The Art of Tetman Callis

“People are impressed with numbers, but the mere existence of data that can be quantified and manipulated is no guarantee of valid results.” – John J. Lentini, Scientific Protocols for Fire Investigation, Second Edition

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“An algorithm is defined by a sequence of steps and instructions that can be applied to data. Algorithms generate categories for filtering information, operate on data, look for patterns and relationships, or generally assist in the analysis of information. The steps taken by an algorithm are informed by the author’s knowledge, motives, biases, and desired […]

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“Never try to put too much into any single piece.  There is always a point beyond which it cannot be improved, and further attempts to improve it will in fact destroy it.” – Douglas R. Hofstadter, Gödel, Escher, Bach

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“A problem is determinate if it has a definite number of solutions, indeterminate if it has an indefinite number of solutions, and impossible if it has no solution.” – G. A. Wentworth, Plane Geometry (emphases in original)

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“In the Valley of Youth, through which all wayfarers must pass on their journey from the Land of Mystery to the Land of the Infinite, there is a village where the pilgrim rests and indulges in various excursions for which the valley is celebrated.  There also gather many guides in this spot, some of whom […]

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“Just as a being may be imagined as having only two dimensions, and living always on a plane surface (in a space of two dimensions), and having no conception of a space of three dimensions, so we may think of ourselves as living in a space of three dimensions but surrounded by a space of […]

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“An interesting application of the theorem relating to similar triangles is this: Extend your arm and point to a distant object, closing your left eye and sighting across your finger tip with your right eye.  Now keep the finger in the same position and sight with your left eye.  The finger will then seem to […]

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“The natural temptation in the nervous atmosphere of America is to listen to the voice of the mob and to proceed at once to lynch Euclid and every one who stands for that for which the ‘Elements’ has stood these two thousand years.  This is what some who wish to be considered as educators tend […]

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“When the time comes that knowledge will not be sought for its own sake, and men will not press forward simply in a desire of achievement, without hope of gain, to extend the limits of human knowledge and information, then, indeed, will the race enter upon its decadence.” — Charles Evans Hughes (quoted by David […]

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“In the present utilitarian age one frequently hears the question asked, ‘What is the use of it all?’ as if every noble deed was not its own justification.  As if every action which makes for self-denial, for hardihood, and for endurance was not in itself a most precious lesson to mankind.  That people can be […]

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“One of the essential properties of intelligence is flexibility.  What does it mean to be an expert at something?  What makes someone an expert is her ability to respond to a completely novel situation—to solve original problems, for example.  Expertise does not only involve having command of a huge amount of factual knowledge—it does not […]

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“Gödel’s incompleteness theorem is one of the great intellectual accomplishments of the twentieth century.  Its implications are so far reaching that it is difficult to overestimate them.  Gödel’s result puts intrinsic limitations on the reach of deductive systems; that is, it shows that given any (sufficiently complex) deductive system, there are results that are beyond […]

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“Mathematics is not a body of facts arranged and justified by a stringent logical structure.  To give a dynamic metaphor that stems from the related field of fluid flow, it is like a turbulent river.  The flow of the water is extremely complex, but every now and again you see the appearance of stable structures, […]

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