Instrument

The nomogram

Before calculators, engineers read answers off paper. Three scales, a straightedge laid across two of them, and the third scale tells you where you land. Each of the six layers has one relation that decides whether a system is affordable, and all six happen to be the kind a chart like this can hold.

Drag either outer handle. The red line pivots and the diamond on the middle scale is your answer. Arrow keys work too, and hold shift to move faster.

HNSW resident memory

M \;\approx\; N\,(4d + 8m), \quad m = 16

N: vectors
M: resident memory
d: dimensions

10M vectors at 1536 dimensions need 63 GB of RAM, resident, before quantization.

That figure — not query latency — is what pushes teams to quantization or to object-storage-native engines.

Every scale is logarithmic, which is what turns each relation into a sum two scales can carry. The full index has the entries these numbers come from.