While mathematics may be viewed as an abstract creation, its origins lie in the physical world. The need to count animals and share food supplies led to the development of the concept of numbers. With five-fingered hands, we naturally tended to count in tens. Arithmetic methods were needed to allocate land, organize armies and calculate … Continue reading Hamilton’s Dynamics: a Prescient Framework for Quantum Mechanics
Tag: Hamilton
Hamilton’s Semaphore Code and Signalling System
Sir William Rowan Hamilton (1805-1865) was Ireland's most ingenious mathematician. When he was just fifteen years old, Hamilton and a schoolfriend invented a semaphore-like signalling system. On 21 July 1820, Hamilton wrote in his journal how he and Tommy Fitzpatrick set up a mark on a tower in Trim and were able to view it … Continue reading Hamilton’s Semaphore Code and Signalling System
Terence Tao to deliver the Hamilton Lecture
Pick a number; if it is even, divide it by 2; if odd, triple it and add 1. Now repeat the process, each time halving or else tripling and adding 1. Here is a surprise: no matter what number you pick, you will eventually arrive at 1. Let's try 6: it is even, so we … Continue reading Terence Tao to deliver the Hamilton Lecture
The Mathematics of Fair Play in Video Games
Video games generate worldwide annual sales of about $150 billion. With millions of people confined at home with time to spare, the current pandemic may benefit the industry. At the core of a video game is a computer program capable of simulating a range of phenomena in the real world or in a fantasy universe, … Continue reading The Mathematics of Fair Play in Video Games
Maths and Poetry: Beauty is the Link
Mathematicians are not renowned for their ability to reach the deepest recesses of the human soul. This talent is usually associated with great artists and musicians, and a good poet can move us profoundly with a few well-chosen words [TM173 or search for “thatsmaths” at irishtimes.com]. William Rowan Hamilton, whose work we celebrate during Maths Week, was … Continue reading Maths and Poetry: Beauty is the Link
Symplectic Geometry
For many decades, a search has been under way to find a theory of everything, that accounts for all the fundamental physical forces, including gravity. The dictum ``physics is geometry'' is a guiding principle of modern theoretical physics. Einstein's General Theory of Relativity, which emerged just one hundred years ago, is a crowning example of … Continue reading Symplectic Geometry
Kepler’s Vanishing Circles Hidden in Hamilton’s Hodograph
The Greeks regarded the heavens as the epitome of perfection. All flaws and blemishes were confined to the terrestrial domain. Since the circle is perfect in its infinite symmetry, it was concluded by Aristotle that the Sun and planets move in circles around the Earth. Later, the astronomer Ptolemy accounted for deviations by means of … Continue reading Kepler’s Vanishing Circles Hidden in Hamilton’s Hodograph
The Many Modern Uses of Quaternions
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 … Continue reading The Many Modern Uses of Quaternions
The next Hamilton
William Rowan Hamilton was Ireland's greatest mathematician. His name is heard thousands of times every day throughout the world when researchers use the Hamiltonian function that encapsulates the dynamics of a vast range of physical systems. He achieved fame early in life and remains one of the all-time great scientists. [TM099, or search for “thatsmaths” at … Continue reading The next Hamilton
Old Octonions may rule the World
This week’s That’s Maths column in The Irish Times (TM055, or search for “thatsmaths” at irishtimes.com) is about octonions, new numbers discovered by John T Graves, a friend of William Rowan Hamilton. On this day in 1843, the great Irish mathematician William Rowan Hamilton discovered a new kind of numbers called quaternions. Each quaternion has … Continue reading Old Octonions may rule the World
Robots & Biology
The article in this week’s That’s Maths column in the Irish Times ( TM037 ) is about connections between robotics and biological systems via mechanics. The application of mathematics in biology is a flourishing research field. Most living organisms are far too complex to be modelled in their entirety, but great progress is under way … Continue reading Robots & Biology
Admirably Appropriate
The topic of the That’s Maths column ( TM026 ) in the Irish Times this week is the surprising and delightful way in which mathematics developed for its own sake turns out to be eminently suited for solving practical problems. Symbiosis between pure and applied mathematics The power of mathematics is astonishing. Time and again, … Continue reading Admirably Appropriate
Santa’s TSP Algorithm
This week's That's Maths column ( TM011 ) discusses the challenge faced by Santa Claus: he has about a billion homes to visit in one night, so he needs to be smart in picking his route. The challenge he faces is called the Travelling Salesman Problem, or TSP. Although he won't reveal his secret, Santa … Continue reading Santa’s TSP Algorithm
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