It's not the math
UD muses on fractals and math showing intelligent design.
Leads to a different set of musings. The math isn't the interesting part. The PURPOSE of a branched network is more interesting.
Living things have two distinct forms of branching and tributaries. One is single-directional, the other is non-directional.
As I noted earlier,
jellyfish and one-celled animals have non-directional nets.
A directed net can be directed inward or outward.
Both directions are balanced in more complex animals and plants.
Blood circulation branches inward toward the lungs and heart with 'exhausted' blood, then outward from the lungs with 'renewed' blood.
The nerve net runs both ways in separate afferent and efferent channels. The separate pressure-sensing nerves in the skin branch inward toward the brain; the brain processes their inputs with more inward gathering and integration, then reaches a decision and sends it out through the spine, branching to only the muscles needed for the response.
= = = = =
Nets in human communities or organizations repeat the same simple/complex distinction.
A small town or small business is a jellyfish. Not much division of labor, no fixed direction of information. Everyone knows everything and everyone does everything. There is a boss or mayor, and there are a few specialized ganglia like the bank or post office or grain elevator, needed to deal with the outside world.
A nation or big business is more like a mammal, with highly specialized organs and precisely defined afferent and efferent channels.
Small towns or car dealers gather up the economic and cultural needs and preferences of the individual citizens or customers and integrate. The mayor or dealer sends the single representation of the town or customers to the district legislature or district sales manager, who then integrates again and sends to the national management. The national management makes decisions (ideally only the decisions relevant to all the districts) and sends out a bulk package of projects or vehicles to the districts. Each district then retails the package appropriately. Cornville needs irrigation and pickups. Haughty Heights needs a college building and limos.
Branching at all levels in both directions, division of labor and preference at all levels in both directions.
Most important, negative feedback at all levels. When Cornville complains that the district sent an opera performance or an Opera Coupe, the district responds to the error signal and sends out the correct items in the next shipment.
Negative feedback + modularity = life.
= = = = =
Where does math come in? Math loses the purpose, and computers lose it even more.
Math can WRITE equations like the non-directional everything-everywhere-ness of a jellyfish. But math can't SOLVE those equations.
They must be solved by graphs or analog computers. See the Lukyanov water computer,
where a set of input variables stirs up a jellyfish network of intrinsic everywhere feedback, leading to a complex pattern of changing outputs.
Math prefers unidirectional functions. A solvable equation has several inputs and ONE output.
Digital software takes the deficiency even farther. You can't even WRITE
a balanced equation in software. You must only write unidirectional functions. Multiple input arguments, one return value.
Since 1990 we've been running in software mode, and 2020 took the "evolution" even farther.
There are no intermediate modules, no district governments or dealers. Software corporations and governments pull in the inputs from individual citizens or customers all at once, and send out a single bulk package for distribution everywhere according to privilege and security. Accounts with administrator privilege get all of the package, non-admin accounts get nothing.
Everything happens IN PERFECT UNISON ACROSS THE ENTIRE WORLD. All decisions are made in one place,
all murder happens IN UNISON.
The customers and citizens are still sending in their needs and preferences, and many of them still foolishly believe the preferences are connected to the central processor as negative feedback. They aren't. The citizens are screaming
WE ARE SUFFERING AND DYING!
And the central processor treats these pleas as pornography, orgasming endlessly and sending out even more unison bulk shipments. Trillions of free dollars to admin privileges, mayhem and chaos and mass murder to non-admin.
Positive feedback + unison = death.