Law

Pairwise coordination against a shared hub

Coordination cost scales with the number of parties who must agree, not with data volume. A shared vocabulary converts O(N²) pairwise reconciliation into O(N) agreements.

pairwise: \frac{N ( N - 1 )}{2} (or N \times M), through a shared vocabulary: N (or N + M)

$N, M$: Parties; teams, systems or record sources that must agree

Recurring principle: Coordination scales with parties

How it behaves

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

pairwiseshared vocabulary

Data table

Agreements to maintain, by parties
Parties N	series	Agreements
2	pairwise	1
2.1	pairwise	1.16
2.21	pairwise	1.33
2.32	pairwise	1.52
2.43	pairwise	1.74
2.55	pairwise	1.98
2.68	pairwise	2.26
2.82	pairwise	2.56
2.96	pairwise	2.89
3.11	pairwise	3.27
3.26	pairwise	3.69
3.42	pairwise	4.15
3.6	pairwise	4.67
3.78	pairwise	5.24
3.97	pairwise	5.88
4.16	pairwise	6.59
4.37	pairwise	7.38
4.59	pairwise	8.25
4.82	pairwise	9.22
5.06	pairwise	10.3
5.32	pairwise	11.5
5.58	pairwise	12.8
5.86	pairwise	14.3
6.16	pairwise	15.9
6.47	pairwise	17.7
6.79	pairwise	19.7
7.13	pairwise	21.9
7.49	pairwise	24.3
7.86	pairwise	27
8.26	pairwise	30
8.67	pairwise	33.3
9.11	pairwise	36.9
9.56	pairwise	40.9
10	pairwise	45.4
10.5	pairwise	50.3
11.1	pairwise	55.8
11.6	pairwise	61.8
12.2	pairwise	68.5
12.8	pairwise	75.8
13.5	pairwise	83.9
14.1	pairwise	92.9
14.9	pairwise	103
15.6	pairwise	114
16.4	pairwise	126
17.2	pairwise	139
18.1	pairwise	154
19	pairwise	170
19.9	pairwise	188
20.9	pairwise	208
22	pairwise	230
23.1	pairwise	254
24.2	pairwise	281
25.4	pairwise	311
26.7	pairwise	343
28	pairwise	379
29.4	pairwise	419
30.9	pairwise	463
32.5	pairwise	511
34.1	pairwise	564
35.8	pairwise	623
37.6	pairwise	688
39.5	pairwise	760
41.5	pairwise	839
43.5	pairwise	926
45.7	pairwise	1.02K
48	pairwise	1.13K
50.4	pairwise	1.25K
53	pairwise	1.38K
55.6	pairwise	1.52K
58.4	pairwise	1.68K
61.3	pairwise	1.85K
64.4	pairwise	2.04K
67.6	pairwise	2.25K
71	pairwise	2.49K
74.6	pairwise	2.74K
78.3	pairwise	3.03K
82.2	pairwise	3.34K
86.4	pairwise	3.69K
90.7	pairwise	4.07K
95.2	pairwise	4.49K
100	pairwise	4.95K
2	shared vocabulary	2
2.1	shared vocabulary	2.1
2.21	shared vocabulary	2.21
2.32	shared vocabulary	2.32
2.43	shared vocabulary	2.43
2.55	shared vocabulary	2.55
2.68	shared vocabulary	2.68
2.82	shared vocabulary	2.82
2.96	shared vocabulary	2.96
3.11	shared vocabulary	3.11
3.26	shared vocabulary	3.26
3.42	shared vocabulary	3.42
3.6	shared vocabulary	3.6
3.78	shared vocabulary	3.78
3.97	shared vocabulary	3.97
4.16	shared vocabulary	4.16
4.37	shared vocabulary	4.37
4.59	shared vocabulary	4.59
4.82	shared vocabulary	4.82
5.06	shared vocabulary	5.06
5.32	shared vocabulary	5.32
5.58	shared vocabulary	5.58
5.86	shared vocabulary	5.86
6.16	shared vocabulary	6.16
6.47	shared vocabulary	6.47
6.79	shared vocabulary	6.79
7.13	shared vocabulary	7.13
7.49	shared vocabulary	7.49
7.86	shared vocabulary	7.86
8.26	shared vocabulary	8.26
8.67	shared vocabulary	8.67
9.11	shared vocabulary	9.11
9.56	shared vocabulary	9.56
10	shared vocabulary	10
10.5	shared vocabulary	10.5
11.1	shared vocabulary	11.1
11.6	shared vocabulary	11.6
12.2	shared vocabulary	12.2
12.8	shared vocabulary	12.8
13.5	shared vocabulary	13.5
14.1	shared vocabulary	14.1
14.9	shared vocabulary	14.9
15.6	shared vocabulary	15.6
16.4	shared vocabulary	16.4
17.2	shared vocabulary	17.2
18.1	shared vocabulary	18.1
19	shared vocabulary	19
19.9	shared vocabulary	19.9
20.9	shared vocabulary	20.9
22	shared vocabulary	22
23.1	shared vocabulary	23.1
24.2	shared vocabulary	24.2
25.4	shared vocabulary	25.4
26.7	shared vocabulary	26.7
28	shared vocabulary	28
29.4	shared vocabulary	29.4
30.9	shared vocabulary	30.9
32.5	shared vocabulary	32.5
34.1	shared vocabulary	34.1
35.8	shared vocabulary	35.8
37.6	shared vocabulary	37.6
39.5	shared vocabulary	39.5
41.5	shared vocabulary	41.5
43.5	shared vocabulary	43.5
45.7	shared vocabulary	45.7
48	shared vocabulary	48
50.4	shared vocabulary	50.4
53	shared vocabulary	53
55.6	shared vocabulary	55.6
58.4	shared vocabulary	58.4
61.3	shared vocabulary	61.3
64.4	shared vocabulary	64.4
67.6	shared vocabulary	67.6
71	shared vocabulary	71
74.6	shared vocabulary	74.6
78.3	shared vocabulary	78.3
82.2	shared vocabulary	82.2
86.4	shared vocabulary	86.4
90.7	shared vocabulary	90.7
95.2	shared vocabulary	95.2
100	shared vocabulary	100

Worked examples, recomputed

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

Where it appears

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

Data Modeling
What does one row mean, who is allowed to change that answer, and what breaks downstream when they do?
$O (N^{2}) \to O (N)$
Read it in place →
Data Modeling
What does one row mean, who is allowed to change that answer, and what breaks downstream when they do?
$N (N - 1) /2 vs N$
Read it in place →
Data Modeling
What does one row mean, who is allowed to change that answer, and what breaks downstream when they do?
$n (n - 1) /2 pairs$
Read it in place →
Schema Management & Evolution
What happens when the shape of your data changes on its own schedule, and nobody can change the readers, the writers and the old data at the same moment?
$N \times M \to N + M$
N (producers) = $N$ · M (consumers) = $M$
Read it in place →
Data Quality & Validation
How do you check that data is right, when "right" is a claim about the world and not about the bytes?
$n (n - 1) /2 pairs; blocking: blocks \times (2 b)$
Read it in place →
Data Quality & Validation
How do you check that data is right, when "right" is a claim about the world and not about the bytes?
$k (k - 1) /2$
Read it in place →
Metadata, Catalog & Lineage
What can a system prove about its data without reading the data, and how does it know that proof is still true?
$n \times m \to n + m$
Read it in place →
Interfaces & Formats
What can two parties agree on when they cannot talk to each other?
$N \times M \to N + M$
Read it in place →