On Armchair Research and “Computational Archaeology” (Column 341)

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.

Some time ago someone sent me an article from YNET with the enthusiastic headline: “Traces of the measure ‘tefach’ were found in archaeological findings.” The article reports a fascinating result: the size of the tefach was confirmed by archaeological means. The study also supports the (captivating) hypothesis that jar production in that period (the Kingdoms of Judah and Israel, in the 10th–7th centuries BCE) was carried out exclusively by male potters.

The research was conducted by scholars from the Weizmann Institute and the Hebrew University in collaboration with the Israel Antiquities Authority. It mentions institutions with grand names such as “The IAA Laboratory for Digital Documentation and Research in Archaeology,” or the Hebrew University’s “Laboratory for Computational Archaeology.” At first glance this all sounded truly intriguing, so I went to read. At last, I thought to myself, we’ll be able to settle the dispute of the Chazon Ish (and the Noda BiYehuda) versus R. Chaim Naeh; and if we examine the implications for measures of volume such as the “kezayit,” perhaps we even have a chance to get through the upcoming Seder night alive (i.e., without choking on the matzah).

Description of the findings and their interpretation

The researchers relied on three groups of storage and trade jars produced in different places in the Land of Israel. Three hundred jars with an average capacity of 40 liters were scanned in 3D. The study measured shape and size characteristics of the jars—such as volume, height, and maximum diameter—and compared these among the groups. The measurements indicated a lack of uniformity in the sizes measured within each group, but there was one exception: a single dimension that was precisely shared by all the jars—the inner mouth diameter of the jar’s neck. The measured diameter averaged 88–89 mm, which lies in the middle of the commonly accepted range for the “tefach”—a width measure of four fingers—an ancient unit mentioned in the Bible. One hypothesis is that the jar mouths were made in a uniform size to create an opening small enough for effective sealing—important for storage and transport—yet still large enough for easier filling and pouring.

[As part of my armchair research, seated as a researcher in the a priori laboratory for hypothesis-raising in archaeology, I wondered whether the explanation is more prosaic: perhaps there was a single monopolistic producer of jar lids who made only one lid size, and all the manufacturers conformed to that lid size.]

The researchers linked the mouth size to the process of making the jars, in which potters needed to insert a hand inside, or to a size that allows inserting a hand to clean the jars from within after use, or to prevent the entry of impurity (via an opening of a tefach), and so forth. [According to my hypothesis above, this need not be the case, of course. M.A.] In the researchers’ words, “A width that meets all these requirements is the size of a tefach, which is easy for different potters to apply. It would have been natural for ancient potters to adopt the size of the tefach, since it was a widely used unit of length in antiquity, mentioned in Assyrian and Egyptian sources as well as in the Book of the Covenant.” [It’s unclear to me whether they adopted this uniform size—i.e., set a standard unit of length that was transferred among all manufacturers and used in production—or whether each craftsman used his own hands, in which case all the hands of that era would have been of uniform size.]

The researchers buttressed the link between the tefach and the jar-neck diameters by comparing the distribution of jar-mouth sizes with measurements of male and female hand breadths from U.S. Army anthropometric databases. I [M.A.] hope they used measurements from the U.S. Army of that era (i.e., from the appropriate Native American tribe), otherwise we have a worrying anachronism. Oops—turns out they didn’t, since they report assuming that physical hand breadth hasn’t changed over the last three millennia. In any case, the results showed a match between the distribution of jar-mouth sizes and the hand-breadth distribution of men, but not of women.

And the conclusion: these data strengthen the claim that in this case we can clearly identify the use of the ancient tefach, preserved in the jar-manufacturing process, with an average size of 88–89 mm. Moreover, the test supports the hypothesis that the production of these vessels in the period in question was entrusted to male, not female, potters. So much for the study’s conclusions.

Critique from the A Priori Laboratory for Armchair Research and Hypothesis-Raising

The researchers, as noted, assume that finger breadths haven’t changed over three thousand years, measure today’s finger-breadth distribution, and compare it to the historical jar-mouth widths. From this they infer the tefach’s size. And I wonder about the logic of this argument. Seemingly, if we measure finger breadths today and assume the breadth hasn’t changed, we directly obtain the size of the tefach. Why run a field study? The two premises the researchers adopt—without any additional empirical information—by themselves yield, through a simple logical argument, their conclusion. So why, for heaven’s sake, did they need to do “computational archaeology,” use the digital documentation institute’s scans, and analyze the results for this? They could have stayed in their armchairs, posited those two assumptions, and moved straight to typing the paper and sending it to the archaeological journal BASOR.

I’ll go further. My learned predecessors in the Laboratory for A Priori Hypothesis-Raising conducted precisely such an assessment centuries ago. I refer to the halakhic decisors (poskim), who generally assume the measure hasn’t changed, and therefore measure it in their own days and extrapolate to the biblical and Talmudic tefach. It’s a pity the researchers at the computational archaeology lab missed the a priori armchair experiments conducted by Prof. Yechezkel Landau, Prof. Avraham Yeshayahu Karelitz, and Prof. Chaim Naeh, who were centuries—at least decades—ahead of the science of their time. “Turn it and turn it, for everything is in it,” and blessed is He who chose them and their teachings, “for it is your wisdom and understanding in the sight of the nations” (as it says: “and lean not on your own understanding”).

After further thought, a few more possibilities occurred to me. Perhaps their intent was really a study in physical anthropology rather than historical archaeology. That is, maybe the researchers merely wished to empirically confirm the assumption that finger thickness hasn’t changed in three thousand years; for that purpose they assumed the neck diameters reflect a tefach, and then compared them to current U.S. Army data. Here there is an explanation for getting up from the armchair, since such a conclusion does require fieldwork and actual measurement of those diameters. But even this armchair hypothesis doesn’t hold up, since it’s unclear, on this reading, whence their conclusion that the potters were men. Perhaps the jar-makers back then were women, only female finger thickness has changed over the generations? Alternatively, perhaps it was five fingers of men rather than four, and their finger thickness (and maybe women’s too) has increased?

Then I thought perhaps the study’s goal was social-historical: to understand why jar necks were made precisely at that width. Once the researchers discovered that the neck width is a Talmudic/Biblical tefach, the reasons for this captivating riddle became clear: the need to insert a hand to form the jar and to clean it, and also the trade-off between transport (favoring a small opening) and easy pouring (favoring a larger one).[1] I am not an archaeologist, and besides, I too enjoy the occasional bit of silliness, so I will refrain here from commenting on the far-reaching importance of this conclusion.[2]

Don’t think I’m merely a ceremonial head of the famous laboratory I described—this isn’t mere nepotism. I have rich, proven experience in archaeological digs, since as a mischievous youth I joined my Bnei Akiva tribe for an archaeological summer camp where we excavated at Herodion (yes, you hikers there, know that you tread trails I myself carved with the sweat of my brow). I remember that when I was a lad, I cursed the pint-sized Bar Kokhba fighters who lived and fought in tunnels a meter high. Again and again I asked why it was decreed upon me—a Jew eight cubits tall (by a man’s cubit), with a bed of iron—to live a week bent double in their Lilliputian burrows?! In any case, this finding independently supported the widespread hypothesis that the human body has indeed changed since then (height and size have marvelously increased). In light of this experience, I asked myself yet again what basis the researchers have for assuming finger thickness stayed the same (see more below).

Incidentally, Prof. Yechezkel Landau—yes, the same—writes a contrary a priori assumption in his novellae to Pesachim 116b, in these pearly words:

[…] If so, two measures for challah contradict one another, and both are a halakhah le-Moshe mi-Sinai: the measure of 43 eggs and a fifth is a halakhah le-Moshe mi-Sinai, and likewise the mikveh measure is a halakhah le-Moshe mi-Sinai. Necessarily it has changed in our time: either the thumbs have become larger and are bigger than the thumbs in the days of the Tannaim, or the eggs have become smaller and are, in our time, smaller than in the days of the Tannaim. And it is known that the generations decline, and it is impossible that our thumb is larger than the thumbs of the sages of the Talmud. Necessarily, the eggs in our time have diminished. QED.

He claims that the decline of the generations is expressed in a decrease in physical size; therefore our bodies cannot be larger than those of the ancients, and so on.

These groundbreaking a priori findings stand in contrast to the researchers’ hypothesis, but also to the empirical findings from my Herodion “study” above [and to reality as well. But there’s no need to reiterate here that we are dealing with qualitative, a priori armchair research whose methodology obligates a complete disconnect from the facts.]

The Hebrew University’s report

After these questions arose for me, I recalled that more than once I had read reports on various studies riddled with ridiculous flaws, only to find—upon reading the original article—that the problem lay in the journalistic report, not in the research. So I read the Hebrew University’s own brief report on this study. It is almost identical (the journalist copied the overwhelming majority of the summary—see below). However, I did find one relevant change. The academic report states that the “assumption” that finger thickness hasn’t changed over millennia is not just an assumption; it rests on other studies to which the authors refer in their article.

This indeed changes the picture somewhat and adds an important empirical dimension to this weighty sugya. But the need to rise from the armchair remains as unclear as before. Now the assumption that finger breadth hasn’t changed is the outcome of prior empirical studies (or at least supported by them; I didn’t check). Still, if we are equipped with this conclusion and combine it with U.S. Army data regarding current sizes, why is there a need to go into the field and measure jars? From those two premises alone one can infer the size of the tefach without getting up from the armchair (as is our custom in the a priori lab). Above I already discussed other possibilities—namely, that the study aimed to confirm an anthropological or historical hypothesis rather than to test the halakhic-historical claim about the tefach’s size—and I won’t return to that here.

I admit that if I were writing a serious review of this study, I would have had to read the scientific article itself (from the archaeological journal BASOR). I didn’t, because the topic doesn’t interest me enough, and the summaries I read did not whet my appetite. Therefore I must phrase my conclusion cautiously: in light of these reports, it seems the empirical research was superfluous. There was no need to get up from the armchair to reach this conclusion. But you are welcome to read and comment in light of the article itself.

You may then ask why I bother to write this column at all. The answer lies in methodological and logical lessons—in developing an appropriate stance toward various studies and, even more so, toward the journalistic reports about them. I therefore turn to the takeaways.

Lessons on the logical and scientific plane

Science, as distinct from mathematics, is built from empirical information and its logical analysis. The results must include some factual information, and that information doesn’t emerge from logic but from factual premises and the generalizations used in the analysis.

Note, logically speaking, that if we have a valid argument inferring some conclusion X from the set of premises {A, B, C}, then if we add further premises (say, D and E), the argument’s validity is preserved. For example, if I assume that all frogs have wings and that the table before me is a frog, I can infer that my table has wings. Now add the premise that Trump will be elected President of the United States today for a second time. The argument remains valid, of course (only it now contains a superfluous assumption; it would remain valid without it).

Returning to our study, the researchers’ conclusion relies on two premises: 1) the size of the tefach in the U.S. Army today is 89 mm; 2) the size of the tefach hasn’t changed over the last several millennia. From this one may infer: the Talmudic/Biblical tefach is also 89 mm. Indeed, even if we now add the measured widths of jar necks, and perhaps the assumption that they were made by men, and if you like also the premise that a full moon is now shining over Kamchatka, the argument remains valid. Only these additions contribute nothing to it—neither the Kamchatka premise nor the measured jar-neck widths. By the same token we could add the premise that the jars were made only by women, and that women’s hand-breadth changed sinusoidally across the years, with the period dividing the time since then to now with remainder 1—the conclusion would still remain in force.

This problem in their argument is scientific, not logical. It’s unclear why empirical work was required here, rather than sufficing with an a priori armchair study (or: why they’re stealing our laboratory’s livelihood).

Lessons on the journalistic plane

Here we have a common phenomenon: copying a report from the institution directly into a newspaper and presenting it as journalistic coverage. If they had copied verbatim and presented the piece explicitly as a text composed by the Hebrew University, there would have been some honesty. But presenting a spokesperson’s text as a journalist’s report on what occurred at the institution, in my view, violates basic journalistic norms. A journalist should critically examine the facts and their meaning and report on them independently. Imagine what we would say if we heard that a journalist transcribed a text issued by a politician’s spokesperson and presented it as a journalistic report on an event involving that politician (a daily occurrence, of course).[3]

The reasons for this widespread phenomenon are mainly the journalist’s laziness; but in scientific contexts it also reflects the journalist’s inability to examine the matter (because it requires experts). Yet in this case it would have been quite easy to check and pose the researchers some tough questions about their study, since even I—no expert in empirical archaeology (recall, my expertise is a priori armchair research)—managed to do so.

It’s worth knowing—many are unaware—that the appearance of an academic study in the popular press is a status symbol, no less than publication in prestigious journals. I recall that when I was in the Physics Department at Bar-Ilan, the department bulletin board regularly displayed clippings from the popular press reporting on our researchers’ findings. It’s no wonder that scholars and institutions pursue journalists to get their research into the general media—and journalists, of course, oblige (a win-win). This is a lesson for us as media consumers: how we should relate when we read about “groundbreaking” research in various fields. This is especially true in areas (like mathematics or physics) where the journalist lacks the knowledge and capability to truly vet the “breakthrough.”

One more note on armchair research in evolution: the case of finch beaks

In chapter four of my book God Plays Dice, I illustrated the phenomenon of a priori field studies (that is, field studies whose results can be predicted from the armchair) that are very common in the field of evolution, using the Grants’ research on the beaks of finches.[4] To clarify my claims about the tefach study, I’ll describe here the Grants’ experiment and briefly discuss its relevance.

The book The Beak of the Finch describes the fieldwork of Peter and Rosemary Grant in the Galápagos Islands in the Pacific (not far from where Darwin himself worked), mainly on Daphne Major. This work is considered a classic evolutionary field study, and the riveting (and very enthusiastic) book describing it even won a Pulitzer Prize. The Grants visited Daphne Major every year for about twenty years and tracked the development of the finch population on the island. They consistently measured several physical parameters of the finches—such as beak length, wing length, and so on. They found that over those twenty years—and even less—significant changes occurred in several parameters, and they even identified the reasons for those changes. The study demonstrated the evolutionary process in action, and contrary to the common view that evolutionary change requires thousands or millions of years for each step, it turned out—surprisingly—that a relatively small number of years suffices to sample such a process. For our purposes here I’ll describe one of those changes and the explanations found for it.

Chapter five describes the drought of 1977 and its consequences. On the island a plant called Tribulus was widespread; it scatters its mericarps which, after rain, sprout new Tribulus plants. Inside the mericarp are several seeds that can serve as food for finches. But to the finches’ misfortune, these mericarps usually hide under stones, and the common finch struggles to move them. In a normal year the finches do not eat those seeds, since more accessible plants are available. The Tribulus mericarps are hard to crack and are thus a low priority. But as a result of the drought almost all other plant types disappeared, and the finches were forced to subsist on the Tribulus mericarps. In 1973 the finches could hardly crack the hard shell of the Tribulus mericarp, and even those that did paid in great effort and time. Once the soft, accessible seeds vanished, the birds had to contend with the hard mericarps. The medium and small finches could not cope and almost all perished for lack of food. Only finches with strong, longer beaks—able to handle Tribulus mericarps—survived. The finch numbers declined steadily, and in parallel the average beak length and strength of the survivors increased. Thus the drought eliminated certain finch species (such as cactus finches) and selected for stronger, tougher beaks. The average beak length increased by about five to six percent compared to its pre-drought average. Note that such small variations in beak length and strength were what separated those that survived from their fellows who died. Thus far this is natural selection. Afterwards evolution operates: the survivors mated and their offspring were born with beaks as strong as their parents’ (genetics).

We must now ask: what was truly new in this field study? What did we learn at the conceptual level? Seemingly, this result is entirely banal: in a drought, only the hard seeds remain, and those that survive are precisely those able to crack them. Up to this point it’s a tautology. Add to this the principle that those who do not eat die—which doesn’t strike me as particularly groundbreaking—and the genetic datum that beak length is indeed heritable, and the end result is still a tautology. Thus, even without any observation, given the circumstantial facts (the drought, the weather resistance of Tribulus, and the varying capabilities of beaks), simple logic would lead any child to expect these outcomes.

True, without those observations we might not have known that beak length and strength are traits inherited genetically from parents to offspring—but that is a finding that belongs to genetics rather than to evolution per se. One could have reached that result by direct study, unrelated to evolutionary questions (by examining sample and control groups of finches and their offspring). This result does not belong to pure evolution but to its scientific periphery (genetics, etc.). No one disputes that genetics is an empirical science—i.e., falsifiable or confirmable. My debate in the book concerns only the principle of the survival of the fittest. Imagine we already knew that genetic fact that beak length is heritable; the study would seem to lose any theoretical significance.

To see clearly that the thesis proven by the Grants is a tautology (I defined it there as a “practical tautology,” without elaborating here), let’s present the matter as a logical argument:

Claim A: There was a drought.

Claim B: If there is a drought, plants disappear, except for a few hard seeds.

Claim C: Not all birds can crack hard seeds (it depends on their beak length and strength).

Claim D: Those that cannot crack hard seeds (i.e., whose beaks are too weak) have nothing to eat and die.

Claim E: Those that remain alive are precisely those that managed to crack such seeds (i.e., those with strong beaks).

Claim F: Beak strength and length are genetic traits passed from parents to offspring.

Conclusion: The beak strength and length of the offspring will increase after a drought.

It’s easy to see that, given the six premises, the conclusion follows by strict logical inference. This raises the question: what did we learn from the Grants’ study? Claims A–E are banal, self-evident facts that teach us no general principle about nature. No one seriously suggests that the study’s conclusion is that there was a drought that year, or that those who don’t eat die. Claim F is a genetic fact that could be discovered in the lab (not necessarily in the field), and in any case it is not the study’s main novelty. The conclusion, finally, is a simple logical consequence of those six claims.

Weiner himself sensed the problem, and quotes Raymond Pearl (p. 76 of the book):

“According to the opinion of many, surprisingly many, including some quite eminent names in science, it is all the same to show that something is logically necessary and to show that it actually exists. If the rules of formal logic are satisfied, they imagine that the truth has been revealed. No further proof is required. As everyone knows, such an approach has already, in effect, brought the whole theory of evolution to an intellectual bankruptcy…”

Those “eminent men of science” whom Pearl cites are entirely right. It is like a study showing that if there are ten finches on an island and six more arrive, then when we count the finches the total will be sixteen. Thus we have confirmed the (physical, not mathematical) law that 6+10=16. According to Pearl and Weiner, we should not think that if mathematics says so, there is no value in an observation demonstrating it in practice. Alternatively, the Grants’ study is like taking different triangles drawn on paper and measuring their angles to test whether their sums are 180 degrees. That too is a field test of a (practical) tautology. Is there any point or value in such a study? I have serious doubts.

In the evolutionary context it serves, of course, the propaganda needs of a defensive theory and the shoring up of believers’ confidence against their creationist critics. In the context of the biblical tefach, the study looks like conceptual confusion (had it been conducted by religious people I would have thought it too was meant to bolster faith). Substantively such studies are unnecessary. The Grants’ work offers at most a demonstration of evolutionary processes, but I see no substantive conclusion arising from it.[5]

When examining an empirical armchair study, it is advisable to structure the argument as I did here (and above for the tefach). With such a logical structure before us, we must ask which premises are known in advance and which are subject to empirical test. One can treat some premises as known and leave the others; then, if the expected conclusion is obtained, it corroborates the remaining premises. Thus, for example, had we not known there was a drought on Daphne Major, the study could have corroborated that. Had we not known that stronger beaks crack hard seeds more successfully, the study could have corroborated that. But if all the argument’s premises are already known independently prior to the study, then such research has no significance beyond psychological reinforcement for believers. We could have reached the conclusion without getting up from the armchair.

Incidentally, these very days in our A Priori Armchair Research Laboratory, we are considering expanding into evolution, gender studies (though there, all departments everywhere mainly do armchair research), psychology, household management, space science, nuclear physics, computational biology, political science, strategy and governance, history, literature, neuroscience, and more. Consider this column a call for donors—and may the listener find it pleasant.

[1] Thus it is presented in the Hebrew University report mentioned below.

[2] I’ll just note that yesterday I received a post from a well-known businessman who mocked the rabbis’ concern with the correct blessing for a krembo. He wondered at the useless, ridiculous topics to which wise people devote themselves in the 20th century. I replied that his scorn should have been directed at those who devote their lives to television shows—their production, viewing, and critique—and even to politics and other pointless subjects that occupy almost the entire secular public. That strikes me as far more ridiculous. But now I thought perhaps I should also direct him to these studies—some of which he may even be funding. There he can see that even our academy engages burning issues like why jar necks were made 89 mm wide in 10th-century BCE Israel. Shame on the rabbis who deal with the blessing over a krembo cookie instead of devoting their talents and energies to investigating the reason for fixing jar-neck widths…

[3] See, for example, Kalman Liebskind’s comments about the Wikipedia entry “Esther Hayut,” where the site’s editors were asked by the court system’s spokespersons to copy into it text written by their office.

[4] There it was part of my claim that evolution is a tautological theory that is not falsifiable (and therefore, of course, necessarily true). Survival of the fittest is a valid logical-analytic argument.

[5] For this reason, evolutionary researchers consider it very important to demonstrate such a phenomenon and watch it in action. This can have a non-trivial effect on one’s willingness to consider the blind process as an option. As Dawkins explains at length in his book (p. 169ff.), observing an evolutionary process can raise awareness of this option, which we tend to dismiss out of hand. But that claim is problematic, since it is a psychological effect, not a result of scientific significance.