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’## Archive for the 'Irish Times' Category

### Multiple Discoveries of the Thue-Morse Sequence

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

### 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’### Discoveries by Amateurs and Distractions by Cranks

Published January 17, 2019 Irish Times Leave a CommentTags: History, Ramanujan, Recreational Maths

Do amateurs ever solve outstanding mathematical problems? Professional mathematicians are aware that almost every new idea they have about a mathematical problem has already occurred to others. Any really new idea must have some feature that explains why no one has thought of it before [TM155 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Discoveries by Amateurs and Distractions by Cranks’

### Trappist-1 & the Age of Aquarius

Published January 3, 2019 Irish Times Leave a CommentTags: Astronomy, Mechanics

The Pythagoreans believed that the planets generate sounds as they move through the cosmos. The idea of the harmony of the spheres was brought to a high level by Johannes Kepler in his book *Harmonices Mundi*, where he identified many simple relationships between the orbital periods of the planets [TM154 or search for “thatsmaths” at irishtimes.com].

Kepler’s idea was not much supported by his contemporaries, but in recent times astronomers have come to realize that resonances amongst the orbits has a crucial dynamical function. Continue reading ‘Trappist-1 & the Age of Aquarius’

### Consider a Spherical Christmas Tree

Published December 20, 2018 Irish Times Leave a CommentTags: Algorithms, Topology

A minor seasonal challenge is how to distribute the fairy lights evenly around the tree, with no large gaps or local clusters. Since the lights are strung on a wire, we are not free to place them individually but must weave them around the branches, attempting to achieve a pleasing arrangement. Optimization problems like this occur throughout applied mathematics [TM153 or search for “thatsmaths” at irishtimes.com].

Trees are approximately conical in shape and we may assume that the lights are confined to the surface of a cone. The peak, where the Christmas star is placed, is a mathematical singularity: all the straight lines that can be drawn on the cone, the so-called generators, pass through this point. Cones are *developable* surfaces: they can be flattened out into a plane without being stretched or shrunk.

### Random Numbers Plucked from the Atmosphere

Published December 6, 2018 Irish Times Leave a CommentTags: Number Theory

Randomness is a slippery concept, defying precise definition. A simple example of a random series is provided by repeatedly tossing a coin. Assigning “1” for heads and “0” for tails, we generate a random sequence of binary digits or *bits*. Ten tosses might produce a sequence such as 1001110100. Continuing thus, we can generate a sequence of any length having no discernible pattern [TM152 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Random Numbers Plucked from the Atmosphere’

### The “Napoleon of Crime” and The Laws of Thought

Published November 15, 2018 Irish Times Leave a CommentTags: History, Logic

A fascinating parallel between a brilliant mathematician and an arch-villain of crime fiction is drawn in a forthcoming book – *New Light on George Boole –* by Des MacHale and Yvonne Cohen. Professor James Moriarty, master criminal and nemesis of Sherlock Holmes, was described by the detective as “the Napoleon of crime”. The book presents convincing evidence that Moriarty was inspired by Professor George Boole [TM151, or search for “thatsmaths” at irishtimes.com].

Continue reading ‘The “Napoleon of Crime” and The Laws of Thought’

### Johannes Kepler and the Song of the Earth

Published November 1, 2018 Irish Times 2 CommentsTags: Astronomy, Music

Johannes Kepler, German mathematician and astronomer, sought to explain the solar system in terms of divine harmony. His goal was to find a system of the world that was mathematically correct and harmonically pleasing. His methodology was scientific in that his hypotheses were inspired by and confirmed by observations. However, his theological training and astrological interests influenced his thinking [TM150, or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Johannes Kepler and the Song of the Earth’

### Who Uses Maths? Almost Everyone!

Published October 18, 2018 Irish Times Leave a CommentTags: Education

In the midst of Maths Week Ireland, many students may be asking “What use is mathematics and what purpose is served by studying it?” Mathematicians often stress the inherent beauty and intellectual charm of the subject, but that is unlikely to persuade many people, who demand to know how mathematics can be of use and value to them. [TM149, or search for “thatsmaths” at irishtimes.com].

In reality, mathematics is essential in numerous contexts: the diversity is remarkable, and you may be surprised how maths plays a vital role in the everyday work of so many people.

### The Many Modern Uses of Quaternions

Published October 4, 2018 Irish Times 1 CommentTags: Algebra, Hamilton

The story of William Rowan Hamilton’s discovery of new four-dimensional numbers called quaternions is familiar. The solution of a problem that had bothered him for years occurred to him in a flash of insight as he walked along the Royal Canal in Dublin. But this Eureka moment did not arise spontaneously: it was the result of years of intense effort. The great French mathematician Henri Poincaré also described how sudden inspiration occurs unexpectedly, but always following a period of concentrated research [TM148, or search for “thatsmaths” at irishtimes.com].

### Tom Lehrer: Comical Musical Mathematical Genius

Published September 20, 2018 Irish Times Leave a CommentTags: Education, Music, Recreational Maths

Tom Lehrer, mathematician, singer, songwriter and satirist, was born in New York ninety years ago. He was active in public performance for about 25 years from 1945 to 1970. He is most renowned for his hilarious satirical songs, many of which he recorded and which are available today on YouTube [see TM147, or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Tom Lehrer: Comical Musical Mathematical Genius’

### Face Recognition

Published September 6, 2018 Irish Times Leave a CommentTags: Algorithms, Computer Science, Social attitudes

As you pass through an airport, you are photographed several times by security systems. Face recognition systems can identify you by comparing your digital image to faces stored in a database. This form of identification is gaining popularity, allowing you to access online banking without a PIN or password. [see TM146, or search for “thatsmaths” at irishtimes.com].

### The Miraculous Spiral on Booterstown Strand

Published August 16, 2018 Irish Times Leave a CommentTags: biology, Geometry, Geophysics

We all know what a spiral looks like. Or do we? Ask your friends to describe one and they will probably trace out the form of a winding staircase. But that is actually a helix, a curve in three-dimensional space. A spiral is confined to a plane – it is a flat curve. In general terms, a spiral is formed by a point moving around a fixed centre while its distance increases or decreases as it revolves [see TM145, or search for “thatsmaths” at irishtimes.com].

Continue reading ‘The Miraculous Spiral on Booterstown Strand’

### Tides: a Tug-of-War between Earth, Moon and Sun

Published August 2, 2018 Irish Times Leave a CommentTags: Fluid Dynamics, Geophysics

All who set a sail, cast a hook or take a dip have a keen interest in the water level, and the regular ebb and flow of the tides. At most places the tidal variations are **semi-diurnal**, with high and low water twice each day [see TM144, or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Tides: a Tug-of-War between Earth, Moon and Sun’

### The Empty Set is Nothing to Worry About

Published July 19, 2018 Irish Times 1 CommentTags: Arithmetic, Set Theory

Today’s article is about nothing: nothing at all, as encapsulated in the number zero and the empty set. It took humanity millennia to move beyond the counting numbers. Zero emerged in several civilizations, first as a place-holder to denote a space or gap between digits, and later as a true number, which could be manipulated like any other. [see TM143, or search for “thatsmaths” at irishtimes.com].

### Trigonometric Comfort Blankets on Hilltops

Published July 5, 2018 Irish Times Leave a CommentTags: Geophysics, Maps, Spherical Trigonometry

On a glorious sunny June day we reached the summit of Céidín, south of the Glen of Imall, to find a triangulation station or *trig pillar*. These concrete pillars are found on many prominent peaks throughout Ireland, and were erected to aid in surveying the country [see TM142, or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Trigonometric Comfort Blankets on Hilltops’

### Optical Refinements at the Parthenon

Published June 21, 2018 Irish Times Leave a CommentTags: Geometry, History

The Parthenon is a masterpiece of symmetry and proportion. This temple to the Goddess Athena was built with pure white marble quarried at Pentelikon, about 20km from Athens. It was erected without mortar or cement, the stones being carved to great accuracy and locked together by iron clamps. The building and sculptures were completed in just 15 years, between 447 and 432 BC. [TM141 or search for “thatsmaths” at irishtimes.com].

### Leopold Bloom’s Arithmetical Adventures

Published June 7, 2018 Irish Times Leave a CommentTags: Arithmetic, Puzzles

As Bloomsday approaches, we reflect on James Joyce and mathematics. Joyce entered UCD in September 1898. His examination marks are recorded in the archives of the National University of Ireland, and summarized in a table in Richard Ellmann’s biography of Joyce (reproduced below) [TM140 or search for “thatsmaths” at irishtimes.com].

### Mathematics at the Science Museum

Published May 17, 2018 Irish Times Leave a CommentTags: Education, History

The new Winton Gallery at London’s Science Museum in South Kensington holds a permanent display on the history of mathematics over the past 400 years. The exhibition shows how mathematics has underpinned astronomy, navigation and surveying in the past, and how it continues to pervade the modern world [see TM139, or search for “thatsmaths” at irishtimes.com].

### Stan Ulam, a mathematician who figured how to initiate fusion

Published May 3, 2018 Irish Times Leave a CommentTags: Algorithms, Fluid Dynamics, Set Theory, Topology

Stanislaw Ulam, born in Poland in 1909, was a key member of the remarkable Lvov School of Mathematics, which flourished in that city between the two world wars. Ulam studied mathematics at the Lvov Polytechnic Institute, getting his PhD in 1933. His original research was in abstract mathematics, but he later became interested in a wide range of applications. He once joked that he was “a pure mathematician who had sunk so low that his latest paper actually contained numbers with decimal points” [TM138 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Stan Ulam, a mathematician who figured how to initiate fusion’

### Fourier’s Wonderful Idea – II

Published April 5, 2018 Irish Times Leave a CommentTags: Analysis, History

**Solving PDEs by a Roundabout Route**

Joseph Fourier, born just 250 years ago, introduced a wonderful idea that revolutionized science and mathematics: any function or signal can be broken down into simple periodic sine-waves. Radio waves, micro-waves, infra-red radiation, visible light, ultraviolet light, X-rays and gamma rays are all forms of electromagnetic radiation, differing only in frequency [TM136 or search for “thatsmaths” at irishtimes.com].

### Cubic Skulduggery & Intrigue

Published March 15, 2018 Irish Times Leave a CommentTags: Algebra, History

Babylonian mathematicians knew how to solve simple polynomial equations, in which the unknown quantity that we like to call *x *enters in the form of powers, that is, *x* multiplied repeatedly by itself. When only *x* appears, we have a linear equation. If *x*-squared enters, we have a quadratic. The third power of *x* yields a cubic equation, the fourth power a quartic and so on [TM135 or search for “thatsmaths” at irishtimes.com].

### Reducing R-naught to stem the spread of Epidemics

Published March 1, 2018 Irish Times Leave a CommentTags: Epidemiology, medicine

We are reminded each year to get vaccinated against the influenza virus. The severity of the annual outbreak is not known with certainty in advance, but a major pandemic is bound to occur sooner or later. Mathematical models play an indispensable role in understanding and managing infectious diseases. Models vary in sophistication from the simple SIR model with just three variables to highly complex simulation models with millions of variables [TM134 or search for “thatsmaths” at irishtimes.com]. Continue reading ‘Reducing R-naught to stem the spread of Epidemics’

### Galileo’s Book of Nature

Published February 15, 2018 Irish Times Leave a CommentTags: Astronomy, History, Mechanics

In 1971, astronaut David Scott, standing on the Moon, dropped a hammer and a feather and found that both reached the surface at the same time. This popular experiment during the Apollo 15 mission was a dramatic demonstration of a prediction made by Galileo three centuries earlier. Galileo was born in Pisa on 15 February 1564, just 454 years ago today [TM133 or search for “thatsmaths” at irishtimes.com].

### Staying Put or Going with the Flow

Published February 1, 2018 Irish Times Leave a CommentTags: Algorithms, Geophysics, Numerical Analysis

The atmospheric temperature at a fixed spot may change in two ways. First, heat sources or sinks may increase or decrease the thermal energy; for example, sunshine may warm the air or radiation at night may cool it. Second, warmer or cooler air may be transported to the spot by the air flow in a process called advection. Normally, the two mechanisms act together, sometimes negating and sometimes reinforcing each other. What is true for temperature is also true for other quantities: pressure, density, humidity and even the flow velocity itself. This last effect may be described by saying that “the wind blows the wind” [TM132 or search for “thatsmaths” at irishtimes.com].

### The Heart of Mathematics

Published January 18, 2018 Irish Times Leave a CommentTags: biology, Fluid Dynamics, medicine

At five litres per minute the average human heart pumps nearly 200 megalitres of blood through the body in a lifetime. Heart disease causes 40 percent of deaths in the EU and costs hundreds of billions of Euros every year. Mathematics can help to improve our knowledge of heart disease and our understanding of cardiac malfunction [TM131 or search for “thatsmaths” at irishtimes.com].

### Energy Cascades in Van Gogh’s Starry Night

Published January 4, 2018 Irish Times Leave a CommentTags: Fluid Dynamics, Geophysics

“*Big whirls have little whirls that feed on their velocity,*

*And little whirls have lesser whirls, and so on to viscosity.*“

We are all familiar with the measurement of speed, the distance travelled in a given time. Allowing for the direction as well as the magnitude of movement, we get velocity, a vector quantity. In the flow of a viscous fluid, such as treacle pouring off a spoon, the velocity is smooth and steady. Such flow is called laminar, and variations of velocity from place to place are small. By contrast, the motion of the atmosphere, a fluid with low viscosity, can be irregular and rapidly fluctuating. We experience this when out and about on a gusty day. Such chaotic fluid flow is called turbulence, and this topic continues to challenge the most brilliant scientists [TM130 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Energy Cascades in Van Gogh’s Starry Night’

### Darker Mornings, Brighter Evenings

Published December 21, 2017 Irish Times Leave a CommentTags: Astronomy, Time measurement

Today is the winter solstice, the shortest day of the year. We might expect that the latest sunrise and earliest sunset also occur today. In fact, the earliest sunset, the darkest day of the year, was on 13 December, over a week ago, and the latest sunrise is still more than a week away. This curious behaviour is due to the unsteady path of the Earth around the Sun. Our clocks, which run regularly at what is called mean time, move in and out of synchronization with solar time [TM129 or search for “thatsmaths” at irishtimes.com].

### The Star of Bethlehem … or was it a Planet?

Published December 7, 2017 Irish Times 1 CommentTags: Astronomy

People of old were more aware than we are of the night sky and took a keen interest in unusual happenings above them. The configuration of the stars was believed to be linked to human affairs and many astronomical phenomena were interpreted as signs of good or evil in the offing. The Three Wise Men or Magi were astrologers, experts in celestial matters, and would have drawn inferences from what they observed in the sky [TM128 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘The Star of Bethlehem … or was it a Planet?’

### Slingshot Orbit to Asteroid Bennu

Published November 16, 2017 Irish Times Leave a CommentTags: Astronomy, Mechanics

The *Voyager 1* and *Voyager 2* spacecraft have now left the solar system and will continue into deep space. How did we manage to send them so far? The *Voyager* spacecraft used gravity assists to visit Jupiter, Saturn, Uranus and Neptune in the late 1970s and 1980s. Gravity assist manoeuvres, known as **slingshots**, are essential for interplanetary missions. They were first used in the Soviet Luna-3 mission in 1959, when images of the far side of the Moon were obtained. Space mission planners use them because they require no fuel and the gain in speed dramatically shortens the time of missions to the outer planets.

### Modular Arithmetic: from Clock Time to High Tech

Published November 2, 2017 Irish Times Leave a CommentTags: Arithmetic, Time measurement

You may never have heard of *modular arithmetic*, but you use it every day without the slightest difficulty. In this system, numbers wrap around when they reach a certain size called the modulus; it is the arithmetic of remainders [TM126 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Modular Arithmetic: from Clock Time to High Tech’

### Learning Maths has never been Easier

Published October 19, 2017 Irish Times Leave a CommentTags: Education, Ireland, Recreational Maths

Maths is hard: many people find it inscrutable and have negative attitudes towards maths. They may have bad memories of school maths or have been told they lack mathematical talents. This is unfortunate: we all have the capacity to apply reasoning and logic and we can all do maths. Given the vital role mathematics plays in modern society, there is an urgent need to help young people to become more numerate and comfortable with mathematics. With a wealth of online resources, learning maths has never been easier. [TM125 or search for “thatsmaths” at irishtimes.com].

### Andrey Markov’s Brilliant Ideas are still a Driving Force

Published September 21, 2017 Irish Times Leave a CommentTags: Algorithms, Statistics

Imagine examining the first 20,000 letters of a book, counting frequencies and studying patterns. This is precisely what Andrey Markov did when he analyzed the text of Alexander Pushkin’s verse novel *Eugene Onegin*. This work comprises almost 400 stanzas of iambic tetrameter and is a classic of Russian literature. Markov studied the way vowels and consonants alternate and deduced the probabilities of a vowel being followed by a another vowel, by a consonant, and so on. He was applying a statistical model that he had developed in 1906 and that we now call a Markov Process or Markov chain. [TM123 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Andrey Markov’s Brilliant Ideas are still a Driving Force’

### Euler and the Fountains of Sanssouci

Published September 7, 2017 Irish Times Leave a CommentTags: Applied Maths, Euler, Fluid Dynamics

When Frederick the Great was crowned King of Prussia in 1740 he immediately revived the Berlin Academy of Sciences and invited scholars from throughout Europe to Berlin. The most luminous of these was Leonhard Euler, who arrived at the academy in 1741. Euler was an outstanding genius, brilliant in both mathematics and physics. Yet, a myth persists that he failed spectacularly to solve a problem posed by Frederick. Euler is reputed to have bungled his mathematical analysis. In truth, there was much bungling, but the responsibility lay elsewhere. [TM122 or search for “thatsmaths” at irishtimes.com].

### It’s as Easy as Pi

Published August 3, 2017 Irish Times Leave a CommentTags: Archimedes, Geometry, Number Theory, Pi

Every circle has the property that the distance around it is just over three times the distance across. This has been known since the earliest times [see TM120 or search for “thatsmaths” at irishtimes.com].

The constant ratio of the circumference to the diameter, denoted by the Greek letter pi, is familiar to every school-child. You might expect to find a proof in Euclid’s *Elements of Geometry*, he could not prove it, and he made no mention of the ratio (see last week’s post).

### Quadrivium: The Noble Fourfold Way

Published July 20, 2017 Irish Times Leave a CommentTags: Arithmetic, Astronomy, Geometry, History, Music

According to Plato, a core of mathematical knowledge – later known as the Quadrivium – was essential for an understanding of the Universe. The curriculum was outlined in Plato’s *Republic*. The name Quadrivium means four ways, but this term was not used until the time of Boethius in the 6^{th} century AD [see TM119 or search for “thatsmaths” at irishtimes.com].

It is said that an inscription over the entrance to Plato’s Academy read “Let None But Geometers Enter Here”. This indicated that the Quadrivium was a prerequisite for the study of philosophy in ancient Greece.

### Robert Murphy, a “Brilliant Meteor”

Published July 6, 2017 Irish Times Leave a CommentTags: History, Ireland

“A brilliant meteor that flared intensely but all too briefly”; this was how Des MacHale described the Cork-born mathematician Robert Murphy in his biography of George Boole, first professor of mathematics in Cork. Murphy was a strong influence on Boole, who quoted liberally from his publications [see TM118 or search for “thatsmaths” at irishtimes.com].

### Fractal Complexity of Finnegans Wake

Published June 15, 2017 Irish Times Leave a CommentTags: Algorithms, Fractals

Tomorrow we celebrate Bloomsday, the day of action in *Ulysses*. Most of us regard Joyce’s singular book as a masterpiece, even if we have not read it. In contrast, *Finnegans Wake* is considered by some as a work of exceptional genius, by others as impenetrable bafflegab [See TM117 or search for “thatsmaths” at irishtimes.com].

### Beautiful Patterns in Maths and Music

Published June 1, 2017 Irish Times Leave a CommentTags: Music

The numerous connections between mathematics and music have long intrigued practitioners of both. For centuries scholars and musicians have used maths to analyze music and also to create it. Many of the great composers had a deep understanding of the mathematical principles underlying music. Johann Sebastian Bach was the grand master of structural innovation and invention in music. While his compositions are the free creations of a genius, they have a fundamentally mathematical basis [See TM116 or search for “thatsmaths” at irishtimes.com].

### Yves Meyer wins 2017 Abel Prize

Published May 18, 2017 Irish Times Leave a CommentTags: Applied Maths, Wave Motion

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 life from 1802 to 1829, made dramatic advances in mathematics. Meyer was chosen for his development of the mathematical theory of *wavelets*. [See TM115 or search for “thatsmaths” at irishtimes.com].

### When Roughly Right is Good Enough

Published May 4, 2017 Irish Times Leave a CommentTags: Algorithms, Education

How high is Liberty Hall? How fast does human hair grow? How many A4 sheets of paper would cover Ireland? How many people in the world are talking on their mobile phones right now? These questions seem impossible to answer but, using basic knowledge and simple logic, we can make a good guess at the answers. For example, Liberty Hall has about 16 floors. With 4 metres per floor we get a height of 64 metres, close enough to the actual height. Problems of this nature are known as Fermi problems. [TM114 or search for “thatsmaths” at irishtimes.com].

### The Water is Rising Fast

Published April 20, 2017 Irish Times Leave a CommentTags: Fluid Dynamics, Geophysics

Seventy percent of the Earth is covered by water and three quarters of the world’s great cities are on the coast. Ever-rising sea levels pose a real threat to more than a billion people living beside the sea. As the climate warms, this is becoming a greater threat every year [TM113 or search for “thatsmaths” at irishtimes.com].

### The Improbability Principle

Published April 6, 2017 Irish Times Leave a CommentTags: Probability, Statistics

*Extremely improbable events are commonplace.*

“It’s an unusual day if nothing unusual happens”. This aphorism encapsulates a characteristic pattern of events called the *Improbability Principle*. Popularised by statistician Sir David Hand, emeritus professor at Imperial College London, it codifies the paradoxical idea that extremely improbable events happen frequently. [TM112 or search for “thatsmaths” at irishtimes.com].

Modern science is big: the gravitational wave detector (LIGO) cost over a billion dollars, and the large hadron collider (LHC) in Geneva took decades to build and cost almost five billion euros. It may seem that scientific advances require enormous financial investment. So, it is refreshing to read in *Nature Biomedical Engineering *(Vol 1, Article 9) about the development of an ultra-cheap centrifuge that costs only a few cents to manufacture [TM111 or search for “thatsmaths” at irishtimes.com].

### Enigmas of Infinity

Published March 2, 2017 Irish Times Leave a CommentTags: Analysis, History, Logic

Children sometimes amuse themselves searching for the biggest number. After trying millions, billions and trillions, they realize that there is no end to the game: however big a number may be, we can always add 1 to produce a bigger number: the set of counting numbers is infinite. The concept of infinity has intrigued philosophers since antiquity, and it leads to many surprises and paradoxical results [TM110 or search for “thatsmaths” at irishtimes.com].

### The Spire of Light

Published February 16, 2017 Irish Times Leave a CommentTags: Applied Maths, Mechanics

Towering over O’Connell Street in Dublin, the Spire of Light, at 120 metres, is about three times the height of its predecessor [TM109 or search for “thatsmaths” at irishtimes.com]. The Spire was erected in 2003, filling the void left by the destruction in 1966 of Nelson’s Pillar. The needle-like structure is a slender cone of stainless steel, the diameter tapering from 3 metres at the base to 15 cm at its apex. The illumination from the top section shines like a beacon throughout the city.

### Voronoi Diagrams: Simple but Powerful

Published February 2, 2017 Irish Times 2 CommentsTags: Algorithms, Geometry

We frequently need to find the nearest hospital, surgery or supermarket. A map divided into cells, each cell covering the region closest to a particular centre, can assist us in our quest. Such a map is called a Voronoi diagram, named for Georgy Voronoi, a mathematician born in Ukraine in 1868. He is remembered today mostly for his diagram, also known as a Voronoi tessellation, decomposition, or partition. [TM108 or search for “thatsmaths” at irishtimes.com].

### The Library of Babel and the Information Explosion

Published January 19, 2017 Irish Times Leave a CommentTags: Arithmetic, Topology

The world has been transformed by the Internet. Google, founded just 20 years ago, is a major force in online information. The company name is a misspelt version of “googol”, the number one followed by one hundred zeros. This name echoes the vast quantities of information available through the search engines of the company [TM107 or search for “thatsmaths” at irishtimes.com].

Long before the Internet, the renowned Argentine writer, poet, translator and literary critic Jorge Luis Borges (1889 – 1986) envisaged the Universe as a vast information bank in the form of a library. The Library of Babel was imagined to contain every book that ever was or ever could be written.

Continue reading ‘The Library of Babel and the Information Explosion’