## More of the matrix stuff

The really interesting thing about network matrices is they can represent any formal system. More to the point, anything mathematical in nature (systems of equations, computer programs, flowcharts, org charts) can be represented by a list of objects and a binary matrix.

Here’s an example organization chart, where 1 indicates a subordinate and 0 indicates the person in that row is not a subordinate:

[USAREUR HHBN, HSC, OPS Co., I&S Co., CMD GRP, IG, OJA, PAO, OCHAP, G3, G6, G1, G2, G4, G8, ODCSENG]

[0, 1, 1, 1, 0, 0, 0, 0, 0, 0…] (Three direct subordinates, HSC, OPS Co, and I&S Co)
[0, 0, 0, 0, 1, 1, 1, 1, 1, 0…] (Six subordinates)
[…]

Imagine taking all sixteen rows and concatenating them into a single binary number 256 digits long. (In practical reality we could shorten this a great deal- for instance, all of the relationships are unidirectional which obviates the bottom-left half of the square.) Given the preliminary list of objects, this integer would comprehensively describe their formal arrangement.

Here’s the OODA loop:

[Orient, Observe, Decide, Act]

[0, 1, 0, 0]
[0, 0, 1, 0]
[0, 0, 0, 1]
[1, 0, 0, 0]

Here’s a computer program:

[a <- 1, b = 1?, a <- a * b, b <- b – 1, end]

[0, 1, 0, 0, 0]
[0, 0, 1, 0, 1]
[0, 0, 0, 1, 0]
[0, 1, 0, 0, 0]
[0, 0, 0, 0, 0]

Again, remember that this is just a list of black box functions connected by arrows. The arrows themselves are fully described by a single binary number.

Here's a bit of Nock:

[2 [6 [[28 29] [30 [62 63]]]]] = [2 6 [28 29] 30 62 63]

The right side can be represented thus:

[2, 6, 28, 29, 30, 62, 63]

[0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0]
[0, 0, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0]

What if the relationships weren’t black boxes, but were actually operations and instructions? Maybe truth tables? Then we’d have us a real algorithm, I think. I’m still trying to figure out how that would be done.