We have made thee neither of Heaven nor of Earth,
Neither Mortal nor Immortal
~ Giovanni Pico della Mirandola, Oration on the Dignity of Man
These themes, of mortality and immortality, and of the different substrates, have been twining themselves around me recently. It seems everything I do returns me to this topic, and I need to start dealing with it in the only form I know how. Everything connects to this theme, from Kierkegaard to Kauffmann– that is, from theology to physics. And it all relates to time, the growth in complexity, and acceleration.
Let me start with the phases of matter. Earthly versus heavenly stuff– these are solids and liquids/gasses1 respectively. In physics, we might use water to illustrate– what does it mean that ice is solid? It means it doesn’t change its structure over time. In this sense structures formed in ice are immortal– write your name in defects in an ice crystal and it will be there for a long time. And what does it mean that water is liquid? It has very little long-range order and the relationships between atoms are described by statistical metrics. Fluid is ethereal, intangible, heavenly– and any structures formed within it are mortal, finite and fleeting.2
1 For my purposes liquid and gas are the same– you can simply say fluid. The world we humans live in happens to be gaseous, but we could just as easily live in water, these media are the same in all the ways that matter.
2 But wait, I hear you object– heaven is immortal, earth is the mortal real! This is the core inversion of Christian theology and we will go over it in more detail later. But notice that even Giovanni orders them so– Heaven / Earth, Mortal / Immortal. But in some sense these are just different meanings of mortality.
But you can form structures in a fluid. Because the very act of ‘forming’ implies changing over time. In fact this relationship between solid and fluid– between a persistent substrate and a changable one, between an immortal object and a changable realm– is at the heart of everything we do. How does a classical sculptor place a shard of matter in the future? With liquid metal, in the fluid realm, they work– but their work is solid matter and therefore immortal. Or they take a piece of the world, the earth, a piece of rock– marble. They expose it to the fluid world with machinery, and then at that interface between solid and fluid they chip away at it, sending chunks flying– flying, mark you! A very fluid form of motion– across the room until they have “removed all the excess”.
In the physics of complex systems, the human realm looks like a thin skin of dynamical activity on the surface of an aggregate of solid matter (a planet). This realm is known as the Edge of Chaos. It is closely related to the concept of criticality.
It is easy to illustrate criticality– here is an Ising model at the critical temperature. The lattice is a grid of atoms, each of which can be ‘up’ or ‘down’. The atoms interact with their neighbours, and the temperature controls how much randomness there is in the system. At the critical temperature, the system is poised between order and disorder– structures form and dissolve, neither frozen nor chaotic. This is the edge of chaos.
Open full interactive lattice simulator with this config
Compare this to the low-temperature regime– the solid phase. Here the thermal fluctuations are too weak to overcome the coupling between neighbours, so the lattice freezes into large, stable domains. Structures here are immortal, but nothing new can form. This is earth, rock, ice.
Open full interactive lattice simulator with this config
Using the lattice simulator’s tracking feature, you can select a structure at criticality and trace it backwards and forwards through time, producing a spacetime sculpture– a record of how a structure was born, lived, and died. Here is one such structure, extruded through time. You can drag to rotate it.
A spacetime structure from the Ising model at criticality, traced through ~200 frames.