Mathematics, Blueprint of the Physical World

Ever since the beginning of time, or since the time when man began to measure the physical world, Mathematics and the physical world have been inseparable. Mathematicians measured everything in the physical world and the physical world, on the other hand, had been proven to be “real” through mathematics. Is Mathematics then the blueprint of the physical world? Or man’s creative intellect simply found mathematics in the physical world? The Platonic view that “mathematical concepts actually exist in some weird kind of ideal reality just off the edge of the Universe” (Stewart, 2006) theorizes that mathematics is ever present in the physical world. From this context, it is something not invented but is being discovered and rediscovered as man learns about his physical world. It is out there as something constant. But is this hypothesis accurate?

Now looking back into the history of mathematics, Thales and other Ionian philosophers in 560 B.C. speculated about the physical world. They formulated theorems that would explain the universe beyond what is observable. They assumed that all questions about Universe and Nature can be answered; and the answers are in mathematical equations or principles (Beccera & Barnes, 2005). It seems then again that they are making blue print of the physical world out of mathematics. However there are those who claim that mathematics is merely another invention of man or a product of man’s creative genius. In 1908 Henri Poincare presented an insightful idea about Mathematical invention in his essay Mathematical Creation (Liljedahl, 249). Then in 1943 Jacques Hadamard conducted his own investigation based on a series of questionnaire about the psychology of Mathematical creations. His Psychology of Mathematical Invention in the Mathematical Field characterized the creative process in mathematics and defined the stages of mathematical invention (Liljedahl, 250). Then in 2002, Peter Liljedahl made similar survey which claimed and demonstrated man’s thought process as a factor in mathematical invention (Liljedahl, 253). All these stages into arriving at mathematical discoveries claimed that man himself, due to his own thought process invented mathematics.

Similarly, at present, scientists have been trying to find the same answers in some of the mysteries in life. Just a few years ago Gerald S. Hawkins found that there are geometric theorems in patterns of crop circles. For instance, in one of the equilateral triangle in between an outer and inner circle, the area of the outer circle is precisely four times that of the inner circle. Other numerical relationships include diatonic ratios and whole number ratios. As Hawkins commented, “These designs demonstrate the remarkable mathematical ability of their creators” (Peterson, 1996). Hawkins discovered that with the use of Euclidian geometry he can prove four theorems in the areas in the crop circle patterns.  Moreover, there was a fifth theorem which Hawkins stated, “involves concentric circles which touch the sides of a triangle, and as the [triangle] changes shape, it generates the special crop-circle geometries,” (Peterson, 1996).  But what is surprising in this fifth theory is that even in Euclid’s works and in all the other reference books he consulted, Hawkins found no reference to this theorem (Peterson, 1996). When he challenged others to demonstrate this fifth theory, none answered. But the theorem came up again and again in the crop circles.

So what does this tells us about the whether mathematics is the blueprint of the physical world? It tells us that math is part of nature just waiting to be discovered or put into perspective as blueprints should; which is exactly what Hawkins did with the crop circles. The crop circles have proven that the geometric theorems are its blueprint; and that they (the crop circles) are not mere creative designs made by whoever made them. To prove the point, historically, mathematics is always being discovered and rediscovered to describe nature and it is used to connect one scientific fact into the next. As they are discovered and connected, man derives a better understanding of his physical world. For instance, we see this in Einstein’s Theory of Relativity and Quantum Mechanics which are mathematically accurate when measured in the physical world. There is also the String Theory which scientist claims has proven mathematically that there are actually ten dimensions in the physical world (Berman, 2007).

For years, man has been trying to measure the universe and his surroundings through mathematics. From the crop circles to this new discovery of String Theory, we see all the other things in the universe having mathematics as its blueprint. Again we see this blueprint in Aristotle’s mathematical models which explains planetary motions, in Ptolemy mathematical model of his Ptolemaic Universe, in Copernicus’ elaborate mathematical equations, in Kepler’s elliptical orbits, in Newton’s law of gravity, and in Einstein’s presentation of the universe in his theory of relativity. In all these, even up to the present, scientists have proven that Mathematics is not a mere instrument of measurement which man created for his fancy. Mathematics show what is real and once they are proven, show the actual blueprint of the physical world.

References

Becerra, Linda and Barnes, Ron. 2005. The Evolution of Mathematical Certainty. University of

Houston. Math Horizons, September 2005 Issue, p 13 – 17.

Retrieved 17 February 2008 from

http://www.maa.org/mathhorizons/pdfs/september_2005_13.pdf

Berman, David. 2007.  String theory: From Newton to Einstein and beyond. Plus Math.org

Retrieved 17 February 2008 from

http://plus.maths.org/issue45/features/berman/index.html

Liljedahl, Peter. 2004 Mathematical Discovery: Hadamard Resurrected.

 International Group for the Psychology of Mathematics Education, 28th Bergen,

 Norway, July 14-18, 2004, p 249-246

Peterson, Ivan. 1996. Crop Circles: Theorems in Wheat Fields. Science News Online

   http://www.sciencenews.org/pages/sn_arch/10_12_96/note1.htm

Stewart, Ian. 2006. Think Maths: Is mathematics the grand design for the Universe, or merely a

figment of the human imagination? New Scientist magazine, Issue 2058, November 30, 1996, p 38