[ExI] Chips The Size Of[interplanetary] Dust [and matrioshkabrains]

[Russell Wallace]

On 9/3/07, spike <spike66 at comcast.net> wrote:
> Russell, this turns into an interesting question of autonomous manufacturing
> optimization and launching of nodes, as well as optimization of the use of
> energy from sunlight.

*nods* Well, for initial bootstrap there are other considerations; on
the one hand, you don't want the up front cost to be too big, on the
other hand there'll be mining of materials from asteroids, gas giants
etc, and the machines needed to do this efficiently will have a
certain preferred size range. In this context I'm only considering the
most efficient configuration of the final Dyson sphere.

> Imagine you have a signal you wish to transmit distance x.  You can do it
> with one transmitter and one receiver, but you could put another receiver at
> x/2, amplify the signal and retransmit another x/2 to distance x.  This way
> you actually have two transmitters, but each one requires only one fourth as
> much power as in the first case, so together they only require half as much
> power.  Now imagine three receivers and transmitters, each transmitting a
> distance x/3.  Each requires one ninth as much power, so together they
> require a third as much power as in the first case.  And so on.  Cool, huh?
> Perhaps you worked the same problem.

Ah, interesting. I don't recall having come across that one before,
and your solution makes sense when transmitter count is the only
variable being considered; but there are factors you're not taking
into account:

1. Transmitter size matters, and with fewer larger nodes you can
afford to make the transmitters bigger. A 2 meter dish at 2 megameter
range gives the same beam footprint as a 1 m dish at 1 Mm (or you can
take part of the benefit in the ability to use longer wavelength
photons, which have less energy).

2. Similarly, receiver size also matters.

3. Most importantly, with big nodes you can eliminate most of the
transmitters completely, replacing them with wires that don't spill
photons into space. Alternatively you can think of this as the
ultimate limiting case of your solution: if more transmitters in the
chain are more efficient, use a wire = a chain of transmitters that
are all in contact with each other.

> As for station keeping, as the node size scales downward, gravity becomes
> less the driver and electrostatic forces ever more important.

Okay, but electrostatic isn't the only option, nor necessarily the best one.

There's photon pressure as Eugen observes - this scales down with
thickness, but doesn't care about width.

There are also magnetic forces, which are arguably easier to control
than electrostatic. These scale better to large sizes than
electrostatic does.

> My intuition tells me that building an M-brain is optimized by making the
> individual nodes as small as our technology permits.

*nods* Mine tells me it's optimized by making the nodes as large as
reasonably practical, the above being some of the reasons.