Let me introduce you to a wonderful gentleman, Manfred Clynes. I met him in Sydney during the late 1970s and have a signed copy of his book before me as I type. But I get ahead of myself. Let me tell you a little about him first.
He grew up in Vienna, Austria, during the late 1920s and early 1930s. In 1938, his family emigrated to Australia to escape the Nazis (they were Jewish). Within a couple of years, now aged 15 and having just learned calculus, Manfred invented an inertial guidance system for aircraft that used piezoelectric crystals. Authorities dismissed his invention, but an almost identical system was used in aircraft during the latter half of WWII.
He subsequently trained in engineering and music, becoming a very accomplished concert pianist. He also pursued studies in the psychology of music and it was at about this time that he became a friend of Albert Einstein (they were both at Princeton University).
Shortly after this, he performed research in the fields of neurophysiology and neuroscience, inventing the CAT computer for electrical brain research (not to be confused with the CAT scan ... a different thing altogether). In collaboration with Nathan Kline, he explored how technology and the human body could work together. It was Manfred Clynes and Nathan Kline who invented/coined the term CYBORG in 1960! You have him to thank for that. So, if you ever watched Six Million Dollar Man, or have seen the Terminator movies, or something similar, you will be familiar with the concept of cyborg (although these movies do not quite depict what Manfed had in mind).
I hope you can see that you really need to read the Wikipedia article about him!
Now to the mathematics ... because I haven't yet told you what I think is his most amazing discovery!
When I met him in the late 1970s, he had just begun what was to be a very fulfilling ten years of research and music making at the NSW Conservatorium of Music in Sydney, Australia. He had been carrying out some fascinating research that I want to share with you here (in summary form). I apologise to Dr Clynes if I have incorrectly described some of the process. This is my simplification of it.
He, and others, had noticed that, when people conducted a musical work by Beethoven, for example, there was a similarity in their hand movements. Also, the movements seemed to change pattern when pieces were played by a different conductor. There was a different pattern for Mozart, another one for Mendelssohn, and so on. He asked the questions, "Is there something of the composer in the music itself?" and "Can this 'something' be identified?"
Being an engineer, he constructed a small button that recorded vertical and horizontal pressures and asked people to press the button in time with music so that he could record their reactions, just like tapping one's finger on a table. He found that the vertical and horizontal pressure curves were consistent for a given composer whether or not the subject had music training. The equipment meant that he was now able to MEASURE reponses.
Because of his background in psychology, he hypothesised that it was something of the EMOTIONAL makeup of the composers that was conveyed through their music. So, he asked people to think of a time in their life when they experienced a particular raw emotion ... love, joy, anger, hatred, awe, etc. ... all the time while pressing on the sensor button. He found that the pressure curves/patterns for each emotion were quite distinct and were universally shared across gender, nationality and cultures. This suggested that we ALL experience such emotions in the same way.
Excited by this, he then wondered if he had stumbled upon some way of identifying or measuring emotion in humans. He decided to turn the process around and apply it in reverse! He asked volunteers to sit and have their finger attached to the sensor button. This time, he only asked them to report what they were feeling when he made the button vibrate/oscillate according to the pattern for specific emotions. He found that vibrating part of a person's body in this way CAUSED THEN TO FEEL THAT EMOTION. He would play the pressure patterns for anger/rage, for example, and subjects would report feeling unaccountably enraged (without being aware of what signals were being given to them)!
Don't you find this to be exciting research?
He called these patterns "Sentics." His book is called Sentics: The Touch of Emotions ~ A revolution in understanding how we experience and communicate emotion. The enthusiastic forword was written by Yehudi Menuhin (I hope you know of him).
Manfred combined his love of engineering and mathematics with his passion for music, psychology and the human body to discover these wonderful things. He has since applied his understanding of these sentic patterns to synthesised music, so that computer-generated music 'feels' warm and emotional, as though a human played it, instead of clinical. Some examples are on YouTube.
I hope you enjoyed learning about how mathematics has been used, in this way, to investigate the wonderful world of music and emotions.
Don't forget to read about this fascinating man, who turned 90 this year (2015), and is still 'going strong!'