For Einstein, insight did not come from logic or mathematics. It came, as it does for artists, from intuition and inspiration. As he told one friend, “When I examine myself and my methods of thought, I come close to the conclusion that the gift of imagination has meant more to me than any talent for absorbing absolute knowledge.” Elaborating, he added, “All great achievements of science must start from intuitive knowledge. I believe in intuition and inspiration…. At times I feel certain I am right while not knowing the reason.” Thus, his famous statement that, for creative work in science, “Imagination is more important than knowledge”.
But how, then, did art differ from science for Einstein? Surprisingly, it wasn’t the content of an idea, or its subject, that determined whether something was art or science, but how the idea was expressed. “If what is seen and experienced is portrayed in the language of logic, then it is science. If it is communicated through forms whose constructions are not accessible to the conscious mind but are recognized intuitively, then it is art”. Einstein himself worked intuitively and expressed himself logically. That’s why he said that great scientists were also artists.
Einstein first described his intuitive thought processes at a physics conference in Kyoto in 1922, when he indicated that he used images to solve his problems and found words later. Einstein explicated this bold idea at length to one scholar of creativity in 1959, telling Max Wertheimer that he never thought in logical symbols or mathematical equations, but in images, feelings, and even musical architectures. Einstein’s autobiographical notes reflect the same thought: “I have no doubt that our thinking goes on for the most part without the use of symbols, and, furthermore, largely unconsciously”. Elsewhere he wrote even more baldly that “no scientist thinks in equations”.
Anyone in science education reading this?!
Einstein only employed words or other symbols (presumably mathematical) — in what he explicitly called a secondary translation step — after he was able to solve his problems through the formal manipulation of internally imagined images, feelings, and architectures. “I very rarely think in words at all. A thought comes, and I may try to express it in words afterwards,” he wrote.
Einstein expanded on this theme in a letter to fellow mathematician Jacques Hadamard, writing that “the words of the language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be ‘voluntarily’ reproduced and combined…. The above mentioned elements are, in my case of visual and some of a muscular type…. Conventional words or other signs [presumably mathematical ones] have to be sought for laboriously only in a secondary stage, when the associative play already referred to is sufficiently established and can be reproduced at will”.
In other interviews, he attributed his scientific insight and intuition mainly to music. “If I were not a physicist,” he once said, “I would probably be a musician. I often think in music. I live my daydreams in music. I see my life in terms of music…. I get most joy in life out of music”. His son, Hans, amplified what Einstein meant by recounting that “whenever he felt that he had come to the end of the road or into a difficult situation in his work, he would take refuge in music, and that would usually resolve all his difficulties”. After playing piano, his sister Maja said, he would get up saying, “There, now I’ve got it”. Something in the music would guide his thoughts in new and creative directions.
No historian of science seems to have taken these musical and intuitional comments of Einstein seriously, but we think there is something very important to be gleaned from his personal testimony. What did Einstein mean when he told Wertheimer that he often thought in terms of musical architectures? We can’t know for certain at this far remove, and Wertheimer never asked, but the engineer-composer Robert Mueller investigated further.
According to Mueller, Einstein’s friend Alexander Mozskowski says “that Einstein recognized an unexplainable connection between music and his science, and notes that his [Einstein’s] mentor Ernst Mach had indicated that music and the aural experience were the organ to describe space”. Music also embodies time. Could music have therefore provided Einstein with a connection between time and space through its combination of architectonic, or structural, nature combined with its spatial and temporal aspects? Mueller has conjectured that the physicist’s “disposition to architectonic logics of abstraction was formulated by Einstein’s early musical experiences, and even enlarged by a constant struggle for musical experiences which helped him build a rich mental perceptual fabric of space and time in which to perform his scientific theorizing”.
These speculations about music, space and time in Einstein’s imaginative thinking certainly fit with something the physicist told the great pioneer of musical education, Shinichi Suzuki: “The theory of relativity occurred to me by intuition, and music is the driving force behind this intuition. My parents had me study the violin from the time I was six. My new discovery is the result of musical perception”. They also fit with the manner in which Einstein expressed his greatest praise for a fellow scientist. Neils Bohr’s work on the structure of the atom, Einstein said, was “the highest form of musicality in the realm of thought”.
Wow! Anyone looking for connections between music, mathematics, and physics? How about intuition and reason? Einstein shows us how it all connects. But what do our students typically get, especially in high school and college? They get math without music. They get science without images, feelings and intuition. They get knowledge without imagination. Not only does intuition go undeveloped, many math and science teachers do not give credit to answers (even though they may be correct) that are not explicated by detailed logic. What these teachers appear not to understand is that translating intuitive insights into words or mathematical symbols is a secondary process that can - and should be — be taught just as explicitly as translating from one language and another.
So much for Einstein’s admission that he often had a feeling he was right without being able to explain it. So much for experiencing space-time through music. So much for working out ideas in images and feelings and musical architectures for which there are no words or symbols. So much for sitting down at the piano and letting the music show the way.
No wonder so many of our students don’t like math and science: what is there to imagine and feel? Where is the art in their learning?