“To be attached to the subdivision, to love the little platoon we belong to in society, is the first principle (the germ, as it were) of public affections. It is the first link in the series by which we proceed towards a love to our country and to mankind.”
—Edmund Burke, Reflections on the Revolution in France (1790)

Fractals are a beautiful geometric phenomenon, and also a profound natural emergence of non-linear dynamical systems. They are characterised by the repetition of their structure at each level of magnification.¹ This structure arises because the rules of construction apply at every level.

To my mind, social relations are the perfect example of non-linear dynamics in action:

Causes: They experience feed-back effects.; Their dimensions are continuous.; They are highly complex.
Effects: They cycle around in close but never-repeating loops.; They have strong threshold effects.; And they exhibit fractal self-similarity.

In this essay, we will consider the fractal element of the core social relation of family.

Family-Proper

The atomic building-block of the familial fractal—what we might call level one—is the family itself, the house-hold or direct inheritance. The family exhibits, as an emergent property and as an archetype, several properties that will become familiar across this essay.

Loyalty

The members of a family exhibit loyalty to each other. This is not a mere happenstance but an evolutionary imperative: absent loyalty, the family group will be out-competed by united rivals. Loyalty includes self-sacrifice, the superficially paradoxical subjection of a lower, more intense tier (in this case, level zero, the individual), to a higher tier for a higher good. Individual-level analysis in the manner of the economists cannot explain this except as irrationality, but as a group behaviour it is not only explicable, but unavoidable.

This loyalty also applies in reverse, that a healthy family group will sacrifice collectively for the good of the individual. Indeed, understood properly this is the same thing. The sacrifice made by the group is also of necessity a sacrifice made by individuals, and the sacrifice made for the group is also a sacrifice made for individuals.²

Resemblance

Family members are innately alike, and become more alike through the emotional and physical proximity that naturally follows from healthy family behaviour. On this pillar of resemblance rests, bio-psychologically, many (all?!) of the other traits. It is important that this is bio-psychological: a resemblance that is purely conceptual is weaker than one that is rooted in blood. Step-children and adopted children have significantly worse outcomes than natural children even when they are superficially similar in appearance.³ A thousand subtle and subconscious differences scream silently from the uncanny valley: “I am not as you!”. Legally, there is no difference between the step- or adopted child and the natural one; morally, if you assert the smallest difference between them a cacophony of women will emerge to screech at you about how terrible you are⁴; and yet it is true.

The importance of resemblance is not merely descriptive. Because these philosophical traits of the family relationship are evolutionary, that is, emergent and adaptive, they are therefore necessary in the sense of the alternative being excluded by self-contradiction. A family group that does not resemble each other, physically, emotionally, and mentally, will be out-competed by more cohesive groups.

sum θoətiz abaʊt fraktəl familiiyiz [wip]

“tə biiʸ atacəð tə ðə sub-diviʒən, tə luv ðə litəl plətʊʊn wii biloŋ tʊʊʷ in səsaiətii, bii ðiiʸ umθ prinsipəl (ðə juəm, az it did biiʸ) ov publik afekʃəniz. it bii ðiiʸ umθ link in ðə siəriiz bai wic wii prəsiid təwʊədz a luv tə wiis kuntriiʸ and tə man-kaind.”
—edmənd buək, riflekʃəniz on ðə revəlʊʊʃən in frans (1790)

fraktəliz biiʸ a byʊʊtifəl jiiəmetrik fənominən, and oəlsoʊʷ a prəfaʊnd nacərəl imuəjəns ov non-liniiə dainamikəl sistəmiz. dii bii kariktəraizəð bai ðə repitiʃən ov diis strukcəʳ at iic levəl ov magnifikeiʃən.¹ ðis strukcəʳ araiz bikuz ðə rʊʊliz ov kənstrukʃən aplaiʸ at evrii levəl.

tə miis maind, soʊʃəl rileiʃəniz bii ðə puəfekt egzampəl ov non-liniiə dainamikiz in akʃən:

kʊəziz: diiʸ ekspiəriiəns fiid-bak efektiz.; diis daimenʃəniz bii kəntinyʊʊəs.; dii bii hailii kompleks.
efektiz: dii saikəl araʊnd in kloʊs but nevə-ripiitiŋg lʊʊpiz.; dii hav stroŋ θreʃoʊld efektiz.; and diiʸ egzibit fraktəl self-similaritiiʸ.

in ðis esei, wii wil kənsidə ðə fraktəl elimənt ov ðə kʊə soʊʃəl rileiʃən ov familii.

familii-propə

ðiiʸ atomik bildiŋ-blok ov ðə familiiəl fraktəl—wot wii mait koəl levəl um—bii ðə familiiʸ itself, ðə haʊs-hoʊld oə dairekt inheritəns. ðə familiiʸ egzibit, az an imuəjənt propətiiʸ and az an aəkitaip, sevrəl propətiiyiz ðat wil bikum fəmilyəʳ akros ðis eseiʸ.

loiəltii

ðə membəriz ov a familiiʸ egzibit loiəltii tʊʊʷ iic uðə. ðis biiʸ not a miə hapənstans but an iivəlʊʊʃəneriiʸ imperətiv: absənt loiəltii, ðə familii grʊʊp wil biiʸ aʊt-kəmpiitəð bai yʊʊnaitəð raivəliz. loiəltiiʸ inklʊʊd self-sakrifais, ðə sʊʊpəfiʃəlii parədoksikəl subjekʃən ov a loʊwə, mʊəʳ intens tiəʳ (in ðis keis, levəl zoʊ, ðiiʸ individyʊʊəl), tʊʊʷ a haiə tiə foəʳ a haiə gʊd. individyʊʊəl-levəl analisis in ðə manəʳ ov ðiiʸ ikonəmistiz not kan eksplein ðis eksept az iraʃənalitii, but az a grʊʊp biheivyəʳ it bii not oʊnliiʸ eksplikəbəl, but unəvoidəbəl.

ðis loiəltiiʸ oəlsoʊʷ aplaiʸ in rivuəs, ðat a helθii familii grʊʊp wil sakrifais kəlektivlii foə ðə gʊd ov ðiiʸ individyʊʊəl. indiid, undəstandəð propəlii ðis bii ðə seim θiŋ. ðə sakrifais meikəð bai ðə grʊʊp biiʸ oəlsoʊʷ ov nesesitiiʸ a sakrifais meikəð baiʸ individyʊʊəliz, and ðə sakrifaisiz meikəð foə ðə grʊʊp biiʸ oəlsoʊʷ a sakrifais meikəð foəʳ individyʊʊəliz.²

rizembləns

familii membəriz biiʸ ineitliiʸ alaik, and bikum mʊəʳ alaik θrʊʊ ðiiʸ imoʊʃənəl and fizikəl proksimitii ðat nacərəlii foloʊ from helθii familii biheivyə. on ðis piləʳ ov rizembləns rest, baiyoʊ-saikəlojiklii, meniiʸ (oəl?!) ov ðiiʸ uðə treitiz. it biiʸ impʊətənt ðat ðis bii baiyoʊ-saikəlojikəl: a rizembləns ðat bii pyʊəlii kənsepʃʊʊəl bii wiikə ðan um ðat bii rʊʊtəð in blud. step-caildiz and adoptəð caildiz hav signifikəntlii wuəs aʊt-kumiz ðan nacərəl caildiz iivən wen dii bii sʊʊpəfiʃəlii similəʳ in apiərəns.³ a θaʊn sutəl and sub-konʃəs difrənsiz skriim sailəntlii from ðiiʸ unkanii valii: “mii bii not az ðii!”. liigəlii, ðeə bii noʊ difrəns bitwiin ðə step- oəʳ adoptəð caild and ðə nacərəl um; morəlii, if ðiiʸ asuət ðə smoəlist difrəns bitwiin diiʸ a kakofəniiʸ ov wʊməniz wil imuəj tə skriic at ðiiʸ abaʊt haʊ teribəl ðii bii⁴; and yet it bii trʊʊ.

ðiiʸ impʊətəns ov rizembləns bii not miəlii diskriptiv. bikuz ðiiz filəsofikəl treitiz ov ðə familii rileiʃənʃip biiʸ evəlʊʊʃənerii, ðat biiʸ, imuəjənt and adaptiv, dii bii ðeəfoə nesəseriiʸ in ðə sens ov ðiiʸ oltuənətiv biiyiŋᵍ eksklʊʊdəð bai self-kontrədikʃən. a familii grʊʊp ðat not rizembəl iic uðə, fizikliiʸ, imoʊʃənəliiʸ, and mentəlii, wil biiʸ aʊt-kəmpiitəð bai mʊə koʊhiisiv grʊʊpiz.