Anyone know if the ancient Hebrew used a base-10 number system???
David Richardson
Please reply directly to me, and include references if possible
-david richardson
supr...@leland.stanford.edu
Jeremy A Horwitz
Similar to the Greeks, they used their alphabet for numerals. Aleph
(the first hebrew letter) represents 1, Beth 2, ..., Yod 10, Koph 20,
..., Tav 400.
jeremy
Jeffleader
According to Georges Ifrah, in his book
"From One to Zero" (cribbed heavily from
Danzig's earlier book "Number"), the
Hebrew alphabet was used numerically
in a manner similar to that used by the
Greeks: That is, the letters aleph-->teph
were 1-9, yod-->tsade were 10, 20, ...90,
and qoph-->tav were 100, 200, 300, 400.
But, for example, 35 would be written as
5 30; 50 was also used as an intermediate
base. Two dots over a letter for 1-9 meant
thousands, e.g. aleph with 2 dots over it
was 1000. Ifrah cites one case of writing
the year 5739 as 9 30 300 400 5000 on a
gravestone. So, 10 was essentially a base
but not in the sense of a positional base 10
system for writing numbers; as Dantzig says,
"In all Indo-European languages, as well as
Semitic...the base of numeration is 10, i.e.,
there are independent number words up to
ten, beyond which some compounding
system is used until 100 is reached. All
those languages have independent number
words for 100 and 1000."
-Jeff Leader
Santa Clara Univ.
Karen Condie Hunt
>Even though you may have named numerals based on "ten",
>there are many variations of base-10 systems that aren't
>precisely our current system as pointed out in
>the book "From One to Zero". Just because there are
>numerals doesn't mean there is a place system to
>facilitate computing (e.g. remember the problems with
>Roman numbers).
>Also, there may be artifacts of earlier non-ten base
>systems (e.g. special names for five, twelve-twenty,
>and twenty-county in Romance languages).
>I do not know how much of this occurs in classical
>Hebrew.
Not much of this occurs in classical Hebrew, if my Biblical Hebrew textbook
is to be believed. It is true that there is no nice place system for
easier computing, but things aren't as bad as for Roman numerals. Since
several postings have already mentioned the alphabet letter correspondence
with numbers (aleph=1, beth=2, yodh=10, kaph=20...), I'll focus on the
words for the numbers.
One through nine:
1 'ehad
2 shnayim (note: the ayim is a dual ending. Hebrew did singular,
dual, and plural for its endings/declensions.)
3 shalosh
4 'arba`
5 hamesh
6 shesh
7 sheba`
8 shemoneh
9 tesha`
Nothing special for 5, 9, or any others unless you count the dual ending on
2. (I'm cheating a little above -- 1 and 2 are given masculine forms while
3-9 are given feminine forms here. I did this because the numbers are
simpler that way.)
10 `eser (feminine form again)
11-19 are done as 1 10, 2 10, 3 10, etc.
For example, 13 is shelosh `esreh
3 10
(The form is for feminine again, and the vowels are strange because that's
just the way Hebrew was/is.)
Now there is an alternate number for 11, so maybe this is a bit of what
you want, but it is not really interestingly different (`ashteh `asar
instead of 'ahad `asar). Similarly there are different spellings here
and there for 12, 17, and 19, but these are not meaningful.
The only place where I see some of what you want in classical Hebrew is in
the number 20. The rules for 30,40,...90 are that they are plurals of
3,4,...9. But 20 is slightly different:
20 `esriym (plural, not dual, of 10)
It is suspected that it once was dual of 10, *`esrayim, but
how could one tell? The consonants are the same, and older
Hebrew writing didn't have vowels marked at all.
Similarly, 200 is dual of 100 rather than being done like 300-900 are.
(300-900 are done by the equivalent of "three of hundreds", "four of
hundreds", etc.) The exact same pattern happens in thousands -- namely,
2000 is dual of 1000, while 3000-9000 are "n of thousands".
Just to throw in an oddity now. Compound numbers like 23, 32, 675 and such
seem to be able to be given in any order 3+20 or 30+2 or 600+5+70 or whatever
turned the writer on.
I hope this helps.
Richard Ottolini
Robert Israel
Depends on how "ancient" you mean. As far as I know there is no evidence
that this system (known as "gematria") was used before the Hellenistic period.
In the Bible, all numbers are written out in full using words.
--
Robert Israel isr...@math.ubc.ca
Department of Mathematics (604) 822-3629
University of British Columbia fax 822-6074
Vancouver, BC, Canada V6T 1Y4
Gerry Myerson
wrote:
>
> In the Bible, all numbers are written out in full using words.
Shush! Don't led the fundamentalists hear this, they'll insist that
we all do this from now on! Imagine trying to write a paper about
Skewes' number under these circumstances....
Gerry Myerson (ge...@mpce.mq.edu.au)
Mike McCarty
Gerry Myerson <ge...@mpce.mq.edu.au> wrote:
)In article <4ipomo$4...@nntp.ucs.ubc.ca>, isr...@math.ubc.ca (Robert Israel)
)wrote:
)>
)> In the Bible, all numbers are written out in full using words.
)
)Shush! Don't led the fundamentalists hear this, they'll insist that
)we all do this from now on! Imagine trying to write a paper about
)Skewes' number under these circumstances....
)
)Gerry Myerson (ge...@mpce.mq.edu.au)
Untrue. They were not written out in full in words. They used a
numerological technique, somewhat similar to Roman Numerals, but using
all the letters of the alphabet (actually, more similar to the Greek
Numeration system).
Mike
--
----
char *p="char *p=%c%s%c;main(){printf(p,34,p,34);}";main(){printf(p,34,p,34);}
I don't speak for DSC. <- They make me say that.
Robert Israel
|> )In article <4ipomo$4...@nntp.ucs.ubc.ca>, isr...@math.ubc.ca (Robert Israel)
|> )wrote:
|> )>
|> )> In the Bible, all numbers are written out in full using words.
|> Untrue. They were not written out in full in words. They used a
|> numerological technique, somewhat similar to Roman Numerals, but using
|> all the letters of the alphabet (actually, more similar to the Greek
|> Numeration system).
Well, I don't know what Bible you're looking at. In the currently accepted
Hebrew text of the Bible, as far as I know, all numbers are written out in
words. If you have a counterexample, please quote chapter and verse.
David Karr
>isr...@math.ubc.ca (Robert Israel) wrote:
>>
>> In the Bible, all numbers are written out in full using words.
>Untrue. They were not written out in full in words. They used a
>numerological technique, somewhat similar to Roman Numerals, but using
>all the letters of the alphabet (actually, more similar to the Greek
>Numeration system).
Perhaps this disagreement stems from the fact that many printed
copies of the Hebrew Bible contain a Greek-style numerical system
(but using the Hebrew letters) to enumerate the chapters, verses,
and other things that need to be annotated. But these aren't part
of the original text, are they? I was under the impression that
that entire number system was a later invention, and that it is
hardly ever used for numbers greater than 999.
-- David A. Karr (ka...@cs.cornell.edu)
Karen Condie Hunt
Indeed the chapter numbers and verses and such are not part of the original
text. They date from the Masoretes, a group of scholars who preserved teh
text of the Hebrew Bible as best they could under pre-typesetting and
pre-mimeographing conditions. They worked from the 1st Century AD through
the 10th Century, and the Hebrew Bible as we have it today is their
Masoretic Text. (Apart from a few corrections due to a few other texts
such as the Dead Sea Scrolls.) The only other place in the Bible where
you'll find the Greek-style enumeration is in the Masorah at the end of
each Book. One can think of the Masorah as a type of error-correcting-
code, naming such things as the middle word or verse of the book, counting
the sumber of "sections" and verses, and a few other tidbits as this.
That number system only began to be used in Hebrew in the Hellenistic times
(not surprisingly, considering that it is styled after the Greek numbering
method.) This would be at earliest around 200BCE. -- I'm not positive of
the dates here. When did Alexander do all his conquests again? Anyway,
this was then.
Karen Hunt
Someday my .sig will come...
Michael Wodzak
that any "big" number in the Good Book is 40 (Noah's flood etc).
I always have pictured this as the amount that two guys could count
together with their fingers and toes.
Michal
Dann Corbit
In ancient Hebrew, numbers were spelled out. Sometime after the exile to
Babylon, the Jews adopted to some extent the practice of using their alphabetic
letters as symbols of numerical figures. However, this usage does not appear
even in postexilic Hebrew Bible manuscripts. One of the oldest extant specimens
of Hebrew writing is the inscription taken from the Siloam water tunnel (probably
from the time of Hezekiah's reign [745-717 B.C.E.]), in which the measurements
are written out in full. Spelling out the numbers provides an added measure of
accuracy and dependability in the manuscripts of the Hebrew Scriptures, which
have been copied many times, for, in copying, a numeral is usually easier to
mistake than a word.
In Hebrew, numbers above ten are a combination of words, such as 12 (two and ten)
(Ge 14:4), except that 20 is the plural of ten; 30 a plural word derived from three;
40 a plural word derived from four, and so on. One hundred is a separate word;
200 is the dual form. Other "hundreds" are composed of two words, as, 300. The
highest number expressed by one Hebrew word is 20,000, the dual form of 10,000
(myriad). Larger numbers are a combination of words. For example, at 1 Chr 5:18
the number 44,760 is, literally, forty and four thousand and seven of hundreds
and sixty. A million is written as a thousand thousands. (2Ch 14:9) Rebekah's
family blessed her, saying: "O you, our sister, may you become thousands times
ten thousand [literally, thousands of myriads]." (Rebekah's posterity actually
came to number many millions.) (Ge 24:55, 60) In Daniel's vision Jehovah is shown
as having "ten thousand times ten thousand [literally, a myriad of
myriads]" standing before him.-Da 7:10.
--
The opinions expressed in this message are my own personal views
and do not reflect the official views of Microsoft Corporation.
In fact, I'm just a subcontractor, not an employee, so pull in your claws.
Karen Condie Hunt
I'd say you are half-way out to lunch. :) While the Bible is fond of using 40
years to indicate a rather long period of time (The time in the wilderness
during the Exodus, various "then the land was at peace for 40 years" lines in
the Book of Judges, even a few New Testament passages in Acts that refer to
the Old Testament.), they were quite capable of using larger numbers.
In fact your Noah's flood reference refers to 150 days as well
as your 40 days. I could give references up to your ears of other times and
places where years, ages, sizes, and whatever else are given with numbers
noticeably larger than 40.
Some think that this 40 years is supposed to refer to 1 or 2 generations of
people. They would therefore claim that no accuracy should be implied here.
How much one agrees with this depends on one's theological bents, so that
discussion should IMHO stay out of sci.math.
Karen Hunt
Someday my .sig will come....
Ariel Scolnicov
jmcc...@sun1307.spd.dsccc.com (Mike McCarty) writes:
>isr...@math.ubc.ca (Robert Israel) wrote:
>>
>> In the Bible, all numbers are written out in full using words.
>Untrue. They were not written out in full in words. They used a
>numerological technique, somewhat similar to Roman Numerals, but using
>all the letters of the alphabet (actually, more similar to the Greek
>Numeration system).
Perhaps this disagreement stems from the fact that many printed
copies of the Hebrew Bible contain a Greek-style numerical system
(but using the Hebrew letters) to enumerate the chapters, verses,
and other things that need to be annotated. But these aren't part
of the original text, are they? I was under the impression that
that entire number system was a later invention, and that it is
hardly ever used for numbers greater than 999.
You won't find the greek-style in the actual text. The number system
is a bit awkward for large numbers. The first 9 letters have values
1-9, the next 9 are 10-90 (jumping tens), and finally there's
100-400. If you want to get into the higher hundreds, you can repeat
letters (so 700 is tav shin). If you want thousands, what you
(usually) do is start again from the lower letters (for the
thousands), then write the hundreds normally. This year is 5756, which
is spelled out
hei tav shin nun vav
(`hei' is the fifth letter of the alphabet, with value 5 -- but here
it has value 5000).
Note that there is no fixed convention for expressing thousands or for
the order of the letters. This is *great* if you're into mysticism --
every word in the Bible can be converted into a number, and an
equivalence relation on the set of words can be defined (according to
their numeric values). There's a slight difficulty due to the fact
that the numbering system didn't exist at the time the text was
written, but what's history between friends?
On a more pragmatic note, every book in the bible can end with a
checksum, which gives the number of verses (so nobody can sneak in
some new ones, or take out the ones they don't like). The checksum
often takes the form of a versicle, with some of the letters
marked. The sum of the values of the marked letters is the number.
-- David A. Karr (ka...@cs.cornell.edu)
--
Ariel Scolnicov
Toby Bartels
>If you want thousands, what you
>(usually) do is start again from the lower letters (for the
>thousands), then write the hundreds normally. This year is 5756, which
>is spelled out
> hei tav shin nun vav
>(`hei' is the fifth letter of the alphabet, with value 5 -- but here
>it has value 5000).
A place value system (like ours) base 1000!
-- Toby
to...@ugcs.caltech.edu
David Karr
>If you want thousands, what you
>(usually) do is start again from the lower letters (for the
>thousands), then write the hundreds normally. This year is 5756, which
>is spelled out
> hei tav shin nun vav
I looked at a calendar (printed in Israel for Israel---e.g. it has
Shabbat times for cities like Tel Aviv) in the office of one of my
co-workers, and it had only
tav shin nun vav
in other words, only 756; the thousands digit was simply omitted.
I found the exact same thing on a US-printed calendar that I dug up
(only difference is the Shabbat times were for New York City).