Comments on: A Common Upper Ontology for Advanced Placement tests http://haleyai.com/wordpress/2008/04/18/a-common-upper-ontology-for-advanced-placement-tests/ systems that know and understand and think and learn Thu, 28 Aug 2008 08:26:53 +0000 http://wordpress.org/?v=2.3.1 By: szisk http://haleyai.com/wordpress/2008/04/18/a-common-upper-ontology-for-advanced-placement-tests/#comment-282 szisk Mon, 07 Jul 2008 17:24:15 +0000 http://haleyai.com/wordpress/2008/04/18/a-common-upper-ontology-for-advanced-placement-tests/#comment-282 A few errors and quibbles, plus one fundamental disagreement: 1.) One second of arc is 1/(360*60*60)th = 1/1,296,000 of a circle, not 1/3,600. 2.) Ratio vs fraction - you assume fractions allow only integers for numerators or denominators but this is true only in the simplest maths and not at all in physics or chemistry. The point of SI (or other unit systems) is that everything has an explicit unit or an explicit lack of a unit, so almost no calculations are done against bare numbers. Your distinction between fractions and ratios here does not seem to serve your argument. However, I certainly agree that a ratio can be between any two related quantities, whether the result has an explicit or implicit unit or not. Finally, 3.) I have a basic disagreement with your statement: "... the physicists and chemists who defined the the International System of Units overlooked [angles]." SI was intended to define units and relationships unambiguously to replace the hodge-podge of units and measurements that existed in different locations prior to the French Revolution. The radian was an SI supplemental dimensionless unit until 1995, after which it was relegated to a derived unit. Same goes for the steridian. A few errors and quibbles, plus one fundamental disagreement:
1.) One second of arc is 1/(360*60*60)th = 1/1,296,000 of a circle, not 1/3,600.
2.) Ratio vs fraction - you assume fractions allow only integers for numerators or denominators but this is true only in the simplest maths and not at all in physics or chemistry. The point of SI (or other unit systems) is that everything has an explicit unit or an explicit lack of a unit, so almost no calculations are done against bare numbers. Your distinction between fractions and ratios here does not seem to serve your argument. However, I certainly agree that a ratio can be between any two related quantities, whether the result has an explicit or implicit unit or not.

Finally,

3.) I have a basic disagreement with your statement: “… the physicists and chemists who defined the the International System of Units overlooked [angles].” SI was intended to define units and relationships unambiguously to replace the hodge-podge of units and measurements that existed in different locations prior to the French Revolution. The radian was an SI supplemental dimensionless unit until 1995, after which it was relegated to a derived unit. Same goes for the steridian.

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