Presented to Emperor Wu of Han 漢武帝 (r. 140–87 bce) in 139 bce by his uncle, Liu An 劉安 (c. 179–122 bce), the second king of Huainan 淮南,Footnote 1 under the simple title of Neishu 內書 (Inner Writings),Footnote 2 Huainanzi 淮南子 (lit. Masters of Huainan) is comprised of twenty-one treatises (xun 訓), often called “chapters.”Footnote 3 These chapters encompass an encyclopedic range of subjects, including the fundamental nature of man, the realm, and the cosmos. While broad in coverage, the text’s many strands nevertheless feed into its overarching purpose of edifying a royal reader, presenting him with “a compendium of everything a modern monarch needs to know.”Footnote 4
As a “fundamentally political work,”Footnote 5 Huainanzi contributes a distinct model of sage rulership. This model consists in, among other features, ruling through wuwei 無為, or “non-action.” The cosmological context of governance through wuwei, however, appears to be paradoxical. The Huainanzian sage-ruler’s “non-action” is underpinned by his capacity to straddle reality at a patterned level of myriad forms, on the one hand, and at a level beyond the bounds of form, on the other. This begs the question, how can one reality simultaneously show two such structurally antithetical faces? And how can the sage-ruler’s program encompass both at once? In this article, I suggest that a heuristic of fractal and Euclidean geometries, simplified from modern mathematics, offers one way to embrace and make sense of this seeming paradox at the heart of Huainanzian political cosmology.
The Geometrical Heuristic
“Euclidean” refers to the classical geometry of shapes with whole integer (up to three) dimensionality. I use the term to refer to the geometry that the non-mathematician intuitively leverages in order to model objects encountered in their lived surroundings. Importantly for this article, the term serves as a heuristic for modelling the world in terms of regular, complete, and discrete forms that readily map onto the layperson’s mental Cartesian grid. “Fractal,” by contrast, refers to the nonintuitive geometry of shapes with non-integer, or fractional, dimensionality. These “dimensionally discordant” shapes exhibit the same detail at all levels of magnification, such that any part or division represents a structural facsimile of any other.Footnote 6 In short, they are self-similar. By virtue of this structural recursion, fractal shapes contain no juncture at which any part may be distinguished from any other, no obvious “point of entry” for the viewer.Footnote 7 Their dimensionality is theoretically endless.
Descriptive fractal geometry developed in earnest in the 1960s and 1970s, as advances in computing, specifically iterative modelling of complex natural systems, made these shapes quickly reproducible.Footnote 8 While fractal geometry as a sub-field of modern mathematics is clearly anachronistic with respect to the intellectual universe of Huainanzi,Footnote 9 its descriptions of its strange shapes and their features offer a ready-made language by which to excise some of the more difficult aspects of Huainanzi’s model of reality. This language is especially apt to open up Huainanzi because the text makes heavy use of a roster of nesting and other regressive or iterating structures of its own.
Native Nesting-Type Structures in Huainanzi: The Current Scholarship
Huainanzi draws extensively on an eclectic range of texts in the early Chinese canon. Tobias Zürn argues that the text’s composition process is to be understood as a kind of “highly intertextual” weaving (jingwei 經緯).Footnote 10 For perhaps this and other reasons, the text was categorized by imperial librarians in the late Western Han as “miscellaneous” (za 雜 or zajia 雜家).Footnote 11 The label stuck through the centuries, and the proposition that Huainanzi might constitute a highly coherent textual, literary, and conceptual artifact has gained traction in Chinese Studies only recently.Footnote 12 Within the context of this burgeoning research on Huainanzi’s overlooked consistencies, scholars such as Andrew Meyer and Benoît Vermander have begun to explore the text’s use of sometimes fractal-like, limited-depth nesting and other regressive or iterating structures, at both the conceptual and the compositional levels.Footnote 13
Scholars have long been aware of the important role that microcosm–macrocosm themes hold in the Huainanzi enterprise, where, as with many texts of the era, figures such as the nonary “magic” square regularly recur.Footnote 14 As early as 1962, Benjamin Wallacker noted, in the preface to his translation of the “Binglüe xun” 兵略訓 (“Military Strategy”) chapter, that Huainanzi’s universe is one in which “[e]ach unique phenomenon is both part of and equal to the great unity of the cosmos.”Footnote 15 This observation has been echoed in Michael Puett’s To Become a God (2002), which found that the principle that “humanity is a microcosm of the universe” is a key component in the text’s soteriology, as well as in Judson B. Murray’s suggestion (2004) that the postface “Yaolüe” 要略 (“Summarizing the Essentials”) has an “ever-broadening” nesting structure that “can be said to consist of both a summary and summaries, and summaries of the summary and summaries, and so forth.”Footnote 16
The 2010 English translation of The Huainanzi went further, asserting that a compounding “root-and-branches” (benmo 本末) figure informs the entire text’s construction on the macro-level.Footnote 17 Per Major and his team, root-and-branches forms both the text’s “central organizing metaphor” and “the most fundamental dynamic principle conditioning the phenomenal realm,”Footnote 18 as well as a “compositional principle.”Footnote 19 A chapter devoted to the topic, authored by Meyer, in the related 2014 collected volume The Huainanzi and Textual Production in Early China, discusses the various manifestations of the root-and-branches figure throughout Huainanzi.Footnote 20 According to this research, the first eight chapters, addressing topics in the abstract milieus of metaphysics, cosmogony, and proto-science, constitute the text’s “root” (ben), while the latter twelve chapters, addressing the concrete application of this “root” knowledge in military strategy, agriculture, political persuasion, et cetera constitute its “branches” (mo).Footnote 21 Meyer further refined the conceptual metaphor in a 2023 response to Vermander, expanding on root-and-branches as a cosmogonic pattern and its relationship to qi 氣 (vital breath, energy-matter) metaphysics, as well as discussing the limitations of the eight-and-twelve grouping of the chapters.Footnote 22
In “Edit by Number,” Vermander posits that a sophisticated and intentional numerology-based compositional rhetoric, formed as an interleaving “double circle,” informs Huainanzi’s overarching structure.Footnote 23 “[E]ach series of ten chapters [1 to 10 and 11 to 20] draws a circle, the second one centred on Potency”—which is to say, de 德, the applications of dao 道—and “the first one on the Way”—dao itself.Footnote 24 Vermander shows how this structural rhetoric produces an endless, interlocking series of squares and circles, embodying “[t]he issue at stake [which] is to relate heavenly matters (represented by the circle) to (squared) earthly ones” at the level of the text’s overall composition.Footnote 25
The fractal cosmological heuristic applied in this article echoes the nesting schema that this scholarship has uncovered at different levels of Huainanzi’s construction, particularly the root-and-branches image.Footnote 26 In fact, a fractal schema can be thought of as a modern elaboration upon Huainanzi’s root-and-branches model, innovating a heuristic from the text that is then applied back to it. (This, in turn, further defines the root-and-branches image. Huainanzi’s native structural metaphors, such as root-and-branches, the numerological double circle, and weaving, are often seen to elaborate one another, and the endless combinations of the text’s overlapping images keep it exegetically open and alive.Footnote 27 Elaborating new images on the basis of the existing roster could therefore be regarded as playing into the text’s work.) Unlike the aforementioned structures, however, a fractal figure is not an uncovered construct of the text, but a tool applied for thinking through the structural paradox of formed formlessness that undercuts Huainanzi’s cosmic schema.
Process
Given Huainanzi’s prohibitively large size, this article is based in the analysis of selected extracts.Footnote 28 This analysis grew out of separate chapter studies, where I noticed that these readings built upon one another to produce a view of Huainanzian sage rule as wedded to a distinct cosmological context. These chapters also encompass the full breadth of the text, ranging from the third to the twentieth chapter, and so go some way to represent its overarching argumentative cycle, from “root” to “branch.”
I start by developing an interpretation of Huainanzi’s cosmic schema, grounded in the metaphysics of qi. First, referring to a cosmogonic passage from chapter three, “Tianwen xun” 天文訓 (“Patterns of Heaven”), I sketch out the structure of the Huainanzian cosmos in its earliest moments, identifying some of the principles of qi metaphysics in the process. Next, I extend this tentative sketch in reference to the evidence of chapter four, “Dixing xun” 墬形訓 (“Forms of Terrain”). I show that this tentative sketch of the early Huainanzian cosmos also represents the structure of the familiar lived world and its myriad forms. (At the same time, I further develop the working understanding of qi metaphysics, which lays groundwork for the later discussion of Huainanzi’s “dual” cosmology.) From there, I introduce the issue of the paradox of formed formlessness. Referring to extracts drawn from chapter six, “Lanming xun” 覽冥訓 (“Perceiving the Obscure”), I describe the phenomenon of resonance. I show how this phenomenon reveals another, strange domain of experience alongside the familiar lived world, with the mechanics of the resonance phenomenon itself seemingly interleaving these two, structurally distinct aspects of reality. Next, reading extracts from chapter twenty, “Taizu xun” 泰族訓 (“Highest Conglomeration”), I show how the resonance phenomenon outlined in “Lanming xun” is leveraged in the context of statecraft; there, resonance appears to be a definitive feature of the Huainanzian model of rule through non-action. This demonstrates the contextual importance of Huainanzi’s “dual” cosmic schema for its model of rulership.Footnote 29
In a section entitled “Putting It All Together,” I assemble the evidence of the four preceding sections to discuss how Huainanzi’s model of the familiar lived world can represent one and the same reality alongside its structural opposite, such as allows resonance to be possible. I suggest that thinking in terms of fractal versus Euclidean geometry offers one way through the apparent paradox of ruling (per Huainanzi’s rubric) amid highly ordered forms from a position of formlessness, in addition to articulating the tricky qi metaphysics that underpins this dual cosmology. In the concluding section, I segue from these findings into discussion of other, related aspects of Huainanzi’s thought and construction onto which a fractal heuristic may shed new light.
The Early Cosmogonic World and Qi Metaphysics
“Tianwen xun” documents patterns governing atmospheric and celestial phenomena, addressing topics in astronomy, astrology, and meteorology.Footnote 30 In this part of the article, I produce a tentative sketch of the young Huainanzian cosmos described in “Tianwen xun’s” opening passage, which is an account of the formation of the heavens and earth. I identify the principles of qi metaphysics that, per the passage, drive the cosmogonic process.Footnote 31
Before the cosmos’ earliest moments, separate things were yet to emerge; all was an indivisible unity. From this primordial formlessness, qi eventually emerged, of which the “clear and bright” sort became heaven, while the “heavy and turbid” sort became the earth. The joined “essence” of the newly formed heaven and earth became yin 陰 and yang 陽,Footnote 32 and the “essence” of yin and yang went on to become the four seasons, the “essence” of which finally went on to become the “myriad things,” referring to all remaining things.
天墬未形，馮馮翼翼，洞洞灟灟，故曰太昭。
道始于虛霩，虛霩生宇宙，宇宙生氣。
氣有涯垠，清陽者薄靡而為天，重濁者凝滯而為地。清妙之合專易，重濁之凝竭難，故天先成而地後定。
天地之襲精為陰陽，陰陽之專精為四時，四時之散精為萬物。
積陽之熱氣生火，火氣之精者為日；積陰之寒氣為水，水氣之精者為月；日月之淫為精者為星辰，天受日月星辰，地受水潦塵埃。
When the heaven and terrains were not yet formed, [all was] a crashing, soaring, gushing, roaring [profusion], and thus was called “Supreme Beginning.”Footnote 33
Dao began in empty vastness; the empty vastness gave birth to time and space; time and space gave birth to qi.
Qi had shores and boundaries: the clear and bright fluttered [out] to become heaven; and the heavy and turbid curdled to become earth. The converging of the clear and fine was localized and easy; the curdling of the heavy and turbid was exhaustive and difficult. Thus, heaven was completed first and earth fixed after.
The joined essence of heaven and earth became yin and yang; the specialized essence of yin and yang became the four seasons; and the scattered essence of the four seasons became the myriad things.
The hot qi of accumulated yang gave birth to fire, and the essence of fire qi became the sun; the chilly qi of accumulated yin gave birth to water, and the essence of water qi became the moon. The essence of the excess [qi] of the sun and moon became the stars and constellations. Heaven received the sun and moon, stars and constellations [while] earth received the rivers and floods, dirt and dust.Footnote 34
The pivotal moment in this cosmogonic process comes when qi coalesces the first distinct things, demarcating “shores and boundaries” from the sheer, contiguous topography of the primordial cosmos. This initial qi,Footnote 35 through movements of conjoining, rarefication, and accumulation, goes on to coalesce all things, from the mythical to the mundane.Footnote 36 As Fung Yu-lan 馮友蘭 formulates it, “Huainanzi uses its theory of qi to describe the material causes of the constitution and emergence of the myriad things.” (⟪淮南子⟫還用氣的學說，講一些說明了萬物構成和發生的物質原因).Footnote 37
Through its radical transformations, which I collectively refer to as differentiation, qi coalesces things with diverse characteristics, belonging to diverse sorts.Footnote 38 The first differentiation in “Tianwen xun’s” cosmogony yields the abstract energies yin qi and yang qi. Subsequent differentiations yield diverse “myriad things.” These differentiations are, Fung explains, “the result of the physical properties of the dual qis of yin and yang mechanistically impacting on one another” (萬物的形成和差別，是陰陽二氣的物理性能機械地互相作用的結果).Footnote 39 This is also how qi is able to coalesce things belonging to opposite sorts: from yang qi there is derived a hot qi, which forms fire with its burning heat, while from yin qi there is derived a chilly qi, forming water with its dark, cool characteristics. Throughout these various differentiations, however, qi remains fundamentally singular: the qi that forms fire is still qi, just like the qi that forms water.Footnote 40
These properties may be represented diagrammatically as a simple bifurcation. The two individual lines represent two coalescences of differentiated qi, and two discrete things (Figure 1).
Figure 1. Differentiating qi.
In “Tianwen xun’s” metaphysical paradigm, it is through this differentiation of singular qi that all things eventually coalesce (“And the scattered essence of the four seasons became the myriad things”).Footnote 41 In other words, phenomenal reality in its entirety consists most fundamentally in a singular qi. This reality may be diagrammatically represented as a many-tiered bifurcating structure, wherein each bifurcation represents a differentiation of qi (see Figure 2). The first bifurcation represents primordial qi differentiating to coalesce the first discrete things at the dawn of cosmic time, while the cascade of successive bifurcations represents derivative differentiations of qi, generating younger things and sorts.
Figure 2. Huainanzi’s overarching cosmic schema.
This representation notably aligns to the “root-and-branches” expositional motif identified by Meyer, who argues that the Huainanzian cosmos “began as a unitary, undifferentiated, and infinitely potent ‘root’ and evolved through successive stages of ramification into ever-more-variegated cosmic branches.”Footnote 42
The Familiar Natural Order
“Dixing xun” is a cosmographical treatise, describing the spatial configurations of various terrestrial and mythical, semi-terrestrial realms. It also documents the biological, topographical, meteorological, and geological phenomena, both mundane and mythical, that populate these realms.Footnote 43 In this section, I corroborate and develop the tentative diagrammatic representation of the Huainanzian cosmos in Figure 2 against evidence drawn from across “Dixing xun.” By showing how similar biological, geological, and meteorological sorts emerge and thrive in proximity to one another, linking this “eco-structure” to qi dynamism, “Dixing xun” demonstrates how the principles of qi differentiation continue to structure reality long after the cosmogonic era, defining the contours of the familiar natural world against the same branching structure diagrammatized in Figure 2.
The following extract, from the beginning of “Dixing xun,” describes the configuration of the Nine Provinces: eight at each of the points and corners of the compass and a ninth at the center.Footnote 44 Each of these provinces is described as an “earth” (tu 土), and a great diversity of characteristics is observed among these nine earths. The earth of the northern province, for example, is “completed” (in the sense of mature or ready), while the earth of the southern province is “sumptuous.”
何謂九州？ 東南神州曰農土，正南次州曰沃土，西南戎州曰滔土，正西弇州曰并土，正中冀州曰中土，西北台州曰肥土，正北泲州曰成土，東北薄州曰隱土，正東陽州曰申土。
What are the Nine Provinces called? To the southeast is Shen Province, called Agricultural Earth; to the south is Ci (or Zi) Province, called Sumptuous Earth; to the southwest is Rong Province, called Abounding Earth; to the west is Yan Province, called Ripe Earth;Footnote 45 in the center is Jì Province, called Central Earth;Footnote 46 to the northwest is Tai Province, called Fat Earth; to the north is Jǐ Province, called Completed Earth; to the northeast is Bo Province, called Lurking Earth; to the east is Yang Province, called Prolonging Earth.Footnote 47
The Eight Winds blow into the Nine Provinces from the eight compass directions. Again, each directional wind has its own characteristic. The northern wind, for example, is “chilling” while the southern is “tremendous.”
何謂八風？東北曰炎風，東方曰條風，東南曰景風，南方曰巨風，西南曰凉風，西方曰飂風，西北曰麗風，北方曰寒風。
What are the Eight Winds called? The northeastern one is called Scorching Wind; the eastern one is called Ordering Wind;Footnote 48 the southeastern one is called Auspicious Wind;Footnote 49 the southern one is called Tremendous Wind;Footnote 50 the southwestern one is called Cool Wind;Footnote 51 the western one is called Lofty Wind; the northwestern one is called Fearsome Wind;Footnote 52 the northern one is called Chilling Wind.Footnote 53
Among these earths and winds, it appears that those sharing similar characteristics are found in the same compass direction. For example, “sumptuous” earth and “tremendous” wind are both found in the south. This is corroborated in the following extract, which describes the south as full of virile, humid, vigorous, overgrown, and sharp things.
南方，陽氣之所積，暑濕居之，其人脩形兌上，大口決眦，竅通於耳，血脈屬焉，赤色主心，早壯而夭；其地宜稻，多兕象。
The south is where yang qi accumulates; heat and damp reside there. Its people are long of form and sharp on top; with big mouths and open canthuses; their apertures are connected to their ears. Blood and blood-vessels belong to it (the south);Footnote 54 the color crimson is lord over the heart. [Its people] are stout early on but die young. Its land is suited to rice, with many rhinoceros and elephants.Footnote 55
These are characteristics shared by human inhabitants of the southern lands beyond the Nine Provinces, who are identified by their ferocious demeanors and fearsome body modifications.
凡海外三十六國，… 自西南至東南方，結胷民、羽民、讙頭國民、裸國民、三苗民、交股民、不死民、穿胷民、反舌民、豕喙民、鑿齒民、三頭民、脩臂民。
Beyond the oceans there are thirty-six lands, … From the southwest to the southeast, [there are] the Knot-chested people,Footnote 56 the Feathered people, the people of the Huantou land,Footnote 57 the people of the Naked Land, the three Miao peoples, the Joined-thigh people, the Undying people, the Pierced-chest people, people of twisted tongues,Footnote 58 the Hog-snouted people, the Chisel-toothed people, the Three-headed people, and the Long-upper armed people.Footnote 59
Overall, one can conclude that things sharing similar characteristics are found in the same environment. This phenomenon of proximal characterization is corroborated in the following two extracts, the first of which matches diverse peoples to local kinds of earth, while the second matches metals and minerals with kinds of water.
堅土人剛，弱土人肥，壚土人大，沙土人細，息土人美，秏土人醜。
People of hard earth are unyielding; people of yielding earth are fat; people of black, gravelly earth are big; people of sandy earth are slight; people of replenishing earth are beautiful;Footnote 60 and people of used-up earth are ugly.Footnote 61
白水宜玉，黑水宜砥，青水宜碧，赤水宜丹，黃水宜金，清水宜龜。
White water is suitable for jade; black water is suitable for whetstone; blue-green water is suitable for aquamarine jade; red water is suitable for cinnabar; yellow water is suitable for gold; and clear water is suitable for turtles.Footnote 62
Each people lives on an earth with which they share characteristics; each geological deposit is suited to a type of water with which it shares characteristics. People who have slight builds are found near to fine, sandy earth, while black-colored whetstone is suited to black waters. Just as intense, overgrowing things are found together in the south, slight, fine things are found together, black-colored things are found together, and so on.
The next extract describes this same pattern of things sharing similar characteristics belonging to the same environment.
土地各以其類生，是故山氣多男，澤氣多女，障氣多喑，風氣多聾，林氣多癃，木氣多傴，岸下氣多腫，石氣多力，險阻氣多癭，暑氣多夭，寒氣多壽，谷氣多痹，邱氣多狂，衍氣多仁，陵氣多貪。
輕土多利，重土多遲，清水音小，濁水音大，湍水人輕，遲水人重，中土多聖人。
Each [thing] from the earth and on the land gives birth according to its sort. For this reason, the qi of mountains increases males; the qi of marshes increases females; the qi of ramparts increases muteness, the qi of wind increases deafness; the qi of forests increases infirmity; the qi of wood increases hunched-ness; the qi of coastal areas increases swollenness; the qi of stone increases strength; the qi of precipitous inaccessible [areas] increases goitre; the qi of heat increases premature death; the qi of cold increases longevity; the qi of valleys increases rheumatism; the qi of hillocks increases crookedness; the qi of flatlands increases humaneness; the qi of mounds increases covetousness.
Light earth increases [interest in] profit; heavy earth increases languor. Clear water decreases [the volume of] sounds; turbid water increases [the volume of] sounds; the people of torrential waters are light; the people of placid waters are heavy; the central earth yields many sages.Footnote 63
Clearly, sorts propagate locally. Another extract documents this localized proliferation of sorts (lei 類) (here, “downy-haired,” “feathered,” and “hairy” etc.) over generations.Footnote 64
生海人，海人生若菌，若菌生聖人，聖人生庶人，凡
者生於庶人。
羽嘉生飛龍，飛龍生鳳皇，鳳皇生鸞鳥，鸞鳥生庶鳥，凡羽者生於庶鳥。
毛犢生應龍，應龍生建馬，建馬生麒麟，麒麟生庶獸，凡毛者生於庶獸。
介鱗生蛟龍，蛟龍生鯤鯁，鯤鯁生建邪，建邪生庶魚，凡鱗者生於庶魚。
介潭生先龍，先龍生玄黿，玄黿生靈龜，靈龜生庶龜，凡介者生於庶龜。
Downy-haired gave birth to Sea-Man,Footnote 65 Sea-Man gave birth to Agaric Ancestor, Agaric Ancestor gave birth to sages, and the sages gave birth to common people. All downy-haired things are born from common people.
Feathered Excellence gave birth to Flying Dragon, Flying Dragon gave birth to Phoenix, Phoenix gave birth to the luan bird,Footnote 66 and the luan bird gave birth to the common birds. All feathered things are born from common birds.
Hairy HeiferFootnote 67 gave birth to Winged Dragon,Footnote 68 Winged Dragon gave birth to Virile Horse,Footnote 69 Virile Horse gave birth to the qilin, and the qilin gave birth to common beasts. All furry things are born from common beasts.
Armored Scales gave birth to Sea Serpent,Footnote 70 Sea Serpent gave birth to Ginormous Fishbone,Footnote 71 Ginormous Fishbone gave birth to Virile Fish,Footnote 72 and Virile Fish gave birth to common fish. All scaly things are born from common fish.
Armored Abyss gave birth to First Dragon, First Dragon gave birth to Profound Softshell, Profound Softshell gave birth to Divine Tortoise, and Divine Tortoise gave birth to common turtles. All armored things are born from common turtles.Footnote 73
As the passage beginning “Each [thing] from the earth and on the land” makes plain, there is a causal relationship between the sort of things that pre-exist in (and constitute) a given environment and the sort of new things that emerge there. Taking the first example given in that same extract, the sturdy, upright, “male” mountain “yields” a preponderance of “maleness” within the population emerging nearby. The opening line (“Each [thing] from the earth and on the land gives birth according to its sort”) substantiates this, asserting that “sort” is the precedent according to which things, with their particular characteristics, emerge and grow. Reading on in the same extract, the catalogue of topographical and meteorological things affirms that this proximal sorting is a function of qi.
皆象其氣，皆應其類。
故南方有不死之草，北方有不釋之冰，東方有君子之國，西方有形殘之尸。寢居直夢，人死為鬼。
All [things] resemble their qi, all respond to their sort.
Thus, in the south are grasses that do not die; in the north is ice that does not dissolve; in the east are lands of civilized men; in the west are the barbarian peoples of the Xing Can.Footnote 74 Sleeping and living is a constant dream, and people become ghosts when they die.Footnote 75
Each thing has its own particular qi.Footnote 76 This qi is that which this thing “resembles,” which is to say, its sort. (“Qi” and “sort” occupy parallel positions within the laconic formula “All [things] resemble their qi, all respond to their sort,” encoding their relationship.) And if it is a thing’s qi that determines its sort, then, factoring in the principle of localized sort propagation, one may posit that it is the qi of pre-existing things within a given environment that ultimately determines the sort of new things that emerge therein. This is corroborated in the following extract, which documents the pale qi of “weak earth” yielding generations of things of a “white” sort, whereas the abyssal qi of “female” earth yields generations of “dark” things.
弱土之氣，御于白天，白天九百
生白礜，白礜九百
生白澒，白澒九百
生白金，白金千
生白龍，白龍入藏生白泉，白泉之埃上為白雲，陰陽相薄為雷，激揚為電，上者就下，流水就通，而合于白海。
牝土之氣，御于玄天，玄天六百
生玄砥，玄砥六百
生玄澒，玄澒六百
生玄金，玄金千
生玄龍，玄龍入藏生玄泉，玄泉之埃上為玄雲，陰陽相薄為雷，激揚為電，上者就下，流水就通，而合于玄海。
The qi of weak earth is governed by white heaven; after nine hundred years white heaven gives birth to white arsenic; after nine hundred years white arsenic gives birth to white mercury; after nine hundred years white mercury gives birth to white metal (silver); after a thousand years white metal gives birth to white dragons; white dragons go into hiding and give birth to white springs; the precipitate of the white springs rises to become white clouds, yin and yang weaken one another and become thunder, are agitated and become lightning; what has risen then goes down, and flowing water passes without resistance to combine with the white sea.
The qi of female earth is governed by dark heaven; after six hundred years dark heaven gives birth to dark whetstone; after six hundred years dark whetstone gives birth to dark mercury; after six hundred years dark mercury gives birth to dark metal;Footnote 77 after a thousand years dark metal gives birth to dark dragons; dark dragons go into hiding and give birth to dark springs; the precipitate of the dark springs rises to become dark cloud, yin and yang weaken one another and become thunder, are agitated and become lightning; what has risen then goes down, and flowing water passes without resistance to combine with the dark sea.Footnote 78
In sum, the cosmographical evidence of “Dixing xun” suggests that the Huainanzian world of familiar (and more distant) surroundings is governed by the following principles: first, each thing has its own particular qi; second, this qi determines this thing’s sort; third, the qi of pre-existing things determines the sort of new things that emerge in the nearby environment.
The tentative interpretation of the Huainanzian cosmos diagrammed in Figure 2 conforms to these principles. This figure, to recap, shows a singular qi coalescing an infinity of things, in their diverse, even opposite, sorts; this reflects the first two principles. The flowering of diverse things represented within Figure 2 is a function of qi differentiation, the same phenomenon that accounts for the localized propagation of diverse things, in their many sorts, within “Dixing xun’s” evidence. To summarize from this evidence, “new” things in the environment are new coalescences of already differentiated qi that exists nearby, in and as older things, and this sharing of the same kind of differentiated qi manifests in the shared characteristics of newer and older things. Referring to the example “[t]he qi of mountains yields more males,” the qi that coalesces the mountains is transacted to the human population flourishing nearby, such that both manifest sturdy, upright, “male” characteristics.
In short, the localized propagation of the same sorts of things is the manifestation of differentiated qi moving through generation after generation of proximate thing. These localized “qi ancestries” are represented in the various (theoretically infinite) pathways that extend through Figure 2. It is these ancestries that give the inhabited world its familiar, reliable contours: these organisms here, those minerals there; this sort over here, that sort over there.Footnote 79 In this way, the bifurcations of Figure 2 serve as a skeletal representation not only of the distant young cosmos, a sparser reality of divine celestial forms, but also of the still-evolving here and now, the busy, highly patterned reality of the familiar natural order.Footnote 80
Resonance and the Two-Faced Cosmos
“Lanming xun,” the sixth Huainanzi chapter, documents correlations in the behaviors of remote things. These correlated behaviors suggest that things are able to affect one another without any direct transaction of physical force. “Lanming xun” refers to this mysterious entanglement with the terms gan 感 (“affecting”) and ying 應 (“responding”), which commentators have since concatenated into the term ganying 感應, or “resonance.”Footnote 81 In this third set of readings, I show how “Lanming xun’s” resonance phenomena work with reference to the qi-based processes underpinning them. I show that these resonance mechanics imply the seemingly paradoxical interleaving of the familiar natural order with another, structurally antithetical aspect of reality. I draw out the features of this “other aspect” of reality based on the text’s evidence.
The following extract, opening an arc that Charles Le Blanc describes as “the most important passage” in the chapter, documents several instances of things affecting one another at a distance: the arrival of the east wind prompts wine to turn clear; silkworm silk affects the shang 商 string on a lute; a drawing in ash affects the moon; distrust between lords and ministers causes discordant arcs to appear in the atmosphere.Footnote 82
夫物類之相應，玄妙深微，知不能論，辯不能解。
故東風至而酒湛溢，蠶咡絲而商弦絕；或感之也。畫隨灰而月運闕，鯨魚死而彗星出；或動之也。
故聖人在位，懷道而不言，澤及萬民。君臣乖心，則背譎見於天；
神氣相應徵矣。
故山雲草莽，水雲魚鱗，旱雲煙火，涔雲波水；各象其形類，所以感之。
As a principle, the mutual resonance of things in their sorts is profoundly fine and deeply subtle. Knowledge cannot [be used to] discuss it, and disputation cannot unravel it.
Thus, the east wind arrives and wine turns clear and overflows;Footnote 83 the silkworm spits out silk and the shang string [on a lute] severs.Footnote 84 It is that something affects them. An ellipsisFootnote 85 is drawn in ash and the moon’s halo is depleted;Footnote 86 a whale dies and comets appear. It is that something stirs them.
Thus, a sage occupies the throne, cherishes dao and does not speak, and his beneficence reaches the myriad people. If lords and ministers are antagonistic [in] their hearts, then back-to-back arcs [about the sun] are seen in heaven.Footnote 87 It is the sign of spirit qi mutually responding.
Thus, mountain clouds are [like] grassy undergrowth; water clouds are [like] fish scales. Drought clouds are [like] smoldering flames; downpour clouds are [like] vacillating waters. Each resembles its form and sort, affecting [the other] in this way.Footnote 88
Many of these mutually resonant pairs share characteristics. Antagonistic feelings between lords and ministers can be synesthetically schematized as back-to-back shapes in the atmosphere; the moon and an ellipsis drawn in ash are both cold, gray, and dry and have a circular form. Where shared characteristics are not immediately intuited by the modern reader, they are understood from early Chinese agrarian knowledge: the east wind comes at the same time of year as sediment settles in wine, turning it clear, and both events are moreover connected to “wood” among the five phases. Newly exuded silk fibers are as fragile and brittle as the shang string, the highest note on a lute. Overall, most of these resonating pairs belong to the same sort as one another, a point that the passage highlights by prefacing these instances as “the mutual resonance of things in their sorts.”Footnote 89
Reading extracts from “Tianwen xun” and “Dixing xun” in the previous two parts, I concluded that things’ sorts are determined by the kind of differentiated qi of which they are coalesced. These remote interactions between same-sorted things, which Le Blanc calls “relative resonance,”Footnote 90 may therefore be understood more precisely as remote interactions between coalescences of the same kind of differentiated qi.Footnote 91 The above “Lanming xun” passage corroborates this, going on to present two further instances of relative resonance that it explains as functions of similarly differentiated qi.
夫陽燧取火於日，方諸取露於月。天地之間，巧歷不能舉其數，手徵忽怳不能覽其光。然以掌握之中，引類於太極之上，而水火可立致者，陰陽同氣相動也。此傅說之所以騎辰尾也。
The fusui burning mirror takes fire from the sun, and the fangzhu square receptacle takes dew from the moon.Footnote 92 [Consider all that is] between heaven and earth: even a skilled calendarian is unable to enumerate its number; even a hand that traces the dim and indistinct is unable to grasp its lights. This is so, and yet one uses what’s within the palm of one’s hand to draw out sorts up to the Supreme Extremity. And that fire and water are able to be summoned, [this] is because the like qi of yin and yang stir one another. This is how Fu Yue bestrode the Tail.Footnote 93
The heat of the sun magnifies on the surface of a fusui burning mirror because their fiery yang qis “stir one another,” while the watery dew of the moon collects overnight in a fangzhu square receptacle because their watery yin qis interact.Footnote 94 This connection between relative resonance and differentiated qi is corroborated in the “Dixing xun” passage cataloguing localized concentrations of differentiated qi (“All things resemble their qi”), which segues into descriptions of instances of relative resonance.
磁石上飛，雲母來水，土龍致雨，燕鴈代飛，蛤蠏珠龜，與月盛衰。
Lodestone flies up;Footnote 95 mica draws water.Footnote 96 The earthen dragon makes rain arrive;Footnote 97 swallows and wild geese fly after one another. Clams, crabs, pearls, and tortoises wax and wane with the moon [phases].Footnote 98
This model of relative resonance can be understood against the representation of the Huainanzian cosmos in Figure 2, in which each line represents a discrete thing, a coalescence of an individual kind of differentiated qi. These individual lines link up through various pathways representing continuations of kinds of differentiated qi, coalescing generations of things belonging to the same or related sorts. Collectively, these pathways represent the familiar natural order: the everyday lived world in which events and interactions among the discrete yet relationally defined “myriad things” pattern themselves along predictable, regular contours. Relative resonance, as the routine interaction of similar-sorted things, not only follows but maintains the familiar natural order. The relative resonance phenomenon accordingly may be represented as interactions within and along the same pathways on Figure 2, diagrammatized in Figure 3.
Figure 3. A pathway in Huainanzi’s world-schema, representing the range of relative resonance.
In addition to relative resonance, there is a second category, which Le Blanc terms “total resonance.” This refers to remote interactions between things of any sort. The following extract from “Lanming xun’s” opening passage recounts two legendary instances of total resonance, wherein two human agents remotely neutralize patient entities of separate, non-human sorts.
武王伐紂，渡于孟津，陽侯之波，逆流而擊，疾風晦冥，人馬不相見。於是武王左操黃鉞，右秉白旄，瞋目而撝之，曰：「余任天下，誰敢害吾意者！」於是，風濟而波罷。
魯陽公與韓構難，戰酣日暮，援戈而撝之，日為之反三舍。
King Wu attacked Zhòu and forded at the Meng ford.Footnote 99 The Marquis of Yang’s waves reversed flow and struck them.Footnote 100 The brisk wind was gloomy and murky, [such that] the cavalry could not see one another. At this, King Wu grasped his yellow battle-axe in his left hand and gripped his white mao banner in his right. His eyes wide, he brandished these, saying, “I am charged with the realm; who would dare harm my ambition?!” With this, the winds abated, and the waves ceased.
Enmity had bred between the Duke Luyang and the Hán, and the battle reached fever pitch as the sun was setting.Footnote 101 [The Duke] took his halberd and brandished it, and the sun went back three stations for him.Footnote 102
Another extract from Le Blanc’s “most important” arc in “Lanming xun” demonstrates the difference between total and relative resonance using the allegory of tuning a lute.
今夫調弦者，叩宮宮應，彈角角動，此同聲相和者也。
夫有改調一弦，其於五音無所比，鼓之而二十五弦皆應，此未始異於聲，而音之君已形也。
Now, when someone tuning his [lute] strings strikes the gong note, the gong note [on other lutes] responds; when he plucks the jue note, the jue note stirs [on other lutes]. This is because like sounds harmonize with one another.
Someone changes the tuning of one string [such that] it does not match up to any of the five notes, and, upon hitting it, all twenty-five strings respond.Footnote 103 This is because there was yet to be [any] differentiation between sounds, but that which is lord over [musical] notes had already been formed.Footnote 104
In a first scenario, someone plucks a string on a lute with standard tuning, and so causes the same strings (which is to say, strings of the same sort) on other lutes nearby to reverberate. This represents relative resonance. In a second scenario, a string on the first lute is given a special tuning, and plucking this string causes all strings on other lutes to reverberate. This illustrates total resonance, wherein things remotely stimulate one another regardless of sort.
Whereas relative resonance describes routine occurrences that follow and reaffirm the familiar natural order, total resonance appears to describe the subversion of this natural order. Much how the special lute tuning cuts right across the pitch distinctions that bring harmonic order to music, King Wu and Duke Luyang disrupt the processes of nature, mollifying raging winds and rivers and reversing the sun’s passage across the sky. A further “Lanming xun” passage affirms this subversive impact of total resonance within the familiar natural order, using the analogy of divine birds.
鳳凰之翔至德也，雷霆不作，風雨不興，川谷不澹，草木不搖，而燕雀佼之，以為不能與之爭於宇宙之間。
還至其曾逝萬仞之上，翱翔四海之外，過昆侖之疏圃，飲砥柱之湍瀨，邅回蒙汜之渚，尚佯冀州之際，徑躡都廣，入日抑節，羽翼弱水，暮宿風穴。
當此之時，鴻鵠鶬鸖莫不憚驚伏竄，注喙江裔，又況直燕雀之類乎！
When the soaring of phoenixes is fully powerful, thunder and lightning do not strike; wind and rain do not rise up; the river plains and vales do not deluge; the grasses and trees do not shake. The swallows and sparrows mocked them (the phoenixes), thinking them unable to compete with them between the eaves and ridge piece [of the roof].Footnote 105
Then [a moment] came when they (the phoenixes) passed again and again at a height of ten thousand fathoms, soared and circled beyond the four seas, passed through the wilderness gardens of the Kunluns, drank from the rushing rapids of the Dizhu [mountain],Footnote 106 wheeled back and forth over the islets of the Shrouded Mire,Footnote 107 and lingered at the border of Ji Province; [they] passed directly through Douguang,Footnote 108 went in [with] the sun where it breaks off [its course], [washed] their feathers and wings at the Weak Waters,Footnote 109 and at dusk lodged in the Wind Cavern.Footnote 110
At that moment, there were none among the wild geese, swans, oriels, and cranes that were not startled, shrinking down in their nests and sticking their beaks in the banks of the rivers. Just how much more [was this the case for] such sorts [of birds] as swallows and sparrows!Footnote 111
By the reckoning of swallows and sparrows, even the ability to fly quickly between the eaves of a barn represents a supreme achievement. Phoenixes, however, can travel vast distances in impossibly little time, sojourning at otherworldly sites inaccessible to earthly beings, and venturing to the fringes of the world.Footnote 112 Their fantastic transit violates all apparent physical laws and is incomprehensible from a standpoint within the bounds of the everyday lived world, as evidenced in other birds’ reactions to the spectacle: even moderately-sized birds—wild geese, swans, oriels, and cranes—are bewildered into submission, to say nothing of the little swallows and sparrows.Footnote 113
The familiar natural order does not proffer any epistemological frame by which to anticipate or understand the phenomenon of total resonance. Rather, from a standpoint within this order, total resonance (in stark contrast to relative resonance) appears to completely subvert all laws and patterns; it is as improbable as the phoenixes’ transit appears with respect to the little birds’ frame of reference. If one tries diagrammatizing total resonance on Figure 2, as in Figure 4, the result is the awkward bisection of its pathways, reflecting the unsuitability of the familiar natural order as a basis for a positive account of how (or where) total resonance happens. Clearly, some other aspect or dimension of Huainanzian reality beyond the familiar natural order is required in order to account for total resonance.
Figure 4. How total resonance initially appears.
The “Tianwen xun” cosmogonic passage seen in the section “The Early Cosmogonic World” evokes the exotic nature of reality before the cosmos’ earliest moments, “[w]hen the heaven and terrains were not yet formed.” This was a formless, primordial unity; all was “a crashing, soaring, gushing, roaring [profusion]” comparable to an ocean of un-isolatable waterdrops. No “things” had yet emerged from any “other,” to speak in terms of the familiar natural order. The following “Lanming xun” extract, which follows on directly in the text from the lute-tuning passage, describes a state mirroring the chaotic formlessness described in “Tianwen xun’s” cosmogony. This state, which the chapter calls “great connectedness” (da tong 大通), refers to the experience of the human total resonance agent.
故通於太和者，惛若純醉而甘臥以游其中，而不知其所由至也。純溫以淪，鈍悶以終，若未始出其宗，是謂大通。
Thus, the one who is thoroughly connected through to supreme harmony is dim as if plain drunk and roams within it, sweetly asleep, not knowing whence they came. Submerged in clean warmth, terminated in dull mugginess, as if they had not yet begun to emerge from the ancestor: this is what is referred to as great connectedness.Footnote 114
One who decomposes into “great connectedness” experiences themselves devolving to a point where they outwardly appear “dim as if plain drunk … sweetly asleep, not knowing whence they came,” relinquishing that which marks them as a distinct individual. They appear “as if they had not yet begun to emerge from the ancestor,” anteceding the latter order of discrete things. This appears to be an experience of reality as, like “Tianwen xun’s” primordial reality, un- or “pre”-differentiated qi, wherein individual things have yet to emerge. A human agent enmeshed therein faces no gap nor lag in affecting “other” things, with which “they” constitute a sheer, singular, analytically indivisible whole, and “interactions” become the “intra-actions” of a unified qi.Footnote 115 This is how an agent may achieve resonance with patient entities that, at the level of the latter natural order, belong to a different sort. Whereas relative resonance happens automatically and routinely within the familiar natural order, total resonance becomes possible only for the exceptional individual who passes beyond the veil of everyday experience to achieve oneness with “the ancestor,” reflected in “Lanming xun’s” association of the phenomenon with exceptional beings like phoenixes.
Arriving at this account of total resonance, an area requiring further explanation becomes apparent. This area is touched on in the next section of the passage recounting the actions of King Wu and Duke Luyang.
夫全性保真，不虧其身，遭急迫難，精通於天。若乃未始出其宗者，何為而不成！夫死生同域，不可脅陵，勇武一人，為三軍雄。
They kept intact their nature and preserved their trueness, not forfeiting their bodies; met with crisis and pressed with difficulty, their essence connected through to heaven. Just like ones who had not yet emerged from the ancestor, what feat could they not accomplish! They took life and death to be the same territory, unable to be coerced or bullied; their courage and martial spirit was such that either alone could have become the hero of three armies.Footnote 116
The passage affirms that, in these two cases, enmeshment with great connectedness did not require either agent to irreversibly relinquish the human form they possess within the default natural order. Even though great connectedness, like “Tianwen xun’s” primordial formlessness, appears to be structurally antithetical to, and incompatible with, the familiar natural order, the total resonance agent exists simultaneously in these two aspects of reality, their resonance act straddling both domains.
How can this be possible? How can one reality encompass both a division-based order of finite things, and the boundless, indivisible unity that this order carved itself out of at the beginning of time? How can individual things be both things unto themselves, “not forfeiting their bodies,” and part of a primordial whole (“not yet emerged from the ancestor”)? Qi, the energy-substance in which all reality is constituted, encompasses this duality in its own ontology: throughout the differentiations whereby it fixes the myriad things in their sorts, it is nevertheless, per the evidence of “great connectedness,” a fundamentally undifferentiated, infinitely mutable unity. The hot qi that forms fire yet constitutes a singular substance with the cool qi that differentiates water. How, too, can this be?
Before proposing a way through the seeming paradox of a patterned-yet-formless reality, it is instructive to gauge the extent to which these questions hold relevance beyond the subject matter niche of “Lanming xun” by examining Huainanzi’s final full chapter, “Taizu xun.” As its title (“Highest Conglomeration”) suggests,Footnote 117 this chapter synthesizes the diverse insights of the preceding nineteen and applies these in an exposition of the sage-ruler’s approach in governance.Footnote 118 In all matters, the sage-ruler operates on the basis of “sincerity” (cheng 誠), or a “sincere heart” (cheng xin 誠心). While Huainanzi’s concept of “sincerity” has many facets, I show that in several key instances, this refers to a state that enables the sage-ruler to perform total resonance. This important role for total resonance within the text’s ideal of rulership elevates the understanding of its mechanisms to a key concern for the Huainanzian enterprise as a whole.
Total Resonance in the Supreme Performance of Politics
The concept of sincerity is introduced in a passage near the beginning of “Taizu xun,” which details instances of relative resonance in nature.
夫溼之至也，莫見其形而炭已重矣；風之至也，莫見其象而木已動矣。日之行也，不見其移；騏驥倍日而馳，草木為之靡；縣熢未轉而日在其前。
故天之且風，草木未動而鳥已翔矣；其且雨也，陰曀未集而魚已噞矣。以陰陽之氣相動也。
故寒暑燥溼，以類相從；聲響疾徐，以音相應也。故⟪易⟫曰：「鶴鳴在陰，其子和之。」
As a principle, at the arrival of moisture, none sees its shape, and yet coal is already heavier. At the arrival of wind, none sees its likeness, and yet wood has already moved. At the passage of the sun, one does not see its movement; fine steeds gallop to double [the speed of] the sun,Footnote 119 [with] grasses and timber blown away by them, [arriving] before distant beacon lamps [can complete] a turn, and yet the sun is still in front of them.
Thus, when heaven is about to [send] wind, the grasses and wood have yet to move and yet birds have already taken flight. When it is about to [send] rain, overcast gloom has yet to gather and yet fish already gawp [at the surface]. This is because they move one another with the qi of yin and yang.
Thus, heat and cold, damp and dryness follow each other according to sort; sounds and echoes, rapid or slow, respond to each other according to tone. Thus, the Yi [jing] says, “The crane cries out in the shadows; her child sings back to her.”Footnote 120
Coal responds to wetness (both are dark and yin); birds respond to the wind; fish respond to the rain. (The extract explains that these things “move one another with the qi of yin and yang,” as “heat and cold, damp and dryness” respond to one another on the basis of “sort,” supporting the earlier conclusion that resonance phenomena are functions of qi.) A parallel is drawn between these responses and the instantaneous response shared between sounds and their echoes. This recalls the “Lanming xun” extract, discussed in the previous part, that illustrates the principles of resonance using the analogy of notes played on a lute. The excerpt affirms this comparison by citing an example of automatic response between similar things in the foundational literature, a couplet from the sixty-first hexagram in the Yi jing 易經 (Classic of Changes), “Zhong fu” 中孚 (“Center Returning”).Footnote 121 This couplet describes baby cranes calling out in response to the cries of their unseen mother.
The passage continues by presenting another example of resonance, this time enacted by a legendary ruler.Footnote 122
高宗諒闇，三年不言，四海之內寂然無聲；一言聲然大動天下。是以天心呿唫者也。
故一動其本而百枝皆應，若春雨之灌萬物也，渾然而流，沛然而施，無地而不澍，無物而不生。
When Gaozong [went into] ritual mourning, he did not speak for three years. [There was] nothing but silence within the four seas. [Then] with a single utterance he greatly moved the realm; this is because he opened and closed [his mouth] with the heart of heaven.
Thus, move its root [but] once and the hundred branches all respond, like spring rain suffusing the myriad things. In pitching [waves] it flows; in copious [torrents] it spreads. There is no place that it does not inundate; there is no thing that it does not give birth to.Footnote 123
With only the faintest of sounds, Gaozong moves not one or two remote things, but all things in the realm. This resonance performance is analogized as heavy, relentless spring rains that spread everywhere, drenching everything. The passage goes on to define the general resonance performance of the sage on the basis of this example.
故聖人者懷天心，聲然能動化天下者也。
故精誠感於內，形氣動於天，則景星見，黃龍下，祥鳳至，醴泉出，嘉穀生，河不滿溢，海不溶波。
Thus, the sage is one who holds in their breast the heart of heaven and is able to move and transform the realm with a sound.
Thus, [when] rarefied sincerity is affected from within and the qi of [their] shape is moved by heaven, spectacular stars appear, the yellow dragon descends, the propitious phoenix arrives, springs of sweet wine burst forth, and excellent grains grow. The Yellow River does not swell to bursting; the seas do not billow and surge.Footnote 124
When “rarefied sincerity is affected from within” the sage and “the qi of [their] shape is moved by heaven,” all sorts of wonderful, mythical things are stimulated to appear in profusion, while threats on the other hand are quelled.
The feats of sage-rulers (like Gaozong) refer to subtle interactions between things of any sort, and as such constitute exemplar performances of total resonance. (The passage’s identification of qi as the material factor in this agrees with earlier analysis.) The concept of sincerity is introduced as the catalyst for these feats. It is when “rarefied sincerity is affected from within” the sage (who “holds in their breast the heart of heaven”) that “the qi of [their] shape is moved by heaven” and the feats of resonance described take place. In the section “Resonance and the Two-Faced Cosmos,” I posited that total resonance is possible for individuals who slip beyond the default, everyday experience of reality into “great connectedness,” a rare and strange experience of the sheer, analytically indivisible wholeness of un- or pre-differentiated qi. Interactions that fall outside the limits of the familiar natural order become possible within great connectedness as “intra-actions” between as-yet un-emerged things. One of the meanings of sincerity, then, is the special attitude or state whereby this elusive experience of reality can be reached, in turn allowing an individual to perform total resonance and, in the case of the ruler, rule through it.Footnote 125
Another “Taizu xun” extract describes the features of the realm when this is ruled by a sage whose regime is led by his “sincere heart.”
聖主在上，廓然無形，寂然無聲，官府若無事，朝廷若無人。無隱士，無軼民，無勞役，無寃刑。四海之內，莫不仰上之德，象主之指，夷狄之國，重譯而至，非戶辯而家說之也。
推其誠心，施之天下而已矣。⟪詩⟫曰：「惠此中國，以綏四方。」內順而外寧矣。
[When] a sage-ruler is positioned above, he is secluded and without shape, silent without a sound. [His] offices and bureaus [are] as if without business, [his] court and halls as if without men. [There are] no reclusive scholars, no disenfranchised people, no harsh labor, and no unjust punishment. Within the four seas, none do not gaze up to [his] virtue as superior and emulate [his] instructions as ruler. [In] the domains of the Yi and Di, [these instructions] arrive [through] repeated translation; it’s not that [anyone] is contending [them] from door to door or persuading family after family.Footnote 126
He does nothing more than promote his sincere heart and spread it out [through] the realm. The Shi [jing] says, “Care for these central domains, to pacify the four directions.”Footnote 127 When all goes agreeably in the interior, the exterior is tranquil.Footnote 128
When a sage is in power, his governance does not appear at all active. He is passive in his personal presentation, and his personnel and buildings also appear dormant. Society is nevertheless inclusive (“[There are] no reclusive scholars, no disenfranchised people”) and the people are reverent to him (“none do not gaze up to [his] virtue as superior and emulate [his] instructions as ruler”). These positive effects moreover extend to foreign peoples, not through concerted canvassing efforts, but through a natural osmosis and attraction.Footnote 129 The couplet from “Min lao” 民勞 (“The Commonfolk are Burdened”) reaffirms the axiom that the state of society directly under the ruler’s control has an impact on, and is reflected in, the state of domains beyond. This is, to make a connection with another term that appears throughout Huainanzi, governance by non-action (wuwei), a term echoed throughout the extract’s opening line (wu xing 無形 [“without shape”]; wu sheng 無聲 [“without a sound”]; wu shi 無事 [“without business”]; wu ren 無人 [“without men”]).Footnote 130 The extract concludes that all of this is achieved simply because the ruler “[promotes] his sincere heart and [spreads] it out [through] the realm.”
From there, the passage presents several episodes from legend that affirm the distinction of sincerity as a basis for governance.
太王亶父處邠，狄人攻之，杖策而去。百姓攜幼扶老，負釜甑，踰梁山，而國乎岐周，非令之所能召也。
秦穆公為野人食駿馬肉之傷也，飲之美酒，韓之戰，以其死力報，非券之所責也。
密子治亶父，巫馬期往觀化焉，見夜漁者，得小即釋之，非刑之所能禁也。
孔子為魯司寇，道不拾遺，市買不豫賈，田漁皆讓長，而辬白不戴負，非法之所能致也。
夫矢之所以射遠貫牢者，弩力也；其所以中的剖微者，正心也；賞善罰㬥者，政令也；其所以能行者，精誠也。
故弩雖强，不能獨中；令雖明，不能獨行。
[When] Ancestral King Danfu was situated in Bin and the Di attacked it, he departed leaning on his cane. [With] the common folk leading the young by the hand and supporting the elderly, shouldering cooking pans and steaming pots, they crossed over Mount Liang and [set up] a walled city in Qi Zhou.Footnote 131 This is not [something] that decrees could muster.
[When] Duke Mu of Qin furnished the hinterland people with fine wine [to drink] on account of his pain at [seeing] them feeding on the meat of fine steeds, they recompensed [him] with fatal efforts at the battle of Han[yuan].Footnote 132 This is not [something] that contracts could compel.
[When] Fuzi governed [the fief of] Danfu, Wuma Qi went to observe the transformations [brought] by him. He saw [how] those who fished by night would catch small [fish] only to release them.Footnote 133 This is not [something] that punishments could forbid.
[When] Confucius was the Minister of Criminal Affairs for Lu, [passers-by] did not pick up [things] lost on the road and [vendors] did not hike the prices up at market. In tilling and fishing, all yielded to [their] seniors, and the white-haired [elders] were not laden with burdens. This is not [something] that laws could impel.
As a principle, [although] the means by which arrows fly far to pierce through hard [materials] is the power of the crossbow, the means by which they strike the mark and slice through the minute is the rectified heart. [While] rewarding goodness and penalizing violence are decrees of governance, the means by which they can be applied is rarefied sincerity.
Thus, even when the crossbow is strong, it cannot strike [the mark] unassisted; even when decrees are enlightened, they cannot be applied unassisted.Footnote 134
Ancestral King Danfu, Duke Mu of Qin, Fuzi, and Confucius achieved changes in the populace’s behavior such as would be unobtainable through the usual direct tools of government, such as decrees and punishments. The passage clarifies that the sage-ruler does not necessarily dispense with these tools entirely, explaining that where these exemplary leaders employed these tools, their full utility remained contingent upon the leaders’ demonstration of “rarefied sincerity,” much as a perfect crossbow shot requires the direction of a virtuoso archer’s rectified heart. Sincerity’s lynchpin role in ideal governance is reaffirmed in a further section, which plainly states that it is only through sincerity that the ruler’s project (here, covering the people with dao) is achieved.Footnote 135
必自精氣所以與之施道。故攄道以被民，而民弗從者，誠心弗施也。
It must be from rarefied qi that one propagates the dao with them (decrees). Thus, [when] one spreads out the dao to cover the people, if they do not follow it, it is because a sincere heart does not spread it [to them].Footnote 136
In sum, sincerity is central to Huainanzi’s construct of sage governance, and one of its key functions therein involves unlocking the ruler’s capacity to realize actions unhampered, both at home and abroad, all while remaining quite passive within the familiar natural order—in short, to act through non-action.Footnote 137 Where usual instruments of governance are limited by the physical laws of the natural order, the sincere-hearted ruler, dissipated amid the singular, “rarefied” qi of great connectedness, bypasses this order entirely, meeting no obstruction in acting upon “other” things, with which they constitute a cosmic whole. This is how, to gloss a line from the “Lanming xun” passage that opens section “Resonance and the Two-Faced Cosmos,” “a sage occupies the throne, cherishes dao and does not speak, and his beneficence reaches the myriad people.”
Putting It All Together: A Way Through the Structural Paradox
Huainanzi presents a formula for governance that begins with the ruler’s cultivation of a sincere heart, sending him beyond the veil of everyday reality and into an experience of “great connectedness.” There, political projects are realized limitlessly through the non-action of total resonance. This model of rulership, however, rests on what appears to be a paradoxical model of reality. This is a model of reality that, as indicated in the conclusion to section “Resonance and the Two-Faced Cosmos,” superimposes a highly patterned domain of discrete, finite forms upon a structurally antithetical domain of endless formlessness, with the sage-ruler’s actions encompassing the two as one.Footnote 138
The “Taizu xun” passage cited in the opening of the section “Total Resonance in the Supreme Performance of Politics” above is directly preceded in the text by a description of heaven arranging the myriad things into discrete and predictable orders.
天設日月，列星辰，調陰陽，張四時。日以暴之，夜以息之，風以乾之，雨露以濡之。
其生物也，莫見其所養而物長；其殺物也，莫見其所喪而物亡。此之謂神明。聖人象之。故其起福也，不見其所由而福起；其除禍也，不見其所以而禍除。
遠之則邇，延之則疎；稽之弗得，察之不虚。日計無算，嵗計有餘。
Heaven set up the sun and moon, arrayed the stars and constellations, attuned yin and yang, and set forth the four seasons. The day exposes [things] to the sun, the night replenishes them; the wind dries them, and the rain and dew moisten them.
When it (heaven) gives birth to things, in no case does it show [the way] that it nourishes [them] and yet things [still] grow; when it kills things, in no case does it show [the way] that it loses [them] and yet things [still] perish. It is this that we call “numinous brightness.” The sage resembles this, thus, when he engenders good fortune, he does not show what he derives [this] from and [still] good fortune is engendered; when he clears away catastrophe, he does not show what he uses and [still] catastrophe is cleared away.
[Put] it at a distance, and it gets near; draw it in, and it makes itself scarce; examine it, and it will not be gotten; scrutinize it and it will not be empty. Reckon it [on the scale of] days and it is incalculable; reckon it [on the scale of] years and it is superfluous.Footnote 139
Heaven arrays the sun and moon, yin and yang, the stars, seasons, day and night, wind and rain, and even the life and death cycles of mortal things, and the ebb and flow of their fortunes. From there, the passage considers the ways in which heaven achieves these arrangements: heaven’s actions and reactions appear counterintuitive and immeasurable, to the point of impossibility, with respect to the laws that structure the everyday natural order. Much how the little birds in the “Lanming xun” passage are unable to comprehend the phoenixes’ flight, the familiar, known world and heaven’s sphere of limitless activity are so unlike that the former proffers no epistemological framework for making sense of events in the latter.
The above passage, considered simply, is a contingent meditation on the distinction between finite and infinite processes. Here, the utility of a fractal versus Euclidean geometrical heuristic, juxtaposing discrete and (endlessly) continuous dimensionality, becomes apparent. I suggest that Huainanzi’s apparent superposition of great connectedness—the infinitely connected unity of undifferentiated qi—and the familiar natural order—the aggregate of finite, local, and sorted qi-coalesced things—within, and as, reality can be understood in reference to these geometrical registers. Similar to how information about complex natural phenomena in our world may be modelled using either geometry, Huainanzi’s two, structurally distinct domains refer to representations of the same, subtle reality, with the experience of great connectedness referring to the “fractal” cosmic figure, and the familiar natural order referring to the same, parsed out into discrete “Euclidean” forms.
As noted in the introduction, unlike normal finite systems in which each new level is governed by a new set of rules, a fractal is structured at all possible levels, including the whole, by the same rule.Footnote 140 Higher orders of complexity mushroom from one simple recursive operation, which encodes an infinity of microcosmic levels, extending all the way down. As such, any possible level both is in the whole, as its part, and is the whole, not only as its perfect structural facsimile, but also as a seamless integrant within this same true, infinite and infinitely divisible whole, where discrete “levels” are circumscribed from “others” on a purely synthetic basis. These attributes of fractal geometry reflect great connectedness’ features of infinite self-sameness, infinite divisibility (amounting to perfect uniformity), infinite scope and extensibility, an absolute degree of internal connectedness, as well as chaotic muddledness.Footnote 141 By contrast, Euclidean shapes, clearly bounded with their full integer dimensionality, model the discrete forms of the familiar natural order. Using figure 2 as a corollary, great connectedness corresponds to this shape taken holistically, as a fractal whole, with the structural rule of bifurcation reiterating ad infinitum.Footnote 142 The familiar natural order, by contrast, corresponds to individual finite lines and finite local arrangements thereof, decontextualized from the endless structural iterations of the fractal whole, divesting these “parts” of the fractal attributes that emerge when nested in situ relative to “one another.” These are branches when seen removed from the fractal net of branches.
Thinking about the Huainanzian cosmos in this way, the actions of the total resonance agent, straddling both great connectedness and the familiar natural order, need not imply a paradox. These experiential domains have all along corresponded to the same ineffable cosmic reality, with the abyssal dimensionality of the former occluded by the finite structural rubrics that apply in the latter. To attempt to apprehend great connectedness from a standpoint within the familiar natural order is akin to attempting to describe a fractal set in Euclidean terms. Thus, “Lanming xun’s” description of the total resonance agent’s decomposition out of the familiar natural order and into great connectedness likens this process to a sweet stupefaction, as the agent unlearns the declarative patterns of isolation and division on which the familiar order hangs, falling back into the infinitesimally fractional dimensionality across which “they” have always, in fact, been endlessly spread. This agent, assented to the fractal integrity of great connectedness, may universally affect any individual “thing” within the latter natural order, with which “they” (to speak in terms of this order) constitute a unity, with the resulting appearance within that order of scattered resonance events. Any “part” within great connectedness can act on the whole inasmuch as the whole may act on itself.
At this point, there is a distinction to be made between the examples of total resonance discussed in section “Resonance and the Two-Faced Cosmos” and the sage-ruler’s total resonance performance (governing through non-action). The “Lanming xun” passage recounting the episodes of King Wu and Duke Luyang remarks, “What feat could they not accomplish!” This indicates that there is nothing stopping the pair, devolved into great connectedness, from resonating with all things. The scope of their resonance acts are curtailed by their focus on specific patients within the latter order. This passage goes on to muse “how much more” this resonance scope would extend for one whose intent lies beyond the pair’s “seeking fame.”
彼直求名耳，而能自要者尚猶若此，又況夫宮天地，懷萬物，而友造化，含至和，直偶於人形，觀九鑽 一，知之所不知，而心未嘗死者乎！
If that which those [two, King Wu and the Duke Luyang], who were just directly seeking fame, were able to demand of themselves could yet be like this, then how much more [could be demanded in the case of] one who makes heaven and earth his palace, cherishes the myriad things, befriends the creator, harbors utmost harmony, simply lodges in human form, observes nine and penetrates through to one, and [takes] that which knowing does not know,Footnote 143 and [does so] with a heart that has never known death!Footnote 144
Going beyond this limited resonance scope to affect all things is the preserve of “one who makes heaven and earth his palace.” This is the resonance performance of “Taizu xun’s” sage-ruler: like Gaozong, whose performance was described in an earlier extract using the image “move its root [but] once and the hundred branches all respond,” “Taizu xun’s” ruler achieves a global, ambient resonance with all things in the realm. This may be diagrammatized as the intra-action of all lines in the shape in Figure 2, per Figure 5, showing the fractal whole intra-acting across itself.Footnote 145 The constant uniformity of this resonance effect across the familiar natural order accounts for the sage’s appearance of quiet, harmonious non-action therein, just like “Lanming xun’s” phoenixes at their fullest power.
Figure 5. The theoretical full scope of total resonance.
Conclusion: “Resemblance” in the Philosophy and Text of Huainanzi, The Fractal View
I have argued that Huainanzi’s sage-ruler is defined by his capacity for total resonance, whereby he enacts a form of governance by “not doing.” As I have also shown in connection with evidence drawn from across the text, total resonance is made possible by the overlaying of great connectedness with the familiar natural order. Vermander argues that Huainanzi’s “Way,” such as the ruler must seek to master, is “a paradoxical shape.”Footnote 146 Echoing this finding (which Vermander makes with respect to Huainanzi’s intentional conceptual design), I have suggested that the relationship between these two seemingly structurally incompatible domains can be understood using the heuristic of representing (parts of) the same figure with different geometrical paradigms.Footnote 147 The “great connectedness” of singular undifferentiated qi corresponds to the root-and-branches diagrammatization of the Huainanzian cosmos in Figure 2 when taken as a fractal whole, with the rule of bifurcation appearing at all magnifications. Meyer, in his elaboration of the root-and-branches schema, asserts that Huainanzi’s cosmos is characterized by an underlying immutable sameness; this characteristic is formalized in the structural sameness of a fractal heuristic.Footnote 148 The familiar natural order of separate things, on the other hand, corresponds to Figure 2’s finite lines and their finite local arrangements, circumscribed from the structural context whence the shape’s fractal attributes emerge.Footnote 149 I accordingly suggest that the sage-ruler’s total resonance performance, moving in and between both domains, can be understood with this heuristic. Through the work of cultivating a sincere heart, unlearning the world’s ordering patterns, the sage-ruler sees the fractal wood for the individually sorted trees. Enmeshed in fractal connectedness, he bypasses the limitations of traditional instruments of government in the familiar natural order, impacting the realm limitlessly through the non-action of total resonance.
The “Taizu xun” passage cited in the previous part states that the sage himself “resembles” (xiang 象) the “numinous brightness” that is heaven’s extraordinary, inscrutable workings, which correspond to events in great connectedness.Footnote 150 (In the passage, this point is emphasized by its placement at the center of a syntactically parallelized stanza.) To say that the sage mimics or resembles reality and its domains is, however, only part of the story. As noted in the conclusion to the previous part, governance by non-action is achieved through global, ambient total resonance, the scope of which encompasses not just any but all things in the natural order. Referring again to the fractal heuristic, this is an affirmation of the indistinguishability of part and whole, including the sage-ruler’s own indistinguishability from the realm. This leads into the point that the sage-ruler who achieves an apprehension of the cosmos as a fractal whole is not himself external to it. Having previously experienced himself as a discrete thing, his decomposition into great connectedness encompasses an experience of “himself” as a seamless integrant therein—the part that is also the cosmic whole. Each “thing” that “he” then resonates with is also, from “his” standpoint within great connectedness, a part that is also the whole. The sage’s global resonance with all things, then, is a part that is also the whole interacting with itself through each part, which are also that same whole; in effect, the sage-ruler’s resonance act retraces, and performs, the dive into recursion whence the fractal cosmic set arises.Footnote 151
As indicated in the introduction, fractal-like recursions are found elsewhere in Huainanzi. Given their role in articulating a nesting cosmology that, the text claims, is a facsimile of a nesting lived world beyond it, the inclusion of nesting motifs at different levels of the text’s composition, as identified by Murray and Vermander, can also be regarded as a kind of performative recursion.Footnote 152 Through its replication in the text structure, Huainanzi’s nesting cosmology becomes a facsimile of a facsimile of a lived world, performing the spatial regression that forms its thesis; not only are both text and cosmic schema in the world as resident parts, but they are the world. By a similar logic of fractal recursion, the sage-ruler, achieving wuwei, not only resembles and aligns with the cosmos, but becomes the cosmos. It is not so much the case that “he” enacts “his” political will, but that he serves as a conduit among the forms of the natural order for the cosmos as a whole—to which, again, he is equivalent—to shape and regulate itself, via the crux of the realm’s political center.Footnote 153 As much as total resonance appears, from a standpoint within the familiar natural order, as a shortcut by which the ruler can reshape the realm in line with “his” will, when a ruler enacts total resonance in its fullest scope, the material changes that follow are in fact merely the secondary effects of his ascension to his position as heaven and earth, cosmos and realm, “his” will and designs engulfed amid a greater performance of the cosmic whole and its harmonious structural equivalences.Footnote 154 Through all this, the sage-ruler nevertheless retains “his own” form amid the profusion of delightfully diverse myriad things that make up the vibrant, beautifully-woven world of everyday lived experience (for this is, after all, the same reality, simply under what I have likened to a different geometrical register). As noted by Griet Vankeerberghen and Matthew Hamm, the sage’s role encompasses defining and leading the people in the patterns and guidelines of culture (wen 文), “the collection of technologies and social institutions” through which humanity attempts to accord with the “existing patterns [li 理] of the cosmos”—the familiar natural order.Footnote 155 The harmony of the dao’s expressions in and as great connectedness and the familiar natural order, the two ontological “registers” of the universal substrate, qi, is thereby sustained at equilibrium.Footnote 156
In summary, the heuristic of fractal and Euclidean geometry not only offers a way to understand the seemingly dual structure of Huainanzian reality underpinning its model of rulership, but moreover provides a language by which to articulate some of the subtleties of the ruler’s function in maintaining cosmic harmony.Footnote 157 I have suggested that this function encompasses both representation and correlation between cosmos and sage, on the one hand, and cosmos and sage being and becoming one another, on the other. Huainanzi’s (often layered) use of mimicry, allegory, metaphor, and other representational figures is a recurrent interest in the most recent wave of Huainanzi scholarship from the late 2010s and 2020s.Footnote 158 The term “homology” is often seen in this scholarship in support of arguments to the effect that Huainanzi constructs relationships that go beyond representation, to constitute performative iterations, doublings, or other becomings.Footnote 159 As an addition to the existing conceptual repertoire for articulating the kinds of isomorphisms and evocations that Huainanzi, as a philosophical and literary text, uses to build relationships, the fractal heuristic offers a language for describing sets or systems in which all (structural) equivalences between elements are becomings: all would-be isomorphisms collapse into, and are, the mapped element itself. This would appear to be a useful concept to have in hand while thinking through the complex relational and ontological events of the Huainanzian universe, its text, and its associated system of concepts.
This recent wave of Huainanzi scholarship has also shown that the iterative and performative dimensions of the text’s uses of homology enable it to generate meaning in sensuous, intuitive, experiential, and other non-declarative ways.Footnote 160 (These scholars note that this strategy of meaning-making embodies the workings of dao, aligning with the text’s understanding of how wisdom of dao may be gotten at. “[M]usic and sound,” Peter Tsung Kei Wong asserts, “are relatively closer to the Way.”)Footnote 161 It appears to be a rule of this scholarship to work from an assumption that the text is saying more than it says, and with good reason: Huainanzi exhibits an exceptional understanding of how to encode, and not just declare, meaning. The postface “Yaolüe” recommends Huainanzi as an eternal account of phenomenal reality, a “final sage” transcending any finite contingent application, and I would suggest that a further application of a fractal heuristic is as the articulation of a specific way in which Huainanzi encodes infinity, sidestepping the impossible task of expounding the same through finite language.Footnote 162 Like Benoît Mandelbrot’s (1924–2010) early computer-rendered fractals, Huainanzi’s cosmos can, in one sense, be thought of as a set that iterates itself on the basis of a single operation.Footnote 163 Invariant under changes of scale, the fractal encodes instructions for replicating itself at any other level. In a similar way, Huainanzi leverages its limited text space to build not just a world, but a world that keeps building itself, over and over, erupting with a bewildering procession of endless forms from a deceptively simple structural principle.
As reflected in the name of Meyer’s article “Root, Branches, Numbers, Weaving, and Structural Rhetoric in the Huainanzi,” there can be no one conclusive interpretation of Huainanzi’s structural logic and rhetoric. It is impossible to fix a single image. Vermander’s research specifically highlights “the ‘computational’ nature of the Huainanzi, namely, its capacity to reach similar results through different itineraries” (even “suggest[ing] that the Huainanzi works as a mathematical table, as the one found in the Tsinghua 清華 manuscripts for instance”).Footnote 164 The different organizing “homologies” that scholars have identified within Huainanzi can be “computed” together, much how Meyer regards the numerological One-to-Ten sequence of Vermander’s “double circle” rhetoric as an expression of the “proliferation of ‘branch’ phenomena from the origin-point of the One.”Footnote 165 With Huainanzi—in a further characteristic paradox—it seems that the greater the proliferation of approaches to the text, the nearer one gets to it. These endless possibilities, as Vermander argues on behalf of the “reciprocal production” of squares and circles at the level of Huainanzi’s chapter-by-chapter composition, keep the text in constant motion.Footnote 166 The fractal cosmic figure is also a structure that is never foreclosed and is, in this sense too, in constant motion; it thereby renders obsolete all other cosmological projects, past, contemporary, and future, reaching towards “Yaolüe’s” bold proclamation of absolute comprehensiveness.
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