The origins of science were mixed with the mystical from early on. In the ancient world, the greatest attention was paid to the movement of the stars and planets not for its own sake, but for how they would affect the events and actions of kings and nations. Later, on in the 1600's western european men of letters were alchemists and astrologers.
Over time, science moved further away from these two studies and chose instead to concentrate on "practical" considerations such as agriculture and husbandry. These men adopted what has been called the Baconian method, named after Sir Francis Bacon. This despite the strong evidence that Bacon was an alchemist and perhaps even practiced astrology.
Science became more rational and under the period of the Enlightenment, it finally abandoned any notion of magic, metaphysics and eventually married itself to mathematics. This union of the two disciplines accomplished great breakthroughs in understanding the universe and nature. Western science then discovered the mathematical nature of nature. This realization led to an attempt to quantize every phenomena observed in nature. This almost exclusive obsession with mathematical quantification has also become the very soul of science.
There are however certain voices that are beginning to question this blind allegiance to mathematics in the sciences. The former Jacob Schwartz, professor of Mathematics and Computer Science and founder of the Computer Science department at New York University wrote an article entitled, The Pernicious Influence of Mathematics on Science. We will quote this article extensively because of its relevance. He stated:
Schwartz then laid bare one of the critical problems mathematics faces when applied to science:
science tries to deal with reality that even the most precise sciences normally work with more or less ill-understood approximations toward which the scientist must maintain an appropriate skepticism. Thus, for instance, it may come as a shock to the mathematician to learn that the Schrodinger equation for the hydrogen atom, which he is able to solve only after a considerable effort of functional analysis and special function theory, is not a literally correct description of this atom, but only an approximation to a somewhat more correct equation taking account of spin, magnetic dipole, and relativistic effects; that this corrected equation is itself only an ill-understood approximation to an infinite set of quantum field-theoretical equations; and finally hat the quantum field theory, besides diverging, neglects a myriad of strange-particle interactions whose strength and form are largely unknown. The physicist, looking at the original Schrodinger equation, learns to sense in it the presence of many invisible terms, integral, integrodifferential, perhaps even more complicated types of operators, in addition to the differential terms visible, and this sense inspires an entirely appropriate disregard for the purely technical features of the equation which he sees. This very healthy self-skepticism is foreign to the mathematical approach.
This article is so devastating to the common way mathematics is used in the sciences that one see a crisis approaching when the mathematical models will dramatically fail, thus perhaps bringing the entire mathematical/science edifice into partial disrepute.
Finally, at the risk of quoting the entire article, Schwartz unmasked what many of us have suspected all along about the way mathematics is being used in the sciences.
We present to you a documentary named Dangerous Knowledge on the slow realization on the part of mathematicians in the late 19th and early 20th century on weakening pillars supporting mathematics as sure fire way to understand the structure of the universe. If you cannot see the embedded video here is the link: http://bit.ly/gX70nj.
In our final part 4b of this article we will consider the radical new direction Science might choose to go to escape the dilemma it finds itself in.