Chapter XIX: Elegance And Complexity | The Philosophy Of Science by Steven Gussman [1st Edition]

        “There is grandeur in this view of life, with its several powers, having been originally breathed by

        the Creator into a few forms or into one; and that, whilst this planet has gone circling on according

        to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most

        wonderful have been, and are being evolved."

        – Charles Darwin^I

        “If you can't explain it simply, you don't understand it well enough.”

        – Attributed to Albert Einstein^II

        In philosophy of science, elegance (a term most commonly associated with the field of physics) is an important concept to get right, and there are many ways to misunderstand it.  Elegance does not really mean simplicity; relative simplicity is required, but not sufficient for elegance.^III  The elegant description of a phenomenon is the one which explains as much of the empirical evidence as possible, within the most minimal framework.  The tool used to achieve this is either called Occam's razor or the principle of parsimony, and it effectively means that if one has two competing hypotheses for explaining an empirical phenomenon, and one of them accounts for the evidence with a much simpler picture, then that is the one to take as provisionally true.^IV

        Ontologically, the universe really does appear to be amazingly elegant: the project of science is the taming of complexity by explaining broadly diverse outcomes as emerging from few and simple laws.^V  It is believed that all of the biodiversity of life arose from the elegant process of evolution by natural selection operating on a single common ancestor.^VI  Sir Issac Newton showed that the same law of the gravitational force governs the motions of orbiting planets and apples falling from trees (it is easy to take such a unification for granted, today).^VII  Physicists believe that all motion in the cosmos is ultimately explicable by just four fundamental forces, two of which have already been unified; indeed, many believe a grand unified theory (GUT) awaits discovery in which motion can be understood as arising from a single fundamental force of nature.^VIII  But simplicity is a relative term; what is important is that the most simple explanation that explains the data is selected (meaning that a simpler and perhaps more aesthetically pleasing model which nevertheless misses when it comes to explaining some significant empirical phenomenon does lose to a more complicated theory which accounts for more features of the ontology).  That said, Nobel prize winning physicist Steven Weinberg (one of three men responsible for unifying the theories of electromagnetism and the weak nuclear force into the theory of the electroweak force) made a provocative and subtle argument that elegant theoretical frameworks are so important, and empirical evidence so practically fallible, that it can be wise to accept a significantly more elegant theory which explains the vast majority of the empirical data even when another description has only slightly better empirical agreement at the cost of being an ugly data-fitting model, because it is likely closer to the mechanical truth of the situation (and in the future, a deeper or otherwise modified theory may account for the last bits of empirical discrepancy without the need for the ugly data-fitting).^IX  Conversely, computational physicist Max Tegmark has argued, I think wrongly, that Occam's razor is not to be applied to the ontology described by one's theory, but to the mathematical description of it!^X  In this way, he claims that a simpler equation with many solutions (including but not limited to those that appear to describe our cosmos) is better than a more complicated equation that limits its solution range to just that which appears to reflect our cosmos (although he would argue that those “extra” predictions really are physically manifest, somewhere).  It is partially through this reasoning that he allows for multiverses of universes very much unlike our own.  Of course, there is little stopping one from using ever more bluntly-simple equations whose solutions contain, among other things, something like our world.  But they will never do so with much precision, and we will never know if those other worlds it describes actually exist.  When applying Occam's razor to our potential theories, we should be most worried about removing extra concepts that don't seem to be necessary to explaining the universe we observe, even if that means the addition of terms in our mathematical descriptions.  Often, in any event, the simplification of our conceptual framework will coincide with the simplification of our mathematical description (for example, all of Kepler's laws of planetary motion are encapsulated as consequences of Newtons' single universal law of gravitation).^XI

        Some scientists have balked at the idea that nature is elegant.^XII  In my experience, this comes from the higher level sciences, particularly medicine, because these people deal with realms that can leave one feeling helpless: the human body is quite complex and it can be difficult (and at times, practically impossible, given the current state of knowledge) to figure out what is causing a particular symptom in a particular body.  In the case of medicine, this unfortunate state of events can bare its head during life-or-death situations.  Here one must again remember the difference between elegance and mere simplicity: our theories must explain the phenomena and no less.  That doesn't mean that some phenomena aren't relatively complex, and clearly the human body is a far more complex system than, say, a hydrogen atom!  Here it is worth making a distinction: complexity is to complication what elegance is to simplicity.  Yes, complex systems are in some sense “complicated”, but it's the application of classic reductionism (or, reducible emergence) to these problems that makes them scientifically tractable.^XIII  Some have seen the advent of complexity and so-called chaos theory as the death-knell for the scientific tools of reductionism and isolation.  But properly understood, these tools may never die: they reflect basic ontological facts about reality.  In fact, the discoverers of complexity and chaos theory do not tend to interpret their topics of study in this way at all: they approach them in the spirit of a classical scientific ethic.^XIV

        In fact, we have always used an enlightened, multi-tiered version of reductionism and isolation.  This is what the ontological stack is all about.  Statistical mechanics views many-particle systems as a whole—one composite object (say, a volume of gas), rather than isolating each atom; but this composite object is, crucially, still treated as isolated from others, say, the gas' container, because this would obfuscate the point being made.  In-principle, every object except the most fundamental particles are composite-objects which we may treat as parts or as a whole depending on the level of abstraction and which lens is most insightful and elegant for explaining a given phenomenon.  Besides statistical mechanics, we have atomic theory in which an atom is treated as a single composite-object; below that, we have subatomic particle physics in which we treat the quarks and electrons making up the atom as individual objects.  It is a crucial part of scientific judgment to know which things (and when) to treat as the same or different.  Symmetry is the treating of things as the same (say, all of the forces of nature unifying at high energies such as at the big bang), and symmetry breaking is the recognition of difference (for example, the fact that in today's cooler universe, the four forces are evidently separated in some way).^XV  No one is stopping anyone from doing such things as scientists have always done; this is how the shouts that we have “reached the limits” of normal scientific research, of utilizing reductionism and isolation,^XVI are based on a straw-man argument of how these tools have been used, so far; and is itself misguided, prone to permitting fallacies such as irreducible emergence and illogical anti-isolationism where we make no smart distinction between composite objects.  Emergent abstraction is how we have always tamed complexity.  The theories that await discovery concerning such complex phenomena as the brain ,or societies, as clever as their content must be, will not deviate from the normal philosophy of science to do so.

        Complexity groups such as The Santa Fe Institute, for example, approach the problem of complexity by investigating whether complex systems (these are highly networked systems involving many moving parts whose individual nature do not obviously imply the collective behavior that nevertheless emerges from their interaction) follow any universal, substrate-independent laws.^XVII  This would be a sort of complexo-dynamics similar to thermodynamics (the study of many-particle physical systems that gives rise to macroscopic features such as temperature and phase-transitions).  Regardless of what a gas is made of, chemically, it follows the laws of thermodynamics (specifically, statistical mechanics).  Those at the Santa Fe Institute are wondering if any such elegant laws similarly govern facets of both your brain (a complex neural network) and, say, stock markets (the complex system of economic transactions and reactions).^XVIII  On the other hand, the whole point of chaos theory is that practically pseudo-random outcomes of even in-principle deterministic laws can be expected if the system is sensitive to slight changes in input (of the kind expected from empirical measurement, which can never be infinitely precise or accurate).  This does not void the in-principle reality of the existence of those elegant laws, it merely places a practical limitation on how useful they can be in the real world, under real measurement conditions.  In Charles Darwin's and Gregor Mendel's time and before, one could easily imagine calling all of biodiversity a “complex system”, and one might have been forgiven for thinking no elegant explanation would ever be proposed, if the connections between grass, and fish, and man were even noticed.  And the biosphere is a complex ecosystem.  But we don't tend to chiefly think of it in those terms today (at least not in the sense of being an irreducible mystery), because the neo-Darwinnian synthesis brought it all down to a hard science, and we understand that whatever the complexity of biodiversity, all of life ultimately emerged from the elegant law of evolution by natural selection operating on a single common genetic ancestor.^XIX

        The scientific ethic must never be to fetishize mystery, the limitations of the scientific method, and the inability to know!^XX  Precisely the opposite: we confidently enter the unknown in the spirit of discovery.

Footnotes:

0. The Philosophy Of Science table of contents can be found, here (footnotephysicist.blogspot.com/2022/04/table-of-contents-philosophy-of-science.html).

I. I retrieved this quote from an untitled page edited by Christopher J. Earle (Gymnosperm Database) (last modified in 2006) (https://www.conifers.org/topics/darwin.htm#:~:text=There%20is%20grandeur%20in%20this,most%20wonderful%20have%20been%2C%20and) which further cites The Origin Of Species by Charles Darwin (Barnes & Noble Classics) (1859 / 2004) (pp. 384) (though I have not yet read this famous work).

II. See the BrainyQuote entry for this quoate: https://www.brainyquote.com/quotes/albert_einstein_383803. Another common version is, “If you can't explain it to a six year old, you don't understand it yourself,” see the goodreads entry for this quote: https://www.goodreads.com/quotes/19421-if-you-can-t-explain-it-to-a-six-year-old.

III. For more on elegance, see The Elegant Universe by Greene (pp. 166-169, 368-369, 385, 387); “A Profusion Of Place” by Gussman (https://footnotephysicist.blogspot.com/2020/03/a-profusion-of-place-part-i-of-unity.html); and “In Defense Of Philosophy (Of Science)” by Gussman (https://footnotephysicist.blogspot.com/2021/05/in-defense-of-philosophy-of-science.html).

IV. See “In Defense Of Philosophy (Of Science)” by Gussman (https://footnotephysicist.blogspot.com/2021/05/in-defense-of-philosophy-of-science.html#FN20A).

V. For more on this topic, see the “Consilience” chapter.

VI. See "Carl Sagan - COSMOS - Evolution" by Sagan, Druyan, and Soter (https://www.youtube.com/watch?v=gZpsVSVRsZk) which is I believe from the “One Voice In The Cosmic Fugue” episode of Cosmos: A Personal Voyage by Sagan, Druyan, and Soter; and "Phylogeny" by Prum (https://www.edge.org/response-detail/27179) in This Idea Is Brilliant edited by Brockman (pp. 262-263).

VII. See Cosmos by Sagan (pp. 72-73); Parallel Worlds by Kaku (pp. 24-25); and Our Mathematical Universe by Tegmark (pp. 36, 248-249)

VIII. See Parallel Worlds by Kaku (pp. 84-85) and The Elegant Universe by Greene (pp. 175-178).

IX. See To Explain The World by Weinberg (pp. 150-151) and “In Defense Of Philosophy (Of Science)” by Gussman (https://footnotephysicist.blogspot.com/2021/05/in-defense-of-philosophy-of-science.html#FN21B).

X. See Our Mathematical Universe by Tegmark (pp. 363)

XI. See Our Mathematical Universe (at least pp. 248-249) and Cosmos by Sagan (pp. 72-73).

XII. See "The Pursuit Of Parsimony" by Jonathan Haidt (Edge / Harper Perennial) (2014 / 2015) (https://www.edge.org/response-detail/25346) and "The Clinician's Law Of Parsimony" by Gerald Smallberg (Edge / Harper Perennial) (2014 / 2015) (https://www.edge.org/response-detail/25415) both from This Idea Must Die edited by Brockman (pp. 493-498) (although I think both of these writers are confused about the proper construal of Occam's razor in the first place).

XIII. For more on this topic, refer to the “Reductionism And Emergence” chapter.

XIV. See The Physics Of Wall Street by Weatherall (pp. 131-132, 136-149).

XV. See Parallel Worlds by Kaku (pp. 84-85).

XVI. For examples, see "The Human Brain Will Never Understand The Universe" by Karl Sabbagh (Edge / Harper Perennial) (2006 / 2007) (https://www.edge.org/response-detail/10848), "It's OK Not To Know Everything" by Marcelo Gleiser (Edge / Harper Perennial) (2006 / 2007) (https://www.edge.org/response-detail/11093), "The End Of Insight" by Steven Strogatz (Harper Perennial) (2007), and "Navigating By New Scientific Principles" by Rupert Sheldrake (Harper Perennial) (2007), all from What Is Your Dangerous Idea? edited by Brockman (pp. 102-104, 128-131, 201-203); and “Unification” by Marcelo Gleiser (Edge / Harper Perennial) (2014 / 2015) (https://www.edge.org/response-detail/25455), "We'll Never Hit Barriers To Scientific Understanding" by Martin Rees (Edge / Harper Perennial) (2014 / 2015) (https://www.edge.org/response-detail/25519), "The Mind Is Just The Brain" by Tania Lombrozo (Edge / Harper Perennial) (2014 / 2015) (https://www.edge.org/response-detail/25290), "Knowing Is Half The Battle" by Laurie R. Santos and Tamar Gendler (Edge / Harper Perennial) (2014 / 2015) (https://www.edge.org/response-detail/25436), "Nature = Objects" by Scott Sampson (Edge / Harper Perennial) (2014 / 2015) (https://www.edge.org/response-detail/25532), "The Scientific Method" by Melanie Swan (Edge / Harper Perennial) (2014 / 2015) (https://www.edge.org/response-detail/25398), "Opposites Can't Both Be Right" by Eldar Shafir (Edge / Harper Perennial) (2014 / 2015) (https://www.edge.org/response-detail/25486), "Essentialist Views Of The Mind" by Lisa Barrett (Edge / Harper Perennial) (2014 / 2015) (https://www.edge.org/response-detail/25400), and "The Illusion Of Scientific Progress" by Paul Saffo (Edge / Harper Perennial) (2014 / 2015) (https://www.edge.org/response-detail/25511), all from This Idea Must Die edited by Brockman (pp. 5-8, 167-169, 271-273, 312-314, 361-364, 392-395, 406-408, 499-502, 542-543).

XVII. See The Physics Of Wall Street by Weatherall (pp. 131-132, 136-149).

XVIII. See The Physics Of Wall Street by Weatherall (pp. 131-132, 136-149).

XIX. I have since become aware that this argument was independently made by the great physicist John Archibald Wheeler, see Parallel Worlds by Kaku (pp. 187). See also Cosmos by Sagan (pp. 271-272).

XX. See The God Delusion by Dawkins (pp. 152) and The Demon Haunted World by Sagan (pp. 304-306).