Artistic Experience I

"Music is a science which should have definite rules; these rules should be drawn from an evident principle; and this principle cannot really be known to us without the aid of mathematics. Notwithstanding all the experience I may have acquired in music from being associated with it for so long, I must confess that only with the aid of mathematics did my ideas become clear and did light replace a certain obscurity of which I was unaware before." (Jean-Philippe Rameau, "Treatise on Harmony reduced to its natural principles", 1722)

"Music is like geometric figures and numbers, which are the universal forms of all possible objects of experience." (Friedrich Nietzsche, "Birth of Tragedy", 1872)

"A scientist worthy of the name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature. [...] we work not only to obtain the positive results which, according to the profane, constitute our one and only affection, as to experience this esthetic emotion and to convey it to others who are capable of experiencing it." (Henri Poincaré, "Notice sur Halphen", Journal de l'École Polytechnique, 1890)

"Art is a human activity consisting in this, that one consciously, by means of certain external symbols, conveys to others the feelings one has experienced, whereby people so infected by these feelings, also experience them." (Leo Tolstoy, "What is Art?", 1897)

"True artistic experience is never passive, for the spectator is obliged to participate, as it were, in the continuous or discontinuous variations of proportions, positions, lines and planes. Moreover, he must see clearly how this play of repeated or non-repeated changes may give rise to a new harmony of relations which will constitute the unity of the work. Every part becomes organized into a whole with the other parts. All the parts contribute to the unity of the composition, none of them assuming a dominant place in the whole." (Theo van Doesburg, 'Grundbegriffe der neuen Gestaltenden Kunst', 1921-23)

"Just as music comes alive in the performance of it, the same is true of mathematics. The symbols on the page have no more to do with mathematics than the notes on a page of music. They simply represent the experience." (Keith Devlin, "Mathematics: The Science of Patterns", 1994)

"Music is the pleasure the human soul experiences from counting without being aware it is counting." (Gottfried W Leibniz)