Thursday, March 31, 2011

Greatness in humility

“Where you find the greatness of the Holy One, blessed be He, there you find His humility.”
Talmud Bavli, “Megillah” 31a

What is the meaning of the above statement? What does it mean for G-d to be humble, to be great and to be both? In my mind, I see a few levels:
  1. In the simple meaning, His greatness and His humility can be found “in the same place”, at the same time. These two characteristics coexist, simultaneously, side-by-side. For instance, G-d creates the Universe every single second; He is holy, awesome and exalted; the angels praise Him daily, and the righteous are in awe of Him. Yet, He cares about the needs of every single worm, and we can address Him with the simplest of requests. “Kadosh, kadosh, kadosh...”, yet “poseach es yadecho...”.

    (In the words of Talmud, quoting from Dvorim: He is “The King of kings, the Supernal Being above all supernal beings, and Master of all masters — and yet, He judges on behalf of the orphan and the widow.”)

    This may teach us (who are supposed to “walk in the paths of Hashem”) that no matter how great and important we may (perceive ourselves to) be, we must still find time and space for even the most unimportant of creatures, events and people. Furthermore, we cannot be haughty about our station — the true greatness is evidenced by humility.

  2. Alter Rebbe asks a question in Tanya: how is it possible for us to say that G-d — the great exalted G-d — cares about what we eat, what we wear, what we do in our everyday lives? He answers: because Torah is really G-d’s Will and Wisdom, stemming from His Essence, and piercing each of the spiritual worlds, enveloping itself in the “garments” of each of the worlds, until it reaches the material world and envelops itself in the physical matters: in the physical food, in the meat of kosher animals for consumption and skin for parchments, in the wool for tzitzis, etc.

    And don’t say that G-d cares only about the spiritual because He Himself is so exalted and above the material. First of all, G-d is as high above the spiritual as above the material. Second, “where you find His greatness, you find His humility” — G-d’s “greatness”, i.e., His exalted Will and Wisdom, descend into this world to envelop themselves in the material matters, to become accessible to us, such that we, through performing mitzvos, can make a Dwelling for G-d in the physical Universe.

  3. Looking at Seider Hishtalshelus, the spiritual chain of the worlds and G-d’s Lights and Vessels, there is a point, where we see that we cannot go any higher. It’s the most “lifnei” and the most “le’ma’alah” one can get. Above all the worlds, above all tzimtzumim, above all definitions, powers and potentials. There, we say, is the true greatness of G-d. Well, “where you find His greatness, you find His humility”. Even that exalted level above all comprehension is merely G-d’s “humility” — His lowering Himself from His Essence to have connection to His creation.

    This is the concept of yedias ha’shlila, study through negation: one first learns about the worlds and Lights of G-d, how exalted, beautiful and awesome they are. About G-d’s creation of everything every single moment out of nothing. About His bringing of His spiritual Universe out of nothing through His Lights and His vessels, and all their intricate interactions and mysteries, a glimpse of which is barely accessible to human understanding after years of work. And after all that, we know that this “greatness” is nothing but G-d’s humility.

  4. Wherever you find G-d’s ability to reveal Himself (His “greatness”), through His Light — you find equally His ability to conceal Himself through His vessels and tzimtzumim. Both stem equally from G-d. “Hashem Elokeinu, Hashem Echod.” One cannot say that G-d is only infinite, for that way one limits Him too. G-d can express Himself through finitude as well as through infinity.

  5. At the moment where you observe G-d’s “humility”, His concealment of Himself, you actually observe His greatness. Revelations, Lights, spirituality, Upper Worlds, the souls and the angels — that’s not the true greatness of G-d. The vessels and tzimtzumim, the power to conceal and to limit and not to shine (“yecholto she lo lehoir”, or, lower, “koach ha’gvul”), the physicality and materiality — and, finally, the human body. All of these are, despite being expressions of G-d’s “humility”, so to speak, are actually expressions of His Greatness, expressions of His Essence.

    In that case, why do we need the Light? In order to reveal that His Humility is actually His Greatness.

Monday, March 28, 2011

Proving that G-d exists

From Wikipedia, Gödel's proof of G-d's existence:

The proof



\text{Ax. 1.} & \left\{P(\varphi) \wedge \Box \; \forall x[\varphi(x) \to \psi(x)]\right\} \to P(\psi) \\

\text{Ax. 2.} & P(\neg \varphi) \leftrightarrow \neg P(\varphi) \\

\text{Th. 1.} & P(\varphi) \to \Diamond \; \exists x[\varphi(x)] \\

\text{Df. 1.} & G(x) \iff \forall \varphi [P(\varphi) \to \varphi(x)] \\

\text{Ax. 3.} & P(G) \\

\text{Th. 2.} & \Diamond \; \exists x \; G(x) \\

\text{Df. 2.} & \varphi \text{ ess } x \iff \varphi(x) \wedge \forall \psi \left\{\psi(x) \to \Box \; \forall x[\varphi(x) \to \psi(x)]\right\} \\

\text{Ax. 4.} & P(\varphi) \to \Box \; P(\varphi) \\

\text{Th. 3.} & G(x) \to G \text{ ess } x \\
\text{Df. 3.} & E(x) \iff \forall \varphi[\varphi \text{ ess } x \to \Box \; \exists x \; \varphi(x)] \\
\text{Ax. 5.} & P(E) \\
\text{Th. 4.} & \Box \; \exists x \; G(x)

Modal logic

The proof uses modal logic, which distinguishes between necessary truths and contingent truths.
truth is necessary if its negation entails a contradiction, such as 2 + 2 = 4; by contrast, a truth is contingent if it just happens to be the case, for instance, "more than half of the earth is covered by water". In the most common interpretation of modal logic, one considers "all possible worlds". If a statement is true in all possible worlds, then it is a necessary truth. If a statement happens to be true in our world, but is false in some other worlds, then it is a contingent truth. A statement that is true in some world (not necessarily our own) is called a possible truth.
property assigns to each object, in every possible world, a truth value (either true or false). Note that not all worlds have the same objects: some objects exist in some worlds and not in others. A property has only to assign truth values to those objects that exist in a particular world. As an example, consider the property
P(s) = s is pink
and consider the object
s = my shirt
In our world, P(s) is true because my shirt happens to be pink; in some other world, P(s) is false, while in still some other world, P(s) wouldn't make sense because my shirt doesn't exist there.
We say that the property P entails the property Q, if any object in any world that has the property P in that world also has the property Q in that same world. For example, the property
P(x) = x is taller than 2 meters
entails the property
Q(x) = x is taller than 1 meter.
The proof can summarized as:
IF it is possible for a rational omniscient being to exist THEN necessarily a rational omniscient being exists.

Friday, March 25, 2011

A little cell magic in Matlab

Imagine we have four variables: x, y, std, and stdErr. Each variable is an array. So, we have a series of x-values, y-values, and, because each y-value is really an average of a set of values, we also have standard deviation and standard error assigned to each x.

These variables are part of a structure, called curve. So, we have our fields:
Now, for whatever reason, I have pre-allocated 100 values (empty) to all my variables. Some of them are empty; some are filled. I want to get rid of the empty values. I know that I have N non-empty values. So, then:
newCurve.x = curve.x (1:N, 1);
% newCurve.x gets assigned values from 1st to Nth from curve.x along
% the 1st column

newCurve.y = curve.y (1:N, 1);
newCurve.std = curve.std (1:N, 1);
newCurve.stdErr = curve.stdErr (1:N, 1);
That does the job, doesn’t it? Well, surely so, but... it’s a bit boring. Unimaginative. Repetitive. Imagine I had fifty fields in my curve structure. I don’t want to copy-paste the same line fifty times, making corrections for a new variable each time. So, can we make this process a bit streamlined?

Well, my idea is to convert the structure into a cell; convert a cell into a matrix; use Matlab’s simple matrix operation (seen above for the matrix with size 1) to select the non-empty in the matrix; convert the matrix back into a cell, and convert the cell back into a structure. So, I have really only three steps — except that I have to tell the cell2struct function what the resulting structure’s headings are, so I have to have another line of code with those (Update: using fieldnames function, I can skip that step).

    %% a little cell magic

    %converting to a matrix
    curve_mat = cell2mat( struct2cell(curve)' );

    %assigining non-zero values to a cell from the matrix
    shortCurve_cell = num2cell( curve_mat(1:N,:), 1);

    %converting back to a structure with field names = those of curve
    newCurve = cell2struct (shortCurve_cell, fieldnames(curve), 1);

With only four fields, I don’t really save much space (just one line of code), but you would with fifty... But that’s not the point. The point is that a soul of a former C-programmer sings when it looks at the second piece of code.

The next step is to automate the process further by writing a function outputCurve = removezeros (inputCurve, numFilled) that will take a curve structure and the number of filled values and return a structure with zero values removed. The above code will be in the function.

If you know of an even more elegant way of doing this (I am new to Matlab, so I don’t really know cell manipulation well), please comment.

By the way, in the end, if we plot the newCurve using errorBar function, we get the following:

Wednesday, March 23, 2011

Harnessing the mind: binah vs. tvunah

Source. (Click on the link also to read the text description of what binah and tvunah are, what the differences between them is and how to apply them.)

Monday, March 14, 2011

Two types of foolishness

In the ma’amor Bosi LeGani, we learn that we can create the Dwelling for G-d in this world by turning shtus d’l’yuma, the foolishness of the world, into shtus d’kedusho, the foolishness of holiness.

What is meant by the former? Being too absorbed in the wordly things for their own sake. Clothes, food, jewelry, gadgets, computer games, politics, your job. What is meant by “the foolishness of holiness”? Serving Hashem with utmost devotion, breaking even boundaries in holiness — the limitations and excuses one has set up for oneself not to grow in Torah matters. Regarding this the Rebbe says:

The way to break out of the bounds and restrictions imposed by the animal soul is to conduct oneself according to the Shulchan Aruch and to study ethical writings. This enables a person to realize that materiality is utterly worthless. As a result he will free himself of the restrictions of the animal soul, and of course from the restrictions of the body. However, when it comes to freeing oneself from restricting bounds in holy matters, that's quite a different story.

Exactly what are the latter restraints?

Concerning the study of Torah a man might argue: It’s enough for me that I am one of the “supporters of the Torah”; it's enough that I study “one chapter in the morning and one chapter in the evening”; the shiur after davenen will suffice; studying without exerting the soul or the  flesh will be quite enough; it's enough that I study nigleh, the revealed plane of the Torah: do I have to study Chassidus as well?!

Concerning avodah, i.e., davenen, the same individual argues that it's quite enough that he arrives at shul in the middle of davenen; according to the Shulchan Aruch he can then skip most of Pesukei DeZimrah, the psalms of praise — i.e., three-quarters of the davenen — so long as he prays together with the congregation. Surely it's enough that he hastily churns and chops his way through the words, without taking time off to think what they mean. If he does think about what the words mean, without meditating for a moment on Whom he is addressing, then surely that's more than enough. As to the earnest frame of mind that is supposed to precede prayer, he discharges this obligation by clasping his hands like a servant before his master; now, having done that, he can allow his thoughts to fly hither and thither...

Concerning tzedakah, this individual argues that the Shulchan Aruch itself lays down limits. There is a certain quota required by the Torah, deoraysa, and there is a certain quota required by the Sages,deRabbanan — and surely he is not obliged to give away more than the prescribed minimum. As to giving away more than a fifth of his income, then this is not only not obligatory, but (he argues) forbidden! For did not the Sages say that “he who gives freely should not give away more than a fifth”?

Besides, this individual argues, in no area of his life should a man make more stringent demands on himself than the Torah requires him to. For this stance he quotes the Talmud Yerushalmi: “Let the Torah's prohibitions suffice for you!” “Tell me,” he protests, “am I expected to be more pious than the Yerushalmi?!” In similar vein such a man contends that it is not proper to expect him to do things that go beyond the letter of the law: if only he would conduct himself according to the law, he says, according to the Shulchan Aruch…

These arguments derive from the limitations of one’s mindset — including the limitations of one’s mindset in holy matters.
 But what does it mean to convert the foolishness of the world[ly matters] into the “foolishness” of holiness?

The Rebbe explains in Bosi LeGani (Tes-Vov) that this means, on one level, taking the energy that you invest into the worldly things and re-investing it into holy things. You are not going to skip a meal, are you? If you’re hungry, you’re hungry — you will drop everything and go eat lunch. You are not going to go to sleep a little late, are you? “Sorry, I am tired; good night.” If you’re reading a book or watching a movie, you can become so absorbed in them that you will becoming completely unaware of the world around you.

Well, use the same attitude towards the holy matters. Don’t delay (or, G-d forbid, skip) learning or davening just like you wouldn’t delay or skip a meal or going to sleep. Become as absorbed in davening and learning Torah as you’re absorbed in, lehavdil, watching a fascinating movie or reading a captivating book. Run to do a mitzva as fast as you run to move your car if you know you may get a ticket. When you’re wondering whether you should “take it easy” in some concept of kedusha, replace mentally this concept with some aspect of your everyday material life, and ask yourself whether you’d take it easy there.

Then take that energy of mental investment into the worldly things (and for every one of us, this is individual: for instance, I don’t care about following sports, but I like reading fantasy; I don’t care about clothes, but I care about gadgets or computer programs; I am bored in a jewelry shop, but bring me to a bookstore, and I will get lost there¹ — for someone else, however, the list can be quite different) and apply that energy to kedusha.

¹ I know, “nerd alert”...

Sunday, March 13, 2011

Of vessels and shuckling

As I have stated in the last post, people show two extreme forms of davening: 1) davening with many outbursts of emotions in a form of exclamations, gesticulations, etc., and 2) davening very quietly and motionlessly.

Two reasons can exist for each form. For the first form, one of the reasons is that the person is fake. Or, giving him limud zchus, he is not faking his emotions intentionally, but he gets excited by the emotions (sometimes artificially induced) themselves, not by Elokus. I.e., he knows he must feel emotions about Eibeshter, and he thinks (erroneously) that when one feels these emotions, one is supposed to cry out and shake his hands, so he does the latter... and sure enough, he feels something, but it’s not directed at the Eibeshter; it’s directed at himself.

For the second form, a person can be quiet because he doesn’t really feel anything when he davens — either artificial or real. He just says the words, and maybe he even knows their meaning, but no emotions are produced in his mind. So, he is quiet.

But what about those who daven properly? Those who feel emotions, and the emotions are directed to Elokus, and yet they either cry out and express themselves outwardly or are very quiet.

When Alter Rebbe was nistalek, there was a question about who was going to be the next Rebbe of Chabad Chassidus. Some Chassidim favored the Mitteler Rebbe, Alter Rebbe’s son, and some favored Reb Aaron Strashiler, the Mitteler Rebbe’s former chavrussa. Now, to be sure, both had Rebbishe neshamos. But there was a difference in their avoida: when Reb Aaron davened, he was very expressive outwardly, and when Mitteler Rebbe davened, he was absolutely quiet and motionless.

One chossid remarked once on this difference. He said: Reb Aaron brings very great Oiros (Supernal Lights) into his neshama when he davens. But the lights are so great that they cannot be contained by the keilim (vessels) of his neshamo, and as a result, the Light “spills over” and creates a sort of emotional exothermic reaction, with Reb Aaron expressing himself very greatly.

Mitteler Rebbe, the chossid continued, also brings down great Oiros. But his neshama’s keilim are big enough to incorporate the Oiros into themselves. As a result, he davens motionlessly, because all the “energy” of the Lights is absorbed.

The difference is, said the chossid, that the Light that Mitteler Rebbe brings down stays, since it has become internalized into his neshamo...

The lesson for us (whose keilim are miniscule, and who cannot bring down great Oiros) is that we can become very emotional during davening and feel like we are surrounded by holiness. And then we can finish davening, take off tefillin and tallis, zip up the tallis bag, and go on being the same selves that we had been before the davening. That is a result of not internalizing the Light that one brings down into his neshamo during davening.

The way to avoid that is daven b’avoido — prepare oneself before davening by learning about Eibeshter and Elokus, daven slowly and deliberately, and think intently and deeply about what one has learned, trying to “see” Eibeshter in the words of prayer. To make sure, when talking to the Eibeshter, to force oneself to really address Him and not the pages of the siddur or the wall. And when one experiences emotions, not let them spill out, but keep them inside, burning like the hidden flame inside a coal.

It doesn’t always work — neither from day to day, nor from page to page, but it is important to keep trying and keep pushing.

Thursday, March 10, 2011

Quiet and dry

One rap star, who had once claimed to be a part of Chabad movement, remarked, upon his apparent “conversion” to a different branch of Chassidus, that he was not inspired by Lubavitch style of davening. “A Lubavitcher whispers when he davens,” he said. “[A member of another Chassidic group] screams.”

(When I heard this story for the first time, I remarked: “It is not polite to yell at the Eibeshter.”)

I have heard a story about one “Polish” Chossid remarking that Chabad is like a handgun without a flint. A complicated mechanism, with the many hammers and springs and wheels... but the spark is not there.

And true — Chabad Chassidim (the real Chassidim) and especially Rebbeim have always been known for the very quiet nature of their avoidas ha'lev, the service of prayer. Why is that?

I heard today a description of three levels of avoida in the Beis HaMikdosh. The first level was karbonos, the sacrifices. In order to burn all the meat, the kohanim burnt large pieces of wood, stacked on top of each other. The fire was roaring — Gemara remarks that sometimes things would be thrown off the platform by the fiery winds. The combustion of the fire was fighting with the moisture of the wood and the flesh: two opposites, one trying to overcome another in a roaring struggle.

When Menoira was lit, it was silent. The flame burnt the finest, purest olive oil. This was no struggle. A peaceful co-existence of the flame, the wick and the oil.

When the ketores (the incense) was lit, there was neither flame nor smoke. Apparently, when the incense was dried very well (and made into a very fine powder), it would not even give off smoke (the smoke is a result of moisture remaining in the incense); nor would it burn with a flame. It just quietly smoldered away, releasing the smell.

The first level of service represents the struggle between the spiritual (fire) and the physical (water), the struggle between the G-dly Soul and the Animal Soul. As the former tries to subdue the latter (in a process called iskafia), their fight releases much heat, passion and noise.

The second level represents a union between the spiritual and the physical — and, likewise, the union between the G-dly and the Animal Soul, where the first transforms the second in an act of ischapcha. The flame and the oil co-exist in shleimus, and there is no need for all the noise and outward expressions of the combustion. And yet, two distinct entities exist on this level — albeit at peace with each other.

On the third level, the level of ketores (which, according to Chassidus, corresponds to Atzmus Ve’Mahus of Hashem), not only is there no noise or struggle, not only is there no outward release of “emotions” (even in a form of a quiet smoke) — there is not even a separation between the flame and its fuel. There is complete unity. Similar to Achdus Hashem, the Oneness of G-d — Oneness not only in His Essence, but also with His Creation, both spiritual and physical, both Light and Darkness.

The first Rebbe of Chabad, Shneur Zalman of Liadi, was known to say, while davening: “Ich vil nisht Gan Eiden Tachton. Ich vil nisht Gan Eiden Elyon. Ich vil Dich Alein.” (“I don’t want the Upper Gan Eiden. I don’t want the Lower Gan Eiden. I want You Alone.”) Rebbeim Chabad were not satisfied with having His Light. They wanted His Essence too. And they reached what they wanted. But that is not what is special. What is special is that their shared Him with their Chassidim.

Also see on the subject: “Emotions which have not been internalized