DS
Extension C · Toroids and Grids
मण्डल

Toroids and Grids

The Geometry of Memory, Grids, and Intelligence
— Dileep Saxena
Einstein within a toroidal grid form
Scroll to explore
I

The Torus and Attractors

Toroids · Manifolds · Memory Surfaces · Grids

Toroids mesmerise my orientation towards neuroscience... an amazing field holding key vantage links — and open up an infinitely rich tapestry into vital manifolds for 'Attractors'.

Interactive torus — colorful wireframe with orbiting particles

Literature is abuzz with information dance on never-ending, no limits — the tarpaulins, as if it is lining an inner surface boundary of black holes.

Its memory records, abstract possibilities, rich in spatial-temporal-tensor-tags play to rewind (Past) or extrapolate (Future), relating to present.

Consciousness is the only comprehensible spotlight that is available to our perceptions. We try to unravel these complex concepts by crawling along "grids".

Colorful Torus — hexagonal grid columns in spiral wraps
Colorful Torus — hexagonal grid columns in spiral wraps
II

Grids and Action Potentials

Virtual Grids · Neuronal Tug of War · Balanced Potentials

But again, these virtual grids in discussion are the balanced state of opposing neuronal action-potentials. In neural nets always a tug of war is perpetually on between positively charged against negatively charged potentials / field, (here lies our interneuronal dominance).

Grid structure is created, and their virtual maintained existence is all-through supported by neuronal action-potentials.

III

Hexagonal Properties

Nascent Neural Nets · Dynamic Potential Boundaries · Six-Node Relations

In any nascent neural net this dynamic play of potential balanced boundary finally settles for grid structure of "hexagonal" properties.

Aim of maturing of neural nets in brain circuits is always to seek a balanced circuit in hexagonal relations. The anatomical locations of these "six" neuronal nodes are never geometric or, as conventional shapes we understand.

But neuronal grids in hexagonal relationships are actually in terms of electrical potentials, irrespective of anatomical locations and properties.

Hexagonal torus — tiles covering the toroidal surface
Hexagonal torus — tiles covering the toroidal surface
IV

Grid Manifolds and Memory

Foetal Cortical Activity · Toroidal Surfaces · Golden Spiral Ratio

Since the very initial cortical electrical activity generation while in early creation — foetal age, first activity mostly in network formation revolves around finding ways to weave this grid manifolds.

Actual play of building up complex behaviors require memory use. And, manifolds wrapped up into toroidal virtual surfaces provide unlimited potentials for memory storage. Hexagonal matrix on surface as spirals — almost at golden spiral ratio — offer a never ending-story!!

Hexagonal grid torus — spiral wrapping lines with pulsing illumination
V

Evolution as Conductor

Unlimited Memory · Speed of Abstraction · Directing Intelligence

Here is what becomes even more fascinating: unlimited memory potential space is just now waiting for a system more and more efficient, in speed of creation, of weaved concepts with more and more abstracted in space and time.

This is actually "Evolution" filling in role of "conductor" directing brain capacity for better and even better intelligence.

VI

Artificial Intelligence Parallel

Exponential Growth · Processing Power · Memory Loops

After all, this is what we see now in exploding, exponential growth of artificial intelligence!

What is required for its rapid emergence?

Answer would present itself in powerful processing and unending memory loops and storage.

(Of course, AI requires a higher energy cost consumption against our organic brains.)

Grid cell attractor network — hexagonal node connections
Grid cell attractor network — hexagonal node connections

Toroidal Geometry — the deeper mathematical foundations...

▶ TOROIDAL GEOMETRY — UNDER CONSTRUCTION

Memory weaved in time — spatial tensors on the torus...

▶ TOROIDS AND GRIDS AS MEMORY IN TIME WITH SPATIAL TENSORS — UNDER CONSTRUCTION