Advanced mathematics is providing new ways to see a picture, listen to sounds and analyse information. The use of mathematical tools allows the user to zoom in and see the finest detail or back up and take in the broader view.
The tools in question are known as "wavelets", explained Prof Ingrid Daubechies, who last night delivered the annual Hamilton Lecture, which focuses on mathematics.
Wavelets are a new approach used in the analysis of sounds, images and many other types of information, she told her audience in Dublin last night.
"They are mathematical tools that really come as a result of maths developed by mathematicians, engineers, physicists and computer scientists."
Prof Daubechies is professor of applied and computational mathematics at Princeton University, New Jersey. The title of her talk was: "A mathematical microscope: wavelets and their application".
The technique is akin to taking apart an onion, she said. You can get deeper and deeper into the image or sound by passing through layer after layer of information. How deep you go depends on the level of resolution required by the application. "You adjust your accuracy or resolution to the scale where you work," she explained.
The wavelet tools are algorithms, mathematical formulas that perform a given function. They can be connected together to achieve a particular result, for example compressing and decompressing images or sounds.
Engineers and mathematicians have been using algorithms in this way for many years, but about 20 years ago the full potential of using them in this way began to emerge.
The Federal Bureau of Investigation in the US chose a wavelet-based system to analyse the millions of fingerprints it holds on file. "That was one of the first non-specialist applications of wavelets," Prof Daubechies said.
The system searches for near matches before zooming in to very specific details such as the location of individual sweat glands on the finger.
The annual Hamilton Lecture highlights the life and work of one of Ireland's greatest scientists, William Rowan Hamilton (1805-1865).