Reading “The Artist and the Mathematician” by Amir Aczel, is one of those frustrating experiences, like trying to get a decent suntan on a patchy cloudy day in Wellington. It’s the only day you’ll have free for months, and the clouds keep blocking the way, but you know the UV rays are tanning you anyway, it’s just too cold when the clouds are blocking the heat for it to be pleasant.
(BTW: it’s about the Bourbaki phenomenon in mathematics and how it influenced structuralist philosophy. But the really interesting stuff is the mathematics, and Alexandre Gröthendieck, and sadly that is not much of what the book is about. I’d like to find a good read about Gröthendieck’ s mathematics, not the guy himself, although his life is fascinating )
Actually, truth be told, I’ve read a couple of books on the topic of structuralism, and every one of them was as annoyingly vague about defining exactly what structuralism is! They beat around the topic, mentioning it’s importance in displacing existentialism as the new philosophy for the 20th century, and how structuralism eventually gave way to post-modernism, but they never actually define what it is exactly. And they talk about the influences on structuralism, which as the anthropologist Claude Levi-Strauss, the linguist Roman Jakobson and the mathematicians Bourbaki. And you just have to either give up and look up Wikipedia, or imagine they’ve defined structuralism implicitly through bulk force of examples. I guess that’s ok, but it is still frustrating, especially for someone who likes to sprint to the mint of a goal of understanding rather than jog and slog.
So in this post I’m going to tell you what structuralism is in essence in sprint fashion, and then link it to something less boring than foundational mathematics and philosophy. And to do this I am not going to consult Wikipedia. You can do that yourself. My version is a subjective impression. (So I may have left out some essential features, but too bad. I apologise in advance if I tread upon any academic toes.)
Structuralism is merely a guiding philosophy. So it can be applied to almost any intellectual endeavours. The core essence of structuralism are the principles:
(P1) Everything (objects, thoughts, ideas, … can be studied as a system comprised of component parts. Structuralism first says, “identify the system of interest and isolate it’s parts”.
(P2) To understand any phenomena (physical or intellectual), you should  find the relationships between the irreducible component parts.  Abstract away (i.e., ignore entirely) any non-essential features, such as properties that are not inherently part of the most basic structure of your system, i.e., those properties which are not connected by any relationship to the principle components your wish to study. Then,  analyse (if this is your intent) the whole system by using any and whatsoever tools you have available or can find or invent that reveal the interactions between these parts and the effect the state of the whole system has on these relationships.
(P3) To understand a system it is not necessary to break it up into the absolute minimalist parts possible, but rather to analyse it at some level of abstraction: this could be a complete reduction to atomistic parts (physicists do this), or a near reduction but only down to molecular level (chemists do this), or it could be any manner of chunking of components from chemical up to biological, or (as cosmologists prefer) stellar or galactic chunks. But structuralism applies not just to nature, the same levels of chunking can be performed on ideas, such as language, art, economic systems, religions, you name it, any system. And what isn’t a system?
To elaborate upon these core principles of structuralism I’d just add a few comments:
(1) Even a single subatomic particle is a “system”, albeit the simplest kind, one with only one component part. Having only one part merely makes structuralist study of an elementary particle pretty boring. (Only it’s not really. But that’s because quantum mechanics makes a grand ‘vacuum field’ out of all elementary particles, so it’s never just a single entity. But that’s another essay.)
(2) Examples are plenty: In Anthropology: The mathematician Andrei Weil helped Claude Levi-Strauss organise the study of kinship relations in human societies using the mathematical apparatus of Group Theory. Their data was the patterns of allowed marriages amongst Australian Aboriginal families. They ignored (abstracted away) all things like wealth and material possessions, geography, etc. In Linguistics: Jakobson and then later Chomsky and successors, have had tremendous success understanding language (origins, acquisition, learning, evolution, the whole gamut …) by abstracting away spelling and meanings and analysing using logic just the grammar or deep structure. How did they do this? Well, taking away spelling and meaning leaves you with no workable communicative language for sure, but it does leave behind a skeleton of all languages. That’s the power of structuralism. It gets rid of stuff you do not need, and leaves just the essentials, which makes analysis much easier and less clouded.
The linguists were not interested in communication you have to understand. Their goal was to understand how language is acquired and developed across human life times, and how it evolves across civilisation time frames. Since you do not need to know about the poetry and literature of a society for such studies, you can abstract out the word meanings, and just leave very abstract relations between types of words (nouns, adjectives, verbs, etc.). Worrying about lyrics and poetry is just a distraction for linguists who want to study language universals, sine anything requiring translation is not a universal. But relationships between the way a language links nouns and adjectives and verbs is something universal, or if it’s not, then there should be some deeper structure which is universal (one hopes). And indeed, that was what Chomsky discovered.
In fact, so universal were Chomsky’s discoveries about structure of languages that they even apply to computer languages! They apply to fictional languages like Klingon. And they will probably apply to extraterrestrial species languages, if we ever contact extraterrestrials.
In Economics every economist who develops a mathematical model for features of a subsystem within an economy is applying structuralism. They may not call it structuralism, but that’s what it is. It’s the same in most other sciences. In Mathematics, well, I mean mathematics itself is almost entirely structure, perhaps the purest form of structuralism known. Although pure structure does not quite define mathematics, it is a large part of what mathematics is — the particular structures of numbers and geometry and sets and categories.
Why Structuralism is Not In Vogue
The laughable thing is that structuralism is put into practise all the time, every day, by most people in most professions. This still includes artists, but most prominently it means scientists in any discipline, mathematicians (of course), politicians, business managers, sometimes lawyers (although that particular profession is a bit dark for me). There is no field of human intellectual endeavour these days that does not have professional tools that in some form or another embody the above principles of structuralism. And, of course and naturally and obviously and all those cliché’s, structuralism was practised for millennia before it ever had the label “structuralist”. The ancient Greek philosophers were structuralists, as were the ancient Egyptian linguists, as were the Stone Age artists and inventors and speakers.
So when we say structuralism is “not in vogue”, this just means it is not considered trendy in circles of philosophy where it is discussed (or used to be discussed) as a guiding principle. It’s been supplanted by post-modernism, which is less well-defined and entirely useless for doing anything actual practical and helpful in this world. So if you consider yourself a “structuralist” and feel that post-modernism is a rabbit-warren of confusing and contradictory ideas with no logical basis, then you are not alone. Maybe post-modernism has some importance to the world, but other than generating a lot of dry academic papers (and pretty much limited only to literature and philosophy journals) over the last fifty years or so, I cannot find it.
OK, I know I’m not being fair to post-modernists. But come on! What are the real fruits of post-modernist ideas? I am open to opinons, and will admit I might be wrong about post-modernisms (lack of useful impact) impact on society. If there is a good idea within it’s scope I guess the idea that human beings and our ideologies are not fixed and static, and that people with different world views do not necessarily have wrong world views, and that ambiguity and paradox are possible and signify a coexistence of differences that may have a deep hidden resolution which we are just too dumb to figure out. These are useful ideas because they give one a reason for believing in the possibility of peace.
The peace which comes from realising there are always more than two ways of seeing things, and none of them might be perfect. That’s my positive gloss on post-modernism, and if it is halfway correct and valid then let’s celebrate post-modernism. But I think the literary criticism and philosophical movements associated with post-modernism have not really contributed such positve ideas on a global reach. They should have, by my humble reading, and I’m a bit mystified why they have not been so forceful. But maybe that’s just a demonstration of my own ignorance. I’ll leave readers to comment on that (typically one doesn’t appreciate their own ignorance until informed of it by others).
Structuralism on the other hand has immediate and clear practical use and is really quite a helpful sort of way of thinking about the world, or about the part of life you are interested in. It has transcended philosophy because it is hardly discussed in philosophy any more, and yet is used by practical people every day.
My pet theory on this is that when ordinary people start to take up a branch of philosophy it starts to become boring for philosophers. Philosophers (most of them I suspect, at least those who call themselves philosophers) have some kind of built-in ego drive which forbids them from thinking of themselves as ordinary. (But, I also suspect, the very best philosophers go against this grain, and are truly humble and consider themselves as the most ordinary of people.)
But be warned. Structuralism is not everything. Plenty of stuff falls outside it’s scope. Nevertheless, it is a vastly useful philosophical method, because it is so general and has proven practical worth.
One question I am currently interested in is whether structuralism has anything to offer our understanding of spirituality. You know what I mean by spirituality? No? Well, it’s not ghosts and stuff.
Spirituality is a very natural and easily understood aspect of human existence. It means things like love, justice, honesty, compassion, kindness, wisdom (and knowledge), forgiveness, mercy, friendliness, and all such similar virtues and attributes of divinity. That’s all.
Whatever concerns these things is precisely what I refer to as spiritual reality. It’s a separate reality to physics because none of it can be reduced to physics. But it is connected to physics through the existence of sentient intelligence, like human beings. Human beings have an ability to comprehend and innately feel spiritual reality, but you cannot isolate it from human interaction and existence. Without sentient intelligence to comprehend these abstract things, there is no spirituality.
So is there structure and pattern and relation between spiritual realities?
Here’s a visual puzzle: what does the following diagram represent?
(Hint: the bite out of the apple is a misdirection. It’s nothing to do with a computer technology/company.)
I’ll leave that question hanging here for a while I think. It’s good to ponder. For a start you need to have a clear idea in your mind of what is meant by a spiritual reality, and what systems it might imply and what structure there is within those systems.
It’s a difficult area of analysis because spiritual reality is already highly abstracted. It ignores physical stuff, and concentrates our attention on the high level interactions between spiritual entities. So human beings are a physical form of spirituality. But to study spirituality we want to drop as much of our biology and physics as possible, retaining only what is minimally necessary for understanding the abstractions of love and mercy and justice et cetera.
One of the great things about this way of thinking is that “negative abstract concepts” like hate, oppression, injustice, do not have the same status as the associated positive concepts. The negatives are merely the absence of the positive. So, to take a physical analogy as illustration, darkness is the absence of light. Light (photons or electromagnetic waves) are a reality, it is stuff (structure in spacetime if you wish to know) which exists. Darkness and shadow do not have such an independent existence, they are the absence of light photons, they exist only as secondary reality, their existence depends upon the prior existence of light and an object which blocks the light and another object which receives the light and shows up the shadow.
You might disagree or find flaw in this idea, the idea that spiritual negatives are merely absences. But it does seem to pan out when you think deeply about it. Take hatred, often seen as a highly active emotion. You really hate someone (let’s say). How can this ever be interpreted as merely the absence of love for this person? Perhaps they’ve done something so horribly evil that there is simply no way you can ever find anything about them to love. So you hate them. Thinking deeply about this, really it is this persons actions or speech or other outward behaviour or appearances which you are hating. These are not the person themselves. You have no idea what is or has been going on in their head. They could be a totured psychopath. Or a deeply misunderstood person. And when you really think about it hard, you do not really hate them, but you feel incredibly sorry and sad for their condition. They become pitiful, in a very literal sense, you feel absolute pity for them. You think that their death might be the happiest thing that could happen for them (in the extreme case — I do not advocate death penalties — just the idea of their death seems like the best release for everyone, them, you, society). In any case, you find little love for this person, and in the end you pity them. Hatred was an emotion you felt along the way, but it has dissolved in the end (some people never get through to this stage and will hate for the rest of thier lives, and ironically this is in turn slightly pitiable, but I guess we can’t be judging how people feel, feelings are what they are, and I only know they can change over time). If it does dissolve, that is good I think, but it still leaves no love.
So there you have it, an absence of love, revealed, eventually, as a source of prior hatred. Because when you’ve finally reached the stage of feeling utter sorrow and sadness for someone who just cannot in any way be loved, you can only be happy and let go of your hatred if you leave the loving of this tragic person up to some higher power, some entity more capable than yourself for dispensing a measure of love. At the very least, you might be able to say that, “if this person had had more love earlier in their life then maybe I would not have ended up hating them so much.” Maybe you can’t say this, but you might be able to accept it as a possibility? You move on. Or at least, I hope you would.
The (hate)=(absence of love) example is the most extreme I could think of, so it suffices to make the point. I won’t elabrate further.
The late William Hatcher wrote about spiritual minimalism and paved the way for us. Sadly he is not with us to help continue. But I think there are some good things that can emerge from spiritual minimalism. Not the least of which is a deeper understanding of how differing human approaches to happiness and well-being are related, and how the divergent religious beliefs that co-exist in the world are distractions which hide deeper and more peaceful and enduring universals of peace and societal cohesion and unity within a greater diversity.
It is the dark/light analogy which interests me after reading Hooper Dunbar’s lectures, printed in “Forces of Our Time” (Hooper C. Dunbar, George Ronald, Oxford, 2010). The subtitle of his lectures is, “The Dynamics of Light and Darkness“, but it’s not a physics book on optics!
It is a book about the forces which shape individuals and society. By “individuals” we mean any sentient being living within a complex society. And so, when you think about it for a while, you realise these “forces” he is talking about must be abstractions of the notion of “force” borrowed form physics. So Dunbar must be using an analogy or metaphor here. And I would very much like to understand it better because I think it will add to the question (or to the answer) of how structuralism can be applied to understanding human spirituality, and thus help me to escape from the vague stuff about spirituality that comes under the heading of “New Age” or “Mystical”.
I try to avoid mysticism, since it is literally a mystery to me. But I know such things (human spirituality) is not approachable with hard sciences either, because nothing subjective can be made completely scientific. But, with some help, and with some creative analogies and metaphors, I think some structure can be found. (A very new-agey Bahá’í once suggested this was possible to me! — that was after a lecture I had given on quantum mechanics and it’s implications for the harmony of science and religion — for which I concluded there was no current analytical connection between this physics and religion, but there were a few philosophical bridges only, such as the possibility for free will in a universe with non-deterministic laws.)
The launching point I had for this essay was the following brief excerpt from Forces of Our Time (page 6.):
“Another profound and important tool for investigating spiritual reality is the awareness that spiritual truths are expressed at every level of creation. There is a crossover between truths at one level of being and those at another level of being, so that if we understand a relationship or pattern of physical reality, we will find that the same relationship exists not only in varying instances within the physical world itself but also, in a higher set of circumstances, in the spiritual realm.”
That’s pretty exciting to me. If it all pans out. But who’s to say it does? Is this guy Dunbar on to something or is this just philosophical hot air? He continues,
“Knowledge of nature and spiritual knowledge are essentially the same thing because the physical world that scientists study can be seen as an expression of spirit — as tangible reflections of spiritual truths.”
It gets a bit vague though, since the connections are tenuous. One fairly concrete analogical connection is with Love and Gravity. Gravity is the universal attractive force in the celestial sphere (the physical cosmos in other words). Love is likewise (the universal attractive force) in the spiritual sphere.
I guess my problem is that this really is only a metaphorical connection, and it can only ever be such between physical and spiritual. But let’s play with this and see where it goes. If there is anything to Dunbar’s philosophy (and as I understand it he is speaking primarily of the ideas he has borrowed from Bahá’í philosophy) then there should be a lot more structure which can be related by this primary analogy from Gravity to Love.
(That’s the puzzle solution BTW ‐ the apple was my symbol for gravity, you know … Newton and all …)
My next post, Forces In and Out of Time picks up this topic and takes it further.
Parting Thoughts of Structuralism
The irony about trying to understand the definition of structuralism is that the very idea it encapsulates is so incredibly general that it is hard to pin it down without examples, and the essence of structuralism is so simple that it hardly merits a definition. It is simply what one has to do in order to understand any system comprised of many parts. You have to break apart it’s structure (and there is often more than one way of doing so, which adds to the apparent ambiguity of the idea of structuralism) and extract the essential relationships between the parts, and forget about the non-essentials.
There is an art to this of course, since if you fail to ignore some non-essential relationship or parts, then you will have too complicated a structure which will perhaps defy or at least hinder a useful analysis.
And what is “a useful analysis”? Well, this too is frustratingly vague or too general. But I would define it as anything which helps to achieve your purposes. So first you need a purpose. If it to discover and label the underlying similarities across a vast family of languages then a useful structural analysis will consist in an abstract of language which can be shown to be an umbrella structure covering all the languages in the family. But it will be a description at a high level of types of word (a deep level correspondence), not at the word-words correspondence level itself (that’d be a machine translators purpose, and would be described as a surface level structural correspondence).
Another example: if you wished to understand how market crashes arise in economics you would not bother with the structure of prices of commodities in economics, but would instead study (probably) the interactions between agents using the pricing systems, since that is where the euphoria and panics in market bubbles and crashes happens.
OK, that’s all for now. Later I hope to write more on structure of spiritual reality, if it’s possible. It’s all unknown territory to me, so please send in any comments if you are still reading!