ALEPH – The Unending One

ויקרא אל-הים לאור יום ולחשך קרא לילה ויהי-ערב ויהי-בקר יום אחד: (בראשית א:ה)

And G-d called the light Day, and the darkness It called Night. And there was evening and there was morning, one day. (Jewish Publication Society Bible, 1917 Genesis 1:5)

אלף שנים* בעיניך כיום אתמול כי יעבר ואשמורה בלילה: (תהלים צ:ד)

A thousand years in Your eyes are as a day, yesterday, surely it will pass, and I will watch in the night. (My translation – Psalm 90, Verse 4)

*The Hebrew word שנים can be translated both as 'years' and as 'two'.

In her book FIRE with FIRE, (Random House 1993) author Naomi Wolf keenly observes: "Either/or thinking is the natural mental reaction to a perception of scarcity. When people feel they have no options, they cling to the assurances of polarized certainties. It is only when people feel rich in confidence and space that they dare to pursue the subtleties of what Gloria Steinem calls both/and thinking. Feminism must embrace this psychology of plenty." If this is true of feminists, it is all the more true of mathematicians, scientists and linguists, who would plumb the secrets of creation itself. Hebrew Alphanumerics is the arithmetic that describes a universe of superabundance, of endless potential, as well as actuality because it is the arithmetic that does not posit that there is one value per integer.

"…the Hebrew alphabet is a complete cycle. The final tzadik (ץ) equals 900 and thus, the alef equals both one and one thousand. Indeed, in Hebrew the same spelling is used for the name of the letter alef, and elef, meaning "one thousand." 

Noting this phenomenon, Rabbi Avraham Abulafia (b. 1240) interprets the question איכה ירדף אחד אלף** ( דברים ל"ב:ל - Deuteronomy 32:30 "How can one purrsue one thousand!") to mean: One, the first number, follows after one thousand in a complete and perfect cycle." (See: http://tinyurl.com/bk6a3)

The following quote from the ENCYCLOPAEDIA JUDAICA CD-ROM EDITION, Text © Keter Publishing House Ltd., 1997 entry: 'Alef : "The alef was rewarded by starting the Decalogue (אנכי Anokhi; "I") and by denoting the highest number, (elef, "thousand")" is based upon a famous midrash (homily) from Yalkut Shimoni, Parshat Bereishit, Allusions 1-2. The original Hebrew text and my English translation, which are to be found on the following URL: http://tinyurl.com/qs2rh, discuss the relationship of the letter א to the numbers one and 1000 and refers to the above-cited Biblical passage. **. The quaint and "folksy" flavor of the simple meaning of the midrash belies the profundity of the teachings. As with all Hebrew texts, the underlying mathematical lattices, which provide the ground for much hermeneutics and exegesis, are wholly untranslatable. We will not discuss the below-the-surface meanings of the passage in the space of this work. We will treat only how they relate to the alphanumeric principles that we will be demonstrating herein.

This paper will, inter alia, demonstrate why 1000 is "the highest number".

We learn, from the quotes above, that Hebrew alphanumerics is as old as the Bible itself. In fact, on one level the entire Bible is an instruction as to how to use the alphanumerical system. The claim that Hebrew "gematria" was developed subsequently to the numerology of the Greeks simply because the use of the word "gematria" to refer to these studies is relatively recent is patently absurd (See: http://tinyurl.com/jllof). This method of hermeneutics and exegesis, as well as simply reading Hebrew, is as old as the language itself. Scribes in Hebrew are, and always were, called סופרים (sofrim, meaning 'those who count' as well as 'those who produce books'). The Hebrew word for book is ספר (sefer). The Hebrew word for number is מספר (mispar) from the self-same radical. Reading, writing and calculation are one and the same in classical Hebrew. Hebrew was never read without consideration of the numerical values of the letters until the knowledge was lost among the majority of the People during the Diaspora after the destruction of the Second Temple. In every generation the ancient system was preserved lovingly, and expanded upon, by the few.

There are numerous examples in the Dead Sea scrolls in which a scribe has used the final forms of words either at the beginning of a word or somewhere thereafter, but not at the end. Alternatively, there are many instances where the final form of a letter is not used at the end of a word, where it "should have" been. These are obviously not errors, for it is found a large number of times in various fragments and it is often the case that in the very same sentence wherein the anomaly occurs, the word is spelled again "correctly". This bears out the position that the use of the aleph-bet as a complete alphanumerical cycle that begins with the letter א (aleph), equaling one, and ending with the letter ץ (tzaddi sofit ), equaling 900, brings us to the next "cycle" where the letter א is equal to 1000 is very ancient. However, we do not know, cannot know, which cycle "comes first". That is, just as it is true that 1000 follows 900, it is true that the value one, and the other values for the letter א, some of which we will demonstrate in the space of this paper, follow ץ = 900 as well. The scribes of HaYachad (the Dead Sea Sect) utilized the final forms as they did in very deliberate calculations of their texts (See: Dead Sea Scrolls CONCORDANCE, The Non-Biblical Texts from Qumran, by Martin G. Abegg, Jr. with James E. Bowley & Edward M. Cook.& in Consultation with EMANUEL TOV, © Koninklijke BRILL NV, Leiden/Boston 2003). There is a hapax legomenon in the Hebrew Bible in which the final form of the letter ם (mem sofit) is not used at the end of a word. That is the word לםרבה in The Book of Yeshayahu (Isaiah, 8^th-7^th C. BCE), Chapter 9, Verse 6. We learn, then, that the Prophet Yeshayahu used this reckoning as well.

The arithmetical aspects of verse 32:30 from the book of Deuteronomy are not cited above in its entirety. The entire passage reads:

איכה ירדף אחד אלף ושנים יניסו רבבה...

How can it be that one follows after a thousand, and two puts ten thousand to flight…? (my translation)

In this paper we shall demonstrate how.

Having demonstrated the antiquity and authenticity of the reckoning of the Hebrew letter aleph (א) as both one and 1000, let us go on to prove that, in fact, there is no end to the substitution values of א, all of which are operational always.

א (aleph) = 1 = 1000

By simple deduction, the next letter, which is ב (beit), must be:

ב (beit) = 2 = 1001 = 2000

The names of the Hebrew letters are transliterated herein. In more advanced methods of calculation the names of the letters are taken into account. For our present purposes, however, it is enough to recognize the letter only.

These are what I call the "basic" values of the letters, extrapolating from the fact that א = 1 = 1000:

ג (gimmel) = 3 = 1002 = 2001 = 3000

ד (dalet) = 4 = 1003 = 2002 = 3001 = 4000

ה (heh) = 5 = 1004 = 2003 = 3002 = 4001 = 5000

ו (vav) = 6 = 1005 = 2004 = 3003 = 4002 = 5001 = 6000

ז (zayin) = 7 = 1006 = 2005 = 3004 = 4003 = 5002 = 6001 = 7000

ח (chet, guttural ch) = 8 = 1007 = 2006 = 3005 = 4004 = 5003 = 6002 = 7001 = 8000

ט (tet) = 9 = 1008 = 2007 = 3006 = 4005 = 5004 = 6003 = 7002 = 8001 = 9000

י (yud) = 10 = 1009 = 2008 = 3007 = 4006 = 5005 = 6004 = 7003 = 8002 = 9001 = 10,000

It is essential to bear in mind that all of the above values for each of the letters are operational always and concurrently. It is not possible to know which of the values is "the correct one" at any one given time or under given circumstances. They are always all correct under all circumstances. This is what is meant by "both/and thinking" in this context. We shall see that the number system is one of heretofore unrecognized superabundance. We need only to surrender our emotional ties to a system of numerical reckoning that is based on this-or-that thinking, and make the leap to this-and-that thinking. The numbers are conjunctions of values, not disjunctions.

We choose which value or values to consider for a given letter when reckoning it. The more we choose to consider, the greater and richer the universe we describe.

It is possible to continue, of course, with all of the letters of the aleph-beit, but as will be amply demonstrated, we have already stepped far into the depths of the astronomical.

As we have seen above, our tradition has explained how and why 1 = 1000, that is איכה ירדף אחד אלף – how one can follow one thousand, how one and 1000 are both values for א. We shall go further and demonstrate ושנים יניסו רבבה... – 'and two puts 10,000 to flight', that is, exceeds it.

Using the very same logic we use in classical arithmetic: א must be ב - א. For the sake of clarity for the English-speaking reader, we will adopt the convention of writing the arithmetical expressions in this work from left to right. ב – א is to be read ב minus א, not א minus ב. Since we cannot "know", but rather we can only choose, the expression ב – א can mean 2 – 1 = 1 and 2 – 1000 = -998*** and 1001 – 1 = 1000 and 1001 – 1000 = 1 and 2000 – 1 = 1999*** and 2000 – 1000 = 1000.

***When a value for א that we have not seen before is generated as a result of our computations the value will appear in bold type the first time it is generated.

At this juncture it is important to note an interesting phenomenon. The Hebrew word for 'less'; 'fewer'; 'minus' is פחות. The most basic and commonly reckoned value for the letter פ (peh) is 80. The word עוד (pronounced 'ōd', which is the sound-alike etymon of the English word 'add'), means 'more'; 'again'; 'also' likewise has a value equal to 80

(ע = 70 + ו = 6 + ד = 4). If we consider the letter ו, which when used as a prefix often means 'and', in the word פחות and use it as such before the word עוד, we see that the Hebrew word פחות contains the words עוד (more) and ועוד (and more; yet more; and again; and also). One cannot "subtract" in Hebrew without adding.

We already know that א is 1 and 1000. Now, in considering א as ב – א, we have proven that it is also equal to -998 and 1999.

Therefore,

א = -998 = 1 = 1000 = 1999

The revelation of a negative value for א is fantastic. It opens the door to the discovery of endless negative, as well as positive, values for א.

In order to keep matters wieldy, at this juncture we will be demonstrating the values that are generated for א only, and those merely by subtracting the "basic" values of the letters from one another in order to arrive at the values for א, not considering the values for א that we see being generated. Of course those calculations should be made. As they are matters of normal arithmetic according to normal arithmetical laws, it is left to the reader to continue as she or he will.

Next we consider א as ג – ב.

3 – 2 = 1

3 – 1001 = -998

3 – 2000 = -1997

2001 – 2 = 1999

2001 – 1001 = 1000

2001 – 2000 = 1

3000 – 2 = 2998

3000 – 1001 = 1999

3000 – 2000 = 1000

We now see that:

א = -1997 = -998 = 1 = 1000 = 1999 = 2998

The repetitions we will see in this paper are presented for two purposes. First, they demonstrate the internal consistency of our system. Second, and certainly not less important, the repetition helps us to think of arithmetic differently. Just as we practiced the arithmetic we learned as children in order to learn it by rote, so we must do the same to learn this system of arithmetic, which is a vastly more complex and elastic superset than the one we were taught.

א = ד – ג

4 – 3 = 1

4 – 1002 = -998

4 – 2001 = -1997

4 – 3000 = -2996

1003 – 3 = 1000

1003 – 1002 = 1

1003 – 2001 = -998

1003 – 3000 = -1997

2002 – 3 = 1999

2002 – 1002 = 1000

2002 – 2001 = 1

2002 – 3000 = -998

3001 – 3 = 2998

3001 – 1002 = 1999

3001 – 2001 = 1000

3001 – 3000 = 1

4000 – 3 = 3997

4000 – 1002 = 2998

4000 – 2001 = 1999

4000 – 3000 = 1000

We have demonstrated that:

א = -2996 = -1997 = -998 = 1 = 1000 = 1999 = 2998 = 3997

א = ה – ד

5 – 4 = 1

5 – 1003 = -998

5 – 2002 = -1997

5 – 3001 = -2996

5 – 4000 = -3995

1004 – 4 = 1000

1004 – 1003 = 1

1004 – 2002 = -998

1004 – 3001 = -1997

1004 – 4000 = -2996

2003 – 4 = 1999

2003 – 1003 = 1000

2003 – 2002 = 1

2003 – 3001 = -998

2003 – 4000 = -1997

3002 – 4 = 2998

3002 – 1003 = 1999

3002 – 2002 = 1000

3002 – 3001 = 1

3002 – 4000 = -998

4001 – 4 = 3997

4001 – 1003 = 2998

4001 – 2002 = 1999

4001 – 3001 = 1000

4001 – 4000 = 1

5000 – 4 = 4996

5000 – 1003 = 3997

5000 – 2002 = 2998

5000 – 3001 = 1999

5000 – 4000 = 1000

Subtracting the "basic" values of the letter ה from the "basic" values of the letter ד reveals the following values for the letter א:

א = -3995 = -2996 = -1997 = -998 = 1 = 1000 = 1999 = 2998 = 3997 = 4996

א = ו – ה

6 – 5 = 1

6 – 1004 = -998

6 – 2003 = -1997

6 – 3002 = -2996

6 – 4001 = -3995

6 – 5000 = -4994

1005 – 5 = 1000

1005 – 1004 = 1

1005 – 2003 = -998

1005 – 3002 = -1997

1005 - 4001 = -2996

1005 – 5000 = -3995

2004 – 5 = 1999

2004 – 1004 = 1000

2004 – 2003 = 1

2004 – 3002 = -998

2004 – 4001 = -1997

2004 – 5000 = -2996

3003 – 5 = 2998

3003 – 1004 = 1999

3003 – 2003 = 1000

3003 – 3002 = 1

3003 – 4001 = -998

3003 – 5000 = -1997

4002 – 5 = 3997

4002 – 1004 = 2998

4002 – 2003 = 1999

4002 – 3002 = 1000

4002 – 4001 = 1

4002 – 5000 = -998

5001 – 5 = 4996

5001 – 1004 = 3997

5001 – 2003 = 2998

5001 - 3002 = 1999

5001 – 4001 = 1000

5001 – 5000 = 1

6000 – 5 = 5995

6000 – 1004 = 4996

6000 – 2003 = 3997

6000 – 3002 = 2998

6000 – 4001 = 1999

6000 – 5000 = 1000

Our consideration of א as ו – ה has revealed that:

א = -4994 = -3995 = -2996 = -1997 = -998 = 1 = 1000 = 1999 = 2998 = 3997 = 4996 = 5995

א = ז – ו

7- 6 = 1

7 – 1005 = -998

7 – 2004 = -1997

7 – 3003 = -2996

7 – 4002 = -3995

7 – 5001 = -4994

7 – 6000 = -5993

1006 – 6 = 1000

1006 – 1005 = 1

1006 – 2004 = -998

1006 – 3003 = -1997

1006 – 4002 = -2996

1006 – 5001 = -3995

1006 – 6000 = -4994

2005 – 6 = 1999

2005 – 1005 = 1000

2005 – 2004 = 1

2005 – 3003 = -998

2005 – 4002 = -1997

2005 – 5001 = -2996

2005 – 6000 = -3995

3004 – 6 = 2998

3004 – 1005 = 1999

3004 – 2004 = 1000

3004 – 3003 = 1

3004 – 4002 = -998

3004 – 5001 = -1997

3004 – 6000 = -2996

4003 – 6 - 3997

4003 – 1005 = 2998

4003 – 2004 = 1999

4003 – 3003 = 1000

4003 – 4002 = 1

4003 – 5001 = -998

4003 – 6000 = -1997

5002 – 6 = 4996

5002 – 1005 = 3997

5002 – 2004 = 2998

5002 – 3003 = 1999

5002 – 4002 = 1000

5002 – 5001 = 1

5002 – 6000 = -998

6001 – 6 = 5995

6001 – 1005 = 4006

6001 – 2004 = 3997

6001 – 3003 = 2998

6001 – 4002 =1999

6001 – 5001 = 1000

6001 – 6000 = 1

7000 – 6 = 6994

7000 – 1005 = 5995

7000 – 2004 = 4996

7000 – 3003 = 3997

7000 – 4002 = 2998

7000 – 5001 = 1999

7000 – 6000 = 1000

Our list of values for א continues to grow. We now see that:

א = -5993 = -4994= -3995 = -2996 = -1997 = -998 = 1 = 1000 = 1999 = 2998 = 3997 = 4996 = 5995 = 6994

א = ח – ז

8 – 7 = 1

8 – 1006 = -998

8 – 2005 = -1997

8 – 3004 = -2996

8 – 4003 = -3995

8 – 5002 = -4994

8 – 6001 = -5993

8 – 7000 = -6992

1007 – 7 = 1000

1007 – 1006 = 1

1007 – 2005 = -998

1007 – 3004 = -1997

1007 – 4003 = -2996

1007 – 5002 = -3995

1007 – 6001 = -4994

1007 – 7000 = -5993

2006 – 7 = 1999

2006 – 1006 = 1000

2006 – 2005 = 1

2006 – 3004 = -998

2006 – 4003 = -1997

2006 – 5002 = -2996

2006 – 6001 = -3995

2006 – 7000 = -4994

3005 – 7 = 2998

3005 – 1006 = 1999

3005 – 2005 = 1000

3005 – 3004 = 1

3005 – 4003 = -998

3005 – 5002 = -1997

3005 – 6001 = -2996

3005 – 7000 = -3995

4004 – 7 = 3997

4004 – 1006 = 2998

4004 – 2005 = 1999

4004 – 3004 = 1000

4004 – 4003 = 1

4004 – 5002 = -998

4004 – 6001 = -1997

4004 – 7000 = -2996

5003 – 7 = 4996

5003 – 1006 = 3997

5003 – 2005 = 2998

5003 – 3004 = 1999

5003 – 4003 = 1000

5003 – 5002 = 1

5003 – 6001 = -998

5003 – 7000 = -1997

6002 – 7 = 5995

6002 – 1006 = 4996

6002 – 2005 = 3997

6002 – 3004 = 2998

6002 – 4003 = 1999

6002 – 5002 = 1000

6002 – 6001 = 1

6002 – 7000 = -998

7001 – 7 = 6994

7001 – 1006 = 5995

7001 – 2005 = 4996

7001 – 3004 = 3997

7001 – 4003 = 2998

7001 – 5002 = 1999

7001 – 6001 = 1000

7001 – 7000 = 1

8000 – 7 = 7993

8000 – 1006 = 6994

8000 – 2005 = 5995

8000 – 3004 = 4996

8000 – 4003 = 3997

8000 – 5002 = 2998

8000 – 6001 = 1999

8000 – 7000 = 1000

Proceeding with our method, we have now proven that:

א = -6992 = -5993 = -4994= -3995 = -2996 = -1997 = -998 = 1 = 1000 = 1999 = 2998 = 3997 = 4996 = 5995 = 6994 = 7993

א = ט – ח

9 – 8 = 1

9 – 1007 = -998

9 – 2006 = -1997

9 – 3005 = -2996

9 – 4004 = -3995

9 – 5003 = -4994

9 – 6002 = -5993

9 – 7001 = -6992

9 – 8000 = -7991

1008 – 8 = 1000

1008 – 1007 = 1

1008 – 2006 = -998

1008 – 3005 = -1997

1008 – 4004 = -2996

1008 – 5003 = -3995

1008 – 6002 = -4994

1008 – 7001 = -5993

1008 – 8000 = -6992

2007 – 8 = 1999

2007 – 1007 = 1000

2007 – 2006 = 1

2007 – 3005 = -998

2007 – 4004 = -1997

2007 – 5003 = -2996

2007 – 6002 = -3995

2007 – 7001 = -4994

2007 – 8000 = -5993

3006 – 8 = 2998

3006 – 1007 = 1999

3006 – 2006 = 1000

3006 – 3005 = 1

3006 – 4004 = -998

3006 – 5003 = -1997

3006 – 6002 = -2996

3006 – 7001 = -3995

3006 – 8000 = -4994

4005 – 8 = 3997 5004 – 8 = 4996

4005 -1007 = 2998 5004 – 1007 = 3997

4005 – 2006 = 1999 5004 – 2006 = 2998

4005 – 3005 = 1000 5004 – 3005 = 1999

4005 – 4004 = 1 5004 – 4004 = 1000

4005 – 5003 = -998 5004 – 5003 = 1

4005 – 6002 = -1997 5004 - 6002 = -998

4005 – 7001 = -2996 5004 - 7001 = -1997

4005 - 8000 = -3995 5004 – 8000 = -2996

6003 – 8 = 5995 7002 – 8 = 6994

6003 – 1007 = 4996 7002 – 1007 = 5995

6003 – 2006 = 3997 7002 – 2006 = 4996

6003 - 3005 = 2998 7002 – 3005 = 3997

6003 – 4004 = 1999 7002 – 4004 = 2998

6003 – 5003 = 1000 7002 – 5003 = 1999

6003 – 6002 = 1 7002 – 6002 = 1000

6003 – 7001 = -998 7002 – 7001 = 1

6003 – 8000 = -1997 7002 – 8000 = -998

8001 – 8 = 7993

8001 – 1007 = 6994

8001 – 2006 = 5995

8001 – 3005 = 4996

8001 – 4004 = 3997

8001 – 5003 = 2998

8001 – 6002 = 1999

8001 – 7001 = 1000

8001 – 8000 = 1

9000 – 8 = 8992

9000 – 1007 = 7993

9000 – 2006 = 6994

9000 – 3005 = 5995

9000 – 4004 = 4996

9000 – 5003 = 3997

9000 – 6002 = 2998

9000 – 7001 = 1999

9000 – 8000 = 1000

Having subtracted the "basic" values of the letter ט from those of the letter ח, we have determined the following:

א = -7991 = -6992 = -5993 = -4994= -3995 = -2996 = -1997 = -998 = 1 = 1000 = 1999 = 2998 = 3997 = 4996 = 5995 = 6994 = 7993 = 8992

א = י – ט

10 – 9 = 1 1009 – 9 = 1000

10 – 1008 = -998 1009 – 1008 = 1

10 – 2007 = -1997 1009 – 2007 = -998

10 – 3006 = -2996 1009 – 3006 = -1997

10 – 4005 = -3995 1009 – 4005 = -2996

10 – 5004 = -4994 1009 – 5004 = -3995

10 – 6003 = -5993 1009 – 6003 = -4994

10 – 7002 = -6992 1009 – 7002 = -5993

10 – 8001 = -7991 1009 – 8001 = -6992

10 – 9000 = -8990 1009 – 9000 -7991

2008 – 9 = 1999

2008 – 1008 = 1000

2008 – 2007 = 1

2008 – 3006 = -998

2008 – 4005 = 1997

2008 – 5004 = -2996

2008 – 6003 = -3995

2008 – 7002 = -4994

2008 – 8001 = -5993

2008 – 9000 = -6992

3007 – 9 = 2998

3007 – 1008 = 1999

3007 – 2007 = 1000

3007 – 3006 = 1

3007 – 4005 = -998

3007 – 5004 = -1997

3007 – 6003 = -2996

3007 - 7002 = -3995

3007 – 8001 = -4994

3007 – 9000 = -5993

4006 – 9 = 3997

4006 – 1008 = 2998

4006 – 2007 = 1999

4006 – 3006 = 1000

4006 – 4005 = 1

4006 – 5004 = -998

4006 – 6003 = -1997

4006 – 7002 = -2996

4006 – 8001 = -3995

4006 – 9000 = -4994

5005 – 9 = 4996

5005 – 1008 = 3997

5005 – 2007 = 2998

5005 – 3006 = 1999

5005 – 4005 = 1000

5005 – 5004 = 1

5005 - 6003 = -998

5005 – 7002 = -1997

5005 – 8001 = -2996

5005 – 9000 = -3995

6004 – 9 = 5995

6004 – 1008 = 4996

6004 – 2007 = 3997

6004 – 3006 = 2998

6004 – 4005 = 1999

6004 – 5004 = 1000

6004 – 6003 = 1

6004 – 7002 = -998

6004 – 8001 = -1997

6004 – 9000 = -2996

7003 – 9 = 6994

7003 – 1008 = 5995

7003 – 2007 = 4996

7003 – 3006 = 3997

7003 – 4005 = 2998

7003 – 5004 = 1999

7003 – 6003 = 1000

7003 – 7002 = 1

7003 – 8001 = -998

7003 – 9000 = -1997

8002 – 9 = 7993 9001 – 9 = 8992

8002 – 1008 = 6994 9001 – 1008 = 7993

8002 – 2007 = 5995 9001 – 2007 = 6994

8002 – 3006 = 4996 9001 – 3006 = 5995

8002 – 4005 = 3997 9001 – 4005 = 4996

8002 – 5004 = 2998 9001 – 5004 = 3997

8002 – 6003 = 1999 9001 – 6003 = 2998

8002 – 7002 = 1000 9001 – 7002 = 1999

8002 – 8001 = 1 9001 – 8001 = 1000

8002 – 9000 = -998 9001 – 9000 = 1

10,000 – 9 = 9991

10,000 – 1008 = 8992

10,000 – 2007 = 7993

10,000 – 3006 = 6994

10,000 - 4005 = 5995

10,000 – 5004 = 4996

10,000 – 6003 = 3997

10,000 – 7002 = 2998

10,000 – 8001 = 1999

10,000 – 9000 = 1000

We shall end our calculations in the space of this work with figuring the values of א by considering א as י – ט. Having done so may now add yet another two values for א to our list.

א = - 8990 = -7991 = -6992 = -5993 = -4994= -3995 = -2996 = -1997 = -998 = 1 = 1000 = 1999 = 2998 = 3997 = 4996 = 5995 = 6994 = 7993 = 8992 = 9991

Using this method of extrapolation to discover values for the letter א, all of which are as true as the value 1 and the value 1000, our list of new values grows slowly. Each step shows the validity of the step before and the system is proven to be perfectly internally consistent.

We can continue in a number of ways. We can compute values of א by considering the various "basic" values of the remainder of the letters of the aleph-beit. We can, having extrapolated more than the "basic" values of the letter א, i.e., 1 and 1000, use those values for arriving at more values for the other letters. For instance, choosing a value for א arbitrarily, we have learned that one of the values of א is -8990. ב, then, being א + א, would have to equal -8990 + -8990 = -17,980. Is this value consistent with our system? Yes, it is. If we add -17 to -980, we will arrive at -997. We know that one of the values for א is -998. A value of -997 for the letter ב, i.e., one more than a value for ,א is perfectly consistent. We have answered the question that the Hebrew Bible poses to us quoted above: "How can it be that one chases a thousand, and two puts ten thousand to flight…?" We have seen how and why it is that the letter א is equal to both 1 and 1000 and other values. We have now also seen a value for the letter ב that is larger than 10,000.

We can also consider ב as the values of ב multiplied by the values of א. Once again choosing a value for א arbitrarily, let us say 9991, and a value for ב arbitrarily, 2 for instance, we have:

2 x 9991 = 19,982. Is this value consistent with our system? Once again, it is. If we compute 19 + 982 we arrive at 1001, one of the "basic" values for the letter ב.

Will the system work if we begin by adding an extrapolated value for ב, i.e., a value other than 2, 1001 and 2000, with itself? Well, if a value for א is -2996. Then a value for ב must be -2996 + -2996 = -5992. Adding -5 to -992, we arrive at the value -997. We have arrived at the value -997 for the letter ב by way of another computation above and we know that one of the values for א is -998. Therefore, since the value -997 for the letter ב is perfectly consistent with our system we know that we do not diverge from internal consistency when we begin our considerations with an extrapolated value of a letter.

Is consistency maintained if we multiply an extrapolated value for the letter ב by an extrapolated value for the letter א in order to arrive at yet another extrapolated value for the letter ב? An extrapolated value for the letter ב is 1999 + 1999 = 3998. Adding 3 + 998 we arrive at 1001, a "basic" value for ב. We know we are correct thus far. If we multiply the extrapolated value for ב 3998 by -998 (an extrapolated value for א), we arrive at the product -3,990,004. Is -3,990,004 a value for the letter ב? Let's break the figure down. The sum -990,000 is necessarily identical to -990 in gematria because a number multiplied by 1 is identical with itself. Since in gematria 1 = 1000, -990 must equal -990,000. -990 multiplied by all of the other valuees for א will likewise all be identical. We now see that -3,990,004 can be rewritten as -3994. The figure -3000 is identical to -3. If we add -3 to -994 we will arrive at -997. This, we have seen, is a value of the letter ב. It is one more than the value of -998 for the letter א.

The world of Hebrew alphanumerics is both very familiar and quite strange to us upon encountering it initially. It is familiar because classical arithmetic is a subset of Hebrew alphanumerics. Yet, it is also strange because we are asked to surrender what we have learned about what numbers are. The possibilities, and the responsibility for choosing, are vastly greater employing Hebrew alphanumerics than when we employ classical arithmetic theory. As we have seen, the computations are eminently simple, no more complicated than the arithmetic that we grew up with. The only difficulty in accepting this system is overcoming the hurtle of our emotional attachment to a number theory that is characterized by and which describes scarcity. We need only open ourselves to the possibility of superabundance and this system becomes abundantly clear and filled with the joyous understanding that all that we experience, all that exists, in actuality and in potentiality, exists on an infinite number of planes concomitantly because for every value there is an infinite number of substitution values.

Doreen Ellen Bell-Dotan, Tzfat, Israel

DoreenDotan@gmail.com