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 Graham’s Maze Game: TestFlight Help
 Königsberg Bridges
 Weber’s Law
 Baboon Counting Algorithms
 Place Value
 Jevons’es Data
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 Counting Cormorants
 Otto Koehler
 Primed Number Lines
 Even 3dayold Chicks Do It
 Seriation
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 Number Names and Words
 What Counts
 Counting Ants
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 William Tutte’s Hidden Past
 Missing Pullover Found
 Spatial Representation of Number
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 Subitising
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Tag Archives: Logic
Königsberg Bridges
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
Posted in Architecture, Enumeration, Geometry, Logic
Tagged Architecture, Design, Enumeration, Geometry, Logic
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Baboon Counting Algorithms
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
Posted in Architecture, Brain Physiology, Enumeration, Logic
Tagged Architecture, Brain Physiology, Enumeration, Logic
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Place Value
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
Posted in Architecture, Classification, Enumeration, Logic
Tagged Architecture, Classification, Enumeration, Logic
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Jevons’es Data
In 1871 the early economist and logician William Stanley Jevons published an article in Nature “The Power of Numerical Discrimination” (Jevons 1871) According to Jevons, Sir William Hamilton had clearly stated the problem: “Assuming that the mind is not limited to … Continue reading
Posted in Architecture, Brain Physiology, Enumeration, Randomness
Tagged Brain Physiology, Enumeration, Logic, Randomness
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Otto Koehler
Numerical Competence in Animals The German zoologist Otto Koehler (18891974) 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
Posted in Architecture, Brain Physiology, Design Methods, Enumeration, Logic
Tagged Architecture, Brain Physiology, Design Methods, Enumeration, Logic
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Even 3dayold Chicks Do It
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
Posted in Architecture, Brain Physiology, Enumeration, Logic
Tagged Architecture, Brain Physiology, Enumeration, Logic
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Seriation
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
Posted in Architecture, Classification, Enumeration, Logic
Tagged Classification, Enumeration, Logic
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Number Names and Words
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 base10 and use ten singledigit number names, … Continue reading
Posted in Architecture, Classification, Enumeration, Logic
Tagged Architecture, Classification, Enumeration, Logic
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What Counts
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
Posted in Architecture, Brain Physiology, Embodiment, Enumeration, Logic
Tagged Architecture, Brain Physiology, Embodiment, Enumeration, Logic
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William Tutte’s Hidden Past
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
Posted in Architecture, Design Methods, Geometry, Logic, Tiling
Tagged Aperiodic Tiling, Architecture, Design Methods, Geometry, Logic, Tiling, Turing Machines
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