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Rav Hirsch also appears to define efes as something other than zero mamash: being used up, a distant end, or valueless.⁴ I believe that this is, in part, due to everything in life being in a constant state of Flux. As Heraclitus quipped, “the only constant is change.” There is no absolute zero. When the ledger hits zero, the book is discarded. When we try to place a value on zero, we are insinuated that there is another beginning. Perhaps the aleph was not allowed to begin the Torah because it is used with efes. This seems to be the thrust from the Arizal. On sefer Eitz Chaim, Rabbi Shabtai Teicher comments on the notion of “above Chochma: the huili, Keter”:

⁷-From Tohu to Bohu appears to mirror the Yiddish word eppes which means something or a little bit of anything. Curiously, the aleph of efes assumes an ayin in eppes which is more of a guttural sound. This is probably what led Isaac Mozeson to connect the reverse (pei samach) to the hapax legomenon פסה in Tehillim 72:16. See idem, Origin of Speeches; see also Klein Dictionary, פִּסָּה. Without this opening in the throat, we are left with a closed dental lisp of samech. See also Aryeh Kaplan, cmt., Sefer Yetzirah: The Book of Creation, Samuel Weiser, Inc. NY 1990 p.102 (explaining interchangeable letters); see also Rashi, Vayikra 19:16. Samech is a closed loop or a chain like a Syrian semkath ܣ. See Etymological Dictionary of Biblical Hebrew, p. 203, s.v., פסס. Psst! Is not Edenics fun?

Rav Hirsch also appears to define efes as something other than zero mamash: being used up, a distant end, or valueless.⁴ I believe that this is, in part, due to everything in life being in a constant state of Flux. As Heraclitus quipped, “the only constant is change.” There is no absolute zero. When the ledger hits zero, the book is discarded. When we try to place a value on zero, we are insinuated that there is another beginning. Perhaps the aleph was not allowed to begin the Torah because it is used with efes. This seems to be the thrust from the Arizal. On sefer Eitz Chaim, Rabbi Shabtai Teicher comments on the notion of “above Chochma: the huili, Keter”:

⁷-From Tohu to Bohu appears to mirror the Yiddish word eppes which means something or a little bit of anything. Curiously, the aleph of efes assumes an ayin in eppes which is more of a guttural sound. This is probably what led Isaac Mozeson to connect the reverse (pei samach) to the hapax legomenon פסה in Tehillim 72:16. See idem, Origin of Speeches; see also Klein Dictionary, פִּסָּה. Without this opening in the throat, we are left with a closed dental lisp of samech. See also Aryeh Kaplan, cmt, Sefer Yetzirah, p.102 (explaining interchangeable letters); see also Rashi, Vayikra 19:16. Samech is a closed loop or a chain like a Syrian semkath ܣ. See Etymological Dictionary of Biblical Hebrew, p. 203, s.v., פסס. Psst! Is not Edenics fun?

The dilemma that follows (our intellectual Tohu v’Bohu) defines our bechira (sourced in Daat): do we side with Hashem or our own alien opinion? Without Hashem, efes takes on a negative meaning: destruction.⁸ In modern Hebrew, efes is also a derogatory term (i.e., dapar efes – lowest score of the low) meaning loser or idiot. Rabbi Dov Linzer notes:

If the Ein Sof B”H¹⁷ is One, then Ein is zero. Hashem is called the Endless One and not the Beginningless One (Ein Techila).¹⁸ If He were called the Beginningless One, it would be impossible to speak about Him at all. But we are able to conceive of Him to some small extent through His creation. This is a beginning, but it has no end¹⁹ – “for indeed it does have a beginning, namely, the Luminary Who can freely choose to illuminate or not to illuminate. As Rambam states,²⁰ ‘This is what the Prophet says: והוי-ה אלקים אמת – “And the L-rd G‑d is true,” meaning that He alone is the truth; nothing else is true as He is.’ For absolute truth is that which exists independently of everyone and everything else – a condition which can be ascribed solely to G‑d Himself, Whose existence derives from His very own essence and being. In contrast, all that which issues from Him exists only by His volition and sufferance, and not independently.”²¹ So too does our number system begin at zero, but it has no end. In this context, it is impossible to ascribe any negative numbers because there are no negative traits associated with Hashem.²²

Another way of looking at Ein is through science. Michael J. Alter writes: “An atom is made up of a nucleus and its orbiting electrons. Physics has determined that despite its diminutive size, the nucleus (comprised of neutrons and protons) contains the predominate amount – more than 99.9 percent of the mass of the atom. The electrons are by comparison just clouds of moving fluff. Thus, atoms are mainly empty space. Hence, science and the kabbalah concur that matter is composed chiefly of nothing.”²³ In a manner, Hashem is quite literally found everywhere and is everything.

It is known that the “stones are [Hebrew] letters. When the tzaddik prays with these letters and binds (me-kasher) himself to the supernal wisdom (hokhmah elyonah), as is known, he has already entered the gate of eternity/nothingness (shaar ha-ayin). He will elevate his heart until it is as if G-d’s power is in it. At that moment he achieves complete nullity (efes mukhlat). As such, everything is divine power (koach) and his [the tzaddik’s] speech is from the speech of G-d that created the world. The world of speech (olam ha-dibbur) is drawn from the supernal wisdom (chokhmah) which is the pleasure (ta’anug) and playfulness (sha’ashuim) that G-d gets from the world. And now he [the tzaddik] speaks only for the playfulness (sha’ashua) of G-d. And through this the letters return to their original source, which is the wisdom (chokhmah) from which they were drawn.²⁸

¹  -  Ibn Ezra on Isaiah 34:12 (Ain); Ibn Ezra on Isaiah 41:12 (Lo).

²  - See Duties of the Heart, First Tr. On Unity 5.

³  - Kedushat Levi, Exodus, Ki Tisa.

⁴  - Etymological Dictionary of Biblical Hebrew by Matityahu Clark, p. 15.

⁵  - Genesis 1:2.

⁶  - Isaiah 40:17.

⁷  - From Tohu to Bohu appears to mirror the Yiddish word eppes which means something or a little bit of anything. Curiously, the aleph of efes assumes an ayin in eppes which is more of a guttural sound. This is probably what led Isaac Mozeson to connect the reverse (pei samach) to the hapax legomenon פסה in Tehillim 72:16. See idem, Origin of Speeches; see also Klein Dictionary, פִּסָּה. Without this opening in the throat, we are left with a closed dental lisp of samech. See also Aryeh Kaplan, cmt., Sefer Yetzirah: The Book of Creation, Samuel Weiser, Inc. NY 1990 p.102 (explaining interchangeable letters); see also Rashi, Vayikra 19:16. Samech is a closed loop or a chain like a Syrian semkath ܣ. See Etymological Dictionary of Biblical Hebrew by Matityahu Clark, Samson Raphael Hirsch, p. 203, s.v., פסס. Psst! Is not Edenics fun?

⁸  - Rashi on Isaiah 34:12.

⁹  - See Ibn Ezra on Numbers 22:35:2 (defining efes as howbeit); see also Ber Rab 40:4 (attributing efes to the Gk word hafes). I believe that this is referring to the word ἄφεσις or aphesis. Ironically, aphesis or Apheresis linguistically speaking is when the initial vowel is let go to produce a new word. In Greek (and Russian) there’s no initial ‘h’ even though the apostrophe (in classical Gk) denotes such. Therefore, hafes becomes efes.

The weak (rapha) hei in Hebrew is also quiescent. There is an example of this in the word ‘hevel’ found in Kohelet 1:2. “Vanity is something empty of substance, it is zero. However, when combined with something of substance, such as Torah study, it adds value to it, in the same manner that a zero that is placed next to a number adds value to it.” Mashal Umlitzah.

¹⁰  - Bamidbar 13:28.

¹¹  - “He writes subsequently that their sin consisted of the word אפס, that though they had spoken truthfully, and had reported on what they had been asked to report, that word means ‘zero,’ in the sense that the chances of accomplishing one’s objective were ‘zero,’ non existent.” Shenei Luchot HaBerit, Torah Shebikhtav, Sh’lach, Torah Ohr.

¹²  - Ramban on verse 27.

¹³  - Radak on Gen 1:31:

¹⁴  - “It’s Good Because I Say So” on parashat Shelach; see “One Wrong Word” by Rav Yaakov Beasley.

¹⁵  - The word used here is keitz, which is understood to mean the ends of physicality as we see in the writings of Rebbe Nachman:

“‘All ÆFSei the earth have seen’—In other words, the physical matter of the thing becomes EFeS (worthless) <and emptiness, as explained above>.” Likutei Moharan 94:3 (cit. Tehillim 98:3).

¹⁶  - Radak on Ps 2:8.

¹⁷  - There is a basic difference between the way man looks at things and in the way G-d looks at things. Man begins with the phenomena that he sees and hears and proceeds by means of those phenomena to comprehend or assume the existence of other less familiar phenomena. Such unfamiliar phenomena may exist only in the abstract, never to be perceived visually or aurally. G-d, on the other hand, proceeds in the opposite fashion. Sof ma’asseh bamachashavah techillah, the final product had been envisaged at the very outset. This is the way He operates. Every manifestation of any phenomenon represents merely a step planned and necessary to lead to the ultimate total structure. Having planned the final product, He comprehends the significance of every step, every constituent part, even if it is apparently unrelated to the whole. He is aware that such a phenomenon is indispensable, an integral part of the whole to be revealed later. Akeidat Yitzchak 49:1:4.

¹⁸  - If we think of this eternal return in terms of sefirot, then the beginning is keter. “Similarly, keter contains within it the ultimate goal which it seeks to attain. The aim of every plane of reality is to reveal the Infinite Light appropriate to that plane of reality. Thus, keter contains within itself the endpoint which it desires to achieve. And when it has achieved that desired endpoint, it ceases to drive further. This is the meaning of the statement of the Sages in Sefer Yetzira (1:7): “the end is wedged in the beginning, and the beginning is wedged in the end.” The purpose of the emanation of the sefirot which is expressed in keter is to unfold the level of Infinite Light appropriate for that plane of reality, all the way through the various stages of development (i.e., through the various sefirot) to the final revelation and manifestation of that light in the sefira of malchut. Thus, keter is “wedged” in the lowest sefira, malchut. And malchut is wedged in the highest sefira, keter, for it is the end-point which fulfills the purpose of the entire emanation.” Rabbi Moshe Miller on Keter.

¹⁹  - Mezritcher Magid in Imrei Tzadikim, quot. In Torat HaMagid (Tel Aviv, 5729), vol. II, p. 162, trans. In Meditation and Kabbalah by Aryeh Kaplan, p. 303.

²⁰  - Hil. Yesodei HaTorah 1:4.

²¹  - Reishit Goyim Amalek, ch. 1.

²²  - Cf., Tanya, Shaar HaYichud VeHaEmunah 9 (86b).

²³  - Why the Torah Begins with the Letter Beit, p. 5, by Michael J. Alter.

²⁴  - See Breshis 14:14.

²⁵  - This was also the case with Hebraic hieratic numerals as they did not need an attendant zero. See “The Use of Hieratic Numerals in Hebrew Ostraca and the Shekel Weights” by Yohanan Aharoni; “The Hieratic Scribal Tradition in Pre-exilic Judah” by David Calabro.

However, according to Otto Neugebauer, the origins of the sexagesimal system are not as simple, consistent, or singular in time as they are often portrayed. See Neugebauer, O. (1969), “The Exact Sciences in Antiquity”, Acta Historica Scientiarum Naturalium et Medicinalium, Dover, 9: 17–19. This is why we find fractions. It appears that with the dumbing down of civilization, society moved to a base fifty system briefly, as we find with the different types of shekels, see “Money, Prices and Market in the Ancient Near East” by Bert van der Spek (of VU Univ. Amsterdam), p. 30, Yale Univ. New Haven, Economics Dep’t, Economic History Sem., March 30th, 2015, before settling for base ten (and now with binary basically ruling the world). This system, though, will return in the future (as is needed to weigh a few things in the third Temple). However, this system also appears to be eternally incomplete as there has never been a true sexagisimal system with sixty different symbols.

²⁶  - The Tzemach Tzedek on Iggeret Hakodesh, Epistle 21.

²⁷  - Gen. 28:1.

²⁸  - The Maggid of Mezritch, Torat ha-Maggid, vol. 1, 73a/b. Cf., 1, 76a.

I too am very curious about the first use of zero as a concept in Judaism. Maybe Harel of Torah Thoughts would know.

Which characters of alphabet means zero according to gematric rules?

If we accept that Gematria is more than just comparing two words with the same numerical meaning, but that each number represents a Divine theme like we see most emphatically with seven and ten, then zero or nothing would be best represented by the characters אין rather than some glyph. Efes then as well as now carries a negative connotation.

since which time did Jews consider zero as a character equivalent to other alphabet characters=numbers?

Probably Egypt, but not in any script we’re used to.

if zero appears in gematria now, but didn’t at gematria’s beginning, how were adapted gematria perceptions?

The word kind of evolved with the times, eventually taking on more esoteric and mystical meanings.

Could somebody point me to further reading?

The dilemma that follows (our intellectual Tohu v’Bohu) defines our bechira (sourced in Daat): do we side with Hashem or our own alien opinion? Without Hashem, efes takes on a negative meaning: destruction.⁸ In modern Hebrew, efes is also a derogatory term (i.e., dapar efes – lowest score of the low) meaning loser or idiot. Rabbi Dov Linzer notes:

If the Ein Sof B”H¹⁷ is One, then Ein is zero. Hashem is called the Endless One and not the Beginningless One (Ein Techila).¹⁸ If He were called the Beginningless One, it would be impossible to speak about Him at all. But we are able to conceive of Him to some small extent through His creation. This is a beginning, but it has no end¹⁹–“for indeed it does have a beginning, namely, the Luminary Who can freely choose to illuminate or not to illuminate. As Rambam states,²⁰ ‘This is what the Prophet says: והוי-ה אלקים אמת – “And the L-rd G‑d is true,” meaning that He alone is the truth; nothing else is true as He is.’ For absolute truth is that which exists independently of everyone and everything else – a condition which can be ascribed solely to G‑d Himself, Whose existence derives from His very own essence and being. In contrast, all that which issues from Him exists only by His volition and sufferance, and not independently.”²¹ So too does our number system begin at zero, but it has no end. In this context, it is impossible to ascribe any negative numbers because there are no negative traits associated with Hashem.²²

Another way of looking at Ein is through science. Michael J. Alter writes: “An atom is made up of a nucleus and its orbiting electrons. Physics has determined that despite its diminutive size, the nucleus (comprised of neutrons and protons) contains the predominate amount–more than 99.9 percent of the mass of the atom. The electrons are by comparison just clouds of moving fluff. Thus, atoms are mainly empty space. Hence, science and the kabbalah concur that matter is composed chiefly of nothing.”²³ In a manner, Hashem is quite literally found everywhere and is everything.

It is known that the “stones are [Heb] letters. When the tzaddik prays with these letters and binds (me-kasher) himself to the supernal wisdom (hokhmah elyonah), as is known, he has already entered the gate of eternity/nothingness (shaar ha-ayin). He will elevate his heart until it is as if G-d’s power is in it. At that moment he achieves complete nullity (efes mukhlat). As such, everything is divine power (koach) and his [the tzaddik’s] speech is from the speech of G-d that created the world. The world of speech (olam ha-dibbur) is drawn from the supernal wisdom (chokhmah) which is the pleasure (ta’anug) and playfulness (sha’ashuim) that G-d gets from the world. And now he [the tzaddik] speaks only for the playfulness (sha’ashua) of G-d. And through this the letters return to their original source, which is the wisdom (chokhmah) from which they were drawn.²⁸

¹-Ibn Ezra on Isaiah 34:12 (Ain); Ibn Ezra on id. 41:12 (Lo).

²-See Duties of the Heart, First Tr. On Unity 5.

³-Kedushat Levi, Exodus, Ki Tisa.

⁴-Etymological Dictionary of Biblical Hebrew by Matityahu Clark, p. 15.

⁵-Genesis 1:2.

⁶-Isaiah 40:17.

⁷-From Tohu to Bohu appears to mirror the Yiddish word eppes which means something or a little bit of anything. Curiously, the aleph of efes assumes an ayin in eppes which is more of a guttural sound. This is probably what led Isaac Mozeson to connect the reverse (pei samach) to the hapax legomenon פסה in Tehillim 72:16. See idem, Origin of Speeches; see also Klein Dictionary, פִּסָּה. Without this opening in the throat, we are left with a closed dental lisp of samech. See also Aryeh Kaplan, cmt., Sefer Yetzirah: The Book of Creation, Samuel Weiser, Inc. NY 1990 p.102 (explaining interchangeable letters); see also Rashi, Vayikra 19:16. Samech is a closed loop or a chain like a Syrian semkath ܣ. See Etymological Dictionary of Biblical Hebrew, p. 203, s.v., פסס. Psst! Is not Edenics fun?

⁸-Rashi, Is 34:12.

⁹-See Ibn Ezra on Numbers 22:35:2 (defining efes as howbeit); see also Ber Rab 40:4 (attributing efes to the Gk word hafes). I believe that this is referring to the word ἄφεσις or aphesis. Ironically, aphesis or Apheresis linguistically speaking is when the initial vowel is let go to produce a new word. In Greek (and Russian) there’s no initial ‘h’ even though the apostrophe (in classical Gk) denotes such. Therefore, hafes becomes efes.

The weak (rapha) hei in Hebrew is also quiescent. There is an example of this in the word ‘hevel’ found in Ecc 1:2. “Vanity is something empty of substance, it is zero. However, when combined with something of substance, such as Torah study, it adds value to it, in the same manner that a zero that is placed next to a number adds value to it.” Mashal Umlitzah.

¹⁰-Nm 13:28.

¹¹-“He writes subsequently that their sin consisted of the word אפס, that though they had spoken truthfully, and had reported on what they had been asked to report, that word means ‘zero,’ in the sense that the chances of accomplishing one’s objective were ‘zero,’ non existent.” Shenei Luchot HaBerit, Torah Shebikhtav, Sh’lach, Torah Ohr.

¹²-Ramban, v 27.

¹³-Radak, Gen 1:31:

¹⁴-“It’s Good Because I Say So” on parashat Shelach; see “One Wrong Word” by Rav Yaakov Beasley.

¹⁵-The word used here is keitz, which is understood to mean the ends of physicality as we see in the writings of Rebbe Nachman:

“‘All ÆFSei the earth have seen’—In other words, the physical matter of the thing becomes EFeS (worthless) <and emptiness, as explained above>.” Likutei Moharan 94:3 (cit. Teh 98:3).

¹⁶-Radak, Ps 2:8.

¹⁷-There is a basic difference between the way man looks at things and in the way G-d looks at things. Man begins with the phenomena that he sees and hears and proceeds by means of those phenomena to comprehend or assume the existence of other less familiar phenomena. Such unfamiliar phenomena may exist only in the abstract, never to be perceived visually or aurally. G-d, on the other hand, proceeds in the opposite fashion. Sof ma’asseh bamachashavah techillah, the final product had been envisaged at the very outset. This is the way He operates. Every manifestation of any phenomenon represents merely a step planned and necessary to lead to the ultimate total structure. Having planned the final product, He comprehends the significance of every step, every constituent part, even if it is apparently unrelated to the whole. He is aware that such a phenomenon is indispensable, an integral part of the whole to be revealed later. Akeidat Yitzchak 49:1:4.

¹⁸-If we think of this eternal return in terms of sefirot, then the beginning is keter. “Similarly, keter contains within it the ultimate goal which it seeks to attain. The aim of every plane of reality is to reveal the Infinite Light appropriate to that plane of reality. Thus, keter contains within itself the endpoint which it desires to achieve. And when it has achieved that desired endpoint, it ceases to drive further. This is the meaning of the statement of the Sages in Sefer Yetzira (1:7): “the end is wedged in the beginning, and the beginning is wedged in the end.” The purpose of the emanation of the sefirot which is expressed in keter is to unfold the level of Infinite Light appropriate for that plane of reality, all the way through the various stages of development (i.e., through the various sefirot) to the final revelation and manifestation of that light in the sefira of malchut. Thus, keter is “wedged” in the lowest sefira, malchut. And malchut is wedged in the highest sefira, keter, for it is the end-point which fulfills the purpose of the entire emanation.” Rabbi Moshe Miller on Keter.

¹⁹-Mezritcher Magid in Imrei Tzadikim, quot. In Torat HaMagid (Tel Aviv, 5729), vol. II, p. 162, trans. In Meditation and Kabbalah by Aryeh Kaplan, p. 303.

²⁰-Hil. Yesodei HaTorah 1:4.

²¹-Reishit Goyim Amalek, ch. 1.

²²-Cf., Tanya, Shaar HaYichud VeHaEmunah 9 (86b).

²³-Why the Torah Begins with the Letter Beit, p. 5, by Michael Alter.

²⁴-See Breshis 14:14.

²⁵-This was also the case with Hebraic hieratic numerals as they did not need an attendant zero. See “The Use of Hieratic Numerals in Hebrew Ostraca and the Shekel Weights” by Yohanan Aharoni; “The Hieratic Scribal Tradition in Pre-exilic Judah” by David Calabro.

However, according to Otto Neugebauer, the origins of the sexagesimal system are not as simple, consistent, or singular in time as they are often portrayed. See Neugebauer, O. (1969), “The Exact Sciences in Antiquity”, Acta Historica Scientiarum Naturalium et Medicinalium, Dover, 9: 17–19. This is why we find fractions. It appears that with the dumbing down of civilization, society moved to a base 50 system briefly, as we find with the different types of shekels, see “Money, Prices and Market in the Ancient Near East” by Bert van der Spek (of VU Univ. Amsterdam), p. 30, Yale Univ. New Haven, Economics Dep’t, Economic History Sem., March 30th, 2015, before settling for base 10 (and now with binary basically ruling the world). This system, though, will return in the future (as is needed to weigh a few things in the third Temple). However, base 60 also appears to be eternally incomplete as there has never been a true sexagisimal system with 60 different symbols.

²⁶-Tzemach Tzedek on Iggeret Hakodesh, Epistle 21.

²⁷-Gen. 28:1.

²⁸-The Maggid of Mezritch, Torat ha-Maggid, vol. 1, 73a/b. Cf., 1, 76a.

With respect to Mr. Schœmann, his answer does not actually answer anything. I too am very curious about the first use of zero as a concept in Judaism. Maybe Harel of Torah Thoughts would know.

OP:

Which characters of alphabet means zero according to gematric rules?

If we accept that Gematria is more than just comparing two words with the same numerical meaning, but that each number represents a Divine theme like we see most emphatically with seven and ten, then zero or nothing would be best represented by the characters אין rather than some glyph. Efes then as well as now carries a negative connotation.

since which time did Jews consider zero as a character equivalent to other alphabet characters=numbers?

Probably Egypt, but not in any script we’re used to.

if zero appears in gematria now, but didn’t at gematria’s beginning, how were adapted gematria perceptions?

The word kind of evolved with the times, eventually taking on more esoteric and mystical meanings.

Could somebody point me to further reading?

Arturo answers:

To be sure, as mentioned by mi yodeya:

¹ - Ibn Ezra on Isaiah 34:12 (Ain); Ibn Ezra on Isaiah 41:12 (Lo).

² - See Duties of the Heart, First Tr. On Unity 5.

³ - Kedushat Levi, Exodus, Ki Tisa.

⁴ - Etymological Dictionary of Biblical Hebrew by Matityahu Clark, p. 15.

⁵ - Genesis 1:2.

⁶ - Isaiah 40:17.

⁷ - From Tohu to Bohu appears to mirror the Yiddish word eppes which means something or a little bit of anything. Curiously, the aleph of efes assumes an ayin in eppes which is more of a guttural sound. This is probably what led Isaac Mozeson to connect the reverse (pei samach) to the hapax legomenon פסה in Tehillim 72:16. See idem, Origin of Speeches; see also Klein Dictionary, פִּסָּה. Without this opening in the throat, we are left with a closed dental lisp of samech. See also Aryeh Kaplan, cmt., Sefer Yetzirah: The Book of Creation, Samuel Weiser, Inc. NY 1990 p.102 (explaining interchangeable letters); see also Rashi, Vayikra 19:16. Samech is a closed loop or a chain like a Syrian semkath ܣ. See Etymological Dictionary of Biblical Hebrew by Matityahu Clark, Samson Raphael Hirsch, p. 203, s.v., פסס. Psst! Is not Edenics fun?

⁸ - Rashi on Isaiah 34:12.

⁹ - See Ibn Ezra on Numbers 22:35:2 (defining efes as howbeit); see also Ber Rab 40:4 (attributing efes to the Gk word hafes). I believe that this is referring to the word ἄφεσις or aphesis. Ironically, aphesis or Apheresis linguistically speaking is when the initial vowel is let go to produce a new word. In Greek (and Russian) there’s no initial ‘h’ even though the apostrophe (in classical Gk) denotes such. Therefore, hafes becomes efes.

The weak (rapha) hei in Hebrew is also quiescent. There is an example of this in the word ‘hevel’ found in Kohelet 1:2. “Vanity is something empty of substance, it is zero. However, when combined with something of substance, such as Torah study, it adds value to it, in the same manner that a zero that is placed next to a number adds value to it.” Mashal Umlitzah.

¹⁰ - Bamidbar 13:28.

¹¹ - “He writes subsequently that their sin consisted of the word אפס, that though they had spoken truthfully, and had reported on what they had been asked to report, that word means ‘zero,’ in the sense that the chances of accomplishing one’s objective were ‘zero,’ non existent.” Shenei Luchot HaBerit, Torah Shebikhtav, Sh’lach, Torah Ohr.

¹² - Ramban on verse 27.

¹³ - Radak on Gen 1:31:

Even though, as a result of these six “days” of G’d’s creative endeavour, something had been lost forever, i.e. the אפס, the absolute nothingness which had preceded creation of the universe, silence this very “nothingness” had now become inextricably interwoven with the “something,” all the phenomena which G’d had called into existence, G’d described the sum total as good.

Maimonides, in commenting on the words והנה טוב מאד,, (Moreh 3,10) writes: “even death, which appears to constitute a return to אפס to nothingness, G’d considered as something positive, constructive, seeing it is only a prelude to rebirth, albeit sometimes in a different guise than that the previous incarnation. Death is perceived as the result of the ‘nothingness’ which had preceded the universe having become an integral part of this universe. Hence it had become a necessary phenomenon. [these words are mine, I am not sure that I could literally translate the words of Maimonides, themselves a translation, rendered differently by different super-commentaries, such as Crescas, Shem Tov, and Afudi, as well as Abravanel. Ed.]

¹⁴ - “It’s Good Because I Say So” on parashat Shelach; see “One Wrong Word” by Rav Yaakov Beasley.

“‘All ÆFSei the earth have seen’—In other words, the physical matter of the thing becomes EFeS (worthless) <and emptiness, as explained above>.” Likutei Moharan 94:3 (cit. Tehillim 98:3).

¹⁶ - Radak on Ps 2:8.

¹⁷ - There is a basic difference between the way man looks at things and in the way G-d looks at things. Man begins with the phenomena that he sees and hears and proceeds by means of those phenomena to comprehend or assume the existence of other less familiar phenomena. Such unfamiliar phenomena may exist only in the abstract, never to be perceived visually or aurally. G-d, on the other hand, proceeds in the opposite fashion. Sof ma’asseh bamachashavah techillah, the final product had been envisaged at the very outset. This is the way He operates. Every manifestation of any phenomenon represents merely a step planned and necessary to lead to the ultimate total structure. Having planned the final product, He comprehends the significance of every step, every constituent part, even if it is apparently unrelated to the whole. He is aware that such a phenomenon is indispensable, an integral part of the whole to be revealed later. Akeidat Yitzchak 49:1:4.

¹⁸ - If we think of this eternal return in terms of sefirot, then the beginning is keter. “Similarly, keter contains within it the ultimate goal which it seeks to attain. The aim of every plane of reality is to reveal the Infinite Light appropriate to that plane of reality. Thus, keter contains within itself the endpoint which it desires to achieve. And when it has achieved that desired endpoint, it ceases to drive further. This is the meaning of the statement of the Sages in Sefer Yetzira (1:7): “the end is wedged in the beginning, and the beginning is wedged in the end.” The purpose of the emanation of the sefirot which is expressed in keter is to unfold the level of Infinite Light appropriate for that plane of reality, all the way through the various stages of development (i.e., through the various sefirot) to the final revelation and manifestation of that light in the sefira of malchut. Thus, keter is “wedged” in the lowest sefira, malchut. And malchut is wedged in the highest sefira, keter, for it is the end-point which fulfills the purpose of the entire emanation.” Rabbi Moshe Miller on Keter.

¹⁹ - Mezritcher Magid in Imrei Tzadikim, quot. In Torat HaMagid (Tel Aviv, 5729), vol. II, p. 162, trans. In Meditation and Kabbalah by Aryeh Kaplan, p. 303.

²⁰ - Hil. Yesodei HaTorah 1:4.

²¹ - Reishit Goyim Amalek, ch. 1.

²² - Cf., Tanya, Shaar HaYichud VeHaEmunah 9 (86b).

²³ - Why the Torah Begins with the Letter Beit, p. 5, by Michael J. Alter.

²⁴ - See Breshis 14:14.

²⁵ - This was also the case with Hebraic hieratic numerals as they did not need an attendant zero. See “The Use of Hieratic Numerals in Hebrew Ostraca and the Shekel Weights” by Yohanan Aharoni; “The Hieratic Scribal Tradition in Pre-exilic Judah” by David Calabro.

However, according to Otto Neugebauer, the origins of the sexagesimal system are not as simple, consistent, or singular in time as they are often portrayed. See Neugebauer, O. (1969), “The Exact Sciences in Antiquity”, Acta Historica Scientiarum Naturalium et Medicinalium, Dover, 9: 17–19. This is why we find fractions. It appears that with the dumbing down of civilization, society moved to a base fifty system briefly, as we find with the different types of shekels, see “Money, Prices and Market in the Ancient Near East” by Bert van der Spek (of VU Univ. Amsterdam), p. 30, Yale Univ. New Haven, Economics Dep’t, Economic History Sem., March 30th, 2015, before settling for base ten (and now with binary basically ruling the world). This system, though, will return in the future (as is needed to weigh a few things in the third Temple). However, this system also appears to be eternally incomplete as there has never been a true sexagisimal system with sixty different symbols.

Krieger delves into this further (cit. Mathematics in the time of the pharaohs by Richard J. Gillings, p. 257), writing:

²⁶ - The Tzemach Tzedek on Iggeret Hakodesh, Epistle 21.

²⁷ - Gen. 28:1.

²⁸ - The Maggid of Mezritch, Torat ha-Maggid, vol. 1, 73a/b. Cf., 1, 76a.

Arturo answers:

To be sure, as mentioned by mi yodeya:

¹ - Ibn Ezra on Isaiah 34:12 (Ain); Ibn Ezra on Isaiah 41:12 (Lo).

² - See Duties of the Heart, First Tr. On Unity 5.

³ - Kedushat Levi, Exodus, Ki Tisa.

⁴ - Etymological Dictionary of Biblical Hebrew by Matityahu Clark, p. 15.

⁵ - Genesis 1:2.

⁶ - Isaiah 40:17.

⁷ - From Tohu to Bohu appears to mirror the Yiddish word eppes which means something or a little bit of anything. Curiously, the aleph of efes assumes an ayin in eppes which is more of a guttural sound. This is probably what led Isaac Mozeson to connect the reverse (pei samach) to the hapax legomenon פסה in Tehillim 72:16. See idem, Origin of Speeches; see also Klein Dictionary, פִּסָּה. Without this opening in the throat, we are left with a closed dental lisp of samech. See also Aryeh Kaplan, cmt., Sefer Yetzirah: The Book of Creation, Samuel Weiser, Inc. NY 1990 p.102 (explaining interchangeable letters); see also Rashi, Vayikra 19:16. Samech is a closed loop or a chain like a Syrian semkath ܣ. See Etymological Dictionary of Biblical Hebrew by Matityahu Clark, Samson Raphael Hirsch, p. 203, s.v., פסס. Psst! Is not Edenics fun?

⁸ - Rashi on Isaiah 34:12.

⁹ - See Ibn Ezra on Numbers 22:35:2 (defining efes as howbeit); see also Ber Rab 40:4 (attributing efes to the Gk word hafes). I believe that this is referring to the word ἄφεσις or aphesis. Ironically, aphesis or Apheresis linguistically speaking is when the initial vowel is let go to produce a new word. In Greek (and Russian) there’s no initial ‘h’ even though the apostrophe (in classical Gk) denotes such. Therefore, hafes becomes efes.

The weak (rapha) hei in Hebrew is also quiescent. There is an example of this in the word ‘hevel’ found in Kohelet 1:2. “Vanity is something empty of substance, it is zero. However, when combined with something of substance, such as Torah study, it adds value to it, in the same manner that a zero that is placed next to a number adds value to it.” Mashal Umlitzah.

¹⁰ - Bamidbar 13:28.

¹¹ - “He writes subsequently that their sin consisted of the word אפס, that though they had spoken truthfully, and had reported on what they had been asked to report, that word means ‘zero,’ in the sense that the chances of accomplishing one’s objective were ‘zero,’ non existent.” Shenei Luchot HaBerit, Torah Shebikhtav, Sh’lach, Torah Ohr.

¹² - Ramban on verse 27.

¹³ - Radak on Gen 1:31:

Even though, as a result of these six “days” of G’d’s creative endeavour, something had been lost forever, i.e. the אפס, the absolute nothingness which had preceded creation of the universe, silence this very “nothingness” had now become inextricably interwoven with the “something,” all the phenomena which G’d had called into existence, G’d described the sum total as good.

Maimonides, in commenting on the words והנה טוב מאד,, (Moreh 3,10) writes: “even death, which appears to constitute a return to אפס to nothingness, G’d considered as something positive, constructive, seeing it is only a prelude to rebirth, albeit sometimes in a different guise than that the previous incarnation. Death is perceived as the result of the ‘nothingness’ which had preceded the universe having become an integral part of this universe. Hence it had become a necessary phenomenon. [these words are mine, I am not sure that I could literally translate the words of Maimonides, themselves a translation, rendered differently by different super-commentaries, such as Crescas, Shem Tov, and Afudi, as well as Abravanel. Ed.]

¹⁴ - “It’s Good Because I Say So” on parashat Shelach; see “One Wrong Word” by Rav Yaakov Beasley.

“‘All ÆFSei the earth have seen’—In other words, the physical matter of the thing becomes EFeS (worthless) <and emptiness, as explained above>.” Likutei Moharan 94:3 (cit. Tehillim 98:3).

¹⁶ - Radak on Ps 2:8.

¹⁷ - There is a basic difference between the way man looks at things and in the way G-d looks at things. Man begins with the phenomena that he sees and hears and proceeds by means of those phenomena to comprehend or assume the existence of other less familiar phenomena. Such unfamiliar phenomena may exist only in the abstract, never to be perceived visually or aurally. G-d, on the other hand, proceeds in the opposite fashion. Sof ma’asseh bamachashavah techillah, the final product had been envisaged at the very outset. This is the way He operates. Every manifestation of any phenomenon represents merely a step planned and necessary to lead to the ultimate total structure. Having planned the final product, He comprehends the significance of every step, every constituent part, even if it is apparently unrelated to the whole. He is aware that such a phenomenon is indispensable, an integral part of the whole to be revealed later. Akeidat Yitzchak 49:1:4.

¹⁸ - If we think of this eternal return in terms of sefirot, then the beginning is keter. “Similarly, keter contains within it the ultimate goal which it seeks to attain. The aim of every plane of reality is to reveal the Infinite Light appropriate to that plane of reality. Thus, keter contains within itself the endpoint which it desires to achieve. And when it has achieved that desired endpoint, it ceases to drive further. This is the meaning of the statement of the Sages in Sefer Yetzira (1:7): “the end is wedged in the beginning, and the beginning is wedged in the end.” The purpose of the emanation of the sefirot which is expressed in keter is to unfold the level of Infinite Light appropriate for that plane of reality, all the way through the various stages of development (i.e., through the various sefirot) to the final revelation and manifestation of that light in the sefira of malchut. Thus, keter is “wedged” in the lowest sefira, malchut. And malchut is wedged in the highest sefira, keter, for it is the end-point which fulfills the purpose of the entire emanation.” Rabbi Moshe Miller on Keter.

¹⁹ - Mezritcher Magid in Imrei Tzadikim, quot. In Torat HaMagid (Tel Aviv, 5729), vol. II, p. 162, trans. In Meditation and Kabbalah by Aryeh Kaplan, p. 303.

²⁰ - Hil. Yesodei HaTorah 1:4.

²¹ - Reishit Goyim Amalek, ch. 1.

²² - Cf., Tanya, Shaar HaYichud VeHaEmunah 9 (86b).

²³ - Why the Torah Begins with the Letter Beit, p. 5, by Michael J. Alter.

²⁴ - See Breshis 14:14.

²⁵ - This was also the case with Hebraic hieratic numerals as they did not need an attendant zero. See “The Use of Hieratic Numerals in Hebrew Ostraca and the Shekel Weights” by Yohanan Aharoni; “The Hieratic Scribal Tradition in Pre-exilic Judah” by David Calabro.

However, according to Otto Neugebauer, the origins of the sexagesimal system are not as simple, consistent, or singular in time as they are often portrayed. See Neugebauer, O. (1969), “The Exact Sciences in Antiquity”, Acta Historica Scientiarum Naturalium et Medicinalium, Dover, 9: 17–19. This is why we find fractions. It appears that with the dumbing down of civilization, society moved to a base fifty system briefly, as we find with the different types of shekels, see “Money, Prices and Market in the Ancient Near East” by Bert van der Spek (of VU Univ. Amsterdam), p. 30, Yale Univ. New Haven, Economics Dep’t, Economic History Sem., March 30th, 2015, before settling for base ten (and now with binary basically ruling the world). This system, though, will return in the future (as is needed to weigh a few things in the third Temple). However, this system also appears to be eternally incomplete as there has never been a true sexagisimal system with sixty different symbols.

Krieger delves into this further (cit. Mathematics in the time of the pharaohs by Richard J. Gillings, p. 257), writing:

²⁶ - The Tzemach Tzedek on Iggeret Hakodesh, Epistle 21.

²⁷ - Gen. 28:1.

²⁸ - The Maggid of Mezritch, Torat ha-Maggid, vol. 1, 73a/b. Cf., 1, 76a.