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Scott Horstman
Vendor- Backyard Observatories
Reged: 03/11/04
Posts: 8074
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Quote:
Have you considered that some societies may have adopted the number we call pi as 1.
How could you order 1 Big Mac at the drive through? Wouldn't the kid have to give you 3.14159265 of them? Man to think how bad they screw the orders up NOW! 
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matt
Vendor (Scopemania)
Reged: 07/28/03
Posts: 10362
Loc: Chaville, France
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Quote:
BTW, the degree is not exactly arbitrary. I understand that it size was chosen by the Babylonians because they did not like fractions. 360 is divisible by 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 & 360. This unit was natural to them.
It's certainly convenient, but arbitrary nonetheless, just like the 24 hour day and the 60 minute hour.
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astrotrf
professor emeritus
Reged: 09/30/07
Posts: 709
Loc: Rodeo, NM
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Quote:
Have you considered that some societies may have adopted the number we call pi as 1. They may then consider the radius of a circle as an irrational number. It is the ratio between the two that I assert that they will know.
I don't really see this as being likely. Firstly, a society will invent counting long before they realize that the ratio of the diameter to the circumference of a circle is a constant. Secondly, a diameter, being straight, is an easy thing to measure, and will be determined first before any circumference is measured. Thirdly, adopting pi as one would make counting the number of berries in your hand a quite difficult process. 
It would sure make first-grade arithmetic a trying course! 
Quote:
BTW, the degree is not exactly arbitrary. I understand that it size was chosen by the Babylonians because they did not like fractions. 360 is divisible by 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 & 360. This unit was natural to them.
Well, it *is* an arbitrary choice, but it is NOT a haphazard one.
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Terry (astrotrf)
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HiggsBoson
Pooh-Bah
Reged: 02/21/07
Posts: 1118
Loc: Kal-li-fornia
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Quote:
Quote:
BTW, the degree is not exactly arbitrary. I understand that it size was chosen by the Babylonians because they did not like fractions. 360 is divisible by 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 & 360. This unit was natural to them.
It's certainly convenient, but arbitrary nonetheless, just like the 24 hour day and the 60 minute hour.
My point was to one person a choice is arbitrary and to another it makes since. I thought that the 360 degree choice was silly until I learned of those who made the choice. What I am suggesting is that we are in a poor position to understand the choices of an ET society which we currently can not imagine. The Babylonians liked to be able to divide things without the use of fractions. Who can blame them? Their choice reflected their concerns at that time. They probably thought it was brilliant.
The degree can be divided in to minutia. They choose 60 minutia per degree. They choose to sub divide minutia again forming the second minutia of a degree. Hence, minutes and seconds. These are different from arbitrary choices.
I do not know why there are 24 hours in a day but I am confident that it made since to someone at the time. What I am suggesting is that it may be difficult for us to understand the choices of a society with which we have little in common. This dose not make their choices arbitrary.
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Michael
ATM: 6" F/9 Newtonian Travel Scope
ATM: 12.5" F/4.5 Real Soon Now...
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HiggsBoson
Pooh-Bah
Reged: 02/21/07
Posts: 1118
Loc: Kal-li-fornia
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Quote:
Quote:
Have you considered that some societies may have adopted the number we call pi as 1. They may then consider the radius of a circle as an irrational number. It is the ratio between the two that I assert that they will know.
I don't really see this as being likely. Firstly, a society will invent counting long before they realize that the ratio of the diameter to the circumference of a circle is a constant. Secondly, a diameter, being straight, is an easy thing to measure, and will be determined first before any circumference is measured. Thirdly, adopting pi as one would make counting the number of berries in your hand a quite difficult process.
It would sure make first-grade arithmetic a trying course!
Not if you were born into a world where the circle is considered more important than a line. Recall that during the development of Astronomy people were obsessed with the perfection of the sphere! So much so that they attempted to force all orbits to be constrained to the surface of spheres. This made since to them and it influenced what they felt was reasonable.
Quote:
Quote:
BTW, the degree is not exactly arbitrary. I understand that it size was chosen by the Babylonians because they did not like fractions. 360 is divisible by 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 & 360. This unit was natural to them.
Well, it *is* an arbitrary choice, but it is NOT a haphazard one.
Perhaps we have different definitions of the word arbitrary.
If n + infinity = infinity then in an example using real numbers the choice of n is arbitrary. Any choice of n is a useful as any other. A choice that is based upon a preference is not arbitrary to me.
In most movie theaters a ticket cost a fixed amount for all choices of seats. To the theater owner your choice is arbitrary. To you it is not. Some people are shorter and choose to sit near an outside aisle so that they can view the screen across the aisle. This would prevent the case where a tall person entering late sits in front of you and blocks your view of the screen. Others hate this choice because people walking in and out will temporarily block their view. Others will want to sit 1/3 of the way between the screen and the projector because this best duplicates the field of view of the photographer. Still others will want to sit in the back because they want the screen to fit into a smaller field of view. To the viewer these choices are not arbitrary even if we do not understand why the choices were made.
For me a choice is not arbitrary if it matters to the person making the choice.
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Michael
ATM: 6" F/9 Newtonian Travel Scope
ATM: 12.5" F/4.5 Real Soon Now...
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astrotrf
professor emeritus
Reged: 09/30/07
Posts: 709
Loc: Rodeo, NM
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Quote:
Perhaps we have different definitions of the word arbitrary.
Yes, there are several different connotational meanings of the word. I think, also, that we're looking at the choice from different ends.
I'm looking at it from the a priori end. If someone asked me how to divide a circle, I'd say "Well, the choice is completely arbitrary, in that anything you choose will work. But if you pick 360, it has these nice properties."
I believe you're looking at it from the fait accompli end. You'd say, "360 has these nice properties, so that was deliberately chosen as the way to divide a circle rather than something arbitrary."
To a mathematician, arbitrary means "chosen at random" (and that's the sense in which you are using the word). A more layman-like definition would be "chosen subject only to judgment".
I think we would both agree that the choice of how to divide a circle was unrestricted, and was made based on the desirable arithmetic properties of the number 360.
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Terry (astrotrf)
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matt
Vendor (Scopemania)
Reged: 07/28/03
Posts: 10362
Loc: Chaville, France
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"arbitrary" does not mean "bad", although people often use the word "arbitrary" in the "dictatorial" sense, as in "coach made the arbitrary choice of moving Bubba to tight end". They mean it as in "coach is a clueless dictator". In fact, good or bad, the choice IS arbitrary, since it is a choice. Coach puts Bubba at TE because it fits his schemes and allows Timmy to play fullback. The guy who divided the day into 24 hours and the circle into 360 ° did it because it was convenient for him.
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Matt
CI700 mount with various scopes on top.
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HiggsBoson
Pooh-Bah
Reged: 02/21/07
Posts: 1118
Loc: Kal-li-fornia
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Yes to all. I think we agree.
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Michael
ATM: 6" F/9 Newtonian Travel Scope
ATM: 12.5" F/4.5 Real Soon Now...
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