B"H
DEFINITION
of ZERO, INFINITY and ONE
In
HEBREW ALPHANUMERICS
The following is an excerpt
from the first section of a book that I am writing that discusses the presence
of the names of the vowels and the cantillation marks
in תורה entitled מאוצר אור החלופים - פרשת
מקץ. The first section of the book is almost complete and can be
found on:
http://www.geocities.com/dordot2001/ParshatMiketzAdditions.html
Within
the words פני
הארץ that appear in verse מא:נו in ספר
בראשית, פרשת מקץ we see the word אפס if we add the letters נ + י to arrive at
the value ס. Although we will not be discussing פרשת ויגש, the next פרשה in ספר בראשית, in the space of this paper; it behooves us to
mention that we encounter the word אפס twice in פרשת ויגש,
in verses מז:טו
and מז:טז. Actually, we encounter the word אפס many, many times in פרשת מקץ. First, let us notice some of the cases in
which we find the anagram/imperfect permutation1 of the word אפס, that being אףס. There is
certainly no difficulty finding instances in which the name יוסף is preceded or succeeded by a word that contains
the letter א in פרשת
מקץ, thus we would find the word אףס in all of those instances, including in the verse
presently being discussed, within the contiguous words יוסף את. While the
presence of a ף, and not a regular פ, in the word אפס may not seem convincing or intellectually
satisfying at first sight, it is, in fact, very important to notice. The letter ף is, of course,
equal to 800. One חלוף for the value 800 is the word שרש, which is at once a biological, linguistic as well
as a mathematical term, being the analog of the English terms root and radical.
The word פעמים and the expressions כל פעם and נ פעם are also equal to 800. In addition to the word שרש, the letter ף should be
understood to be the three arithmetical terms פַעֲמַיִם
and/or פְעָמִים and/or נ
פעמים concomitantly. Therefore the
name of the letter אל"ף can be read ל"א פעמים
(i.e. 31 x 2 and/or taken 31 times), while the word אףס can be read ס"א פעמים
(i.e., 61 x 2 and/or taken 61 times). The letter ף is also equal
to the expression כל
פעם, as we have indicated. The letter therefore should indicate
constancy in the mind of the reader.
1 By perfect
permutation the author intends a result of the performance of a חלוף or חלופים that is an
anagram the value of which is exactly equal to the original letter, word,
expression, sentence etc. that the חלוף or חלופים was/were performed on. If the חלוף or חלופים was/were
performed on letters, words, phrases, etc., that are not themselves nor do they
contain any letters that have a סופית form, the anagram will always be
a perfect permutation. If however, we
perform a חלוף or חלופים on letters that do have a סופית form, or on
words, phrases etc., that contain a letter or letters that have a סופית form, and
thus the value of the letter or letters may change if it/they is/are placed at
the end of a word (and sometimes elsewhere in a word, as we find in the hapax legomenon the word לםרבה, which
begins Chapter 9, Verse 6 of the Book of ישעיהו, and is found quite often in the
Dead Sea scrolls), the resulting anagram will be either a perfect or an
imperfect permutation. An imperfect
permutation is the result of performing a חלוף or חלופים in which a regular letter or
regular letters have become a סופית or סופיות or a סופית or סופיות have become
a regular letter or regular letters after the חלוף or חלופים was/were performed, and thus the
value of the resulting value of the anagram is not that of the original letter,
word, expression, sentence, etc.
We
can also find many cites in פרשת
מקץ in which the word אפס appears to us as we are accustomed to seeing it,
written with a regular פ, within discrete words or within contiguous words.
A verse within which the word אפס appears written with a regular פ within two contiguous words is מא:מט. Herein we
find the words אין
מספר within which the word אפס is easily discerned. The presence of the word אפס in the phrase אין מספר
is significant. On the one hand the word
אפס can be taken literally to mean no number, no
quantity of or zero. On the other hand, we see from the context in which the
phrase appears that the expression אין
מספר, within which the word אפס appears, is a number so great that it is
incalculable. The contention that the Hebrew word אפס also means the
innumerable, as well none at all, is substantiated by verse בראשית טו:ה,
in which the words אם-תוכל
לספר appear. We find the word אפס within the words אם-תוכל לספר
as well as in the expression אין
מספר that we find in verse בראשית מא:מט. Thus the meanings innumerable as well as
nothing are the purely numerical Hebrew conceptions of what אפס is – nothing at all and/or a number so vast that it
is not within human capability to grasp the sum, if indeed there be a sum at
all. The fact that the expression אין-סוף contains the word אףס, while in the inflections אין-סופי and אין-סופית we see the word אפס written with a
regular פ, lends further support to the understanding that
the word אפס is both zero and number without end for us. If we
transliterate the English word infinite into Hebrew letters, thus: אין-פינית we see the word of negation אין at once. The
letters remaining after we subtract the word אין from the
transliterated word אין-פינית are פינית, the transliteration of the word finite, quite
obviously. We can add one of the יוד"ין to the letter נ in order to
arrive at the value of the letter ס. After doing so, switch the order of the letters ס and פ such that the ס comes first.
We now see that the word infinite after being transliterated into Hebrew
letters and having a very simple גימטריא
and חלוף performed on it becomes אין ספית. Does the reader wonder where the “missing” ו is that is needed to complete the expression אין-סופית? We have
learned about the expanding and contracting of letters. Any letter יו"ד or ת"ו contains a ו . (This is obviously true of the names of the
other letters that contain the letter ו as well. The examples of the letters יו"ד and ת"ו are being mentioned here specifically because the
transliterated English word infinite contains both when transliterated into
Hebrew letters). The letter ו contained in the names of other letters can be
expanded into its name, producing another ו. (In fact, the
expansion of the letter ו can go on indefinitely because the name of the
letter ו"ו is perfectly symmetrical. Each ו expands into
two ו"וין when expanded into its name ad infinitum.)
Therefore, there is no problem whatsoever writing אין-ספית,
the original result we obtained from performing a transliteration, addition of
letters and changing of the order of two letters on the English word infinite,
as אין-סופית, the correctly spelled Hebrew compound word that
means infinite. One of the cites in which the word אפס appears within
one word is another verse that opens with the word ויפתח, namely מב:כז.
Within verse מב:כז
we see the word מספוא and the compound word את-כספו, both of which
clearly contain the word אפס written with a regular פ. With these
examples, the author is confident in the readers' ability to find many more
examples of where the word אפס appears within פרשת מקץ
and elsewhere in תנ"ך.
Yet,
for all of the considerations of the meaning of the word אפס above, there is one simple fact that we have
overlooked. The consonants of the word אפס equal to 141. Since this פרשה is פרשת
מקץ and we have seen again and
again that the גימטריא of the name of the vowel קמץ plays a most prominent role in this פרשה, any word that contains the value 41 should be
considered carefully as the גימטריא
of the name of the vowel קמץ and whatever the remainder may be. The word אפס is equal to קָ. The word עָל is equal to
the consonants of the word אפס as well. A
word such as מִקְרָא contains the word אפס within it
too. If we consider the two סגולין that punctuate the word אֶפֶס we see that taken together their value is 99
x 2 = 198, or קבוצ. Therefore the word אֶפֶס, in toto, equals ק
+ ָ + ֻ. Do you see how we are
treating אפס as a mathematical concept, but yet very, very
differently than does classical mathematics?
Arriving
at the definition of one in Hebrew alphanumerics
involves analysis of the masculine and feminine forms of the word, to wit: אחד and אחת.
The
Hebrew word אחד is made up of the letters א, ח -ד and the various values of each letter must be
considered in order to understand the various values of the Hebrew concept
one. The Hebrew letter א is equal to both one and one thousand. By inference, then, the value of the Hebrew
letter ד must be 4, 1003, 2002, 3001 and 4000. The values of
the letter ח are: 8, 1007, 2006, 3005, 4004, 5003, 6002, 7001
and 8000.
The
operative totals of the word אחד would be an addition of all of the values for each
of the letters concomitantly. Therefore,
אחד equals thirteen (which is also the simplest value
for the word אהבה, which means 'love' in Hebrew), 1012, 2011, 5008,
9004, etc.
In
the
פ
+ ע + מ + י
+ ם
+ ר + ב +
ו + ת =
80 + 70 + 40 + 10 + 600 + 200 + 2 + 6 + 400 = 1408
Since one and one thousand are
identical according to the tradition of alphanumeric Hebrew, the value 1408 is
identical to 409. The simplest value of
the word אחת, the feminine form of the word meaning 'one' in Hebrew, is
likewise 409. By way of examining the unique alphanumeric properties of Hebrew
we have proven that the feminine number 'one' in Hebrew is identical to 'many
times'.
The following is a brief list
of some more חלופים for the number 'one' in the feminine
form in Hebrew:
אחת = 409 = שבתון = 1408 = עולם שבת = יוצרת שבת =
אבות* = באות = תבוא
*This חלוף
is of special interest. We see that the word אבות
is a simple חלוף for the word אחת. The concept of אבות
is not only masculine, it is also plural, yet it is a relatively apparent חלוף
that one who is accustomed to performing חלופים
will easily arrive at.
It should be clear to the
reader that this is an approach to mathematics, and linguistics for that
matter, far more comprehensive than that of the Western tradition. While mathematics as we have inherited them
from the Egyptians and the Greeks exists in Hebrew mathematics as a subset, it
is only a subset. The entire system of
Hebrew mathematics is far more comprehensive.
Doreen Ellen Bell-Dotan, Tzfat
קיץ ה,תשתס"ד