Does Reality Add Up?
In the August issue of Scientific American, Mario Livio explores – Why Math Works – Is math invented or discovered? A leading astrophysicist suggest that the answer to the millenia-old question is both. Here’s what Mario offers in brief:
The deepest mysteries are often the things we take for granted. Most people never think twice about the fact that scientists use mathematics to describe and explain the world. But why should that be the case?- Math concepts developed for purely abstract reasons turn out to explain real phenomena. Their utility, as physicist Eugene Wigner? once wrote, “is a wonderful gift which we neither understand nor deserve.”
- Part of the puzzle is the question of whether mathematics is an invention (a creation of the human mind) or a discovery (something that exists independently of us). The author suggests it is both.
Cosmic Mathematics
- The Golden Ration – Ancient Greek mathematicians first studied what we now call the golden ratio because of its frequent appearance in geometry. The division of a line into “extreme and mean ratio” (the golden section) is important in the geometry of regular pentagrams and pentagons. Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.
- Fractal Geomentry – A fractal is “a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,” a property called self-similarity. Roots of the idea of fractals go back to the 17th century, while mathematically rigorous treatment of fractals can be traced back to functions studied by Karl Weierstrass, Georg Cantor and Felix Hausdorff a century later in studying functions that were continuous but not differentiable; however, the term fractal was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning “broken” or “fractured.” A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion. There are several examples of fractals, which are defined as portraying exact self-similarity, quasi self-similarity, or statistical self-similarity. While fractals are a mathematical construct, they are found in nature, which has led to their inclusion in artwork. They are useful in medicine, soil mechanics, seismology, and technical analysis.
- Holographic Universe – In a larger and more speculative sense, the theory suggests that the entire universe can be seen as a two-dimensional information structure “painted” on the cosmological horizon, such that the three dimensions we observe are only an effective description at macroscopic scales and at low energies. Cosmological holography has not been made mathematically precise, partly because the cosmological horizon has a finite area and grows with time
Our Western spiritual understanding has grown distant from its roots; Plato’s and Pythagoras’s spiritual training required the utmost rigor of logic and precision of discrimination. Pythagoras taught spirituality through instruction in mathematics, and Plato instituted mathematics as part of the curriculum of his academy. Logical debates were part of Plato’s spiritual training, a practice inspired by Socrates. The originators of our Western thought conceived of mystical experience and logical discrimination as two sides of the same capacity for knowing. The contemporary assumptions are radically otherwise; the major thrust of thought now is that mystical experience and logical thought are not only divergent but also incompatible. – Inner Journey Home, A.H. Almaas
It’s enough to make my mind spin! When it comes to the question of whether or not it all adds up, I guess the answer is – how is it going in your corner of the multiverse?
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