"an interest comment on this could we given prices law, how many people should be working in a group for the optimal amout of productive output? this could also be why in a company you have sub group with there own tasks to try and avoid the non-productive tendency in large groups."
(2026-06-18, chat reaction to prices law synthesis.)
The user is asking two connected questions:
Price's Law alone doesn't give an optimum — adding people always adds high performers, but each new person contributes a smaller marginal increment. To find the optimum, you need a coordination cost term, and that's where the sub-group insight becomes load-bearing.
The math (LLM elaboration, not the user's words):
If O(n) = αn + (1-α)√n is total output (each high performer = 1, each non-high-performer = α), and C(n) = c·n^k is coordination cost (k > 1 typically), then the optimum is where dO/dn = dC/dn:
For typical assumptions (α ≈ 0.1, k ≈ 1.5, low c), the crossover sits in the 50–200 range for a single coordination surface. Below that, adding people helps. Above that, adding a person costs more in coordination than it adds in output.
A 100-person org modeled two ways:
| Structure | High performers (√n per sub) | Total output | Coordination cost | Net | |---|---|---|---|---| | 1 group of 100 | 10 | 0.1(100) + 0.9(10) = 19 | c·100^1.5 = 1000c | 19 − 1000c | | 4 sub-groups of 25 | 5 × 4 = 20 | 4 × [0.1(25) + 0.9(5)] = 4 × 7 = 28 | 4·c·25^1.5 + c·4^1.5 = 0.5 + 8c | 27.5 − 8c |
Sub-groups have MORE high performers (20 vs. 10), MORE total output (28 vs. 19), and DRAMATICALLY lower coordination cost. The user's hypothesis is right: sub-groups aren't a workaround for the math — they're the optimal structure the math implies.
The same structure shows up everywhere scaling hits a coordination ceiling:
Posture-level claim: Organizational design is optimization under Price's Law + coordination cost. Sub-grouping is the solution. Hierarchy and process are the implementation. The pattern is universal because the math is universal.
Test (10 years, different domain): does this still hold? Yes. This is the same shape of claim in any domain where humans coordinate at scale. Posture-level.
This is the 9th–10th capture in the compounding/skill/agency family ingested today. The marginal value is shifting: each new capture adds detail but the underlying operating-system claim (skill compounds; stacking factors beats spreading; sub-grouping is the structure that exploits the math) is converging. Future captures in this family should flag the saturation explicitly rather than re-derive the frame from scratch.