Start your day with a healthy breakfast

Who can count accurately how many layers this picture contains?

Up and down

When Jews were crossing the sea, two events happened. One: the Heavens descended down to the Earth. Two: the Earth was elevated up to the Heavens.

Alter Rebbe explains in a ma'amor that sea represents G-d's Speech, which is the sphera of Malchus of Atzilus. All three concepts — sea, speech and Malchus — have in common that they exist both to unite and to separate. (Interestingly, this is also the idea seen in the mitzva of Havdala.)

In order to express his thoughts to others, a person must speak. But at the same time, speech separates the one who receives the person's ideas from the person's mind. Once spoken, thoughts do not exist anymore in the same state as they did in the mind. They are made accessible, crystallized — and also limited.

Similarly, the sphera of Malchus of Atzilus exists to create the lower worlds, to direct to them the light of its own world — but at the same time, Malchus separates the three created worlds from Atzilus.

In this way, it is also similar to the sea. Malchus is called "the great sea", because, just like "all rivers fall into the sea", the six emotional spheros (Ze'er Anpin) collect their lights into Malchus. And just like the sea separates the marine creatures from the earth creatures, since the former cannot breath above the water and the latter cannot breath below it, Malchus of Atzilus makes sure that the phenomena of Atzilus cannot exist in the created worlds (they would "suffocate" from such limited Light) and that, conversely, the created beings cannot ascend into Atzilus (since they can only receive the Light in a limited form through the vessels of their worlds and would "dissolve" in Atzilus).


This, then, was what happened during the Kriyas Yam Suf, the splitting of the Sea of Reeds: the Great Sea, Malchus of Atzilus, split. Two views (that of the Zohar and that of Arizal) exist regarding what happened:

1. The limitation of Malchus of Atzilus was stopped so that the Lights of Atzilus could descend and unite with the physical universe below and Jews inhabiting it.
2. When Malchus "split", the Jews were elevated into Atzilus.

One of the views places emphasis on the fact that the Jews were able to continue walking on dry land towards their destination. If there was a sea on their way — then the sea split, but that's not the main point. The other view's emphasis is on the fact that Jews were plunged into the middle of the sea. The dry-land aspect of the journey was only a means for the Jews to survive their journey into the realm normally uninhabitable.

Alter Rebbe explains in his ma'amor that both these points of view are correct: the Heavens split and the Supernal Lights were able to reach the physical Universe and the Jews, and, at the same time, Jews themselves were elevated to the level of the Supernal Lights.

Kriyas Yam Suf was an event that prepared the Jews for the receiving of Torah. The two spiritual aspects of the Splitting corresponded to two aspects of Mattan Torah: the fact that it was received (by Jews) and the fact that it was given (by G-d). On the one hand, Jews are never lofty enough to receive the Wisdom and Will of HaKodosh Boruchu Himself. On the other, G-d is too lofty and elevated above the physical aspects of the world for His Will to be associated with them. Both these limitations (so to speak) were broken at the Kriyas Yam Suf.

This explains what Torah and mitzvos accomplish. On the one hand, they elevate the person who performs them to the state of holiness ("asher kideshanu bemitzvoisav..."). On the other, they introduce G-dliness into the physical aspects of the world and the levels of our souls associated with them, creating a dwelling in the lower worlds for G-d.

On the more abstract level, the two aspects correspond to yichuda ila'ah and yichuda tata'ah: the Upper Unity and the Lower Unity. The first is the concept that ein od milvado — there is nothing but G-d, in a simple, literal sense. Even though on our level of reality, the worlds exist, in relationship to G-d's Essence, nothing exists. (Imagine this as the function of y = 1/x taken to infinity. The larger the x, the smaller the y — but still always finite. But when x = ∞, then y = 0, mamosh.) And obviously, our point of view is "wrong" when compared with G-d's point of view. On the ultimate level of truth, nothing but G-d exists.

The concept of Lower Unity corresponds to the idea of G-d's unity with all of creation. From this point of view, all of the worlds exist, but they are still completely one with G-d, in a perfect (albeit complex) unity. This is revealed by the fact that He creates them all every single moment (or, to put it more correctly, He creates their every moment). That His thought pervades them all. That for Him, they exist as one point, with all dimensions compressed into a single idea.


For our avoida, this means that two levels of bittul exist. These two levels are represented by two colors of flame (and two colors of tzitzis strings): white and blue. Flame is a symbol of bittul: the desire of the soul to "rise" and nullify itself to G-d. There is the "blue" level, the part of the flame that hugs the wick. Then there is the white level, the part of the flame which never even touches the wick.

In our lives, the blue flame corresponds to the idea of realizing and revealing G-d's omnipresence in our lives (on the one hand, the flame rises from the candle; on the other, it is still connected to the wick). The fact that everything that happens in our lives is connected to G-d and is only due to G-d's Will and Kindness. And, respectively, that everything that we do in our lives must be connected to G-d. We cannot do anything "stam". Everything must be, one way or another, an aspect of avoidas Hashem.

And then there is the level where nothing but G-d exists. This level is achieved in our avoida through contemplation about G-d, as we learn about Him in Chassidus, during davening, on Shabbos and holidays. On this level, not only is G-d one with the world, but G-d is One — the only one.

As Alter Rebbe's ma'amor teaches, both aspects are extremely important and both aspects are the part of our journey to Har Sinai — to the point in the world's history, where G-d's Essence will be revealed. And this time, not for a short time only, as it happened during Mattan Torah, but forever. May it happen speedily in our days.

Teshuva with the help of G-d

(curvature of space and time, according to Einstein's General Theory of Relativity — source)

In one of the previous posts, I wrote:

So, some people say that [...] an electron is actually a four-dimensional wave. Its interaction with quantum labeler changes its energy such that it becomes collapsed. Its interaction with quantum eraser restores the same energy level and restores the electron's wave — but, it restores it back in four dimensions (including the time), such that the electron is now a wave "again", not just in the space, but also in the time, including the point in the past where it passed through the slit. 

(I think this would be a good moshol for teshuva that [one] could use. When a person does teshuva, he goes back and erases his sin — in fact, turns his sin into a mitzva. This is because, although to our perception, we exist as a point on the time line, always moving forward, in reality, we exists in all possible dimensions at the same time. And, by making teshuva, we interact, with G-d's help, with ourselves in the past.)

I wrote "with G-d's help" deliberately, and not just because it is customary to do so when you're saying that you will accomplish something (i.e., as a more frum way of saying "hopefully"). There was some thought at the back of my mind when I was writing the above, but I didn't attend to it fully at the time. This morning, I thought more about it.

In reality, perhaps the moshol is not the most accurate. Because even though according to the above model, the electron is a four-dimensional wave (and there are other models that don't require that), there is no indication that we exist as a four-dimensional being, and that our past is as much an aspect of our reality as the present. I.e., there is no indication that we, "ourselves", can interact with our past, just like we can interact with our space by picking up a cup¹.

On the other hand, for G-d Almighty, past, present and future exist as one reality on the same level. The space, time, and whatever other physical or spiritual dimensions — all exist as one point, one singularity, for G-d.

(As an aside, I wanted to mention that my professor of German would sometimes show us German movies — for 15 minutes at the end of every class. After he was done with a particular DVD, he would "rewind" it, like one would a tape. And by that I mean he would press << on his DVD remote and wait until the movie reached the beginning. Eventually, someone explained to him that you don't have to rewind DVDs, just like you don't have to "rewind" books. Although, of course, a movie or a novel do no exist on a DVD or in a book as one single nekuda...)

That is why, if we reach to the Essence of G-d, to the point above all structure, space and time, we are able to change the past, so to speak, since past and present there are one. We do this by reaching to our yechida sh'b'nefesh, the essence of our soul, by performing teshuva, repentance. This is really the point of Yom Kippur — why it is so holy. Not that it is the day on which the sins are forgiven, but that it is the day on which we are one with Hashem, and on that level, a) no separations (sins) can exist between us and Him, and b) we are able to nullify our sins or even change them into mitzvos.

That is why the concept of teshuva is so important in Chassidus. If you will, teshuva is the reason why the world was created. The world exists as a seemingly separate entity from G-d. Our job is to reveal G-d's Essence in the world, to reveal oneness of G-d with the world. So, this is the ultimate teshuva — teshuva for the whole world. Space and time, perhaps. Because by revealing that the world is one with G-d today, we go back in the time and transform the "sin" (so to speak) — the existence of the world for all millenia in a state of concealment of G-d — into a "mitzva", revelation of G-d. We show that all the existence of the world, even in a form of concealment, was only for the purpose of (eventual) revelation of G-d in the world.

This way, we achieve perfect oneness of G-d with the world — not just with the space of the world, but also with the time of the world. May it happen speedily in our days.

___________
¹ Of course, nothing we do even in our everyday reality is "by ourselves". Everything we do is with the help of G-d, since G-d is creating the Universe every second. So, if I want to move a cup, I have to will it, and then G-d responds to that with the Universe re-created with cup moved (plus everything that needs to happen in my brain, muscles, etc., for me to move my hand).

Which means that on the one hand, when we punch someone's nose, we are asking Hashem to do something not nice. On the other hand, when someone punched us in the nose, it was really Eibeshter that did so — the other guy's decision to do so is between him and Eibeshter. Our nose would not get punched had we not deserved it.

First to space

Today is the 50th anniversary of the flight of the first man to space, Yuri Gagarin, sent there by the Soviet Union. He boldly flew... etc., etc.

To commemorate this, a few jokes:

Russians sent the first man to space. They also sent the first satellite to space, the first dog and the first hot-dog (when the first dog was on the way down).

Russians send the first man to space. A Ukrainian shepherd calls out to another Ukrainian shepherd:
— Mikola!
— What?
— Russians flew to space!
— All of them?
— No, just one.
— So, why are you bothering me?

Americans spent millions of dollars and decades of research on developing a pen that would work in zero gravity. Russians use pencils.

All jokes aside, when Gagarin came back, he said: "The Earth is very beautiful. Treasure it."

Consciousness and quantum mechanics

To clarify what I said in one of the previous posts about consciousness and quantum mechanics. (This is from a very limited and probably very erroneous understanding of this topic. Alternatively, you can just skip the mumbo-jumbo below and just watch this — no discussion of four-dimensional waves can happen without a reference to this scene.)

From what I understand, the idea is that measurement affects what "decision" the electron makes. According to some people, measurement is congruent with human consciousness. In reality, that's not necessarily the case, because just measurement alone (i.e., interaction with a non-conscious measuring device), without the consciousness, is enough to collapse the wave.

The same goes for Schrödinger's Cat. According to the "paradox", until you open the box with the cat, the cat exists as both alive and dead, and then your measurement (and, some people would say, consciousness) influences the reality.

(By the way, Schrödinger himself never postulated this as the state of events — he used his Cat as an argument ad absurdum to show that our understanding and mathematical apparatus of quantum mechanics are incomplete. But, interestingly enough, around the same time, Einstein, Podolsky and Rosen published a paper, in which they showed that, following mathematics of quantum mechanics, you can have a state of events when particles are separated spatially and yet are instantaneously linked to each other. I.e., just because they are far apart from each other doesn't mean they are distinct, independent entities. This was also an ad absurdum paper, but this phenomenon was shown to be true — it is now known as quantum entanglement. So, not all ad absurdums are absurd.)



Anyway, the point is that it doesn't require consciousness to collapse a function. What actually is required is measurement, but why that is the case is unclear. Some people say it's the interaction with the "macro-world" which collapses the function (in which case, Schrödinger's cat is exclusively dead or exclusively alive as soon as the electron interacts with the poisonous gas machine). But, recently they've done another experiment, in which they "labeled" the electron itself as having passed through either right or left slit (this way, one would know, once the electron reaches the screen, which slit it had passed through). Well, if you do that, you, as expected, collapse the interference pattern.



But then, if you put a "quantum eraser" between the slits and the screen, which will erase the "label" from the electron, you actually restore the interference pattern. So, when the electron interacts with the macro-world once, this collapses the wave function. But, if it interacts with the world twice, this restores the wave function! So, in the end, what's important is whether the electron's passage through one or the other slit is measured. If it is measured, the wave collapses. If the measurement information is erased, the wave is restored.



Again, this doesn't necc. say anything about the importance of consciousness. I think that we just have no idea what really happens when the electron wave collapses.

The unique thing about the Quantum Eraser experiment is that once electron wave collapses at the slit, there is no way that interaction of the electron's wave with itself can happen — but then, if you put up the quantum eraser, it restores the interference pattern... meaning, it is as if it told the electron: "Now go back to the past and actually interfere with yourself".

So, some people say that this shows that an electron is actually a four-dimensional wave. Its interaction with quantum labeler changes its energy such that it becomes collapsed. Its interaction with quantum eraser restores the same energy level and restores the electron's wave -- but, it restores it back in four dimensions (including the time), such that the electron is now a wave "again", not just in the space, but also in the time, including the point in the past where it passed through the slit. (I think this would be a good moshol for teshuva that Tzvi Freeman et al. could use. When a person makes a teshuva, he goes back and erases his sin — in fact, turns his sin into a mitzva. This is because, although to our perception, we exist as a point on the time line, always moving forward, in reality, we exists in all possible dimensions at the same time. And, by making teshuva, we interact, with G-d's help, with ourselves in the past.)

If you want an illustration of this concept, just watch this scene.

But, another interpretation of the Quantum Eraser experiment could be that when a wave function collapses, it does not collapse "completely", so to speak. It just passes from the state where it influences reality to the state where it does not, but it (and its interaction with itself) always exists in potential, alongside with the electron's "collapsed" path.

So, imagine that when electron passes through the two slits, all the possible paths it can take exist simultaneously — and interfere with each other in a wave-like fashion. Then, when the electron is "labeled", its wave function collapses, and only one of the paths exists "in reality". The other paths, however, do not disappear. They are still out there, hanging like punctured lines, "in potential".

If the electron is allowed to reach the screen, the potential paths and their potential interactions are never allowed to influence the reality of the electron's trajectory.

If, however, the electron interacts with the quantum eraser, the latter reverses whatever effect the quantum labeler did (by restoring the energy levels to the former, etc.). This restores the electron's state as a wave and all the "potential" possible paths become real (all at once) again — as well as their, so far only potential, interactions.

In this interpretation, there is no need to do something as esoteric as imagining the electron as a four-dimensional wave interacting with itself not only in space, but also in time. Although, perhaps the concept of potential paths existing in a state of semi-reality is even more esoteric.

Update: Regarding probabilities, a conversation in the kitchen:
— Did you know that on average, a human foot sweats a cup a day?
— Not my foot.
— I said “on average”.
— Just sayin’. My feet don’t sweat no cups per day.

Real and imaginary

(can you guess what function this is?)

Looking at the graph above made me think about how in "historic" sciences, such as Evolutionary Biology or Geology, we extrapolate the existing state of the world backwards in time to try to paint a picture of the past. This is like standing on the right part of the "blue" graph above (the "real" graph) and looking backwards, to x < 0.

But what if the world did not exist in the same state of "reality"? For example, it existed not in a material form, like today, but in some sort of spiritual form. And today, when we look at the world, we find the remnants of those "spiritual" processes (as they "materialized" themselves once the world passed x = 0) and, trying to interpret them, create a distorted picture of the past (since we have access only to the "real" part of the "function").

For instance, Evolutionary Biology shows relationship between species. Extrapolating back billions of years, it interprets it as descent with modification due to natural selection. And, considering that today descent with modification due to both natural and human selection is observed, that there is no reason to believe that it did not happen in the past, and that there is evidence consistent with the descent with modifications due to natural selection, all this seems to present strong evidence in favor of Theory of Evolution. (Even though many mechanisms are not clear, and many aspects of the evidence remain unexplained. So, nu, in every set of ideas you have holes and gaps. From physics to, lehavdil, Gemara. Just because there is a discontinuity in the function doesn't mean that we can't work with the function.)

But what if descent with modification did happen (and there may even have been selection), but not in "nature", since the nature, with the rest of the physical world, did not exist? Perhaps what really happened was some sort of evolutionary "spiritual" process that happened before the creation of the world and, during the first week 6771 years ago, "created" the species (which would not contradict G-d creating the species, since "He and His life-giving emanations are one; He and His garments are one" — i.e., G-d envelops Himself and becomes one with the spiritual tools with which He creates the worlds and all that is in them).

And now we see merely the material "shadow" of those spiritual events.



(Yes, I know I am misusing the concept of imaginary and real numbers. This is just a graphic illustration. There need not be a strict coherence between the moshol and the nimshal. Also, you can interpret "imaginary" as a product of our extrapolation, or you can say that "imaginary" = spiritual, while "real" = material.)

Wave function build-up and the skier of Charles Addams: the gist

[Since people have ADD, I split my last post in two parts.]

This is known as a collapse of wave function.

In his book, Wheels, Life and Other Mathematical Amusements, Martin Gardner asks:

Single-panel gag cartoons, like Irish bulls, are often based on outrageous logical or physical impossibilities. Lewis Carroll liked to tell about a man who had such big feet that he had to put his pants on over his head. Almost the same kind of impossibility is the basis of a famous New Yorker cartoon by Charles Addams of a woman skier going down a slope. Behind her you see her parallel ski tracks approaching a tree, going around the tree with a track on each side and then becoming parallel again. 

Suppose you came on a pair of such ski tracks on a snowy slope, going around a tree exactly as in Addams's cartoon. Assume that they are, in truth, tracks made by skis. Can you think of at least six explanations that are physically possible?

In his Answers section, after listing the possibilities, he jokingly brings a cartoon by J. Hart. I call this situation a wave function build-up:

Wave function build-up and the skier of Charles Addams: background

Everyone knows about wave function collapse. (If you don't want to read about it, skip to the quote from Martin Gardner.)

In short, imagine you wanted to determine where I am right now. Without knowing my exact location, but knowing where I might be, you can assign probabilities to a number of locations. I can be at my home. I can be at work. I can be on my way in between. I can be in a grocery store. I can be shopping for a new pair of headphones at BestBuy. And so on. I can also be in Maryland — but with much lower probability than in the above places, although probability greater than zero. Probability of me being on the moon right now is very-very close to zero. Probability of me being in Alpha Centaura solar system is zero.

So, you can draw a "probability cloud", with each location's density proportional to the probability of my being there.



At different times, my probability cloud changes shape. For instance, on Shabbos, it becomes restricted to the walking distance around my house, and it's densest at my house, my shull, and the homes of the few people that I go to lunch to on Shabbos with my wife. Around Peisach time, my probability wave will shift to Skokie, when I will be visiting my in-laws. And so on.

The interpretation of the probability cloud regarding me is that I may be found in any of the locations on the cloud. In reality, however, at any given moment of time, I am at only one of those locations. It's not like 50% of me is at my work, 40% is at home, and 10% on the highway in between. The probability cloud is a result of your lack of precise knowledge about my location. If you put a GPS device on me, my probability cloud in your measurement will shrink to whatever the limitations of the device's accuracy are (e.g., plus-minus ten meters).

Well, in the quantum world, it's different. An electron's probability cloud has reality. The electron really exists at the same time in all the places represented by its probability cloud — the greater the probability, the more it exists there. It's as if the electron's metzius was smeared over the space.


(different shapes of electron's orbitals)


Well, if you make an experiment of shooting an electron (or any other quantum "particle") through two slots many times, as everyone knows, the collection of the marks on the screen where the electron hits will have interference pattern — a pattern similar to what you would see if you sent two waves of any kind through two slots (e.g., waves of water or a wave of light).

As waves go through space, they interfere with each other, partially cancelling each other in some places and super-imposing on each other in others, forming this pattern in the end:



In contrast, if you shoot a bunch of pellets through two slots, those pellets that pass through will form two parallel bars of marks on the screen — since the pellets don't interfere with each other (as waves do) when they fly.



(Watch this cartoon for a description of the whole experiment.)

Now, if you shoot a bunch of electrons at the screen, they will form wave-like interference patterns seen above. This suggests that electrons interfere with each other as waves when they fly through space. But, even more shockingly, if you shoot electrons one at a time, the interference pattern will be the same (with each bright bar representing places of greater probability for the electrons to hit the screen). It's as if the electron is interfering with itself when flying through space — which means that it doesn't fly as a particle, but as a probability wave, a wave of metzius, if you will, which interferes with itself just like a water wave passing through two slits.



In the last part of the experiment, if you put a detector next to one of the slits, to see if the electron "really" passes through the slit, the interference pattern forming on the screen will be only two bars. It's as if when you observe the electron, you force it to pick a slit. While flying unobserved, the electron is free to be as "scatter-brained" and indecisive as it wants (or as its wave function dictates). But, when meeting a detector (and, whatever Tzvi Freeman tells you, it's not the human consciousness that the electron meets, but simply a piece of macro-world, a detector, which will work even if the human being with his consciousness went to lunch), the electron has to make a decision, and it will decide for sure that it wants to fly through the one slot only or through the other.

This is known as wave function collapse.

[Continued in the next post.]

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.

Proving that G-d exists

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

The proof

Symbolically:

Modal logic

The proof uses modal logic, which distinguishes between necessary truths and contingent truths.

A 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.

A 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.

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:

curve.x
curve.y
curve.std
curve.stdErr

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).


Thus:

    %% 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:

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.)

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”...

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.

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”

Compromise

“The Rebbe never-ever permitted or encouraged compromising ourselves to save another Jew. The Rebbe would always say: ‘You have to bring the Jew to Torah, not Torah to the Jew.’”
— Rabbi Yossi Paltiel, “Chassidic dress” (part of What is Chassidus series)

Bad grammar kills

Maybe it doesn't kill bodies, but it definitely kills minds and souls.

After ruling Libya for decades, people are wondering for how long Col. Gaddafi can stay in power.

Who ruled Libya for decades? The "kernel" or the people? From the sentence, it reads like the latter. The correct sentence options would be:

People are wondering: after ruling Libya for decades, how long Col. Gaddafi can stay in power?

Or:

After Col. Gaddafi's rule of Libya for decades, people are wondering how long he can stay in power.

Think before writing. Please. It's almost as important as showering and brushing your teeth.

In other news: retzuos painted black on both sides may be past nisht. Stay tuned.

iPhones kill

Time Warp Project from Uirá Lamour on Vimeo.

Also, obviously, American music and not wearing seat belts while driving at fast speeds.

This clip shows that wearing a seat belt at low speeds, in the city, is completely useless. A seat belt would do nothing to prevent this guy from banging his head. In fact, his having banged the head, the seat belt would probably make it harder for him to get out of the car (since it’s difficult to fumble with the seat belt with a concussion).



P.S. Actually, I’ve watched the first clip again, and it seems that when the guy looks up, he is still in his lane, and it is the other car that crashes into him, suddenly — which, considering the speed at which he was driving, would be difficult to avoid anyway. So, what is the clip trying to say: if you look down to text or change the track on your phone/iPod, then another car might crash into you? Also, nobody spends that much time looking down. You look down, look up, look down, etc. Not that it’s not still dangerous...

Message of the day

Don’t be frum from birth. Be frum from growth.

Marx would be happy

More information here.



This reminds me:

There is no such thing as an equal exchange. At the point of exchange, both buyer and seller consider themselves to be better off as a result of the exchange. In a system of extensive specialization and division of labor, most goods are produced for exchange. Specialized producers have little, if any, direct use for the goods they have produced; under the principle of diminishing marginal utility, the marginal utility of a unit of production is virtually zero as far as they are concerned. They place a higher valuation on the money that they can get for their goods. On the other hand, consumers or buyers value the goods obtained more highly than the money spent to acquire them. Exchanges can occur only when there are differences between the subjective valuations expressed by the parties of the exchanges.
        The failure to consider this subjective orientation led to the unfortunate notion of the "economic man," which depicted every participant in the market economy as relentlessly seeking at every turn to maximize his monetary position. This idea is unrealistic because what people actually seek in every action is a maximum psychic or subjective profit.
        There are numerous examples of people forgoing additional monetary wealth because they deem the "cost" to be greater than its worth. There are investors who resist monetarily rewarding investments in industries whose products they find objectionable. Marketers have recognized that consumers sometimes consider factors besides the purchasable good and its related price. The availability of parking, the courtesy of clerks, and "store personality" now receive attention in discussions of merchandising. Wealthy entrepreneurs who continue to involve themselves in profit making even in their old age are undoubtedly motivated in many cases by something besides money. People often consider factors in addition to wages in deciding on a career or particular job.
        The point of these examples is to demonstrate that people are not "economic men" in the classical sense and that money is not the ultimate basis of valuation. Even when dealing with money matters, people do not calculate monetarily in utmost detail every step and decision. They maximize subjectively but not monetarily, because monetary calculation must be sacrificed when its requirements on time and energy are recognized. 

[source]

And:

Big Surprise: Fair Coffee is a Scam
Fairness with Your Coffee?
The Fairness of "Unequal" Exchange

I also find it fascinating that even though it’s presumably “worker-owned”, it still needs a board of directors (with outside members).