12 Issues for the Future
251
On the other hand, if the empiricist view holds, our classical logic and
mathematics are inadequate to explain all of physics, and perhaps we should
be seeking to develop a different logic for this purpose.
It is not surprising that our classical logic works so well in the macro world
of classical physics. This is after all the world in which we, and our intelligence, have evolved, and for which classical logic is tuned. No hominid or
primate has ever played with toys of molecular dimensions, nor travelled at
speeds close to the velocity of light. Had our ancestors been exposed for many
thousands of years to the wonderfully strange world of Alice in Quantumland
[11], the logic that we now use would arguably be different.
It is a very surprising thing that mathematics describes the physical world
so well. Wigner [12] and Manning [13] in two separate thought-provoking
papers have explored this enigma under the title: The Unreasonable Effectiveness of Mathematics. Classical mathematics, based on long chains of logical
reasoning from a few basic assumptions (axioms), is routinely used to explain
observed physical phenomena. It is also used by engineers to construct
bridges, aircraft and other complicated structures, with full confidence that
they will function as planned. Symmetries in mathematical equations have led
to the prediction of new (and at the time yet unobserved) physics, e.g. radio
waves, inferred from the equations of Maxwell (see Chap. 5), and antimatter,
from Dirac’s equation (see Chap. 8).
Despite the astounding success of classical mathematics in so many areas
of physics, there are cases where it falls surprisingly short. Newton’s law of
gravity was one of the spectacular early successes of physics. It explains the
orbiting of one celestial body about another with great precision; however, the
addition of an extra body to the celestial system renders the problem insoluble using classical mathematics, and its solution requires an approximation
method.
When we realise that most of the world comprises many bodies, both
small and large, interacting with each other, the limitations of the bottomup approach become clear. When the number of interacting bodies becomes
immense, physicists have devised statistical methods (statistical physics and
thermodynamics) to successfully describe this domain. However, that still
leaves an intermediate region where solutions to important problems are
difficult to obtain.
In Chap. 2, we discussed alternative approaches to the traditional bottomup approach to the laws of physics, involving statistical and pattern recognition methods. Recently, an approach to solving the three-body problem using
neural networks has been investigated [14]. Neural networks are computers
constructed from parallel arrays of processors. They are not programmed in
251
On the other hand, if the empiricist view holds, our classical logic and
mathematics are inadequate to explain all of physics, and perhaps we should
be seeking to develop a different logic for this purpose.
It is not surprising that our classical logic works so well in the macro world
of classical physics. This is after all the world in which we, and our intelligence, have evolved, and for which classical logic is tuned. No hominid or
primate has ever played with toys of molecular dimensions, nor travelled at
speeds close to the velocity of light. Had our ancestors been exposed for many
thousands of years to the wonderfully strange world of Alice in Quantumland
[11], the logic that we now use would arguably be different.
It is a very surprising thing that mathematics describes the physical world
so well. Wigner [12] and Manning [13] in two separate thought-provoking
papers have explored this enigma under the title: The Unreasonable Effectiveness of Mathematics. Classical mathematics, based on long chains of logical
reasoning from a few basic assumptions (axioms), is routinely used to explain
observed physical phenomena. It is also used by engineers to construct
bridges, aircraft and other complicated structures, with full confidence that
they will function as planned. Symmetries in mathematical equations have led
to the prediction of new (and at the time yet unobserved) physics, e.g. radio
waves, inferred from the equations of Maxwell (see Chap. 5), and antimatter,
from Dirac’s equation (see Chap. 8).
Despite the astounding success of classical mathematics in so many areas
of physics, there are cases where it falls surprisingly short. Newton’s law of
gravity was one of the spectacular early successes of physics. It explains the
orbiting of one celestial body about another with great precision; however, the
addition of an extra body to the celestial system renders the problem insoluble using classical mathematics, and its solution requires an approximation
method.
When we realise that most of the world comprises many bodies, both
small and large, interacting with each other, the limitations of the bottomup approach become clear. When the number of interacting bodies becomes
immense, physicists have devised statistical methods (statistical physics and
thermodynamics) to successfully describe this domain. However, that still
leaves an intermediate region where solutions to important problems are
difficult to obtain.
In Chap. 2, we discussed alternative approaches to the traditional bottomup approach to the laws of physics, involving statistical and pattern recognition methods. Recently, an approach to solving the three-body problem using
neural networks has been investigated [14]. Neural networks are computers
constructed from parallel arrays of processors. They are not programmed in