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Re: More on precision semantics

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Tue, 26 Jul 2011 09:31:10 +0200

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 ```We have all been exposed to decreasing precision. Think about those decimal rounding excercises one did in elementary school... 1.02 --> 1.0 --> 1 1.0236 --> 1.024 --> 1.02 --> 1.0 --> 1 1.09 --> 1.1 --> 1 1.59 --> 1.6 --> 2 Compare the number 1 that was rounded to the nearest whole number with 1.06 (a number clearly expressed to 1/100s place)? They are, of course, "equivalent". In complete sentences "The number 1 and 1.06 rounded to the nearest whole number are equivalent". What are we comparing when we compare 1994-03-02 with 1999-12-12? We are comparing them to the day within the International standard calandar year. Two events whose date value is reported as "1994-03-02" are said to share the same day, namely "1994-03-02". We can't say they occured at the same instant in time, only the same day. Two events too that are reported as occuring at 12:30 on the same day are not said to have occured at the same instant, only the name minute on the same day (date with minute precision). With time this continues all the way down to our most precise measure. Here we can speak of the same CGPM time (measured in SI seconds) but not the same instant--- unless, of course, we define the semantics of "same instant" to be as equivalent decimal seconds rounded to the tenth decimal place (we have much more precise measures of time than the standard based upon Caesium 133 but its that which is "standard"). When I compare now "1994" with "1994-03-02" what am I doing? I am-- not unlike with 1.06 and 1 above-- comparing at a decreased precision. "1994" and "1994-03-02" share the same year. Just as I could not talk about the decimal places to the right of a number given to me rounded to the nearest whole number, I can't talk about the month, day or time of a date "rounded" to year.   -- Edward C. Zimmermann, NONMONOTONIC LAB http://www.nonmonotonic.net Umsatz-St-ID: DE130492967 ```