Month: July 2020

Last time we looked at the imprecise pairing of chaoplexity with scientific modeling and dubious use of quantum mechanics to explain a spontaneously appearing universe. My final example of suspect mathematics in science is even more metaphysical, string theory.

In the first half of the 20^th century it must have appeared that the fundamental nature of matter was finally elucidated with Niels Bohr’s model of the atom with three readily understandable subatomic particles: electrons, protons, and neutrons. Unfortunately, that hope was brief since astronomers were already finding other particles in cosmic radiation. Later research using particle accelerators led to the unsightly Standard Model of Particle physics wherein subatomic particles like the proton are made up of still smaller particles called quarks of which there are dozens with odd names like the down quark or the charmed antiquark; coming in ‘flavors’ arbitrarily called red, green, and blue; and with spin of 0, 1, or 2.³

Such a disconcertingly complex outcome led many physicists to seek a still ‘smaller’ and simpler explanation underlying this particle ‘zoo.’ At that point string theory comes on the scene. The general theory is simple enough – particles are not points, but “string-like” and can be (1) stretched like rubber bands; more energy when stretched and less when contracted, and (2) vibrate like rubber bands. With work physicists and mathematicians were able to make string theory work by joining it to supersymmetry leading to the more coherent superstring theory. Here at last was a theory that could unify physics, a theory of everything; explaining  all of the particles, the forces, and the laws of motion, and accommodating special relativity and quantum theory.⁴

However there are problems. First superstring theory is actually many equally coherent theories, each requiring more than the commonly accepted  four dimensions – in fact 10 in all (the remaining six being tiny curled up dimensions). String theory depends on only one constant, but requires many additional seemingly arbitrary constants to explain the standard model. The theory is contingent on supersymmetry which is not visible in the natural world. The theory itself appears to be untestable. Last is the question of how the differences between unified particles and forces is to be explained.⁵

Some physicists are dubious of superstring theory. Richard Fenyman dislikes the tendency to explain or discount anything inconsistent with the theory. Sheldon Glashow scoffs that it cannot be demonstrated and has not led to a single experimental prediction.⁶ Lee Smolin bemoans the incredible resources diverted to this theory to the exclusion of other research based on the scientific community’s rigid belief in the theory or ‘groupthink’, referencing Kuhn’s book on scientific paradigms at one point. Others believe string theory’s greatest strength is its beauty, suggesting it qualifies as aesthetics.⁷

None of this is intended to diminish science which for the most part is the best system for identifying “truth” known to humanity. However my goal is to remind readers that the mathematics underpinning science and some resulting theories are not certain, some not even in an empirical context. Next time we look at one more concern with science as certainty, issues of connection.

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¹Horgan, John, The End of Science, Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, 1996. ISBN 0-201-62679-9, page 191.

²Ibid. Page 202.

³Hawking, Stephen, A Brief History of Time, Bantam Books, New York, 2009. ISBN: 978-0-307-29117-2, pages 86-89.

⁴Smolin, Lee, The Trouble with Physics, Houghton Mifflin Company, Boston, 2007. ISBN: 978-0-618-91868-3, pages 103-112.

⁵Ibid., page 117-123.

⁶Ibid., page 125.

⁷Horgan, John, The End of Science, Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, 1996. ISBN 0-201-62679-9, page 70.

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Having trouble leaving a question or comment?  E-mail me at gregoryciliberti@gmail.com

“God used beautiful mathematics in creating the world.”– Paul Dirac, Nobel Laureate in Physics, 1933.      “

In the last post I noted that mathematics developed independently of science over thousands of years until the Age of Reason when several great minds yoked them initiating a revolution in science. However, by the early 20^th century, cracks began to show both in the proposition that mathematics is absolute and in the application of increasingly abstract mathematics to empirical reality. The doubts inherent in these mathematical speculations and modeling is the subject of this post.

Our first example is the area of chaos theory and complex system analysis which John Horgan labels chaoplexity.¹ While basic science depends on the assumption of the uniformity of simple systems in generating scientific laws, most of reality is complex. So while we can predict the product of the mixing of two chemicals in a test tube it is unclear what this tells of about chemical reactions occurring in Earth’s primordial soup. On the face of it, chaos theory’s central tenant that highly complex systems inevitably lead to unpredictability appears to be logically inconsistent with predictive modeling.

In addition scientific models are prone to structural problems including speculative assumptions and bias in the choice of inputs. Nancy Cartwright, a philosopher of science, considers numerical models nothing more than “a work of fiction.”² Nonetheless experts constantly forecast future events based on this method including portentous phenomena such as climate change and the course of pandemics.

A second example is quantum mechanics and uncertainty, which is inscrutable at best and irrational at worst. Still some physicists use the probabilistic nature of matter in space-time implied by this theory to argue that even if nothing at all existed before the big bang, there was an infinitesimal chance that a singularity would appear spontaneously. Since there was an infinite period in which this could occur, the appearance of the universe from naught is a reasonable explanation (everything just came from nothing!). This too seems illogical since there would have been no time and no environment in which a spontaneous event could occur.

This theory does not appear empirical at all, rather a mathematical labyrinth requiring assumptions and contortions which are of course beyond non-mathematicians. In fact, this theory seems closer to metaphysics than strict science,and lay persons are expected to accept its “truth” on faith in the knowledge of the experts, a circumstance hauntingly reminiscent of the assertion of priests in early religions.

(continued next post)

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Having trouble leaving a question or comment?  E-mail me at gregoryciliberti@gmail.com