Award: Best use of a physics analogy in a halakhic or metahalakhic teshuvah

The subject line speaks for itself. The 2006 award goes to Rabbi Gordon Tucker's teshuva, "Halakhic and Metahalakhic Arguments Concerning Judaism and Homosexuality". This post does not address the content of the teshuva or the politics surrounding it, but only the use of a physics analogy that most rabbis of any denomination would not have been able to come up with.

The context is a discussion of the role of legal positivism in halakha.

So for the broadest range of questions that may arise – be they queries about the kashrut of microbial enzymes, or the use of a shaliah le-kabbalah in giving a get, or the permissibility of driving on Shabbat to be a shomer for a corpse – the teshuvot are bound to be written in the positivist style. In addition to there being many good reasons to reason this way, there are, in the large majority of cases, no good grounds not to. We are all positivists in the same way that we all use Euclidean geometry and Newtonian mechanics to solve the broadest range of problems in the configuration of space and in the dynamics of motion. Euclid and Newton are not only perfectly suited to the small scale of the billiards table; their relative simplicity and linear quality serve us well in most of the tasks we face. But despite the fact that Euclid and Newton are splendid and irreplaceable tools in most ordinary matters, we need to know that their “local success” does not necessarily translate into “global success”. When Einstein measured, during a solar eclipse, the light of a distant star that passed very near the large mass of the darkened sun, he demonstrated that we either had to concede that space was not Euclidean, or that light did not travel in straight lines near large gravitational fields. We know, in other words, that there are those phenomena that lie outside the domain of normal observation, that lay bare to us the need for more sophisticated, less simple tools of analysis that can be extremely disorienting at first. But that is the only way that progress is made.

This is the sense in which we are all positivists in law. It is a splendid and irreplaceable tool for the ordinary questions that law is called upon to answer. But then there are the analogues of Einstein’s landmark experiment, the hard cases of law, hard cases like the one before us in this paper. For we are dealing with a case in which the logic of the system and its precedents do not fit well with the personal experiences and narratives of gay and lesbian Jews, and with the growing moral senses of the community.

As far as I am aware, the physics is entirely correct. Classical mechanics is an elegant and internally consistent theory. It also happens to match up well with the physical universe, for a limited range of cases. These properties don't necessarily have to coincide -- one could come up with elegant and consistent theories that have no relationship to physical reality (like a universe in which F=mj, or heck, this is what they once thought non-Euclidean geometry was), and though we assume that physical reality is consistent (or else all bets would be off when it comes to science), it's not necessarily going to obey the simplest or most elegant laws possible.

And, in fact, the correspondence between classical mechanics and physical reality falls apart when you look at very small or very large things, travel at high velocities, etc. Classical mechanics as a theory is unharmed, and continues to be useful in the same cases in which it was useful, but new theories (quantum mechanics; special and general relativity) are required to describe the physical universe in those other domains of observation.

So Tucker is making this same point about halacha. (I'm not sure I agree with him -- i.e. my own views are even less "Newtonian", i.e. the opposite reason from why the other teshuvot submitted to the CJLS would disagree with him --but my opinions are beyond the scope of this post.) He would define a "classical" theory of halachic jurisprudence that is useful in everyday cases, but recognize that this theory does not correspond to reality in all cases, and develop another theory that applies to those cases.

Where is the boundary between the "ordinary questions" and the "hard cases"? It's an old question (aka challot devash me'eimatai mitame'ot mishum mashkeh? This cryptic reference to be explained in another post upon request. Hint: Psalm 19:10-11), and different people may arrive at different conclusions.

Another point that Tucker doesn't mention but that may strengthen his analogy: The "exceptions" to classical mechanics aren't just freak occurrences, but appear all the time. For example, atoms and molecules can't be explained with classical mechanics, and require quantum mechanics. Many famous things are made of atoms and molecules! Likewise, gay and lesbian people aren't anomalous; they're everywhere.

Question for Rabbi Tucker: Certainly, it's not convenient to use relativity or quantum mechanics to describe everyday situations at human scales (between atoms and galaxies), but it's possible. The correspondence principle says that quantum mechanics reduces to classical mechanics for large enough systems. Likewise, special and general relativity reduce to classical mechanics when v << c (velocity is much less than the speed of light) and we're looking at small masses and small chunks of space. Does your "enhanced halakhic method" obey an analogous correspondence principle? That is, if only the enhanced method were applied, would it arrive (albeit via more effort) at the same results as the positivist method would (in the cases for which you think a positivist approach is valid)? And if not, then would complementarity be a better physics analogy?

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Going back to the physics, in addition to the obvious reasons why classical mechanics is useful even though "more correct" theories exist (an engineer building a bridge doesn't need or want to consider relativistic effects, which would make the calculations much more difficult), there are also pedagogical reasons for this, which are foremost in my mind as a high school physics teacher.

And maybe these reasons aren't so different: similar to the (discredited) theory that ontogeny recapitulates phylogeny, perhaps individual science learning recapitulates scientific development. For my master's project in science education, I looked at how students' mental models undergo Kuhnian paradigm shifts. (This idea wasn't original, and the conditions for a paradigm shift appear in a 1982 article in Science Education by George J. Posner et al., but I was looking more closely at the mechanism of this paradigm shift and the "reactive intermediates".)

So just as classical mechanics had to be developed before Einstein could come up with relativity or Schrodinger could come up with wave mechanics, perhaps students need a foundation in classical mechanics before they can understand "modern physics".

Some students who come into first-year physics with lots of enthusiasm about the subject struggle because they're not able to bracket the "hard cases" while first looking at a simplified model. We make simplifications all the time, and not just the kind where we use classical mechanics instead of quantum mechanics or relativity: high school physics is filled with frictionless surfaces and massless strings and rigid bodies and point masses and point charges and elastic collisions and negligible air resistance and negligible electrical resistance and such. Some students are always asking "But wouldn't it break?" or "But what about the curvature of the earth?" or "What if you were going near the speed of light?". And those are excellent questions to ask. After you get the basic concept and are ready to consider more advanced applications. But if you don't allow for some approximations on the way there (like the famous spherical chicken), you'll be paralyzed and will never gain mastery of the basic concepts. (One of my colleagues had to say to a freshman physics class "Einstein was never born!") It's important to ask questions all the time, and it means that these students are thinking seriously about how physics applies to the real world and not just plugging-and-chugging by rote, but it's also important to learn how to use a simplified model to come up with an approximate answer, and then evaluate this result to see whether it's close enough or whether we have to consider other parameters.

Sometimes this process occurs during first-year physics itself. When we start in the fall, we assume that Earth's gravitational field is uniform (so gravitational acceleration is constant, gravitational potential energy is simply mgh, etc.), and then in December or so, we do the "gravity" unit and see what happens when you get far away from Earth's surface that you can't assume that g is always 9.8 m/s² anymore.

That said, there's still some value in giving students a taste of more "advanced" physics even if they're not going to get all the way there from first principles, because these theories are such an essential part of our current understanding of the physical universe. Even though high school students certainly aren't going to master classical mechanics to the level that Einstein understood it just before publishing his groundbreaking papers in 1905, they should still get some appreciation of physics developments of the last century. For example, the standard Regents curriculum includes the Bohr model and a superficial look at the Standard Model. If there were more time in the school year, I would go further -- I would love to develop a way to teach quantum mechanics concepts (not the Bohr model, but the real thing) to first-year physics students, and I already do relativity with my AP students after the AP test.

So the point is that in physics education, there is a place both for using simplified models and looking beyond those models.

As I learned today from a student, we're not even consistent in the simplified models that we teach. In AP, we've been doing integrals to find the electric fields due to various charge distributions, and a student asked an excellent question: if charge is quantized, then what does "dq" (an infinitesimal amount of charge; essential for setting up an integral) mean, and how can we talk about these continuous charge distributions? She was totally right. We teach from the beginning (starting way back in chemistry) that charge is quantized, and there are these discrete little charged particles. But then we teach classical electromagnetism, which is really all about continuous charge distributions, with concepts like (finite) charge density. (Note: Maxwell's equations predate the discovery of the electron!) So the answer is that when we're talking about an infinite line of charge with linear charge density λ, we're ignoring the fact that charge is quantized and operating within a theory in which it isn't, and then we can argue that this is close enough to our universe when we're looking at macroscopic things, since the quantum of charge is really really small on that scale. (And "infinite" really just means that L >> r.)

So do these rantings about physics pedagogy have any analog in the study of halacha? Perhaps the introductory Talmud student who is always asking "Did they really have to sacrifice an animal? That's sick and inhumane!" and "Does God really care?" and "Where are all the women?" is analogous to the introductory physics student who is always asking "But isn't light also a particle?" and "What about air resistance?" and "What about the rotation of the earth?". That is, they're both asking very very important questions (you'll have a hard time designing an airplane if you never stop ignoring air resistance!), but in order to develop an understanding of Talmudic methodology / physics methodology (which will assist later on in answering those important questions), it may be helpful to put aside those questions temporarily and focus on one thing at a time.

On the other hand, it's also important to develop, from the beginning, some understanding of the more complex questions, and to begin grappling with those questions, so that the student of halacha/physics understands that halacha/physics is not just a formal system or an intellectual exercise, but is intended as a model for the real world.

(model n. 1. a systematic description of an object or phenomenon. 2. a standard or example for imitation.)