How many wormholes does it take to interconnect the structure of a given ISO and keep the whole thing from thinking at a snails pace? You'd be surprised. Here are some basic figures. (Note: this is a generic baseline-friendly illustration only; exact and even generic architectures vary quite widely according to type of archailect, toposophic level, sephirotic or other orientation, and so on).
Basic Info: Length of a human brain: 15cm
Cyber thought speed: 1 million times faster than human.
Based on the above a cyber-mind operating at electronic speeds could be 1 million times larger than a human brain and still think at the speed of a human. This gets us:
(NOTE: When give a mind node size, I am assuming a cubical structure. Sizes are the length of a side of the cube. This extends all the way up to Jupiter node sizes. I realize such an ISO is almost certainly going to be spherical, but the numbers were easier to work dealing with cubes.)
Cyber mind node sizes/speeds:
150km = human thought speed (3,375,000 km3) 1500km = 1/10 human thought speed (3,375,000,000 km3)
15000km = 1/100 human thought speed (3,375,000,000,000)
MOON BRAIN: (the size of Luna):
Diameter: 3476 km Volume: 42,000,000,000 km3 (approximate)
Using a modular structure with each module being a particular size we get:
150km = 12,400 modules. (approx, and allowing space for access paths, power sources, etc.). In order to maintain human thought speeds we would need to put a wormhole gate in each module with all modules linking to one or more central switchboards. However, the number of wormholes becomes unwieldy. So lets be clever:
Step 1: Double the size of each module:
300km on a side = 27 million km3 = 1556 modules (Better, but still a lot). Reduces thought speed to 1/2 human normal in each module.
Step 2: 'Cubing'
Arrange the cubical modules in groups of 26 built around a central wormhole bus. Imagine an array of modules looking something like a Rubik's cube (reference to an Old Earth mathematical toy). A layer of three rows of three modules on the top and bottom (9 modules each), with a middle layer of 8 modules arranged around a central cubical cavity that is equal in size to a module. Can put a lot of stuff in there probably, but the main thing is the wormhole gate at the center.
Each module in the Cube communicates with the central wormhole via optical transmitters or fiber optic lines coming from the modules face, edge, or vertex depending on where the module is in the array.
Instead of one wormhole for each module, we now have 26 modules using one wormhole, with a minimal drop in thought speed. Between the 1/2 human speed of the modules and the distance from the edges of the modules to the wormhole bus, thought speed for a Cube should be between 1/2 and 1/3 of human normal.
Taking our 1556 modules mentioned above and dividing by 26 gets us: 60 wormholes.
Each wormhole bus would link to a central switchpoint within the structure which would route signals from one module to another at high speed. Could also have clusters of Cubes linked to intermediate switch points which are in turn linked to a central point if didn't want to have everything running thru one potential bottleneck. Central switchpoints would probably be near the center of the structure and in close proximity to inter-brain (interplanetary/interstellar) comm. links as well.
So for an investment of 60 wormholes, you get a Moon-brain that operates only 2-3 times slower than a human.
JUPITER BRAIN: (The size of Jupiter):
Diameter: 143,000 km. Volume: 2,924,207,000,000,000 km3
To do this we need bigger modules. Otherwise the sheer number of modules overwhelms even the advantages gained by Cubing and the number of wormhole gates becomes astronomical. But if the modules become too big than thoughtspeed slows down to a huge degree. So need to strike a balance.
1500km module (10x slower than human) = 866,432/26 = 33,324 wormholes 4500km module (30x slower than human) = 32,090/26 = 1,234 wormholes 6000km module (40x slower than human) = 13,538/26 = 521 wormholes 7500km module (50x slower than human) = 6,932/26 = 267 wormholes
The last two lines in particular are fairly modest numbers of wormholes and would still permit the creation of a mind moving a better than glacial speeds. However, there is one other trick we can use if we want to make the investment in wormholes.
Using the 'Cube' design architecture and 5 'internal' wormholes inside a 7500km module, we can speed up its operations to only 10x slower than human. Applying this to the last line in the comparisons above and we end up with a total of 1335 wormholes. This is 1/25 the number of wormholes that would be required if we used 1500km modules operating at 1/10 human normal. For a moderate investment in additional wormholes we get a huge increase in system performance
A Dyson Swarm needs a very different set up from a mass beam supported shell and so on. Here is a basic design for a simple system:
Take 48 Jupiter nodes as described above and arrange them in a Klemperer Rosette around a star in the plane of the ecliptic at about 1 AU out. Now move inward a distance equal to 1/10 of an AU and repeat. Do this about 10 times and you will have a large of array of Jove brains extending from very close to the sun outward. Actually the inner bands would have to be less than 1/10 of an AU apart so they don't hit the sun. Or move everything out by 1/10 of an AU. But that's a minor matter.
When completed you will have some 480 Jupiter brains orbiting your star. Now, within each Jupiter brain set up a wormhole relay. Use 24 wormholes per 'level' to link each Jupiter brain to its counterpart on the opposite side of the sun (the have 2 mouths remember, so you only need half as many wormholes as brains). Use another 24 to link 'around the track' along each levels orbit. Finally use 48 wormholes to link to the J-brains on the next level closer to the star. The last level won't need this since they have no lower level to link to. Unless the system is linked to other stars, as in the larger archailects
When all is said and done you will have 912 wormholes linking your system together.
Now replicate this process with a set of polar orbiting Jupiter brains at 90 degrees from the first set. Do it two more times at 45Â° to the 'left' and 'right' as you look at the star. When completed you will have 1920 Jupiter brains orbiting the star and intercepting rather a lot of light. Additional structures can of course be put in close proximity to the star to catch it all or you can just keep building processing nodes until all the light is blocked. Multiply your 912 wormholes by 4 to connect the whole thing and you get 3648 wormholes. Plus whatever you need to link the 4 different planes of Jove nodes and interstellar links, if any. A whole lot of wormholes, but maybe not enough to really link things to an acceptable level. But then again, if you have a neutron star based weylforge (e.g. the Crab nebula pulsar puts out something like 100,000 times the sun's power output), a few thousand wormholes are a fairly minuscule investment.