Michael Caswell, a 4th year undergraduate at Simon Fraser University has just given me permission to post his essay on aesthetics in science where he argues against future research driven by aspirations of order and beauty. I hope you enjoy this essay as much as I have.
All were destined to perish , except a chosen few, a very few. […] But never, never had any men thought themselves so wise and so unshakable in the truth as those who were attacked. Never had they considered their judgments, their scientific deductions, or their moral convictions and creeds more infallible.
– From Crime and Punishment by Feodor Dostoevsky (461).
We now live in an age where there is a sense of unease with the ravenous manner in which humanity has embraced rational thought and it’s associated notion of truth. If Dostoevsky was concerned with the permeating and dominating influence of science and rational thought in 1866, if he were to look on the world today he would surely think that the apocalypse of the rational plague was upon us (461). In the world today our faith in science and the various “truths” which are produced is truly fanatic within the scientific populace. But when rational scientific thought and the effective mastery over nature that it provides have created the “comfortable” world of cell phones and overnight intercontinental flights the question arises: why exactly is this a problem? Friedrich Nietzsche comes forward with a strong answer, explaining that it is not the technology and convenience that science provides us with which is at issue, but rather that science has, through it’s evolution out of the Platonic and Christian ideals, established a “metaphysical faith” in a concept of “truth” which is anything but healthy (Genealogy, 152). According to Babette E. Babich Nietzche considered science the “technique (art) of uncovering the Platonic ideal of truth in the phenomenal world (both theoretically and experimentally)” (Babich, 147). Nietzsche asserts that faith in the Platonic ideal of truth necessitates the invention of a metaphysical faith in a “true” world as separate from “this” world, a creation that he describes as “our most dangerous attempt yet to assassinate life” (Will, 314).
These “artists” of the Platonic ideal passionately assert that their craft of mathematical and rational logic is motivated by a stimulus akin to that which compelled Michelangelo to create his great sculptures, an aesthetic ambition to create beauty (Chandrasekhar, 61). However much the scientist and artist may both lay claim to the holy grail of beauty, it cannot be argued that the essence of the beauty created and quested after in science as compared to art is vastly different. Be this as it may the scientific concept of rational or deterministic beauty has long motivated the form and character of scientific theory and thought. As such, the concept of “beauty” in science must lie at the heart of how rational thought could represent such a “dangerous attempt […] to assassinate life” (Will, 314). As Neitzsche says: “At bottom, it has been an aesthetic taste that has hindered mankind most: it believed in the picturesque effect of truth” (Will, 262). If aesthetics are the core motivator and justification for science (Chandrasekhar, 60) then any revision of the scientific aesthetic will likewise result in a revision of the types of theories that are developed and embraced. A new aesthetic steering science away from the abstract concept of the “true world” and toward an aesthetic based on revision and tumult is brooding in the depths of modern scientific theory, fighting a valiant battle against the aesthetics of the deterministic ideal.
In order to understand why scientists create the theories they do one must come to understand the nature of their motivating aesthetic. Here I will consider the concept of beauty in the most blatantly rational of the sciences - physics. As the great physicist Kepler once said “mathematics is the archetype of the beautiful” expressing the physicists obsession with mathematical beauty. In his book Truth and Beauty: Aesthetics and Motivations in Science physicist S. Chandrasekhar defines with all the shameless audacity of the scientist the concept of beauty as deriving from two major elements. The first element of beauty he has borrowed from the physicist Heisenburg, it is beauty in the mathematical sense, seen as “the proper conformity of the parts to the whole” (Chandrasekhar, 70). The second criterion of rational beauty Chandrasekhar borrows from another world class scientist Francis Bacon, which he describes as “strangeness in the proportion” (70). In order for a physical theory to be beautiful according to Chandrasekhar it must exhibit these two very different properties of “conformity of the parts” and “strangeness in proportion” (70).
The concept of proper conformity of the parts is most easily understood in the example of a mathematical theory. By its very nature mathematics consists in pure logical consistency and derives from rational thought, thus proper conformity of the parts is explicitly imposed. At every step along a derivation the mathematician takes great care to adhere to the logical axioms he has chosen to restrict his progression. He defines the entities of his world. First the “things” and the “actions”, then the mathematical “laws” of his universe are all laid down by the creativity of his mind. He then operates strictly within the “laws” he has invented to build a complex framework of theorems from the “substance” of his world. This is the game that the mathematician plays, molding from the ductile fabric of his mind, a factory of the utmost logical integrity and complexity. Defined from within in this way, his factory of truth is impervious to any exterior assault, it is in fact a thing that is “true-in-itself” (in the tautological sense).
When the mathematician builds his truth factory from the invincible mental mortar of logic, he often pauses to look back on the towering edifice that is growing beneath his feet. If he has expressed a complex set of relations in a simple way, thus increasing the efficiency of his factory construction, he thinks this is beautiful, because it allows him to create even more relations which are ever more beautiful than the first. For example the equation: 1+2+3+ … + n = n(n+1)/2 can be considered a simple yet beautiful relation. With the concept of “number” and the actions of “add” and “multiply” one can reduce the problem of adding up any number of integers no matter how large by applying the simple formula on the right. He has thus created beauty. To one unaccustomed to spending long nights manipulating mathematical equations (as Neitzsche was) this sort of beauty may seem quite moronic, and it certainly did to Neitzsche (Brobjer, 21). As he says in his essay “On Truth and Lie in an Extra Moral Sense”: “ When someone hides something behind a bush and looks for it again in the same place and finds it there as well, there is not much to praise in such seeking and finding. Yet this is how matters stand regarding seeking and finding “truth” within the realm of reason” (Truth, 6). Nietzsche is certainly correct in his remark, the type of truth that the mathematician “discovers” when he writes down 1+2+3+ … + n = n(n+1)/2 is nothing but a tautology, the mathematician has simply expressed something in a new way, in a simpler, more “beautiful” way. But in so doing he has also increased the power and beauty producing capability of his rational faculty. The truth and the beauty in this creation lies solely in the proper relationship of the parts to the whole, in the “simplicity” and “elegance” of the result with relation to the relative “complexity” and “ugliness” of the left hand side’s unruly string of integers. The beauty lies in taking the complex into a simple form, in the creation of “complex simplicity”.
The game of the mathematician, although innocent within it’s own anthropomorphic universe causes problems when the regularities in the world are interpreted according to an anthropomorphic rational system like mathematics (Will, 337). For Nietzsche “to understand” means “to be able to express something new in the language of something old and familiar” (Will, 266). In the age of rampant scientific practice and education this form rational mathematical thought has become very familiar. Our world has come to be understood in terms of an anthropomorphic framework, and the concepts of “truth” and the “true” world are achieved “through forgetfulness” of the anthropomorphic origins (Truth, 3). Nietzsche argues that: “It is an illusion that something is known when we possess a mathematical formula for an event: it is only designated, described, nothing more!” (Will, 335). While it is certainly true that the mathematical creation of complex simplicity does help one to “understand” something, Nietzsche makes the point that this understanding is not equivalent to real knowledge as the understanding created is simply a description of anthropomorphic origin. This “illusion” of real knowledge created by mathematical beauty is extremely pervasive, and forms the foundation of the scientific concept of “truth” that Nietzsche abhors. The error occurs when the rational beauty of complex simplicity is equated with truth. Ryerson cites the two Latin Mottos: “Simplex sigillum veri – The simple is the seal of the true” and “Pulchritudo splendor veritatis - Beauty is the splendor of truth” in his discussion of the scientific concept of truth (Ryerson, 54). As the great physicist Albert Einstein once said: “If nature leads us to mathematical forms of great simplicity and beauty – by forms I am referring to coherent systems of hypotheses, axioms, etc. […] we cannot help thinking that they are “true,” that they reveal a genuine feature of nature” (Chandrasekhar, 65). Thus, when the scientist “finds” mathematical simplicity in nature, he finds this simplicity beautiful and equates it to “truth”. Thus beauty is the heart of the error.
If the scientific aesthetic is at the heart of the erroneous conceptualization of truth, then changes in the motivating aesthetic of science will lead to changes in the notions and even the types of truth found by science. As J. W. N. Sullivan said “The measure of the success of a scientific theory is, in fact, a measure of it’s aesthetic value” (Chandrasekhar, 60). According to Poincare the “the scientist does not study nature because it is useful to do so, rather the scientist studies nature because he finds beauty in it” (Chandrasekhar, 59). The scientist has equated truth and beauty and thus lets his aesthetic intuition guide his work. Hermann Weyl once said with regard to his scientific career: “ My work always tried to unite the true with the beautiful; but when I had to choose one or the other, I usually chose the beautiful” (Ryerson, 52). Thus the scientist comes to value beauty above truth. This is of course reflected in his theories of nature. As Chandrasekhar says “a theory developed by a scientist, with an exceptionally well-developed aesthetic sensibility, can turn out to be true even if, at the time of its formulation, it appeared not to be so” (Chandrasekhar, 66). This is a phenomenon of the utmost potential and danger, that “incredible fact that what the human, at its deepest and most profound, perceives as beautiful finds its realization in external nature” (Chandrasekhar, 66). The danger lies in the fact that when we forget that “all that conformity to law which impresses us so much in the movement of the stars and in chemical processes, coincides at bottom with those properties which we bring to things”, we may not realize when our aesthetic “sensibility” (i.e. “those properties which we bring to things”) is corrupt and no longer vitalizing for life (Truth, 7). However if we realize that the creative power of our aesthetic sensibility is purely anthropomorphic we can shape the way in which we understand the world and thus what we understand to be “true”.
This brings us to the second criterion discussed above for the beauty of a scientific theory, that property of “strangeness in the proportion” which seems to contradict pure rationality and which has experienced a revolution with the development of quantum mechanics. Strangeness here can be thought of as meaning “exceptional to a degree that excites wonderment and surprise” (Chandrasekhar, 70). Historically all the great theories of science certainly exhibited this property, from Copernicus to Newton, and from Maxwell to Einstein, all of their great theories of nature were truly exceptional, with “strangeness” (in that sense) to the highest degree. Einstein’s theory of relativity is exceptionally strange in this sense as it melds together with striking logical consistency and elegance concepts (time and space, matter and energy) which were before thought of as being truly independent. His equations which were arrived at “by qualitative arguments of a physical nature combined with an unerring sense for mathematical elegance and simplicity” (Chandrasekhar, 71) reveal at every turn apparent contradictions (E.g. the “twin paradox” etc.) and utterly surprising results (E.g. time dilation, space contraction, black holes etc.) which are in opposition to our everyday intuitions about the world. Yet when one looks carefully enough at the contradictions and bizarre results of the theory, the mathematics prevails to explain everything precisely. This is almost always the case with a scientific theory of this sort. One is at first struck with amazement and bewilderment with the suggestions of the theory, then after careful considerations of the mathematics which underlie the description one comes to the conclusion that it does after all “make sense” and a level of understanding is achieved. After experimental verification has erased all doubt, ones faith in the theory and the deterministic world that it describes are solidified. This type of strangeness effects one to conclude that, as Nietzsche says, “so far as we can penetrate here – from the telescopic heights to the microscopic depths – everything is secure, complete, infinite, regular, and without any gaps” (Truth, 7). The experience one feels when digesting this type of complex simplicity certainly inspires one to believe as Nietzsche did that “science will be able to dig successfully in this shaft forever, and the things that are discovered will harmonize with and not contradict each other” (Truth, 7).
But Nietzsche was wrong. The Physicists have dug deep into this pit of knowledge, and what they found smiling up at them from the depths of rationality was the uncanny monster of quantum mechanics. At the pinnacle of our rational scientific thought and observation we now have two dominant theories, both amazingly accurate in their own realm of applicability, yet both in striking contradiction to one another. Greene laments that “like the mixing of fire and gunpowder, when we try to combine quantum mechanics and general relativity, their union brings violent catastrophe” (Greene, 118). And as Greene says, this can make a physicist “deeply unsettled by the fact that the two foundational pillars of physics as we know it are at their core fundamentally incompatible” (Greene, 130). He goes on to say that “[the] equations of general relativity cannot handle the roiling frenzy of quantum foam” (Greene, 129), and that the “frenzy is the obstacle to merging general relativity and quantum mechanics” (Greene, 120). It is this “roiling frenzy of quantum foam” which sets quantum mechanics apart from classical physics, relativity included, and it is this which is so opposed to the classical scientific aesthetic.
When one considers the world view posed by quantum mechanics one is struck with a sense of a very different “aesthetic” at work. As Greene says, “if you ponder the descriptions of Einstein’s work […] with adequate intensity, you will […] recognize the inevitability of the conclusions we have drawn. Quantum mechanics is different” (Greene, 87). While still being thoroughly mathematical, the theory of quantum mechanics has produced a revolutionary aesthetic which must embrace a sense of frenzy as being fundamental to nature. For example, while relativity will attempt to tell you the exact position and velocity of a given object in space at any time given the initial conditions, the theory of quantum mechanics will tell you that you can never know the exact position and velocity of anything simultaneously, and in fact, it only describes the motion of particles in a fundamentally probabilistic way. The role of probability in quantum mechanics is central to why a new aesthetic is required in order to embrace it. While in normal life probability pops in places where it “merely reflects our incomplete knowledge” like at a roulette table or a coin toss (where if we knew the initial conditions a classical theory would, at least theoretically, yield a precise result) quantum mechanics “injects the concept of probability into the universe at a far deeper level” (Greene, 105-106). This injection of probability, implies that, for example, the best one can do when predicting the motion of an object, is to determine the chances that it will turn up here as opposed to there – it presses no necessity of action on the particle and in effect, gives the particle a “choice” as to where it would “like” to end up (Greene, 108). In short “quantum-mechanical uncertainty tells us the universe is a teeming, chaotic, frenzied arena on microscopic scales” (Greene, 120). In other words the theory is at it’s core not based on the deterministic beauty of complex simplicity, but on a concept of chaotic freedom.
This probabilistic interpretation of nature was (and is) “downright unacceptable” to many physicists who maintain a classical aesthetic sensibility (Greene, 107). Einstein was a striking example of a physicist who could simply not accept the aesthetics of quantum frenzy, saying that “God does not play dice with the universe” (Greene, 107). This is amazing coming from a man of the gymnastic mental flexibility of Einstein; here was a man who could revolutionize our conception of time and space, of matter and energy, yet was unable to accept a universe that contained “choice”, and “frenzy” because his deterministic aesthetic forbid it. Einstein, like his equations, could not handle the roiling quantum foam.
This irrational beast of quantum mechanics is perhaps not something that any rational creature can “handle” in the sense of understanding. As Richard Feynman once said: “I think I can safely say that nobody understands quantum mechanics” (Greene, 87). Greene goes on to explain that “those who use quantum mechanics find themselves following rules and formulas laid down by the “founding fathers” of the theory – calculational procedures […] – without really understanding why the procedures work or what they really mean” (Greene, 87). This unintelligibility of the theory can be understood as the inevitable result of creating a theory of nature with a foundation built on quantum foam – a “frothing, turbulent, twisted form” (Greene, 127), an “arena of the universe in which the conventional notions of left and right, back and forth, up and down (and even before and after) loose their meaning” (Greene, 129). In this uncanny arena where nothing is familiar there can certainly be no understanding in terms of Nietzsche’s sense of expressing “something new in the language of something old and familiar” (Will, 266).
An “aesthetic” sensibility capable of accepting the quantum mechanical frenzy would certainly also embrace Nietzsche’s conceptualization of knowledge and truth. According to Babette E. Babich Nietzsche “describes the ‘total character of the world’ as ‘chaos in all eternity – in the sense not of a lack of necessity but of a lack of order, arrangement, form, beauty, wisdom, and whatever other names there are for our aesthetic anthropomorphisms’” (Moore, 142). The theory of quantum mechanics certainly reflects this “chaos” in the quantum froth and represents the greatest “victory of [the] scientific method over science” (Will, 261) that we have yet seen. The very existence of the quantum froth, existing in such striking opposition to the classical conceptualizations which came before it has inspired a commonplace skepticism in science which would not have been previously acceptable. The quantum froth has effectively destroyed what Babich calls “the positivist confidence that knowledge is both possible (in theory) and attainable (in practice), that ‘all the riddles of the universe could be known and fathomed’” (Moore, 135). It has destroyed this positivist confidence because it says that fundamentally our knowledge of the universe is limited (in both theory and practice), and that the central riddle of the universe, the froth or chaos itself, is not “fathomable”. The theory has forced scientists to embrace a skeptical view which is summed up by Claude Bernard’s remark that “[those] who have an excessive faith in their ideas are not fitted to make discoveries” (Chandrasekhar, 68). The aversion to “excessive faith” has even forced some scientists to accept the anthropomorphic nature of their “discoveries” and agree with Pauli’s conclusion that “one should never declare that theses laid down by rational formulation are the only possible presuppositions of human reason” (Chandrasekhar, 67). This skepticism toward the inevitability of the rational formulations of their theories leads the scientist to the more profound and nihilistic conclusion that as Nietzsche says “this condition of existence is perhaps only accidental and perhaps in no way necessary” (Will, 273). Brian Greene expresses a similar sentiment when he says “it is possible that even more basic features of the universe […] also have a direct dependence on historical evolution – evolution that itself is contingent upon the initial conditions of the universe” (Greene, 365). This is most profoundly expressed in the concept of the “multiverse” as described by Greene as “a wildly excessive collection of universes with an insatiable appetite for variety”, with our particular universe being the way it is simply “because if they weren’t, we wouldn’t be here to notice”, in short – by accident (Greene, 368).
Yet I must complain that scientists are certainly not embracing the Nietzschean ideal of “chaos in all eternity” to the extent that Nietzsche would have hoped. For in the same breath as Greene expresses the concept of the multiverse, with all it’s “insatiable appetite for variety” he makes an appeal for physicists to “contemplate ways in which the apparent randomness of the multiverse can be tamed” (Greene, 369). It would seem that the state of affairs is not that different from Nietzsche’s times when he said that because science comes from the “intellect’s dislike of chaos” it cannot resist the urge to put “an end to the complete confusion in which things exist, by hypotheses that “explain” everything” (Will, 324). Greene and other physicists have, instead of embracing a new “aesthetic” of chaos, embarked on a epic quest to save the classical aesthetic of beauty with the creation of an exact “ultimate theory”, the ultimate expression of complex simplicity that they hope will unite relativity and quantum mechanics with a deterministic world view and explain away the quantum froth, not as fundamental to nature, but only as “apparent randomness” (Greene, 369). These scientists, though possessing an advanced level of skepticism, and the knowledge that truth may be only “metaphor” as Neitzsche advocates sill have a nauseating hope for their classical conceptualization of truth and beauty which has been so nurtured and so successful in the past. Perhaps the fundamental issue is that too much exposure to rational beauty necessitates the rational plague of “the geek” which so afflicted that great scientist Charles Darwin in his later years. He says of his disorder: “My mind seems to have become a kind of machine for grinding general laws out of large collections of facts, but why this should have caused the atrophy of that part of the brain alone on which the higher tastes [(Poetry, music etc.)] depend, I cannot conceive” (Ryerson, 56). Seen in this light, it is not surprising that the sickly scientists of the world cannot really accept as beautiful anything but rational beauty, for this would require that part of the brain so atrophied by disease. Perhaps we are asking too much of science that it should overcome its plague. Perhaps Nietzsche was right when he described science as “an intermediary station, at which the more intermediary, more multifarious, more complicated natures find their most natural discharge and satisfaction – all those who should avoid action” (Will, 325). The responsibility to advance beyond current aesthetic sensibilities would then rest on a new type of man who is immune to the plague of rationality, and who could understand the discovery of the quantum froth as a signpost for change – and then take action.
Works Cited:
Babich, Babette E. “Nietzsche’s Critique of Scientific Reason and Scientific Culture: On ‘Science as a Problem’ and Nature as Chaos” from Nietzsche and Science. Edited by Gregory Moore and Thomas H. Brobjer. Ashgate Publishing Limited. 2004
Brobjer, Thomas H. “Nietzsche’s Reading and Knowledge of Natural Science: An Overview” from Nietzsche and Science. Edited by Gregory Moore and Thomas H. Brobjer. Ashgate Publishing Limited. 2004
Chandrasekhar, S. “Beaty and the Quest for Beauty in Science” From Truth and Beauty : Aesthetics and Motivations in Science. Edited by S. Chandrasekhar. The University of Chicago. 1987.
Dostoevsky, Feodor. Crime and Punishment. Trans. Jessie Senior Coulson. W. W. Norton & Company, Inc. 1989.
Greene, Brian. The Elegant Universe : Superstrings, hidden dimensions, and the quest for the ultimate theory. First Vintage Books. 2000
Nietzsche, Frederic. “On Truth and Lies in an Extra-Moral Sense,” from The Nachlass. Trans. Walter Kaufmann & Danielle Breazeale, 1873
Nietzsche, Frederic. On the Genealogy of Morals. Trans. Walter Kaufmann and RJ Hollingdale. Random House, Inc. 1967.
Nietzsche, Frederic. The Will to Power. Trans. Walter Kaufmann. New York Random House inc. 1967.
Ryerson, Edward and Ryerson Nora. “Shakespeare, Newton, and Beethoven, or Patterns of Creativity.” From Truth and Beauty : Aesthetics and Motivations in Science. Edited by S. Chandrasekhar. The University of Chicago. 1987.
All were destined to perish , except a chosen few, a very few. […] But never, never had any men thought themselves so wise and so unshakable in the truth as those who were attacked. Never had they considered their judgments, their scientific deductions, or their moral convictions and creeds more infallible.
– From Crime and Punishment by Feodor Dostoevsky (461).
We now live in an age where there is a sense of unease with the ravenous manner in which humanity has embraced rational thought and it’s associated notion of truth. If Dostoevsky was concerned with the permeating and dominating influence of science and rational thought in 1866, if he were to look on the world today he would surely think that the apocalypse of the rational plague was upon us (461). In the world today our faith in science and the various “truths” which are produced is truly fanatic within the scientific populace. But when rational scientific thought and the effective mastery over nature that it provides have created the “comfortable” world of cell phones and overnight intercontinental flights the question arises: why exactly is this a problem? Friedrich Nietzsche comes forward with a strong answer, explaining that it is not the technology and convenience that science provides us with which is at issue, but rather that science has, through it’s evolution out of the Platonic and Christian ideals, established a “metaphysical faith” in a concept of “truth” which is anything but healthy (Genealogy, 152). According to Babette E. Babich Nietzche considered science the “technique (art) of uncovering the Platonic ideal of truth in the phenomenal world (both theoretically and experimentally)” (Babich, 147). Nietzsche asserts that faith in the Platonic ideal of truth necessitates the invention of a metaphysical faith in a “true” world as separate from “this” world, a creation that he describes as “our most dangerous attempt yet to assassinate life” (Will, 314).
These “artists” of the Platonic ideal passionately assert that their craft of mathematical and rational logic is motivated by a stimulus akin to that which compelled Michelangelo to create his great sculptures, an aesthetic ambition to create beauty (Chandrasekhar, 61). However much the scientist and artist may both lay claim to the holy grail of beauty, it cannot be argued that the essence of the beauty created and quested after in science as compared to art is vastly different. Be this as it may the scientific concept of rational or deterministic beauty has long motivated the form and character of scientific theory and thought. As such, the concept of “beauty” in science must lie at the heart of how rational thought could represent such a “dangerous attempt […] to assassinate life” (Will, 314). As Neitzsche says: “At bottom, it has been an aesthetic taste that has hindered mankind most: it believed in the picturesque effect of truth” (Will, 262). If aesthetics are the core motivator and justification for science (Chandrasekhar, 60) then any revision of the scientific aesthetic will likewise result in a revision of the types of theories that are developed and embraced. A new aesthetic steering science away from the abstract concept of the “true world” and toward an aesthetic based on revision and tumult is brooding in the depths of modern scientific theory, fighting a valiant battle against the aesthetics of the deterministic ideal.
In order to understand why scientists create the theories they do one must come to understand the nature of their motivating aesthetic. Here I will consider the concept of beauty in the most blatantly rational of the sciences - physics. As the great physicist Kepler once said “mathematics is the archetype of the beautiful” expressing the physicists obsession with mathematical beauty. In his book Truth and Beauty: Aesthetics and Motivations in Science physicist S. Chandrasekhar defines with all the shameless audacity of the scientist the concept of beauty as deriving from two major elements. The first element of beauty he has borrowed from the physicist Heisenburg, it is beauty in the mathematical sense, seen as “the proper conformity of the parts to the whole” (Chandrasekhar, 70). The second criterion of rational beauty Chandrasekhar borrows from another world class scientist Francis Bacon, which he describes as “strangeness in the proportion” (70). In order for a physical theory to be beautiful according to Chandrasekhar it must exhibit these two very different properties of “conformity of the parts” and “strangeness in proportion” (70).
The concept of proper conformity of the parts is most easily understood in the example of a mathematical theory. By its very nature mathematics consists in pure logical consistency and derives from rational thought, thus proper conformity of the parts is explicitly imposed. At every step along a derivation the mathematician takes great care to adhere to the logical axioms he has chosen to restrict his progression. He defines the entities of his world. First the “things” and the “actions”, then the mathematical “laws” of his universe are all laid down by the creativity of his mind. He then operates strictly within the “laws” he has invented to build a complex framework of theorems from the “substance” of his world. This is the game that the mathematician plays, molding from the ductile fabric of his mind, a factory of the utmost logical integrity and complexity. Defined from within in this way, his factory of truth is impervious to any exterior assault, it is in fact a thing that is “true-in-itself” (in the tautological sense).
When the mathematician builds his truth factory from the invincible mental mortar of logic, he often pauses to look back on the towering edifice that is growing beneath his feet. If he has expressed a complex set of relations in a simple way, thus increasing the efficiency of his factory construction, he thinks this is beautiful, because it allows him to create even more relations which are ever more beautiful than the first. For example the equation: 1+2+3+ … + n = n(n+1)/2 can be considered a simple yet beautiful relation. With the concept of “number” and the actions of “add” and “multiply” one can reduce the problem of adding up any number of integers no matter how large by applying the simple formula on the right. He has thus created beauty. To one unaccustomed to spending long nights manipulating mathematical equations (as Neitzsche was) this sort of beauty may seem quite moronic, and it certainly did to Neitzsche (Brobjer, 21). As he says in his essay “On Truth and Lie in an Extra Moral Sense”: “ When someone hides something behind a bush and looks for it again in the same place and finds it there as well, there is not much to praise in such seeking and finding. Yet this is how matters stand regarding seeking and finding “truth” within the realm of reason” (Truth, 6). Nietzsche is certainly correct in his remark, the type of truth that the mathematician “discovers” when he writes down 1+2+3+ … + n = n(n+1)/2 is nothing but a tautology, the mathematician has simply expressed something in a new way, in a simpler, more “beautiful” way. But in so doing he has also increased the power and beauty producing capability of his rational faculty. The truth and the beauty in this creation lies solely in the proper relationship of the parts to the whole, in the “simplicity” and “elegance” of the result with relation to the relative “complexity” and “ugliness” of the left hand side’s unruly string of integers. The beauty lies in taking the complex into a simple form, in the creation of “complex simplicity”.
The game of the mathematician, although innocent within it’s own anthropomorphic universe causes problems when the regularities in the world are interpreted according to an anthropomorphic rational system like mathematics (Will, 337). For Nietzsche “to understand” means “to be able to express something new in the language of something old and familiar” (Will, 266). In the age of rampant scientific practice and education this form rational mathematical thought has become very familiar. Our world has come to be understood in terms of an anthropomorphic framework, and the concepts of “truth” and the “true” world are achieved “through forgetfulness” of the anthropomorphic origins (Truth, 3). Nietzsche argues that: “It is an illusion that something is known when we possess a mathematical formula for an event: it is only designated, described, nothing more!” (Will, 335). While it is certainly true that the mathematical creation of complex simplicity does help one to “understand” something, Nietzsche makes the point that this understanding is not equivalent to real knowledge as the understanding created is simply a description of anthropomorphic origin. This “illusion” of real knowledge created by mathematical beauty is extremely pervasive, and forms the foundation of the scientific concept of “truth” that Nietzsche abhors. The error occurs when the rational beauty of complex simplicity is equated with truth. Ryerson cites the two Latin Mottos: “Simplex sigillum veri – The simple is the seal of the true” and “Pulchritudo splendor veritatis - Beauty is the splendor of truth” in his discussion of the scientific concept of truth (Ryerson, 54). As the great physicist Albert Einstein once said: “If nature leads us to mathematical forms of great simplicity and beauty – by forms I am referring to coherent systems of hypotheses, axioms, etc. […] we cannot help thinking that they are “true,” that they reveal a genuine feature of nature” (Chandrasekhar, 65). Thus, when the scientist “finds” mathematical simplicity in nature, he finds this simplicity beautiful and equates it to “truth”. Thus beauty is the heart of the error.
If the scientific aesthetic is at the heart of the erroneous conceptualization of truth, then changes in the motivating aesthetic of science will lead to changes in the notions and even the types of truth found by science. As J. W. N. Sullivan said “The measure of the success of a scientific theory is, in fact, a measure of it’s aesthetic value” (Chandrasekhar, 60). According to Poincare the “the scientist does not study nature because it is useful to do so, rather the scientist studies nature because he finds beauty in it” (Chandrasekhar, 59). The scientist has equated truth and beauty and thus lets his aesthetic intuition guide his work. Hermann Weyl once said with regard to his scientific career: “ My work always tried to unite the true with the beautiful; but when I had to choose one or the other, I usually chose the beautiful” (Ryerson, 52). Thus the scientist comes to value beauty above truth. This is of course reflected in his theories of nature. As Chandrasekhar says “a theory developed by a scientist, with an exceptionally well-developed aesthetic sensibility, can turn out to be true even if, at the time of its formulation, it appeared not to be so” (Chandrasekhar, 66). This is a phenomenon of the utmost potential and danger, that “incredible fact that what the human, at its deepest and most profound, perceives as beautiful finds its realization in external nature” (Chandrasekhar, 66). The danger lies in the fact that when we forget that “all that conformity to law which impresses us so much in the movement of the stars and in chemical processes, coincides at bottom with those properties which we bring to things”, we may not realize when our aesthetic “sensibility” (i.e. “those properties which we bring to things”) is corrupt and no longer vitalizing for life (Truth, 7). However if we realize that the creative power of our aesthetic sensibility is purely anthropomorphic we can shape the way in which we understand the world and thus what we understand to be “true”.
This brings us to the second criterion discussed above for the beauty of a scientific theory, that property of “strangeness in the proportion” which seems to contradict pure rationality and which has experienced a revolution with the development of quantum mechanics. Strangeness here can be thought of as meaning “exceptional to a degree that excites wonderment and surprise” (Chandrasekhar, 70). Historically all the great theories of science certainly exhibited this property, from Copernicus to Newton, and from Maxwell to Einstein, all of their great theories of nature were truly exceptional, with “strangeness” (in that sense) to the highest degree. Einstein’s theory of relativity is exceptionally strange in this sense as it melds together with striking logical consistency and elegance concepts (time and space, matter and energy) which were before thought of as being truly independent. His equations which were arrived at “by qualitative arguments of a physical nature combined with an unerring sense for mathematical elegance and simplicity” (Chandrasekhar, 71) reveal at every turn apparent contradictions (E.g. the “twin paradox” etc.) and utterly surprising results (E.g. time dilation, space contraction, black holes etc.) which are in opposition to our everyday intuitions about the world. Yet when one looks carefully enough at the contradictions and bizarre results of the theory, the mathematics prevails to explain everything precisely. This is almost always the case with a scientific theory of this sort. One is at first struck with amazement and bewilderment with the suggestions of the theory, then after careful considerations of the mathematics which underlie the description one comes to the conclusion that it does after all “make sense” and a level of understanding is achieved. After experimental verification has erased all doubt, ones faith in the theory and the deterministic world that it describes are solidified. This type of strangeness effects one to conclude that, as Nietzsche says, “so far as we can penetrate here – from the telescopic heights to the microscopic depths – everything is secure, complete, infinite, regular, and without any gaps” (Truth, 7). The experience one feels when digesting this type of complex simplicity certainly inspires one to believe as Nietzsche did that “science will be able to dig successfully in this shaft forever, and the things that are discovered will harmonize with and not contradict each other” (Truth, 7).
But Nietzsche was wrong. The Physicists have dug deep into this pit of knowledge, and what they found smiling up at them from the depths of rationality was the uncanny monster of quantum mechanics. At the pinnacle of our rational scientific thought and observation we now have two dominant theories, both amazingly accurate in their own realm of applicability, yet both in striking contradiction to one another. Greene laments that “like the mixing of fire and gunpowder, when we try to combine quantum mechanics and general relativity, their union brings violent catastrophe” (Greene, 118). And as Greene says, this can make a physicist “deeply unsettled by the fact that the two foundational pillars of physics as we know it are at their core fundamentally incompatible” (Greene, 130). He goes on to say that “[the] equations of general relativity cannot handle the roiling frenzy of quantum foam” (Greene, 129), and that the “frenzy is the obstacle to merging general relativity and quantum mechanics” (Greene, 120). It is this “roiling frenzy of quantum foam” which sets quantum mechanics apart from classical physics, relativity included, and it is this which is so opposed to the classical scientific aesthetic.
When one considers the world view posed by quantum mechanics one is struck with a sense of a very different “aesthetic” at work. As Greene says, “if you ponder the descriptions of Einstein’s work […] with adequate intensity, you will […] recognize the inevitability of the conclusions we have drawn. Quantum mechanics is different” (Greene, 87). While still being thoroughly mathematical, the theory of quantum mechanics has produced a revolutionary aesthetic which must embrace a sense of frenzy as being fundamental to nature. For example, while relativity will attempt to tell you the exact position and velocity of a given object in space at any time given the initial conditions, the theory of quantum mechanics will tell you that you can never know the exact position and velocity of anything simultaneously, and in fact, it only describes the motion of particles in a fundamentally probabilistic way. The role of probability in quantum mechanics is central to why a new aesthetic is required in order to embrace it. While in normal life probability pops in places where it “merely reflects our incomplete knowledge” like at a roulette table or a coin toss (where if we knew the initial conditions a classical theory would, at least theoretically, yield a precise result) quantum mechanics “injects the concept of probability into the universe at a far deeper level” (Greene, 105-106). This injection of probability, implies that, for example, the best one can do when predicting the motion of an object, is to determine the chances that it will turn up here as opposed to there – it presses no necessity of action on the particle and in effect, gives the particle a “choice” as to where it would “like” to end up (Greene, 108). In short “quantum-mechanical uncertainty tells us the universe is a teeming, chaotic, frenzied arena on microscopic scales” (Greene, 120). In other words the theory is at it’s core not based on the deterministic beauty of complex simplicity, but on a concept of chaotic freedom.
This probabilistic interpretation of nature was (and is) “downright unacceptable” to many physicists who maintain a classical aesthetic sensibility (Greene, 107). Einstein was a striking example of a physicist who could simply not accept the aesthetics of quantum frenzy, saying that “God does not play dice with the universe” (Greene, 107). This is amazing coming from a man of the gymnastic mental flexibility of Einstein; here was a man who could revolutionize our conception of time and space, of matter and energy, yet was unable to accept a universe that contained “choice”, and “frenzy” because his deterministic aesthetic forbid it. Einstein, like his equations, could not handle the roiling quantum foam.
This irrational beast of quantum mechanics is perhaps not something that any rational creature can “handle” in the sense of understanding. As Richard Feynman once said: “I think I can safely say that nobody understands quantum mechanics” (Greene, 87). Greene goes on to explain that “those who use quantum mechanics find themselves following rules and formulas laid down by the “founding fathers” of the theory – calculational procedures […] – without really understanding why the procedures work or what they really mean” (Greene, 87). This unintelligibility of the theory can be understood as the inevitable result of creating a theory of nature with a foundation built on quantum foam – a “frothing, turbulent, twisted form” (Greene, 127), an “arena of the universe in which the conventional notions of left and right, back and forth, up and down (and even before and after) loose their meaning” (Greene, 129). In this uncanny arena where nothing is familiar there can certainly be no understanding in terms of Nietzsche’s sense of expressing “something new in the language of something old and familiar” (Will, 266).
An “aesthetic” sensibility capable of accepting the quantum mechanical frenzy would certainly also embrace Nietzsche’s conceptualization of knowledge and truth. According to Babette E. Babich Nietzsche “describes the ‘total character of the world’ as ‘chaos in all eternity – in the sense not of a lack of necessity but of a lack of order, arrangement, form, beauty, wisdom, and whatever other names there are for our aesthetic anthropomorphisms’” (Moore, 142). The theory of quantum mechanics certainly reflects this “chaos” in the quantum froth and represents the greatest “victory of [the] scientific method over science” (Will, 261) that we have yet seen. The very existence of the quantum froth, existing in such striking opposition to the classical conceptualizations which came before it has inspired a commonplace skepticism in science which would not have been previously acceptable. The quantum froth has effectively destroyed what Babich calls “the positivist confidence that knowledge is both possible (in theory) and attainable (in practice), that ‘all the riddles of the universe could be known and fathomed’” (Moore, 135). It has destroyed this positivist confidence because it says that fundamentally our knowledge of the universe is limited (in both theory and practice), and that the central riddle of the universe, the froth or chaos itself, is not “fathomable”. The theory has forced scientists to embrace a skeptical view which is summed up by Claude Bernard’s remark that “[those] who have an excessive faith in their ideas are not fitted to make discoveries” (Chandrasekhar, 68). The aversion to “excessive faith” has even forced some scientists to accept the anthropomorphic nature of their “discoveries” and agree with Pauli’s conclusion that “one should never declare that theses laid down by rational formulation are the only possible presuppositions of human reason” (Chandrasekhar, 67). This skepticism toward the inevitability of the rational formulations of their theories leads the scientist to the more profound and nihilistic conclusion that as Nietzsche says “this condition of existence is perhaps only accidental and perhaps in no way necessary” (Will, 273). Brian Greene expresses a similar sentiment when he says “it is possible that even more basic features of the universe […] also have a direct dependence on historical evolution – evolution that itself is contingent upon the initial conditions of the universe” (Greene, 365). This is most profoundly expressed in the concept of the “multiverse” as described by Greene as “a wildly excessive collection of universes with an insatiable appetite for variety”, with our particular universe being the way it is simply “because if they weren’t, we wouldn’t be here to notice”, in short – by accident (Greene, 368).
Yet I must complain that scientists are certainly not embracing the Nietzschean ideal of “chaos in all eternity” to the extent that Nietzsche would have hoped. For in the same breath as Greene expresses the concept of the multiverse, with all it’s “insatiable appetite for variety” he makes an appeal for physicists to “contemplate ways in which the apparent randomness of the multiverse can be tamed” (Greene, 369). It would seem that the state of affairs is not that different from Nietzsche’s times when he said that because science comes from the “intellect’s dislike of chaos” it cannot resist the urge to put “an end to the complete confusion in which things exist, by hypotheses that “explain” everything” (Will, 324). Greene and other physicists have, instead of embracing a new “aesthetic” of chaos, embarked on a epic quest to save the classical aesthetic of beauty with the creation of an exact “ultimate theory”, the ultimate expression of complex simplicity that they hope will unite relativity and quantum mechanics with a deterministic world view and explain away the quantum froth, not as fundamental to nature, but only as “apparent randomness” (Greene, 369). These scientists, though possessing an advanced level of skepticism, and the knowledge that truth may be only “metaphor” as Neitzsche advocates sill have a nauseating hope for their classical conceptualization of truth and beauty which has been so nurtured and so successful in the past. Perhaps the fundamental issue is that too much exposure to rational beauty necessitates the rational plague of “the geek” which so afflicted that great scientist Charles Darwin in his later years. He says of his disorder: “My mind seems to have become a kind of machine for grinding general laws out of large collections of facts, but why this should have caused the atrophy of that part of the brain alone on which the higher tastes [(Poetry, music etc.)] depend, I cannot conceive” (Ryerson, 56). Seen in this light, it is not surprising that the sickly scientists of the world cannot really accept as beautiful anything but rational beauty, for this would require that part of the brain so atrophied by disease. Perhaps we are asking too much of science that it should overcome its plague. Perhaps Nietzsche was right when he described science as “an intermediary station, at which the more intermediary, more multifarious, more complicated natures find their most natural discharge and satisfaction – all those who should avoid action” (Will, 325). The responsibility to advance beyond current aesthetic sensibilities would then rest on a new type of man who is immune to the plague of rationality, and who could understand the discovery of the quantum froth as a signpost for change – and then take action.
Works Cited:
Babich, Babette E. “Nietzsche’s Critique of Scientific Reason and Scientific Culture: On ‘Science as a Problem’ and Nature as Chaos” from Nietzsche and Science. Edited by Gregory Moore and Thomas H. Brobjer. Ashgate Publishing Limited. 2004
Brobjer, Thomas H. “Nietzsche’s Reading and Knowledge of Natural Science: An Overview” from Nietzsche and Science. Edited by Gregory Moore and Thomas H. Brobjer. Ashgate Publishing Limited. 2004
Chandrasekhar, S. “Beaty and the Quest for Beauty in Science” From Truth and Beauty : Aesthetics and Motivations in Science. Edited by S. Chandrasekhar. The University of Chicago. 1987.
Dostoevsky, Feodor. Crime and Punishment. Trans. Jessie Senior Coulson. W. W. Norton & Company, Inc. 1989.
Greene, Brian. The Elegant Universe : Superstrings, hidden dimensions, and the quest for the ultimate theory. First Vintage Books. 2000
Nietzsche, Frederic. “On Truth and Lies in an Extra-Moral Sense,” from The Nachlass. Trans. Walter Kaufmann & Danielle Breazeale, 1873
Nietzsche, Frederic. On the Genealogy of Morals. Trans. Walter Kaufmann and RJ Hollingdale. Random House, Inc. 1967.
Nietzsche, Frederic. The Will to Power. Trans. Walter Kaufmann. New York Random House inc. 1967.
Ryerson, Edward and Ryerson Nora. “Shakespeare, Newton, and Beethoven, or Patterns of Creativity.” From Truth and Beauty : Aesthetics and Motivations in Science. Edited by S. Chandrasekhar. The University of Chicago. 1987.
