Werner Heisenberg, who won the Nobel Prize for physics for his work on quantum mechanics, has written a very sympathetic essay "Goethe's Image of Nature" (Das Naturbild Goethes). What struck him as most important and revealing in the preface to the Farbenlehre is a phrase in the first paragraph of my long quotation: "the abstraction we are afraid of." Heisenberg comments that these words make clear "where Goethe's path must diverge from that of modern natural science (der gelttenden Naturwissenschaft)."

We can make the point of divergence even more precise. The triumphs of modern physics, form Newton to our time depend on the ingenious use of mathematics, and Goethe tended to disparage mathematics. What he always wanted, in science as in poetry, was Anschauung. There is no exact English equivalent of this German word, which Kant used in an entirely different sense. The verb anschauen means to see or contemplate. Goethe's immense lucidity is inseparable from his habit of seeing things instead of relying from his habit of seeing things instead of relying on pure concepts alone. Kant was not a visual person, while Goethe like to draw and also did delightful watercolors. Although his verbal facility and the power of his language were unsurpassed, he unquestionably agreed with Mephistopheles' sarcastic disparagement of words.

For just where no ideas are
The proper word is never far.

Goethe always could find words for what he saw and felt. He mistrusted works that were not backed up by any experience. And he had no need of mathematical certainty. While those who feel most insecure often crave that, Goethe was strong enough to spurn it. In a conversation with F. von Muller, June 18, 1826, he said:

Mathematics has the altogether false reputation of furnishing infallible inferences (Schlusse). Its whole certainty is nothing more than identity. Two times two is not four, but it is simply two times two, and this we call, abbreviating it, four. Four is by no means something new. And that is how it always is with its deductions in the higher formulas we lose sight of the identity.

Goethe failed to recognize the immense usefulness of mathematics for the natural sciences and especially physics and astronomy. This was a serious shortcoming on his part, and in a book on the development of modern physics he might not merit a great deal of attention. but our concern is with the discovery of the mind, and here the hankering for certainty and the model of mathematics have been extremely harmful, while Goethe's approach has proved to be very fruitful. What was needed was attention to the actions and expressions of the mind and the study of their development.,. And for those whose interest in such a development was not purely theoretical but motivated in some measure by a quest for autonomy, Goethe provided a rich model of that, too.

Newton mathematicized large areas of science. Under his influence mathematical precision and absolute certainty because more that ever part of the very meaning of science. While this view is still dominant among both scientists and laymen, may people, including some scientists, are deeply disturbed by this development, because in one way or another it is so often accompanied by a downgrading of what cannot be measured and quantified. As Goethe's Mephistopheles says in the second scene of the Second Part of Faust, speaking to the Chancellor:

What you can't calculate, you think, cannot be true;
What you can't weigh,, that has no weight for you.

A large part of reality - the part which most engages our feelings and emotions and which one might actually consider the most valuable - is discounted as either inconsequential or even as in some sense unreal.

Championing what cannot be measured or weighed can be but need not be - and in Goethe's case was not - obscurantist. Some people feel threatened by reason and understanding and seek safely in a plea of incomprehensibility. Goethe was not an apostle of feeling in this sense, and he had no wish to downgrade reason or science. On the contrary he has his Mephistopheles say in the short monologue that concludes the scene in which he makes his pact with Faust - and Hegel like to quote this:

Have but contempt for reason and for science,
Man's noblest force spurn with defiance,
Subscribe to magic and illusion,
The Lord of Lies aids your confusion,
And, part or no, I hold you tight.

Far from opposing reason and science, Goethe opposed the notion that all science must be mathematical. For him poetry was not the frosting on an essentially dry and prosaic cake, a make-believe embellishment that covers up the way things truly are. Although some poetry, like some of Faust's effusions, may involve self-deception, Goethe was unwilling to discount either emotion or reason, and he felt that understanding cannot dispense with feeling. I know of no better way to put this point than to say that he pointed the way toward a poetic science. In profoundly different ways, Hegel, Nietzsche, and Freud tried to develop a poetic, nonmathematical science.