Peter, good episode; however, you said that it is weird some Byzantine polemicists considered Islam a form of Christian heresy. Although, their rhetoric was primarily motivated by critiquing Islam there are a number of serious modern scholars such as Crone, Luxenberg (pseudonym) and Crook who have put forward theories which make a similar claim. They have somewhat backtracked a little based on further research but their general hypothesis still stands. 

Great episode! I have greatly enjoyed the podcast thus far, having "binged" them all in three weeks. If I may, I have only two points, both of which regard future podcasts; and from the outset, I apologize if you already had these particular issues in mind:

(1) Byzantine satire. When you discussed ancient philosophy, you mentioned the satirist Loukianos (Lucian). Loukianos was well educated in contemporary philosophy, and he provides various satires of philosophers. These serve not only to "make fun" of the philosopher, but they also provide criticisms for particular philosophical schools that existed at that time. The Byzantines (eastern Romans) continued this tradition, e.g. the Timarion, and continued to satirize philosophers, philosophy, and Christianity, including the fundamental precepts of their belief, usually in dialogues concerning journeys to Hades, in the vain of Loukianos' "Dialogues of the Dead". I realize these figures are satirizing philosophy, and engaging in refutation; not necessarily positing any positive philosophical theories, but I wondered whether this might be an area of interest for you. For example, I have met some philosophers who consider both Dostoyevsky and Camus to be existential philosophers, and others who argue they are not philosophy.

(2) Byzantine aesthetics. In particular, aesthetics as expressed through church architecture. The Byzantines, in general, utilized earlier Latin architectural and aesthetic authors, e.g. Vitruvius (of Vitruvian man fame); neoplatonic conceptions of god, the universe, proportion, and harmony; as well as Christian theology, in order to construct their churches (particularly the characteristic dome). In some sense, these builidings serve as the embodiment of particular Byzantine conceptions of aesthetics, the universe, the nature of god, and the place of the human being within the divinely created universe. Indeed, these Byzantine aesthetics (as expressed through the church) are supposed to have influenced later Ottoman mosque aesthetics, post the conquest of Constantinople in 1453. Admittedly, I may not have expressed this idea in a good manner, as it is not my area of specialty - I am a graduate student in the ancient and medieval history of philosophy - but I have heard other members of my faculty (the centre for Byzantine, Ottoman, and Modern Greek studies at the University of Birmingham, UK) speak of these aesthetical aspects of Byzantine church architecture, and I thought it might be of interest to you and your podcast.

Thank you very much for the podcasts, and all of your hard work in producing them. I can say they have been incredibly useful to the formulation of my own ideas, and introduced me to authors and concepts of which I would otherwise have been ignorant.