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Equation 1 · Part 5 · Typed Tools: Protocols as an Agent's Action Alphabet

multiplication

t: At×Σ  ⇀  Rt×Σt:\ \mathcal{A}_t \times \Sigma \;\rightharpoonup\; \mathcal{R}_t \times \Sigma
multiplication

What this part means

Multiply the quantities on either side.

Its job in the formula

Multiply the quantities on either side.

The passage around this formula

Start with the smallest honest model. A tool is not a function in the mathematical sense, because it touches the world. Write it as a partial map from arguments and world-state to results and world-state: t: At×Σ  ⇀  Rt×Σt:\ \mathcal{A}_t \times \Sigma \;\rightharpoonup\; \mathcal{R}_t \times \Sigma. Four things are named there, and each corresponds to a design decision that is usually made by accident.

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Learn the underlying idea

Multiplication scales one quantity by another. A dot, a cross, or adjacent symbols can indicate a product.

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Sources cited in the article section

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