Perhaps the most straightforward answer to whether the Eye of Horus is mathematical, mystical or medical is yes... all of the above, but diving into the interesting relationships between the three leads to some fascinating discussions around this ancient civilization.
The symbol gets its name from a mythical figure: the god Horus, son of Osiris and Isis, so it ties in to the mythological culture central to ancient Egypt. It also has been linked to several unit fractions with denominators that are powers of 2; this links it as well to the mathematical ideas originating out of this area of the world at that time. Finally, it is also thought to represent the senses as they were know to the ancient Egyptians (smell, sight, thought, hearing, taste, and touch) and mysteriously matches quite well with modern anatomy's understanding of the structure of the human brain, linking it to the ancient culture's understanding of medicine and anatomy.
The different parts of the symbol are thought to correspond to distinct unit fractions as well as specific senses. Figure 1 (taken from ReFaey, Quinones, Clifton, Tripathi, & Quiñones-Hinojosa, 2019) shows the unit fractions related to each section of the symbol. They state, "The 1/2 accounts for the sense of smell, the 1/4 represents sight, the 1/8 represents thought, the 1/16 represents hearing, the 1/32 represents taste, and the 1/64 represents touch" (2019).
The most interesting part is arguably they symbol's potential connection to the anatomy of the brain shown by Figure 2 (also taken from ReFaey, Quinones, Clifton, Tripathi, & Quiñones-Hinojosa, 2019). My own understanding of brain anatomy is not at a level where I could verify the claims laid out; regardless, my pseudoscience-spidey-sense tingles a bit as they try to relate each section of the symbol to the area of the brain that corresponds with that specific sense. Despite this, the discussion is still interesting and well worth reading and thinking about, and whether the ancient Egyptians understood the complex inner-workings of specific areas of the brain (an area of neuroscience that we are barely scratching the surface of today), the Eye of Horus is clearly an interweaving of the math, science and culture of that civilization.
In my own life, and as someone trying to learn how to "properly" take pictures, I have always found the compositional aspect of photography to be incredibly interesting. Understanding different ratios and relationships that work within an image can be one way to both take better photos as well as to dissect and understand my own and other peoples. Some examples are below in Figure 3 (they are not photos I have taken).
Reference
ReFaey, K., Quinones, G. C., Clifton, W., Tripathi, S., & Quiñones-Hinojosa, A. (2019). The Eye of Horus: The Connection Between Art, Medicine, and Mythology in Ancient Egypt. Cureus, 11(5), e4731. https://doi.org/10.7759/cureus.4731



Tim, I agree that the overlay of the Eye of Horus on the cross section of the brain is uncanny and alluring. I also agree that the complexity of neural activity by the structures in question are hard to reduce to the 5+ thought mythology. But fascinating nonetheless! Thank you for sharing your photo interests, and a mini lesson in composition!
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