Equation 3 · Part 4 · Multimodal AI in 2035: Scenarios and Falsifiers

Symbol u^*

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

u^{*}

What this part means

$u^*$ is one factor in the product that computes the quantity on the left.

Its job in the formula

$u^*$ is one factor in the product that computes the quantity on the left.

Full expressionSymbol u^*Article meaning

The passage around this formula

…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

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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See this notation across published equations →

Sources cited in the article section

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