[ExI] Megastructure engineering was Re: Tabby's star
Stuart LaForge
avant at sollegro.com
Wed Dec 14 02:17:37 UTC 2016
Spike wrote:
<Step one in any engineering exercise is the bound the problem. Having
all the rocky mass together in one lump is one extreme which trades away
everything for proximity: latency is minimized. With that solution, it
maximizes heat control problem, since every bit that is flipped way down
below the surface needs to have the resulting heat hauled all the way up
to the surface and radiated away.>
Yes, Spike, I totally agree. I have been doing calculations to bound the
latency issue to help with your project here. Figured out some really cool
stuff along the way.
Ok so it turns out that there is a lower bound on latency. It is called
the Bremermann's Limit. Let's call it B for now. B=c^2/h ~ 1.36E50
bits/kg*sec. It is the maximum possible update rate for a computer memory
or in other words the fastest that a collection of bits can change.
So B could be considered to be the partial derivative of information (I)
with respect to mass (m) and time (t) i.e. B:=dI/dm*dt
Integrating by dm and dt gives us:
I=B*m*t
Now recall from our discussion earlier that the Bekenstein Bound is
maximum amount of information (I) that you can stuff into a given amount
of radial space (r) .
I=K*m*r with K=4*pi^2*c/(h*ln2)
Notice we have two expressions for I right now, one dependent on time and
the other dependent on space. Let's call one Is and the other It.
Setting one I equal to the other I gives us:
Is=It or K*m*r=B*m*t. Canceling the mass gives us an expression for the oh
let's call it the specific information (I') or bits per unit mass:
I':=K*r=B*t.
Notice that we can rearrange this equation to give us a radial velocity(v)
and it's a constant!
v=r/t=B/K
Filling in B and K gives us:
v=c*ln2/(4*pi^2) or .017558*c which is approximately 5.26364E6 meters per
second. Notice this is susbtantially slower than light speed.
This has pretty big consequences for network theory. It means that in a
100% optimized network of 100% optimized computers, information changes
will propagate faster between nodes than within them.
Stuart LaForge
There is a maximum radial velocity for the information update within a
computer and it's *slower* than light!
So let's call the all-the mass-in-one-lump scenario monolithic and the
opoosite extreme "dispersive".
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