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From The Number’s Game: the commonsense guide to understanding numbers in the news, in politics and life, by Michael Blastland and Andrew Dilnot; on wealth and averages:

A Dutch economist, Jan Pen, famously imagined a procession of the worlds population where people were as tall as they were rich, everyone’s height proportional to their wealth (note wealth, not income). A person of average wealth would be of average height. The procession starts with the poorest (and shortest) person first and ends, one hour later, with the richest (and tallest). Not until twenty minutes into the procession do we see anyone at all. So far, they’ve had either negative net worth (owing more than they own) or no wealth at all, and so have no height. It’s a full thirty minutes before we begin to see dwarfs about six inches tall. And the dwarfs keep coming. It is not until forty-eight minutes have passed that we see the first person of average height and average wealth, when more than three quarters of the world’s population has already gone by.

What delays the average so long after the majority have passed? The answer lies in the effect of those who come next. “In the last few minutes,” wrote Pen, “giants loom up… a lawyer, not exceptionally succesful, eighteen feet tall.” As the hour approaches, the very last people in the procession are so tall we can’t see their heads. Last of all, sid Pen (at a time before the fully formed fortunes of Bill Gates and Warren Buffett), we se John Paul Getty. His height is breathtaking, perhaps ten miles, perhaps twice as much.

One millionaire can shift the average more than many hundreds of poor people, one billionaire a thousand times more. They have not this effect to the extent that 80 percent of the world’s population has less than average.

In everyday speech, “average” is a word meaning low or disdained. With incomes, the average is high. The colloquial use, being blunt, thoughtless, and bordering on a term of abuse, distorts the statistical one, which might, according to the distribution, be high, or low, or in the middle, or altogether irrelevant. It is worth knowing which. If only one thought survives about averages, let it be that they are not necessarily anywhere near the middle, nor representative of what’s typical, and that places often called “the middle” by politicians or the media may be far removed. These ideas have been lazily hitched together for too long. It is time for a divorce.

A more narrative explanation is available from The Atlantic.

From “Typologies, taxonomies, and the benefits of policy classification” by Kevin B. Smith (Policy Studies Journal, Sep 2002):

There are two basic approaches to classification. The first is typology, which conceptually separates a given set of items multidimensionally… The key characteristic of a typology is that its dimensions represent concepts rather than empirical cases. The dimensions are based on the notion of an ideal type, a mental construct that deliberately accentuates certain characteristics and not necessarily something that is found in empirical reality (Weber, 1949). As such, typologies create useful heuristics and provide a systematic basis for comparison. Their central drawbacks are categories that are neither exhaustive nor mutually exclusive, are often based on arbitrary or ad hoc criteria, are descriptive rather than explanatory or predictive, and are frequently subject to the problem of reification (Bailey, 1994).

A second approach to classification is taxonomy. Taxonomies differ from typologies in that they classify items on the basis of empirically observable and measurable characteristics (Bailey, 1994, p. 6). Although associated more with the biological than the social sciences (Sokal & Sneath, 1964), taxonomic methods–essentially a family of methods generically referred to as cluster analysis–are usefully employed in numerous disciplines that face the need for classification schemes (Lorr, 1983; Mezzich & Solomon, 1980).

The article then goes on to explain the difficulty of applying the more strict taxonomic classifications to, in this case, policy:

…the empirical qualities of many policies are not immediately apparent. Scholars such as Steinberger (1980), T. A. Smith (1982), and, especially, Schneider and Ingram (1997) make a persuasive case that the very concept of a policy category is a social construction, something rooted in individual perceptions. What distinguishes a redistributive from a regulatory policy is an individual judgment, not an observable, policy-specific equivalent to height or length. This argument is at the heart of critiques of Lowi’s work, and it creates obvious difficulties in making the shift from a typology to a taxonomy.

I also like this lecture outline from a University of Illinois at Urbana Champaign entitled “What Isn’t in a Name?: Terminological Misapprehensions Between 20th-Century Linguistics” that explains why the terms “taxonomy” and “typology” are not unbiasedly embraced:

II. CASE-STUDY 1: TYPOLOGY vs. TAXONOMY — positively- vs. negatively- valued by linguists; negatively- vs. positively-valued by biologists

1. Typology as a laudable goal in linguistics:

a. From the Research Centre for Linguistic Typology (RCLT, La Trobe University) mission statement: “putting forward inductive generalisations about human language”.

b. From Association for Linguistic Typology mission statement: “the scientific study of … cross-linguistic diversity and the patterns underlying it”.

c. Existence of societies like the Association for Linguistic Typology, journals like Linguistic Typology or Sprachtypologie und Universalienforschung, and research centers devoted to typology (RCLT, some of the Max Planck institutes (e.g., at Nijmegen and at Leipzig), etc.)

2. Typology as a tainted term (and concept) in modern biology.

a. In most 20th- (and 21st-) century biology, typology invokes the typological species-concept, an essentialist notion that, along with many other scholars, Mayr (1982) holds responsible for delaying the proposal, defence, and acceptance of legitimate evolutionary ideas prior to Darwin’s 1859 Origin of Species.

b. Mayr 1982:256: In “the essentialist species-concept, … each species is characterized by its unchanging essense (eidos) and separated from all other species by a sharp discontinuity. Essentialism assumes that the diversity of inaminate as well as of organic nature is the reflection of a limited number of unchanging universals (…[cf.] Hull 1975). This concept ultimately goes back to Plato’s concept of the eidos, and this is what later authors had in mind when they spoke of the essence, or ‘nature’, of some object or organism. All those objects [that] belong to the same species … share the same essence”.

c. The link from essence to type is made as follows; cf. Mayr 1982: 256: “The presence of the same essence is inferred on the basis of similarity. Species, thus, were [once] simply defined as groups of similar individuals that are different from individals belonging to other species. Species, thus conceived, represent different ‘types’ of organisms. Individuals… do not stand in any special relation to each other; they are merely expressions of the same eidos. Variation is the result of imperfect manifestations of the eidos”.

3. Taxonomy/taxonomic as a frequent term of reprobation in linguistics.

a. Recall Chomsky’s 1962, 1964 attacks on Post-Bloomfieldian American structuralist phonemics as involving, not (usually) the classical or autonomous phonemic level, but the taxonomic phonemic level. Here, the intended criticism is rather explicit.

b. Only implicit, though, are criticisms like those that we both heard from our own (ca. 1975) linguistics-professors, exhorting us not to act like Post-Bloomfieldian American structuralists; e.g.: “Make generalizations going beyond the original set of facts that you were given; don’t just rearrange the data!” — recall that Greek taxo-nom-ía originally involved, literally speaking, the ‘arrangement-law…’, or ‘law of arrangement…’….

4. Yet taxonomy has long been an extremely positive term in modern biology (and the one positively evaluated use of type in biology involves type specimens, which are employed taxonomically!).

a. Taxonomy is often employed synonymously (e.g., by Mayr) with systematics (and/or classification): “The terms systematics and taxonomy are considered by me as approximately synonymous…[; i]n America…[,] the term taxonomy seems to be preferred…[; i]n the rest of the world…[,] the term systematics seems to be more
widely used” (Mayr 1942/1982: 6n.1).

b. And, as for the importance of systematics: “It is the basic task of the systematist to break up the almost unlimited and confusing diversity of individuals in nature into easily recognizable groups, to work out the significant characters of these units, and to find constant differences between similar ones. Furthermore, [(s)]he must provide these units with ‘scientific’ names which will facilitate their subsequent recognition by workers throughout the world…. Even this ‘lowest’ task of the systematist is of tremendous scientific importance. The entire geological chronology hinges on the correct identification of the fossil key species. No scientific ecological survey should be carried out without the most painstaking identification of all the species of ecological significance. Even the experimental biologist has learned to appreciate the necessity for sound, solid identification work” (Mayr 1942/1982: 9).

From Zen and the Art of Postmodern Philosophy by Carl Olsen (I added paragraph breaks):

Within the context of postmodern art, Mark C. Taylor identifies, for instance, two processes at work: disfiguring and cleaving. These two operations are identified by Taylor in his attempt to grasp the chora, a nonexistent that stands behind being and becoming, makes possible all existences, and forms the essential space where both form and copy are inscribed.

The operation of disfiguring is connected to activities like marring, destroying, deforming and defacing in a process of negation or deprivation that also includes the negation of the notions of calculating, considering, and comprehending. By enacting denegation in the realm of form, the process of disfiguring interweaves revelation and concealment and presences and absence which allows for “both a re-presentation and a de-presentation.” If the artist removes, deforms, or defaces a figure and destroys its beauty, he/she leaves a trace of something that is other, which is itself neither being nor nonbeing, present or absent, immanent nor transcendent.

Associated with the notion of disfiguring is that of cleaving, which suggests both dividing and joining as well as separating and uniting. Cleaving is an operation that allows opposites to emerge and remain suspended in a process that is unthinkable and beyond the distinction of identity and difference.

The dual processes of disfiguring and cleaving are indicative that there can be nothing original from the postmodern perspective because such operations render everything secondary due to the tendency of the postmodern artist to disjoin, fragment, distort, and partially destroy a work of art in order to figure what cannot be figured.

In comparison:

In contrast to a postmodern deconstruction of drawing or consideration of the nature of art in the postmodern era, Dōgen quotes a saying by the Ch’an Master Hsing-yen (Japanese: Kyōgen Shikan): “A painting of a rice cake cannot satisfy hunger.” Many different kinds of people have diligently studied this saying without arriving at an useful understanding of its meaning. Like a similar saying, it is a mere clever expression and possesses no viable relationship to our real experience. To this puzzling statement, Dōgen offers his own interpretation: “The painting of a rice cake can be said to be everything: [Buddhas, sentient beings, illusion, enlightenment]. A rice cake, made from glutinous rice, represents both transitory and unchanging life. The painting of a rice cake actually symbolizes detachment, and we should not think about coming or going, permanence or impermanence when we look at it.” Dōgen offers an nondual interpretation of the saying; he denies the common view that a painting is unreal while the rice cake is real. The painting of the rice cake is not different from the various forms of existence. In other words, an actual rice cake is not different from a painting of a rice cake. Dōgen warns: “Do not try to find a real rice cake outside of the painting, if you do not know what the painting signifies.” From Dogan’s perspective, the painting may or may not appear in its true form: “The true meaning of a painting of a rice cake transcends the distinction of past and present, or birth and destruction.”

Dōgen further develops his interpretation of the painting of the rice cake by discussing unsatisfied hunger, which symbolizes the illusion of sentient beings for Dōgen. Hunger is used as a metaphor and/or symbol by Dōgen to illustrate the condition of illusion. By becoming detached from the opposites of enlightenment and illusion, a person loses his/her hunger. Dōgen indicates the nondualism of his position in the following way: “In reality there is no hunger of rice cake conflicting with each other, but when you think you are hungry the entire world becomes hungry; conversely, if there is a real rice cake it exists everywhere!” Prom this viewpoint, since an eatable rice cake and a pictorial representation of a consumable rice cake are both empty, either one can satisfy a person’s hunger, and are examples of ultimate reality in diverse forms. Moreover, an insightful observer of a painting can see, for instance, both movement and inertia, the way of practice, truth of the Buddha’s teaching and of the painting itself, the entire universe is manifested in the painting, and one can find one’s true self in the painting. Therefore, viewing a painting possesses the potential to lead one to an awakening, which functions to actualize the painting.” Thus a painting, from Dōgen’s perspective, can satisfy one’s hunger.

In other words, by intuiting mediation one can transcend it. But in conclusion:

In comparison to Taylor’s notions of disfiguring and cleaving and his emphasis on the surface of a work of art, Dōgen grasps a depth and mysteriousness (yūgen) to a work of art, whereas Taylor seems content with initiating a nonstop dialectic that gives birth to a double negation, a negation of negation. Dōgen and Taylor agree that we exist in a world of flux, although Taylor disagrees with Dōgen that we can catch a glimpse of the eternal in the world of flux. Rather than disfiguring or cleaving a work of art, Dōgen lets it be itself and does not seek to mark or spoil it in any way.

I’ve already posted the cake recipe from PopCo—a great novel by Alice Butler—so here another part of the back matter: a table of the frequency of occurrence of letters in English from Fletcher Pratt’s Secret and Urgent: the story of codes and ciphers, Blue Ribbon Books, 1939. To be fair, the table above is actually from the only place I could find it on the internet: a 1997 patent for a chordic keyboard who cites “Pratt Fetcher”.

Fletcher Pratt also established a dining club upon which Asimov’s Black Widowers series was based.

Update: Apparently the numbers above are different than what was published in PopCo:

I was really proud of myself last week when I made what I felt was a valid and illuminating numerical comparison: I wrote that the amount of Broadband Stimulus money requested for projects within the state of Alaska—projects serving rural and underserved communities—was on a per-capita basis about equal to the federal poverty level for a 2-person household. For those of us who work on access and inclusion (and even those that don’t), that’s a much more meaningful statement than writing “about $15,000″.

I have a degree in math, but at the post-calculus level numbers serve little specialized purpose other than to check your work. One of the professors I now work beside, Marilyn Frankenstein, teaches how to make numbers relevant and meaningful by contextualizing them. She does her studies integrating mathematics and numerical literacy into social justice work (I do work within the College of Public and Community Service, after all), which all falls under Radical Math (which is a funny name if you find math funny).

That all being said, you shouldn’t provide a number without a reason. And since you’re providing the number for a reason, that reason should be apparent. If you expect someone to think “That’s a really big number” you should tell them it’s a really big number and help them understand just how big it is. A number without meaning is just data, and data is boring. If you’re giving someone data and expecting it to have meaning you’re making someone else do extra work by analyzing that data and coming to the conclusion you already have: the reason you thought the number was important in the first place.

The problem with numbers is that within the sphere of other numbers, there isn’t any reference points (other than perhaps zero). And there are a lot of them. More than you can count (hah!).

The problem with people is that we can only remember 3 or 4 things at a time. This means that we tend to bunch the infinite space of numbers into a very small number of groups: nothing, a little, a bunch, and a whole heck of a lot. The way we group things is not by some property of the number itself, but rather by the context it’s given in. By contextualizing numbers and giving them meaning, you move them from data (boring!) to useable information: it is not the numbers themselves that will stick with us, but the meaning they represent.

To show this, I made up 2 different surveys and sent them to my friends on Facebook and whoever happens to follow me on Twitter. In the first survey I asked people to place someone who makes $1 Million/year and someone who makes $1 Billion/year on a 10 point scale of Poor to Rich. Nearly all responses placed $1 Million/year between 7 and 10; and placed $1 Billion/year between 8 and 10; both very Rich. Nearly half of the responses placed both incomes as equivalent at a 10: the mostest richest.

I admit that many of my friends are Americorps alums, nonprofitty folks and other liberal ilk, but the point I want to make is that there isn’t a whole lot of difference, within the context of rich and poor, between someone who makes $1 Million/year and someone who makes $1 Billion/year. Myself, I split incomes into about 5 different levels:

• less than $12k/year: been there, done that
• $12k – $30k/year: limited fun
• $30k – $50k/year: the expected earnings potential for my career trajectory
• $50k-$100k: The job of my dreams and/or did I just go corporate?
• $100k+: Cloud 9

Now I didn’t ask people specifically about themselves, but there are a few things to notice using myself as an example. There are only a few levels (I condensed 100,000 whole numbers into just 4 groups, plus a 5th group for everything else) and there are more groups for smaller numbers than there are for larger numbers (it’s logarithmic-ish: the group sizes are 12, 18, 20, 50, infinity). Also, the numbers are in relation to what I know: what I’m making right now is in the middle and there are 2 groups above and 2 groups below.

So on to the 2nd survey: I asked people where the number 1 Million would fall on a number line between 0 and 1 Billion. This is actually a pretty  typical “aha!” classroom example and a good number of people got it right (many of my friends are also nerds). What’s interesting is the 25% percent of people (1 out of 4) who got it wrong; they chose 3, 5 or 7: exactly where you would divide a 10 point scale into quarters or maybe a few did it by thirds. That’s the expected thing to do if you don’t know this particular trick (and is also a good strategy in Trivial Pursuit).

So what’s the answer? On a 10 point scale, the answer is actually zero, but since that wasn’t an option in my survey, the most correct answer was 1.

The number 1 Billion is 1,000 times larger than the number 1 Million: and 1,000 still is a big number (hilariously, large numbers are made up of many zeros). Compared to 1 Billion, the number 1 Million is rather pale and insignificant….

…unless you’re talking about something meaningful like someone’s salary. In which case, they’re very much the same.

And if you place them in terms of money that’s been wasted through fraud, for example, then the differences should be made apparent because as I’ve shown adding a bunch of zeros just won’t do it on their own.

When numbers are placed in context to things we know and have experience with, they take on actual meaning. This is from the Pew Research Center’s Excellence in Journalism Project’s Principles of Journalism:

7. IT MUST STRIVE TO MAKE THE SIGNIFICANT INTERESTING AND RELEVANT

Journalism is storytelling with a purpose. It should do more than gather an audience or catalogue the important. For its own survival, it must balance what readers know they want with what they cannot anticipate but need. In short, it must strive to make the significant interesting and relevant. The effectiveness of a piece of journalism is measured both by how much a work engages its audience and enlightens it. This means journalists must continually ask what information has most value to citizens and in what form. While journalism should reach beyond such topics as government and public safety, a journalism overwhelmed by trivia and false significance ultimately engenders a trivial society.

I’m not saying we all should strive to be journalists, but I think we should strive to make the significant interesting and relevant. To be fair, false significance can be a powerful rhetorical device when it comes to numbers: just watch your evening news the next time they breathlessly “break” a story about public employees making “gasp!” $60k/year. “How dare they make twice the local average income level?!” …because that’s how averages work.

Another example: in my last post about doing the layout for Survival News (“the voices of low income women”), I noted that if the newspapers in circulation were spread out, they would completely cover the John Hancock Building in Boston up to its 20th floor. That’s much more fun and meaningful than only writing “4,000 copies” (the building has already been covered with plywood, so why not?).

And now to the entire reason I wrote this post: I would like to point out that at 40 tabloid-sized pages, the latest edition of Survival News has 52 square feet of copy and graphics: that’s about the same surface area as your refrigerator.

From Jacques Racière’s The Future of the Image (translated by Gregory Elliot):

The imprint of the thing, the naked identity of its alterity in place of its imitation, the wordless, senseless materiality of the visible instead of the figures of discourse–this is what is demanded by the contemporary celebration of the image or its nostalgic evocation: an immanent transcendence, a glorious essence of the image guaranteed by the very mode of its material production. Doubtless no one has expressed this view better than the Barthes of Camera Lucida, a work that ironically has become the bible of those who wish to think about photographic art, whereas it aims to show that photography is not an art. Against the dispersive multiplicity of the operations of art and games of signification, Barthes wants to assert the immediate alterity of the image—that is, in the strictest sense, the alterity of the One. He wants to establish a direct relationship between the indexical nature of the photographic image and the material way it affects us: the punctum, the immediate pathetic effect that he contrasts with the studium, or the information transmitted by the photograph and the meanings it receives. The studium makes the photograph a material to be decoded and explained. The punctum immediately strikes us with the affective power of the that was: that —i.e. the entity which was unquestionably in front of the aperture of the camera obscura, whose body has emitted radiation, captured and registered by the black chamber, which affects us here and now through the ‘carnal medium’ of light ‘like the delayed rays of a star.

Fortunately, Racière repudiates a hierarchical distinction:

…the semiologist who read the encoded message of images and the theoretician of the punctum of the wordless image base themselves on the same principle: a principle of reversible equivalence between the silence of images and what they say. The former demonstrated that the image was in fact a vehicle for a silent discourse which endeavored to translate into sentences. The latter tells us that the image speaks to us precisely when it is silent, when it no longer transmits any message to us. Both conceive the image as speech which holds its tongue. The former mad its silence speak; the latter makes this silence the abolition of all chatter. But both play on the same inter-convertibility between two potentialities of the image: the image as raw, material presence and the image as discourse encoding a history.

From “Business of Design”, a section of David Barringer’s excellent book There’s nothing funny about design:

Definitions

Quality of life depends on quality of mind, which depends on quality of language. Heightened experience requires both practiced sensory perception and the vocabulary with which to render its significance to yourself and others.

To convey impressions of your own experience to others, you are often bound to language as the flatbed truck for that conveyance, even when your experience is not linguistic or textual but visual, auditory, tactile, and olfactory.

To savor experience you must define experience, and definitions involve the abuse of words.

It is for future designers to convey odors that summarize a poem, sounds that describe the texture of a touch, and images that define an odor.

To enhance your perception, you must exercise your imagination. Expand the control room of your mind to include maps of the surrounding dimensions of experience, as measured and reduced by sight, sound smell, touch, etc. Construct these maps in leisure, with fine concentration, to guide your judgments in times of haste and fury.

I love that first paragraph for its similarity to previous musings on self, language and consciousness.

Apparently conservatives have a new statement named for Mount Vernon, George Washington’s home. The new Mount Vernon Statement is modeled on the 1960s conservative Sharon Statement (named for William F. Buckley’s home), though it’s slightly ironic considering the Sharon Statement was quite firm on state’s rights and Washington was a Federalist. From comparing the statements, it appears that the conservatives have made their peace with the Federal government:

Mount Vernon Statement:

The conservatism of the Constitution limits government’s powers but ensures that government performs its proper job effectively. It refines popular will through the filter of representation. It provides checks and balances through the several branches of government and a federal republic.

Sharon Statement:

THAT the genius of the Constitution – the division of powers – is summed up in the clause that reserves primacy to the several states, or to the people in those spheres not specifically delegated to the Federal government;

And of course we need to compare that to the liberal Port Huron Statement (named for the SDS conference where it was written):

How shall the “public sector” be made public, and not the arena of a ruling bureaucracy of “public servants”? By steadfast opposition to bureaucratic coagulation, and to definitions of human needs according to problems easiest for computers to solve. Second, the bureaucratic pileups must be at least minimized by local, regional, and national economic planning — responding to the interconnection of public problems by comprehensive programs of solution. Third, and most important, by experiments in decentralization, based on the vision of man as master of his machines and his society.

In both style and content, the Mount Vernon Statement is much closer to the lefty Port Huron Statement than the Sharon Statement. Today’s conservatives are about “recommitment” and “natural fusion”; they ask rhetorical questions (“Isn’t this idea of change an empty promise or even a dangerous deception?”); and feel the need to buttress arguments by appealing to the authority of our founders: “The self-evident truths of 1776 have been supplanted by the notion that no such truths exist.”

Those kids in the 60s were a kick-to-the-face. Today, not so much.

…Ok, one more:

Mount Vernon Statement:

A Constitutional conservatism based on first principles provides the framework for a consistent and meaningful policy agenda. … It encourages free enterprise, the individual entrepreneur, and economic reforms grounded in market solutions.

Sharon Statement:

THAT the market economy, allocating resources by the free play of supply and demand, is the single economic system compatible with the requirements of personal freedom and constitutional government, and that it is at the same time the most productive supplier of human needs;

In comparison, a verb like “encourages” sounds pretty weak.

From Karen Armstrong’s A History of God:

In 529 the emperor Justinian closed the ancient school of philosophy in Athens, the last bastion of intellectual paganism: its last great master had been Proclus (412-485), an ardent disople of Plotinus. Pagan philosophy went underground and seemed defeated by the new religion of Christianity. Four years later, however, four mystical treatises appeared which were purportedly written by Denys the Areopagite, St. Paul’s first Athenian convert. They were, in fact, written by a sixth-century Greek Christian, who has preserved his anonymity. The pseudonym had a symbolic power, however, which was more important than the identity of the author Pseudo-Denys managed to baptize the insights of Neoplatonism and wed the God of the Greeks to the Semitic God of the Bible.

Denys was also the heir of the Cappadocian Fathers. Like Basil, he took the distinction between kerygma and dogma very seriously. In one of a his letters, he affirmed that there were two theological traditions, both of which derived from the apostles. The kerygmatic gospel was clear and knowable; the dogmatic gospel was silent and mystical. Both were mutually interdependent, however, and essential to the Christian faith. One was “symbolic and presupposing initiation,” the other “philosophical and capable of proof—and the ineffable is woven with what can be uttered.” The kerygma persuades and exhorts by its clear, manifest truth, but the silent or hidden tradition of dogma was a mystery that required initiation: “It effects and establishes the soul with God by initiations that do not teach anything,” Denys insisted, in words that recalled Aristotle. There was a religious truth which could not adequately be conveyed by words, logic or rational discourse. It was expressed symbolically, through the language and gestures of the liturgy or by doctrines which were “sacred veils” that hid the ineffable meaning from view but which also adapted the utterly mysterious God to the limitations of human nature and expressed the Reality in terms that could he grasped imaginatively if not conceptually.

The hidden or esoteric meaning was not for a privileged elite but for all Christians. Denys was not advocating an abstruse discipline that was suitable for monks and ascetics only. The liturgy, attended by all the faithful, was the chief path to God and dominated his theology. The reason that these thruths were hidden behind a protective veil was not to occlude men and women of goodwill but to lift all Christians above sense perceptions and concepts to the inexpressible reality of God himself. The humility which had inspired the Cappodocians to claim that all theology should be apophatic became for Denys a bold method of ascending to the inexpressible God.

In fact, Denys did not like to use the word “God” at all—probably because it had acquired such inadequate and anthropomorphic connotations. He preferred to use Proclus’s term theurgy, which was primarily liturgical: theurgy in the pagan world had been a tapping of the divine mana by means of sacrifice and divination. Denys applied this to God-talk, which, properly understood, could also release the divine energeiai inherent in the revealed symbols. He agreed with the Cappedociens that all our words and concepts for God were inadequate and must not be taken as an accurate description of a reality which lies beyond our ken.
Even the word “God” itself was faulty, since God was “above God,” a “mystery beyond being.” Christians must realize that God is not the Supreme Being, the highest being of all heading a hierarchy of lesser beings. Things and people do not stand over against God as a separate reality or an alternative being, which can be the object of knowledge. God is not one of the things that exist and is quite unlike anything else in our experience. In fact, it is more accurate to call God “Nothing”: we should not even call him a Trinity since he is “neither a unity nor a trinity in the sense in which we know them.” He is above all names just as he is above all being. Yet we can use our incapacity to speak about God as a method of achieving a union with him, which is nothing less than a “deification” (theosis) of our own nature. God had revealed some of his Names to us in scripture, such as “Father,” “Son” and “Spirit,” yet the purpose of this had not been to import information about him but to draw men and women toward himself and enable them to share his divine, nature.

In each chapter of his treatise The Divine Names, Denys begins with a kerygmatic truth, revealed by God: his goodness, wisdom, paternity and so forth. He then proceeds to show that although God has revealed something of himself in these titles, what he means is not himself. If we really want to understand God, we must go on to deny those attributes and names. Thus we must say that he is both “God” and “not-God,” “good” and then go on to say that he is “not-good” The shock of this paradox, a process that includes both knowing and unknowing, will lift us above the world of mundane ideas to the inexpressible reality itself. Thus, we begin by saying that:

of him there is understanding, reason, knowledge, touch, perception, imagination, name and many other things. But he is not understood, nothing can be said of him, he cannot be named. He is not one of the things that are [nor is he known in any of the things that are: he is all things in everything and nothing in anything].”

Reading the Scriptures is not a process of discovering facts about God, therefore, but should be a paradoxical discipline that turns the kerygma into dogma. This method is a theurgy, a tapping of the divine power that enables us to ascend to God himself and, as Platonists had always taught, become ourselves divine. It is a method to stop is thinking! “We have to leave behind us all our conceptions of the divine. We call a halt to the activities of our minds!’” We even have to have our denials of God’s attributes behind. Then and only than shall we achieve an ecstatic union with God.

When Denys talks about ecstasy, he is not referring to a peculiar state of mind or an alternative form of consciousness achieved by an obscure yogic discipline. This is something that every Christian can manage in this paradoxical method of prayer and theoria. It will stop us talking and bring us to the place of silence: “As we plunge into that darkness which is beyond intellect, we shall find ourselves not simply running short of words but actually speechless and unknowing” Like Gregory of Nyssa, he found the story of Moses’ ascent of Mount Sinai instructive. Moses had climbed the mountain, he did not see God himself on the summit but had only been brought to the place where God was. He had been enveloped by a thick cloud of obscurity and could see nothing: thus everything that we cm see or understand is only a symbol (the word Denys uses is “paradigm”) which reveals the presence of a reality beyond all thought. Moses had passed into the darkness of ignorance and thus achieved union with that which surpasses all understanding: we will achieve a similar ecstasy that will “take us out of ourselves” and unite us to God.

The preceding’s length can be compared to the first 14 lines of Lao Tzu’s Tao Te Ching (translation by S. Mitchell):

The tao that can be told
is not the eternal Tao
The name that can be named
is not the eternal Name.

The unnamable is the eternally real.
Naming is the origin
of all particular things.

Free from desire, you realize the mystery.
Caught in desire, you see only the manifestations.

Yet mystery and manifestations
arise from the same source.
This source is called darkness.

Darkness within darkness.
The gateway to all understanding.

So where does that leave us (emphasis mine):

Dessys’s method became normative in Greek theology. In the West, however, theologians would continue to talk and explain. Some imagined that when they said “God,” the divine reality actually coincided with the idea in their minds. Some would attribute their own thoughts and ideas to God—saying that God wanted this, forbade that and had planned the other—in a way that was dangerously idolatrous. The God of Greek Othodoxy, however, would remain mysterious, and the Trinity would continue to remind Eastern Christians of the provisional nature of their doctrines. Eventually, the Greeks decided that an authentic theology must meet Denys’s two criteria: it must be silent and paradoxical.

The following quote is from Zen and the Art of Motorcycle Maintenance by Robert Pirsig. (The John mentioned is the protagonist’s buddy who wants to escape modern technological life via a motorcycle he deigns to tune-up):

Precision instruments are designed to achieve an idea, dimensional precision, whose perfection is impossible. There is no perfectly shaped part of the motorcycle and never will be, but when you come as close as these instruments take you, remarkable things happen, and you go flying across the countryside under a power that would be called magic if it were not so completely rational in every way. It’s the understanding of this rational intellectual idea that’s fundamental. John looks at the motorcycle and he sees steel in various shapesand has negative feelings about these steel shapes and turns off the whole thing. I look at the shapes of the steel now and I see ideas. He thinks I’m working on parts. I’m working on concepts.

I was talking about these concepts yesterday when I said that a motorcycle can be divided according to its components and according to its functions. When I said that suddenly I created a set of boxes with the following arrangement:

And when I said the components may be subdivided into a power assembly and a running assembly, suddenly appear some more little boxes:

And you see that every time I made a further division, up came more boxes based on these divisions until I had a huge pyramid of boxes. Finally you see that while I was splitting the cycle up into finer and finer pieces, I was also building a structure.

This structure of concepts is formally called a hierarchy and since ancient times has been a basic structure for all Western knowledge. Kingdoms, empires, churches, armies have all been structured into hierarchies. Modern businesses are so structured. Tables of contents of reference material are so structured, mechanical assemblies, computer software, all scientific and technical knowledge is so structured—so much so that in some fields such as biology, the hierarchy of kingdom-phylum-class-order-family-genus-species is almost an icon.

The box “motorcycle” contains the boxes “components” and “functions.” The box “components” contains the boxes “power assembly” and “running assembly,” and so on. There are many other kinds of structures produced by other operators such as “causes” which produce long chain structures of the form, “A causes B which causes C which causes D,” and so on. A functional description of the motorcycle uses this structure. The operator’s “exists,” “equals,” and “implies” produce still other structures. These structures are normally interrelated in patterns and paths so complex and so enormous no one person can understand more than a small part of them in his lifetime. The overall name of these interrelated structures, the genus of which the hierarchy of containment and structure of causation are just species, is system. The motorcycle is a system. A real system.

To speak of certain government and establishment institutions as “the system” is to speak correctly, since these organizations are founded upon the same structural conceptual relationships as a motorcycle. They are sustained by structural relationships even when they have lost all other meaning and purpose. People arrive at a factory and perform a totally meaningless task from eight to five without question because the structure demands that it be that way. There’s no villain, no “mean guys’ who wants them to live meaningless lives, it’s just that the structure, the system demands it and no one is willing to take on the formidable task of changing the structure just because it is meaningless.

But to tear down a factory or to revolt against a government or to avoid repair of a motorcycle because it is a system is to attack effects rather than causes; and as long as the attack is upon effects only, no change is possible. The true system, the real system, is our present construction of systematic thought itself, rationality itself, and if a factory is torn down but the rationality which produced it is left standing, then that rationality will simply produce another factory. If a revolution destroys a systematic government, but the systematic patterns of thought that produced that government are left intact, then those patterns will repeat themselves in the succeeding government. There’s so much talk about the system. And so little understanding.