The Data EngineeringBeta

Model

Loop gain

Stability is a ratio, capacity is a level, and only the ratio decides whether you come back.

total work = 1 + R + R^{2} + \dots = \frac{1}{1 - R} (R < 1), unbounded for R \geq 1

$R$: Branching factor; units of further work each unit of degraded work creates

Recurring principle: Local optimizations compose badly

How it behaves

One input on the horizontal axis, the others held fixed.

Data table

Total work a disturbance causes, by loop gain
Gain R	Total work ÷ the disturbance
0	1×
0.012	1.01×
0.025	1.03×
0.037	1.04×
0.049	1.05×
0.061	1.07×
0.074	1.08×
0.086	1.09×
0.098	1.11×
0.11	1.12×
0.123	1.14×
0.135	1.16×
0.147	1.17×
0.159	1.19×
0.171	1.21×
0.184	1.23×
0.196	1.24×
0.208	1.26×
0.221	1.28×
0.233	1.3×
0.245	1.32×
0.257	1.35×
0.269	1.37×
0.282	1.39×
0.294	1.42×
0.306	1.44×
0.319	1.47×
0.331	1.49×
0.343	1.52×
0.355	1.55×
0.367	1.58×
0.38	1.61×
0.392	1.64×
0.404	1.68×
0.416	1.71×
0.429	1.75×
0.441	1.79×
0.453	1.83×
0.466	1.87×
0.478	1.91×
0.49	1.96×
0.502	2.01×
0.514	2.06×
0.527	2.11×
0.539	2.17×
0.551	2.23×
0.564	2.29×
0.576	2.36×
0.588	2.43×
0.6	2.5×
0.613	2.58×
0.625	2.66×
0.637	2.75×
0.649	2.85×
0.661	2.95×
0.674	3.07×
0.686	3.18×
0.698	3.31×
0.71	3.45×
0.723	3.61×
0.735	3.77×
0.747	3.96×
0.759	4.16×
0.772	4.38×
0.784	4.63×
0.796	4.91×
0.808	5.22×
0.821	5.58×
0.833	5.99×
0.845	6.46×
0.857	7.02×
0.87	7.68×
0.882	8.47×
0.894	9.46×
0.906	10.7×
0.919	12.3×
0.931	14.5×
0.943	17.6×
0.956	22.5×
0.968	31×
0.98	50×

Worked examples, recomputed

Every number the mechanisms quote for this relationship is recomputed from it, so none of them disagrees with it.

R = 0.5 → 2 units in total

Where it appears

Each mechanism states it in its own names. The general symbol each name stands for is shown with it.

Emergent Failure Dynamics
What happens when nothing is broken, every component is healthy, and the system's own response to stress makes the stress worse?
$1 + R + R^{2} + \dots = 1/ (1 - R)$
Read it in place →

Linear probing: probes by load factor

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