Category Archives: Logic

Numerical Separators

Posted on November 1, 2022 by Graham Shawcross

With a base 10 place value number system, Britain and America use the period as the radix symbol, to separate integers and decimals, and use a comma to separate groups of digits; for example, they would write 3,200,100.56 Other Europeans … Continue reading →

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Königsberg Bridges

Posted on March 7, 2016 by Graham Shawcross

Background The great Swiss mathematician Leonhard Euler, who had been asked by the Mayor of Danzig to provide a solution to the Königsberg Bridge problem, sent him this disdainful reply: “. . .  Thus you see, most noble Sir, how this type of … Continue reading →

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Baboon Counting Algorithms

Posted on October 2, 2015 by Graham Shawcross

Human counting can be thought of as a kind of condition controlled logic where counters increment a sequence of labels “one, two, three four…” until some condition is met. (Cantlon et al. 2015) The diagram below illustrates some, but not all, … Continue reading →

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Place Value

Posted on September 24, 2015 by Graham Shawcross

Laplace “The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance … Continue reading →

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Otto Koehler

Posted on June 23, 2015 by Graham Shawcross

Numerical Competence in Animals The German zoologist Otto Koehler (1889-1974) was the first scientist to convincingly demonstrate numerical competence in animals. The first part of this post is based upon a panel from Counting on neurons: the neurobiology of numerical competence” (Nieder … Continue reading →

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Even 3-day-old Chicks Do It

Posted on February 9, 2015 by Graham Shawcross

An interesting series of experiments has recently been reported in Science.  (Regani et al 2015). These strongly support the idea that many animals and humans represent numbers by a mental number line where smaller values are located on the left … Continue reading →

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Seriation

Posted on January 31, 2015 by Graham Shawcross

This is Archie, our then 3 year old grandson, after spontaneously reassembling a sawn up branch and being asked to pose with it for his delighted grandfather. Seriation is defined as “the forming of an orderly sequence” and was apparently first used in this sense in the 1650s. … Continue reading →

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Number Names and Words

Posted on September 23, 2014 by Graham Shawcross

Number Names George Lakoff has pointed out that we do not normally distinguish numbers from what might be more properly be called number names. (Lakoff 1989)  The most common number naming systems adopt base-10 and use ten single-digit number names, … Continue reading →

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What Counts

Posted on September 23, 2014 by Graham Shawcross

Numerical Abilities As well as being able to roughly compare continuous quantities, humans and animals of various sorts share a method of recognising small numbers of objects or sequences of events that is independent of language.  See Subitising and  Counting Ants Both … Continue reading →

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William Tutte’s Hidden Past

Posted on April 16, 2014 by Graham Shawcross

If William Tutte is remembered at all by architects, it is for his contribution to solving the problem of Squaring the Square . (Tutte 1958) A solution using Graph Theory and Kirchhoff’s Laws for electrical flow in wires that was subsequently used in Philip … Continue reading →

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