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There is an old tradition commonly referenced in the yeshiva community that Masekhet Ketubot is the "Shas Kattan" of Talmud Bavli, that is, it contains ideas that connect to just about every other area of Shas (short for "Shisha Sidrei," all six orders of the Mishnah). The source and force of this idea is the subject of this question on Mi Yodeya.

Personally, I have thought that this doesn't really seem to be the case; although Ketubot does indeed have a lot of cases involving civil law and connects to many topics covered in tractates Bava Metzia, Bava Batra, and Shevu'ot, and one encounters the laws of Shabbat and Yom Tov in the first 10 pages, it doesn't contain much from Zera'im, Kodshim or Taharot (or Mo'ed really). There seem to me to be much better candidates for Shas Kattan, such as Pesachim or Nedarim, when one considers all six orders of the Mishnah.

My question is - and one that is worth a bounty of lots of extra points from me - would there be a way to computationally determine which tractate has the most varied connections to other tractates in Shas?

There are a few (valid) ways one might interpret this question, which could produce different results, but I'm happy to reward any good attempt with lots of bounty points. See below for some possible approaches. Additionally/alternatively, can you make (or reference) a visualization showing the Talmud's interconnectivity with something like a chord diagram? Or a similar kind of visualization that can help display what the "real Shas Kattan" would look like? (Sefaria has some nice visualizations here, but none that answer my specific question about the Talmud Bavli).

Computationally speaking, which tractate of Talmud Bavli is the real "Shas Kattan"?


Possible Approaches

Page-by-page Seder Score: give each page of talmud a score between 0-6 for its "order connectivity breadth," defined by the number of orders (out of the 6 orders, or sedarim of the Mishnah) cross-referenced by a single page, and then find the Tractate with the highest score averaged across its pages.

Simple Point-Per-Tractate Score: for each tractate, give one point for every other unique tractate (in Mishnah, Talmud, or Tosefta) referenced, with the possible highest score of 63. Perhaps it would be "more fair" to divide that score by the number of words in the given tractate.

Exponential Discounting of Repeated Tractate References: what I believe would be the most accurate reflection of 'shas-kattan-ness' would be to score each tractate's references as follows: give one point for every unique Tractate referenced. For the second time that tractate is referenced, give 0.5 points, then the third time, give 0.25, etc. (So, for example, if a tractate quotes Berakhot once and Shabbat thrice, it will have a score of 1 + 1.75 = 2.75). Again, perhaps divide the final score by number of words in the tractate for fairness

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  • Of course you're looking at "actual Shas" kattan ... not "the much smaller piece of Shas that yeshivas typically cover, to the exclusion of all else" kattan ...
    – Shalom
    Commented May 9 at 19:34
  • @Shalom but that's the thing, people call it "Shas kattan," not "fifty-yeshivihe-blatt-kattan". But it's also not just a new yeshivish thing; this term has a long pedigree, see this article by Tuvia Preschel Commented May 9 at 23:10

1 Answer 1

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Before you scroll down, here's a challenge: according to my research, there's only a single tractate in Talmud Bavli that cites all 62 other tractates of Shas. Can you guess which one it is?


So... Even though this question has been bountied it seems like nobody else cares much, so I did some work to figure this out on my own. I don't know about using Sefaria's API (it seems not so well designed for answering these kinds of cross-referencing talmud questions), but Sefaria does have a list of links which already counts up the number of cross-references that exist throughout the Sefaria library.

I used this to collect the number of times any tractate of Shas was quoted by each tractate of Talmud Bavli.

Below is a table of how many unique other tractates are cited by each tractate of the Talmud Bavli. In this case, a 'citation' counts whether it is a reference to the Mishnah, Tosefta, Talmud Yerushalmi, or Talmud Bavli to any one of the 63 tractates in Shas. According to this table, there is only a single tractate which manages to reference all the others: Chullin!

I also used a slightly more complex scoring method to account for multiple references to the same tractate, where each additional citation garners incrementally smaller points in a geometric series. The results don't do much to change the rankings overall but can help with a few tie-breakers, and so I've sorted the table below first by "unique references" and then by this more complex score.

Tractate Unique Tractates Referenced Exponential-Decrease-Score
Chullin 62 116.89577852011915
Eruvin 58 104.11961320040427
Menachot 58 104.1098582111299
Berakhot 56 101.77476863324046
Gittin 55 99.0613626539598
Bekhorot 55 95.35521305304428
Avodah Zarah 55 93.15401339507207
Bava Metzia 54 96.7636258301427
Pesachim 53 98.12823985467958
Niddah 52 91.59834762607352
Shabbat 51 93.73074903174845
Bava Batra 51 93.48292022838086
Bava Kamma 51 91.50913565878997
Chagigah 51 87.70597839355469
Kiddushin 50 90.7797232517002
Ketubot 48 86.27256274083626
Sukkah 47 84.69956454820817
Beitzah 47 79.6522365808487
Megillah 45 77.95748043013737
Arakhin 45 76.91127727914136
Sotah 45 76.47444889880535
Sanhedrin 44 83.24673657807102
Nazir 44 78.29042801260948
Makkot 44 75.13363409041631
Keritot 44 71.53747296286747
Nedarim 43 75.31631442904472
Shevuot 41 72.194636791005
Temurah 41 70.44600623844599
Rosh Hashanah 40 68.44915628246963
Moed Katan 37 63.7000732421875
Horayot 37 56.52581787109375
Yoma 36 71.1487001739068
Zevachim 36 70.46337077020688
Yevamot 36 69.9527091364871
Meilah 35 54.75389099120366
Taanit 33 57.51600646972656
Tamid 20 26.12499237060547

And behold, the connectedness of Shas:

Web of connections for Shas


There is another possible way of interpreting "shas kattan"-ness, which would refer to how well balanced all of the citations are in terms of being a more fair representation of all of Shas. Although I don't think anyone had this in mind when referring to Kesubos as "Shas Kattan," it nevertheless seems like an interesting to me. In case this is interesting to anyone else, I'll show the results of my data here, but once again Chullin appears to be the winner (except maybe Bekhorot; both of them have very similar calculated deviations from an expected set of values of 1/6 citations to each Seder).

enter image description here

For a colorblind-friendly version, click here.

Another question we can ask of Masekhet Ketubot (or any tractate): does it have the most references to Nashim and Nezikin, compared to any other tractate? If not Shas Kattan, is it at least "Bas Kattan" (for ב סדרים)? The answer to that question is also no; all three "Bava"s beat Ketubot if you sum up citations to both Nashim and Nezikin. Here are some of the heavy-hitters in terms of "Bas Kattan":

Tractate Citations to Nashim Citations to Nezikin
Ketubot 689 385
Gittin 627 311
Kiddushin 502 284
Bava Kamma 279 854
Bava Metzia 334 775
Bava Batra 401 706

Another legitimate approach would be to understand the term "shas kattan" as a non-literal reference to "all the topics in the Torah," and ask the question: which tractate of Talmud Bavli covers the most unique topics? This question is much more difficult to answer simply because there were no tools which identified "topics" as they appear in the Talmud in the same way that people have been identifying talmudic cross-references since R. Nissim Gaon in the 11th century.

But today, we have Sefaria! Included in the Sefaira database and API docs is a way to identify which topics come up in any source. So I also tried to count up all the unique topics that show up anywhere throughout each tractate of Talmud Bavli. In reality, topic ontology is kind of messy; there are ways that I could have been stricter/more rigorous in counting topics but this simple count is also interesting, for all its issues.

Here's a chart of all the tractates ordered by most topics identified according to Sefaria's topic links (along with the "Unique Tractates Referenced" number in the third column, as explained above)

Tractate Topics Count Unique Tractates Referenced
Shabbat 1133 51
Sanhedrin 1038 44
Berakhot 954 56
Pesachim 864 53
Bava Batra 781 51
Sotah 708 45
Bava Metzia 680 54
Ketubot 678 48
Eruvin 662 59
Yevamot 634 36
Kiddushin 630 50
Chullin 623 63
Gittin 616 55
Bava Kamma 611 51
Yoma 592 36
Avodah Zarah 577 55
Nedarim 541 43
Megillah 537 45
Taanit 488 33
Menachot 462 59
Chagigah 394 51
Rosh Hashanah 393 40
Niddah 384 52
Sukkah 351 47
Zevachim 313 36
Bekhorot 310 56
Moed Katan 293 37
Arakhin 289 45
Makkot 272 44
Nazir 251 44
Shevuot 242 41
Beitzah 217 47
Keritot 193 44
Horayot 183 37
Temurah 177 41
Meilah 104 35
Tamid 101 20

Here's a jupyter notebook with the code and figures, for anyone interested.

Of course, all this has a huge asterisk: it relies on the "Link Number"s and "Topic Link"s provided by Sefaria, and it's hard to say to what extent this information reflects the actual cross-references number (and, of course, how to define a "topic" and identifying associated sources is notoriously tricky)

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    Thanks! I hope you or someone continues this, and makes a blog. So, does Tamid not quote Taharot at all, or is the graph too small there? That seems to be the only gemara that is missing a single reference to a whole seder? Is Niddah that much better than Chullin here for fractional link count - is it by eye you are saying that or did you calculate and compare scores? I recently saw this video about analyzing the connectedness of wikipedia, using math to work out "communities" based on connections etc: youtu.be/JheGL6uSF-4. Would love if someone would do the same here, if useful
    – Rabbi Kaii
    Commented Apr 8 at 21:49
  • If you remove self-referencing, what does the fractional link count chart look like?
    – Rabbi Kaii
    Commented Apr 8 at 21:51
  • No, but I just assumed it contained self references because Berachot has a lot of Zeraim references?
    – Rabbi Kaii
    Commented Apr 8 at 22:34
  • Sefaria's connections are added by mesorat hashas, algorithmacally, and by random people. their topic pages are generally taken from somewhere specific such as aspaklaria.info
    – Mordechai
    Commented May 9 at 14:43
  • @Mordechai yes I know, thanks, but I didn't want to get into the details. I'm very thankful to Sefaria that the connections actually contain information about where they come from (it's called "dataSource" in the ref-topic-links) and so I could have filtered out the topics index by source reliability. But however you slice it, there are still going to be some issues with rigorousness and balance so I just decided to keep them all Commented May 9 at 16:02

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