Philosophy 101

 
Under New Management
 
Avatar
 
 
Under New Management
Total Posts:  56
Joined  05-10-2007
 
 
 
29 March 2008 13:40
 

I’m taking a philosophy class (mostly inspired by this forum) and my professor has posted a lecture that I believe shows a gross lack of understanding of the subject he is attempting to teach. There are many errors, like it doesn’t seem that he can even add.  Example: 1 – 1 – 2 – 3 – 5 – 8 – 13 – 21 – 34 – 57 – 91….etc.  What this?  21 + 34 = 57?  There are pictures but I am only submitting the text

Is someone able to read this and tell if I am correct. 


The Golden Ratio (Phi) and
the Construction of the Natural World

  Everyone who gets through high school has heard of pi (?), a number whose function Pythagoras discovered:  it represents the ratio between the radius of a circle and its area.  Very few people, however, have ever heard of pi’s more powerful brother Phi (?) , a number that explains almost everything else in the cosmos.  Like pi, it is an irrational number (the decimal places never end) and like pi it was discovered by Pythagoras.  He started out with a simple mathematical phenomenon and ended up believing he had unlocked the secret of the universe:

  Start with the first number—1—and then add to it the previous number—0—.  The result is a new 1.  Now add the previous number—the old 1—and you get 2.  Add the previous number—the new 1—and you get three.  Add the previous number—2—and you get 5.  You can keep doing this until the cows come home (that is English for ad infinitum).  The series of numbers generated this way looks like this at the beginning:

1 – 1 – 2 – 3 – 5 – 8 – 13 – 21 – 34 – 57 – 91….etc.

  The remarkable properties that Pythagoras discovered in this series and that we will start looking at shortly, were lost when the barbarians overturned the Roman Empire and destroyed ancient civilization in the fifth and sixth centuries A.D.  They were rediscovered in the middle ages by Leonardo of Pisa, who was nicknamed “Fibonacci” and that is the name by which the series is known today:  the Fibonacci series.  It is a name and an idea you should know.

  The Fibonacci series is more than just a simpleminded way to waste time.  Pythagoras noticed that these numbers are found all throughout nature:  the number of peas in a pod, the number of pigs in a litter, the number of eggs in a nest, the number pine needles in a bundle or petals on a daisy—all of these will tend to be one of the Fibonacci numbers.  There is a reason why you don’t see four-leafed clovers

The individual piece are arranged in sets of spirals that conform to the Fibonacci series.  And pineapples have 8 and 13 spirals of external “scales” on them.  It seems that Mother Nature speaks mathematics, and with a Fibonacci accent.


Fibonacci Numbers Generate Shapes

  Another remarkable property of this series of numbers is that the ration between any two adjacent numbers is always the same.  Take any two of them side by side and the small one will always be .618034….. the size of the larger one.  This ratio is an irrational number like pi and Pythagoras named it phi .  You can pronounce it “fee” or “f-eye”.  Of course, early in the series the ratio is very rough.  1 : 2 for instance is .5 and 2 to 3 is .6666… but already by 5 : 8 we have .625.  The Phi ratio, .618034…to 1, also runs throughout nature in astonishing ways.

  For instance, if you build an oblong whose sides are Fibonacci numbers (like 3 x 5 or 8 x 13 or 21 x 34, etc.—in other words, any rectangle whose short side is .618034…. the length of the long side) you get a familiar looking shape: 

I will stop there.  When he says,  “the ration between any two adjacent numbers is always the same.”

I think he meant to say ratio, but is that even true.  Is the ratio between any two adjacent numbers always the same?

 
Jehu
 
Avatar
 
 
Jehu
Total Posts:  30
Joined  22-01-2008
 
 
 
29 March 2008 14:16
 

You are quite right, the author was a little sloppy with his arithmetic, and I think you will find that he meant to say that the ratio between the smaller and larger number in each pair tends toward a value of .618034. For example, 1-1 = 1.0, 1-2 = 0.5, 2-3 = 0.6666…’ 3-5 = 0.6, 5-8=0.625, 8-13 = 0.615384615, 13-21 = 0.619047619, 21-34 = 0.617647058, 34-55 = 0.6181818….

So you see, the upper and lower limits of the ratios begin at 1.0 (1-1) and 0.5 (1-2-), and then converge toward a common limit some where between 0.619047619 (12-34) and 0.618181818… (34-55); and the higher the scalar value of the pair, the closer their ratio comes to the common limit 0.618034 – but they can never quite reach this limit.

 
 
Under New Management
 
Avatar
 
 
Under New Management
Total Posts:  56
Joined  05-10-2007
 
 
 
29 March 2008 14:22
 

Thank you very much.  So the statement, “the ratio between any two adjacent numbers is always the same” is false?

 
Jehu
 
Avatar
 
 
Jehu
Total Posts:  30
Joined  22-01-2008
 
 
 
30 March 2008 04:41
 
Under New Management - 29 March 2008 06:22 PM

Thank you very much.  So the statement, “the ratio between any two adjacent numbers is always the same” is false?

Clearly!

 
 
Under New Management
 
Avatar
 
 
Under New Management
Total Posts:  56
Joined  05-10-2007
 
 
 
30 March 2008 23:36
 

Thanks Jehu!!

 
Jehu
 
Avatar
 
 
Jehu
Total Posts:  30
Joined  22-01-2008
 
 
 
31 March 2008 15:47
 

Happy to be of assistance.