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Against Euclidean transcendental intuition. The mind invents the categories in terms of which it perceives the world. "The same aether vibrations which the eye feels as light, the skin feels as heat. The same aerial vibrations which the skin feels as whirring motions, the ear feels as sound." (p. 346). "Kant, however, went further ... [and] considered spatial determinations as little belonging to the real world, 'to the thing in itself,' as the colors which we see belonging to bodies in themselves, and which we rather brought into them through out eyes." (p. 348). Be here there is a strong disanalogy: spatial intuition, according to Kant, contains definite content, namely the Euclidean axioms. The supposed proof of this is that we can all intuit Euclidean geometry and no other geometries. But this proof fails. By the same reasoning one could "prove" that the English language is innate while Swahili is not. Just as we are born with a general language capacity that quickly specialises in response to given environmental conditions, there is every reason to think that our spatial intuition is initially neutral with respect to Euclidean or non-Euclidean geometry and subsequently formed by empirical data. Thus Kant's claim that the Euclidean axioms are innate is: "1. an unproven hypothesis; 2. an unnecessary hypothesis, since it pretends to explain nothing in our factual world of representation that could not also be explained without its help; and 3. a completely unusable hypothesis for the explanation of our knowledge of the real world, since the theorems established by it may first be applied to the relations of the real world after its objective validity has been experimentally proven and determined" (p. 380). Point 3 may be illustrated by the following example (p. 373). Let ABC be an equilateral triangle. Extend AB and AC above A and mark the points b and c on these lines that have the same distance to A as do B and C. Now: does bc=BC? Euclidean geometry says yes; non-Euclidean no. It is not for the mind to decide the outcome: the mind invents the categories in terms of which it perceives the world, but equality or inequality of impressions must depend on equality or inequality in the underlying physical reality, whatever it may be.

"On Academic Freedom in German Universities." "Such was the origin of Universities": "a free confederation of independent men, in which teachers as well as taught were brought together by no other interest than that of love of science; some by the desire of discovering the treasure of mental culture which antiquity had bequeathed, others endeavouring to kindle in a new generation the ideal enthusiasm which had animated their lives" (p. 330). Today "the German student alone has this perfect joy." "He can devote himself to the task of striving after the best and noblest which the human race has hitherto been able to attain in knowledge and in speculation, closely joined in friendly rivalry with a large body of associates of similar aspirations, and in daily mental intercourse with teachers from whom he learns something of the workings of the thought of independent minds." (p. 334). "You, my younger friends, have received in this freedom of the German students a costly and valuable inheritance of preceding generations. ... But freedom necessarily implies responsibility. It is as injurious a present for the weak, as it is valuable for strong characters. Do not wonder if parent and statesmen sometimes urge that a more rigid system of supervision and control, like that of the English, shall be introduced even among us. There is no doubt that, by such a system, many a one would have been saved who is ruined by freedom. But the State and the Nation is best served by those who can bear freedom, and have shown that they know how to work and struggle, from their own force and insight and from their own interest in science." (pp. 334-335). "Another point in which German Universities are distinguished from the English and French ones ... is that we start with the object of having instruction given, if possible, only by teachers who have proved their own power of advancing science. ... The English and French ... lay more weight ... on what is called the 'talent for teaching'---that is, the power of explaining the subjects of instruction in a well-arranged and clear manner, and, if possible, with eloquence, and so as to entertain and fix the attention. ... I am by no means prepared to defend what is, frequently, our too great contempt for form in speech and in writing. It cannot ... be doubted that many original men, who have done considerable scientific work, have often an uncouth, heavy, and hesitating delivery. Yet I have not infrequently seen that such teachers had crowded lecture-rooms, while empty-headed orators excited astonishment in the first lecture, fatigue in the second, and were deserted in the third. Anyone who desires to give his hearers a perfect conviction of the truth of his principles must, first of all, know from his own experience how conviction is acquired and how not. ... A teacher who retails convictions which are foreign to him, is sufficient for those pupils who depend upon authority as the source of their knowledge, but not for such as require bases for their convictions ... [Thus] The free conviction of the student can only be acquired when freedom of expression is guaranteed to the teacher's own conviction---the liberty of teaching." (pp. 335-336).

"The Relation of Optics to Painting." Small particles in the air scatter light. "The colour of the light reflected by the opaque particles mainly depends on their magnitude. When a block of wood floats on water, and by a succession of falling drops we produce small wave-rings near it, these are repelled by the floating wood as if it were a solid wall. But in the long waves of the sea, a block of wood would be rocked about without the waves being thereby materially disturbed in their progress." Since blue light has the shortest wavelength it is most easily scattered. That is why the sky is blue: while the red and yellow rays pierced through the atmosphere, the blue ones were deflected down to us. "Conversely, the denser turbidity consists mainly of coarser particles, and is therefore whitish. As a rule, this is the case in the lower layers of air, and in states of weather in which the aqueous vapour in the air is near its point of condensation. On the other hand, the light which reaches the eye of the observer after having passed through a long layer of air, has been robbed of part of its violet and blue by scattered reflections; it therefore appears yellowish to reddish-yellow or red, the former when the turbidity is fine, the latter when it is coarse. This the sun and the moon at their rising and setting, and also distant brightly illuminated mountain-tops, especially snow-mountains, appear coloured." "The high transparent landscapes of mountain regions, which so often lead the Alpine climber to under-estimate the distance and the magnitude of the mountain-tops before him, are also difficult to turn to account in a picturesque manner. Views from the valleys ... are far better; not only do they allow the various distances and magnitudes of what is seen to stand out, but they are on the other hand favourable to the artistic unity of colouration." (pp. 286-287)

Hermann von Helmholtz was quite simply one of the most important German scientists of the 19th century. However, what becomes so clear when one peruses the collection edited by David Cahan is that Helmholtz has much of interest to say to philosophers, artists, musicians, and historians. This collection includes his most important public addresses on a wide range of topics and provides a clear portrait of the breadth of Helmholtz's contributions to science and intellectual life. This provides in English what is lacking in the original German editions - a readily available, inexpensive edition of Helmholtz's highly influential work.