For many years there has been an ongoing debate about the importance of phase changes in music. Some people claim that we cannot hear the effects of phase errors, others claim that we can. Who is right? The figure below shows a waveform of a perfect fifth, with components in the ratio for various values of the phase-shift. Despite the different appearances, all sound pretty much the same.

Continue reading ‘Don’t be Phased by Waveform Distortions’## Archive for February, 2019

### Don’t be Phased by Waveform Distortions

Published February 28, 2019 Occasional Leave a CommentTags: Fourier analysis, Music, Wave Motion

### Multiple Discoveries of the Thue-Morse Sequence

Published February 21, 2019 Irish Times Leave a CommentTags: Algorithms, Number Theory

It is common practice in science to name important advances after the first discoverer or inventor. However, this process often goes awry. A humorous principle called Stigler’s Law holds that no scientific result is named after its original discoverer. This law was formulated by Professor Stephen Stigler of the University of Chicago in his publication “Stigler’s law of eponymy”. He pointed out that his “law” had been proposed by others before him so it was, in a sense, self-verifying. [TM157 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Multiple Discoveries of the Thue-Morse Sequence’### Folding Maps: A Simple but Unsolved Problem

Published February 14, 2019 Occasional Leave a CommentTags: Combinatorics

Paper-folding is a recurring theme in mathematics. The art of origami is much-loved by many who also enjoy recreational maths. One particular folding problem is remarkably easy to state, but the solution remains elusive:

**Given a map with M ****×**** N panels, how many different ways can it be folded? **

Each panel is considered to be distinct, so two foldings are equivalent only when they have the same vertical sequence of the L = M *×* N layers.

### Rambling and Reckoning

Published February 7, 2019 Irish Times Leave a CommentTags: Arithmetic, Recreational Maths

A walk on the beach, in the hills or along a river bank provides great opportunities for mathematical reflection. How high is the mountain? How many grains of sand are on the beach? How much water is flowing in the river? [TM156 or search for “thatsmaths” at irishtimes.com].

While the exact answers may be elusive, we can make reasonable guesstimates using basic knowledge and simple mathematical reasoning. And we will be walking in the footsteps of some of the world’s greatest thinkers.

Continue reading ‘Rambling and Reckoning’