What do you believe in?
"I believe in the indomitable human spirit and the amazing capacity we have for understanding the world; for love, joy and happiness. Science not only does not take away any of those things, it adds to the sum of human knowledge.
When I look through my little telescope in my backyard at the planets, moon or Andromeda galaxy that is 2.9 million light-years away, I can enjoy the beauty of the night sky and appreciate it on an emotional level. Then I can think that the photons of light that are landing on my retina left 2.9 million years ago, when we were just barely bipedal hominids in Africa, and are just now arriving tonight. Boy, that's just awe-inspiring.
To me, that's what it means to be spiritual -- what makes your spine tingle. It's what gives you a sense of awe and wonder and transcendence. It doesn't matter to me if you call it God or the cosmos. We're all talking about the same thing, whether it's religious people or New Age spiritual people or Buddhists or scientists. We're all talking about having a sense of awe and wonder at something grander than ourselves."
- Michael Shermer, founder of the Skeptics Society, in an interview with Kevin Berger from salon.com.
My stomach is doing backflips, I have goosebumps, the hairs on my arms are standing on end and my pulse has quickened. I'm not preparing to speak in public (uuurgh).. instead, this is the reaction I get when I listen to a select few of my most loved pieces of music. It feels similar to going on a rollercoaster, and no matter how many times I listen, at a certain point in each track (usually a key change, or resolution of some sort of chord progression), my body will produce the same response, and usually I'll be grinning like an idiot. I have been moved to tears more than once by a piece of music, and similarly, felt so happy I could almost burst. It has never ceased to amaze me. Music is a collection of sound waves. That's all it is, and most of it isn't even 'real' - just synthetic sounds created on a computer. And yet these sound waves, upon entering my ear canals, somehow have the power to activate those areas of my brain where feelings such as blissful happiness, sadness and nostalgia are generated and processed. I love it.
A lot of interest has been created by neuroscientists recently regarding the relationship between the brain and music. I am obviously no neuroscientist, but nevertheless find the whole topic fascinating. Specifically, why certain pieces of music are more 'moving' or enjoyable than others. It seems, I have read (not very extensively), that we enjoy music that is a challenge to us. To some people this may be surprising - you would think our brains would like nice melodies that follow simple patterns and are 'pretty'. To others (usually people with some musical training) this notion will not surprise - the idea of tension and release in music has been around forever. But why? It is, apparently, to do with the way our brains learn. We learn by association - if this, then this. Our brains have been programmed (whether innately or as a result of culture is under debate) to expect certain things to happen in music. Run up a major heptatonic scale: C,D,E,F,G,A,B,.. and your brain will "hum" the last C, even if it isn't there. Music that creates the most brain activity, avoids this association - avoids giving us what we expect to happen. Satisfaction and pleasure are experienced when the association is eventually made.
There is a tonic note in music - a note that feels like 'home'; the most 'significant' note of a song. Even someone with absolutely no musical training would be able to recognise the tonic chord in a song. Good composers will (traditionally) studiously avoid this note until the very end of a piece of music, creating anticipation throughout the piece by suggestively moving towards it but never quite reaching it, and then creating a satisfying sense of resolution at the conclusion, when it is finally reached. Leonard Meyer, who wrote a book on the subject in the 1950s, dissected Beethoven's String Quartet in C-sharp minor - considered a masterpiece by many. By taking apart and analysing 50 measures of the quartet, he demonstrated how Beethoven created a clear rhythmic and melodic pattern, and then carefully presented many variations of it, almost the same as the first but not quite, and all while avoiding a straight expression of the tonic chord - which he saved until the end. Some people believe the emotion in music arises from it's "connotative" meaning - that is, its similarity or ability to mimic or remind us of real-life situations and experiences; instead Meyer suggests that the emotion in music comes from the composition of the music itself - the confusion and conflict created in the piece and the brain's natural tendency to dislike, avoid and reject this, followed by the satisfaction when a resolution is reached.
I don't know a whole lot about this topic so please excuse me if some of my interpretations are incorrect. Much of how all this happens is still largely unknown - we know so much more about sight and vision than we do about sound and hearing.
During a recent visit to the Science Museum in London (now amongst my favourite places on earth), I came across a display of 'Klein Bottles', made by British glassblower Alan Bennett. Not being a mathematician, the thing that first stuck me was the beauty and detail of the work, but as I read on, the mathematical basis of these 'bottles' was what really intrigued me. A Klein Bottle is what is called a 'non-orientable surface'. It has no inside or outside, and no boundary (a sphere, on the other hand, also has no boundary, but is an orientable surface). No inside or outside? Sound impossible? Have a look:
Inside becomes outside, outside becomes inside. It's confusing and mysterious and beautiful. A 'true' Klein bottle can only exist in 4 dimensions, so the bottles made by glassblowers are 3-dimensional representations of 'true' Klein bottles. If dissected into two halves, the Klein Bottle produces two Mobius Strips - a well known phenomenon produced most commonly by taking a (two-sided) strip of paper, twisting it, and gluing the ends together to create a (one-sided) figure. Bennett experimented further with his Klein Bottles, creating more and more complex bottles which, when dissected, produced ever-expanding numbers of Mobius Strips.
History is littered with mathematicians who, inspired by the splendor of the mathematical world, have transformed their 'work' into works of art. After all, the ancient and ultimate challenge of many artists was to successfully represent a 3-dimensional scene or object, in a 2-dimensional format. Architecture is the ultimate crossroad of art and mathematics; check out this 'Klein Bottle House' by McBride Charles Ryan in Hawthorn:
Historically, artists/mathematicians such as Leonardo da Vinci, Giovanni Battista Piranesi and Piero della Francesca explored and utilised this relationship - uncovering and unlocking the secrets of perspective and accurately representing the human anatomical form, but the correlation continues today, inspiring artist such as Nikki Graziano - a photography and mathematics student.
Recently I've begun realizing that mathematics isn't the boring, static subject that I studied in school, but rather, fascinating and relevant - not only in art, but also in nature (which is another observation for another day..)
Hello! An explanation - the name of this blog is a reference to H.G Wells' "The Door In The Wall", a short story written in 1906. The story was referred to by Aldous Huxley in his book "The Doors of Perception" (full text) - a fascinating account of his first experience with mescaline - charting the previously unexplored regions of his consciousness. The title of Huxley's work was derived directly from a statement made by William Blake in around 1791:
"If the doors of perception were cleansed, everything would appear to man as it is - infinite"
Incidentally, it was also this quote that inspired the name of the band The Doors.