250
R. Barrett and P. P. Delsanto
Today, we still may not know whether there are intelligent forms of life on
other exoplanets, 2 but we do know that here on earth we are the result of an
evolutionary process that has led us inexorably to our current position as the
most intelligent of earth’s animals.
In Chap. 2, we have discussed the nature and origin of classical logic.
This way of thinking, as encapsulated in mathematics, is at the very heart
of science, and thus responsible for most of our technological development.
We saw in Chap. 2 that both the platonic (aka a priori) and empiricist (aka a
posteriori ) viewpoints have their followers. In the platonic view, mathematics
is “out there”, describing the physical world, and just waiting to be discovered by humans, or presumably other intelligent life forms. In the empiricist
view, mathematics is a human invention like any other, which may or may
not describe the physical world. It would probably be true to say that most
mathematicians would favour the former view over the latter.
In Chap. 4, we saw how Gödel’s incompleteness theorems whipped the rug
out from under rigorous mathematicians in their attempts to construct all
of mathematics by logical deduction from a limited number of basic axioms.
Essentially such an approach results in a system that either has contradictions,
or truths that can never be proved. As physics is based on mathematics, we
might expect the same arguments to apply, i.e. there will be some physical
“truths” that can never be derived from theory. This was the basis of Stephen
Hawking’s change of heart about the unlikelihood of a “theory of everything” that we described in Chap. 4, and follows directly from the platonic
viewpoint.
We see from the above paragraph that a change of perception of the nature
of reason (from a priori to a posteriori) is by no means just an abstruse
academic game, but has very important ramifications. If the platonic point
of view applies, then Gödel demands that physics must follow mathematics,
and physicists should explore which “truths” can never be explained in our
current view of the universe.
We saw an example of this type of investigation in Chap. 4, where Toby
Cubitt, a quantum-information theorist at University College, London, and
co-workers, found that the problem of determining whether there is an
energy gap between the lowest energy levels in a material is undecidable. This
team also wants to study a related important problem in particle physics,
exploring why the particles that carry the weak and strong nuclear forces have
rest mass, while photons have no rest mass. This question may also fall into
the “undecidable” class.
2 Exoplanets are planets that orbit a sun in another solar system, and not our sun.
R. Barrett and P. P. Delsanto
Today, we still may not know whether there are intelligent forms of life on
other exoplanets, 2 but we do know that here on earth we are the result of an
evolutionary process that has led us inexorably to our current position as the
most intelligent of earth’s animals.
In Chap. 2, we have discussed the nature and origin of classical logic.
This way of thinking, as encapsulated in mathematics, is at the very heart
of science, and thus responsible for most of our technological development.
We saw in Chap. 2 that both the platonic (aka a priori) and empiricist (aka a
posteriori ) viewpoints have their followers. In the platonic view, mathematics
is “out there”, describing the physical world, and just waiting to be discovered by humans, or presumably other intelligent life forms. In the empiricist
view, mathematics is a human invention like any other, which may or may
not describe the physical world. It would probably be true to say that most
mathematicians would favour the former view over the latter.
In Chap. 4, we saw how Gödel’s incompleteness theorems whipped the rug
out from under rigorous mathematicians in their attempts to construct all
of mathematics by logical deduction from a limited number of basic axioms.
Essentially such an approach results in a system that either has contradictions,
or truths that can never be proved. As physics is based on mathematics, we
might expect the same arguments to apply, i.e. there will be some physical
“truths” that can never be derived from theory. This was the basis of Stephen
Hawking’s change of heart about the unlikelihood of a “theory of everything” that we described in Chap. 4, and follows directly from the platonic
viewpoint.
We see from the above paragraph that a change of perception of the nature
of reason (from a priori to a posteriori) is by no means just an abstruse
academic game, but has very important ramifications. If the platonic point
of view applies, then Gödel demands that physics must follow mathematics,
and physicists should explore which “truths” can never be explained in our
current view of the universe.
We saw an example of this type of investigation in Chap. 4, where Toby
Cubitt, a quantum-information theorist at University College, London, and
co-workers, found that the problem of determining whether there is an
energy gap between the lowest energy levels in a material is undecidable. This
team also wants to study a related important problem in particle physics,
exploring why the particles that carry the weak and strong nuclear forces have
rest mass, while photons have no rest mass. This question may also fall into
the “undecidable” class.
2 Exoplanets are planets that orbit a sun in another solar system, and not our sun.