Sunday, February 3, 2008

Terumah, Shemos 25:15, The Physics of Metaphysics: The Aron Hakodesh and Its Badim

(As always, other divrei Torah on this Parsha can be accessed by clicking "Terumah" in the Label Column.)

Several utensils of the Mishkan had carrying-poles, 'Badim,' used when the Mishkan was taken apart and transported to the next encampment. These were the Shulchan, the Mizbeichos, and the Aron. The badim of the Aron, were, however, unique. The Torah says lo yasuru, they shall never be removed. Unlike the other badim, which were removed when the Mishkan was at rest, the badim of the Aron remained in place permanently both in the Mishkan and the Beis Hamikdash.

Reb Meir Simcha of Dvinsk explains that the poles of the other utensils were purely utilitarian.  Their purpose was their functionality; they served to enable carrying the utensils, and they had no intrinsic or symbolic significance beyond that. The badim of the Aron, on the other hand, were absolutely not utilitarian. Chazal, and several pesukim in Tanach, tell us that the Aron was miraculously not only weightless, but it actually carried those that carried it– “nosei es nos’av.” Therefore, there was no need for the badim to enable carrying the Aron, since it could have been carried by one person who would simply point it in the desired direction. If they were not utilitarian, they must have been essential to the form and identity of the Aron, and this is why they were permanently affixed to it.

Many meforshim speculate as to the symbolic logic of this unique trait, but that is not the focus of this discussion. (Some approaches: the Badim represent the supporters of Torah, the Zevuluns. Torah can not exist without both the lomdim and the supporters. While it may appear that they are the ones who carry the Lomdei Torah, in truth it is the Lomdei Torah that carry them. It says "Semach Zevulun," it doesn't say "Smach Yissochor"-- the primary beneficiary is Zevulun. Another-- this teaches that Torah has no geographic or temporal limitations. Another-- A Torah that is static, that is not shared, is not Torah at all. Another-- The purpose of Limud Hatorah is Ahl Menas La'asos.)

The Gemara in Yoma, Kiddushin, and Bova Basra, says that“Aron she’asa Moshe lo haya min hamidah.” “The Ark made by Moshe was not part of the measure.” This means that the chamber, the Adytum Sanctum Sanctorum (of the Beis Hamikdash, not the Mishkan), which contained the Aron, was twenty Amos square; the Aron, placed in middle toward the front, was two and one half Amos wide, and one and a half high and deep. But when you measured the room from the left side to the Aron, you would have ten Amos; from the right side to the Aron was also ten Amos. The Aron itself was two and one half wide. But when you measured the room from the far left to the far right, it was only twenty Amos. The strange thing is that the floor had Amah-square tiles, and the Aron sat on two and one half tiles, and you should have been able to count the number of tiles in the room. Nonetheless, it was not min haminyan, just as Moshe Rabbeinu’s grave appeared next to the people down below when you were looking from above, and above when you were looking from below.

It seems to me that the idea that it didn’t have a determinable position is related to the fact that it was “nosei es nosav,” because they both stem from the fact that the Aron was not tied to a specific position, and it had no physical mass that would occupy a fixed position.

This lack of position and mass did not indicate unstableness or impermanence. On the contrary— because it was superior to physical matter, it could not be tied to a particular place, it could not be defined by any relationship to physical things, including spatial position, which is a matter of its relativity to physical things. It was not insubstantial, it was trans-substantial. Its holiness, when containing the luchos, elevated it to a state in which it was free from the material characteristic of being tied to a specific place. So we can understand why when one measured from the right there were ten amos to the Oron, and when one measured from the left there were ten amos to the Oron, and when one measured from the right to the left wall there were twenty amos; because the metaphysical kedusha of the Oron contradicted its being in a determinable place, so the very attempt to measure and and determine the position of the Oron resulted in its not being in the area you are measuring. This might be similar to the idea of “Hu m’komo shel olom.” You may refer to this concept as the Kant/(H)eisenberg Uncertainty Principle.”

Now, let us think about “Aron nosei es nos’ov.” Gravity is a function of spatial relation. The Aron had no spatial relation to its surroundings; in the Kodesh Kadashim, it was on the right side just as much as it was on the left side, meaning it could not be defined as being 'located' on either side.  If the Aron was not physically proximate even to its immediate position, it could not be affected gravitationally. This is why gravity did not act on the Aron. Even the people who carried it, apparently, were unaffected by gravity, since while they were carrying it they were serving it and were, at that moment, accessories appurtenant to the Oron.

Additionally, the Rogatchover says, the Aron was not subject to the passage of time. He says this in three places: Shemos 16:33, Teshuvos II 28, and Teshuvos Dvinsk II 43:4.

Several years ago, I sent an email to Dr. Barry Simon, the eminent IBM Professor of Mathematics and Theoretical Physics at Caltech and a frum and learned man, asking what he thought about this concept.

He answered (drumroll please) that it was "wrong on many levels." If the Aron had no mass, then it would have to move at the speed of light. So it was not behaving in a manner consistent with the rules of physical matter that have been observed; it was a neis, and that’s all.  His field of expertise, he said, was the laws of physics, not nissim.

So did you just waste five minutes reading this? I hope not. Even nissim conform, to some extent, to teva. The great nissim were emplaced at the time of Bri'as Ha'olam, during the eve of Shabbat. It stands to reason that the nissim of the Aron have some physical logic. Exactly what that logic is, however, remains unclear for the moment. But I believe that this approach, while speculative and not mathematically provable, might have some small element of validity, if not as a maskana, at least as an interesting hava amina.


  1. The idea of speed of light and mass and all that other scientific stuff is also discussed by Josh in his post here:
    I barely have a layperson's understanding of these areas, so I can't comment.

  2. The fact that an object has no volume need not mean that it has no mass. To the contrary, the smaller its volume, the larger the gravitational effect that its mass would have.

    Hence, as per Prof. Simon's objection, the concept of nosei es nos'av would not seem to be symptomatic of a lack of mass, but rather of an independent gravitational force that counteracts the gravitational force of the earth - although if the aron has mass one would have to postulate the generation of some force that enables its separation from the surface of the earth when its carriers "lift" it up.

    Of course, there's no reason that nosei es nos'av need be based on an opposing gravitational force - it could also be based on an analog of an electromagnetic force or of weak or strong interactions, but I'm not sure exactly where one would go from there.

  3. Josh, I didn't suggest that the Aron had no volume. I said that since the Aron had no relationship to any particular point in the physical universe, it could therefore not effect or be effected by objects that had a specific position. Then I said that an object that is completely uneffected by gravitational forces would have to be analogous to an object that had no mass.
    Chaim, thanks for the reference to Josh's site. Josh, thanks for making what was already murky murkier. Now I know how the members of my shiur feel when I'm discussing the difference between Psik Reisha delo nicha lei and Melacha she'eina tzricha legufa.

  4. I'm not sure I would play this game -- assessing the physics of something ascribed to a violation of nature. That said...

    In relativistic terms, gravity is the shape of spacetime in a given region. If the presence of the aron compressed the space around it to compensate for the room of the Qodesh haQadashim that it occupied (a different version of the game than yours), it would have a negative mass. (Like dark energy.) Negative mass would mean gravitational repulsion. Not only would the aron not fall, but could actively lift itself the people carrying it "nosei es nos'av". And actually, its not flying away when not held down would be a neis.

    Also, space is altogether distorted by the luchos themselves, in which text carved all the way through said the same thing from both sides, rather than the back having a mirror image.


  5. Micha, that's why I was pleased with the title-- the physics of metaphysics.

    Anyway, the letters on the back of the luchos were in reverse order, as the Gemara in Haboneh (104a) says, ואמר רב חםדא כתב
    שבלוחות נקרא מבפנים ונקרא מבחוץ כגון
    נבוב בובן ה<(רהב בהר) םרו ורם
    although I know that this Gemara is mysterious (Tosfos) and is said to comprise deep secrets, but pashut pshat is that although the individual letters came out unreversed, they did come out in reverse order.