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Matheology § 192
Posted:
Jan 18, 2013 8:06 AM


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 restmass 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 HawkingBekenstein 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/astroph/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



