The Navigational Skills of the Marshall Islanders

For thousands of years, the Marshall Islanders of Micronesia have been finding their way around a broadly dispersed group of low-lying islands, navigating apparently without effort from one atoll to another one far beyond the horizon. They had no maps or magnetic compass, no clocks, no weather forecasts and certainly no GPS or SatNav equipment … Continue reading The Navigational Skills of the Marshall Islanders →

Hokusai’s Great Wave and Roguish Behaviour

Hokusai's woodcut “The Great Wave off Kanagawa”. “The Great Wave off Kanagawa”, one of the most iconic works of Japanese art, shows a huge breaking wave with foam thrusting forward at its crest, towering over three fishing boats, with Mt Fuji in the background [TM158 or search for “thatsmaths” at irishtimes.com]. This woodcut, produced by … Continue reading Hokusai’s Great Wave and Roguish Behaviour →

Don’t be Phased by Waveform Distortions

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 $latex {3 : … Continue reading Don’t be Phased by Waveform Distortions →

Gravitational Waves & Ringing Teacups

Newton's law of gravitation describes how two celestial bodies orbit one another, each tracing out an elliptical path. But this is imprecise: the theory of general relativity shows that two such bodies radiate energy away in the form of gravitational waves (GWs), and spiral inwards until they eventually collide. Energy and angular momentum are carried … Continue reading Gravitational Waves & Ringing Teacups →

Waves Packed in Envelopes

In this article we take a look at group velocity and at the extraction of the envelope of a wave packet using the ideas of the Hilbert transform. Interference of two waves A single sinusoidal wave is infinite in extent and periodic in space and time. When waves interact, the dynamics are more interesting. The … Continue reading Waves Packed in Envelopes →

Wavelets: Mathematical Microscopes

In the last post, we saw how Yves Meyer won the Abel Prize for his work with wavelets. Wavelets make it easy to analyse, compress and transmit information of all sorts, to eliminate noise and to perform numerical calculations. Let us take a look at how they came to be invented. Fourier's Marvellous Idea. In … Continue reading Wavelets: Mathematical Microscopes →

Yves Meyer wins 2017 Abel Prize

On 23 May King Harald V of Norway will present the Abel Prize to French mathematician Yves Meyer. Each year, the prize is awarded to a laureate for “outstanding work in the field of mathematics”. Comparable to a Nobel Prize, the award is named after the exceptional Norwegian, Niels Henrik Abel who, in a short … Continue reading Yves Meyer wins 2017 Abel Prize →

Modelling Rogue Waves

There are many eyewitness accounts by mariners of gigantic waves – almost vertical walls of water towering over ocean-going ships – that appear from nowhere and do great damage, sometimes destroying large vessels completely. Oceanographers, who have had no way of explaining these 'rogue waves', have in the past been dismissive of these reports [TM090, or search for … Continue reading Modelling Rogue Waves →

For Good Comms, Leaky Cables are Best

A counter-intuitive result of Oliver Heaviside showed how telegraph cables should be designed [see this week’s That’s Maths column (TM066) or search for “thatsmaths” at irishtimes.com]. Robert Halpin In Wicklow town an obelisk commemorates Robert Halpin, a Master Mariner born at the nearby Bridge Tavern. Halpin, one of the more important mariners of the nineteenth … Continue reading For Good Comms, Leaky Cables are Best →

How Big was the Bomb?

By a brilliant application of dimensional analysis, G.I.Taylor estimated the explosive energy of the first atomic blast, the Trinity Test (see this week’s That’s Maths column in The Irish Times, TM053, or search for “thatsmaths” at irishtimes.com). Physicists, engineers and applied mathematicians have an arsenal of problem-solving techniques. Computers crunch out numerical solutions in short … Continue reading How Big was the Bomb? →

The Biggest Harp in Ireland

This week’s That’s Maths column in The Irish Times (TM052, or search for “thatsmaths” at irishtimes.com) is about "Samuel Beckett Playing Bridge in Dublin". Mathematics Models Nature The life of Pythagoras is shrouded in myth and legend. He was born on the island of Samos and travelled to Egypt, Mesopotamia and possibly India before arriving … Continue reading The Biggest Harp in Ireland →

White Holes in the Kitchen Sink

A tidal bore is a wall of water about a metre high travelling rapidly upstream as the tide floods in. It occurs where the tidal range is large and the estuary is funnel-shaped (see previous post on this blog). The nearest river to Ireland where bores can be regularly seen is the Severn, where favourable … Continue reading White Holes in the Kitchen Sink →

Interesting Bores

This week’s That’s Maths column in the Irish Times ( TM036 ) is about bores. But don't be put off: they are very interesting. According to the old adage, water finds its own level. But this is true only in static situations. In more dynamic circumstances where the water is moving rapidly, there can be … Continue reading Interesting Bores →

Ducks & Drakes & Kelvin Wakes

The theme of this week’s That’s Maths column in the Irish Times ( TM021 ) is Kelvin Wakes, the beautiful wave patterns generated as a duck or swan swims through calm, deep water or in the wake of a ship or boat. Group Velocity A stone dropped in a pond generates waves in a beautiful changing … Continue reading Ducks & Drakes & Kelvin Wakes →