PREFACE
Eugene Wigner, a theoretical physicist involved in the early development of
nuclear energy, asked an interesting question in a 1960 paper entitled The Unreasonable
Effectiveness of Mathematics in the Natural Sciences. His question concerned
the remarkable relationship between nature and our mathematical modelling of
it. How is it that human beings are able to more or less accurately mimic natural
processes by the use of mathematical constructs? He was unable to provide a
convincing explanation, in part because he hesitated to take the mystery out
of the subject.
Let us look at that question. What do the workings of nature, or the universe,
and mathematics have in common? It would seem obvious that they are both characterised
first and foremost by logic, otherwise we, as logical beings, would not be able
to understand or manipulate either - our entire civilisation is founded on that
premise. Now the real question arises: “What is logic?”. Rather
than attempt to delve into the logic of logic, which sounds alarmingly like
metaphysics, I suggest we just accept that, for all human intents and purposes,
logic is simply the way we see the universe working. Our brains having evolved
from, as an integral part of, this universe, they naturally contain the method
which created them, whatever that may be. In fact our mind is a primitive but
evolving working model, a physical analog, of the functioning universe and logic
is nothing more than a memory of that phenomenon. We therefore perceive the
way the universe works, the way our brain works, as logical. Whatever that method
may be, they correspond to each other. As simple as that!
Now this notion of memory of the cosmos has interesting implications, and brings
to mind the ancient conundrum as to whether mathematical relationships are discovered
or invented. Obviously the answer is neither - they are remembered since they
originate in our memory of the common logic contained in our universe and in
our mind. What do we mean by mathematical relationships anyway? Why mathematics
is simply the study of the natural and logical sequencing of events or states:
if X then Y, so if Y then Z, and so on literally ad infinitum. The relationships
follow in a logical sequence or progression, a process of evolution ruled by
logic, just like nature, and there again lies the correspondence between nature,
mathematics and our mind. It is therefore not at all surprising that mathematics
can be used to model nature, assuming of course that the right questions are
asked, that the relevant variables are identified for insertion into the equations,
that the relationships extrapolated correspond accurately to those existing
in nature, and therein lies the problem for the researcher. This assumes of
course that he possesses that essential quality, a consuming desire to know
and understand.
The urge to know is what makes us human, right? - not true at all! It is actually
humbling to realise that the urge to know is not what distinguishes us from
other animals. This urge is instinctive, part of the survival kit of all creatures,
residing in the nervous system or even earlier, at the molecular level. It gave
rise to memory, enabling bits of information to be stored, manipulated and adapted
over time. Useful stuff.
The desire to understand is an altogether different thing. What is the difference
between knowing and understanding? It is a difference of degree only, but a
fundamental one. It is the difference between on the one hand acquiring hard
information for an immediate, or at best anticipated, purpose, and on the other
hand speculating about relationships between the bits of information themselves
and, more significantly, between them and the wider field of unknown, potential
information. It is the difference between knowing that two and two equals four
and understanding the impact that mathematics has and will have on the development
of our civilisation. It is a question of placing things in a context and then
broadening that context, ultimately to include all existence. It is also unlikely
that any creatures on Earth other than humans were ever capable of that.
Since it is a question of degree, inevitably the one leads to the other; knowledge
becomes understanding. But in order to get there knowledge must submit to a
process of transformation, not of its information content, but in the way the
information is processed, the manner and order in which the bits are fitted
together. The point is that understanding cannot be attained without first gathering
and then ordering the relevant bits of information into a coherent picture,
a structure, a theory. The story of civilisation, the history of knowledge and
understanding, boils down to that - the daily struggle to squeeze out minute
details of information which can then be processed and confirmed by universal
experience and which, when they add up to a sufficiently critical mass, may
yield an insight, a conceptual phase transition to a broader, higher level of
understanding, perhaps to a fundamental change in our perception of ourselves.
This higher level unfortunately cannot be inherited; it has to be attained individually
by each of us through our own personal efforts. Like the embryo that relives
the stages of evolutionary history as it develops in the womb, our mind must
be led to evolve through all the transitions of understanding, one by one, toward
ever greater subtlety and complexity.
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