An old philosophical dilemma: how can individuality exist if everything in the universe is connected? Or, the other way around: how can connectedness exist if every object is unique? It is usually played out as a paradox. Technically it is just two characteristics of the same system.
Here is how.
Integrated Information Theory: two numbers
Giulio Tononi proposed the measure Φ (phi) — integrated information. Φ measures how much a system behaves as a whole. The higher Φ, the more unified the system.
Beside Φ lives a second number — the diversity of states the system can occupy. Call it D. D measures how many distinguishable configurations the system can sustain.
Φ and D are different quantities. You need both.
High Φ, low D — a monolith. A crystal. Unified but uniform. One state, repeated everywhere.
High D, low Φ — a pile of sand. Many parts, each in its own state, with no binding. Diverse and formless.
Consciousness lives in the regime where both are high. Many states — and all of them bound into one experience.
What this does for "unity and multiplicity"
Two characteristics of one system complement each other. Unity is Φ. Multiplicity is D.
A human is a system with fairly high Φ (you experience the world as a whole rather than as disconnected sensations) and very high D (thousands of distinguishable thoughts, feelings, perceptions per day).
A beehive has higher Φ than a single bee, but lower than a human brain (on current estimates). The hive's D is enormous: thousands of bees, each in their own state.
Planet Earth as an active biosphere — possibly — has even higher Φ and D. No firm numbers exist: measuring Φ at that scale requires instruments we do not yet have.
Where this is being tested
Φ can be approximately measured in small systems. Tononi et al. (2014, Annual Review of Neuroscience) is a review of the attempts. Modern approximations (PCI — Perturbational Complexity Index) are used clinically to assess levels of consciousness in coma patients (Casali et al., 2013, Science Translational Medicine). PCI distinguishes healthy wakefulness, sleep, anaesthesia, and persistent vegetative state.
Φ is being estimated in practice — approximately. Exact computation is impossible; approximation works.
The philosophical dilemma "unity vs multiplicity" in this frame becomes an engineering question: for each system — what Φ, what D. Each system sits in its own region of the (Φ, D) plane. The argument stops.
What stays open
Why integratedness comes with an inside experience — David Chalmers's hard problem of consciousness. IIT registers the correlation between Φ and consciousness. The mechanism — why high integratedness feels — is outside the theory.
Chalmers does not claim the answer doesn't exist. He claims no amount of Φ data replaces the answer to "why does Φ correlate with feels-like-something". An honest edge.
Practical takeaway
When someone says "everything is one, everything is connected" — ask for precision. In what sense? With what Φ? High Φ — an integrated system where each part carries information about the whole. Low Φ with high D — a collection whose links are more imagined than real.
Graph theory applied to connectivity. No mysticism.
Unity and multiplicity are two coordinates, not a paradox. The question is where we sit on that plane.