I’ve been diving into The Almagest, translated by G.J. Toomer, and the first chapter gave me deep insights into philosophy, mathematics, and the nature of knowledge. Here are my key takeaways:
1️⃣ The Divide Between Practical and Theoretical Philosophy
Philosophy is divided into two parts: practical and theoretical. Practical philosophy can often be learned through experience—people can possess moral virtues without formal teaching. Theoretical philosophy, on the other hand, requires instruction and study. Practical wisdom improves through action, while theoretical knowledge grows through deep inquiry.
2️⃣ Mathematics as the Most Certain Knowledge
The discussion highlights three divisions of theoretical philosophy: physics, mathematics, and theology. Physics studies the material and changing world, making it unstable and uncertain. Theology deals with what is beyond perception, making it speculative. Mathematics, however, remains unchanging, eternal, and the most reliable form of knowledge. It serves as a bridge between the material and the divine, capable of supporting both physics and theology.
3️⃣ Mathematics as Our Language for the Physical World
One passage that truly stood out to me was:
"As for physics, mathematics can make a significant contribution. For almost every peculiar attribute of matter becomes apparent from peculiarities of its motion from place to place. Thus, one can distinguish the corruptible from the incorruptible—whether it undergoes motion in a straight line or in a circle, heavy from light, or passive from active, whether it moves towards the center or away from the center."
This is a beautiful description of how mathematics allows us to describe the nature of the physical world—how we categorize motion, weight, and forces. Mathematics has been our human language for encoding the attributes and qualities of reality. But now, with the rise of AI and machine learning, we are seeing a new way to represent the physical world—through neural network weights.
What if these AI systems, by learning from vast amounts of data, could encode the laws of physics in ways we can’t yet fully comprehend? Could these neural networks serve as a new kind of mathematical language, capturing not just the mechanics of the universe, but perhaps even the deeper truths that theology seeks to understand?
This makes me wonder—are we at the beginning of a paradigm shift in how we define and discover truth? Would love to hear your thoughts!
#Philosophy #Mathematics #AI #MachineLearning #Physics #TheAlmagest #Knowledge #IntellectualGrowth