The symbolic Eye was divided into six parts, each part being associated with one of the six senses, as well as with a specific fraction. The Ancient Egyptians considered thought to be a sense, in addition to the five senses we often think of today.
The seven liberal arts and sciences are, of course, ways of thinking. The most important of which we all know, and it is that which is most obviously represented within the Eye (but which cannot be understood without arithmetic, which in turn cannot be understood without logic, which in turn cannot be understood without rhetoric, which in turn cannot be understood without grammar).
As stated by Bro. Richard Marcus:
"As infants, we are unable to speak. We must learn words to describe everything. Words organize our thoughts. Language is essential for learning. As we progress up the Winding Stairs, we learn to speak with eloquence and grace, which is rhetoric. We learn to use logic to make our arguments persuasive and true. We advance up the lessons to higher levels of arithmetic, geometry, and music. These require abstract thinking and greater levels of concentration. As we mature in life, we gain PERSPECTIVE and WISDOM as we enjoy the glorious works of creation, the stars and planets, astronomy, and the DIVINE."
Bro. Marcus continues by stating:
"The sense of SEEING is developed in Geometry. We grow in PERCEIVING which STRUCTURES are in ORDER and which ones are not well arranged. We acknowledge that geometric is the foundation of architecture."
Of course, one must have an understanding of geometry to understand music, it being made of wholes, halves, fourths, eighths, sixteenths, etc., which are the fractions depicted by the Ancient Eye. More complex fractions can be created by adding the symbols/fractions together, as can ratios.
The Eye of Horus can be associated with either the right eye or the left eye. The Ancient Egyptians associated with the right eye with the Sun, and the left with the Moon. It has been suggested that the Eye of Horus being torn out referred to a solar eclipse - something even an EA sees reference to in the midst of solemn ceremony. And what is this but astronomy?
Unrelated associations? Could be - I'm a Speculative Mason, and so I speculate.