Some Thoughts About “Reality Is Scalar”

[Galilée] déclare que dans tous ces phénomènes il faut mesurer tout ce qui est mesurable, et tâcher de rendre mesurable tout ce qui ne l’est pas directement.
[“[Galileo] declares that in all these phenomena we must measure all that is measurable, and try to make measurable all that is not directly so.”]
—Thomas-Henri Martin, Galilée: Les Droits de la Science et la Méthode des Sciences Physiques (1868)

When we describe the world, we often use categories to do so. We say that there are red objects and blue objects, poor folks and rich folks, lions and tigers, etc ad inf. These categories are useful to us, because they provide useful rules of thumb for understanding the world and predicting what the effects of our and others' actions will be. We can predict that a lion will behave differently to a tiger, or a red object will match some other object better than a blue one.

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Where we go wrong is to think that those categories that we apply to the world for our convenience are absolute. Taking the colour example, in truth these are just ranges on a scale, and fuzzy ranges at that, which we group into convenient bands. English is developed enough that we have basic colour names to a fairly high degree of specificity, but there are many languages with far fewer basic colour names, and even in English the cross-over points between different colours are fuzzy, ill-defined.

Our categories are useful only insofar as they correspond to real differences within scalar ranges. In particular, there are often threshold effects: tipping points at which a major change in some property of the object occurs, even when there is little change in that property outside of those ranges. Temperature and states of matter are a good example of this. For many basic substances there are two temperature thresholds where the substance undergoes a rapid and significant—and real—change in its properties: the melting / freezing point; and the boiling / condensing point. Water at 90°C behaves differently to water at 10°C, but in some important ways they are still more similar to each other than either is to water at 110°C. The temperature is scalar in a linear way; the state of matter depending (largely) on the temperature is scalar in a stepped way. Around the thresholds, the stepped scale moves faster, and is observable as a scale: for example, within the narrow range around the melting / freezing point, melting is a process rather than a binary switch. These differences in properties between ranges are real, but that does not make the categories absolute in themselves; we could usually choose different boundaries if it were useful to us to do so. For example, today we distinguish gases and plasmas because it is useful to do so, but we did not before, and in future we may distinguish differently again.

Where do categories tend to arise, especially in nature? At some point we do need to make decisions, and because those decisions are categorical, we must crystallise the spectrum into categories corresponding to the decisions we need to take. The feedback effect from those decisions in turn forces scalar reality to diverge and categorise. An excellent example is the binary division between the sexes: a thousand million years of sexual reproduction, with millions of millions of sex acts every day, have reïfied those mating decisions into (by the scalar standards of the natural world) an unusually rigid and uniform system of sex differences. Speciation results from the same effect: aeons of mating decisions resulting in visibly categorical outcomes.

The problematic effects of treating scalar reality as categorical (sometimes called “binary thinking”, the most extreme version of the error) appear in many places. Most of all, due to the forcing effect of decision-making, they stem from our treating our decisions as iron laws rather than pragmatic guidelines. Because reality is scalar, even when there are extreme threshold effects, there will always be edge cases that cannot be appropriately covered by iron laws. It may sometimes even be more appropriate to treat the edge cases as a category in themselves, but either this is precluded by categorical thinking rigidly insisting on its categories, or the edge cases are treated so rigidly as their own category that their similarities to their adjacent categories on the continuous scale are themselves ignored.

This is especially true in the social sciences and moral philosophy¹, because they themselves exist in the central portions of the reality scale between hard material reality, where it is usually obvious to think in a scalar fashion, and pure concept, where it is unproblematic or even appropriate to think in categorical terms. The social and moral domains are precisely about how our concepts map to underlying behaviours that are impossible to measure precisely, and where our decisions are of profound personal importance. But just because it is difficult for us to measure socio-moral properties does not mean that those properties are purely conceptual, and therefore categorical rather than scalar. While there are cases where we do not realise that our decisions have been reïfied into categories², in practice the more common error is treating our descriptive categories as defining reality itself.


sum θoətiz abaʊt “riiyalitii bii skeilə”

[Galilée] déclare que dans tous ces phénomènes il faut mesurer tout ce qui est mesurable, et tâcher de rendre mesurable tout ce qui ne l’est pas directement.
[“[galileiyoʊ] dikleə ðat in oəl ðiiz finomənoniz wii must meʒər oəl ðat bii meʒərəbəl, and trai tə meik meʒərəbəl oəl ðat bii not dairektlii soʊ.”]
—tomas-onrii maətan, galilei: lei dwa də la siiyons ei la meθod dei siiyons fiziik (1868)

wen wii diskraib ðə wuəld, wii oftən yʊʊz katigəriiyiz tə dʊʊ soʊ. wii sei ðat ðeə bii red objektiz and blʊʊw objektiz, pʊə foʊkiz and ric foʊkiz, laiyəniz and taigəriz, ets. ad inf. ðiiz katigəriiyiz bii yʊʊsfəl tə wii, bikuz dii prəvaid yʊʊsfəl rʊʊliz ov θum foər undəstandiŋ ðə wuəld and pridiktiŋg wot ðiiy efektiz ov wiis and uðər-iis akʃəniz biiyil. wii kan pridikt ðat a laiyən biheivil difrəntlii tʊʊw a taigə, oər a red objekt macil sum uðər objekt betə ðan a blʊʊw um.

weə wii goʊ roŋ bii tə θink ðat ðoʊz katigəriiyiz ðat wiiy aplai tə ðə wuəld foə wiis kənviiniiyəns biiy absəlʊʊt. teikiŋ ðə kulər egzampəl, in trʊʊθ ðiiz bii just reinjiz on a skeil, and fuzii reinjiz at ðat, wic wii grʊʊp intʊʊ kənviiniiyənt bandiz. ingliʃ bii diveləpəð inuf ðat wii hav beisik kulə neimiz tʊʊw a feəlii hai digriiy ov spesifisitii, but ðeə bii menii langwijiz wið faə fyʊʊwə beisik kulə neimiz, and iivən in ingliʃ ðə kros-oʊvə pointiz bitwiin difrənt kuləriz bii fuziiy, il-difainəð.

wiis katigəriiyiz bii yʊʊsfəl oʊnliiy insoʊfaər az dii korispond tə riil difrənsiz wiðin skeilə reinjiz. in pətikyələ, ðeə biiy oftən θreʃoʊld efektiz: tipiŋ pointiz at wic a meijə ceinj in sum propətiiy ov ðiiy objekt əkuə, iivən wen ðeə bii litəl ceinj in ðat propətiiy aʊtsaid ov ðoʊz reinjiz. temprəcər and steitiz ov matə biiy a gʊd egzampəl ov ðis. foə menii beisik substənsiz ðeə bii tʊʊ temprəcə θreʃoʊldiz weə ðu substəns undəgoʊw a rapid and signifikənt—and riil—ceinj in hiis propətiiyiz: ðə meltiŋ / friiziŋ point; and ðə boiliŋ / kəndensiŋ point. wʊətər at 90°s biheiv difrəntlii tə wʊətər at 10°s, but in sum impʊətənt weiyiz dii bii stil mʊə similə tʊʊw iic uðə ðan aiðə bii tə wʊətər at 110°s. ðə temprəvə bii skeilər in a liniiyə wei; ðə steit ov matə dipendiŋg (laəjliiy) on ðə temprəcə bii skeilər in a stepəð wei. araʊnd ðə θreʃoʊldiz, ðə stepəð skeil mʊʊv fastər, and biiy obzuərvəbəl az a skeil: foər egzampəl, wiðin ðə naroʊ reinj araʊnd ðə meltiŋ / friiziŋ point, meltiŋ biiy a proʊses raəðə ðan a bainərii swic. ðiiz difrənsiz in propətiiyiz bitwiin reinjiz bii riil, but ðat meik not ðə katigəriiyiz absəlʊʊt in diiselfiz; wii kʊd yʊʊʒʊʊwəlii cʊʊz difrənt baʊndəriiyiz if ðat biiyid yʊʊsfəl tə wii tə dʊʊ soʊ. foər egzampəl, tədei wii distingwiʃ gasiz and plazməriz bikuz ðis bii yʊʊsfəl tə dʊʊ soʊ, but wii dʊʊwid ðis not bifʊər, and in fyʊʊcə wii mei distingwiʃ difrəntliiy agen.

kwes katigəriiyiz tend tʊʊw araiz weər, espeʃəliiy in neicər? at sum point wii niid tə meik disiʒəniz, and bikuz ðoʊz disiʒəniz bii katigorikəl, wii must kristəlaiz ðə spektrəm intʊʊ katigəriiyiz korispondiŋ tə ðə disiʒəniz wii niid tə teik. ðə fiidbak efekt from ðoʊz disiʒəniz in tuən fʊəs skeilə riiyalitii tə daivuəj and katigəraiz. an ekselənt egzampəl bii ðə bainərii diviʒən bitwiin ðə seksiz: a θaʊn mail yiəriz ov sekʃʊʊwəl riiprədukʃən, wið mailiz ov mailiz ov seks aktiz evrii dei, reiyifaiyiv ðoʊz meitiŋ disiʒəniz intʊʊ (bai ðə skeilə standədiz ov ðə nacərəl wuəld) an unyʊʊʒʊʊwəlii rijid and yʊʊnifʊəm sistəm ov seks difrənsiz. spiiʃiiyeiʃən rizult from ðə seim efekt: iiyoniz ov meitiŋ disiʒəniz rizultiŋg in viziblii katigorikəl aʊtcəmiz.

ðə probləmatik efektiz ov triitiŋ skeilə riiyalitiiy az katigorikəl (sumtaimiz koələð “bainərii θinkiŋ”, ðə moʊst ekstriim vuəʒən ov ðiiy erə) apiər in menii pleisiz. moʊst ov oəl, jʊʊ tə ðə fʊəsiŋg efekt ov disiʒən-meikiŋ, dii stem from wiis triitiŋg wiis disiʒəniz az aiyən loəriz raəðə ðan pragmatik gaidlainiz. bikuz riiyalitii bii skeilər, iivən wen ðeə biiy ekstriim θreʃoʊld efektiz, ðeə oəlweiz biiyil ej keisiz ðat kan not biiy aproʊpriiyətlii kuvərəð baiy aiyən loəriz. ðeə mei sumtaimiz iivən bii mʊər aproʊpriiyət tə triit ðiiy ej keisiz az a katigəriiy in diiselfiz, but aiðə ðis bii priklʊʊdəð bai katigorikəl θinkiŋg rijidliiy insistiŋg on hiis katigəriiyiz, oə ðiiy ej keisiz bii triitəð soʊ rijidliiy az diis oʊn katigərii ðat diis similaritiiyiz tə diis ajeisənt katigəriiyiz on ðə kəntinyʊʊwəs skeil bii diiselfiz ignʊərəð.

ðis biiy espeʃəlii trʊʊw in ðə soʊʃəl saiyənsiz and morəl filosəfii¹, bikuz dii diiselfiz egzist in ðə sentrəl pʊəʃəniz ov ðə riiyalitii skeil bitwiin haəd mətiəriiyəl riiyalitii, weə ðis bii yʊʊʒʊʊwəliiy obviiyəs tə θink in a skeilə faʃən, and pyʊə konsept, weə ðis biiy unprobləmatik oər iivən aproʊpriiyət tə θink in katigorikəl tuəmiz. ðə soʊʃəl and morəl dəmeiniz bii prisaisliiy abaʊt haʊ wiis konseptiz map tʊʊw undəlaiyiŋ biheivyəriz ðat biiy imposibəl tə meʒə prisaisliiy, and weə wiis disiʒəniz biiy ov prəfaʊnd puəsənəl impʊətəns. but just bikuz ðis bii difikəlt foə wii tə meʒə soʊʃyoʊ-morəl propətiiyiz miin not ðat ðoʊz propətiiyiz bii pyʊəlii konsepcʊʊwəl, and ðeəfoə katigorikəl raəðə ðan skeilə. wail ðeə bii keisiz weə wii riiyəlaiz not ðat wiis disiʒəniz biiyiv reiyifaiyəð intʊʊ katigəriiyiz², in praktis ðə mʊə komən erə bii triitiŋg wiis diskriptiv katigəriiyiz az difainiŋg riiyalitiy hiiself.