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R. Barrett and P. P. Delsanto
Clearly logic is an important component of the brain’s activities, but it is
certainly not the only component, nor probably the most important for our
daily survival. Pattern recognition, which enables us to separate objects into
particular classes, even if we have never seen them before, is a vital part of
human learning. We all know a tree when we see one, and do not attempt
to teach it to heel, in the belief that it is a dog. The extraction of patterns
has played a vital role in our survival. It is a facility that is trained into the
minds of infants by their earliest childhood experiences. Pattern Recognition is currently being incorporated into computers in research into “machine
learning”, with the aim of further developing Artificial Intelligence.
2.4 Complexity
The bottom-up logical approach has been the traditional modus operandi of
physics. For instance, the laws of interaction of particles were proposed by
Newton and others, and the result was the science of classical mechanics. The
orbits of planets, and the paths of rockets, have been deduced from these laws
by the use of mathematics. Different laws were formulated for the interaction of high-velocity bodies by Einstein, leading to relativistic mechanics, and
by Heisenberg, Schrödinger and others for sub-atomic particles, leading to
Quantum Mechanics. Deductions from these laws have led to the prediction
of phenomena that have been observed experimentally.
Difficulties arise when attempts are made to apply these physical laws to
scenarios with large numbers of interacting particles. It is not because anyone
believes the laws do not work. Rather, it is that the mathematics of the problems becomes intractable. As an example, Newton’s Theory of Gravity yields
an exact analytical solution only for the case of two interacting bodies. One
might imagine the situation of the earth revolving about the sun. The orbit
of the earth can only be predicted analytically if we disregard the presence of
the earth’s moon, and of the other planets and their moons.
However, we know that during the Apollo missions, NASA predicted the
paths of their spacecraft very precisely. How was this possible? Numerical
methods have been developed which involve computing the effect on the
rocket’s trajectory of one body (the sun or the earth), and then refining
the estimates obtained by repeating the calculations, including more and
more “perturbations” from hitherto neglected gravitational sources (i.e. other
planets and moons). Such a procedure is time-consuming, and only possible
because of the development of fast modern computers.
R. Barrett and P. P. Delsanto
Clearly logic is an important component of the brain’s activities, but it is
certainly not the only component, nor probably the most important for our
daily survival. Pattern recognition, which enables us to separate objects into
particular classes, even if we have never seen them before, is a vital part of
human learning. We all know a tree when we see one, and do not attempt
to teach it to heel, in the belief that it is a dog. The extraction of patterns
has played a vital role in our survival. It is a facility that is trained into the
minds of infants by their earliest childhood experiences. Pattern Recognition is currently being incorporated into computers in research into “machine
learning”, with the aim of further developing Artificial Intelligence.
2.4 Complexity
The bottom-up logical approach has been the traditional modus operandi of
physics. For instance, the laws of interaction of particles were proposed by
Newton and others, and the result was the science of classical mechanics. The
orbits of planets, and the paths of rockets, have been deduced from these laws
by the use of mathematics. Different laws were formulated for the interaction of high-velocity bodies by Einstein, leading to relativistic mechanics, and
by Heisenberg, Schrödinger and others for sub-atomic particles, leading to
Quantum Mechanics. Deductions from these laws have led to the prediction
of phenomena that have been observed experimentally.
Difficulties arise when attempts are made to apply these physical laws to
scenarios with large numbers of interacting particles. It is not because anyone
believes the laws do not work. Rather, it is that the mathematics of the problems becomes intractable. As an example, Newton’s Theory of Gravity yields
an exact analytical solution only for the case of two interacting bodies. One
might imagine the situation of the earth revolving about the sun. The orbit
of the earth can only be predicted analytically if we disregard the presence of
the earth’s moon, and of the other planets and their moons.
However, we know that during the Apollo missions, NASA predicted the
paths of their spacecraft very precisely. How was this possible? Numerical
methods have been developed which involve computing the effect on the
rocket’s trajectory of one body (the sun or the earth), and then refining
the estimates obtained by repeating the calculations, including more and
more “perturbations” from hitherto neglected gravitational sources (i.e. other
planets and moons). Such a procedure is time-consuming, and only possible
because of the development of fast modern computers.