Equation 6 · Part 3 · AI Memory Systems and the Bandwidth Wall in 2035: Scenarios, Signals, and Falsifiable Predictions

Symbol t_0

\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}.

t_0

What this part means

$t_0$ occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Its job in the formula

$t_0$ occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Full expressionSymbol t_0Article meaning

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…

Read this part in the article →

Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

See this notation across published equations →

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.