On 07 Dec 2014, at 10:32, Cedric Knight wrote:
On 06/12/14 17:56, [email protected] wrote:
World's oldest computer may be older than previously thought
<http://groups.google.com/group/everything-list/t/2ecc8efb138742df?utm_source=digest&utm_medium=email
>
Bruno Marchal wrote:
Well, to be sure, we don't have evidence that the antikythera
mechanism is authentically Turing universal, but it is sure that it
is close. Very impressive discovery.
...
It is QM which has made possible the invention of the transistor. The
machine of the ancient were closer to Babbage machine, but the
current one use transistor, which has made possible their speeding up
and the miniatuirization.
I wonder if you missed the word "analog" in the news story.
Now I remind, I saw a video on this sometime ago. Good point!
To avoid
possible confusion, the Antikythera Mechanism was not a digital or
programmable "computer", but basically a system of gears which took
the
continuous input of a date and produced the rising and setting times
of
celestial features. Although it was mechanical like the analytical
engine, it would perhaps be better compared to a slide rule (if you
remember how calculations were done in an analogue way before
calculators)
Yes, it is a physical rendering of the continuous homomorphism from R*
without zero to R+, known as logarithm.
I am enough old to have play with such slide rule at school!
It is clever than the Antikythera, as it transforms a complex
iteration (multiplication) into a simple one (addition), and without
the need of the computation of a table of logarithm. I ask myself when
such slide rule appeared. I am pretty sure that the disocvery of
logarithm (by Neper, also known as Napier) is the real start of the
industrial revolution.
than to any idea of a general-purpose digital computer
invoking Babbage, Turing or von Neumann.
You are right, making such machine not just less than universal, but
not even belonging to a class of machines admitting a universality
notion. I commented to much quickly.
To be sure, we can always accelerate any computer by an arbitrary
factors on almost all input sby just programming them differently.
Well, there is some horrendously inefficient code out there (see May's
Law), but I'm sure the people forecasting your weather would be
interested in how they can accelerate their computing devices by
programming them differently :) .
I was alluding to the Gödel's length of proof theorem, or the similar
(but not completely equivalent) speed-up theorem of Blum.
Unfortunately it is not practical, except perhaps for long term open
processes, like life is a theory of evolution. Could play some role in
the origin of physics too, as those unbounded speed-up appears also in
the universal dovetailing. Those speed-up result are not constructive,
or when they are, they are correct for all inputs ... with a finite
numbers of exceptions, which limit direct applicability. For the
weather, we still have to better listen to birds and frogs ...
But this is another type of (non practical) speed-up, and for all
practical purposes, we can say that the machine of the ancient, and
Babbage machine are much slower and "antic" than your PC.
The Antikythera Mechanism was perhaps "slower" if you include the
human
operation and read-off, but IMHO it shouldn't be directly compared
to a
PC because, however impressive and beautiful it may have been, it was
still a single-purpose analogue device.
You are right.
Bruno
CK
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