Equation 3 · Part 1 · Multimodal AI in 2035: Scenarios and Falsifiers

Symbol C

C(t) = \mathbb{1}\!\left[U(t) \ge u^{*}\right] \cdot \mathbb{1}\!\left[R(t) \ge r^{*}\right]

C

What this part means

C is part of the quantity the equation computes from the expression on the right.

Its job in the formula

C is part of the quantity the equation computes from the expression on the right.

Full expressionSymbol CArticle meaning

The passage around this formula

…system stitched together from several vendors’ best components does not consolidate the market around any one of them. Consolidation is therefore better modelled as a conjunction than an average: $C(t) = \mathbb{1}\!\left[U(t) \ge u^{*}\right] \cdot \mathbb{1}\!\left[R(t) \ge r^{*}\right]$ . C(t) stays at zero however high either term climbs alone. Axis A determines whether U(t) can plausibly clear $u^{*}$ within this article’s horizon; Axis B determines whether R(t) can. Neither can be inferred from the other, which is why they are kept as two axes rather than folded into one.

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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