The Experiment as Mediator

“It does not follow that the hunter [investigator of nature]
who has killed the game must also be the cook
[mathematician] who prepares it. By chance, a cook may
go along the hunt [for knowledge], and be a good shot;
but he would be very wide off the mark if he were to
maintain that to be a good shot, one must also be a good cook”

This following chapter will try to present and interpret some of Goethe’s remarks on the theory of science. As his utterances on epistemological questions are sporadic, I will try to concentrate on one of his essays, The Objective and Subjective Reconciled by Means of the Experiment.*This is one of the most famous of his essays on scientific theory in general, and has been used and interpreted by many. Instead of following these interpretations, in the first part at least, I attempt to give a general outline, and only discuss certain details later.

The essay itself is closely connected to the two Conributions to Optics I-II. In fact it is an exposition of the theoretical background that could not have been expressed in the two Beiträge.** In the beginning Goethe stresses the important difference between simply living in the world, where an individual looks at everything “with reference to himself”, and when the individual wishes to “observe the things of Nature in themselves and in their interrelations” with “a vigorous urge toward knowledge”. The latter is the scientific way of looking at Nature, and the whole of Der Versuch is about the difficulties of this way of looking at the world.

The main task of a real scientist is quiet, unbiased investigation. A botanist should not be influenced by “either the beauty or the utility of plants” he should “study their formation, their relationship to the rest of the plant world”. Thus the aesthetic appreciation (if by this we mean the preference of the aesthetically pleasing to the less so), which is by many considered to be a give-away sign of Goethe’s dilettante science, is ruled out as unwanted, indeed dangerous, at the very beginning.¹

The unbiased observation of nature leads to “clear concept of … parts and … relationships” of phenomena. But when drawing the conclusions based on observations the observer has to be very cautious. He must be “distrustful of himself even in his most zealous efforts”, and even if it is a “hypothetical impossibility”, we must do our best to be as careful as we can be.

“No one will deny that experience has and should have the greatest influence in natural science”, and, although the mind is very ingenious as to how these experiences are “comprehended, collected, arranged, and developed” we have to be very distrustful with these results.

It is very useful to study the works of “outstanding men”, and realize their strengths and weaknesses. By seeing where they went wrong we can hopefully prevent ourselves from going astray following their paths.*** But it is just as useful to have others to keep us on the right track. So to “produce outstanding results” it is crucial that the “interest of several people” be “focused upon one subject”. The importance of open research communities also means that “the greatest obstacle to the scientist may be the envy prompting him to exclude others from the honour of a discovery, or an immoderate desire to treat and work out a discovery exclusively in his own way.”

This latter notion is commonplace for us, but it was not so obvious for an 18^th century scientist. And as “each science in itself is such a massive thing that it will occupy many individuals, and cannot be mastered by one individual alone” it is more than useful, indeed “impossible to exaggerate the necessity for sharing of ideas, for co-operation, criticism, and opposition”, because:

Thus in science we have to do “the reverse of what the artist finds advisable”. While the artist “does right not to allow his work of art to be viewed until it is finished”, “in things scientific it is beneficial to share each individual experience with others”. Also, unlike the writer who is boring if “he leaves nothing to the imagination; the scientist must work indefatigably”, to clear away all possible sorts of misunderstanding.

After these general remarks Goethe talks about experiments in detail. He defines it in the following way:

But however useful one experiment is, it can only have value in combination and in connection with others. But connecting and combining two experiments “demands more strictness and discernment than even astute observers ordinarily require of themselves”. It is exactly here that we can make the most serious mistakes. The human intellect has a tendency to jump to conclusions too easily and establish connections between phenomena that are not inherently connected. There is a “mountain” of “inner enemies”: “imagination, impatience, rashness, self-complacency, rigidity, conventionality, prejudice, sloth, frivolity, fickleness, and all the rest, all lurk in ambush here to surprise and overpower”.

To warn against this danger Goethe sets up paradoxes, which he later explains in detail:

As every experience represents an isolated part of our knowledge, it makes only sense in a context. But as the context depends on our experiences and how we interpret them it is very important to decrease the theory-ladenness of this ‘context’. But how is this possible, when Goethe himself notes that “I myself have often noticed my own tendency to commit this error.”

Even if we cannot dispose of this problem Goethe finds it important to investigate the conditions when we are more prone to commit this mistake. It usually happens when “we take more delight in our concept of a thing than in the thing itself, or more correctly, we have joy in a thing only insofar as we form an idea about it”. This explains our inclination to “hypotheses, terminologies, and systems”, which cannot be condemned as it “arises logically from the organization of our nature”.

How are we to avoid the tension between the singularity and individuality of experiences on the one hand and the powerful striving of our intellect towards unifying and integrating exterior things? It seems that theories trying to bridge this gap “find greater approval than they merit and are maintained longer than is warranted”. These “retard and weaken the advance of the human intellect, though admittedly fostering it in some respects”, as we do not get closer to the understanding of nature, only to our thought-structures. The sparser the data available the “greater the ingenuity” of the intellect, the more detached the theory can be from reality. To complicate things even more, and:

These structures tend to survive for centuries, as the students are more than willing “to admiringly assimilate as much as possible of their master's mode of thought”, until someone ventures to “attack the sacrosanct”, and to reinterpret the data by taking the theory less seriously.

So much for Goethe’s criticism of authority and rigidity of science. But if he warns us about rashly connecting facts and building a theory, he must also explain how this fallacy is to be avoided. His solution is not as radical as many believe. Recognizing the intellect’s inevitable tendency to form hypothesis it is evident that this predisposition cannot be changed. All one can do is to reduce it’s effect on how the facts are interpreted. What Goethe proposes is to build up a ‘super-experiment’, to establish a series of experiments which “directly adjoin and touch each other”. Goethe sees all these experiments as the manifold aspects of the same experiment. In a letter to Schiller in January 1798 he calls this the pure phenomenon, and in his Farbenlehre the Urphenomenon. His attempt with the two Contributions to Optics is this, to help his reader to re-experience this ‘higher experiment’.

For Goethe the highest duty of a scientist is to strive towards “experiments of this higher type”, as this is the point when, within our human limits, we can best understand nature. The method of building up the ‘higher experiment’ is that of a mathematician’s, it proceeds step by step, by “deriving one fact from the preceding one”. Natural sciences in Goethe’s view can reach the exactness and purity of mathematics. Just as mathematical proofs are “always expositions and recaþitulations, never mere arguments, sciences should not be argumentative, as the task here is not that of clever debaters using their wit and imagination in connecting isolated instances, but the ‘unveiling’ of nature’s inherent structure. Arguments, that is “the direct application of an experiment to prove a given theory” is dangerous, because they stress our preconceptions, not the order of nature.

Instead of a detailed discussion following the summary of the essay only a few important notions are discussed concerning Goethe’s views on the theory of science around the time of the Contributions to Optics.

The Experiment as Mediator... starts very Baconian by stressing that man tends to see everything in relation to himself. In general the essay is not too far from our concepts of how scientific investigation should be carried out, but there are few obvious differences. For Goethe the experiment is suggested to the scientist by prior observation, not by any prior hypothesis, as modern theory of science would say. Also the experiment itself means something different for us and for Goethe. In modern science the experiment is used to test or extend a theory or a theoretical proposition. The phenomena are merely given, the theory is what makes sense of them, gives them order. For Goethe phenomena have intrinsic importance, and they bear certain affinities and relationships to other phenomena.²

The most significant detachment from our trains of thought is Goethe’s description of the ‘experiment of a higher kind’. It presupposes continuity within the phenomenal world, as if, with infinitesimally small changes, one could depart from one experiment and arrive at the other. In this way the experiments are connected to each other, cannot and should not be interpreted on their own, as it can easily cause misinterpretations. A single phenomenon, a single experiment can prove nothing; it is a member of a great chain, and is significant only within this context.³ For these reasons Goethe takes sides with us and is against the mainstream of the science of his age in the question of the validity of the experimentum crucis. For him one or a few experiments lead neither to picking the true hypothesis, nor to falsify the false ones.

His solution is 'das reine Phenomenon’, a super-experiment amalgamating a series of experiments that should be the final stage in science. This ‘pure phenomenon’ is reached by varying different conditions under which a certain phenomenon appears.⁴ We grasp a single dynamic phenomenon in the multiplicity. This sequence of experiments (in Contributions to Optics): "constitutes as it were just one experiment, presents just one experience from the most manifold perspectives. Such experience, which consists of several others, is obviously a higher kind. It represents the formula under which countless single examples [Rechnungsexempel] are expressed."⁵

Goethe is empirical but not an empiricist. He doesn't claim that connections between phenomena can be derived from pure experience. Immediate experience is only half reality, and that is why we have to be very careful when connecting phenomena, as we can easily impose our habits of thought on nature. An experiment is only a 'mediator', an aid to knowledge; but in itself an experiment doesn't prove anything. The whole notion of causality is discredited “For we are not looking for causes here, but for conditions under which phenomena appear”,⁶ as causal explanation is only a useful tool for explaining occurrences, but not necessarily the most telling.

For modern scientists theories are always hypothetical. It is impossible, and often even useless to try to prove any theory ‘beyond doubt’. Goethe realises this source of mistake, and this is one of the reasons why he condemns Newton’s theory of white light and colours, which pretends to be more than a theory, but claims a truth-value equivalent to the observations from which they spring forth. But instead of sticking to our ‘decentralised’ way of looking at science as a solution, he comes up with certain claims for certainty.

Although Goethe remained suspicious of any proof by means of experiments to the end of his days, this doesn't mean that we can't be certain about anything. According to Sepper "this essay and the Farbenlehre as a whole are predicated on the notion that we can achieve an extraordinarily high degree of certainty - about the experiments, not about propositions."

This is unusual for us, as we most often prefer the theory to the phenomena, our hypotheses make sense of our experiments, and thus the theory derived from experiences gains unconsciously ontological priority. There is a big difference between the two views one being based on experience, the other on a particular way of conceiving this experience.

Goethe’s main concern is that once we find a reasonably plausible explanation, we stick to it, and start to cherish it too much. "But one must not in principle be content with hypotheses, believing with them one has acquired all possible knowledge of the area, let alone confuse these hypotheses with properly objective knowledge, as is manifestly the case in classical mechanical physics according to its ontological claims, and as Goethe finds, for example, in Newton's theory of colour."⁷

It is true that the human spirit can't bear to leave the isolated phenomena, and it tries to comprehend by grouping them in whatever way it can⁸ and that "theories are usually the premature conclusions of an impatient understanding which would prefer to get the phenomena out of the way" as Goethe said, but we must try not to jump to conclusions (or, shall we say jump to theories). The aim is to find every factor which contributes to the appearance of the phenomena. Once reaching this elemental level a resynthesis can take place. "The proximate goal of Goethe's method is to achieve what he called a naturgemässe Darstellung, a presentation in accordance with nature ... Goethe’s physical science of color is thus morphological in much the same way that his other sciences are..."⁹

Theory is different for Goethe and Newton. "Theory for Goethe is not a set of propositions or a mathematical modeling; rather it is more akin to something suggested in the root meaning of ancient Greek theoria, which was the activity of the spectator, a seeing and recognizing, a sense also conveyed by the German Anschauung ("onlooking," a perhaps simpler and more faithful rendering than the usual "intuition").¹⁰

For Goethe, the basis of much of our modern science, a "decisive apercu is to be regarded as an inoculated disease: One does not get rid of it till one has fought the disease through".¹¹ As an apercu can be true, false or both, and who is to tell, if we ourselves believe in its truth so strongly?

"Let man seek nothing behind the phenomena, for they themselves are the theory"¹² can be the summary of Goethe’s comments on theory. For him an unbound theory is inferior to a theory that acknowledges it’s bounds. Mathematization in itself is no problem, but any theory where mathematics appears more exacting than it really is is inferior than one not pretending to do this.¹³

The best way to escape these traps is to gain good empirical basis and only then should the search for causes start, otherwise we can make serious mistakes. "Things which have nothing in common cannot be understood, the one by means of the other..."¹⁴ as Spinoza said, but by rash judgement and not rigorous criticism of our own hypotheses this is exactly what we will end up doing.

”I have heard myself criticised as if I were an
opponent, an enemy, of mathematician general,
which in fact noone can value more highly than I”

Goethe for most is considered the typically unmathematical thinker. Like Buffon he is against quantification of phenomena. And it is true that Goethe’s mathematical education was not even near to that of Leibniz, Spinoza or Newton. But it is untrue that he despised mathematics as such. He admired Euclid and his way of demonstrating, while Newton threw Euclid away as “trifling”, and read Descartes instead.¹⁶ Goethe also praises the pure mathematics of Plato and Pythagoras but opposes certain ways of using it in Physics.¹⁷ He does not condemn Galileo for using mathematics, indeed holds that mathematical symbolization has the potential to become nearly identical in the highest sense with the phenomena that it represents, as a sort of Urphänomen, but still holds that mathematical descriptions are dangerous as:

Contrary to these negative utterances, which are more aimed at extreme symbolization, and the loss of phenomena than at mathematics in particular (see Chapter 9) many consider Goethe‘s own method resembling mathematics.

Heisenberg claims that there are resemblances between modern theories of symmetry and Goethe's elaboration of the morphology of colour phenomena. In a posthumous manuscript he writes "Goethe derives straight-line boundaries from a curved boundary by performing what amounts to a continuous deformation of space".²⁰

Sepper believes that one of the intriguing aspect of Goethe's exposition of the phenomena is that it incorporates a fundamental concept of modern mathematics and mathematical physics, the limit of a series, potentially if not actually infinite.²¹ But while this limit is usually an abstract aid in mathematics, for Goethe it becomes phenomenal.

It is true that Goethe himself writes in Die Farbenlehre, that he has learnt his method from the mathematicians. What Goethe values and means here is the logical structure of mathematics. By this method he means the same as Spinoza by ‘moro geometrico’ and Leibniz’s ‘mathesis universalis’.²²

His method is to construct a theory, where one link leads to another in a ‘clearly discernible chain of inferences’.²³ ‘His aim is to arrive at a comparatively small number of simple, well-defined elements, corresponding to the axioms of geometry, that is, expressions which are not further reducible to others, but express basic concepts in the system from which the other elements are derived’.²⁴

Goethe realizes "that it [mathematics] is particularly useful, especially when it is employed in the solution of technical problems".²⁵ However he considers systematizations of the purely mathematical-physical aspects of the phenomena partial, and sets specific demands for scientific method, a task in which Newton fails.

"What is exact in mathematics except exactness itself? And this again, is it not a consequence of the feeling of truth?"²⁶ This truth can be grasped by other means as well,**** not only mathematics, which is only one manifestation of it. As he writes it in one of his maxims: "Mathematics is ...an organ of the higher inner sense". What is important is how this ‘truth’ of the ‘higher sense’ can be acquired, and this is where a scientist must learn from a mathematician. And as our mathematical ability is strictly speaking not 'innate', is developed by systematic use, similarly it is possible to develop a similar capacity in other, qualitative areas. And although one may doubt this, but it seems hardly rejectable in principle.²⁷

The whole essay on Der Versuch als Vermittler can be taken as an explanation why we prefer conceptions of phenomena to phenomena themselves. It is one of Goethe’s early writings on theory. By late 1794 he will claim that there might be many legitimate ways of conceiving things. And from 1798 the historical part of the Farbenlehre slowly emerges.

Goethe’s vision of the world of living organisms, a unity where everything is in reciprocal relations determined his way of thinking about plants and animals. Now he transforms the notion of gradual series from natural history to physical science.²⁸ The archetypal phenomenon developed from the Typus. With both concepts his aim was to portray the phenomena with the least possible intrusion of the intellect into nature’s inherent rules.

What is unusual about Goethe’s starting point is that it does not seek the relationship between idea and sense-world outside of man, as "for it there is no sense world (nature) without idea outside of man." Only man is able to perceive what is one separated, and picture nature devoid of ideas. "Therefore one can say: for the Goethean world view the question, "How do idea and sense-perceptible things come together?", which has occupied the evolution of Western thought for centuries, is an entirely superfluous question."²⁹

For this reason he seeks no final solution in mathematics or causality, both of which are very much anthropocentric. This separates him from the rationalistic tradition, which, merging with empiricism has been the mainstream of modern science. In a letter to Schiller 19, Jan. 1798 he writes:

He recognizes quantification, mathematization as they help in our systematization of nature. In spite of this he claims that his ‘gentle empiricism’, that tries to control the work of the intellect is a better way of understanding nature. He does not claim that one is good, the other bad. Rationalism is only fallacious if it does not accept its own limitations (which was, for the most part, true for Newton’s theory of white light and colours). His method, therefore, can only be better, not good. And even if it is better in getting to know nature, it is not necessarily a better way of doing science.

* Written in 1792-1793; published in Natural Science in General; Morþhology in Particular, Vol. II, No. 1 (1823). The original title is Der Versuch als Vermittler von Objekt und Subjekt .
** Goethe found it unnecessary to ‘theorize’ in these two Contributions. He was probably still under some Baconian influence, and he preferred to present his theories separate from the experiments.
*** It is not hard to see that this, as so many parts of the essay, is directed against Newton. Whether Goethe’s criticism stands or falls is to be discussed in the other chapters.
****For Goethe this is called 'Schauen', and is nothing other than what we call in mathematics ‘capacity to grasp'. Walter Heitler characterizes this 'Schauen' or the 'Anschauende Urteilskraft' [perceptive power of thinking] as lying 'somewhere between observation and intuition'.

1.   See for example Stephenson (1995) p.67 “The projection, by the imagination, of a sensuous-conceptual image on to nature to yield the aesthetic insight which he calls the Urphänomen is but the most comprehensive of such symbolic acts.” Stress on the ‘aesthetic insight’!
2.   Sepper (1988) p.64
3.   MuR 156
4.   See more in ‘Erfahrung und Wissenschaft’
5.   Sepper (1988) p.70
6.   LA, I, 3, p.308
7.   Hegge (1987) p.213
8.   Sepper (1988) p.68
9.   Sepper (1988) p.70
10. Sepper (1988) p.17
11. HA, 14: 263
12. MuR 916
13. Sepper (1988) p.179
14. Spinoza quoted in Hegge (1987) p. 197
15. In Über Mathematik und deren Missbrauch
16. as Freelance (1938) shows it.pp. 9-10 citing Brewster (1663). Later: Newton changes his attitude probably under Barrow’s tuition ad influence in 1664
17. MuR 573
18. Nisbet (1972) p.49
19. LA, I, 9, p.367
20. quoted in Sepper (1988) p.74
21. Sepper (1988) p.74
22. Hegge (1987) p. 201 (A misprint here: ‘more geometrico’)
23. ibid.
24. Hegge (1987) p.202
25. from Materialen zur Geschichte der Farbenlehre, translated in Hegge (1987) p. 216, fn.
26. From his Maximen und Reflexionen
27. see more about the topic in Hegge (1987)
28. Nisbet (1972) p.39
29. Steiner (1985) p. 17