And what kind of light would that be? Lazy…? :grin:

Andymonk,

In the interest of being open-minded, I’ll ask this question despite my misgivings:

Why, exactly, do you think this (or any) design is something other than a pretty picture? You said something vague and mystical about the pattern of creation or some such, but as Occam pointed out, that doesn’t actually mean anything, at least without further explication to show those of us without any special insight what you’re talking about. What are we supposed to learn from this picture.

mckenzievmd - 11 June 2007 04:08 PM

What are we supposed to learn from this picture.

There is actually one very interesting thing about this pattern. And that is “60-degree angle”. 60-degree angle is the only measurement you can find with a piece of rope (and two hands) without any calculations. Once again, draw a circle and a second one (same size) with its centre at the edge of the first one. Join the middle of the first circle and the cross point of the two circles and the two centres of the circles and you’ll find it’s exactly 60 degrees. This is very useful indeed. This way you can find a perfect 90-degree angle in about ten seconds…and all you need is a piece of rope! I have thought about this a long time ago and came to a conclusion (I might be wrong) that this is the reason why circle is divided into 360 degrees. Find 60, multiply it by 6 and you get 360. 360 is the smallest possible number of degrees in circle that will enable you to find a perfect 90-degree angle on top of the Mount Everest…if you ever needed to…

Wanted a mystery, Andymonk? Here you have one!

George - 11 June 2007 04:28 PM

360 is the smallest possible number of degrees in circle that will enable you to find a perfect 90-degree angle on top of the Mount Everest…if you ever needed to… !

I am wrong on this one. If we divide the circle into 60 degrees for example (instead of 360) we could also find a perfect right angle using the same method. (Only that it would now be 15-degree angel and not a 90-degree one.) It wouldn’t work, though, if we were to divide the circle into 100 degrees for example.

Does anybody know why a circle is divided into 360 degrees?

I think it’s the Babylonians’ fault. Something about theere being ~360 days in the year and how far the sun moves each day. Something anyway with a nonsensical historical root that’s too entrenched to change now.

There are all sorts of numeric artifacts that when we, as human beings focused on pattern recognition see, say, “Wow, isn’t that weird?”  No, it’s just part of the interwoven structure of mathematics.  For example, when I was in elementary school, I was fascinated when I saw that 37 times any multiple of three from 3 to 27 gave a number that was a three numeral repetition of that multiple.  For example, 37 X 18 is 666.  I played with it for a while until I realized it was pretty much to be expected, and not nearly as fascinating as I thought it was.  Thank goodness I had never been indoctrinated with theism or I would have seen some nefarious import to that 666.   

Occam

I once read the “reason” why number seven is considered a lucky number: when the aliens came from the outer space, after a long journey they encountered the Solar system and our planet was the seventh one counting from Pluto.

But the 360 degrees in a circle is not quit the same thing. It doesn’t have to be 360. It can be any number as long as it’s divisible by 6. I just would like to know why 360. Why not 120 or 720? Would 120 degrees in a circle be too big and 720 too small? Maybe Brennen is right: it could have something to do with the 365 days in a year….

George, that’s a beautiful example of people defining a cause based on the effect.  However, did the aliens miss the recently discovered body farther out than Pluto and larger than it?  And, how did they happen to define planets the way astronomers did recently, but not the way they are doing now of deciding Pluto (and the farther out body) are no longer planets but planetoids or sub-planets or whatever nomenclature they’ve come up with?

Defining the number of segments into which to devide a circle seems to be based on ease of use.  I’m getting frustrated because I can’t remember -  there was some unit (radian?) that was used for some purpose and was 57.3 degrees as I recall.  In other words, 360 degrees isn’t sacrosanct.

Occam

Occam

For once I have reason to be thankful for being “numerically challenged.” I never was at risk of seeing the hand of God in the patterns of mathematics because I’m far too stupid to see the patterns. For that reason, I’m probably wrong here, but I always thought of mathematics as primarily descriptive, representative of reality but not “embedded” in the very fabric of reality. Sure, as a good representation it has to have some true correlation to the real thing. But as Occam says, there aren’t really 360 degrees in a circle, it’s just one of probably many effective ways to represent a circle. If we had 12 digits, we’d do our math in base 12 (which I still don’t really understand, despite the cute little educational cartoon Schoolhouse Rock had about it when I was a kid). The problem is when we mistake our representations for the reality itself. We think our metaphors for describing the universe are the universe, and God is born, or we think a pretty picture contains some pattern fundamental to reality, or we think math IS reality instead of just our way of representing it.

And now I’ll sit back and watch the smarter folks demolish the ideas in the above rant. 

mckenzievmd - 11 June 2007 09:52 PM

If we had 12 digits, we’d do our math in base 12

This is exactly the reason why I wanted to find out why there are 360 degrees in a circle and not 100. Not to repeat myself, but it wouldn’t work with 100 degrees. It’s interesting that time is also measured in some form of a system based on Imperial units. Why is this? Is it because a second is very close to one palpitation of our heart? And there are also twelve notes in an octave scale on a piano for example: seven white ones and five black ones. Another interesting one is carbon: “The relative isotopic mass is the relative mass of the isotope, scaled with carbon-12 as exactly 12.” (Wikipedia) I know I am just cherry picking, but numbers 12, 24, ...60, etc., have seemed to have served us well.

George - 11 June 2007 04:28 PM

There is actually one very interesting thing about this pattern. And that is “60-degree angle”. 60-degree angle is the only measurement you can find with a piece of rope (and two hands) without any calculations. Once again, draw a circle and a second one (same size) with its centre at the edge of the first one. Join the middle of the first circle and the cross point of the two circles and the two centres of the circles and you’ll find it’s exactly 60 degrees. This is very useful indeed. This way you can find a perfect 90-degree angle in about ten seconds…and all you need is a piece of rope!

That is actually a very cool result. Sometimes I think it would be really neat to have a math class with this sort of ‘ancient’ everyday knowledge.

George, sure 100 degrees would work.  It’s just that the calculations would be miserable.  Sort of like, I loved it when we had an 8% sales tax but hated it when they changed it to 8.25%.  I could add all the taxable items then multiply by 8, divide by 100 and add it to the total while I was in the check-out line.  It has to be an appreciably longer line now before I can do that with 8.25. 

Humans have been using math since before recorded history, and they’ve found and used those relationships that allowed them to operate more easily and effectively.

Numbers which are made up of products of simpler numbers are extremely easy to use because we can break them down into their factors.  12=2 X 2 X 3,  60= 2 X 2 X 3 X 5. 

And there’s nothing special about one of the isotopes of carbon containing six protons and six neutrons, that is, having an atomic weight of twelve.  It’s just the same as one of the isotopes of of oxygen has an atomic weight of sixteen.  Each of the elements are identified by the number of protons they have in their nucleus.  It starts with hydrogen having one proton and ends (naturally occuring ones) with uranium having 92 protons. 

One of the things that micturates me off is when people get carried away with ideas based on observations, but with less knowledge of the underlying functioning.  A great example, is “Stupid” whoops, sorrry, “Intelligent Design”.  If one doesn’t understand statistics and probability and can’t conceive of large numbers, both of individuals and of time, and doesn’t know about how mutations work, one can’t see that evolution is quite reasonable.

Another problem is the idea that we have to have answers for all our questions.  “How did the universe come into being?”  Saying, “That’s a good question.  Let’s gather all our data and have our most brilliant scientists study the bejabers out of it (like Einstein, Hawking, et al) and be satisfied that we don’t know the answer yet, is a hell of a lot more rational than saying, “God did it” without any empirical evidence to back that statement up.

Rant over.  (sorry for the multiple lines, Brennen, especially because you said it much more succinctly than I did.)

Occam

“micturates me off”
 

Occam - 12 June 2007 12:06 PM

George, sure 100 degrees would work.  It’s just that the calculations would be miserable.

Agreed. A 60-degree angle would read as 16.67 degrees in a 100-degree circle. Again, I wonder if this (the 60-degree angle) was responsible for creating the 360 degrees in a circle. I am not looking for a mystery, Occam, I am just being curious.

Re. the carbon, I heard that carbon is “special” precisely because its weight is 12; all other elements are measured using carbon’s atomic weight ( ). But you’re the chemist: if you say it ain’t special then it ain’t special…

The most common isotope of carbon does have an atomic weight of only a tiny hair over twelve (the electrons contribute a bit) but the actual atomic weight is 12.011 because of the carbon thirteen (an extra neutron), and usually a bit of carbon 14 (the ratio of that to the carbon 12 is what they use for radio-carbon dating).  Similarly, hydrogen has only one proton and one electron, but its atomic weight is 1.008 because of the very small amount of deuterium (it has a neutron) and trace amounts of tritium (with two neutrons). 

Occam

(Thanks, Brennen.  The program screwed up and lost my post, but using your suggestion, I had a backup copy.)