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Equation 6 · Part 12 · AI Memory Systems and the Bandwidth Wall in 2035: Scenarios, Signals, and Falsifiable Predictions

Denominator: log_2(B_1 / B_0)

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}.
log⁡2 ⁣(B1/B0)\log_2\!\left(B_1 / B_0\right)

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

log2(B1/B0)g_2(B_1 / B_0) occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the surrounding passage

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