Mathematics Survey

Those who are creative often shy away from math. This is partly the fault of many education systems around the world that at an early age make young people choose between the humanities and the sciences. I cannot remember at school anyone who choose both math and art as their specialist topics. In the Renaissance as in ancient Greece the two disciplines were seen as complimentary.

Leonardo da Vinci was not only an outstanding artist he was also a draftsman, an inventor and a mathematician . He looked for the mathematical formulas that underlay beauty. It is da Vinci that bought the idea of the golden ratio to many people’s attention. It is found throughout nature and is one of the most fundamental principles of design. The golden ratio seems inherently ‘right’. It can be expressed in math as:

 

 

 

 

 

 

From this formula you can get a rectangle that can inform the design of tables, whiteboards and also the spacing of sections on a website.

Another mathematical aspect to design can be found in the Fibonacci sequence of numbers:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 etc.

This sequence is derided from adding the last two numbers together to get the next number in the sequence. Thus 1 +2 =3. 2+3 =5. 3+5=8 and so on. It is interesting to note that the bigger the numbers get the closer their relationship conforms to the golden ratio.

The Fibonacci sequence is particularly useful for graphic design. It gives us the correct proportions between font sizes and also the relative values for column sizes. For website design it is good to start with a content width of 987 pixels to make it easy to calculate the relative sizes of columns.

Finally, modern design has been greatly influenced by fractals. These are mathematically governed images that appear to magnify at each iteration. It is like the zoom on a camera; only with fractals the image quality never becomes blurred. Designers often have fractals moving and /or  rotating with each iteration to produce striking effects.

It is clear from these 3 examples that much of the best design is mathematically based. The more we can use math in design the easier it will be on the eye. For website design maths can be a powerful to grab the user’s attention.

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Music is written in a notational form that can be easily converted to mathematical symbols. Through doing so it soon becomes apparent that the basis of all music that is commonly thought of as ‘beautiful’ uses repetition.

A motif in music is introduced and then it is repeated and altered. The setting up of expectation of repetition in music and then fulfilling or dashing that expectation explains the dynamic of music. It is a series of patterns essentially that is behind the aesthetics of all music from chamber music to death metal.

This sets up an interesting question: is it possible to write music that is totally absent of pattern? This is different to random music – rather music that has patterns but no pattern is repeated. To do this math is needed.

John Costas was hired by the US Navy to solve the problem with the sonar ping. For the ping to work a sound with patterns where no pattern was repeated was needed. He solved the problem by using the Prime Number Theory developed by Evariste Galois. Each component of the ping was mathematically related to the next but no pattern was repeated.

The speaker in the talk (Scott Rickard) used the work of Costas that borrowed from Evariste Galois to write a piece of music without repetition. It should be the ugliest piece of music ever written as it is devoid of repeating patterns.

In a sense this music realizes the dream of the composer Schoenberg in his movement called ‘the emancipation of the dissonance’.

After listening to the talk and musical piece on TED it is worth reading the comments
(http://www.ted.com/talks/lang/en/scott_rickard_the_beautiful_math_behind_the_ugliest_music.html) as it details some of the key points of what is pattern? How does the mind perceive pattern? How is math converted to music?

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