Published January 19, 2017
Tags: 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].
Artist’s impression of the Library of Babel [Image from Here].
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’
Published January 12, 2017
The picture below is of a sculpture piece called Intuition, which stands in front of the Isaac Newton Institute (INI) in Cambridge. It is in the form of the Borromean Rings, a set of three interlocked rings, no two of which encircle each other.
“Intuition”. A sculpture piece in front of the Isaac Newton Institute [Photograph courtesy of S J Wilkinson].
Continue reading ‘On Knots and Links’
Published December 29, 2016
Tags: Geometry, Topology
The idiom “square peg in a round hole” expresses a mismatch or misfit, often referring to somebody in the wrong profession. It may also indicate a difficult or impossible task but, of course, it is quite simple to fit a square peg in a round hole, hammering it in until the corners are tight against the circular boundary of the hole. Since the peg may be oriented at any angle, there are an infinite number of ways to fit a square within a circle. In contract, for a boomerang-shaped hole, there is just one way to draw a square with its vertices on the curve.
Continue reading ‘Unsolved: the Square Peg Problem’
Published September 22, 2016
Tags: Graph Theory, Topology
We wrote about the basic properties of Venn diagrams in an earlier post. Now we take a deeper look. John Venn, a logician and philosopher, born in Hull, Yorkshire in 1834, introduced the diagrams in a paper in 1880 and in his book Symbolic Logic, published one year later. The diagrams were used long before Venn’s paper, but he formalized and popularized them. He used them as logical diagrams: the interior of each set means the truth of a particular proposition. Unions and intersections of sets correspond to the logical operators OR and AND.
Continue reading ‘Venn Again’s Awake’
Networks are everywhere in the modern world. They may be physical constructs, like the transport system or power grid, or more abstract entities like family trees or the World Wide Web. A network is a collection of nodes linked together, like cities connected by roads or people genetically related to each other. Such a system of nodes and links is what mathematicians call a graph [TM078; or search for “thatsmaths” at irishtimes.com ].
Continue reading ‘It’s a Small – Networked – World’
Published August 4, 2015
Tags: Algorithms, Euler, Topology
Leonhard Euler considered a problem known as The Seven Bridges of Königsberg. It involves a walk around the city now known as Kaliningrad, in the Russian exclave between Poland and Lithuania. Since Kaliningrad is out of the way for most of us, let’s have a look closer to home, at the bridges of Paris. [TM073: search for “thatsmaths” at irishtimes.com ]
Continue reading ‘The Bridges of Paris’
Published April 30, 2015
Tags: Geometry, Topology
A climber sets out at 8 a.m. from sea-level, reaching his goal, a 2,000 metre peak, ten hours later. He camps at the summit and starts his return the next morning at 8 a.m. After a leisurely descent, he is back at sea-level ten hours later.
Is there some time of day at which his altitude is identical on both days? Try to answer this before reading on.
Continue reading ‘Brouwer’s Fixed-Point Theorem’