Equation 6 · Part 1 · AI Memory Systems and the Bandwidth Wall in 2035: Scenarios, Signals, and Falsifiable Predictions

Symbol τ

\tau = \frac{t_1 - t_0}{\log_2\!\left(B_1 / B_0\right)} = \frac{2025 - 2022}{\log_2(2.0 / 0.82)} \approx 2.3 \ \text{years}.

\tau

What this part means

the doubling time implied by the data.

Its job in the formula

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

Full expressionSymbol τArticle meaning

Where the article explains it

where $B_0$ is the bandwidth at reference year $t_0$ and $\tau$ is the doubling time implied by the data.

The passage around this formula

where $B_0$ is the bandwidth at reference year $t_0$ and $\tau$ is the doubling time implied by the data. Solving for $\tau$ from the two JEDEC anchor points gives $\tau = \frac{t_1 - t_0}{\log_2\!\left(B_1 / B_0\right)} = \frac{2025 - 2022}{\log_2(2.0 / 0.82)} \approx 2.3 \ \text{years}$ . Extrapolated naively, ten more years at that doubling time — roughly 4.3 further doublings — would put per-stack bandwidth near 39 terabytes per second by 2035. That number…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

[13] AI and Memory Wall ↗

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