Tuesday, February 5, 2013

Perfume and the Pre-Socratics 7: Pythagoras and the Importance of Proportion

Pythagoras stands apart from the other pre-Socratic philosophers for having focused primarily on mathematics rather than observable phenomena to be explained in terms of other observable phenomena such as air, earth, fire, and water. In the view of Pythagoras, number is the first principle of the universe, which is ordered in a mathematical sense. The word cosmos, which means order, was first applied to the world by Pythagoras, although some of the other pre-Socratic philosophers are now referred to as cosmologists and regarded as the earliest scientists in human history.

The colony founded by Pythagoras is sometimes characterized as having been a religious cult of sorts, yet his prodigious contributions to the history of mathematics are beyond dispute and have to a large extent saved his legacy. Every child learns the Pythagorean theorem in grade school:

a2 + b2 = c2

The sum of the square of each of the two sides of a right triangle is equal to the square of its hypotenuse.

Pythagoras was essentially the founder of the discipline of mathematics. In his view, embraced still today by modern thinkers, numbers reflect structures in the universe, beginning with 0, 1, 2, and 3, corresponding to the zero-dimensional point, the one-dimensional line, the two-dimensional plane, and the three-dimensional volume of space. Later mathematicians have worked in many more dimensions, but everything started back in ancient times with this man in awe of the mathematical beauty inherent in the universe.

Unlike Parmenides, whose contribution, that “All is one,” may escape attention by the vast majority of humanity past, present, and future, Pythagoras provided us with the foundations of all modern applied science and physics.

Many people dislike mathematics, or at least they claim to dislike mathematics. In truth, they appear not to understand mathematics. It was never presented to them in the proper way and from the proper perspective. They were forced by martinet schoolmarms to memorize the principles of mathematics rather than being taught how to deduce them.

As a result, mathematics remains for such people an arcane, inaccessible, and even painful subject. Because physics is the most directly mathematical of the sciences, requiring the use of many abstract formulas and mathematical concepts, it, too, has left many people with bad memories. Organic chemistry is another case where the logic of the theory must be understood in order to achieve an understanding of the profound beauty which it embodies.

It is unfortunate that many teachers of these subjects either do not themselves grasp the essential logic involved or else they are for some reason unable to communicate it to their students. The truth is that mathematics exhibits a profound beauty in its aesthetic simplicity and symmetry, as do the more theoretical of the sciences.

To see the patterns of mathematics in these disciplines requires that one ascend above the formulas to the spheres from which they derive, and this was naturally Pythagoras' strong suit. Among the theories devised by human beings, mathematics offers the one source of and glimpse into eternity, because nothing that happens on the planet which we happen by chance to inhabit will ever change the truths of mathematics.

Psychologists have discovered correlations between mathematical and musical ability, and not without reason: all of music is grounded in the proportions of mathematics. In this way the beauty of mathematics is inherent to that of music. Most people never study music seriously and have no idea why the compositions of J.S. Bach are perfect or what is meant when someone makes this claim, which may strike them as the ravings of a zealot. People who have never studied and played an instrument may enjoy music in a superficial way, but they will never be able fully to grasp the highest pleasure of musical art, to participate directly in its production, which can be likened to traveling to another sphere of reality.

Is there a parallel mathematical universe, where musicians and physicists interact? In a sense, yes. They are privy to secrets to which most people have no access. Plato, who arrived on the scene in ancient Greece a bit later than Pythagoras, attempted to capture the distinction between mundane appearance and eternal truth with his theory of the Forms and the Allegory of the Cave, to which, he claimed, most people are effectively chained. We remain mired in delusion and tricked by images cast on the wall by politicians and other shucksters who wield flickering candles to persuade us to believe in their opportunistic lies. Plato's Allegory of the Cave has never been more relevant than today, as images and packaging have come to take precedence over content in the internet age.

Plato was influenced by all of the pre-Socratic philosophers in one way or another, but his metaphysics reflects a belief in truth and and beauty clearly captured by the Pythagorean world view. The realm of knowledge is separate from the realm of opinion or mere belief, which is a fluctuating sea of ideas deriving from the contingent ephemera of the perceived world. Beyond the realm of the senses lies the realm of truth. This is the insight of Pythagoras which explains the magical effect of music and also the more mathematical sciences, at least to their practitioners.

It is probably worth observing here that in the worldview of Plato and some of his pals, art and beauty are not at all the same thing, despite the common tendency on the part of modern people to conflate them. Plato disliked poets because he thought of them as deceivers or even liars. Beauty and Truth are absolute and immutable Forms in which both instrumental music and perfume would seem to be able to participate because they cannot “lie”. Why? Because they are non-representational and therefore have no propositional content

All of this poses problems for people who erroneously conflate beauty and art. The two are conceptually distinct. A naturally existing canyon is beautiful. When Christo “wraps” it, he thereby creates a work of art—one which many local residents may regard as ugly. We shall return to the important distinctions between art and beauty, art and design, and truth and artifice, in future episodes of the History of Philosophy Refracted through Perfume.

Valley Curtain, 1970-2
by Christo and Jeanne-Claude

The Pythagorean-Perfume Connection

As we have seen in the other theories of pre-Socratic philosophers, perfume has been omitted or deleted from the version of the story to survive. It might seem that since the world of mathematics is divorced form the senses and the world of perfume is intimately connected to sense perception, that the two do not intersect.

By that argument, however, it should follow that because we apprehend music through our ears, therefore, it can have nothing to do with the eternal realm of mathematical truth. These misunderstandings arise when we make the same mistake as the schoolteacher who forces his students to memorize mathematical formulas rather than teaching them how to deduce them from first principles.

Most people wear perfume in the way in which they listen to music and balance their checkbook. They use perfume functionally, just as they use music for entertainment and numbers for the math needed to accomplish this or that task. Music is there in the world and they hear it, and perfume is there in the world, so they use it, But their limited appreciation of perfume's beauty is similar to the person who enjoys the chirping of birds or the sound of rain in the springtime. It's there, and they notice it, and it gives them pleasure, but that's where their understanding ends.

There is more to perfume than just the superficial scent, just as there is more to music than the sound waves by which we apprehend it. Pythagoras, as a master of mathematics, no doubt appreciated perfume as well, having recognized that the mathematical proportions so crucial to music are equally important to perfume.

Any professional perfumer will aver that the distinction between a masterpiece and a disaster may lie only in the proportions used. The ingredients of a perfume are obviously very important, but even more important, once the basic shape and demeanor of the perfume have been determined, are the precise proportions of the various components used. We laypersons might consider a comparison in the case of cooking: a dash of salt may perfect a batch of carrot ginger soup. A spoonful may ruin it by rendering it inedible.

Lists of notes are only the most basic way of approaching perfume. The experience of perfume is subjective and intimate, and the joy of perfume is found at the first level in the judicious proportions of ingredients combined by a skilled perfumer. But the perceiver contributes to the creation as well, just as the beauty of a poem emerges only upon its conscious appreciation by an interpreter. Poetry, too, pace Plato, exhibits mathematical proportions of cadence and rhythm, in addition to the use of colorful metaphors to produce something far more valuable than the sum of the letters used to write it.

Pythagoras no doubt recognized that perfume, like music and poetry, offers a transcendent glimpse into the only certainty in the universe: mathematics. The heavens may fall, but the truth will persist. The truth is unassailable. Behind all of the deceptive techniques used to market fragrances in the modern world, there is a reality. Not all that glitters is gold, and hidden treasures are out there, ready to be found by those who do not allow themselves to be distracted by all of the hype and folderol and focus instead upon the quality of the perfumes which they seek out and test.

We may disagree about which precise perfumes achieve a transcendent level of beauty, but that is because we perceive them from our own peculiar and idiosyncratic starting points, which are determined not only by our biological constitution, but also all of our past experiences and memories. Just as people exhibit various degrees of awareness about other aspects of reality, we should expect them to disagree, too, when it comes to perfume. We are all on a journey, and while our perceptions may sometimes coincide, often they do not.

The music of the spheres is ringing in the background, beckoning us to seek out the truth by whatever means available to us. We are fortunate to be among the select few to have access to perfume, through which we are able to travel to an olfactory universe unknown to the vast majority of humanity but nonetheless real.


  1. Bravo, sherapop! You somehow made me somewhat interested in math. :P

    1. Hello, Hayven, and thanks for your comment!

      I'm happy that you are ready to give math another chance, even if only "somehow" and "somewhat" ! ;-)

  2. I don't think one can measure talent or beauty with mathematics. There were numerous examples of the purfect from the composition or technique point but completely soulless poetry or painting peaces. Yes, a wrong proportion can kill an otherwise great composition.But there is no formula to the right proportion. At least for natural ingredients: those differ not only from region to region but also from one year to another.

    Also, you need some knowledge to apreciate something that you don't like naturally; but if something moves you - be that music, sound of an ocean or a perfume - do you really need to know anything else?

    1. Dear Undina,

      It's so nice to read you here! Perhaps in honor of you and Rusty I should post a fresh image of HRH Emperor Oliver...

      Yes, you are right: proportion is necessary but not sufficient. Recipes alone don't seem to work. Not only because natural ingredients vary from year to year, but also because one needs inspiration. How many soulless perfumes have been composed using top-notch ingredients carefully combined? I'd venture to say: many!

      Above I was suggesting only that those who miss the beauty in mathematics fail to see the crystalline symmetries and that the people who love mathematics do appreciate them. I did not mean to suggest that right proportion is the *only* reason why a perfume is beautiful, just that without it, it will not be beautiful and may even be a mess. It's really a very abstract concept, though, and cannot be quantified in any simplistic way.

      As you say: "there is no formula to the right proportion." In the case of perfume, the situation is inordinately complex because of different people's variable sensitivities to all of the various components. That's just one of the reasons why "one perfumista's treasure is another one's trash"... Another reason is of course fundamental difference in taste.

      I also agree with you about the fact that we may intuitively sense that something is wonderful without learning more about the theory. I play the piano and really never connected music theory with my own performance experience. To me, they are completely different things. I do believe, however, that we may intuit the symmetries and proportions, even if we are unable to articulate them—or simply prefer not to.

      I find that playing the piano is a completely different experience from examining the score. Perhaps I could compare the distinction to writing versus editing. They involve very different skills and are quite different modes of experience, even though both involve text. In writing, one produces text. In editing, one attempts to refine it. These are distinct modes of consciousness, in my experience, although it is true that while writing may one see fit to edit and suddenly switch out of writing mode. The disanalogy is that in performing music one cannot suddenly "switch gears" without disrupting the performance! Of course, in a practice room one can do that...

      Your final question, "do you really need to know anything else?" seems like a version of "I know what I like", and I definitely believe that such a maxim applies in the case of perfume. It does not matter who else in the universe exalts or scorns a perfume beloved to us. If we love it, then we love it. That's all that matters!

      Thank you so much for raising these questions, Undina!

  3. *waves HELLO : *

    <--- knows zilch about math but love to see this post as I do love symmetry ;)

    Just wanted to let you know I read here... not always respond....
    but still greatly appreciated your word wizardry <3


    1. Thank you, Guusje! Very nice to see you here! I know how busy you are these days... ;-)


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