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Topic: Matheology § 192
Replies: 1   Last Post: Jan 18, 2013 2:50 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 192
Posted: Jan 18, 2013 2:50 PM

In article
WM <mueckenh@rz.fh-augsburg.de> wrote:

> 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 today¹s 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 Moore¹s 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 Moore¹s 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

WM, as usual, conflates mathematics with physics, but to true
mathematicians, mathematics is free to ignore physical limitations, and
often does so quite fruitfully.

The mathematics of the real number line and Euclidean geometry ignore
physical limitations, giving us, among other things, always another
point between any two given points, a density of points that physics
rejects, even though Euclidean geometry and calculus depend on it.

So it is WM's WMYTHEOLOGY and general lunacy which separates him from
real mathematics and exiles him to the kook's corner of fanaticism.
--

Date Subject Author
1/18/13 mueckenh@rz.fh-augsburg.de
1/18/13 Virgil