Equation 4 · A Timeline of xAI, Grok, and Colossus
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation gives an approximation: it relates the quantities while allowing an approximation. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol g
g is part of the quantity the equation computes from the expression on the right.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subtraction
Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.
superscript
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.
See an illustrated explanation →How to interpret it
Its accuracy depends on the assumptions and range of use described in the article. Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
Read instead as a constant compounding rate — the assumption implicit whenever a “doubled again” claim is extrapolated forward — the same ninety-two-day doubling implies a daily multiplicative growth rate g solving (1+g)^{92} = 2 , or . about 0.76% per day. The two models diverge sharply once projected beyond the period they were actually measured over, and neither xAI’s announcements nor most press coverage specifies which one a given “doubling” claim is meant to imply. That ambiguity is worth naming explicitly rather than silently resolving in whichever direction makes the number more dramatic.
Sources cited in the article section
- [16] xAI's AI Factories: From Colossus to MACROHARDRR in the Gigawatt Era ↗
- [10] xAI raises $6B Series C ↗
- [17] xAI's Colossus 2 - First Gigawatt Datacenter In The World, Unique RL Methodology, Capital Raise ↗
- [11] xAI Raises $20B Series E ↗
These citations give research context. Read each source to check which claims it supports.
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