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Helmholtz and the Psychophysiology of Time

Claude Debru

University Paris VII Denis Diderot

Argument

After having measured the velocity of the nervous impulse in the 1850s, Helmholtz begandoing research on the temporal dimensions of visual perception. Experiments dealing withthe velocity of propagation in nerves (as well as with aspects of perception) were carried outoccasionally for some fifteen years until their final publication in 1871. Although the temporaldimension of perception seems to have interested Helmholtz less than problems of geometryand space, his experiments on the time of perception were technically rather subtle andseminal, especially compared with experiments performed by his contemporaries, such asSigmund Exner, William James, Rudolf Hermann Lotze, Ernst Mach, Wilhelm Volkmann,and Wilhelm Wundt. Helmholtzs conception of the temporal aspects of perception reflectsthe continuity that holds between psychophysiological research and the Kantian philosophicalbackground.

1. Introduction

William James quotes Helmholtz often in The Principles of Psychology, generally withpraise, but occasionally with severe judgments. Because these judgments are based ondeep insight regarding the German psychophysiological literature, they can be usefulas a starting point for discussing Helmholtzs physiological work on the mechanismsof sensation, its philosophical background, and its implications. In the course of thisdiscussion, we will take into account the transformation of Helmholtzs conceptionsby comparing the first and second editions of the Handbuch der physiologischen Optik.

Commenting on Helmholtzs Handbuch, James writes:

Can I find fault with a book which on the whole I imagine to be one of the four or fivegreat monuments of human genius in the scientific line? If truth impels I must fain try,and take the risks. It seems to me that Helmholtzs genius moves most securely when itkeeps close to particular facts. At any rate, it shows least strong in purely speculativepassages, which in the Optics, in spite of many beauties, seem to me fundamentallyvacillating and obscure. (James [1890] 1983, 908)

One of the occasions for criticism is given by the following passage from the

Handbuch:

Science in Context 14(3), 471492 (2001). Copyright Cambridge University PressDOI: 10.1017/0269889701000175 Printed in the United Kingdom


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The only respect, in which a real agreement of our perceptions with reality can takeplace is the time sequence of the events with their different properties. Simultaneity,succession, the regular return of simultaneity or succession can take place as well in

sensations as in the events. The external events as well as their perceptions unfold in time;accordingly, the time relations of the latter can be the faithful picture of the former.(Helmholtz 1867, 445)1

In William James view, this philosophy is unfortunately too crude (James [1890]1983, 591). The Americans judgment is perhaps too severe, since Helmholtzrecognizes in that same passage that the time-succession of sensations is not anentirely faithful picture of external events, due to differences in propagation times ofthe nerves to the brain. Perhaps Helmholtz considered James criticisms favorably, for

that passage was omitted from the second edition of the Handbuch (1896). However,in an address delivered in 1892, he repeated his earlier comments:It is only in respectto the temporal course that sensations can be images of the course of the events(corrections being reserved) (Helmholtz 1896, 358).

The present article will analyze Helmholtzs experiments on time perception in thecontext of similar attempts by other physiologists, and will discuss the philosophicaldimensions of the research and comments he devoted to time perception (see alsoDebru 1999), with emphasis on the evolution of his philosophy regarding therelationship between time and causality, on one hand, and his relation to Kantianism,on the other hand.

2. The Velocity of Propagation in Nerves and Subsequent Experiments

Helmholtzs experiments and ideas on the physiological and psychological aspects oftime were initiated by his measurements of the propagation velocity of the nervousimpulse (1850), which he carried out on the sciatic nerve and the gastrocnemiusmuscle of the frog. According to the physiologist Charles Marx, these measurements

yielded the first new datum in nerve physiology since Antiquity (Marx 1969, 16).Using available electrical techniques, including Pouillets galvanometer, Helmholtzwas able to measure the time interval between the stimulation of the frogs sciaticplexus and the response of the gastrocnemius muscle. For a distance of about 50 to60 millimeters, the intervals ranged from 0.0014 to 0.0020 seconds (Helmholtz1850a, 7173; 1850b, 204206). Frederic Holmes and Kathryn Olesko commentedon the methodological issues involved in this research and concluded that Helmholtz

1 On the whole topic of our study, remarks have been already made by Schiemann 1997, 234, 266, 272, 280,314, 330. Schiemanns remarks were made from a more epistemological point of view. The present paper dealsfirst with Helmholtzs physiological researches. On Helmholtzs epistemology, see also Heidelberger 1998,

924.

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modified the condition of experimental physiology due to his concern for theaccuracy of measurements (Holmes and Olesko 1993, 52).

The theme of measurement errors has become particularly prominent since 1823,

when the Knigsberg astronomer Friedrich Wilhelm Bessel stressed the individualdifferences in judging the time at which a star crosses a net in the telescope, thephenomenon called personal equation.2 The problem of accuracy in time intervalmeasurement has several aspects, which were well defined by Helmholtz: technicalaspects (measurement instruments), physiological aspects (the material, nerves, andmuscles used in the physiological experiments), psychological aspects (personalequation), and epistemological aspects (calculation of errors).3

Generally speaking, Helmholtzs experiments on the propagation velocity innerves had two far-reaching consequences: on the one hand, they showed that the

notion of simultaneity between bodily actions and mental representations wasillusory; on the other, they opened the field for further investigation of the time lagbetween stimulation and conscious awareness of stimulation. After having examinedHelmholtzs notebooks, Holmes and Olesko (1993, 52) noted indeed that he hadstarted at that time to extend the scope of his experiments to humans. Thus, theresearch initiated in 1848 presages the time measurements that were performedtwenty years later on the time lag between visual stimulation and visualconsciousness.

This research was in part carried out in collaboration with the Russian physiologist(and assistant) N. Baxt in 1867 at Heidelberg (cf. Koenigsberger 1903, vol. 2, 9395)

and the results appeared in two articles published in 1867 and 1870. In thefirst article,reference was made to earlier attempts. Helmholtz noted that the experiments onmuscles and nerves yielded widely divergent results; this also held for the contributionof Friedrich Kohlrausch (1866). Technical improvements were introduced in order toachieve greater precision. In the new series of experiments of 1867, Helmholtzborrowed from Etienne-Jules Marey the use of the thumb muscles (instead of musclesof the limbs), thereby eliminating the reaction of too many muscles when thestimulation was performed on a higher level of the nervous trunk (cf. Helmholtz1883, 933934). In the second series of experiments (Summer 1868/Winter 1869)the accuracy of the time measurements was further improved by the use of a newly

constructed Pendelmyograph, a device by which the oscillations of a pendulum

2 Christoph Hoffmann, in a personal communication, pointed out that this expression is not found in Besselsoriginal work.3 Helmholtz devoted a full lecture at Knigsberg to several of these aspects (Helmholtz 1850c). He startedfrom the psychological limits partly due to the slowness of the awareness process itself (the very subject of hislater researches on time psychology). He described various technological devices to improve the accuracy ofthe measurements of very small time intervals, a problem of great relevance in contemporary physics,electricity, and optics. He discussed their use in physiological experiments, and presented preliminary resultson the human. He concluded with the idea that the workings of the nervous system produce a delay in

perception and consciousness.

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induce stimulations at fixed time intervals yielding results in the order of less than amillisecond (cf. Helmholtz 1883, 940).4

In a next step, Helmholtz extended the scope of time measurements to the

emergence of conscious visual sensations. This implied a significant move from purephysiology to the psychological part of sense physiology, a field defined in the firstedition of the Handbuch as separate from pure psychology (cf. Helmholtz 1867, 427).Once again, a key issue of psychophyics as fostered by Fechners Elemente derPsychophysik of 1860 became the subject matter of a lively debate. In the Handbuch,Helmholtz expressed doubts about the overall validity of the Weber-Fechner-lawconcerning the sensation of light intensity. He stressed its merely approximatecharacter and offered a modified mathematical formula to cover the whole range ofstimulus intensities (ibid., 312313).

3. Time Sense and Psychophysics

Let us briefly take a look at research that was carried out more or less in parallel withthat of Helmholtz on the temporal dimension of perception. Ernst Mach was amongthe physicists and physiologists who were discussing most fervently the new notionsof Fechner. Indeed, he lectured on psychophysics at the University of Vienna (cf.Mach 1863) and compared several hypotheses of thinkers belonging to differentschools of thought with one another, for example, those of the statistician and

astronomer Qutelet; those expressed by Johann Friedrich Herbart in his writings onmathematical psychology; Fechners psychophysics; the ideas of Helmholtz andWundt; and Ernst Heinrich Webers approach (cf. Mach 1863, 242). In addition, hediscussed the conceptions of Wilhelm Volkmann, Johannes Czermak, and RudolfHermann Lotze. Mach commented particularly on the already published parts ofHelmholtzs Physiological Optics as well as the theories of colors and tones of WundtsBeitrge zur Theorie der Sinneswahrnehmungen of 1862. In this important contribution,Wundt had referred to mental processes that take place between sensation andperception asunconscious inferences.This notion had previously been proposed byHelmholtz and would later be elaborated in the concluding part of theHandbuch.

Mach also mentioned Czermaks paper on time sense, but added that he hadalready begun experiments on this problem in the autumn of 1860 (cf. Mach 1863,260). The general conclusion of Machs text is worth quoting: Physics, physiologyand psychology stay in an indestructible relationship, so that for each of these sciencessalvation can only be found in cooperation with the other ones, and that each of themcan be considered as an auxiliary science for the other ones (ibid., 365).

4 This means that Helmholtz was indirectly reaching the order of time dimensions of the neurophysiologicalprocesses as they are described today. Similar research was later pursued by Sigmund Exner, who explicitly

referred to the Hemholtz-Baxt experiments (Exner 1873).

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Czermak is apparently the first experimentalist who named, and investigatedtimesense (Zeitsinn) (cf. Czermak 1857, 231). This term was coined in analogy with theterm space sense (Raumsinn) as defined by Weber in 1852 in the famous study onthe spatial sensitivity of the skin. Now, Czermak proposed a program for time senseresearch (and quite remarkably also for the sense of velocity) in the same terms asWeber, advocating the method of the just noticeable difference (JND), and raised thequestion whether the same time interval was estimated identically by different senses.As previously mentioned, Mach began to study time perception in 1860 from theviewpoint of the Weber-Fechner law, and published the first results in 1863. HisResearches on the time sense of the ear (cf. Mach 1865a) appeared two years laterand was followed by Remarks on the space sense of the ear (cf. Mach 1865b).5 Inthe same year, Machs lectures on acoustics and music were published, whichcontained a long summary of Helmholtzs conceptions (cf. Mach, 1865d), and in1866, a popular account of Helmholtzs treatise for musicians came out (cf. Mach1866).

In his 1865 work on the Zeitsinn of the ear, Mach noted: When I started, someyears ago, to devote myself to physiological-psychological studies in a more intensiveway, I was struck by the lack of work on the theory of the time sense (Mach 1865a,133). By improving the technical devices used in this research, he could show that theears ability to correctly estimate time intervals was far better than that of any othersense. He also estimated the minimal duration sensed by the ear (Mach 1865a, 145).Thus, he could conclusively demonstrate that Webers law was only approximatelyvalid and that time sensitivity decreased for small as well as for large intervals (Weberslaw holds only for intermediate intervals in the range of 0.4 to 0.5 seconds [cf. Mach1865a, 144]).

These results were taken into account by Fechner in his 1877 book In Sachen derPsychophysik. In a chapter devoted to the validity of Webers law in cases of extensivemagnitudes like space and time, he discussed Machs and Vierordts results on timesensation and sought to specify the psychophysical laws for lower and higher timeintervals on the one hand, and for intermediate intervals, on the other hand (cf.Fechner 1877, 174177).

Machs philosophical comments are also worth mentioning. Going back to Kants

theory of time as form of the intuition, the young Viennese professor noted that onewould have toabandon either provisionally or generally the idea of a theory of timesense [cf. in the Kantian sense]. The first serious and solid attempt to construe atheory of time sense is found in Herbart (Mach 1865a, 145). But Mach alsocriticized Herbarts psychology of time, which was based on the assumption that timeseries could be reproduced at will. He pointed out that two melodies of the same

5 No mention of this problem is to be found in Helmholtz s treatise On the Sensations of Tone as a PhysiologicalBasis for the Theory of Music, published in 1863. Indeed, the interpretation of the pitch of a musical tone asproduced by the tones vibrational period was not really relevant to the time sense problem (cf. Helmholtz

[1863] 1954, 11).



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rhythm cannot always be compared, and that there must exist an independent senseof rhythm a sense different from the sensation of tone (cf. Mach 1865a, 147).Linking the problem back to physics, Mach emphasized that this science had to

represent every phenomenon as a function of time. But time was not an independentvariable in all instances, since the movement of the pendulum, which could be takenas a measure of time, was represented by the concept of force, which includes thenotion of time. If we succeed in representing every phenomenon as a function of thependulum movement, this would mean only that all phenomena depended on eachother in such a way that each one could be represented as a function of any other.Time, physically speaking, is thus the representability (Darstellbarkeit) of everyphenomenon as a function of any other (Mach 1865a, 150). In the case of the earstime sensation, this entailed a functional link between the sensation of tone and thesensation of accommodation of the sense organ. Later on, in theAnalysis of Sensations,Mach stressed again the existence of a specific time sensation, which was linked toconsciousness, and thus to an organic process of energy consumption (Mach 1918,204).

4. On the Time Necessary for a Visual Impression to ReachConsciousness

Apparently Helmholtz did not cross the field of time psychophysics as studied byMach and other experimentalists like Ewald Hering and Vierordt. His own work on

the psychophysiology of time was a continuation of his earlier physiological studies ofthe propagation velocity of the nervous impulse, which he subsequently extended tothe psychological subject-matter of the time necessary for the arousal of theconsciousness of an object following the stimulation of the eye. In 1871, Helmholtzand Baxt published the paper,On the time necessary for a visual impression to reachconsciousness (Helmholtz 1883, 947), based on the examination of after-imagesa much studied phenomenon of physiological psychology. According to hisbiographer Leo Koenigsberger, Helmholtz made a significant move by using after-images to discuss the time-course of visual impressions rather than unraveling thefactors (including colors) which affect it (Koenigsberger 1902 vol. 1, 351356).6

The Helmholtz-Baxt experiments used rotating disks with open slots to create avisual stimulus of short duration to allow the after-image to develop, whereupon itwould be extinguished after a variable duration by a second, superimposed visualstimulus. Thanks to this device, it was possible to adequately estimate the duration of

6 The duration of visual sensations and many features of after-images are discussed at length in the Handbuchsfirst edition of 1867. After-images were considered phenomena of the retina that induced continuoussensation when discontinuous stimuli were delivered (cf. Helmholtz 1867, 338). The author also discussesextensively the circumstances that influence positive and negative after-images. The phenomena of after-images have also been used, among others, by Mach to obtain significant results on visual properties, such as

the so-called Machs bands, which were interpreted as a purely retinal phenomenon (Mach 1865c).

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the after-image necessary for the visual stimulus to be recognized. This device hadbeen designed by Sigmund Exner, who combined two different instrumentsconstructed by Helmholtz: an electromagnetic instrument that was able to maintain

a constant speed of rotation while allowing for changes of the rotation frequency, andanother instrument capable of producing visual stimuli of short duration.7 Theapproach of the Helmholtz-Baxt experiments went beyond Exners studies in thatthey used after-images for understanding the relationship between visual mechanismsand consciousness. Under normal conditions, after-images last up to twelve seconds.The interruption of an after-image at an earlier stage than its spontaneousdisappearance made it possible to show that the time it took for a visual stimulus toreach consciousness depended on several factors, which included the total durationbefore the extinction of the after-image, on the one hand, and the structure of thestimulus, on the other. It was shown by measurement that the minimal duration fora stimulus to be perceived (before extinction of the image) was about thirtymilliseconds. To enable the determination of the influence of the stimulus itself,printing type of different sizes were used, smaller type being less rapidlyrecognized.8

Another interesting aspect of these experiments concerns the phenomenon ofattention. Helmholtz noticed that attention could be voluntarily directed towardspoints of a visual space different from the visual fixation point. This phenomenon ofperipheral attention permitted him to draw an important conclusion, which heinterpreted in terms of a modification occurring in the nervous system independentfrom the movement of perceived bodies (see Helmholtz 1883, 952). In a way, it wasassumed that so-called voluntary attention was based on processes in the centralnervous system. Yet, when discussing the phenomenon of peripheral attention in theHandbuch, Helmholtz still used the terminology of aconscious and voluntary effortwhich directs attention independently from the position of the eyes. James quotedthis passage (James [1890] 1983, 414), as well as another relevant passage whereHelmholtz had asserted that the relation of attention to will is, then, less one ofimmediate than of mediate control. According to James, these words of Helmholtzare of fundamental importance (ibid., 399400). Indeed, sustained voluntaryattention bearing on the same object is only possible if there is a renewal of interest.

7 Exner spent some time at Helmholtzs physiological laboratory in Heidelberg and published some of theresults obtained there in the paperOn the time necessary for a visual perception (cf. Exner, 1868). In thiswork, he tried to identify the conditions that influence the time it takes a retinal image to reach consciousness.He enumerated four conditions: light intensity, the size of the visual stimulus and its retinal image, thepresence of an after-image in the absence of the real retinal image, and the place of the image on the retina.Although he did not mention Webers lawa highly controversial topic, as we have seenhe found, for thefirst two conditions (light intensity and size of the image), the same kind of relationship between thegeometric progression of the stimulus and the arithmetic progression of the perception time that was typicalof an entity pertaining to the Weber-Fechner type.8James obviously knew this research, for he mentioned it in the chapter on memory of the Principles (James

[1890] 1983, 610).



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The novelty of a stimulus is a major factor in attentional processes that does not relyonly on will.

In 1871, Baxt published another paper dealing with the temporal dimension of

visual perception that depended on a slightly different and more precise method,which allowed him to take into account, among other things, the time the extinctionstimulus takes to reach consciousness. He was able to demonstrate a relationshipbetween the time it takes a stimulus to reach consciousness and its internal complexity(the number of recognizable objects it contains) (Baxt 1871). Helmholtzs research isalso relevant in another respect. The after-images maximal duration of twelve secondsmentioned by Helmholtz and Baxt was of the same range as the duration of thespecious present, which may be defined, if we follow William James references towork done by Wilhelm Wundt and his pupils, as the maximum filled duration ofwhich we can be both distinctly and immediately aware (James [1890] 1983, 577).The specious present is probably the dozen seconds or less that have just elapsed(ibid., 578).

5. Time Perception and Temporal Errors

Many theoretical consequences could be drawn from the exploration of the timedimensions of perception. Going back to Helmholtzs statement that the timedimension is the only one in which perception agrees with reality, it seems thatHelmholtz did not really take into account the possibility of temporal illusions,although he did not miss it entirely. Indeed, he does mention it in the followingsentences of the Handbuch:

The sensation of thunder follows the sensation of lightning just as the sonorousdisturbance of the air by the electr ic discharge reaches the observers place later than thatof the luminiferous ether. However, one has to notice here that the time-succession ofthe sensations is not an entirely faithful picture of the time-succession of the externalevents, since the conduction from the sense organs to the brain needs time, and needsdifferent times from different organs. In addition, the time for eye and ear, which isneeded for light and tone to reach the organ, comes now into account. (Helmholtz

1867, 445)

William James did not quote this text entirely. Instead, he felt urged to make somevery critical comments on the theory of truth as copying, which, according to him,Helmholtz implicitly indulged in:

One experiences an almost instinctive impulse, in pursuing such reflections as these, tofollow them to a sort of crude speculative conclusion, and to think that he has at last gotthe mystery of cognition where, to use a vulgar phrase, the wool is short. What morenatural, we say, than that the sequences and durations of things should become known?

The succession of the outer forces stamps itself as a like succession upon the brain. The

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brains successive changes are copied exactly by correspondingly successive pulses of themental stream. The mental stream, feeling itself, must feel the time-relations of its ownstates. But as these are copies of the outward time-relations, so must it know them too

. . . . This philosophy is unfortunately too crude. (James [1890] 1983, 591)

James states the reason why this was the case in a way that is not entirely original. Hegoes on to say:

Between the minds own changes being successive and knowing their own succession,lies as broad a chasm as between the object and subject of any case of cognition in theworld. A succession of feelings, in and of itself, is not a feeling of succession. And since,to our successive feeling, a feeling of their own succession is added, that must be treated

as an additional fact requiring its own special elucidation, which this talk about outertime-relations stamping copies of themselves within, leaves all untouched. (ibid.)

These remarks constitute the starting-point of the famous question (which remains aneurophysiological puzzle even for todays neuroscientists):To what cerebral processis the sense of time due? (ibid., 594). According to James, time was no exception tothe rule that perception does not reveal itself to be merely a copy of what is perceived.This means that in time perception a particular factor comes into play a factorexpressing the activity of central processes, in whichever way such processes are to beconceived.

Let us briefly look at some developments that seem to have converged on Jamesquestion. His statement that a succession of feelings, in and of itself, is not a feelingof succession, may be found under various guises in earlier authors whom he quotedor mentioned. One of the founders of mathematical psychology, Johann FriedrichHerbart, in his Lehrbuch zur Psychologie (1816), had raised sharp criticisms againstKants theory of space and time as the only proper internal forms of intuition,independent of each other (Herbart 1887, 5657). Indeed, he considered them ratheras serial forms produced upon the occurrence of sensations, and thereby linked theserial character of sensations to the working of arithmetic: Arithmetic is for the

psychologists the remarkable play of a kind of representation always refining itself, ofa series through which one can wander in both ways (ibid., 58). The representing(Vorstellen) of something that possesses temporal character implies the reproduction ofprevious states or events. Thus, the whole process of representation behaves in adifferent way and obeys a different law depending on the viewpoint (things areviewed differently if considered from the beginning or from the end) and on the waythe process as such is kept in consciousness (ibid., 119). According to Herbart, thisfeature was the root of the representation of time. In about the same way as therepresentation of space, which, according to him, was not spatial due to the non-extensive, hence intensive, character of the soul, the representation of time had

something that was not temporal in the sense that it did not flow out (ibid.). The act



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of representing space needed a succession, since it rested on actual reproductions. Two

corollary remarks were made in this context:1) the succession in representing is nota represented succession; and 2) it does not need a finite duration, but only anunnoticeably small time (ibid., 120).

In the essay on the time sense of the ear, Mach (1865a, 145) noted: The firstserious and solid attempt of a theory of time sense is found in Herbart. In addition,Mach used to distinguish between the perception of the temporal course of

representations, on one hand, and the temporal course itself, on the other hand. He

had tried to show that perception was certainly not immediately given by the timecourse. Mach, in contradistinction, departed from Herbarts intention of reducingpsychological space and time to laws of serial reproductions. Regarding time, hepointed out that different melodies displaying the same rhythm could not be

considered an analog series of representations reproducing each other, as they weresaid to be according to Herbart. As previously mentioned, his arguments pointedrather to the existence of an independent sense of rhythm (ibid., 146147).

In his Metaphysics, the physiologist Hermann Lotze discussed the problem of

succession. The attempt to understand the genesis of the feeling of succession in ourrepresentation implies a change of representations in consciousness, sincein this waya change in representations could be present, but still no representation of thischange (Lotze 1884, 294295). For making this representation of change acomprehensible object, Lotze proposed a theory of time signs which turns out to be

an analog of his famous theory of local signs.

Yet another approach was developed by Wundt in the Treatise of PhysiologicalPsychology, a large volume that contains a systematic survey of the results obtained by

experimentalists on the time dimensions of perception (minimum duration fordifferent kinds of visual, acoustic, etc., stimuli to be perceived, minimum time

intervals needed to discriminate stimuli belonging to a series of the same kind or of

different kinds, time lags in the perception of different kinds of stimuli presented insimultaneity). In this survey, Wundt envisaged the possibility of an inversion of order

between two stimuli of different kinds, e.g., visual and auditory. He even pointed out

that such displacements in the series of perceived stimuli could happen for stimuli ofthe same kind. This phenomenon depended on the way attention was directed

towards one of the stimuli, which led to an enhancement of the stimulus intensity(Wundt 1880, vol. 2, 262). But the difficulty of attending simultaneously to twodifferent stimuli was also mentioned; it could, in fact, be the reason why illusions

regarding temporal intervals were possible. These phenomena were thereforecategorized as observational errors that were due to intrinsically mental factors (ibid.,

273; also 6th ed. 1908, vol. 1, 536537).The inversion in the order of stimuli following each other was also recognized as

relevant by James (James [1890] 1983, 598). The chapter on attention of the Principles

follows closely Wundts data and interpretations on serial visual and auditory stimuli.

Wundt explains all these results by his previous observation that a reaction

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sometimes antedates the signal (ibid., 388392).9 Another point of Wundts studiesconcerns the fact that perception was conceived as a temporally discontinuousphenomenon. Once impressions are not simultaneously perceived, they tend to

separate: The psychological nature of our time intuition reveals itself as discrete(Wundt 1880, vol. 2, 263). This notion is not to be found in JamesPrinciples, which,instead, expresses rather straightforward views on the continuous character ofconsciousness: The changes from one moment to another in the quality of theconsciousness are never absolutely abrupt (James [1890] 1983, 231). Consciousnessdoes not appear to itself chopped up into bits (ibid., 233). Thus, when discussingthe law of times discrete flow, James wrote: The discreteness is, however, merelydue to the fact that our successive acts of recognition or apperception of what it is arediscrete. The sensation is as continuous as any sensation can be (ibid., 585).

When trying to answer the question,to what cerebral process is the sense of timedue? James emphasized that it had to bean element present at every moment of theprocess, and this element must bear the same inscrutable sort of relation to itscorrelative feeling which all other elements of neural activity bear to their psychicproducts, be the latter what they may (ibid., 594; emphasis in original). At this point,and before proposing the idea that the sense of time was due to the summation ofstimuli, which entailed the overlap of different brain processes at the same time, Jamessummarized, as has been noted before, several theories regarding the origin of timeorder. Most of these theories relied on the feeling of the pastin his view, clearly aninsufficient and question-begging explanation. In this context, he also mentionedWundts attempts at measuring the shortest time interval whose subjective evaluationcame closest to the truth. This interval

of about three-fourths of a second, which is estimated with the minimum of error, pointsto a connection between the time-feeling and the succession of distinctly apperceivedobjects before the mind. The association time is also equal to about three-fourths of asecond. This association time he regards as a sort of internal standard of duration towhich we involuntarily assimilate all intervals which we try to reproduce, bringingshorter ones up to it and longer ones down. (Ibid., 596597)

This association time was one of the elements that allowed James to conclude thatthe phenomenon of stimuli summation played a role in the perception of time:Theamount of the overlapping determines the feeling of the duration occupied. Whatevents shall appear to occupy the duration depends on just what processes theoverlapping processes are (ibid., 598). When introducing Wundts law ofdiscontinuous succession in time, of percepts we cannot easily attend at once, he

9 The temporal inversion of stimuli has recently acquired a great significance in neuroscience, mainly in the

work of Benjamin Libet.



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mentions that the brain processes corresponding to the percepts were distributed overdifferent phases. He adds:

If our theory of time-feeling be true, empty time must then subjectively appear toseparate the two percepts, no matter how close together they may objectively be, for,according to that theory, the feeling of a time-duration is the immediate effect of suchan overlapping of brain-processes of different phasewherever and from whatever causeit may occur. (Ibid., 600; emphasis in original)

But James also devotes a paragraph in the same chapter of the Principles to the factthat we have no sense for empty time. The empty time alluded to here followedclosely Wundts remarks and may be conceived of as the result offluctuations of thebrain processes occurring in different phases. Indeed, James last words on the causeof time perception, which was also structured, as previously mentioned, by the so-called specious present, were: This causeprobably the simultaneous presence ofbrain-processes of different phasefluctuates; and hence a certain range of variationin the amount of the intuition, and its subdivisibility, accrues (ibid., 604).10

Why did Helmholtz encounter such difficulties in admitting, in the first edition ofthe Handbuch, that time perception was no exception to the general rule ofperception and this rule implied that there exists a lack of conformity(Uebereinstimmung) between the act of perception and the perceived object? It seemsthat the privileged status of time as the universal form of intuitiona principle drawnfrom KantsTranscendental Aesthetics ( 4) of the Critique of Pure Reason (see Kant [1787]1968, vol III, 57B 46)constituted the metaphysical background of Helmholtzsown thinking. Traces of this privileged status of time are to be found in theintroductory paragraphs ofDie Erhaltung der Kraft, which asserts that the task ofnatural science is to reduce all natural phenomena to ultimate invariable causes, andthat these causes should be found in forces which are invariable according to time(Helmholtz 1847, 5).11

But a second look is needed which focuses on the relevancy of time from thestandpoint of psychology. In the first edition of the Handbuch, where Fechner ismentioned in connection with investigations into the nature of after-images,

Helmholtz did not seem to have any serious interest in the kind of theorizing

10 As a comment on the specious present and on the time order problem, it is worth mentioning a remarkmade by Wittgenstein: Is it not this way: the phenomenon (specious present) contains time, but is not withintime? Its form is time, but has no place within time. Whereas language flows in a temporal fashion(Wittgenstein 1989, 98).11 Michael Heidelberger has rightly pointed out that Helmholtz has been led to his metaphysical standpointof the Erhaltung der Kraft by Kants Metaphysical Foundations of Natural Science (Heidelberger 1998, 11).Heidelberger sees this metaphysical standpoint as typical of Helmholtzs first phase, before Helmholtz becameinfluenced by Faradays empiricism. Helmholtzs metaphysical standpoint in the introduction of the Erhaltungder Kraftis particularly clear in the use of the causality principle. This principle (or the principle of sufficient

reason) is the first and essential foundation of the conservation law.

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exemplified by psychophysical parallelism in the Fechnerian idealistic-monisticfashion, nor did he make use of this concept. Surely, after having theorized on theconservation of energy, he could no longer consider the metaphysical idea of

psychophysical parallelism as a useful one. But in the attempts at clarifying therespective domains of physiology and psychology on visual perception, Helmholtzasserted that he had to consider the content of sensation from the point of view ofthe perceptually relevant features (for instance, direction or distance). This task couldbe carried out entirely by means of (purely) natural-scientific (naturwissenschaftlichen)methods. And yet, he went on to say that he would refrain from speaking of mentalactivities and of the laws involved in perception, since he lacked hard facts and clearand universal principles relating to this field of research. He therefore separated thepsychological aspects of sensory physiology from psychology in the narrower sense ofthe term (see ibid., 427). In the Handbuchs first edition, the emphasis was clearlymore on physiology than on psychology. But it turns out that these were notHelmholtzs last words.

6. Time as Internal Intuition: the Psychological Foundation of Arithmetic

In 1887, Helmholtz published the famous text Zhlen und Messen erkenntnistheoretischbetrachtet, an investigation into the psychological foundation of arithmetic in relationto time. The peculiar combination of empiricism and Kantianism is clearly stressed for

both fields, geometry and arithmetic.

In earlier writings I endeavoured to show that the axioms of geometry are notpropositions given a priori, but that they are rather to be confirmed and refuted throughexperience. Here I emphasize once again that this does not eliminate Kant s view ofspace as a transcendental form of intuition; in my opinion this merely excludes just oneunjustified particular specification of his view, although one which has become mostfateful for the metaphysical endeavours of his successors. It is then clear that if theempiricist theorywhich I besides others advocateregards the axioms of geometry nolonger as propositions unprovable and without need of proof, it must also justify itself

regarding the origin of the axioms of arithmetic, which are correspondingly related tothe form of intuition of time. (Helmholtz [1921] 1977, 72)

In the comments on various attempts at providing an axiomatic unfolding ofarithmetic, Helmholtz raised the question as to whetherthe cardinal number of agroup of objects is ascertainable independent of the order in which they arenumbered. He went on: To my knowledge, Mr. Schrder (Lehrbuch der Arithmetikund Algebra. Leipzig 1873, p. 14) was the first to recognize that there a problem liesconcealed; he also acknowledgedin my opinion justlythat there is a task here for

psychology, while on the other hand those empirical properties should be defined



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which the objects must have in order to be enumerable (ibid., 74). With respect toboth the empirical and the strictly Kantian theories set up to solve the problem of

how to derive a general concept of magnitude, Helmholtz drew the readers attentionto Paul du Bois-Reymonds statement that both views were equally possible, sinceboth would equally lead to contradictions. Feeling obliged to give voice to his own

thoughts, he made the forceful statement: I consider arithmetic, or the theory ofpure numbers, to be a method constructed upon purely psychological facts, which

teaches the logical application of a symbolic system (i.e. of the numbers) having

unlimited extent and an unlimited possibility of refinement (ibid., 7475).Helmholtz drew a distinction between numbering (das Zhlen) and numbers

(die Zahlen). The psychological facts involved in arithmetic as a method, were, inhis view, to be found in the definition of numbering rather than in the definition of

numbers as symbols. Numbering is a procedure based upon ourfinding ourselvescapable of retaining, in our memory, the sequence in which acts of consciousnesssuccessively occurred in time (ibid., 7576). In further comments on the so-callednatural numbers, which he depicted as a series of arbitrary symbols whoseparticular succession has been fixed by man as a lawlike one, he explained that thenatural character of these numbers had to do with a special use of numbering, viz.with giving the cardinal number of things. The lawfulness in the series of cardinalnumbers expressed the fact that man could add a new object to the ones which he

had already counted. Helmholtz explained that this method had nothing to do with

the use of particular symbols in a series. The sequence of symbols has been arbitrarily

chosen by our ancestors, and has thus acquired the status of a law of its own, whichdiffered from the lawfulness of the series of the numbers themselves, as described in

the process of numbering qua giving the cardinal number of things. The distinctionbetween numbering and number allowed him to recognize the insufficienciesinherent in the notion ofnaturalness as applied to numbers, to emphasize thedouble meaning of lawfulness in numbering and number, and to stress the symboliccharacter of numbers.

In a comment on this text, Paul Hertz suggests that we should not stop at apsychologistic theory of arithmetic. The psychic is rather, as regards the axioms ofarithmetic, completely coordinated with the physical, and is involved only as anobject

of our cognition. We shall not be allowed to claim that the nature of our cognitionis a ground for the validity of those axioms. This seems also to be the view of

Helmholtz (ibid., 104). This comment raised the question as to the role the scienceof psychology could play in the foundation of arithmetic. Where Helmholtz hadargued that arithmetic was a method drawn from purely psychological facts, Hertz

understood this as meaning that in our reflections upon experiences we gain thoseconcepts which possess a significance projecting beyond the psychic, and which cantherefore inter alia also be applied to the physical (ibid., 104). Thus, in Hertzs view,the role of psychology could well be partly defined along the lines of empiricism (a

position Helmholtz also claimed for himself), in the sense that it was called upon to

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our memory, the recollection of their time sequence remains also12 (ibid., 577578).Helmholtz also stresses that the ordering of internal perceptions or memories in timeseries makes it possible to repeat temporal series of perceptions, to observe, and to

recognize them. Repetitions of the original experience seldom happen in the sameway as the original experience, because perceptions are accompanied by arbitrarybodily movements and modifications which affect the observational process. Hence,the problem of the psychological conditions of time order is addressed in the contextof the general question concerning the conformity between perception and reality.

As the second edition of the Handbuch shows, Helmholtz starts from Kantsconception of the internal sense, but goes beyond the limits of this conception, sincehe tries to give a psychological account of temporal succession. In these laterphilosophical developments on perception, he deals repeatedly with the psychologyof memory in order to give an empirical content to Kants transcendentalism and tofurther the understanding of the psychological basis of induction and of lawfulness inour view of nature. The problem which now arises, however, is that of theunconscious character of memory (ibid., 580). This is clearly a problem of cognitivepsychology.

Strikingly enough, the corresponding passages in the first edition of the Handbuchon the conformity between time series in reality and sensation, which closelyfollowed Kants famous example of cinnaber, is not found in the second edition,although the analysis of the cinnabers color remains. Instead, Helmholtz discusses invery general terms Kants Ding an sich, the transcendental forms of intuition, thequalities of sensation, and the truth of our representations of the external world, andthereby finds himself once again confronted with the issue of the relationshipbetween image and object, but now in the realm of the internal sense. In this realm,one could find the most favorable instance offit (gleichen) or similarity between imageand object. And once more, the problem of memory is addressed, however in aparticular way. Helmholtz does not deal with the relationship between memory andthe original experience, but rather with the conformity between memories of thesame object at different times. He suggests that there is no need to assume thatsecondary memories (images) are exact pictures of the original memory (ibid., 591).This shows that psychological approach to memory has replaced the theory of time

perception as copying. In a further discussion, Helmholtz comments upon the kindof lawfulness which holds for phenomenal experience, and which rests oncorrespondences between sensations and bodily movements. In this discussion, wefind no trace of the previous notion that time could make an exception in thedifference between perception and reality. Rather, we are faced with memorymechanisms and with their unconscious character.

The notion of unconscious inference had already been met in the Handbuchs firstedition (see Helmholtz 1867, 430) in the context of the hypothesis that mental

12 (So lange [die Erinnerungen] uns berhaupt im Gedchtnis stehen bleiben, bleibt auch die Erinnerung an

ihre Zeitfolge.)

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activities, which lead to judgments on external objects, are generally unconscious. In

the second edition, the notion of unconscious inference is defined as inference madewithout linguistic means and without voluntary reflection (Helmholtz 1896b, 601).However, this is not all which the Handbuch is purporting. The temporal order ofconscious experience, and its unconscious mechanisms, whose very existence impliesthat the temporal dimension of the mental no longer corresponds to real time,

constitute barely more than a general framework for the constitution of a stable image(or rather concept) of the world. The explanation for this is to be found in the factthat memory images are purely sensory impressions which do not need to be verbally

described and thus transformed into concepts. Sensory impressions form the basicmaterial upon which our knowledge of the behavior of external objects rests. Theycan be used as elements of linking thoughts with one another without having to be

captured by words (cf. Helmholtz 1896b, 601). It is particularly meaningful that theexample used to corroborate this assertion stems from projective geometry, in which

the representation of a three-dimensional solid body is considered not only as acombination of previously observed perspective images, but also as a concept fromwhich other perspective images can be derived. At this point, Helmholtz concludes

that such a process, which rests upon the activity of unvoluntary and unconsciousmemory, is able to create correlations between representations, which agreeessentially with representations resulting from conscious thinking (ibid., 602). But at

this point, Helmholtz is no longer concerned with correspondences between real andperceived time as an exceptional example ofadaequatio rei et intellectus. Rather, he is

engaged in an enquiry about thepsychologicalmechanisms underlying the formationof knowledge.

In this enquiry, Helmholtz introduces the conceptslawfulness (Gesetzlichkeit) andcausality, which, again, are associated with temporal sequence or order. Thelanguage used to introduce the law of causality (Causalgesetz) is surprisingly Kantian:it is described as a regulative principle (ibid., 593), as an a priori given,transcendental law, which is impossible to prove from experience (ibid., 594). In theCritique of Pure Reason, Kant described the foundations of objective knowledge as anexemplification of mathematical physics; hence, the latter realized the conditions ofpossibility of experience in general. It is well known that in the chapter on theSecond

Analogy of Experience, Kant discussed the foundation of the temporal sequence as thenecessary basis for the notion of causality. He explained that the temporal connection

between perceptions is not brought about by intuition, but rather by the syntheticpower of imagination. Indeed, time itself cannot be perceived. Many philosophersand psychologists seem to agree that we do not have direct experiences of time.

Moreover, perception does not determine the objective relationship betweenphenomena. However, the synthetic power of imagination does not involve the

element of necessity that constitutes an experience. It does not even determine theorder of representations, since human imagination can reverse this order. The

objective, necessary relationship between phenomena must therefore be determined



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in a purely conceptual manner, which imports the element of necessity into thisrelationship: the concept of the relationship between cause and effect, the principleof sufficient reason, are the foundations of all possible experience (Kant [1787] 1968,vol III, 167B 233234).

In another context, Kant discussed the case of simultaneity between cause andeffect, which is the most common case in nature, with the qualification that effectdoes not immediately reach full development. In this discussion, Kant introduced thehighly important distinction between time order (Ordnung) and time course (Ablauf).The temporal order can exist without a real time course, since the temporaldifference between cause and effect can be infinitely small. In this case, therelationship between cause and effect (the order in time) remains something that canbe temporally determined (ibid., 175176B 247248). Another important remarkmade by Kant in the Second Analogy had to do with determining the place of an eventin time. This determination cannot be made by referring to absolute time, becauseabsolute time is not an object of perception. The determination of the place of anevent in time can therefore only arise from the phenomena themselves, according tothe general rule of causality:phenomena must determine their places within time bythemselves and make them necessary in the time order, it means that what follows orhappens must follow what was contained in the preceding state according to a generalrule13 (ibid., 174B 245). It is well known that for Kant, transcendental idealismwas compatible with empirical realism. Indeed, a fully fledged explanation of naturalphenomena rests on intuition (or on perceptual data) as well as on understanding,which confers necessity and universality to that which has been conceptually grasped.In the Second Analogy of Experience, Kant solved the problem of the correspondencebetween the subjective apprehension of phenomenal diversity and the unity ofexperience by means of the conceptual principle of causality or sufficient reason.

Now, according to Helmholtz, the principle of causality is given a priori. However,it does not seem that the strong statements to be found in the Handbuchs secondedition represent his final view. In 1902, Leo Koenigsberger published the followingnote from Helmholtzs Nachlass: The causal law (the presupposition of thelawlikeness of nature) is only a hypothesis and not otherwise provable. Lawlikeness inthe past can never prove lawlikeness in the future (Koenigsberger 1902, vol 1, 247;

see also Meyering 1989, 216). This remark was interpreted by Benno Erdmann assignaling a move towards empiricism (Erdmann 1921, 1112).

8. Concluding Remarks

From Helmholtzs physiological research on the temporal dimension of nervoustransmission and perception to the later speculations on the psychology of

13 (die Erscheinungen mssen einander ihre Stellen in der Zeit selbst bestimmen und dieselbe in derZeitordnung notwendig machen, d.i. dasjenige, was da folgt oder geschieht, muss nach einer allgemeinen

Regel auf das, was im vorigen Zustande enthalten war, folgen)

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knowledge, the borders between physiology and psychology shifted and interest incognitive psychology increased. Physiological research done by Helmholtz up untilthe late 1860s was above all concerned with the issue of accuracy in measurement. It

was physical in spirit. The combination of physiology and physics remained under thedomination of physics. In later years Helmholtzs contribution to physiologydecreased. The Handbuchs 1896 edition was more concerned than the first editionwith speculative developments on the unconscious mechanisms of knowledge. Thepsychology of memory enriched the physiology of perception. However, Helmholtzsconceptual background on the law of causality and on the distinction betweenexternal and internal sense retained a rather classical, and even a Kantian, outlook. Incomparison to Ernst Mach for example, Helmholtz is representative of a type ofconceptually oriented physicist who constructs and applies principles and laws inorder to understand both the world and the nature of knowledge. These laws areinvariable according to time, although they describe relationships between highlyvariable events or processes. Helmholtzs way of thinking about time remainedembedded in the classical view of time as an independent variable in the equations ofmechanics as well as a basic and independent dimension of psychology. On bothpoints, he relied heavily on Kant.

On the occasion of Kants centennial in 1904, the neo-Kantian philosopher AloisRiehl wrote:

Kant remained for a while the man of the physiologists; one put the doctrine of the a

priori forms of experience in connection with the progress of sensory physiology. Butthis is not in this physiological conception of Kant, founded by Helmholtz, . . . that theproper service of the great natural scientist lies for us; we see it more in the fact thatHelmholtz generally attracted attention on Kant, and thus reestablished the connectionbetween philosophy and science interrupted by the speculative systems of Schelling andHegel. (Riehl 1904, 261)

Although a neo-Kantian could not agree with Helmholtzs attempts at devising apsychological interpretation of transcendental concepts, he would recognize that suchwas the scientists intention to fill the framework of possible experience with real

empirical experience. The concepts Helmholtz borrowed from the philosophicaltradition were perhaps not entirely suitable to his psychological or psychophysio-logical purposes, ideas, and discoveries. In this way, he remained much more classicalthan Mach. In one of the many comments on Helmholtzs theory of spaceperception, James states in the Principles of Psychology: Helmholtz, though all thewhile without an articulate theory, makes the world think he has one. He beautifullytraces the immense part which reproductive processes play in our vision of space, andnever . . . does he tell us just what it is they reproduce (James [1890] 1983, 910). Aswith the notion of space, Helmholtzs notion of time revealed similar limits ofempiricism. They also testify to the lasting influence of Kants classification and

terminology of internal versus external sense. James judgment should be compared



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with Alois Riehls praise: It was Helmholtzs extraordinary service, at the time of thehegemony, or perhaps, looking back at the sixties and seventies years, we could saytyranny of the natural sciences, to have pointed out energetically and with the weight

of his authority the right and significance of philosophy for scientific research (Riehl1904, 284).

Acknowledgments

This article was completed during a stay as guest researcher at the Max PlanckInstitute for the History of Science at Berlin (May to June 1999); I am grateful toProfessor Hans-Jrg Rheinberger, Director of this Institute, for his hospitality. I wasable to undertake the writing of this paper during a stay at the Institute of Medical

History of the Albert Ludwig University at Freiburg im Breisgau in February 1999;I am glad to thank its Director, Professor Ulrich Trhler, for his hospitality inFreiburg.

I am also grateful to Pierre and Arlette Buser, Michael Heidelberger, ChristophHoffmann, David Hyder, Rmy Lestienne, Charles Marx, Alexandre Mtraux,Michel Meulders, Jutta Schickore and Henning Schmidgen for their suggestions orhelp. I wish to thank Mrs. Witzel for her help at the Archives of the Berlin-Brandenburg Academy of Sciences.

This paper is a result of the activities of the Helmholtz Working Group of the LouisPasteur University in Strasbourg, whose members are Andr Coret, Gerhard

Heinzmann, Jacques Lambert, Charles Marx, Alexandre Mtraux, Michel Meulders,Philippe Nabonnand. A Conference on Helmholtz and Physiology was organized bythisHelmholtz Academy in Strasbourg in March 1997. Additional working sessionswere also held at the Max Planck Institute for the History of Science and at theHumboldt University in Berlin in February 1998.

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