**From:** Christian Zielinski (*zielinski@transhumanismus.org*)

**Date:** Mon Jan 09 2006 - 08:36:36 MST

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Hello.

Only an idea of the limits of exponential grow of a post-singularity

civilisation:

Let's assume an exponential grow of the technological progress of a type

II-III civilisation.

With growing technology the energy consumption of such a civilisation

should grow too.

Let's assume it for the sake as a linear relation, so that ("~" stands

for proportionality):

Available technology ~ Energy consumption

If the available technology grows exponential, then the same is valid

for the energy consumption:

Energy consumption ~ e^(a t) (with a as scaling factor)

The maximal available energy for the civilisation is all the included

usable energy in the area where the civilisation

has settled. Let's assume it further as a sphere. If the energy is

nearly (in averaged) homogenous

in space, than follows:

Available energy ~ Settled space

With the developed technology it should be possible to expand near the

speed of light.

So the volume of the sphere in space, which the civilisation has already

settled an

is using the energy, grows with the expansion in all three directions of

space:

Settled space ~ (radius of settled sphere)^3

The radius grows at the constant speed of light (r = c t). If we

substitute we get:

Settled space ~ t^3

Because the available energy is proportional to the settled space, it

follows that:

Available energy ~ t^3

So we have an civilisation which energy consumption grows exponential

with time while the

available energy follows only a cubic law:

Energy consumption ~ e^(a t)

Available energy ~ t^3

As the first of this curves is growing faster, we can find a point in

time where the

energy consumption would be greater than the maximal energy which can be

used.

Therefore the technological progress has to slow down. Am I right?

Regards,

Christian Zielinski

-- http://www.transhumanismus.org/ http://www.singularitaet.org/

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