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R. Barrett and P. P. Delsanto
the same manner as a normal computer, but are trained by presenting them
with the output of thousands of calculations carried out with traditional
methods; they learn by experience, in the same way that the human brain
learns to distinguish the image of a tree from that of an egg. They are then
able to use this training to solve different, but similar, astronomical problems
much faster than is possible with a conventional computer. Inherent in this
approach is the difficulty of checking whether the results obtained in this
manner are correct. As we saw in the last Section, this problem will be exacerbated in the near future when quantum computers, with their much faster
speeds, become available.
In attempting to obtain a reason why mathematics is so successful in
theoretical physics, Hamming and later Abbott [15], point their fingers at
humanity. We tend to be selective in which problems we address with mathematics; e.g. there is no mathematical theory of truth, beauty or justice. When
existing mathematics cannot be applied to a particular physical problem, we
try to invent new forms to use. We have already described in Chap. 4 the
extension of our numbering system from simple integers to complex numbers
as the centuries passed, and the need to address more complicated scenarios
arose. In fact, as we have seen in the last paragraph, there are vast domains of
interest where the logical bottom-up approach fails.
Finally, it is suggested that the role of natural selection in the evolution
of our species would have favoured those individuals who can follow long
chains of close reasoning. We should point out, however, that Hamming is
unconvinced on this point.
We have, in earlier Chapters, highlighted the contradictions between the
theories of Quantum Mechanics and Relativity, both of which are formulated with classical logic. In particular, Quantum Mechanics is a probabilistic
theory, where predictions are of a statistical nature, while Relativity is deterministic, with precise predictions of the trajectories of objects. In Quantum
Mechanics, particularly in Quantum Entanglement, the collapse of the wave
function fixes the properties of particles simultaneously, while in relativity
simultaneity is different for different observers who are moving with respect
to each other.
It is entirely possible that scientists will find a way to understand and
accept even the strangest quirks of modern science by stretching the limits
of classical logic. However, it is also possible that a Copernican revolution in
the field of logic, analogous to that which has occurred in our understanding
of our place in the cosmos, might turn out to be a more direct route towards
a better understanding of those parts of the world that are not our natural
R. Barrett and P. P. Delsanto
the same manner as a normal computer, but are trained by presenting them
with the output of thousands of calculations carried out with traditional
methods; they learn by experience, in the same way that the human brain
learns to distinguish the image of a tree from that of an egg. They are then
able to use this training to solve different, but similar, astronomical problems
much faster than is possible with a conventional computer. Inherent in this
approach is the difficulty of checking whether the results obtained in this
manner are correct. As we saw in the last Section, this problem will be exacerbated in the near future when quantum computers, with their much faster
speeds, become available.
In attempting to obtain a reason why mathematics is so successful in
theoretical physics, Hamming and later Abbott [15], point their fingers at
humanity. We tend to be selective in which problems we address with mathematics; e.g. there is no mathematical theory of truth, beauty or justice. When
existing mathematics cannot be applied to a particular physical problem, we
try to invent new forms to use. We have already described in Chap. 4 the
extension of our numbering system from simple integers to complex numbers
as the centuries passed, and the need to address more complicated scenarios
arose. In fact, as we have seen in the last paragraph, there are vast domains of
interest where the logical bottom-up approach fails.
Finally, it is suggested that the role of natural selection in the evolution
of our species would have favoured those individuals who can follow long
chains of close reasoning. We should point out, however, that Hamming is
unconvinced on this point.
We have, in earlier Chapters, highlighted the contradictions between the
theories of Quantum Mechanics and Relativity, both of which are formulated with classical logic. In particular, Quantum Mechanics is a probabilistic
theory, where predictions are of a statistical nature, while Relativity is deterministic, with precise predictions of the trajectories of objects. In Quantum
Mechanics, particularly in Quantum Entanglement, the collapse of the wave
function fixes the properties of particles simultaneously, while in relativity
simultaneity is different for different observers who are moving with respect
to each other.
It is entirely possible that scientists will find a way to understand and
accept even the strangest quirks of modern science by stretching the limits
of classical logic. However, it is also possible that a Copernican revolution in
the field of logic, analogous to that which has occurred in our understanding
of our place in the cosmos, might turn out to be a more direct route towards
a better understanding of those parts of the world that are not our natural