Date: Jan 18, 2013 8:06 AM Author: mueckenh@rz.fh-augsburg.de Subject: Matheology § 192

Matheology § 192

We first consider the total amount of energy that one can harvest

centrally. [...] one finds

E_max = 3.5*10^67 J, comparable to the total rest-mass energy of

baryonic matter within today?s horizon. This total accessible energy

puts a limit on the maximum amount of information that can be

registered and processed at the origin in the entire future history of

the Universe. [...] Dividing the total energy by this value yields a

limit on the number of bits that can be processed at the origin for

the future of the Universe: Information Processed [...] = 1.35*10^120.

[..] It is remarkable that the effective future computational capacity

for any computer in our Universe is finite, although, given the

existence of a global event horizon, it is not surprising. Note that

if the equation of state parameter w for dark energy is less than -1,

implying that the rate of acceleration of the Universe increases with

time, then similar although much more stringent bounds on the future

computational capacity of the universe can be derived. In this latter

case, distributed computing is more efficient than local computing (by

a factor as large as 10^10 for

w = -1.2, for example), because the Hawking-Bekenstein temperature

increases with time, and thus one gains by performing computations

earlier in time. [...]

On a more concrete level, perhaps, our limit gives a physical

constraint on the length of time over which Moore?s Law can continue

to operate. In 1965 Gordon Moore speculated that the number of

transistors on a chip, and with that the computing power of computers,

would double every year. Subsequently this estimate was revised to

between 18 months and 2 years, and for the past 40 years this

prediction has held true, with computer processing speeds actually

exceeding the 18 month prediction. Our estimate for the total

information processing capability of any system in our Universe

implies an ultimate limit on the processing capability of any system

in the future, independent of its physical manifestation and implies

that Moore?s Law cannot continue unabated for more than 600 years for

any technological civilization. {{Not a breathtakingly large

number.}}

[Lawrence M. Krauss, Glenn D. Starkman: "Universal Limits on

Computation" (2004)]

http://aps.arxiv.org/PS_cache/astro-ph/pdf/0404/0404510v2.pdf

Therefore it is not only theoretically wrong that a process can always

be completed when every single step can, but it is already practically

impossible to perform a step the identification of which requires more

than 10^130 bits. At least genuine mathematicans would hesitate to

accept steps that in principle are impossible - that is reserved for

matheologians and lunatics.

Regards, WM