Representation and Nonverbal Thinking: 3. Linguistic Representation – Applications (Column 381)

With God’s help

Disclaimer: This post was translated from Hebrew using AI (ChatGPT 5 Thinking), so there may be inaccuracies or nuances lost. If something seems unclear, please refer to the Hebrew original or contact us for clarification.

In the previous column I described linguistic representation, focusing mainly on the question of verbal thinking. Now we will look at several applications, and conclude with a connection of sorts to Passover.

Halachic implications

Once I dealt with a mishnah in tractate Mikvaot (3:3) about a channel of living water that passes through a mikveh of forty se’ah of drawn water and mixes into it:

A pit that is full of drawn water, and the aqueduct enters it and leaves it— it remains invalid forever until it is calculated that not more than three log of the original [drawn water] remain.

The mishnah addresses the question of from when we may assume that in the mikveh there no longer remain more than three se’ah of drawn water. The early authorities there make calculations with the limited mathematical tools available to them, and it is no wonder they reach results that differ greatly from one another. With a simple differential equation one can show that their calculations are quite mistaken, and at least under certain circumstances this can amount to errors of entire orders of magnitude. The paper on which I wrote up the matter contained a differential equation and its solution (see the link at the end of the column). A collection of mathematical symbols, nothing more. My study partner asked me whether, in my view, that paper should be consigned to genizah?[1] Are these words of Torah? I didn’t know how to answer him, for this equation is indeed a representation of a halachic discussion in the mathematical language. But on the other hand, that is not evident to an external observer looking at the page. To him it could be an engineering calculation or something else entirely, or simply the solution of a differential equation.

The mathematical expressions on the page are a linguistic representation of the halachic ideas— but only if someone is aware of that (and, of course, from the perspective of the author who had that in mind); and this raises the question of the status and importance of the representation. Seemingly it is no different from the Hebrew formulation of the mishnah quoted above, except that here it is written in a mathematical language that can represent many entirely different things with no connection to Torah and halacha. The question is how we should relate to the representation: Is the representation as such words of Torah and does it possess sanctity? In this regard one may also wonder whether what determines is the writer’s intention, or perhaps what the outside observer sees. In the terms of the midrash I cited in previous columns, one may ask whether, from the angels’ perspective, the text given to us at Sinai is Torah, or whether in their view it is just a neutral text—just as the page with the equation appears to one who does not know the mathematical language or does not understand what the equation represents (in their world our commandments have no meaning).

It seems to me that from the discussion conducted in the previous columns one may infer that the representation as such is not Torah. We saw from Shabbat 30 that there is no prohibition on speaking in filthy alleyways if no thought (contemplation) accompanies it. The prohibition is on the thought, and speech merely expresses it. Likewise, when I myself read that paper, words of Torah are in my mind, but the paper itself is like speech without contemplation— that is, a representation whose connection to the represented exists only in the reader’s mind. This is akin to a recording of a Torah class played in a bathhouse with no one listening (except that in our case the signs on the page have no clear Torah significance even if someone sees them). It would seem that such a sheet has no status of words of Torah (though it would be forbidden for me to write or read it in filthy alleyways, because for me, as one who knows and understands the represented content, the writing and reading are accompanied by thoughts of Torah). This is in contrast to a page on which the text of the mishnah (cited above) is written— there it is clear to everyone what it represents; therefore it is reasonable that the representation has sanctity irrespective of the person who wrote or reads it (even if he does not understand Hebrew and does not know Torah).

One might have distinguished between voice and writing on paper by arguing that speech is not Torah, for sound has no substance (see Rambam, Laws of Shofar 1:3, and the commentaries there). There is no cheftza (object) of Torah, and therefore there is no prohibition to speak words of Torah (without contemplation) in a bathhouse. By contrast, a written sheet— even if what is written on it is a generic representation (like an equation)— has substance and perhaps is considered a cheftza of Torah; one might argue that it possesses sanctity as such. Yet by this logic, contemplation too has no substance, and nonetheless there is a prohibition to contemplate words of Torah in filthy places.[2] It therefore seems incorrect to distinguish in this way.

Perhaps one can adduce proof from the law of a Torah scroll that has been erased. The Gemara in Shabbat 115b cites an opinion that if 85 letters remain— as in the passage “And when the ark would travel” (which itself is considered a complete book)— it retains sanctity and one saves it from a fire on Shabbat.[3] So too is the halacha in Rambam and in the Shulchan Aruch. Here we are speaking of letters that do not form words and certainly not meaning, and yet they possess sanctity. Seemingly this proves that sanctity pertains to the representing object itself, not to the content. But upon further analysis of the Gemara, the implication is quite the opposite, for it does not deal with a scroll written ab initio in such a manner, but only with a Torah scroll that was erased and those letters remained. That is, we are dealing with residual sanctity on account of the complete scroll that previously existed. From here it follows that if we had initially written 85 scattered letters, even if in their appropriate locations, this would have no sanctity although the representation is in place. The reason is that sanctity attaches to the content, not to the representation. Such a parchment is in the category of “letters flying in the air while the parchment burns.” Only if there had been a complete book that was erased does the sanctity of the complete book— when there was also a represented content behind the representation— remain intact even after it is erased.

In the same way one can understand another law brought in that sugya, and likewise ruled in halacha, that a Torah scroll written in another language is also sacred and is saved from a fire. Here this is a different representation of the same content, and because the same content stands behind both representations, then even if the representation is different it has sanctity, so long as the same content stands behind it.[4] The conclusion from all this is that when the representation stands by itself and the represented content does not stand behind it, it has no sanctity on its own.

One may also connect this to the law of a Torah scroll written by a heretic, about which the Gemara (ibid. 116) says that even the Divine Names in it have no sanctity (and it is burned).[5] Again, after the novelty that a scroll written by a heretic is a representation that does not represent the original content (since the heretic does not uphold that content), we have here another example of the principle that if there is a representation without the represented content behind it, it has no sanctity as such.

Note on the complexity of the signifier–signified relation: one-two-many systems[6]

In column 220 I brought another example of such a linguistic–cognitive shortfall. Anthropologists know of a phenomenon that appears in several places around the globe: tribes that use a number system called a one-two-many system, that is, a system containing three numbers: 1, 2, and many. Thus, for example, a paper in Nature reported that researchers who studied the Pirahã tribe in Brazil found that they count in this way. The natives were unable to distinguish between different numbers of objects beyond three. True, when presented with a comparison between a pile of twenty batteries and five they could say that twenty is a larger pile, but a comparison between five and seven was already beyond them.

A fascinating debate took place there about the influence of language on thought, and indeed the errors that arise due to linguistic representation. The researchers’ claim was that a linguistic deficit or constraint affects our ability to think and to understand situations. This is the well-known thesis of Benjamin Lee Whorf, an American scholar who dealt with this extensively (his book, Language, Thought, and Reality, was translated into Hebrew). At times this thesis is called the Sapir–Whorf hypothesis (Sapir was his teacher). Thus, because the language of the Pirahã lacked terms for numbers beyond 2, they were unable to think about them and understand them. Some formulate this concisely: language precedes thought.

I argued there that, in my view, this formulation of the thesis is overly simplistic. After all, a term in a language must itself arise somehow. If one does not understand the number 3, one cannot create that term in the language. Therefore, necessarily, thought and understanding precede language. Clearly the full picture is more complex, for once the terms in the language exist, we can use them and better understand the concepts they represent. That is, the process should begin with some level of understanding; subsequently one creates a term in the language, and this circles back to clarify the concept and allows us to grasp it better, use it, and even derive conclusions from it.

A special relationship between signifier and signified: the meaning of Lashon HaKodesh

Rav HaNazir, in his book Kol HaNevuah (Book One, Essay One, sec. 26 and on), discusses the essence of the Holy Tongue compared with other languages. He cites the position of the Rambam (Guide of the Perplexed II:30 and III:8):

The Rambam explains that languages are conventional, and therefore he explains the sanctity of the Holy Tongue by saying it is a refined language. The Ramban (on Exodus 30:13) and the Raavad (in his commentary to Sefer Yetzirah 1:10) took issue with him. He there (in the previous section) explains their view as to why, in their opinion, this language is called the Holy Tongue:

His claim is that biblical Hebrew differs from other tongues because it is not conventional, but essential. In an ordinary language, the term that designates a concept is chosen arbitrarily, and there is no essential connection between them (between signifier and signified). In Kripke’s terminology, that connection is a matter of “the baptism” (see briefly here). But in the Holy Tongue each word has an essential connection with what it signifies. This view is accepted in the esoteric tradition, and accordingly they attribute even the shapes of the letters to meanings connected with what they signify, the roots of words to their meanings, and so on. As it were, the word is hewn, or emanates, from the concept it signifies (there is, of course, a strong Platonic aroma here).

From this Rav HaNazir deduces (sec. 28) the impossibility of translating an idea from one language to another:

The problem is not only translation from one language to another, but first and foremost the very casting of the content into a verbal formulation in any language. In the Holy Tongue this problem does not exist, because the words were created to represent the content precisely (or perhaps the content itself was created out of the words), but in other languages there is an inherent problem in linguistic representation. Here we reach the failures that arise from identifying the linguistic representation with the represented content— and in his view, in the Holy Tongue these failures do not exist. There the linguistic representation precisely and fully matches the represented content.

Immediately afterwards he brings several halachic ramifications of this distinction (sec. 28 there):

The Rambam and the Raavad of course disagree according to their respective positions (the Raavad of Posquières is the author of the glosses).[7] Regarding reading the Megillah, he refers to the dispute between the Rambam and the Rashba and the Ramban in Laws of Megillah 2:4 (the MM there brings the dispute) regarding whether one who knows both the Holy Tongue and a foreign language may read the Megillah also in a foreign language and fulfill his obligation. Here, too, they follow their approaches to the status and meaning of the language.

Implication: ta’ama dekra

According to these views there is no representational gap between the formulation in the Holy Tongue and the content it describes. My thesis regarding conceptual representation still stands even according to them: linguistic representation certainly exists in the Holy Tongue as well, but it does not engender failures and problems. This of course does not apply to the Oral Torah that is written in the Holy Tongue. There the formulators are human beings, and therefore a gap certainly exists even if the writing is in the Holy Tongue.

In my article on the fifth root I discussed the rule that we do not derive laws based on the reason for a verse (ta’ama dekra). I showed there that according to the Rambam one does not do so even where the Torah itself states the reason— i.e., even when there is no concern that we erred in our interpretation and that the reason we offered is incorrect. Why indeed do we not derive laws from the reason for a verse in such cases? I argued there that the underlying assumption of this halacha is that the Torah’s formulation is precise, and therefore if there is a gap between purposive interpretation (ta’ama dekra) and literal interpretation, our purposive interpretation is probably mistaken. Such a gap may exist in other languages and texts, since linguistic formulation is only a representation— not necessarily precise— of the original. But in the biblical text there is complete alignment between the linguistic representation and the represented content, and therefore a precise purposive interpretation should fully accord with what emerges from the literal interpretation. If so, the rule not to derive laws from the reason for a verse is relevant only to a text written by the Holy One, blessed be He, in the Holy Tongue. Here, too, there is an assertion of a precise, one-to-one correspondence between the biblical formulation and the content it expresses.

“There is no earlier or later in the Torah”

The Gemara in Pesachim 6b challenges the rule “there is no earlier or later in the Torah” with the following question:

Rav Menashia bar Tahlifa said in the name of Rav: This teaches that there is no earlier or later in the Torah. Rav Pappa said: We said this only with respect to two topics, but within one topic— what is earlier is earlier and what is later is later. For if you do not say so, [consider:] with regard to a general and a particular— “a general and a particular: the general includes only what is in the particular”— perhaps it is [actually] a particular and a general. And furthermore, “a general and a particular become a general that adds to the particular”— perhaps it is [actually] a general and a particular [in the other order]. If so, even with two topics as well! This works out according to the one who says that a general and a particular that are far from one another are not judged as a general and a particular— fine. But according to the one who says they are judged, what is there to say? Even according to the one who says they are judged— that applies within one topic, but with two topics they are not judged.

The Gemara asks that if the rule “there is no earlier or later in the Torah” also applies when it is a single topic, then we could not expound the hermeneutic derivations of general and particular. Those derivations relate to verses that begin with a general formulation and continue with specific examples, and the order determines the outcome (whether in the verse the general precedes the particular or comes after it). If there is no earlier or later in the Torah even within a single topic, then when we have a formulation of general and particular, it could just as well be a particular and a general, and the outcome of the derivation would be different. In that case, the verse’s formulation would not reflect the true order of things.

There is a very novel assumption here: that the derivations of general and particular are based on the historical order, not the textual order.[8] We would have thought that the order in the verse is determinative for the derivations, since the Holy One wrote the verse in that order so that we would expound it precisely that way. But the Gemara assumes that the derivation is not based on the textual order but on the historical order. That is, if the general part of the verse was stated before the particular part, we must expound it as general then particular— even if the Torah were to write it in the reverse order.

Once again it seems that an assumption is embedded here of exact correspondence between the text and the content it describes. True, the order of events is not preserved, but that very move was apparently made in order to preserve the precision of the representation for our purposes (for the Torah is not a book whose purpose is to teach facts and bare historical sequence).

A homiletical note for Passover

From the sugya in Pesachim it appears that the historical order of events precisely represents the halachic content, and therefore we can derive the laws from the historical order in the most precise way. When the text does not accurately present the historical order, the halachic conclusions derived from the Torah may be skewed. This seems as if history is planned so as to match exactly the halachic consequences that emerge from it.[9]

This recalls a charming homiletical note, which I present here in honor of the approaching holiday. I hope my foray into mysticism will be forgiven. The verse (Exodus 13:8) states: “Because of this the Lord did for me when I went out of Egypt (ba’avur zeh asah Hashem li betzeti miMitzrayim).” The Ramban there cites the Ibn Ezra, who reads the verse at face value: the Exodus and the miracles were done for the sake of the commandments. But the Ramban himself disputes this and holds that the verse should be read with a shin: “Because of this that the Lord did for me when I went out of Egypt, I perform this service.” The straightforward meaning of the verse is, of course, like the Ibn Ezra; nevertheless, to the Ramban that seems implausible. The logical order is the reverse: the events were not done for the commandments; rather, because of the events we perform these commandments.

Yet several later authorities (R. Kook and the Beit HaLevi) explain that history is arranged such that precisely the correct halachic ramifications emerge from it. We do not eat matzah and abstain from chametz because Pharaoh pursued our ancestors and their dough did not have time to leaven; rather, the reverse is true: Pharaoh pursued so that the dough would not leaven, for at that time there is a spiritual imperative to eat matzot and refrain from chametz.

Indeed, reading the Torah at the beginning of the previous chapter (chapter 12) we see that we are commanded to eat the Passover in haste, with staffs and with our shoes on our feet:

“And the Lord said to Moses and to Aaron in the land of Egypt, saying: This month shall be for you the head of months; it shall be the first for you of the months of the year. … And thus shall you eat it—your loins girded, your shoes on your feet, and your staff in your hand; and you shall eat it in haste— it is a Passover to the Lord.”

Note that this revelation occurred on Rosh Chodesh Nisan, that is, two weeks before Pharaoh ever thought to pursue the Israelites leaving Egypt, and already there we are commanded regarding haste. The reason the verse gives for eating in haste is that it is a Passover to the Lord. That is, the haste and the matzot are intrinsic to Passover itself, and the Exodus and the historical events (like the speed and Pharaoh’s pursuit) were pre-planned so that the commandments that seemingly emerge from them would indeed come out as they did. This is admittedly a bit mystical, but it seems hard to ignore this import of the verses.[10]

A happy holiday to us all.

Link to the calculation of the amount of drawn water in Mishnah Mikvaot 3:3.

[1] For the sake of discussion I am ignoring the fact that, strictly speaking, there is no halachic obligation from the letter of the law to consign Oral Torah writings to genizah. My concern here is only the illustration. If you wish, you may discuss whether it is permitted to save that paper from a fire on Shabbat, as we do sacred writings (the early authorities wrote that nowadays, when Oral Torah is written, we may save Oral Torah writings as well).

[2] It is forced to claim that a person who contemplates becomes a cheftza (object) of Torah. One could have said the same regarding a person who speaks words of Torah— but perhaps thought is “absorbed” in a person and identified with him more than the act of speech.

[3] That chapter deals with the prohibition of rescuing objects from a fire on Shabbat, lest one come to extinguish it. Exceptions include food for three meals, clothing needed that day, and sacred writings.

[4] One may discuss to what extent this is full sanctity like a valid Torah scroll; this is not the place.

[5] Plainly the novelty is twofold: that there is an obligation to burn it and that it is permitted to burn it (i.e., it has no sanctity).

[6] The source of this discussion is a thread I opened many years ago in the “Stop Here, Thinkers” forum. It is worth seeing the whole discussion that developed there.

[7] Several later authorities questioned attributing this interpretation to the Raavad. The Ramak and the Chida attribute it to Rabbi Yosef ben Shalom Ashkenazi.

[8] I discussed this in an article in Midah Tovah, 5765, for Parashat Ki Tisa, available here.

[9] Or that the halachic consequences are the result of the historical order, without it having been planned in advance. But in the context of the “general and particular” derivations this is less plausible.

[10] In this connection I once heard someone cite the midrash of our Sages about Lot, who hosted the angels and gave them “unleavened cakes, for they were not leavened.” Rashi there brings the midrash: “It was Passover.” Note that there, too, we are speaking about roughly four hundred years before the Exodus, and our Sages tell us of the eating of matzot. Even if this is not a historical account, it is still apt to ponder the inner logic of this midrash. Eating matzot before the Exodus occurred means that eating matzot preceded the Exodus and was not derived from it. It would seem to be inherent to the season itself, and the events came only to actualize the matter and to cast historical content upon commandments that, in their origin, do not truly derive from it.