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June 5th, 2018, 11:28 PM   #11
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Thanks Mr.Fly, you're the only one who agrees with me...
No.

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June 6th, 2018, 03:36 AM   #12
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June 6th, 2018, 04:20 AM   #13
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This question was an example provided by Vladimir Arnold in his "A mathematical trivium II". Both trivium's I and II are well worth the read if you have time (only a couple of pages). After stating this problem he goes on to say:

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The "correct" answer is area and a square inch. Justification: the degree is the smallest unit of measurement of angle, and the square inch that of area, but the minute can be further divided, for example into seconds. For us this answer is of course preposterous. But American students whom I tested almost always gave precisely this "correct" answer. For a long time I could not understand why this was until a well-known American physicist explained to me his (correct) answer: "The point is that I correctly imagined the degree of stupidity of the person who set these questions".
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June 6th, 2018, 05:20 AM   #14
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June 6th, 2018, 11:39 AM   #15
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a minute can be used as a periodic measure of time like degrees can be used as a periodic measure of angle
In what way is time (typically represented as the nonnegative real numbers) periodic?

You can't mean that after 60 minutes I go back to 1 hour and 1 minute. Because after four quarts of milk you get a gallon and then another quart is one gallon and one quart. I don't see your reasoning.
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June 6th, 2018, 02:02 PM   #16
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In what way is time (typically represented as the nonnegative real numbers) periodic?

You can't mean that after 60 minutes I go back to 1 hour and 1 minute. Because after four quarts of milk you get a gallon and then another quart is one gallon and one quart. I don't see your reasoning.
I mean exactly that. When we tell time we don't generally refer to minutes outside the range of [0,60). Sure hours, days, months, years, tick up, but we generally keep minutes in the range of 0-59. Sure it's possible to refer to lengths of time as cumulative amounts of minutes, but we generally don't.

Your point about quarts and gallons is valid. But I'm going to state w/o justification that minutes are more naturally periodic than quarts. If only that the minute hand traces a circle and there is no real equivalent for quarts. We don't have a gallon clock.
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June 6th, 2018, 04:16 PM   #17
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I mean exactly that. When we tell time we don't generally refer to minutes outside the range of [0,60). Sure hours, days, months, years, tick up, but we generally keep minutes in the range of 0-59. Sure it's possible to refer to lengths of time as cumulative amounts of minutes, but we generally don't.
An angle of 361 degress is the same angle as an angle of 1 degree. A time interval of 61 minutes is not the same time interval as 1 minute.
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June 6th, 2018, 04:54 PM   #18
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An angle of 361 degress is the same angle as an angle of 1 degree. A time interval of 61 minutes is not the same time interval as 1 minute.
no... but it is equivalent to 1 hr 1 minute which is at least as common a way of expressing 61 minutes as saying 61 minutes.

My oven won't let me program in 61 minutes, I have to program in 1 hr 1 minute.

Basically it comes down to your interpretation of the coordinate system for time. Do you like a circular one, like clocks have used for millennia.

Or do you like a linear one, like folks that work with relativity prefer.
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June 6th, 2018, 07:27 PM   #19
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But I'm going to state w/o justification that minutes are more naturally periodic than quarts. If only that the minute hand traces a circle and there is no real equivalent for quarts. We don't have a gallon clock.
A degree is 60 minutes of arc, that is the amount that the earth rotates in 1 hour on it's own axis with respect to the sun. A truly periodic measure.

Edit: pretty sure that I've got something well and truly messed up here, but it's too late to work out what, but there aren't 360 hours in a day.

Last edited by v8archie; June 6th, 2018 at 07:29 PM.
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