With regard to the shechina - the "Divine Presence of God, I have noticed that some grapple with the concept of how God can be more or less present in a given place or time.
A scalar field is a function that assigns a value to every point in space. One way to picture an approximation of this is to imagine a three dimensional grid overlaying the scene in your mind's eye, and place a small LED at each juncture of the lines of the grid. The larger values of the function can be indicated by a brighter light.
To extend this visualization to the shechina, one can identify the degree of the presence of God with the intensity of the light in the above visualization.
However, I have not discerned a satisfactory interpretation of this model with regard to the underlying theological question - of what God being more or less present means - or if it a thing entirely internal, not having an existence in our Universe at all.
Tuesday, March 15, 2016
Tuesday, January 26, 2016
Axioms of Torah
Within Judaism, there are matters of belief and practice. For each smallest question, there tend to be many, many answers. However, there are some statements that can be whittled down to the point that there exists only one formulation that is consistent with Judaism - if that statement is rejected, then the whole system fails (such as the 'exactly one God exists' - any negation of that statement is not consistent with Judaism). However, there are other statements on which there exist multiple 'kosher' positions (almost any detail of almost any thing... although some would disagree).
Similarly, as Rav Kook notes in his discussion of Science & Torah, in particular in I:134 of אגרות הראיה (the 2nd of a series of three on this subject) - The Rambam sets out a relatable dichotomy - that Tanach includes language (i.e. metaphors such as 'the hand of God') and laws that are not 'intrinsic' to the nature of God, or the Godly state to which we strive. Rather, these things are included because they are necessary to achieve God's goals - we, mankind, need these things both to uplift ourselves to the level to enact those goals, as well as to be vehicles to deliver these concepts into our minds as they are.
We can imagine alternate scenarios, histories that might have been, where God would have communicated some things differently, and some things different. For example, if our species had come to be with four arms instead of two, or a secondary heart located elsewhere in our bodies, the verses describing the mitzvah of Tefi would have had some differences, to accommodate that different physiology. Had Avraham said "Sarah is my wife" rather than "Sarah is my sister", events might have played our very similarly, other than the details of the words, and perhaps a Divine intervention to save Avraham rather than protect Sarah.
One way to conceptualize this (the difference between 'Truths that must be so' and 'Truths that could be otherwise') is to relate it to undecidable statements in mathematics. For simplicity, I will assume that any particular gestalt of one's position on every matter is reducible to a self-consistent set of axioms.
Then, consider the axioms of Euclid's Elements:
1. A straight line segment can be drawn joining any two points.
2. Any straight line segment can be extended indefinitely in a straight line.
3. Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center.
4. All right angles are congruent.
5. Given a line, and a point not on that line, exactly one parallel line exists that intersects that point.
For the first four axioms, if you try to build a framework where one is not true - it does not work, the logic falls apart.
For example, you could change axiom 1 to give two unique lines for every pair of points - this is kind of like saying that 2+2=4, but also that 2+2 = 'other 4', and furthermore, 4 does not equal 'other 4' - neither arithmetic nor algebra can function, as you lose one of the most fundamental properties of all - that a thing is equal to itself!
The fifth axiom (It is often referred to as a 'postulate', for reasons which might interest those who enjoy knowing the history of these things) has alternate formulations that are different - each one contradicts the others, yet each generates its own world.
The Parallel Postulate of Euclid can be true - and you end up with 'regular' straight-line-grid, Euclidean geometry. It is true, and Spartanly elegant.
But - you can also reject it.
You can construct a Geometry (a world-measuring from the original Greek, after all) in which no such point exists - and you have the system of geometry of the surface of a sphere - such as the one on which we live*.
You can declare that there exists no limit to the number of lines which can be drawn through that point - and you have hyperbolic geometry (which is rather harder to simply describe).
Each choice yield a different, and true totality - and the existence of each version does not make the others untrue - they are merely describing different things that share much of their underlying nature (they do share 4 axioms out of five, after all).
Similarly, Judaism has statements which are ironclad, absolute. It also has statements which have many possible iterations - each one true, and each not inimical to the others. And - to only ever have but one of those many is too great a tragedy to bear.
*An oblate spheroid, if you wish to be very מדקדק.
Similarly, as Rav Kook notes in his discussion of Science & Torah, in particular in I:134 of אגרות הראיה (the 2nd of a series of three on this subject) - The Rambam sets out a relatable dichotomy - that Tanach includes language (i.e. metaphors such as 'the hand of God') and laws that are not 'intrinsic' to the nature of God, or the Godly state to which we strive. Rather, these things are included because they are necessary to achieve God's goals - we, mankind, need these things both to uplift ourselves to the level to enact those goals, as well as to be vehicles to deliver these concepts into our minds as they are.
We can imagine alternate scenarios, histories that might have been, where God would have communicated some things differently, and some things different. For example, if our species had come to be with four arms instead of two, or a secondary heart located elsewhere in our bodies, the verses describing the mitzvah of Tefi would have had some differences, to accommodate that different physiology. Had Avraham said "Sarah is my wife" rather than "Sarah is my sister", events might have played our very similarly, other than the details of the words, and perhaps a Divine intervention to save Avraham rather than protect Sarah.
One way to conceptualize this (the difference between 'Truths that must be so' and 'Truths that could be otherwise') is to relate it to undecidable statements in mathematics. For simplicity, I will assume that any particular gestalt of one's position on every matter is reducible to a self-consistent set of axioms.
Then, consider the axioms of Euclid's Elements:
1. A straight line segment can be drawn joining any two points.
2. Any straight line segment can be extended indefinitely in a straight line.
3. Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center.
4. All right angles are congruent.
5. Given a line, and a point not on that line, exactly one parallel line exists that intersects that point.
For the first four axioms, if you try to build a framework where one is not true - it does not work, the logic falls apart.
For example, you could change axiom 1 to give two unique lines for every pair of points - this is kind of like saying that 2+2=4, but also that 2+2 = 'other 4', and furthermore, 4 does not equal 'other 4' - neither arithmetic nor algebra can function, as you lose one of the most fundamental properties of all - that a thing is equal to itself!
The fifth axiom (It is often referred to as a 'postulate', for reasons which might interest those who enjoy knowing the history of these things) has alternate formulations that are different - each one contradicts the others, yet each generates its own world.
The Parallel Postulate of Euclid can be true - and you end up with 'regular' straight-line-grid, Euclidean geometry. It is true, and Spartanly elegant.
But - you can also reject it.
You can construct a Geometry (a world-measuring from the original Greek, after all) in which no such point exists - and you have the system of geometry of the surface of a sphere - such as the one on which we live*.
You can declare that there exists no limit to the number of lines which can be drawn through that point - and you have hyperbolic geometry (which is rather harder to simply describe).
Each choice yield a different, and true totality - and the existence of each version does not make the others untrue - they are merely describing different things that share much of their underlying nature (they do share 4 axioms out of five, after all).
Similarly, Judaism has statements which are ironclad, absolute. It also has statements which have many possible iterations - each one true, and each not inimical to the others. And - to only ever have but one of those many is too great a tragedy to bear.
*An oblate spheroid, if you wish to be very מדקדק.
Sunday, November 8, 2015
A very short thought
The Name of God, ש-ד-י, in Gematria (letter-value system) has value 10,4,300, ie 314.
That is all.
If anyone has some nice insight into that, please comment or email me.
That is all.
If anyone has some nice insight into that, please comment or email me.
Tuesday, November 3, 2015
A brief description of the destruction of Sedom et all.
There are a number of points of
archeological evidence that point to the nature of the destruction God wrought upon
Sodom, [G]omorrah (the ‘g’ happened because the ancient ayin was a
glottal stop, like the ‘Ng’ we see in a number of African names today) and the
other cities of the fertile plain by the Jordan river. Together, they point to
an airburst of a comet or other
previously orbital chunk of material, much like the one filmed over Russia a
few years ago, or the Tunguska event.
In Perek יט
|
כג הַשֶּׁמֶשׁ יָצָא
עַל הָאָרֶץ וְלוֹט בָּא
צֹעֲרָה.
|
23 The sun went out over the land, and Lot came to
Tzoar.
|
|
24 Then God caused to rain upon Sodom and upon Gomorrah
brimstone (i.e. sulfur and sulfurous compounds) and fire from Go out of the
sky.
|
Consider the Greek legend of
Phaeton, wherein the son of their sun god stole the sun-chariot, and came too
near the Earth, burning it, and Zeus was forced to explode him with a bolt of
lightning.
This implies a Michael-Bayesque
sequence:
The sun is burning just over the
eastern horizon; the quiet peace of early morning hangs over Sodom, Gomorrah,
and their sister-cities. Westward, in the foothills of what will one day, far
in the future, be known as the Judean hills, six tiny human figures crest the
first large hill, perhaps even a quite small mountain, worthy of the name.
Then –
suddenly – the sun grows suddenly huge, a fiery bull charging. A nameless comet
burns towards some of the most ancient cities of Man, outspeeding its own sound
more than twenty-fold. As it dives ever deeper into the ocean of air, it
shatters into several chunks. Some fly further on, detonating over the glimmering
Mediterranean, over remote & uncivilized Greece, now but a province of a
mighty empire, its great days a double thousand years yet to come.
One
chunk, glowing eye-searing-bright, roars towards the Jordan. Lot’s wife turns
back, stands atop the mountain, one hand shielding her eyes from the glare,
wondering at the sun come so low.
Below
her, behind the shielding bulk of the hill, the men throw Lot and his daughters
to the ground. It is already too late for her.
The
shard hits air so dense at its poly-Mach speed, it shatters as a fluffy snowball
on a car window. But this snowball still carries the energy of multiple
Hiroshimas within it. All that energy now disperses in every direction, a wall
of heat and sound.
Sodom and
her siblings are flattened in an instant, its people disintegrated, the
buildings pulverized, the crops incinerated.
Lot’s wife, too, disappears to the blast wave.
Lot’s wife, too, disappears to the blast wave.
The
blast reverberates off of the surrounding mountains; the nearby cities, Tzoar
among them, in the mountains start at the blast, and gaze at the mushroom
cloud, rising high into the atmosphere.
Avraham
too, sees the rising cloud from deep within the Judean hills – at Eylonei
Mamre, where he had argued their defense the previous evening.
Sunday, September 20, 2015
A thought for Shmini Atzeret
"God is a mathematician" - Plato
It is well-known that people around the globe celebrate mathematics in general, and pi (=3.14159...) in particular, on the dates which correspond to its common approximations.
These dates are March 14, 3.14 by the month-day notation, and July 22, 22/7 by the day-then-month notation.
But the Jewish calendar has its own day for this!
The first day of Succot is the 15 of Tishrei (בְּמִדְבַּר כט:יב וּבַחֲמִשָּׁה עָשָׂר יוֹם לַחֹדֶשׁ הַשְּׁבִיעִי). Hoshana Rabba, six days later, is the 21rst.
And Shmini Atzeret, the great day of closeness between Hashem and His nation - is the 22nd day of the 7 month.
We are His people, and He is our PhD advisor.
It is well-known that people around the globe celebrate mathematics in general, and pi (=3.14159...) in particular, on the dates which correspond to its common approximations.
These dates are March 14, 3.14 by the month-day notation, and July 22, 22/7 by the day-then-month notation.
But the Jewish calendar has its own day for this!
The first day of Succot is the 15 of Tishrei (בְּמִדְבַּר כט:יב וּבַחֲמִשָּׁה עָשָׂר יוֹם לַחֹדֶשׁ הַשְּׁבִיעִי). Hoshana Rabba, six days later, is the 21rst.
And Shmini Atzeret, the great day of closeness between Hashem and His nation - is the 22nd day of the 7 month.
We are His people, and He is our PhD advisor.
Thursday, August 6, 2015
Sarcasm on Parshat Korach
:Parshat Korach begins as follows
וַיִּקַּח קֹרַח, בֶּן-יִצְהָר בֶּן-קְהָת בֶּן-לֵוִי; וְדָתָן וַאֲבִירָם
בְּנֵי אֱלִיאָב, וְאוֹן בֶּן-פֶּלֶת--בְּנֵי רְאוּבֵן.
And so took Korach son of Yitzhar
son of Kehat son of Levi; and Datan and Aviram sons of Eliav, and Oen son of
Pelet, sons Re'uven.
What did they take? In all the rest
of Tanach, The word 'Vayikach' always has a clear object, the person taking,
and a clear subject, the thing being taken. Here, the Torah only tells us who
took!
I conjecture that they, in fact,
took themselves. The language the Torah uses thus indicates that they
took themselves – and from where? They took themselves out of the congregation
of Bnei Yisrael.
Rav Hirsch on this parsha notes
that 'taking', by its very nature, is also to make separate. I note that the
words of separating in ancient Hebrew grow from the root word Kuf Daled Shin -
Kadesh.
When Korach says to Moshe &
Aharon:
'hashem - רַב-לָכֶם--כִּי כָל-הָעֵדָה כֻּלָּם קְדֹשִׁים,
וּבְתוֹכָם יְהוָה; וּמַדּוּעַ תִּתְנַשְּׂאוּ, עַל-קְהַל'
Korach is employing sarcasm - he is
insinuating that his Kahal – the Kahal that just constituted itself
against Moshe and Aharon - is, by merit of having declared themselves separated
to be leaders, more able and more worthy of leadership of Bnei Yisrael than
Moshe – after all, Moshe was chosen by God, but Moshe was a reluctant
leader - he only led because he had to. Korach is saying: Hey! Moshe - Good
News - you can step down now, we got this under control! You don’t have to
carry this burden anymore. It sounds pretty good, without the retrospect…
The adage that "Those who most
seek power are those least fit to wield it" is indicated to be correct in
God's eyes by His response to Korach’s Kahal’s Kedusha-claim. Or maybe, He
simply dislikes sarcastic politicians!
Symbolism of the Rainbow
While walking to shul this past on a recent erev Shabbat, the one upon which the 9th of Av fell this year, I saw a faint rainbow in the clouds. This led to some mind-wandering on my walk, which ended with me pondering the following question:
Why is the rainbow the symbol of the covenant between God and Noach in the 9th Perek of Bereishet:
יב: וַיֹּאמֶר אֱלֹקים, זֹאת אוֹת-הַבְּרִית אֲשֶׁר-אֲנִי נֹתֵן בֵּינִי וּבֵינֵיכֶם, וּבֵין כָּל-נֶפֶשׁ חַיָּה, אֲשֶׁר אִתְּדֶ--לְדֹרֹת, עוֹלָם
12: And God said: 'This is the token of the covenant which I make between Me and you and every living creature that is with you, for perpetual generations
...
טז: וְהָיְתָה הַקֶּשֶׁת, בֶּעָנָן; וּרְאִיתִיהָ, לִזְכֹּר בְּרִית עוֹלָם, בֵּין אֱלֹקים, וּבֵין כָּל-נֶפֶשׁ חַיָּה בְּכָל-בָּשָׂר אֲשֶׁר עַל-הָאָרֶץ
16: And the bow shall be in the cloud; and I will look upon it, that I may remember the everlasting covenant between God and every living creature of all flesh that is upon the earth:
Why is the rainbow chosen as the symbol of this covenant? Why not a torrential downpour? A terrible storm? A dove? A large boat? Why specifically a rainbow?
I propose the following:
The generation of the flood committed many sins - of violence and thievery and so on. Their sins were rooted in Sinat Chinam (Bereishit Rabbah 38:6) - in 'free' hatred (I will discuss that concept further in a future post).
What is one, if not the, root cause of Sinat Chinam? When one sees other people as completely separate from oneself - when any difference from oneself in another makes one's fellow an 'other' - a non-person.
A rainbow, to the human eye, looks like it is made of several distinct and separate bands of color. In reality, the color changes continuously*, without borders, along the width of the rainbow.
This is the symbol for Man - that we should look upon the rainbow, and perceive the symbol, to remember that as different as we may be from one-another there is no wall between us, there is no division that brings forth such a differentiation as between 'person' and 'other' - and when this is abrogated, Mankind once more walks the path of destruction.
May we all endeavor to bring forth, and merit to see, the day when all of humanity will hold this principle in their minds, and teach it to their children, inductively, for all time.
*For the mathematically inclined:
I note that in reality this is not quite true according to a mathematically rigorous usage of continuity, at least in the typical sense with which it is applied in analysis, due the the fundamental graininess of the universe on the smallest scale. I do not think that this negates the nice symbolism, and one can read not 'continuously' but rather 'without borders or sudden changes' if so desired.
Why is the rainbow the symbol of the covenant between God and Noach in the 9th Perek of Bereishet:
יב: וַיֹּאמֶר אֱלֹקים, זֹאת אוֹת-הַבְּרִית אֲשֶׁר-אֲנִי נֹתֵן בֵּינִי וּבֵינֵיכֶם, וּבֵין כָּל-נֶפֶשׁ חַיָּה, אֲשֶׁר אִתְּדֶ--לְדֹרֹת, עוֹלָם
12: And God said: 'This is the token of the covenant which I make between Me and you and every living creature that is with you, for perpetual generations
...
טז: וְהָיְתָה הַקֶּשֶׁת, בֶּעָנָן; וּרְאִיתִיהָ, לִזְכֹּר בְּרִית עוֹלָם, בֵּין אֱלֹקים, וּבֵין כָּל-נֶפֶשׁ חַיָּה בְּכָל-בָּשָׂר אֲשֶׁר עַל-הָאָרֶץ
16: And the bow shall be in the cloud; and I will look upon it, that I may remember the everlasting covenant between God and every living creature of all flesh that is upon the earth:
Why is the rainbow chosen as the symbol of this covenant? Why not a torrential downpour? A terrible storm? A dove? A large boat? Why specifically a rainbow?
I propose the following:
The generation of the flood committed many sins - of violence and thievery and so on. Their sins were rooted in Sinat Chinam (Bereishit Rabbah 38:6) - in 'free' hatred (I will discuss that concept further in a future post).
What is one, if not the, root cause of Sinat Chinam? When one sees other people as completely separate from oneself - when any difference from oneself in another makes one's fellow an 'other' - a non-person.
A rainbow, to the human eye, looks like it is made of several distinct and separate bands of color. In reality, the color changes continuously*, without borders, along the width of the rainbow.
This is the symbol for Man - that we should look upon the rainbow, and perceive the symbol, to remember that as different as we may be from one-another there is no wall between us, there is no division that brings forth such a differentiation as between 'person' and 'other' - and when this is abrogated, Mankind once more walks the path of destruction.
May we all endeavor to bring forth, and merit to see, the day when all of humanity will hold this principle in their minds, and teach it to their children, inductively, for all time.
*For the mathematically inclined:
I note that in reality this is not quite true according to a mathematically rigorous usage of continuity, at least in the typical sense with which it is applied in analysis, due the the fundamental graininess of the universe on the smallest scale. I do not think that this negates the nice symbolism, and one can read not 'continuously' but rather 'without borders or sudden changes' if so desired.
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