He was introducing what
he described as "a daring assault on the very bounds of mathematics", carried
out by two scientists from The University of Auckland -- Professor
Cris Calude (Computer Science) and Professor Boris Pavlov (Mathematics) -- who have collaborated in creating a new theory
of quantum computing which has the potential to alter parameters in mathematics
and physics, as well as computer science.
Professor Greg Chaitin,
who founded the (different but related) field of algorithmic information
theory, also used the word "daring" to describe the work of Cris and Boris.
A professor from the physics department at IBM's T. J. Watson Research Centre in New York, Greg is a four-year Visiting Professor to the University of Auckland, which he visited for the third time just after the article came out.
The first and most unconventional
focus of the article, he says, and the most exciting if it proves to be correct,
concerns a quantum solution offered by Cris and Boris to the "halting problem"
posed by Turing in the 1930s -- which has been seen as an unassailable boundary
to what is computable.
"Most people think quantum
computing will increase the speed at which things can be done but will not
alter what you can compute and what you can't." says Greg. "Now Cris and
Boris have a new mathematical argument that strongly suggests it may be possible
to actually compute things you couldn't compute before, using quantum computing.
This is why there has been some scepticism about the
paper [published in
the inaugural edition of MIT's new journal,
Quantum Information Processing
] -- but it is also why the paper is exciting and
interesting to scientists."
"Really, in the end it's
a trade-off," he says. "When there is no doubt about a piece of research,
the results are not revolutionary. But in an area where there is doubt, they
create both scepticism and excitement."
Cris agrees that in the
end nature will decide what is computable and what is not.
"We have done the mathematics.
Now the work of the experimental physicists and engineers will be decisive
in establishing whether it's real or just a pure mathematical fantasy."
The second part of the
article in New Scientist was
concerned with algorithmic information theory and focused on a new number
-- known as Omega and discovered by Greg.
This number was also
the subject of a later substantial story in Pour La Science, one of the two most prominent French popular
science magazines.
Omega, Greg describes
as "a wildly uncomputable and unknowable number which shocked mathematicians".
Cris adds that the number "had many people intrigued because it is paradoxical
and hard to believe".
What Cris has succeeded
in doing -- against all odds and in collaboration with
Dr. Michael
Dinneen (Computer Science) and PhD student Chi-Kou Shu -- is to compute Omega's
first 64 bits.
This, he says, has allowed
him to catch "just a glimpse" of the shape of the number.
"Cris and his colleagues
have courageously set out to compute the uncomputable," says Greg. "And to
some extent they have succeeded."
Cris and Greg are both
excited by the increasing recognition of information as a fundamentally new
notion in mathematics, computer science and physics.
"There is a tendency to disperse science into small drawers," says Cris. "If you look at mathematics there are 1000 official narrow specialisations -- in physics, it's the same.
"Information, however, is a unifying factor, which in a sense is its beauty because it encourages convergence after a long period of divergence."