Tire Need of Mathematics in' Geography
LUIS I'BEILE, DepariBlnt 01 Geographr, UmenltJ of Ok1aJloma
The existence of the world Is'a natural phenonmenon which Is difficult
to define In terms of four dimensions. The investigation of the nature of our
planet Is a human attempt, which is expressed in many different criteria,
one ot which Is geography. .
To the geographer, his 'field is the descriptive science of space area..
Such a det1n1tlon gives rOQID for both qualitative and quantitative aspects
which are combined necessarily, by nature of the geographer's quest.
The intensity with which the quantitative aspect, that is to say, the
scientific method as used in geography, Is limited to a level far below that
ot the qualltatlve intensity.
The author agrees with the contemporary Italian and German schools
of geography, which stress rightfully the importance of science in
geographical investigations and teachings.
Considering the method of investigation, the science fields in geography
are three:
(1.) The 8cien<:e of the planet,
(2.) The science of relationships, (nature to nature, nature to man,
and man to nature),
(3.) The science of distributions (phenomena in cultural or natural
occurance).
In these three levels, sdence has mathematics as a common language
because it has a spontaneous response from the physical world that is
stUdied. As is for all sciences, mathematics is needed by the geographer
to help coordinate those experiences which the qualitative criteria is
unable to bring to a complete logical system. For it is mathematics, the
technique par excellance, that implements a comprehensive order in the
knOWledge of some fields in geography.
Upon assuming a quantitative attitude, the geographer realizes that
human scientists are operating in a three dimensional space and therefore must apply themselves to some system of scientifi<: induction, deduction and conclusion, all of which are performed mathematically.
To insure the geographer's scientific success a simple procedure Is
here presented, namely the order of scientific procedure in geography:
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