[ExI] Fermi Paradox and Transcension

[Anders Sandberg]

On 14/09/2012 06:14, spike wrote:
>> ...What kind of delay do you expect to exist at each node?
> Mike, this is where I need help from the electronics hipsters and
> datameisters among us.

Just looking at current routers suggests that delays for internet 
packets are on the order of 0.1 ms (see figure 3 of 
http://researchwebshelf.com/uploads/137_P15.pdf ). In current 
internetworking there are bigger delays from the problem of getting 
access to the link layer when there are many devices chattering away, 
not to mention to longer delays (100 ms when sending stuff over long 
distances). Incidentally, due to the refractive index optical fibres are 
not faster than electrical signals, at least over short distances. In a 
Dyson-brain you can send signals at lightspeed through free space - not 
only faster, but they pass right through each other.

Suppose you want to signal to a node x radians away. The straight 
distance is 2R sin(x/2), and will have a delay of 2R sin(x/2)/c and 
energy requirement proportional to R^2 sin(x/2)^2. If you split this 
into N short jumps, each with an internal delay d, then the total delay 
will be Nd + 2RN sin(x/2N)/c and the total energy requirement 
proportional to R^2 N sin(x/2N)^2. (probably some linear term here too 
from the routers)

You can either try to minimize power by using many hops, ending up with 
a longer delay, or minimize delays by going straight across. Total power 
needs decline as 1/N. If x is large (long distance calls) the Nd term is 
completely swamped by the 2RN sin(x/2N)/c term: delay increases by a few 
percent in the x=1 case when you go from straight to 10 hops, but then 
remains close to Rx/c. If x is small (like a distance of 10 meters) then 
the router delays causes the delay to grow linearly with N: there is no 
real advantage in making many short hops, and the energy needs are 
really small too. For intermediary distances like x=0.1 there is a 
transition; the power vs. delay curve has some funky turns that no doubt 
imply opportunity for smart economizing.

In a Dyson shell you are unlikely to want for power in absolute terms. I 
guess the real issue is signal-to-noise: if you are sending things 
through the interior there is a very noisy fusion ball in the centre, 
and there are half a sky of signalling going on. Also, local comms have 
a harder time achieving line-of-sight: it is easy to aim a few degrees 
away from your horizon and hit a remote thoughtplate, but the one a 
kilometre away is obscured by your neighbours. So you might be forced to 
do many small hops just because of that.

I'm not too worried that a Dyson environment will be slower than 
realtime for uploads, at least not for energy and delay reasons 
(remember, there is a *lot* of energy within the 300 km radius 
lightspeed delays force on a human-type mind). Which still doesn't stop 
Spike's scenario from being great fun. The real reason of the slowdown 
is of course competition from the other screensavers.

-- 
Anders Sandberg,
Future of Humanity Institute
Oxford Martin School
Faculty of Philosophy
Oxford University