300
PHVSICS OF THE IMPOSSIBLE
fifty-fifty chance that the final theory would be found in the next
twenty years. But when the year 2000 arrived and there was no consensus on the theory of everything, he changed his mind and said that
there was a fifty-fifty chance of finding it in another twenty years.
Then in 2002 Hawking changed his mind once again, declaring
that Gôdel's incompleteness theorem may suggest a fatal flaw in his
original line of thinking. He wrote, "Some people will be very disappointed if there is not an ultimate theory that can be formulated as a finite number of principles. I used to belong to that camp, but I have
changed my mind ... Gôdel's theorem ensured there would always be
a job for mathematicians. I think M-theory will do the same for physicists."
His argument is an old one: since mathematics is incomplete and
the language of physics is mathematics, there will always be true physical statements that are forever beyond our reach, and hence a theory
of everything is not possible. Since the incompleteness theorem killed
off the Greek dream of proving all true statements in mathematics, it
will also put a theory of everything forever beyond our reach.
Freeman Dyson said it eloquently when he wrote, "Gôdel proved
the world of pure mathematics is inexhaustible; no finite set of axioms
and rules of inference can ever encompass the whole of mathematics ... I hope that an analogous situation exists in the physical world.
If my view of the future is correct, it means that the world of physics
and astronomy is also inexhaustible; no matter how far we go into the
future, there will always be new things happening, new information
coming in, new worlds to explore, a constantly expanding domain of
life, consciousness, and memory."
Astrophysicist John Barrow summarizes this logic this way: "Science is based on mathematics; mathematics cannot discover all truths;
therefore science cannot discover all truths."
Such an argument may or may not be true, but there are potential
flaws. Professional mathematicians for the most part ignore the incompleteness theorem in their work. This is because the incompleteness
theorem begins by analyzing statements that refer to themselves; that
PHVSICS OF THE IMPOSSIBLE
fifty-fifty chance that the final theory would be found in the next
twenty years. But when the year 2000 arrived and there was no consensus on the theory of everything, he changed his mind and said that
there was a fifty-fifty chance of finding it in another twenty years.
Then in 2002 Hawking changed his mind once again, declaring
that Gôdel's incompleteness theorem may suggest a fatal flaw in his
original line of thinking. He wrote, "Some people will be very disappointed if there is not an ultimate theory that can be formulated as a finite number of principles. I used to belong to that camp, but I have
changed my mind ... Gôdel's theorem ensured there would always be
a job for mathematicians. I think M-theory will do the same for physicists."
His argument is an old one: since mathematics is incomplete and
the language of physics is mathematics, there will always be true physical statements that are forever beyond our reach, and hence a theory
of everything is not possible. Since the incompleteness theorem killed
off the Greek dream of proving all true statements in mathematics, it
will also put a theory of everything forever beyond our reach.
Freeman Dyson said it eloquently when he wrote, "Gôdel proved
the world of pure mathematics is inexhaustible; no finite set of axioms
and rules of inference can ever encompass the whole of mathematics ... I hope that an analogous situation exists in the physical world.
If my view of the future is correct, it means that the world of physics
and astronomy is also inexhaustible; no matter how far we go into the
future, there will always be new things happening, new information
coming in, new worlds to explore, a constantly expanding domain of
life, consciousness, and memory."
Astrophysicist John Barrow summarizes this logic this way: "Science is based on mathematics; mathematics cannot discover all truths;
therefore science cannot discover all truths."
Such an argument may or may not be true, but there are potential
flaws. Professional mathematicians for the most part ignore the incompleteness theorem in their work. This is because the incompleteness
theorem begins by analyzing statements that refer to themselves; that