFECIT
William C. Waterhouse
Penn State
Robert Stonehouse
According to the Oxford Classical Dictionary (Numbers, Roman) it was
common in inscriptions to avoid the use of V (and L) - might this
not be an example of that?
ew...@bcs.org.uk