THE WHEEL OF THE NORM

Introduction

'The Wheel', 'the Wheel of the Norm' or 'the Wheel of the Ananorm' is men­tioned in the 'prose poem' To the Early Readers at the very beginning of the Book of Instruments, the first book of the Model of Neutral-Inclusivity, and in The Wheel of the Ananorm, in the last chapter of the Book of Sym­bols, and there­fore of the whole Model. (You can find a copy of these two 'wheel poems' at the end of this doc­u­ment.) It is in the paragraph preceding the latter poem (S.6.2.2.10) where the fol­low­ing ex­pla­na­tion is given of the use of the wheel as a neutral-inclusive symbol:

(The figure of speech used in the Wheel is an ancient one. The word wheel derives from kyklos, meaning circle or wheel, which in turn derives from c(h)ak­ra, al­so meaning wheel. In some prod­ucts of thought levels of con­scious­ness were, or still are, de­pict­ed as wheels or 'chak­ras'. The effect is the more striking because telos in teleology, which means end or pur­pose, derives from cakra too. That is why it is also of great sym­bol­ic sig­nif­i­cance to call the DNI "a tele­o­logical doc­trine". By doing so we further unify the past, pres­ent and future; and this with­out trying to roll back the wheel of history.)

Here i will first discuss the points made in this parenthetical paragraph in more detail. There­after, i will discuss the char­ac­ter­is­tics of the neutral-inclusive Wheel as displayed at the top of this document. (At the bottom you will find a table of the grey tones used in the prototype of the Wheel.)

Wheels in history

Several wheelless millenniums had passed in agriculture and pottery until in the Copper Age, the transitional period between the Stone and the Bronze Ages (roughly, 6500-4300 years ago), the potter's wheel was invented and the first wheeled vehicles were built. (It has not gone unnoticed that the new signs of ad­vanc­ing civilization as man­i­fest­ed, not only in ce­ram­ics, metallurgy and wheeled vehicles, but also in government and law, medicine and ar­chi­tec­ture, writing and weaving, were al­read­y found in so­ci­e­ties that still ven­er­a­ted, un­ex­pect­ed as it, perhaps, may be by andro­centrist male theists, a Supreme Being in the form of a woman.) The early wheel was a solid piece of wood with a hole at the center for an axle. Spoked wheels and chariots did not emerge until the Middle Bronze Age (4200-3550 years ago), after the do­mes­ti­ca­tion of the horse. The number of spokes in wagon wheels varied from 8 to 16, dependent on the diameter of the wheel desired and the load ex­pec­ted. The wheel and axle was one of five or six classical sim­ple machines, among which also the lever, pulley, wedge and screw, with or with­out the inclined plane. There is no rea­son to assume that the wheel ever started as a symbol of cultural sig­nif­i­cance, even tho it may have been in­vent­ed at more than one time and place in­de­pend­ent­ly; and even tho the original idea may have come from a toy builder or artist who was not after any­thing of prac­ti­cal significance.

an about 2560-year-old wooden cart wheel, painted on a Greek oil flask, with only one (pair of) radial spoke(s) which, it seems, has (so far) gone unnoticed in any history or typology of the world's wheels

Chakras in history

The word chakra derives from the same archaic form as wheel and cycle in a family of lan­guages ranging from Bangla to Ice­landic and originating in countries as far apart as Bangla­desh and Iceland. (The term Indo-European for this family is a dubious one.) Unlike the literally or com­par­a­tive­ly objective meanings of wheel and cycle, the meaning of chakra has, in the course of history, also fanned out in sub­jec­tive di­rec­tions which are much more, if not com­plete­ly, of a meta­physical religous or pseudo­scientific brand. No doubt, the disk shape of both the Sun and the wheel helped the former to be turned into a god that il­lu­mi­nates the world, and subsequently the latter as a symbol to be as­so­ci­at­ed with light; or with light and knowl­edge — the same kind of association as we find in the con­tem­po­rary English word to enlighten. And yet, it is one thing to start from the notion of a circle or a cycle and to arrive at the notion of a center, or vice versa, and quite a different thing to use chakra in the sense of a 'psychic energy center' in an esoteric theory. The term chakra simply does not need to be used in a super­naturalist or any such context, if only because in the Vedas the com­pound noun chakravartin is used fig­u­ra­tive­ly for a leader whose wheel moves, or who, from a center of power or influence in an empire, makes the wheel move in all four quarters of the compass. This 'chakra­vartin' was a monarch with military or political pow­er as real as any such person in the present, re­gard­less of that person's also being a chakra­vartin in the little dem­o­crat­ic sense of an ide­al­ized universal ruler.

Dharmachakra

Whereas chakra can be used for some­thing as political or relatively short-lasting as a 'wheel of state', it can also be used for more serious or solemn matters of a denominational and really long-last­ing, if not 'eternal', nature. In Hindu­ism and Buddhism the dharmachakra has become the main symbol of the faith. In the most general sense, dharma refers to a normative system: dharma­chakra may even be trans­lated as wheel of the law. In the case of Sid­dhartha Gautama's doctrine it is im­me­di­ate­ly connected to the Four Noble Truths or the Noble Eightfold Path. (The wheel may have, say, eight, ten, twelve, sixteen or twenty-four spokes, but will be eight-spoked on purpose if it is to represent the Eightfold Path; or twenty-four-spoked if it is to represent a particular collection of twenty-four qual­i­ties.) By starting to teach a new nor­ma­tive doctrine Gautama, or 'the awakened one' (buddha), set, as it were, the wheel of the new dharma in motion. Rather than a wheel-turning king, Gautama became a wheel-turning sage, but not in the sense of a pure phi­los­o­pher; rather in the pre-Na­po­le­on­ic sense of an ideologue, because it is es­pe­cial­ly ideology which must be nor­ma­tive, whether good or bad, right or wrong, or some mixture of the two. (It is said that Gautama's turning of the wheel signified 'a great and rev­o­lu­tion­a­ry change', and such an i­de­o­log­i­cal desire is not in the mind of a sage as philosopher.)

part of  The Wheel for All People, TRINPsite note of the 53rd Northern Mid-Yule (See also  What will Stop the Wheel?, note of the 56th Northern Late Lent, and The Wheel, note of the 67th Southern Late Lent.)

Religious symbols in the Model?

No, there are no sanctified (ex­clu­sive­ly) re­li­gious symbols or, for that matter, concepts in the Model of Neutral-Inclusivity. At the same time, however, for a symbol or concept to be ac­cept­a­ble it cannot be a require­ment that it is not being used in any religion. The require­ment should be that it is not super­naturalist in itself, that it does not come from or lead to a belief detached from na­ture and the natural, but first and foremost that it does not promote the sort of in­sti­tu­tion­al­ized super­naturalism which goes under the banner of religion, steals the state and by its state religionism foists its own pre­cepts and symbols on the total pop­u­la­tion of a whole country. In The neutral-inclusivist's choice of linguistic symbols, a section (S.2.1.2) of the chapter The Use and Nonuse of Linguistic Symbols in the Book of Symbols, it is written: the vocabulary of the person believing in and sup­port­ing the ideal of neutral-inclusivity will or may differ from other vo­cab­u­lar­ies in the fol­low­ing respects after which seven points follow, of which the last one is in the ex­plic­it­ly inclusivistic and veridicalistic use of terms which are tra­di­tion­al­ly theo­de­mo­nis­tic or super­nat­u­ral­is­tic. The example given there is that The Dharma may be used as a literary reference to the Ananorm or the Norm (which itself is a normistic literary reference to the whole nor­ma­tive edifice erected in the three books of the Model). The dharma may refer to the Four Noble Truths or the Noble Eight­fold Path in Gautama's teach­ings, these Truths and this Path are in no way part of the literal meaning or the denotation of dharma or dharma­chakra. The Model dharma stands for the norm of inclusivity, the norm of neutrality, the four pillars of the Norm and the five TRINP values truth, relevance, inclusivity, neutrality and personhood (of which relevance and inclusivity share one pillar). And the neutral-inclusive dharma­chakra is pre­cise­ly the wheel or 'chakra' of that dharma.

No connection at all?

Yes, there is some connection with beliefs which may be classified as "re­li­gions" on account of some super­naturalism, but which are hardly or not theocentrist (for example, because a god needs the same en­light­en­ment as every ordinary mortal). Such beliefs are not mentioned, but hinted at in the second division of the third chapter of the Book of Fundamentals under Proto­neutralism and proto­relevantism. In that sec­tion (F.3.2.4) ancient systems of religious and/or phil­o­soph­i­cal thought are being dis­cussed which somehow relate to the two fun­da­men­tal values of neutrality and relevance. None of these systems recognize neutrality, let alone catenical neu­tral­i­ty, as a supreme value in plain words. And yet, such con­cepts as equality, symmetry, harmony and balance may play a key role in their argumentation and symbolism; con­cepts which are considered '(catenically) neutral' in the Model of Neutral-Inclusivity. Other old trains of thought do not so much focus on a fusion of opposites of which some kind of equilibrium is the result, but rather on the pristine unity of ultimate reality in which nothing changes or, less pristine, in which every­thing changes. Concepts such as unity and oneness are treated as 'inclusive' in the Model, but within a framework which studiously dis­tin­guish­es the truth-con­di­tion­al aspect of living and thinking from its relevancy-con­di­tion­al one. Changes and dif­fer­en­ces which are there truth-con­di­tion­al­ly speaking 'are not there' relevancy-conditionally speaking, if or when they are not relevant.

The teleological part of the Norm

Clearly, teleology is et­y­mo­log­i­cal­ly in­ti­mate­ly related to the Wheel. But how in­ti­mate­ly is it related to the Norm? As ex­plained in Elements of Normative Philosophy, the seventh chapter of the Book of Instruments, in the section Decision-theoretical consequentialism (I.7.4.2), the Model of Neutral-Inclusivity does not use teleology as a synonym of con­se­quen­tial­ism, but uses it in the sense of decision-theoretical value-based ethics which is past-, present- and future-regarding. Therefore, the doctrine of neutral-inclusivity (the DNI) with the values or 'prin­ci­ples' of truth, relevance, inclusivity and neutrality is a te­le­o­log­i­cal system of thought. However, an ethics ultimately based on values is not the same as an ethics ultimately based on rights and/or duties. In the Model the difference between the two is found back in the distinction drawn between a nor­ma­tive doctrine, such as the DNI, and a normative meta­doctrine. It is not until the eighth chapter that this distinction between the (first-order) doctrinal and the metadoctrinal is in­tro­duced and is going to play an e­nor­mous­ly important role in the foundation and de­vel­op­ment of the Norm. The Norm is more than the doctrinal values or principles of the DNI: it comprises the meta­doctrinal principle of personhood as well. The value of personhood and the rights and duties which give it extra weight may very well be defensible within the purview of the DNI, they add something to the Norm to which a purely teleological calculus would do no full justice.

stylized Nanapolarity Catena at the top and bottom of TRINPsite webpages

A neutral-inclusive wheel symbol

As a concrete object a wheel will have three spatial dimensions; nonetheless, as a symbol it has two dimensions which need not be spatial ones either. Now, each separate dimension can be looked at as a separate catena of a neg­a­tiv­i­ty on the left, a positivity on the right (or the other way around) and a neutrality in the center. In an ordinary catena we could place an arrow on or along its axis from left to right and from low to high (or the other way around), to indicate in which direction the values increase (or de­crease) according to a descriptive or factual-modal evaluation. How­ever, a neutral-inclusive Wheel is a symbol of neutralism and/or inclusivism. And the symbol of neu­tral­ism is the Nana­polarity Catena or 'nanacatena', the catena which does not focus on the extremely negative nor on the ex­treme­ly positive but on the neutral, which is expressed by two arrows pointing to each other in the center of the catena or di­men­sion. The neu­tral­i­ty at the center of a nanacatena is its telos, the quality with the highest value in a normative evaluation, the focus of thought and the aim of action, and a quality to be striven for as symbolized by the two arrows point­ing in its direction. But, con­verse­ly, the telos between the two arrows in the symbolic rep­re­sen­ta­tion may also be one of the three other teleological values of the DNI: relevance, in­clu­siv­i­ty or truth. And, by extension, each point between the two arrows could also represent person­hood, the fifth value of the Norm, because also that is a value to be striven for (even tho its meta­doctrinal foundation dis­tin­guishes it from the doctrinal values). An­oth­er way of look­ing at the four-spoked wheel symbol is that each 'catenary' spoke represents one of the four pillars of the Norm. It is even pos­si­ble to think of four extra 'inter­catenary' spokes which cut the quarters between the catenary spokes into two equal halves to represent the same four pil­lars on their own. You would say that the neutral-inclusive wheel symbol needs four, if not eight, spokes to rep­re­sent the Ananorm.

A matter of discipline

Philosophers may unscrupulously offer so-called 'philosophical' ideas and theories which are largely, if not predominantly, the domain of religious, political or other forms of 'ideology' (wheth­er used in a Napoleonic pejorative or in a proper sense). The author of the Model of Neutral-Inclusivity, on the other hand, is honest about this creation being both a phil­o­soph­i­cal and an i­de­o­log­i­cal work. But while its mixed philo­sophical-ideological nature may be the rule rather than the exception, it is not a work in any phil­o­soph­i­cal or ide­o­log­i­cal tradition. Par­tic­u­lar traditions and history in general are there to inspire and to remind the writer and reader, yet certainly not to be taken for granted or, worse, as good arguments in them­selves. The ultimate values espoused in the Model were not taken from a pluralist potpourri of historical, traditional or, for that matter, fash­ion­a­ble con­tem­po­rar­y values with pleasant con­no­ta­tions or ex­cit­ing emotive meanings; nor was the quantity of these values (or of any set of com­mand­ments based on them) reduced in a slapdash or sloppy process to 10 or some such 'wholly rational holy' num­ber (in the nu­mer­al system with the hollow base ten, that is). Instead, the ultimate values were carefully selected one by one, with each choice leading to the next one: from truth to relevance and inclusivity, from relevance to neutrality and from these three to person­hood. In this process, the num­ber of ultimate values was kept as small as possible —a monistic ideal— without jet­ti­son­ing or overlooking what deserved to be kept or to be assigned a place too in the nor­ma­tive structure. What underlay this under­taking was mental discipline pure and simple: mental discipline as displayed in the use of method rather than arbitrary selectivity, and as resulting in innovation rather than in the per­pet­u­a­tion of 'what has always been con­sid­ered useful' and/or 'normal'. An in­te­gral part of this in­de­pend­ent approach is, even more than giving different answers to old questions, the re­for­mu­la­tion of old questions and the for­mu­la­tion of new ones. Would the as­so­ci­a­tion of the number of values of the Norm with the number of spokes in the Wheel in any way be symbolic of the discipline with which the Model was pro­duced? That is the ques­tion ...

The sectoring of the disk

Just as the absolute size of the wheel, that is, the area of the circle, plays no role in the wheel symbol, so the absolute area of a sector plays no role either. What counts for a proper division is that all sectors are of equal size. But what part of the circle should these sectors be? In the case of a quadrant, that is, a quarter of a circle, for instance, the fraction is 1/4, the part number 0.25. (The latter is not a fraction but a number in itself.) It is quite understandable that the disk of the wheel symbol may make a great many people think of the disk of an analog clock. In itself this would not need to be a disaster, if it were not such a chaotic contemporary clock they have been dumbed down with, one which first divides the day, a naturally given unit of time on Earth, into 2 parts, then into 12 parts (called "hours"), then these parts into 60 parts (called "minutes"), then these parts again into 60 parts (called "seconds") and finally these parts of the day into some­thing like 100 or 1000 parts in turn. Such a clock and such a division of the also naturally given unit angle (tra­di­tion­al­ly di­vorced from nature by 'three hundred and sixty degrees') is a freak of culture which does not deserve to be kept taken se­ri­ous­ly, and is completely unsuitable for the design of a neutral-inclusive symbol. There is only one scheme of division which is universal and not ar­bi­trar­y: the division of the full circle into two (half) parts, of each of these parts into 2 (quarter) parts, of each of these parts of parts into 2 (one-eighth) parts, of each of these parts of parts of parts into 2 (one-sixteenth) parts, and so on and so forth. While the division into four parts happens to be related to the number of pillars, the rest is entirely un­re­lat­a­ble to the num­ber of ultimate or other values of the Norm.

From radixes to sectors and spokes

The continuous sub­division of a disk and its parts into two parts may re­mind some of the radix-two numeral system traditionally called "bi­na­ry". By look­ing at it as a con­sis­tent sub­di­vi­sion into halves it is actually a radix-half system. The radix-½-(radix-)2 couple defines the very first super­system among rational numbers, both of part and of whole numbers. The radix-2 ('binary'), radix-4 ('qua­ter­na­ry'), radix-16 ('hexa­decimal') and radix-256 ('du­o­cen­te­hex­a­quin­qua­ges­i­mal') systems are sub­sys­tems of it with transparent cor­re­spond­ences. The radix-⅟16-16 double system (in which ⅟16 or mi and 16 or mu are each other's inverse) is re­mark­a­bly suitable for a universal nu­mer­i­cal vo­cab­u­lar­y —with the ⅟16-16-based wheel as a mimunary wheel— which does not suffer from Greco-Latin exclusivism but is ethnicity-tran­scend­ing; and free from any whole-number bias as well. (Here i am referring, not to the in­no­cent 'whole-number bias' of school­children, but to the way portions, den­i­gra­ting­ly termed "frac­tions", are treated by adults as num­bers created from the ribs of integers.) It follows that there is a very good reason for stop­ping the sub­division of the Wheel after sub­dividing it into one-sixteenth sectors with sixteen spokes to separate them. Never­the­less, it is quite possible to continue by di­vid­ing the disk into 32, 64, 128 or, perhaps, even more im­pres­sive­ly, 256 parts. In theory, we could go on in­definitely, but in practice we would, long before reaching near-infinity, al­ready end up with a solid wheel, the very type of wheel before there were spokes or a need to use them. This too has always been part of the symbolism of the wheel, namely that after a full rotation we will be back where we came from, albeit on a higher level of ac­com­plish­ment.