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To be frank, there was something wrong with the visualizations in the last post, and I did not feel like letting that stand. Thus, here I address some of those issues.[caption id="attachment_481" align="aligncenter" width="901"] Network discipline to person, main cluster [disciplines in light, people in dark][/caption]This is how the network should look or, at least, the main cluster of it. In the last post, I stated that some grammatical as well as the mathematical disciplines were not connected to the main cluster and that turned out to be wrong. But since they are indeed connected, everything gets – once again – a little messier. As regards the cluster on early education in grammar, that one remains separate. I have excluded it from the illustration for that reason.The connection of the mathematical disciplines, which mostly cluster on the right side of the network, comes from three angles. The more pertinent one is the discipline ʿilm al-farāʾiḍ which is now located in the center. Ibn Ṭūlūn's uncle Jamāl al-Dīn and his father-in-law Burhān al-Dīn Ibn ʿAwn both saw to his education in this important field and thus connect it also ḥadīth, fiqh, and uṣūl al-fiqh. This is obviously where one would expect to find it.The second connection comes through ʿilm al-ḥisāb from both ʿUrfa al-Warrāq and ʿAbd al-Nabī al-Mālikī. One connects this subject to the mathematical disciplines, the other one rather to logic, grammar, kalām. The third one derives from Shihāb al-Dīn al-ʿAskarī's [lower right corner] teachings in both water clocks and Lugha and Tafsīr.Still, those mathematical disciplines concerned with time keeping retain their character as a distinguishable subcluster defined by distinct authors and teachers. They are intricately connected to each other by a number of people, including the teachers al-Warrāq and al-Shamsī Ibn Makkī as well as the much more famous author Ibn al-Hāʾim al-Ishbīlī.[caption id="attachment_487" align="aligncenter" width="1193"] Network discipline to person, weighed by number of teachings[/caption]In the central cluster, we can see how Ibn Ṭūlūn's "religious" education was compartmentalized between his teachers. ʿAbd al-Nabī taught him mostly Logic and Taṣrīf, Ibn ʿAbd al-Hādī gave him a wider introduction to logic, history, medicine, Sufism, recitation, and ḥadīth. The real heavy weight in the last field, however, was Ibn Zurayq (also a member of the Ibn ʿAbd al-Hādī family). Shams al-Dīn Ibn Ramaḍān combined ḥadīth with fiqh and several grammatical disciplines.Al-Shams Ibn Makkī, whose name is a bit difficult to make out, is equally if not more important than those figures. That is, he is important in his own sub-cluster which revolves around medicine and the "natural sciences" informing it. Ibn Makkī appears to have been the foremost authority on medicine in his days, "the raʾīs al-aṭibbāʾ of Damascus".And if we look back at Ibn Ṭūlūn's familial relations, we find that his father-in-law, al-Burhān Ibn ʿAwn appears much more influential in his education than his uncle Jamāl al-Dīn Ibn Ṭūlūn. The latter only educated Ibn Ṭūlūn in two disciplines, ḥadīth and farāʾiḍ, whereas the former was equally important in farāʾiḍ and central in both uṣūl al-fiqh and fiqh itself.One last word about the organization of knowledge. ʿIbn Awn's involvement clearly points towards the relevance of normative understandings of how those disciplines should build on one another. You need to know the foundations of law to learn about jurisprudence. But going back to Ibn ʿAbd al-Hādī's teachings, we also see the potential for development of disciplines in interaction with each other. The combination of Sufism and medicine has long been acknowledged in our field. The closeness of recitation and Sufism is equally convincing.What in my opinion seems a promising field of enquiry, however, are the interconnections between history, logic, and ḥadīth that seems to pervade his teachings. Including the connections to "natural sciences" in such an enquiry might prove even more worthwhile.&#160;[cite]