← All parts of this equation

Equation 1 · Part 5 · The Hardest Unsolved Problems in Evaluating xAI's Claims

superscript

uk=10k/2,k∈{1,2,3},u_k = 10^{k/2}, \qquad k \in \{1, 2, 3\},
superscript

What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

Epoch AI, a research organisation that tracks compute at the frontier, publishes exactly this kind of reconstruction for Colossus and states its own confidence in bands rather than single numbers: an estimate graded “Confident” carries roughly ±3x uncertainty, “Likely” roughly ±10x, and “Speculative” roughly ±31x [ 4 ] . Those three multipliers are not arbitrary; they sit at half-order-of-magnitude steps, uk=10k/2,k∈{1,2,3}u_k = 10^{k/2}, \qquad k \in \{1, 2, 3\}. giving u1u_1 ≈\approx 3.16 , u2u_2 = 10 , and u3u_3 ≈\approx 31.6 — which is a formal way of saying that even a well-resourced independent estimate of a frontier training run can be off by an order of magnitude or more, and everyone doing the estimating knows it going in.…

Read this part in the article →

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.

Open the illustrated exponents: repeated multiplication and powers guide →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.