[math-fun] Golden Ratio discovered in uterus
I've just launched a maths blog for the Guardian Here's my first post: the research is serious, but any conclusions need to be taken with a medium to large dosage of salt. http://www.guardian.co.uk/science/alexs-adventures-in-numberland/2012/aug/14... alex
You might want to check out Prof John D Barrow's thoughts on the "golden ratio" in nature. He thinks that many/most of the "occurrences" fall into the same category as those images of Christ appearing on burnt toast -- people "see" the golden ratio because they are primed to look for it. He's measured many of these occurrences, and they don't hold up. His email is J.D.Barrow@damtp.cam.ac.uk. He recently did a very interesting set of videos for the Olympics about the "physics of sport", all of which are available on the web for free download. At 07:23 AM 8/14/2012, Alex Bellos wrote:
I've just launched a maths blog for the Guardian
Here's my first post: the research is serious, but any conclusions need to be taken with a medium to large dosage of salt.
http://www.guardian.co.uk/science/alexs-adventures-in-numberland/2012/aug/14...
alex
The best way to 'test' that a number actually is equal to phi is by drawing a Fibonacci sunflower. Altering the value of 1/phi by just 0.001 causes the sunflower's symmetry to break: Manipulate[ Graphics[Table[ Point[{Re[#], Im[#]} &[Sqrt[n] Exp[2 Pi I k n]]], {n, 1, 300}]], {{k, 0.618, "Reciprocal of phi"}, 0.610, 0.630, 0.001}] Sincerely, Adam P. Goucher
Hi Alex, Unfortunately, as a consequence of this being hosted by the Guardian, I expect all the folks who uncritically see the golden ratio everywhere will now be blathering about golden uteri. I've started making a series of math videos and here's one rebuttal to the golden ratio cult: http://www.youtube.com/watch?v=_gxC8OjoQkQ As to the image on that page, I hope you don't mind if I interpret your use of the middle finger as an editorial comment. I feel it's misleading to show precise metal calipers and print 1.618, as if finger measurements were precise enough to support four significant digits. George http://georgehart.com/ On 8/14/2012 10:23 AM, Alex Bellos wrote:
I've just launched a maths blog for the Guardian
Here's my first post: the research is serious, but any conclusions need to be taken with a medium to large dosage of salt.
http://www.guardian.co.uk/science/alexs-adventures-in-numberland/2012/aug/14...
alex _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
I don't know about you, but I have five significant digits on each hand. On 2012-08-14 16:22, George Hart wrote:
Hi Alex,
Unfortunately, as a consequence of this being hosted by the Guardian, I expect all the folks who uncritically see the golden ratio everywhere will now be blathering about golden uteri. I've started making a series of math videos and here's one rebuttal to the golden ratio cult:
http://www.youtube.com/watch?v=_gxC8OjoQkQ
As to the image on that page, I hope you don't mind if I interpret your use of the middle finger as an editorial comment. I feel it's misleading to show precise metal calipers and print 1.618, as if finger measurements were precise enough to support four significant digits.
George http://georgehart.com/
On 8/14/2012 10:23 AM, Alex Bellos wrote:
I've just launched a maths blog for the Guardian
Here's my first post: the research is serious, but any conclusions need to be taken with a medium to large dosage of salt.
http://www.guardian.co.uk/science/alexs-adventures-in-numberland/2012/aug/14...
alex _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Surprisingly the ratio 1:1 tends to appear a lot.... On 14 Aug 2012, at 21:29, Mike Speciner wrote:
I don't know about you, but I have five significant digits on each hand.
On 2012-08-14 16:22, George Hart wrote:
Hi Alex,
Unfortunately, as a consequence of this being hosted by the Guardian, I expect all the folks who uncritically see the golden ratio everywhere will now be blathering about golden uteri. I've started making a series of math videos and here's one rebuttal to the golden ratio cult:
http://www.youtube.com/watch?v=_gxC8OjoQkQ
As to the image on that page, I hope you don't mind if I interpret your use of the middle finger as an editorial comment. I feel it's misleading to show precise metal calipers and print 1.618, as if finger measurements were precise enough to support four significant digits.
George http://georgehart.com/
On 8/14/2012 10:23 AM, Alex Bellos wrote:
I've just launched a maths blog for the Guardian
Here's my first post: the research is serious, but any conclusions need to be taken with a medium to large dosage of salt.
http://www.guardian.co.uk/science/alexs-adventures-in-numberland/2012/aug/14...
alex _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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The meaning and purpose of life is to give life purpose and meaning. The instigation of violence indicates a lack of spirituality.
Very nice! Now you could take your nautilus shell, make a mold, and manufacture ~160,000 copies & throw them into the ocean to be "found" by the Fibonacci cultists. There are some sea creatures that live in the shells left by dead nautiluses; perhaps they will find these homes more to their liking. On second thought, make the copies out of Fool's Gold. --- Perhaps you could 3D print a middle "finger" that has a large number of joints that approximates a Fibonacci spiral. At 01:22 PM 8/14/2012, George Hart wrote:
Hi Alex,
Unfortunately, as a consequence of this being hosted by the Guardian, I expect all the folks who uncritically see the golden ratio everywhere will now be blathering about golden uteri. I've started making a series of math videos and here's one rebuttal to the golden ratio cult:
http://www.youtube.com/watch?v=_gxC8OjoQkQ
As to the image on that page, I hope you don't mind if I interpret your use of the middle finger as an editorial comment. I feel it's misleading to show precise metal calipers and print 1.618, as if finger measurements were precise enough to support four significant digits.
George http://georgehart.com/
On 8/14/2012 10:23 AM, Alex Bellos wrote:
I've just launched a maths blog for the Guardian
Here's my first post: the research is serious, but any conclusions need to be taken with a medium to large dosage of salt.
http://www.guardian.co.uk/science/alexs-adventures-in-numberland/2012/aug/14...
alex
From 0:20 to 0:40 in his video, George shows a famous picture of the "golden spiral". But as many of you probably know (no doubt including George), this picture is bogus. Specifically, it conflates two different curves: a curve made up of quarter-circular arcs (which isn't a true spiral) and a curve made of true spiral arcs (which isn't tangent to the rectangles).
George doesn't discuss this in his video, since minor issues like this would distract from his main point. But still, I wish the video hadn't used the inaccurate picture. Yes, I'm being a bit picky. At times like this I am reminded of a motto I saw on a tee-shirt once: "I'm not pompous. I'm pedantic. There's a difference." :-) Jim On Tue, Aug 14, 2012 at 4:22 PM, George Hart <george@georgehart.com> wrote:
Hi Alex,
Unfortunately, as a consequence of this being hosted by the Guardian, I expect all the folks who uncritically see the golden ratio everywhere will now be blathering about golden uteri. I've started making a series of math videos and here's one rebuttal to the golden ratio cult:
http://www.youtube.com/watch?**v=_gxC8OjoQkQ<http://www.youtube.com/watch?v=_gxC8OjoQkQ>
As to the image on that page, I hope you don't mind if I interpret your use of the middle finger as an editorial comment. I feel it's misleading to show precise metal calipers and print 1.618, as if finger measurements were precise enough to support four significant digits.
George http://georgehart.com/
On 8/14/2012 10:23 AM, Alex Bellos wrote:
I've just launched a maths blog for the Guardian
Here's my first post: the research is serious, but any conclusions need to be taken with a medium to large dosage of salt.
http://www.guardian.co.uk/**science/alexs-adventures-in-** numberland/2012/aug/14/golden-**ratio-uterus<http://www.guardian.co.uk/science/alexs-adventures-in-numberland/2012/aug/14/golden-ratio-uterus>
alex ______________________________**_________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/**cgi-bin/mailman/listinfo/math-**fun<http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun>
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Hi Jim, Yes, there is more to be said, but I had to use that curve (consisting of quarter circles) because the point I wanted to make is specifically about that curve. The curve is only a ruler-and-compass approximation to an exponential spiral and the differences may be important in some contexts. But it is a much larger error to claim that curve is a model for the nautilus, and that big error is continuously being copied and re-published. E.g., they both appear on the cover of Livio's popular book The Golden Ratio, and inside, his text about them confusingly does not clarify the difference. As to the curve not being a "true spiral" I don't know of a standard definition of "true spiral" that includes the many types of spiral that people often study, but doesn't include that assemblage of quarter circles. As far as I am concerned, it is a "true spiral" that happens not to be C2 continuous. George http://georgehart.com/ On 8/15/2012 11:02 PM, James Propp wrote:
From 0:20 to 0:40 in his video, George shows a famous picture of the "golden spiral". But as many of you probably know (no doubt including George), this picture is bogus. Specifically, it conflates two different curves: a curve made up of quarter-circular arcs (which isn't a true spiral) and a curve made of true spiral arcs (which isn't tangent to the rectangles).
George doesn't discuss this in his video, since minor issues like this would distract from his main point. But still, I wish the video hadn't used the inaccurate picture.
Yes, I'm being a bit picky. At times like this I am reminded of a motto I saw on a tee-shirt once: "I'm not pompous. I'm pedantic. There's a difference." :-)
Jim
On Tue, Aug 14, 2012 at 4:22 PM, George Hart <george@georgehart.com> wrote:
Hi Alex,
Unfortunately, as a consequence of this being hosted by the Guardian, I expect all the folks who uncritically see the golden ratio everywhere will now be blathering about golden uteri. I've started making a series of math videos and here's one rebuttal to the golden ratio cult:
http://www.youtube.com/watch?**v=_gxC8OjoQkQ<http://www.youtube.com/watch?v=_gxC8OjoQkQ>
As to the image on that page, I hope you don't mind if I interpret your use of the middle finger as an editorial comment. I feel it's misleading to show precise metal calipers and print 1.618, as if finger measurements were precise enough to support four significant digits.
George http://georgehart.com/
On 8/14/2012 10:23 AM, Alex Bellos wrote:
I've just launched a maths blog for the Guardian
Here's my first post: the research is serious, but any conclusions need to be taken with a medium to large dosage of salt.
http://www.guardian.co.uk/**science/alexs-adventures-in-** numberland/2012/aug/14/golden-**ratio-uterus<http://www.guardian.co.uk/science/alexs-adventures-in-numberland/2012/aug/14/golden-ratio-uterus>
alex ______________________________**_________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/**cgi-bin/mailman/listinfo/math-**fun<http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun>
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As many mathematicians have pointed out, the Parthenon -- perhaps the most commonly cited manmade example of the golden ratio -- isn't even close. Has anyone in modern times ever performed the experiment that asks subjects to adjust the ratio of a rectangle's sides (maybe via computer graphics) until it is most aesthetically pleasing? I'd be very curious to learn the results of such an experiment. --Dan
I think this is the latest academic research into into the aesthetic pleasingness of rectangles. McManus 2010 http://www.ucl.ac.uk/psychlangsci/staff/cehp-staff/i_mcmanus Conclusion is that the golden rectangle is not the world's favourite rectangle, but that people do have strong preferences, which merit study. alex On 1 Sep 2012, at 18:13, Dan Asimov wrote:
As many mathematicians have pointed out, the Parthenon -- perhaps the most commonly cited manmade example of the golden ratio -- isn't even close.
Has anyone in modern times ever performed the experiment that asks subjects to adjust the ratio of a rectangle's sides (maybe via computer graphics) until it is most aesthetically pleasing?
I'd be very curious to learn the results of such an experiment.
--Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Perhaps this is the web page you meant to post a link to? http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CCIQFjAA... --Dan On 2012-09-01, at 10:21 AM, Alex Bellos wrote:
I think this is the latest academic research into into the aesthetic pleasingness of rectangles.
McManus 2010
http://www.ucl.ac.uk/psychlangsci/staff/cehp-staff/i_mcmanus
Conclusion is that the golden rectangle is not the world's favourite rectangle, but that people do have strong preferences, which merit study.
participants (8)
-
Adam P. Goucher -
Alex Bellos -
Dan Asimov -
Dave Makin -
George Hart -
Henry Baker -
James Propp -
Mike Speciner