In 1943, before any computer ran, McCulloch and Pitts wrote logic as a cell: N binary inputs, integer weights, one threshold. It fires when the weighted sum meets the bar — Σ wᵢ·xᵢ ≥ θ — and nothing else. Set the dials and it becomes AND, OR, or NOT; the truth table below is computed live, never looked up. Down the center, data flows: inputs go in, the neuron decides, the answer comes out. The blue team builds and defends it; the red team tries to break it — including the one function it famously cannot compute.
source W. S. McCulloch & W. Pitts, A Logical Calculus of the Ideas Immanent in Nervous Activity (Bull. Math. Biophysics 5, 1943) — archive.org/details/a-logical-calculus-of-ideas-immanent-in-nervous-activity. Rendered, not quoted.
There is no memory and no lookup. Each input xᵢ is 0 or 1; each weight wᵢ is an integer — positive is excitatory, negative is inhibitory. The neuron adds them and compares to one bar θ:
fire = 1 iff w₁·x₁ + w₂·x₂ ≥ θ
That inequality is a straight line splitting the input square into fires / silent — the neuron can only draw one such line (it is linearly separable). For the current dials:
Boole's algebra of 0 and 1 was a calculus on paper. McCulloch and Pitts gave it a body: the same AND / OR / NOT, now Σ wᵢxᵢ ≥ θ in a threshold cell. the-algebra is this sphere's premise.
This is the first artificial neuron — the seed of the whole AI world. Its own limit (no XOR from one cell) is the next sphere's premise: stack layers, and add a rule to learn the weights instead of setting them by hand. Each sphere is the next one's premise.
The blue team's live check: rebuild the three presets from the raw rule and confirm each equals its Boolean function, then sweep 175 weight/threshold settings and confirm XOR & XNOR are unreachable. If red tampers, this badge is where it shows.
Fed into the neuron: two binary inputs and the parameters that shape it.
| symbol | is | range here |
|---|---|---|
| x₁, x₂ | binary inputs | 0 or 1 |
| w₁, w₂ | integer weights | −2 … +2 |
| θ | threshold (the bar) | −3 … +3 |
A negative weight is an inhibitory synapse — the trick that lets one cell compute NOT. These four rows of (x₁,x₂) — 00, 01, 10, 11 — are the entire world fed into the panel below.
Presets set the dials; every truth-table cell is recomputed from Σ wᵢxᵢ ≥ θ on the spot, never looked up.
| x₁ | x₂ | w₁x₁+w₂x₂ | ≥ θ ? | fire |
|---|
What the cell produces, proven: the three presets realize AND, OR, NOT exactly; a sweep of the dials shows exactly 14 of the 16 two-input Boolean functions are reachable by one neuron — and XOR and XNOR are the two that are not. The current dials' function is above; the totals are the output.
The blue team's witness (left) confirms these numbers live; the red team (right) tries to make them wrong.
And the M–P cell cannot learn: the weights are set by hand, there is no rule that adjusts them from examples. It is all-or-none binary, while real neurons are graded, spiking, and noisy. This is the first neuron, not the last word — the panel lets you hit the XOR wall yourself.
"A single neuron can compute any Boolean function." Cut. Exactly 14 of 16 two-input functions — the sweep in the machine finds XOR and XNOR unreachable by any one cell.
"The McCulloch–Pitts neuron learns its weights." Cut. It has no learning rule; weights are fixed by design. Learning arrives later — Hebb (1949), Rosenblatt's perceptron (1958).
"Real neurons are binary threshold units." Kept, corrected. A deliberate idealization. Biological neurons are graded and stochastic; M–P abstracts them to logic on purpose — that was the point.
The red team's move: nudge the AND preset's threshold by one (θ: 2 → 1). AND now fires on a single input — it has quietly become OR. The blue team's witness (window 7) is watching.
Move the bar and the AND preset stops computing AND — its truth table gains a row it should not have. The witness rebuilds the preset, disagrees with Boolean AND, and turns red. Nothing is faked; the attack is real and it is caught.