Area Speed Dating Near Stanford

First published Wed May 21, 2008; substantive revision Sun Mar 3, 2019

Jan 31, 2021 Kamala Harris’ niece has stopped selling clothing using the vice president's name after flying to the inauguration on a private jet paid for by a Biden donor and writing a children's book about. May 21, 2008 Ernst Mach (February 18, 1838 – February 19, 1916) made major contributions to physics, philosophy, and physiological psychology. In physics, the speed of sound bears his name, as he was the first to systematically study super-sonic motion. He also made important contributions to understanding the Doppler effect.

The frequent excursions which I have made into this province haveall sprung from the profound conviction that the foundations of scienceas a whole, and of physics in particular, await their next greatestelucidations from the side of biology, and especially, from theanalysis of the sensations. [Mach, Analysis of Sensations,Preface to 1st Edition]
  1. Historically, the area was known for forestry and ore deposits which led to heavy mining in the local economy. In recent years, tourism has become the primary industry, accounting for around 300,000 jobs. The area features several ruined military fortifications dating back to the 17th century (see Baroque fortifications in the Black Forest).
  2. Jun 29, 2009 Adding mass to a black hole, however, will increase its size, which led Bekenstein to suggest that the area of a black hole is a measure of its entropy. This conjecture received support in 1971 when Hawking proved that the surface area of a black hole, like the entropy of a closed system, can never decrease (Hawking 1971).

Ernst Mach (February 18, 1838 – February 19, 1916) made majorcontributions to physics, philosophy, and physiologicalpsychology. In physics, the speed of sound bears his name, as he wasthe first to systematically study super-sonic motion. He also madeimportant contributions to understanding the Doppler effect. Hiscritique of Newtonian ideas of absolute space and time were aninspiration to the young Einstein, who credited Mach as being thephilosophical forerunner of relativity theory. His systematicskepticism of the old physics was similarly important to a generationof young German physicists.

In philosophy, he is best known for his influence upon the ViennaCircle (a predecessor of which was named the Ernst Mach Verein), forhis famous anti-metaphysical attitude (which developed into theverifiability theory of meaning), for his anti-realist stance inopposition to atomism, and in general for his positivist-empiricistapproach to epistemology. It is important to note that some of theseinfluences are currently being re-examined, and are now thought to beboth more tenuous and more complicated than was once assumed. He wasalso an important historian of science, and occupied the Chair for thePhilosophy of the Inductive Sciences at the University ofVienna. Although previous philosophers had commented on science andmany scientists had influenced philosophy, Mach more than anyone elsebridged the divide; he is a founder of the philosophy of science.

In psychology, he studied the relationship of our sensations toexternal stimuli. Space, time, color, sound, once the domain ofphysics, were now also being studied by psychologists and conceived ofas not only the stuff of the physical external world but also theelements of our inner experience. Mach was deeply inspired byGustav Fechner’s psychophysics here. Psychologists todayregard him as a founder of Gestalt theory as well as the discoverer ofneural inhibition. Importantly, although in the twentieth centuryhe was better known to philosophers for his influence upon physics andthe philosophy of physics, it was psychology that was the primarydriving force behind his philosophy of science.

In his later years (1901), Mach was appointed to the AustrianParliament, where he was known as a reformer. His intellectualinfluence amongst leftists was so great that Lenin wrote a book,Materialism and Empirico-Criticism, criticizing Machiananti-materialism.

  • 3. Psychology and the Life Sciences
  • 4. Philosophy of Science
  • 5. Physics
  • Bibliography

1. Summary

A broad foundation is laid for the theory in question, and light isshed upon it from new sides, if, in conformity with the stimulus givenby Darwinism, we conceive of all psychical life — includingscience — as biological appearance, and if we apply to the theorythe Darwinian conceptions of struggle for existence, of development,and of selection. [Analysis of Sensations, 49–50]

Mach was a naturalist and a monist, as well as an anti-materialistin the sense of being an anti-mechanist. The connection betweennaturalism and materialism is an important one for Mach.Naturalism, in its simplest sense, is the doctrine that there isnothing beyond nature, not even the organic or mental, and evolution isthus generally a crucial component of it. The materialism of themechanical philosophy is the further view that this nature consists ofmatter in motion, and in particular that psychic phenomena can bereduced to matter in motion. Although materialism can make asmuch use of evolution as naturalism, Mach’s nineteenth centuryevolutionary views influenced his anti-materialism. Whereasmechanistic materialism views nature as an organized system of billiardballs, Mach’s evolutionary perspective viewed nature as a dynamicprocess.

Mach is part of the empiricist tradition, but he also believed insomething like a priori truths. But it is a biologized apriori: what is a priori to an individual organismwas a posteriori to its ancestors; not only does the apriori pre-form experience, but the a priori is itselfformed from experience. It was simultaneously the contradiction andconfirmation of Kantian epistemology. In as much as Kant usedthe a priori to explain how knowledge is possible, Mach usesthe knowledge of the new sciences to explain how an a priori ispossible. One more patch of philosophy, it was thought, yielded toscience.

Mach’s empiricism is complicated. It has its roots inthe belief that knowledge is a product of evolution, that our senses,minds, and cultures have an evolutionary history. It was simpleexperience to which early organisms responded, and it was out of simpleexperiences that the first images of the world were constructed.These constructions became a priori, allowing new and more complicatedunderstandings, and so forth. This process is in a sense repeatedin development; individual development begins through a process of theinteraction of simple sensations with those innate capacities formed inour ancestors. Out of this, more complex understandings arise;the process continues. Science furthers this biological processby bringing our primitive conceptions into contact with newenvironments, thus causing mental adaptation. The one and sameprocess unites all features of activity in nature: the adaptationof early life to primordial environments and the adaptation of modernscience to new data are unified under the principle of experienceforcing adaptation in memory. Though loosely an empiricist inthis sense, he rejected Locke’s tabula rasa, and alignedhimself against the more empiricist Helmholtz and towards the nativistEwald Hering in their famous nature-nurture debates. He is not inthe least a traditional empiricist.

Mach is generally considered a ‘positivist’. However, thistells us little, as positivism is really a collection of traditions,connected often by misunderstandings as much as by actual intellectualagreement. Furthermore, the word today has come to mean something sofar removed from its nineteenth century origins as to be practicallyharmful in understanding the how it was used in the nineteenthcentury. Outside of the social sciences (where it is alive and well),the word ‘positivism’ seems to be used mostly bypost-modernists, deconstructionists, and the Frankfurt school as aword to represent that branch of the enlightenment tradition thatfailed; it has become the ‘other’ which we all know iswrong without having to know what it is. Comte was a Positivist. Mach,too, was a Positivist, but Mach probably has more in common withHusserl than Comte, and certainly more in common with James.

Mach is not a phenomenalist under normal uses of this term, but thiscertainly requires investigation. First, to whatever extent he was aphenomenalist, he was a ‘scientific’ phenomenalist: hisideas were not derived from philosophical skepticism but throughapplication of the results of psychology and evolutionary theory. Heprovides clues as to how we should understand his infamous“elements”—they are related to the thought ofFechner and Ewald Hering. Secondly, he advocated that physics shoulddescribe relations of experience as much as possible; in his time thiswas termed ‘phenomenological physics’. This was clearlymeant as a methodological suggestion, arising out of the way hethought physics could best respond to the challenges presented to itby the life sciences. Thirdly, he writes that his ideas were the sameas Avenarius who had approached questions of the relationship betweenthe psychical and the physical from a physicalisticperspective. Although Mach undoubtedly adopts a sensationalist basis,this foundation is not crucial for Mach. He recognizes thepossibility of other foundations:

… many readers have found a stumbling-block in what theytook, erroneously indeed, to be the general character of my conceptionof the universe. And, to begin with, I must say that anyone who,in spite of repeated protests from myself and from other quarters,identifies my view with that of Berkeley, is undoubtedly very farremoved from a proper appreciation of my position. Thismisconception is no doubt partly due to the fact that my view wasdeveloped from an earlier idealistic phase, which has left on mylanguage traces which are probably not even yet entirelyobliterated. For, of all the approaches to my standpoint, the oneby way of idealism seems to me the easiest and most natural…. Ifeel it to be a piece of particularly good fortune that Avenarius hasdeveloped the same conception of the relation between the physicaland psychical on an entirely realistic, or, if the phrase be preferred,a materialistic foundation … [italics mine;AS: 361–2; see also 358]

Experimental psychology had just been founded. Mach’s elementsare, quite simply, the variables of a major branch of psychology, thenew field of psychophysics. Mach was part of the first generationof physiological psychologists that thought they had broken through theprimeval walls dividing the physical from the mental. Theythought they had solved this ancient problem through a scientific,monistic unification. The physical was characterized by itsability to be quantified: it was part of science.Now, the realm of Geist was falling under the same methodsused so successfully in physics. Following the pioneering work ofFechner, they had measured sensation and found that therelationship of external stimulus to inner response followedmathematical law. Fueled further by developments in evolutionarytheory, their optimism soared, perhaps a bit too high. Asso often happens in periods of scientific optimism, these newdiscoveries called for a philosophy in which they would be athome. Mach not only took up this challenge, but as a physicistalso applied the results of this tradition to the categories ofphysics.

Modern psychologists regard Mach as the forerunner of the idea ofneural nets in perception. He discovered that the eye has a mindof its own; we perceive not direct stimuli but relations ofstimuli. The visual system operates through a process ofcontinual adaptation of the present sensation to previous ones.We do not experience ‘reality’ but rather experience theafter effects of our nervous system’s adaptations to newstimuli. Furthermore, from an evolutionary perspective, it wasnecessary that this relational nature of perception beso. What were once thought of as errors of the brain, Mach showedto be adaptations. His argument is brilliant and he is cited eventoday in psychology textbooks for these contributions.Furthermore, his work in physiology influenced his epistemology.If we perceive not things directly but contrasts of things, then theworld is a biological construction formed through the process of ournervous system adapting to new sensations. Representationalisttheories of perception, which posit a direct correspondence betweenappearance and reality, become untenable.


Mach is also considered by Gestalt theorists to be one of theirforerunners. Christian von Ehrenfels, the founder of Gestalttheory, begins his seminal 1890 paper “ÜberGestaltqualitäten” by reviewing Gestalt ideas inMach’s Analysis of Sensations. These ideas arosein the context of his research on Mach bands where he realized that themind and senses actively contribute to sensation. TheAnalysis of Sensations is full of examples of this sort; itscentral concern is to understand the dynamic relation between ourcognitive structure and experience. Our cognitive structure isitself formed through previous experience, and our current experienceis structured by it in turn.

2. Biography and Early Development

Mach was born in Moravia on Feb 18, 1838. In 1840 his familymoved to a farm in Untersiebenbrunn, Lower Austria. He studiedphysics at the University of Vienna from 1855 to 1861, continuing on asa lecturer until 1864. After spending three years as Professor ofMathematics at Graz, he received a Chair at Prague where he stayeduntil 1895. For the next six years, Mach occupied a Chair in theHistory and Philosophy of the Inductive Sciences at Vienna. Hesuffered a stroke in 1898 and retired in 1901. He died nearMunich in 1916.

He credited his philosophical awakening to reading, at age fifteen,his father’s copy of Kant’s Prolegomena to any FutureMetaphysics:

The book made at the time a powerful and ineffaceable impressionupon me, the like of which I never afterwards experienced in any of myphilosophical reading. Some two or three years later thesuperfluity of the role played by “the thing in itself”abruptly dawned upon me. On a bright summer day in the open air,the world with my ego suddenly appeared to me as one coherentmass of sensations, only more strongly coherent in the ego.Although the actual working out of this thought did not occur until alater period, yet this moment was decisive for my whole view.[AS: 30fn]

Mach attended an Austrian Gymnasium in Moravia, graduating atseventeen, entering the University of Vienna as a student ofmathematics and physics in 1855, and matriculating in 1860.After graduation, he stayed in Vienna as a privat dozent,supporting himself through giving lectures paid for directly bystudents (which means he made very little money).

It was in these years at Vienna that Mach began his interest inphysiology. Johannes Müller and his students had started anew school of physiology in the 1840s. Initially centeredin Berlin, it came to Vienna following the political reforms of 1848 inthe guise of Ernst Brüke and Carl Ludwig, a former a student ofMüller. This new school was characterized not just bya general suspicion of vitalism (though Müller remained a vitalistof sorts), but more by an agreement on the importance of theapplication of physical-chemical methods to the biologicalsciences. Carl Ludwig, Herman von Helmholtz, and Ernst Haeckel alsostudied under Müller. Although his degree was in physics, Machenrolled as a student of the Medical Faculty, taking 22 hours ofclasses in physiology, chemistry, and anatomy. In 1861 he taughta course in physics for medical students, out of which he developed histextbook, Compendium der Physik für Mediciner. Healso published his first article on psychophysics, Über dasSehen von Lagen und Winkeln durch die Bewegung des Auges, where hestudied the relationship between tension in the eye muscles andperception of form. This work also contains Mach’s firstreference to Fechner, whose influential Elements ofPsychophysics was published in 1860. During the next yearsin Vienna, he also taught classes in psychophysics and a class entitledDie Principien der Mechanik und mechanischen Physik in ihrerhistorischen Entwicklung, which possibly marks the start of hisinterest in the history of science (though we do not know the actualcontents of the lectures). Mach was also influenced byHelmholtz’s Die Lehre von den Tonempfindungen.

Mach’s first important scientific contribution was over therecently discovered ‘Doppler theory’. In 1841,Christian Doppler noticed that sound changes in frequency as a sourcemoves toward and away from an observer. By 1845 he hadgeneralized this to include all wave phenomena, including light.Two prominent physicists, Petzval and Ångström, challengedDoppler. Mach devised a simple apparatus that demonstrated thatthe Doppler effect was real, at least for sound. A six-foot tubewith a whistle at one end was mounted so as to rotate in a verticalplane. When the listener stood in the plane of the axis ofrotation no changes in pitch could be heard. But if the observerstood in the plane of rotation, fluctuations in pitch that correspondedto the speed of rotation could be heard. The application of thiswork to Doppler effects with light remained controversial, but Mach isregarded as one of the first to realize the possibility of studying astar’s spectrum to understand its movements [see Blackmore 1972:17–19; Swoboda 1974: 20–75].

Mach was highly influenced by Johann Herbart during this period, notonly through Herbart’s writings, but also through Franz Lott,Vienna’s Herbartian spokesperson and Mach’s goodfriend. In Herbart, Mach found a mechanical approach topsychology and physiology that coincided with Mach’s earlyacceptance of atomism. As his interests shifted to physiology andpsychology, the mechanical models remained, but the atomism became lessimportant. Eventually, the mechanical approach to physiology gaveway to an evolutionary approach, and as the mechanical approach lostground here atomism did as well. This trend increased the deeperMach went into psychophysics, and eventually turned into ananti-mechanistic philosophy in Mach’s mature thought. Machmakes little mention of Herbart in his later writings; for instance,only two brief references are made to Herbart in Analysis ofSensations, both in the context of reflections on his intellectualdevelopment.

In 1864 Mach received an appointment in mathematics at Graz.For the first time he had the money and freedom to carry out his ownexperiments. In 1866 he exchanged his math chair for one inphysics. While at Graz he had personal contact with Fechner andcarried out his important work on Mach Bands. It was in this workthat Mach first made use of evolutionary theory. Mach startedwork on what later became Analysis of Sensations, butapparently was discouraged by Fechner’s criticism. Hereturned to this work twenty years later, after further developing hisown ideas. It was also in Graz that Mach first encountered EwaldHering’s thought, both in physiology and evolution. InMach’s first article on Mach Bands [Mach 1865] he refers toHering, and in 1866 Hering gave his famous address on UnconsciousMemory to the Vienna Academy. In 1867 Mach went toPrague as a professor of physics. He stayed in Prague fortwenty-eight years, until 1895, whereupon he returned to Vienna. It wasin Prague that his mature thought developed.

Mach’s name is, of course, associated with the speed of sound,where Mach 1 means the speed of sound in a given medium. Since thespeed of sound varies with the density of the medium it is travelingthrough, Mach numbers are not absolute quantities but relationalones. In the late 1860s developments in gun and artillery technologyproduced projectiles that traveled faster than sound vibrations. Thiswas realized over a period of time as two effects wereinvestigated—a second loud ‘boom’, distinct from theusual one of the explosion, as well as a different type of wound. Itwas the latter that began Mach’s interest. In 1868 warringEuropean powers had signed The St. Petersburg Declaration that banneda new type of bullet that exploded on impact, thus causing‘crater’ type wounds. Soon thereafter, however, similartypes of ‘crater’ wounds appeared again. Various theoriesover their cause were put forward, leading Mach to investigate. By1885 Mach had worked out the details of supersonic motion, along theway developing high-speed photographic techniques. Most importantlyfor engineers, Mach Number is the ratio of the speed of the object tothe speed of sound in the given medium; his work is essential tomodern aerodynamics, and through it the word ‘Mach’ hasbizarrely entered into popular culture as an icon for razors, soundsystems, fighter pilots, and high speed fuels.

Mach’s early intellectual development was very much a productof the outstanding developments in the sciences of his time.Whereas a generation before, there existed only one truly maturescience, physics, by the early 1860s both psychology and biologyhad entered the scientific scene. Previously, scientificallybased views on reality were essentially Newtonian-mechanistic.After Darwin and Fechner, the new sciences of psychology andevolutionary theory opened up new areas of philosophic-scientificinteraction. The possibility of a new scientific view opened up,one based upon these new sciences, and sought to displace the Newtonianparadigm with one based upon developmental orientations.

3. Psychology and the Life Sciences

3.1 Gustav Fechner

My natural bent for the study of these questions received itsstrongest stimulus twenty-five years ago from Fechner’sElemente der Psychophysik … [AS:xxxvi]

The single greatest influence upon Mach was Fechner; this cannot beoverstated. Fechner’s The Elements ofPsychophysics was published in 1860, but Mach was aware of theideas in it before. The definitive account of Fechner is MichaelHeidelberger’s book Nature from Within [2004].

Fechner founded experimental psychology by developing a method of‘measuring’ the psychical. Our senses havethresholds of perception; that is, given any amount of stimulation of asense, there is an amount more of that stimulation which is requiredfor us to notice it. Furthermore, that amount increaseslogarithmically as the base-line sensation increases. This holdstrue, with complications and variations, for all of oursensations. The import was that there is a mathematicalrelationship between the external world and the inner, between thephysical and the psychological. It was then possible to talkabout these dual aspects of reality in a neutral manner (see NeutralMonism). Fechner uses the word ‘elements’ for thispurpose, and Mach’s elements are directly related to them. Withsome loss, embed Fechnerian methodology within nineteenth century evolutionary theory,and apply it to the categories of physics, and we get Machianepistemology.

3.2 Mach Bands

Free speed dating near me. In 1865 Mach published, “On the effect of the spatialdistribution of the light stimulus on the retina,” the first of aseries of remarkable articles on what are now known today as MachBands.

Mach Bands © Alan Stubbs, from Perceptual Stuff.
Reproduced with permission.

The thin dark bands along the outer edges of the gradients and thethin light bands along the inner edges of the gradients are opticalillusions. The cause of this effect is due to contrast perception; weover process at boundaries and under process where there isconstancy. In fact sensory response can even stop with unchangingstimulation. Mach is credited for discovering lateral inhibition inour sense organs, the idea that our senses pre-process informationbefore sending it to the brain.

Before this period, optical illusions were understood as just that,errors in judgment, quirks of the brain. The sense organs wereseen as simple media with a direct link to the brain. Their onlyrole was to transmit a sensation to the brain, where it was theninterpreted. Mach argued that the processing does notall occur in the brain. The quirks of judgment are not due toprocessing errors in the brain, but innate features of the sensesthemselves.

The immediate significance of this was that it provided a strongargument against direct representationalist theories ofperception. There simply is no isomorphism between reality andappearance. But Mach took this even further, embedding it withinhis evolutionary Fechnerian framework.

Mach argued that perception works through perceiving the relationsbetween stimuli. And this process is at the root of alllife. The same process that drives evolution, drives perception,and even (as we shall see shortly) drives science.

Since every retinal point perceives itself, so to speak, as above orbelow the average of its neighbors, there results a characteristic typeof perception. Whatever is near the mean of the surroundings becomeseffaced, whatever is above or below is disproportionately brought intoprominence. One could say that the retina schematizes andcaricatures. The teleological significance of this process isclear in itself. It is an analog of abstraction and of theformation of concepts. [Mach 1868, in Ratliff 1965: 306]

That which is constant receives less attention, that which variesmust be brought into equilibrium. It is this process of bringingcontrasts into equilibrium which is at the basis of all organicprocesses, evolutionary, developmental, and perceptual. Theorganism is a dynamic system that has innate tendencies toself-regulation and equilibrium. When equilibrium is disturbed,which can happen on a variety of levels, the organism works to form anew equilibrium. The senses are not things that got passivelywritten on, but rather things that interact with environments.Life is not mechanistic but teleological.

And this is not an accident, for can we imagine lifeotherwise? Mach asks us to consider the following:

Let us first ask how we would find our way in the visual world if wewould perceive, not relations of, but only differences in,illumination. One and the same thing in the same surroundingswould become immediately unrecognizable with the slightest alterationof light intensity, such as when a cloud covers the sun. Shouldwe still want to find our way, we would then have to habituateourselves to maintain equal levels of light intensity, for instance byclosing and opening our eyes. In fact, if this god of thepsychophysical law were non-existent, the organism itself would have todevise it and, if the Darwinian theory is correct, it has devisedit. The seeing of light intensity relations, within certainlimits, is necessary for the existence of organisms. [Mach 1868 inRatliff 1965: 300]

We do not perceive the world in itself, Mach claims. If we didwe would perceive chaos. Thus we have evolved senses thatperceive contrasts of perception, relations of perception.Sensations by themselves can have no organic meaning; only therelations of sensations to one another can have meaning.Perception, Mach believed, is never perception of direct stimuli.

3.3 Gestalt Theory

This central Machian insight that perception is always relational andconstructed lies at the origins of Gestalt Theory. The seminal articleof Gestalt Theory, Christian von Ehrenfels’ 1890“Über Gestaltqualitäten,” begins with areview of these ideas, found in Mach’s 1886 Analysis ofSensations. Sensations are not simply raw experiences, but theinteraction of experience with a pre-formed cognitive structure. Forinstance, when we hear a known melody, we recognize it no matter whatkey it is played in. It can be hummed, buzzed, or strummed on aguitar. Furthermore, even if one or more notes are incorrect, we stillrecognize it. Mach asks, “what constitutes a melody?” Itseems incorrect to say that the actual sound vibrations constitute themelody as we have just seen that numerous different sounds can makethe same melody. But on the other hand, it seems empirically odd tosay that a melody is not constituted out of its sounds. The actualmelody, then, exists in our ability to recognize it. It is formed byexperience of one or more examples of the melody, but it is anidealization of that experience. Significantly, the idealizationcaptures not the actual sounds, but the relationships of thesounds to one another. Thus a melody can be sung in a high or lowpitch, etc., but as long as the relationships remain the same werecognize it as the same melody. For Mach, this process is at thebasis of all perception. Experience requires an ‘apriori’, but that a priori is itself formed byexperience. This process is also at the root of evolutionaryprocesses.

3.4 Haeckel, Hering and Evolutionary Theory

Nineteenth century evolutionary theory is complicated in that in thecultures which most obviously experienced a widespread acceptance ofevolution, inspired apparently by Darwin’s 1859 publicationof Origin of the Species, evolutionary ideas had already beenpresent and Darwin’s mechanism for evolutionary change, naturalselection, was not necessarily accepted. Rather, more deeplyteleological accounts of nature were often put forward within anevolutionary framework. Mach came of intellectual age in 1860, rightwhen this explosion of evolutionary ideas was starting. Unlike thedisciplines of psychology and physics, he makes no contributions toevolutionary theory; however, his entire system is located within anevolutionary framework. This framework is not one that he argues for;rather, it was the metaphysics (yes, metaphysics) he adapted from hisnineteenth century German intellectual culture. The two immediateinfluences on Mach in this regard were Herring and Haeckel, or atleast we can turn to their writings to understand the evolutionarytradition Mach was part of.

The greatest popularizer of evolutionary theory in the nineteenthcentury was of course Ernst Haeckel. Although he is now best known forhis infamous maxim, “ontogeny recapitulates phylogeny”,his larger project was to put forward an evolutionary metaphysics; inparticular to offer a monistic unified account of our reality. Hisproject, overlapping significantly with that of Mach and Herring,sought to embed the developments of psychology within a theory ofevolutionary development; evolution was the evolution of not just thespecies but also of the psyche.

In late nineteenth century continental Europe a different notion of‘direction’ existed than the one that Darwin directlyattacked. Whereas the theory of natural selection maintains thatevolution is a directionless process having no guiding factor or endpoint, relying rather on selection within particular environments onrandom variations thrown up by the chaos of nature, Hering, Haeckel,and Mach were part of a German tradition which held that there is aninner telos in nature. Hering and Mach were atheists, and disbelievedin a soul, but still accepted the idea that nature had internaldirection. As will be shown later, this idea of internaldirection extends for Mach all the way up to his ideas on the purposeof science.

Hering was Mach’s close friend, political ally, academicpartner, and second only to Fechner in terms of total influence.Hering was also a fellow Fechnerian (he studied under Fechner), and heshared both Mach’s bio-psychological orientation and nativisttheories of spatial intuition. Hering is known for his work inbinocular vision and for his debates with Helmholtz over color vision,and also for his address to the Imperial Academy of Sciences in Vienna,“On Memory as a Universal Function of OrganizedMatter”.

3.5 Monism

All three were also leaders in the Monist movement. It is no accidentthat one of the oldest philosophy journals is The Monist(started in 1888). A look through its early volumes reveals a mixtureof scientific applications to the various categories of humanexistence. Mach was a frequent contributor, and indeed a good friendof the editor, Paul Carus, who also arranged the English translationand publication of many of Mach’s works. In1906, Monistenbund, a monistic society, was formed with theintention of including everyone who believed that there was only onereality. Haeckel and Ostwald were active members and tried withoutsuccess to bring in Mach with an offer of the presidency in 1912. Machwrote back:

There are as many different monisms as there are people in it.Monism is provisionally a goal, after which we all strive, butis scarcely anything fixed or sufficient … It seems to me… ludicrous to found a kind of religious sect, whilerefusing to consider philosophical questions [as to itsnature]. But this is not so terribly important in so far as themovement is limited to a small circle of intellectuals. But if itexpands more widely, then it will probably let loose a kind ofcounterreformation for which I definitely have no sympathy.[Blackmore 1972: 193–4]

4. Philosophy of Science

4.1 Historical Critique

Mach wrote a number of widely read science history texts; in a sensethey are archaeologies of science, digging at the past to criticallyelucidate the present. Machian history can also be seen in the contextof German nineteenth century thought; Hegel, David Strauss, Nietzsche,and Marx all offered historical frameworks for their varioussocial-philosophical positions. They also saw their own critiques asplaying a crucial role in the new order that was to follow. That is,each of their works placed itself at the juncture of history, wheretheir writing self-consciously was to influence the next stage that ithad predicted. Certainly d’Alembert, Herschel, Whewell, and Mill hadwritten histories of science before Mach, but it was Mach who wrotecritical history in the above sense. The interesting aspect of Mach’scritique was that it actually had an effect upon science. Scienceof Mechanics deserves mention in the history of physics.

4.2 Biological Origins of Science

Mach puts science on a continuum with earlier human activity, infact with earlier animal activity. What began as simpleadaptations that allowed instinctive responses to immediate conditions,gradually evolved into ever more complex capacities forresponse. Gradually life acquired memory and thus anawareness of a wider field of spatial-temporal relations than ispresent immediately to the senses. Memory then grew beyondindividual memory and became communicated culturally. Science isa direct outgrowth of this deep natural process:

Lower animals living under simple, constant and favorable conditionsadapt themselves to immediate circumstances through their innatereflexes. This usually suffices to maintain individuals and speciesfor a suitable period. An animal can withstand more intricate andless stable conditions only if it can adapt to a wider range ofspatial and temporal surroundings. This requires a farsightedness inspace and time which is met first by more perfect sense organs, andwith mounting demands by a development in the life of the imagination.Indeed an organism that possesses memory has wider spatial andtemporal surroundings in its mental field of vision than it couldreach through its senses. It perceives, as it were, even thoseregions that adjoin the directly visible, seeing the approach of preyor foe before any sense organ announces them. What guarantees toprimitive man a measure of advantage over his animal fellows isdoubtless only the strength of his individual memory, which isgradually reinforced by the communicated memory of forebears andtribe. Likewise, what essentially marks progress in civilization isthat noticeably wider regions of space and time are drawn within thescope of human attention. With the partial relief that a risingcivilization affords, to begin with through division of labor,development of trades and so on, the individual’s life is focused on asmaller range of facts and gains in strength, while that of society asa whole does not lose in scope. Gradually the activity of thinkingthus invigorated may itself become a calling. Scientific thoughtarises out of popular thought, and so completes the continuous seriesof biological development that begins with the first simplemanifestations of life.…. Indeed, the formation of scientifichypotheses is merely a further degree of development of instinctiveand primitive thought, and all the transitions between them can bedemonstrated. [KE: 171]

In an article to which Mach often refers, he writes: “Here Iwish simply to consider the growth of natural knowledge in thelight of the theory of evolution. For knowledge, too, is aproduct of organic nature. And although ideas, as such, donot comport themselves in all respects like independent organicindividuals, and although violent comparisons should be avoided, stillif Darwin reasoned rightly, the general imprint of evolution andtransformation must be noticeable in ideas also.” [PL:218] And later, “We are prepared, thus, to regard ourselves andevery one of our ideas as a product and a subject of universalevolution; and in this way we shall advance sturdily and unimpededalong the paths which the future will throw open to us.”[PL: 233]

4.3 Biological Purpose of Science

Once science is placed within an evolutionary context, Mach’steleological views of evolution (see section 3.4) become significantfor his philosophy of science. The developmental processes ofevolution have given rise to this complex human activity we callscience, which now itself is participating in the processes ofevolution. Just as the eye, for instance, has evolved to betteraid us in adapting to a greater variety of landscapes, so science hasevolved to better aid us in adapting to the world:

Science apparently grew out of biological and cultural developmentas its most superfluous offshoot. However, today we can hardlydoubt that it has developed into the factor that is biologically andculturally the most beneficial. Science has taken over the taskof replacing tentative and unconscious adaptation by a faster varietythat is fully conscious and methodical. [KE: 361]

Science is both an outcome of this process (it hasbiological roots), and also now is part of this process (ithas a biological function continuous with other evolutionaryprocesses). Leaves, hearts, brains, eyes, and science are on acontinuum in as much as they arose out of adaptive processes and nowserve the biological function of survival and further adaptation.

Man is governed by the struggle for self preservation: hiswhole activity is in its service, and only achieves with richerresources, what the reflexes accomplish in the lower organisms undersimpler conditions of life. Every recollection, every idea, everypiece of knowledge has a value originally only in so far as it directlyfurthers man in the direction indicated. [PH: 336]

It should be noted that Mach does not argue or provide evidence forthis evolutionary view of science; he seems rather to adopt it fromideas that were being circulated in the later half of the nineteenthcentury. Nonetheless, references to a deep evolutionary perspectivepermeate his writings. For instance:

The biological task of science is to provide the fully developedhuman with as perfect a means of orientating himself as possible.No other scientific ideal can be realized, and any other must bemeaningless. [AS: 37]

And also:

The adaptation of thoughts to facts, accordingly, is the aim of allscientific research. In this, science only deliberately andconsciously pursues what in daily life goes on unnoticed and of its ownaccord. [AS: 316]

This evolutionary perspective even plays a critical role in hisunderstanding of physics. For instance, in his famous exchange withPlanck (see 5.3), Mach repeatedly refers to his biologico-economicaltheory of knowledge as an important part of view of the physicalworld.

4.4 Economy and Unity of Science

One and the same view underlies both my epistemological-physicalwritings and my present attempt to deal with the physiology of thesenses — the view, namely, that all metaphysical elements are tobe eliminated as superfluous and as destructive of the economy ofscience. [AS: xxxviii]

The idea of an economy of nature dates back at least to Linnaeus, ispresent throughout nineteenth century evolutionary ideas, and findsanother home in Mach. Nature is an organized and frugalsystem. Excess exists only in a vestigial sense; everything hasits place. For Darwin, the economy of nature had a ready explanation innatural selection, and the non-economical aspects of nature, such asvestigial organs, took on great significance. A logic of biologytook hold: where once economy was an observed feature of nature,it now became a necessary feature. Even the apparentnon-economical aspects were ultimately economical. Where onceeconomy required explanation, it now became the explanation. Aphenomenon of nature turned into a force of nature. As is typicalfor Mach, widely accepted biological principles become uncriticallyheld cornerstones of his epistemology.

Of course, the metaphor of economy is also used in economics.According to Mach’s own recollections of his intellectualdevelopment in a 1910 essay, “The Guiding Principles of MyScientific Theory,” he first understood science as‘okonomisch’ in 1864, through discussions with hisfriend E. Hermann, a political economist. In the same passage,Mach proceeds to note that he was well prepared for this idea throughhis biological background, and in fact the two combined to form whatbecame his ‘biological-economical theory of knowledge’.[Mach 1910: 30–31]

The purpose of science is to give the most economical description ofnature as possible, because science is to provide conceptions which canhelp us better orient ourselves to our world, and if science isuneconomical then it is useless in this regard. Put another way,Mach’s reason for insisting that economy must be a guidingprinciple in accepting or rejecting a theory is that uneconomicaltheories cannot fulfill their biological function, which, as we haveseen previously, he insists is (in a descriptive sense) the function ofscience. The biological purpose of science is the improvement orthe better adaptation of memory in service of the organism’sdevelopment:

The aim of scientific economy is to provide us with a picture of theworld as complete as possible — connected, unitary, calm and notmaterially disturbed by new occurrences: in short a world pictureof the greatest possible stability. The nearer science approachesthis aim, the more capable will it be of controlling the disturbancesof practical life, and thus serving the purpose out of which itsfirst germs were developed. [PH: 336, italicsadded]

Disturbances in environments cause maladaptations; progressiveadaptation only has meaning in reference to that which is stable.Science must be economical so that a stable basis for our orientationcan be built up, and this leads to a crucial point: as scienceencompasses more and more of the world, and as these theories workthemselves into our unconscious memory, more and more of the worldbecomes part of our pre-existing cognitive structure. That is, the roleof science is to improve our orientation to the world.

Let us look in depth at a discussion of these issues occurring inScience and Mechanics in a chapter entitled “The Economyof Science.” The section occurs toward the end of the book,and begins: “It is the object of science to replace, orsave experiences, by the reproduction and anticipation offacts in thought. Memory is handier than experience, and oftenanswers the same purpose.” [SM: 577] Theeconomical role of science is to allow us to understand and react tonature prior to experience; just as a newborn chicken knows what to doas soon as it is hatched due to its accumulated memory (itdoesn’t need to learn on its own as the learning has already beendone by its ancestors), so we now learn from science how to anticipatethe world. Our memory encompasses more and more of the world,thus allowing better and better orientation.

The drive for economy is itself a biological instinct, which sciencemust thus also fulfill. In a larger sense, economy is tied to theinnate tendency toward survival or search for better orientationdiscussed earlier. Evolution is guided by these principles; lifeas a product of evolution has a tendency toward these principles, andwe as humans have these tendencies hard-wired into us—even to thepoint that our very conception of self-existence arises out of it; inAnalysis of Sensations, the ego is described as arising froman “ideal mental economical unity.” [AS: 22]

An important application of this idea of economy occurs when twotheories, formerly separate, come in contact. For Mach this is acentral concern: he is driven to unify psychology andphysics. At issue here is the economical requirement of needing asingle orientating perspective: “But anyone who has in mindthe gathering up of the sciences into a single whole, has to look for aconception to which he can hold in every department ofscience.” [AS: 312] When theories come incontact with each other, adaptation of one to the other must takeplace: “Epistemological criticism [is not a problem for thephysicist]. But when it is a question of bringing into connectiontwo adjacent departments, each of which has been developed in itsspecial way, the connection cannot be effected by means of the limitedconceptions of a narrow special department. By means of moregeneral considerations, conceptions have to be created which shall beadequate for the wider domain.” [AS: 313] It isuneconomical to have one theory for physics and another for psychology;the mind demands that the two be brought together. Attempts atsuch mutual adaptation have so far been failures and Mach hopes thathis ideas can facilitate this:

To the physicist, qua physicist, the idea of “body”… [assists in] a real facilitation of view, and is not the causeof disturbance…. When, however, physics and psychology meet,the ideas held in the one domain prove to be untenable in theother. From the attempt at mutual adaptation arise the variousatomic and monadistic theories — which, however, never attaintheir end. If we regard sensations, in the sense above defined(p. 13), as the elements of the world, the problems referred to appearto be disposed of in all essentials, and the first and most importantadaptation to be consequently effected. This fundamental view(without any pretension to being a philosophy for all eternity) can atpresent be adhered to in all fields of experience …[AS: 32]

The inherent non-metaphysical unity of the physical and psychical isnot concocted, rather the disunity is what is artificial.Mach’s ideas on the unity of science, then, arise out of hisbio-economical model of science.

4.5 Nature of Scientific Change and Progress

Finally, Mach can be seen as the precursor of what is today one of themajor epistemological metaphors of scientific change. Mach offers aselectionist account of group-level change consisting of selectionupon naturally produced variation, passed on through processes ofheredity. As with Darwinian evolution, scientific variation itself isnot directed. Emphasizing the importance of natural variation, Machhad a Feyerabendian tolerance of nonscientific beliefs—thefamiliar point being that it is better to tolerate some error than risklosing variation which might yield fruit later. As an indication ofvariation’s importance, several chapters in his various books aredirected almost entirely to this subject. Variation is not somethingwhich we consciously produce, but rather something which happens byaccident.

The mind is not able to come up with new ideas on its own, that is,it is unable to direct creativity. Thus, variation is notdirected, but science relies on fantasy, chance, luck, etc., forproduction of its ideas. Once produced, scientists choose thoseideas which best fit the facts. Mach also comments on the debatesover whether reasoning, inductive or deductive, can produce knowledge,arguing that reasoning cannot by itself produce knowledge, but rathercan only operate on existing variation: “Thus syllogism andinduction do not create new knowledge, but merely make sure that thereis no contradiction between our various insights and show clearly howthese are connected, and lead our attention to different sides of someparticular insight, teaching us to recognize it in differentforms. Obviously, then, the genuine source from which theenquirer gains knowledge must lie elsewhere.” [KE:231]

Although the mind cannot direct the creation of ideas, it can directthe selection of them. Selection occurs when thescientists choose the theories, out of the pool of available variation,which best fit the data and other pre-existing ideas. It is alsoworth noting that Mach talks of the tendency for resistance to changeas being both necessary and problematic for science. Mach was notonly one of the founders of Gestalt Theory, but also applied its coreconcepts to the process of science. Packaged together with his use ofhistory to elucidate science, he anticipates Kuhn’s ideas onscientific change and progressive rationality.

5. Physics

Just as the early Mach was influenced by the revolutions inpsychology and biology, the mature Mach was deeply involved in therevolutions in physics, though remaining a critic of the new physicsjust as much as he had been of the old. Both Planck and Einsteinpaid their homage to the person who created a culture of critiquewithin which they developed their ideas. They also came tocriticize what they saw as his stubborn refusal to accept their newideas.

To twentieth philosophy, Mach is best known as a positivist whoinfluenced Logical Positivism, a philosopher of physics who influencedEinstein, and an empiricist who denied the reality of atoms. None ofthis is incorrect, but to understand Mach as limited to physics is ahuge mistake. Mach’s influence upon physics and its philosophy wasenormous; the mistake has been to not understand the roots of Mach’sideas, a mistake which took place early in the twentieth century as anew brand of positivism/empiricism entered the scene (one which turnedaway from the life sciences as the scientific driving force ofpositivist epistemology and focused on the new developments in thefoundations of physics and logic). This encyclopedia has severalentries on the history and philosophy of physics (see links below)which detail Mach’s ideas, contributions, and influences (inparticular, his famous critique of Newtonian Absolute Space and Time,as well as his relationship to Einstein). What follows is a placementof his ideas within the context of his larger thought.

5.1 Space

Mach perhaps writes more about space than any single other topic;the Analysis of Sensations is dominated by discussions aboutit (Chapters 6 to 10 are devoted, more or less, exclusively to it) asis Space and Geometry. His Science of Mechanicscontains his famous analysis of absolute space. The starting point ofMach’s thought is that physiological space is differentfrom geometrical space. The idea of physiological space wasnot new with Mach; apparently initiated by Müller, it wasdiscussed by both Helmholtz and Hering. Physiological space is thespace constructed by our cognitive structure. It is not something weintentionally create, but rather it is a product of unconsciousadaptation, and as such, may be a source of a prioritruths. Geometrical space, on the other hand, is an intellectualconstruction, “reached for the most part by purposefulexperience.” [SG: 5] While physiological space iscompletely psychological, geometrical space is an abstraction onphysiological space. Neither is an ‘objective’ or‘absolute’ space.

Whereas geometrical space is unbounded, infinite, and homogeneous (atleast in its Euclidean form), physiological space is highly bounded,finite, and non-uniform. Geometrical space is detached from ouremotional psyche, but physiological space is intertwined with basicemotions: a tiger nearby in physiological space brings about differentemotions than a tiger far away in physiological space. Similarly,upness and downness, rightness and leftness are not just abstractdirections but have physiological, and thus psychologicalmeaning. When objects in physiological space are moved, their (apparent)sizechanges (similarly, when we move, the size of objects in physiologicalspace also changes). And, importantly, physiological space does not,at least in its origins, have a metric. The origins of physiologicalspace are in unconscious biological need, whereas the origins ofgeometrical space are in physiological space and intellectualdevelopment.

5.2 Measurement

This brings us to the problem of measurement. Normallywhen we measure an interval we believe we are indeed measuring space ortime. However, measurement relies upon comparison.This was important for Mach: we do not measure ‘space’, butrather we compare our spatial sensations. All measurementrequires the use of a standard, and since any standard we pick is ofthe same nature as the thing we are measuring, we do not truly measureanything (if by this we mean an absolute measurement):

But we do not measure mere space; we require a material standard ofmeasurement, and with this the whole system of manifold sensations isbrought back again. It is only intuitional sense-presentations that canlead to the formulation of the equations of physics, and it isprecisely in such presentations that the interpretation of theseequations consists. Thus, though the equations only containspatial numerical measurements, these measurements, also, are merelythe ordering principle which tells us out of what members of the seriesof sensational elements we have to construct our picture of theworld. [AS: 343]

When we measure the spatial dimensions of an object, we are comparingit to an agreed upon standard. Ultimately all standards must havetheir root in physiological comparison. In this way Mach tries tobring physics back into psychology. Physics is based uponmeasurements, but measurements are ultimately physiologicalcomparisons. According to Mach, physics can never escape itsbiological origins. Planck and Einstein accepted Mach’s critique ofthe old physics, that it was under the spell of concepts which werederivative of unreflective development, but rejected Mach’s claim thatphysics was stuck, so to speak, in psychology.

5.3 Anti-Atomism

… the biological-economical interpretation of the cognitiveprocess can perfectly well co-exist on peaceable, and indeed onfriendly, terms with that of present-day physics. The only realpoint of difference which has so far come to light concerns the beliefin the reality of atoms. Here again, Planck can hardly find wordsdegrading enough for such wrong headedness …. After exhortingthe reader, with Christian charity, to respect his opponent, P. brandsme, in the well-known biblical words, as a “falseprophet.” It appears that the physicists are on the way tofounding a church; they are already using a church’s traditionalweapons. To this I answer simply: “If belief in thereality of atoms is so important to you, I cut myself off from thephysicist’s mode of thinking, I do not wish to be a truephysicist, I renounce all scientific respect—in short: Idecline with thanks the communion of the faithful. I preferfreedom of thought.” [“The Guiding Principles of My ScientificTheory of Knowledge and Its Reception by MyContemporaries.” 37–38]

Mach’s opposition to atomism has become one of his best knownlegacies, with Mach seen as an anti-realist about unobservableentities. While anti-realist arguments can indeed be found inMach, their origins lie not in philosophical skepticism but in hisbio-psychological view of science. Furthermore, hisconcerns about atoms were often specific to the various competingtheories of the time. It should be noted that the issue ofatomism was a central scientific controversy of this period; there werea variety of theories of atoms being put forward as well as varietiesof alternatives. In his Principles of the Theory ofHeat, Mach aligned himself with a phenomenological approach tothermodynamics—a temporarily fruitful research program that avoidedthe problems of positing theoretical causal entities.Mach’s experimental research was not in this area, but at stakewas not just the reality of atoms but an understanding ofscience. Mach’s attitude toward atoms was an outgrowth of aview of science.

He became embroiled in a long-standing dispute with Boltzmann,propounder of the kinetic theory of gasses. Boltzmann and Machended up agreeing in essence: if atomic theory was fruitful it shouldbe used, but adopted what today might be considered ananti-metaphysical stance toward a theory that was still largelyunsubstantiated. It is generally agreed that it was not until1905 with Einstein’s study of Brownian motion that the kinetictheory of molecules found full verification.


Mach’s views on atomism are most clearly presented in anexchange with Planck. In 1909 Planck wrote an essay “TheUnity of the Physical World-Picture”, which contained a severecriticism of Mach’s philosophy. Mach replied in 1910, with“The Guiding Principles of My Scientific Theory of Knowledge andIts Reception by My Contemporaries.” Planck responded in1910 with “On Mach’s Theory of Physical Knowledge: AReply.”

At issue were differences on how to make science free of humansubjectivity, and how to achieve a unified science. Planck [1909]argues that while we once defined heat according to sensations, thestudy of heat has gone beyond this, now being under the purview ofelectrodynamics and kinetic theory; similarly, tones and color are nowunderstood as frequencies or wavelengths. Although physics hadits beginnings in the analysis of sense impressions, its currentsuccess is due to removing these anthropomorphic elements. Planckformulates a vision of a human-independent science in reaction toMach’s claim that science is human-dependent.

Planck thought that physics can go beyond psychological dependencyby basing itself on psychologically independent universalconstants: “the constants appearing in the laws of heatradiation in free ether, like the constants of gravity, have auniversal character and involve no reference to any special substanceor any special body” [1909]. They are human-independent in a waythat a unit like a centimeter is not. These constants can be usedto “establish units of length, time, volume and temperature,which must of necessity retain their meaning for all time and for allcultures, even extra-terrestrial and extra-human ones”[1909].

Mach’s response is one of his last statements of position:

I have no doubt that if, somewhere in the universe a creatureorganized like ourselves could make observations … it wouldperceive a universe working similarly to that we ourselves describe…. As for the reality of atoms: I have no doubt that ifatomic theory corresponds to the reality given by the senses, theconclusions drawn from it will also bear some relation to the facts— though what relation remains unclear. The distance fromthe glass of the first dark ring in reflected light corresponds toone-half of the period of Newton’s ‘fits’, but to onequarter of Young and Fresnel’s ‘wavelength’.The findings of atomic theory, likewise, can undergo a variety ofconvenient reinterpretations, even if we are in no great hurry to takethem for realities. [Mach 1910: 36–37]


Thiele (1963) and Blackmore (1972) contain exhaustive bibliographiesof the German editions of Mach’s books, articles, newspaperwritings, and correspondence. Mach’s archive is located in the Deutches Museum in Munich.

Floyd Ratliff’s Mach Bands, in addition to explicating theimportance of Mach’s work in psychology to modern psychology, alsocontains translations of five critical articles written by Mach in1865–68.

Primary Literature

Books in English Translation

[SG]Space and Geometry in the Light of Physiological, Psychologicaland Physical Inquiry. Trans. by T. J. McCormack, La Salle: Open Court, 1960.
[SM]The Science of Mechanics: A critical and Historical Account ofits Development. Trans. by T. J. McCormack, La Salle: Open Court, 1960.
[PL]Popular Scientific Lectures. Trans. T. J. McCormack, La Salle: OpenCourt, 1986.
[KE]Knowledge and Error—Sketches on the Psychology ofEnquiry. Trans. By T. J. McCormack & P. Fouldes, Dordrecht: D. Reidel,1976.
[AS]The Analysis of Sensations and the Relation of the Physical tothe Psychical. Trans. by C. M. Williams, La Salle: Open Court, 1984.
[PE]Principles of the Theory of Heat—Historically andCritically Elucidated.Trans. T. J. McCormack, Dordrecht: D. Reidel, 1986.

Critical Articles and Essays

[1890]“The Analysis of Sensations—Antimetaphysical.”Monist, 1: 48.
[1891]“Some Questions of Psycho-Physics.”Monist, 1: 394–400.
[1892]“Facts and Mental Symbols.” Monist, 2:198.
[1906]“On Physiological, as Distinguished from GeometricalSpace.” Monist, 11: 321.
[1908]“Über den Relativen Bildungswert der Philologischen und der Mathematisch-Naturwissenschaften Unterrichtsfächer.”Vienna.
[1910]“The Guiding Principles of My Scientific Theory ofKnowledge and Its Reception by My Contemporaries.” In S. Toulmin[1970].
[1910a]“Die Organisierung der Intelligenz.” Neue FreiePresse, July 24, Morgenblatt.
[1913]“Psychic and Organic Life.” Monist, 23:1.
[1913a]“Selbstbiographie.” In Blackmore [1992].

Articles on Mach Bands, in Mach Bands, Ed. FloydRatliff.

[1865]“On the effect of the spatial distribution of the lightstimulus on the retina.” 253–271.
[1866]“On the physiological effect of spatially distributedlight stimuli.” 271–284.
[1866b]“On the physiological effect of spatially distributedlight stimuli.” 285–298.
[1868]“On the physiological effect of spatially distributedlight stimuli.” 299–306.
[1868b]“On the dependence of retinal points on oneanother.” 307–320.
[1906b]“On the influence of spatially and temporally varyinglight stimuli on visual perception.” 321–332.

Lectures in Popular Scientific Lectures, Open Court,1986. These were lectures dating from 1863 to 1898. They were firstpublished collectively in English in 1898.

  • The Forms of Liquids. 1–16.
  • The Fibres of Corti. 17–31.
  • On the Causes of Harmony. 32–47.
  • The Velocity of Light. 48–65.
  • Why Man has Two Eyes. 66–106
  • On Symmetry. 89–106.
  • On the Fundamental Concepts of Electrostatics. 107–136.
  • On the Principle of the Conservation of Energy. 137–185.
  • On the Economical Nature of Physical Inquiry. 186–214.
  • On Transformation and Adaptation in Scientific Thought. 214–235.
  • On the Principle of Comparison on Physics. 236–258.
  • On the Part Played by Accident in Invention and Discovery.259–281.
  • On Sensations of Orientation. 282–309.
  • On Some Phenomena Attending the Flight of Projectiles. 309–337.
  • On Instruction in the Classics and the Mathematico-PhysicalSciences. 238–274.

Secondary Literature

Area Speed Dating Near Stanford Field

  • Arens, Katherine, 1985. “Mach’s Psychology of Investigation,”Journal of the History of Ideas, 21: 151–168.
  • Banks, Erik C., 2007. “Machian Elements andPsychophysical Relations” in S. Mori, etal. (eds.), Proceedings of the 23rd Annual Meeting of theInternational Society for Psychophysics, pp. 39–44, available online.
  • –––, 2005. “Kant, Herbart and Riemann,”Kant-Studien, 96 (2): 208–234.
  • –––, 2004. “The Philosophical Roots of Ernst Mach’sEconomy of Thought,” Synthese, 139 (1): 23–53.
  • –––, 2003. Ernst Mach’s World Elements: A Study inNatural Philosophy (Western Ontario Studies in the Philosophy ofScience: Volume 68), Dordrecht: Klumer.
  • –––, 2002. “Ernst Mach’s ‘New Theory ofMatter’ and his Definition of Mass,” Studies in History andPhilosophy of Modern Physics, 33 (4): 605–635.
  • –––, 2001. “Ernst Mach and the Episode of the MonocularDepth Sensations,” Journal of the History of the BehavioralSciences, 37 (4): 327–348.
  • Blackmore, John T., 1972. Ernst Mach; his work, life, andinfluence, Berkeley: University of California Press.
  • –––, 1978. “Three AutobiographicalManuscripts by Ernst Mach,” Annals of Science, 35:401–418.
  • –––, 1992. Ernst Mach—a deeper look:documents and new perspectives (Boston Studies in the Philosophyof Science: Volume 143). Dordrecht: Kluwer Academic Publishers.
  • Blackmore, John T. & Klaus Hentschel, 1985. Ernst Mach alsAussenseiter: Machs Briefwechsel über Philosophie undRelativitätstheorie mit Persönlichkeiten seiner Zeit: Auszugaus dem letzten Notizbuch (Faksimile) von Ernst Mach. Vienna: W.Braumüller.
  • Blüh, Otto, 1970. “Ernst Mach—His Life as aTeacher and Thinker,” in R. Cohen & R. Seeger (eds.),Ernst Mach—Physicist and Philosopher, Dordrecht:D. Reidel, 274–290.
  • Boltzmann, Ludwig, 1900. “The Recent Development of Methodin Theoretical Physics,” The Monist, 11: 226.
  • –––, 1901. “On the Necessity of AtomicTheories in Physics,” The Monist, 12: 65.
  • Brush, Stephen, 1968. “Mach and Atomism,”Synthese, 18: 192–215.
  • Bunge, Mario, 1966. “Mach’s Critique of NewtonianMechanics,” American Journal of Physics, 34:585–596.
  • Butler, Samuel, Marcus Hartog, Ewald Hering, and Eduard vonHartmann, 1910. Unconscious Memory, London:A. C. Fifield.
  • Capek, Mili, 1968. “Mach’s Biological Theory ofKnowledge,” Synthese, 18: 171–191.
  • Carus, Paul, 1911. “Professor Mach and His Work,”Monist, 21: 19–42.
  • –––, 1916. “Professor Ernst Mach,”Monist, 30: 257.
  • Cohen, R. S., 1970. “Ernst Mach: Physics, Perception and thePhilosophy of Science,” in R. Cohen & R. Seeger (eds),Ernst Mach—Physicist and Philosopher, Dordrecht:D. Reidel, 126–164.
  • Cohen, R.S., and R.J. Seeger, 1970. Ernst Mach, physicistand philosopher, Dordrecht: D. Reidel.
  • D’Elia, Alfonsina, 1971. Ernst Mach, La Nouva ItaliaEditrice.
  • Dipert, Randall, 1973. “Peirce on Mach and AbsoluteSpace,” Transaction of the C. S. Peirce Society, 9:79–94.
  • Edgar, Scott, 2013. “The Limits of Experience andExplanation: F. A. Lange and Ernst Mach on Things inThemselves,” British Journal for the History ofPhilosophy, 21 (1): 100–121.
  • Feyerabend, Paul, 1984. “Mach’s Theory of Research and ItsRelation to Einstein,” Studies in History and Philosophy ofScience, 15: 1–22.
  • Frank, Phillip, 1917. “The Importance of Ernst Mach’sPhilosophy for Our Times,” in R. Cohen & R. Seeger, ErnstMach—Physicist and Philosopher, Dordrecht: D. Reidel, 1970.
  • –––, 1949. “Einstein, Mach, and LogicalPositivism,” in Paul Schilpp (ed.), Albert Einstein:Philosopher-Scientist, Evanston: Tudor Publishing, 71–286.
  • Gampier, P., 1990. “Mach and Freud—A Comparison,”Zeitgeschichte, 17: 291–310.
  • Goe, George, 1981. “On a Criticism by Mach onGalileo,” Scientia, 116: 93–99.
  • Haller, Rudolf, 1982. “New Light on the ViennaCircle,” Monist, 65: 25–37.
  • –––, 1982a. “Poetic Imagination andEconomy: Ernst Mach as Theorist of Science,” in Agassi & Cohen (eds.),Scientific Philosophy Today: Essays in Honor of Mario Bunge,Dordrecht: D. Reidel, 71–84.
  • Haller, Rudolf and Stadler, Friedrich, 1988. Ernst Mach—Werkund Wirkung, Vienna: Hölder-Pichler-Tempsky.
  • Harman, P. M., 1982. Energy, force, and matter: the conceptualdevelopment of nineteenth-century physics (Cambridge History ofScience), Cambridge: Cambridge University Press.
  • Hatfield, Gary C., 1990. The natural and the normative:theories of spatial perception from Kant to Helmholtz, Cambridge,MA: MIT Press.
  • Heidelberger, Michael, 1993. Die innere Seite der Natur:Gustav Theodor Fechners wissenschaftlich-philosophischeWeltauffassung, Philosophische Abhandlungen;V. Klostermann.
  • –––, 2004. Nature from Within: Gustav Fechnerand His Psychophysical Worldview, CynthiaKlohr (trans.), Pittsburgh: University of Pittsburgh Press.
  • Hentschel, Klaus, 1985. “On Feyerabend’s Version of‘Mach’s Theory of Research and Its Relation to Einstein,”Studies in the History & Philosophy of Science, 16:387–394.
  • Hering, Ewald, 1864. “On Memory as a General Function ofOrganized Matter,” in Samuel Butler (ed.), UnconsciousMemory, London: Fifield, 1920.
  • –––, 1902. On memory and the specificenergies of the nervous system, Chicago: Open Court.
  • –––, 1942. Spatial sense and movements ofthe eye, Baltimore: The American Academy of Optometry.
  • –––, 1977. The theory of binocularvision, Bruce Bridgeman & Lawrence Stark (trans.), New York:Plenum Press.
  • Hiebert, Erwin, 1967. “The Genesis of Mach’s Early Views onAtomism,” in R. Cohen & R. Seeger (eds.),Ernst Mach—Physicist and Philosopher, Dordrecht:D. Reidel, 79–106.
  • –––, 1968. “The Influence of Mach’s Thoughton Science,” Philosophia Naruralis, 21: 598–615.
  • –––, 1970. “Mach’s Philosophical Use ofHistory,” in Historical & Philosophical Perspectives onScience, 5: 184–213. Ed. R. Stuewer, University of MinnesotaPress.
  • –––, 1976. “An Appraisal of the Work ofErnst Mach: Scientist-Historian-Philosopher,” in Machamer &Turnbull (eds.), Motion and Time Space and Matter, Columbus:Ohio State, 360–389.
  • Hintikka, Jaakko (ed.), 1968. “A Symposium on ErnstMach,” Synthese, 18: 132–301.
  • Hoefer, Carl, 2014. “Mach’s Principle asAction-at-a-Distance in GR: The Causality Question,”Studies in History and Philosophy of Science (Part B: Studiesin History and Philosophy of Modern Physics), 48 (2): 128–136.
  • Hoffmann, Dieter and Hubert Laitko (eds.), 1991. Ernst Mach:Studien und Dokumente zu Leben und Werk, Berlin: Deutscher Verlagder Wissenschaften.
  • Holton, Gerald, 1988. Thematic Origins of ScientificThought, Cambridge, MA: Harvard.
  • Johnston, William, 1972. The Austrian Mind—An Intellectualand Social History 1848–1938, Berkeley: UniversityCalifornia.
  • Kanizsa, Gaetano, 1979. Organization in vision: essays onGestalt perception, New York: Praeger.
  • Laudan, Larry, 1976. “The Methodological Foundation ofMach’s Anti-Atomism and Their Historical Roots,” in Machamer& Turnbull (eds.), Motion and Time Space and Matter,Dordrecht: D. Reidel, 205–225.
  • Machamer, Peter K. and Robert G. Turnbull, 1976. Motion andtime, space and matter: interrelations in the history of philosophyand science, Columbus: Ohio State University Press.
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