Tag Archives: letters

Why Jews are Good at Math

Jewish children learn early on about numbers and their properties

It’s commonly accepted that Jews do well in math and science because there’s such a strong emphasis on learning within their tradition, as well as amongst Jewish families in general. But can good study habits and parental prompting account for the incredibly disproportionate share of awards (Nobel and others) that have been garnered by Jewish mathematicians and scientists?

Why would a people making up such a small percentage (~0.25%) of the global population earn 25% (or more) of the world’s top prizes in economics, physics, mathematics and medicine?

To delve a little deeper into why this might be, we will explore how the structure of the religion may play a crucial role in embedding complex social, mathematical and dimensional associations into the Jewish psyche in very subtle ways.

~

Modes of mathematical unity in progressive dimensions
(as embodied in the Hebrew teachings)

.

First Dimension (numbers)
Ten as One: Accounting 101

The Hebraic numeral system is one of the oldest decimal systems in existence. The letters of the aleph-bet (aleph through yod shown below) have number values according to their placement in the alphabet.

The number ten, yod, is the next logical step in the evolution of unity from the number one, aleph, just as in the modern decimal model. (In a way, yod is a more ‘concentrated’ form of ‘singularity’ than aleph, because aleph also reflects the fundamental duality present in the creation; the division of light from darkness; the division of ‘waters above’ from ‘waters below’. This is visually expressed in how an aleph is drawn. Below, right.)

Great emphasis is placed on the number ten in Jewish lore and practice: Ten are the primary commandments. Ten are the Lost Tribes. One-tenth is for tithing. Ten were the plagues of Egypt. Ten are the Days of Repentance. Ten is the quorum of group prayer. Ten are the Sephirot of the Kabbalistic Tree of Life. Ten were the generations between Adam and Noah. Ten were the generations between Noah and Abraham.

.

Second Dimension (shapes)
Seven as One: A cyclical view of time and space

The most basic 2-dimensional shape is the circle; all points along its perimeter are equidistant from its centre. It takes seven circles (one in the centre and six around it) to achieve the next most efficient (and unified) use of 2D space using multiples of the same-sized circles. (This applies not only to flat [2D] shapes but also to extruded [3D] forms thereof.)

This lesson can be demonstrated at home with cookies of the same variety or equal-sized coins; echoes of it are to be found everywhere in nature, from honeycombs (extrusions) to snowflakes (polarised ions that attract and consolidate water vapours along flat, crystalline planes) to the most common carbon-ring molecules, like benzene or hexane.

The “seven as one” progression engenders the familiar six-pointed star (Star of David or Seal of Solomon) and represents the seven days of the week as individual cycles of equal length (circumference), six of which are equally anchored to the seventh day (Shabbat), the Holy Day.

The seventh is G-d’s day of rest. Seven are the days of the purification cycle. In the seventh year, a field should be left fallow. A debt should be forgiven after seven years. A Jubilee year follows seven times seven years. The Counting of the Omer is seven times seven days. Seven are the days of mourning (Shiva). Seven are the aliyahs. Seven are the windings of marriage. Seven are the wedding benedictions. Seven are the Shepherds; Abraham, Isaac, Jacob, Joseph, Moses, Aaron and David. Seven are the branches of the Menorah in the Tabernacle. Seven-fold would be G-d’s vengeance for the murder of Cain. Lemech lived for 777 years. The Israelites circled Jericho for seven days, after which, its walls came tumbling down.

.

Third Dimension (forms)
Thirteen as One – The unseen aspects of unity

Moving from circles to spheres (2D to 3D), we find that it takes twelve equal-size spheres to enclose (hide) a central sphere of the same size. Each sphere perfectly touches its five neighbours as well as the centre sphere.

Each sphere can symbolise a year in the life of a male child, culminating in the age of Bar Mitzvah (son of the commandments), at thirteen. The kind of man he will be, however, is still for him to determine through his own future decisions. Female children are honoured upon reaching the age of twelve (Bat Mitzvah), signifying their nature as vessels intended to bear the “hidden” unity of a nascent individual.

Thirteen are the tribes; Joseph was split into two tribes, Ephraim and Menashe, whereupon the Levites became the (esoteric) thirteenth tribe. Thirteen are the Articles of Faith as described by Maimonides. Thirteen are the merciful attributes of G-d set down in the Torah. Thirteen are the nodes of Metatron’s Cube in Kabbalah. Adar II is the 13th (semi-hidden, intercalary) month of the year.

Thirteen is at the crux of the Newton-Gregory Problem (year: 1694), defined during an argument between David Gregory and Isaac Newton. Linear calculations and harmonic analysis show that the number of equal-sized spheres touching a common sphere cannot exceed thirteen, but in using this calculation method, thirteen is likewise shown to be impossible — unless, of course, the centre sphere is recognised to be touching itself (i.e. being self-relative as well as relative to the greater whole).

.

The Most Primary Number (The Ultimate One)
One as One as One

This is not the same as aleph’s “#1”, but is The One that cannot and should not be named.

Each of the foregoing modes of unity were derived by projecting “multiples of one” into the most fitting analogs of “oneness” at each basic level of dimensional reality. G-d, meanwhile, is ever One. Ever was and ever will be. There are no multiples.

This primary tenet of monotheistic unity in Judaism is boldly embodied in one of the chief prayers of the religion; the Shèma (which means “to hear”).

Hear, O Israel! The Lord is G-d; The Lord is One.

~

Obviously, a person doesn’t have to be Jewish in order to be smart, but it apparently does help. How much of that effect is due to the influence of community and genetics; the way in which mathematics is woven into the religious culture and narrative; the acquisition of the ability to read and write in either lateral direction — is probably unknowable.
It should, of course, also be stated that none of the preceding is intended to strip credit from persistent and devoted Jewish mothers everywhere for the achievements of their sons and daughters. This has simply been an exercise in reminding us Where Else credit is always rightly due.
.

3 Comments

Filed under Esoterics, Reason

The Tetragrammaton

יהוה

Tetragrammaton:
(Greek; ‘four-letter thing’)
The series of Hebrew letters reading right to left
which comprise the 4-letter sacred name of G-d.

It appears many thousands of times in the Bible;
an ‘ineffable name’, for it should not be spoken.

~

Yod is in the first position. Tenth letter of the alphabet. Numeral: 10

is in the second position. Fifth letter. Numeral: 5

Vav is in the third position. Sixth letter. Numeral: 6

is in the last position. (Same letter as second position.)

~

In Jewish circles, there’s a longstanding prohibition against pronouncing this combination of letters aloud, primarily due to concerns about preserving its sanctity. When it’s read during prayers, it is usually substituted with the word Adonai, meaning Lord. When read informally, it is frequently replaced by Ha’Shem, simply meaning, The Name. If practicing a prayer, some use the hybrid term Ado’Shem.

It is recorded (Tosef., Yoma, ii. 2; Yoma 39b) that during the Second Temple era the High Priest, Simeon Ha’Tzadik, would pronounce The Name, but only on Yom Kippur (the Day of Atonement) and that he would do so ten times. The writings state that Simeon’s pronouncement of the name was so powerful that it was heard all the way to Jericho. But, was that entirely Simeon’s doing or was he blessed with divine assistance?

Our Rabbis taught: In the year in which Simeon the Righteous died, he foretold them that he would die. They said: Whence do you know that? He replied: On every Day of Atonement an old man, dressed in white, wrapped in white, would join me, entering [the Holy of Holies] and leaving [it] with me, but today I was joined by an old man, dressed in black, wrapped in black, who entered, but did not leave, with me. After the festival [of Sukkoth] he was sick for seven days and [then] died. His brethren [that year] the priests forbore to mention the Ineffable Name in pronouncing the [priestly] blessing.

— Men. 109b. Tosaf Sotah 38a

The prohibition against speaking The Name was not adhered to by the Greeks (and others) who interpreted Hebrew, Aramaic and Paleo-Hebrew source texts in a more academic fashion. This eventually spawned of a number of verbal variants, including Yahweh, Yehwih, Yehovah and Jehovah — even Yahoo!

(In the diagram below, the version at top is Paleo-Hebrew; the next is old Aramaic; and the last is Hebrew.)

137px-Tetragrammaton_scripts.svg

There’s wide disagreement about what The Name means, which can partly be blamed on the understandable tendency of linguists to evaluate ‘word problems’ etymologically. The real problem, however, may spring from the possibility that this is not actually a word at all, but a type of symbolic acronym.

So, let’s look at those letters again.

yodThe tenth letter of the aleph-bet is Yod. It can be symbolic of “higher consciousness”, which can be a reference to G-d, or to the loftier aspects of human consciousness, depending on the context in which it’s found. Yod represents the number ten. In Hebrew numeracy, this is the next greater expansion of the number one, insofar as basic numbers are concerned. (Two- and 3-dimensional progressions of unity evolve distinctly toward seven and thirteen, respectively.) Ten is incorporated into Jewish rituals and rites; it is the minimum number of men required for daily prayers and for special observances. It elevates the individual (01) to a greater unity (10) — in both a spiritual and communal sense. In fact, the Hebrew numeric system has been mostly overlooked as a base-ten [decimal] model, despite the fact that it’s clearly an early example of one. This lack of recognition is owed to the generally insular nature of Jewish communities; the early widespread predominance of the Hindu-Arabic numeral system; and the sometimes confusing matter of having numbers that double for letters — and vice versa.

héHé is the fifth letter of the aleph-bet. It is reflective of the first thing that most people will learn to count: the fingers on their hands. Each hand has five fingers; and two hands gives you ten, so it’s interesting to note that this letter is used twice in the same small group of characters. Our hands are miraculous, for it is with them that we do things, create things, even destroy things. They are the primary executors of man’s free will. The name of the letter comes from the Hebrew word ‘take’, which we mostly do with our hands. (There is also a third [hidden] hand within the tetragram; the hand of G-d, represented by the Yod, which derives its name from the same root as the word ‘hand’, yad.)

vavVav, letter number six, is the number of man. Six are the days of man, but the seventh (Shevat/Shabbat/Sabbath) belongs to G-d. Six is the atomic number of Carbon, the element upon which all known life-forms are based. Hé borrows from the Yod its flame-like crown and appends a descending staff below, anchoring the consciousness (of man) to the ground — to his mortal body, and to the earth. The name of the letter, quite appropriately, means ‘hook’. Vav is an apt metaphor of physical man because it’s reminiscent of our central nervous system, which descends from the seat of our consciousness.

From this perspective:

Yod-Hé-Vav-Hé can translate to: ‘G-d Creates, Man Creates’

(It can therefore also mean: ‘G-d Destroys, Man Destroys’.)

It’s sad, but true, that ‘G-d Creates, Man Destroys’ — and it’s granted that G-d can Destroy whatever Man Creates. Happily, though, life isn’t all about destruction.

G-d is also a helper:

G-d [Yod] ‘lends a Hand’ [Hé], Man [Vav] ‘lends a Hand’ [Hé].

It’s not a particular act that makes us similar to G-d.
Like G-d, we may freely choose what to do, and do it.
Unlike G-d, we won’t always make the right decision.

To do evil, or to do good? — the choices are rarely so clear.

Have a piece of cake, or do the dishes? …uh, what kind of cake?

Whatever our individual decisions, actions, and outcomes, The Name implores us (not once, but twice) to think before we act. It even defines a scientific method for improved decision-making over time:

Conceive [Yod] – Perform [Hé] – Evaluate [Vav] – Perform [Hé]

.
The same process can be seen in G-d’s creative work (Genesis 1:2-4):

G-d said, [Yod – pre-conception]
‘Let there be light’, and there was light; [Hé – action]
and G-d saw that the light was good, [Vav – evaluation]
and he separated light from darkness. [Hé – action]

We each have inherited a tiny seed from the Tree of Knowledge of Good and Evil, the germ from which our free will and our conscience both sprout. We must tend them both lovingly in order to grow straight and strong.

“The man has now become like one of us” — Genesis / Bereshith 3:22

~

The Name should not be spoken because it’s sacred.
The Name
cannot be spoken, because it’s not a word.

~

The foregoing analysis examines only a few approaches to G-d’s quadriliteral name; it is not intended to be an exhaustive study. I pray that it does not offend, and I hope that it clarifies for some our connection to G-d through a ‘Name Unspoken’, with a view to understanding how we could be created in the image of ‘One Unseen’.

Last updated: November 17, 2009  3:25 EST

5 Comments

Filed under Esoterics, Reason