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Ernst Mach

tcrms o£ Mach’s sccond and third dcfinitions hc ncvcr intcridcd such a rcstriction. Not only did hc includc spacc and timc as “scnsations” (in the broadcr scnsc), but cvcrything clse as wcll, including a grcat many things for which \vc cvidcntly havc no sensory organs with which to “scnsc” them. In short, cspccially in tcrms of his third defini-tion, hc did not dcfinc what could be rcliably mcasured in terms of scnsations, but defined scnsations in tcrms óf what could be rcliably mcasured! In other words, if it could be rcliably mcasured (andTe-latcd to other things), then rcgardless of what clsc it might be, and rcgardlcss of how we might experiencc it, then it had to be a sensation.^Cł The qucstionable stretch in Mach’s third definition was not that hc rcstriacd “elcmcnts” to sensory qualitics, which hc did not do, but that hc did not make his distiriction bctwccn “measurablc scnsations” and “not yet measurablc scnsations" ovcrt, and kept suggestmg that all scnsations werc “immcdiatcly givcn” in consciousness and wcrc “ccr-tain," as if their charactcr wcrc independent of the way in which they wcrc identified, or misidentified.⁵⁵

Spacc and Time

Mach distinguished bctwccn a number of different kinds of space and timc. Physiolugicul spacc was the spacc we noticc “out thcrc”; it was “immcdiatcly givcn” and as much an “element” as colors or sounds; it was what Mach mcant by "nativistic spacc.” Physical spacc was a “functional depcndency" uscd in physics to help relate sensationś to one another in the most “cconomical” way possiblc. Metric spacc was an idcalized construct devcloped by gcomctricians which might have as many dimensions as could suit the human imagination.

Thesc distinctions bctwccn difTerent kinds of space wcrc apparently first dcvclopcd in the carly and middle i86os. In 1862 and 1863, while Mach was trying to reconcile the atomie theory with his phcnomenal-ism, hc began to speeulate on what kind of spacc would suit atoms as ideas. He came to the conclusion that only an ideational space of morę than thrcc dimensions would be adecjuate.^⁰ But hc argucd against the practicality of his own hypothesis on the grounds that “real” space (i.c., what hc latcr callcd “physiological” spacc) had only three dimensions, and that in science it would be “uneconomical” to usc a space of morę than thrcc dimensions. Mach latcr considcred his notion of more-

.thrcc dimensions an anticipation of Ricmanns multidimensionnl ^l1'ⁿ c,ry. Mach’s rcjcction of the atomie theory as “uneconomical^M gC°^nlLf le ist partly related to his similar rcjcction of the usc of multi-dimen*ion^s in physics as "uncconomical."⁰⁷

M uh^ own interests, cspccially in his latcr ycars, wcrc dircctcd pri- i •i . toward “physiological spacc." And herc hc madc a number of ^^ar! _r distinctions. He hcld that besides_visuaf physiological spacc K wcrc also tactile, haptic, and various cinotionally fclt typcs of ¹ h siological spaccs.⁶⁸ 1 Ic also bclicved that they wcrc somehow related. L coordiiiaicd with one another.

j^ach ™*je somc largely yerbal changcs in his idcas on spacc during iSoorandfearly. ig^^According to his new dchniuons pnmary ^{1 C} was what a fixed, immobilc animal would notice, a bounded. ⁵P^aCC rictrical, tbrcc-dimcnsion.il, visual World (i.e., "physiological" ^asyn v Sccomlary spacc w^fas what a moving animal or person would ^SP‘ who constantly corrccted asymmctrical and bounded features in ^SCC ₀£ symmctrical, gcomctrical, and unboundcd features (i.e., a ‘^,Cr eric” corrcction of "physiological" spacc).⁶⁰ But Mach also added: “Primary spacc cannot be absolutcly supplantcd by sccondary spacc _f "the renson that it is phylogcnctically and ontologically oldcr and

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stronger.

Evcr sińce Saint Augustine madę his famous searching and unsuc-ccssful analysis into the naturę of timc, philosophers, and cspccially phcnomcnalists, havc bccn dissatisfied not only with the understanding of other philosophers concerning this qucstion, but cvcn with their own understanding. Mach was not an cxception. Hc had his own theories of timc, but they pleased ncithcr his critics nor himsclf.⁶¹

Physiological timc was a fccling accompanying the labor of atten-tion "closely cónncćted with pcriodically or rhythmically rcpcatcd pro-cesses."⁸² Hc added, howcvcr, "It is of coursc only for smali times that I hołd that therc is an immediate sensation of timc."®³ Metric timc was a "chronometrie concept" which arose from comparing physical cvcnts with one another and unlikc physiological timc was the same for everyonc.⁰⁴ Physical timc was "the dcpendence of changcs on cach

uim-i.

It would hc a mistakc, howcver, to exaggcrate Mach's confidcncc in his understanding of spacc and timc. Physically spc.iking both wcrc rdations, but as mentioned bcforc, Mach declincd to clarify what hc

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