Which Stage Does the 333x Work?

Ada re-derives this chapter’s own numbers step by step, at full precision

ADA · CALCULATION AUDIT

Which Stage Does the 333x Work?

A predictive maintenance system watches 200 industrial machines, each streaming vibration data at 1,000 samples/second as 16-bit ADC values — a raw pipeline the chapter prices at $259,200/month before any filtering. Hierarchical edge processing collapses that to 3.11 GB/month and $778/month, a combined 333× reduction the chapter credits to biology’s own filtering. This audit asks the question that single headline number hides: which stage — sensor-level decimation or edge-level summarisation — actually does the 333× worth of work?

Companion to the chapter Biomimetic Sensing — every number here comes from that chapter.

Ada: The chapter reports a combined 333x reduction for the 200-machine line and leaves it as one headline number. Let me confirm it, then split it, because the split is where the biological lesson actually lives.

Start from the raw rate and the monthly volume:

• Raw rate: 200 sensors x 1,000 samples/s x 2 bytes = 400,000 bytes/s
• Monthly: 400 KB/s x 86,400 s/day x 30 days = 1,036,800,000 KB = 1,036.8 GB (about 1,037 GB)
• Reduction to the final 3.11 GB/month: 1,036.8 / 3.11 = 333.4x

That matches. Now decompose it. Stage one is decimation, 1,000 Hz -> 100 Hz, an exact 10x. Everything the total does beyond that must come from the later stages:

• Decimation: 10x
• Edge filtering plus gateway compression: 333.4 / 10 = 33.3x

So the sensor-level step you would instinctively credit, sampling less often, is only a 10x slice. The unglamorous middle stage, discard normal behaviour and send summaries, carries a 33.3x factor, more than three times the decimation’s contribution. That is the biomimetic parallel made quantitative: in skin, the receptors are not where the 99% reduction happens, it is the peripheral-nerve and spinal-cord filtering that throws away “nothing changed.” Move the biggest filter to the edge, not the sensor clock, and the cost follows: $259,200 / 333.4 = $777.5, within a rounding step of the chapter’s $778 per month.

Every number above is taken from the chapter’s own material and re-derived step by step.