Skip to content

Instantly share code, notes, and snippets.

View geometer-jones's full-sized avatar

geometer-jones

View GitHub Profile

On Memory Engines: A Geometric Framework of Graded Phenomenality

1. Intro

An apple accelerates under gravity. Every prior instant of the gravitational field is perfectly preserved in its present velocity—nothing is lost, nothing is forgotten. Yet the apple is not conscious. It does not learn, attend, or remember in any felt sense. What it lacks is not contact with the world, but a certain kind of contact with itself.

Consciousness lies at the opposite pole: vivid, self-modulating, historically deep. The difference is whether a system’s own past loops back to push against its present—reinforcing along some dimensions, opposing along others, and in that interplay reshaping what comes next. Call this interplay reciprocation.

Between the apple and a conscious mind lies a continuous thickening of the same operations. This paper develops a geometric framework—a dynamics of complex-valued vectors on unit hyperspheres—that makes this thickening precise. It argues that the structure of phenomenal experienc

Memory Engines: The Geometry of Automatic Abstraction

Imagine an apple falling from a tree. Gravity pulls it faster and faster. Every prior instant of the gravitational field is perfectly preserved in its present velocity; nothing is lost. Yet the apple feels nothing. It does not notice, learn, or care.

Now picture a conscious mind. It does not just fall through time; it feels the falling. It remembers yesterday, anticipates tomorrow, and right now wonders about apples and consciousness.

What is the difference? The apple is pushed only by the outside world. A conscious mind is also pushed by itself, by its own past pressing back against its present. That back-and-forth push creates something new: a living, felt experience.

We call this back-and-forth reciprocation. This idea leads to a surprisingly simple geometric picture of how consciousness grows out of ordinary physics: no extra ingredients required, just the right kind of self-interaction.

Reciprocator

Overview

A Reciprocator is a dynamical memory system whose state is a complex vector (\mathbf{s} \in \mathbb{C}^n) constrained to the unit hypersphere:

$$ |\mathbf{s}| = 1. $$