*January 19, 2025* # The Geometry of Water ![[spanish-river.jpg]] > There’s no reassuring ceiling over you, Moneo. Only an open sky full of changes. Welcome it. > > —Leto, Children of Dune *** I'm thinking about complexity again. ## Three Views of a Secret Scientists, mathematicians, and storytellers all mean something different when they have a "theory". They each cast a spectrum through perception and ideas to enlighten the subject. Scientists mean something like a working model of a thing that can be evaluated against a measurement. Mathematicians mean a self-consistent system that can hold an internal identity. Storytellers understand the outline, and how ideas are brought to life. So, when a theory finally embraces reality, its colour is naturally ambiguous. The white whale of *complexity theory* is a big one: *What is life?* It came with ideas of *emergence* and *self-organization*. We noticed patterns in the way things transcend the sum of their parts, and that sometimes "no shape" ... seems to have a shape? We started to feel our way through a new and shapeless geometry. ## Shadow and Light Today, we think of *geometry* as a two-sided coin. Ancient Greek philosophers were shape-minded. The universe is governed by eternal shapes and their natural resonance. Our true experience is the consequence of how these shapes fit together, overlap, and the harmonies they make. We can find truth if we learn to listen. Islamic philosophers were logic-minded. Borrowing from Indian philosophers, they invented *algebra* which translates to "binding-together". They bound ideas to symbols and grammar to logic, transforming them into truths. We can unfold truth for ourselves. It's hard to see now, but ***it was not obvious*** that the timeless reality of shape, and the unravelling of symbols intersected around a "coin" of geometry. It was René Descartes who finally noticed! If we consider how our sense of spatial geometry and of symbolic logic came about, we may understand them as two *fully independent* lineages that "happen" to meet somewhere. Hear me out. It's like how evolutionary lineages converge onto similar principles just by virtue of living in the same environment—how distant forms of aquatic life end up with fins. ## Water Babies Seals don't need to plagiarize from dolphins; fins and flippers are just really natural and obvious ways to propel yourself and navigate through water. Of course, this isn't *really* obvious from the perspective of a fish, nor is it really a "conscious" decision made by the evolutionary process shaping the animals. Evolution doesn't know about water; it has no conception of fluid mechanics or whatever. Evolution simply reaches and learns what stays. Fins of every kind are a natural consequence of the exploratory process, pressed against the many and various realities of living underwater. Sharks have sharp rigid fins, allowing them to thrust and thrash, move fast and zigzag on dimes to catch prey. Whales have a powerful, level, tail with which they climb for air and dive to insurmountable depth. Goldfish have gorgeous soft fins that mostly keep them upright and pointing in the right direction. All of these fins tell us something about water. ## As Above So if you look at it from this angle, algebra, geometry, and other intelligence are just like that! Elegant, but fragile limbs by which we navigate and manage the hidden substance of reality. As observers above water, we clearly see that every fin reflects the way water works. We see why they are flat and not bulbous. We see why they can be rigid or flexible, round or pointy, and how every variation meshes with countless aspects of underwater life. From the surface, we are still shocked and amazed at the complexity we see. If human stories are fish, we live in their fins. We push outward; guided by laws of beauty, we simply feel our way into new shapes. What emerges is natural, and what stays is beyond our control.