Δευτέρα, 12 Οκτωβρίου 2009

A correction

Bruno Scarpellini was kind enough to point out to me a minor misprint that he discovered. In particular, on page 178 of line 11 froom above, that is, in clause (i) of definition 9.3.4, one has to replace

H(z(\lambda)) dy/d\lambda with H(z(\lambda)) dz/d\lambda,

that is, one has to replace dy with dz.

Some Thoughts on Hypercomputation

Last year I wrote a "paper" on hypercomputation, but since it is not quite ready, I have posted it to the arXives. I believe the "paper" contains some interesting ideas. Anybody willing to have a look at it, can fetch an electronic copy from the following URL:

http://arxiv.org/abs/0910.1494

Δευτέρα, 30 Μαρτίου 2009

Impressions from SPUC09

SPUC09 was an event that was organized by Mark Hogarth and Mike Stannett and it was founded by EPSRC . It attracted researchers from Computer Science, Mathematics, Physics, Biology, Artificial Intelligence, Economics, and Phylosophy. Delagates presented interesting ideas and the discussions that followed each presentation were very vivid. Personally, I had the chance to meet some new friends and to discuss with them some interesting ideas. Also, I had the chance to personally meet people with whom I had exchanged many e-mails in the past.

Black hole evaporation

Recently, István Németi pointed out to me that there is an omission
in my book regarding the feasability of his relativistic hypercomputer.
In particular, the following passage

In 1974, Stephen William Hawking [80] proposed that black holes
emit thermal radiation, now known as Hawking radiation, due
to quantum effects. Thus, any black hole will vanish sometime
in the future. If Hawking radiation is indeed a real phenomenon,
then it is possible that a relativistic computer G will not be
able to finish a particular supertask it was assigned to finish.
The reason is that the black hole that the computer orbits
around might evaporate years before the computer completes its
task. Moreover, Hawking radiation should play a role in cases
in which the black hole has very small mass. For instance, a
black hole of one solar mass will evaporate in 1067
years, while a black hole of 1016 kg will evaporate
in 3 billion years.

the word Morover should be replaced with However and the text should be augmented with a conclusion of the form
Since we are using extremelly large black holes, Hawking radiation
should not concern us, even if it is a real phenomon. In Section 5.4.1
of [140] there is a detailed discussion of Hawking radiation and
relativistic hypermachines.
Apostolos Syropoulos

A "Solution" to Riemann Hypothesis

Riemann hypothesi s is "is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex n...