Which Stage Does the 333x Work?

Which Stage Does the 333x Work?

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

foundations
math-foundations
calculation-audit
sensors
Ada 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.

See the relationship before changing it

The figure reads from left to right. The blue card is final monthly volume. The middle card applies this page's rule. The green card is raw-to-final reduction. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only final monthly volume, so the numeric fixture does not switch without explanation.

Final monthly volume changes raw-to-final reduction An input card leads through the rule reduction = 1,036.8 GB raw / final volume to the raw-to-final reduction result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. Selective edge filtering creates a larger reduction as it discards more uneventful data.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 3.11 GB/month.

  2. 2

    Name the relationship. reduction = 1,036.8 GB raw / final volume

  3. 3

    Substitute with units. 1,036.8 / 3.11 = 333.4 times

  4. 4

    Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.

Predict, then change final monthly volume

Try Predict the direction of reduction = 1,036.8 GB raw / final volume. Test another final monthly volume, then compare raw-to-final reduction.

3.11 GB/month
Chapter baseline
Raw-to-final reduction

Observe Selective edge filtering creates a larger reduction as it discards more uneventful data. Reset final monthly volume to 3.11 and compare raw-to-final reduction.

Explain Selective edge filtering creates a larger reduction as it discards more uneventful data.

Check yourself

What should you do before trusting a moved-control result?
Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.
What does this small model leave out?
Answer: Only final monthly volume moves here. Field effects named in the technical boundary stay fixed.
Try

Begin with 200 sensors at 1000 samples/s and 2 bytes/sample, then follow the 1000 Hz to 100 Hz decimation before the 3.11 GB/month output.

Observe

The raw stream is 400000 bytes/s and about 1036.8 GB/month; decimation supplies 10× while later filtering and compression supply another 33.3×.

Explain

Decimation reduces every waveform uniformly, whereas edge event filtering discards long periods of normal behaviour; that selective suppression creates most of the 333.4× reduction.

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.

Technical boundaries: This rate ledger assumes constant sampling, fixed event prevalence, and a stated final volume; it excludes burst traffic, headers, retransmissions, compression CPU energy, storage replication, and missed-anomaly cost.

Ready: work the ledger before checking it.