← All parts of this equation

Equation 6 · Part 2 · AI Memory Systems and the Bandwidth Wall in 2035: Scenarios, Signals, and Falsifiable Predictions

Symbol t_1

τ=t1−t0log⁡2 ⁣(B1/B0)=2025−2022log⁡2(2.0/0.82)≈2.3 years.\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}.
t1t_1

What this part means

t1t_1 occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Its job in the formula

t1t_1 occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

where B0B_0 is the bandwidth at reference year t0t_0 and τ\tau is the doubling time implied by the data. Solving for τ\tau from the two JEDEC anchor points gives τ=t1−t0log⁡2 ⁣(B1/B0)=2025−2022log⁡2(2.0/0.82)≈2.3 years\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 should not be believed as stated, and the reason it should not be believed is itself the analytically interesting point. A two-point fit is not a trend; it is a line drawn through the only two data JEDEC has actually ratified. And it runs well ahead of the general DRAM-and-interconnect bandwidth scaling documented across two decades of hardware by…

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

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