The impact of computing on society is ever-increasing. Web-based commerce continues to grow and artificial intelligence now pervades our lives. To make wise choices, we need to understand how computers operate and how we can deploy them most constructively. Listen to any computer scientist and soon you will hear the word “algorithm” [TM168 or search for “thatsmaths” at irishtimes.com].
Posts Tagged 'Algorithms'
Algorithms: Recipes for Success
Published August 1, 2019 Irish Times Leave a CommentTags: Algorithms, Computer Science
Cumbersome Calculations in Ancient Rome
Published June 27, 2019 Occasional Leave a CommentTags: Algorithms, History
“Typus Arithmeticae” is a woodcut from the book Margarita Philosophica by Gregor Reisch of Freiburg, published in 1503. In the centre of the figure stands Arithmetica, the muse of mathematics. She is watching a competition between the Roman mathematician Boethius and the great Pythagoras. Boethius is crunching out a calculation using Hindu-Arabic numerals, while Pythagoras uses a counting board or abacus (tabula) and – presumably – a less convenient number system. Arithmetica is looking with favour towards Boethius. He smiles smugly while Pythagoras is looking decidedly glum.
The figure aims to show the superiority of the Hindu-Arabic number system over the older Greek and Roman number systems. Of course, it is completely anachronistic: Pythagoras flourished around 500 BC and Boethius around AD 500, while the Hindu-Arabic numbers did not arrive in Europe until after AD 1200.
Simple Curves that Perplex Mathematicians and Inspire Artists
Published June 20, 2019 Irish Times Leave a CommentTags: Algorithms, Topology
The preoccupations of mathematicians can seem curious and strange to normal people. They sometimes expend great energy proving results that appear glaringly obvious. One such result is called the Jordan Curve Theorem. We all know that a circle has an inside and an outside, and that this property also holds for a much larger collection of closed curves [TM165 or search for “thatsmaths” at irishtimes.com].
Detail from Michaelangelo’s The Creation of Adam, and a Jordan Curve representation [image courtesy of Prof Robert Bosch, Oberlin College. Downloaded from here].
Continue reading ‘Simple Curves that Perplex Mathematicians and Inspire Artists’
Bouncing Billiard Balls Produce Pi
Published May 9, 2019 Occasional Leave a CommentTags: Algorithms, Numerical Analysis, Pi
There are many ways of evaluating 
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].
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.
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].
Jimmy Wales, co-founder of Wikipedia, answering a question. Face detection indicated by squares.
