Journal

The life of an individual, of humanity as a whole, of all living nature on planet Earth, of the Solar System, the cosmos, and perhaps the universe as a whole can be understood as dynamic systems. What makes a system dynamic? Essentially, changes in its state and the rules that govern those changes. A dynamic system can be studied discretely as a sequence of successive “cross-sections”: a series of static states containing certain variables and connected by a temporal scale.

The evolution of a system over time can be represented as a trajectory through its state space, and its entire history as a collection of “cross-sections” of the same system together with the relations between them. (In another model, time itself could also be incorporated into the structure being described rather than treated merely as an external parameter. But we will deliberately leave that model aside for now.) One important property of time is the resolution of its scale: it allows us to determine how frequently to take “snapshots of reality” for different systems, distinguishing relatively stable parameters from variables that change at different characteristic rates.

A sleepless summer night.

At daybreak, I opened the window. The freshness and coolness of the motionless air. Tree branches frozen as if in a still frame. Neither birdsong nor any other sound has yet broken the silence left by the night. The tops of the pines are lit by the sun’s rays passing through pink clouds. The sky is a clear, translucent blue, with a few light white clouds gently drifting towards me.

Statement

Suppose that

1. $P \rightarrow Q$,
2. $Q \rightarrow R$.

Then

A scientific discovery may begin with a fact that does not fit into the existing picture of the world. If the fact itself is well established, but the existing description of reality cannot explain it, this does not necessarily mean that the fact is wrong. Perhaps it is the description itself that is incomplete. I find it interesting to consider that an existing theory may be entirely correct within the domain it describes, while still remaining only one facet of a broader picture of reality.