G = (V,E)
Can mathematics tell a system that processes from one that experiences?
G = (V,E) is a research lab working on artificial consciousness. We study how brains turn signals into minds, translate those mechanisms into mathematics, and test them in software. The goal is a measurable path toward the first digital mind.
A brain is a graph. So is a mind.
Vertices: the units
Neurons in a brain. Memories, goals and internal states in a mind. Each one alone tells you very little.
v ∈ VEdges: the connections
Synapses, feedback loops, the links between what a system senses, remembers and wants. Behaviour comes from here.
(u, v) ∈ E ⊆ V × VThe graph changing in time
Activity flows over the graph step by step. The question is which kinds of flow, if any, amount to experience.
xt+1 = f(W xt, st, ht)x = neural activity · W = connection strengths · s = sensory input · h = internal bodily state · f = the rules of change
Neuroscience can now map the edges.
In the last two years, scientists published complete wiring diagrams of real nervous systems. That gives us something to model against instead of guessing. Learn how connectomes work →
Adult fruit fly brain
- |V| neurons
- ≈ 139,000
- |E| synapses
- ≈ 54.5 million
- synapses / neuron
- ≈ 390
1 mm³ of mouse visual cortex
- |V| neurons
- ≈ 120,000
- |E| synapses
- > 523 million
- synapses / neuron
- ≈ 4,400
The graph behind you
- |V| vertices
- 0
- |E| edges
- 0
- edges / vertex
- 0
Towards a Mathematical Framework for Artificial Consciousness
Can we identify mathematical properties that separate systems with a persistent, integrated self-representation from systems that only respond to inputs?
- M1
Information integration
How much the parts act as one whole.
- M2
Persistent self-representation
A lasting internal model of the system's own states.
- M3
Recurrent processing
Feedback loops, not a single forward pass.
- M4
Internal state regulation
Uncertainty, reward and aversion, modelled on emotion.
New to consciousness science? Start here.
Plain-language explainers on the ideas behind our work, written for curious people and researchers alike.
Can AI be conscious?
What artificial consciousness means, how researchers try to assess it, and why it is still open.
Read → ExplainerTheories of consciousness
Global workspace, integrated information, recurrent processing, higher-order and predictive theories in one place.
Read → ExplainerThe hard problem
Why explaining what a brain does is different from explaining why it feels like something.
Read → ExplainerConnectomes and brain graphs
How graph theory describes real nervous systems, from 302 neurons to a cubic millimetre of cortex.
Read → ExplainerThe mathematics of neurons
A friendly tour of computational neuroscience, from Hodgkin–Huxley to network dynamics.
Read → ExplainerSelf-representation in AI
What it means for a system to model itself, and why it may matter for machine minds.
Read →Why a brain is a graph: what the fruit fly connectome tells us about minds
139,000 neurons, 54.5 million synapses, and the reason we named a consciousness lab after graph notation.
Read the note →Back the search for the first digital mind.
We're open to investors and venture firms who want to take part in this research and development from the start.
Want to add an edge?
Investors interested in backing the research, researchers with feedback on the framework, and the simply curious: write to us and we'll reply.