eanbardsley
Active Member
- Joined
- Jun 26, 2006
- Messages
- 25
Pelorat was a cosmic archeoligist in Foundation's edge, and in Foundation and Earth, searching for Earth. Humanity spread throughout the Galaxy, such an archeology could become very realistic. I have found the ratio 9/5 in the most humanly held sacred aspects of nature, gold, silver, sun, moon, water, air,... and in other things like the most massive planets in the solar system, Jupiter and Saturn, and human body temperature pointing to the earth where that ratio is concerned. If you are interested in the calculations, you can visit my blog which has its link in my profile. Visit the Arthur C. Clarke forum for my calculations showing Arthur C. Clarke to be tuned into something deeply meaningful. Back to cosmic archeology, here is my bit of cosmic archeology:
Raphael, at the JCF forum has pursued four as significant cosmic value, I have pursued nine-fifths. While I have worked with numbers, he has worked with myth and its symbols
In an effort to generate 4 from the golden ratio and 9/5 in connection with the earth and the 22 card cycle of the tarot we begin by finding the equation whose solution is the golden ratio. The golden ratio, or phi, as it is called, is the ratio such that the whole to the greater part is the same as the greater part to the lesser. That is a/b must be the same as b/c if a=b+c. Thus we have the two equations:
1. a/b=b/c
2. a=b+c
From 1 we have: ac=b^2
From 2 we have: c=a-b
These two yield: a(a-b)=b^2
Which can be written: a^2-ab=b^2
Or, a^2-ab-b^2=0
If we divide the last through by b^2, we get: (a/b)^2-(a/b)-1=0
This last is a quadratic in a/b. a/b is the golden ratio and can be found by completing the square. Letting a/b=x, our equation becomes:
3. x^2-x-1=0
We will not solve equation 3 for the golden ratio but will proceed to consider 9/5.
Raphael has presented the sequence: 5,14,,23,32,41,50,59…
Where we begin with five and add nine to each successive term. He has noted that the sum of the digits of each term is five. Thus this sequence embodies the principle of (9/5) a ratio I have found to exist throughout nature from atoms of gold and silver, to the moon and the sun, to water, and air, to the human body temperature and freezing temperature of water, to the very structure of the solar system itself. The above sequence is an arithmetic sequence, the nth term of which is predicted by:
4. a_n=5+9(n-1)
5. a_n=9n-4 (equivalently)
Since the earth is the third planet, then n=3 yeilds:
9(3)-4=27-4=23
As it so happens, 23 is the 9th prime number, and represents the earth. We write, from 5:
6. 23=9x-4
7. 27=9x
8. 9x-27=0
We equate equation 8 with equation 3:
9x-27=x^2-x-1
to find the intersection of 9/5 and the golden ratio at earth orbit, and get:
9. x^2-10x+26=0
Equation 9 can be solved with quadratic equation and has the solutions, (5+i),(5-i)
These are two complex numbers with real parts 5 and 5, and imaginary parts sqrt(-1) and sqrt(-1). They are vectors whose sum are:
(5,1)+(5,-1)=(10,0)
and whose points are separated by:
|(5+i)-(5-i)|=2i
with a modulus of sqrt(5^2+1^2)=sqrt(26)
This generates the triangle with height 5 and base 2i or complex number 5+2i.
The Mandelbrot set is the iteration of a function of complex numbers that generates the fractal given by:
F(z)=z^2+c
If the seed is zero and c is our 5+2i
Then F(0)=(0)^2+5+2i=5+2i
And F(5+2i)=(5+2i)(5+2i)+5+2i=
26+22i
We have generated our 22 cards of the tarot, and our four in that 26-22=4, from 9/5 and the golden ratio.
Furthermore 22=> 2+2=4 and 26=>6-2=4
We have generated four, three times as well, and 3 times four is twelve. Twelve is the most divisible number for its size. It has been Raphael’s suggestion that we express all in a simple truth. This might be a start. Also, 22+26=48 and 48/4=12
Raphael, at the JCF forum has pursued four as significant cosmic value, I have pursued nine-fifths. While I have worked with numbers, he has worked with myth and its symbols
In an effort to generate 4 from the golden ratio and 9/5 in connection with the earth and the 22 card cycle of the tarot we begin by finding the equation whose solution is the golden ratio. The golden ratio, or phi, as it is called, is the ratio such that the whole to the greater part is the same as the greater part to the lesser. That is a/b must be the same as b/c if a=b+c. Thus we have the two equations:
1. a/b=b/c
2. a=b+c
From 1 we have: ac=b^2
From 2 we have: c=a-b
These two yield: a(a-b)=b^2
Which can be written: a^2-ab=b^2
Or, a^2-ab-b^2=0
If we divide the last through by b^2, we get: (a/b)^2-(a/b)-1=0
This last is a quadratic in a/b. a/b is the golden ratio and can be found by completing the square. Letting a/b=x, our equation becomes:
3. x^2-x-1=0
We will not solve equation 3 for the golden ratio but will proceed to consider 9/5.
Raphael has presented the sequence: 5,14,,23,32,41,50,59…
Where we begin with five and add nine to each successive term. He has noted that the sum of the digits of each term is five. Thus this sequence embodies the principle of (9/5) a ratio I have found to exist throughout nature from atoms of gold and silver, to the moon and the sun, to water, and air, to the human body temperature and freezing temperature of water, to the very structure of the solar system itself. The above sequence is an arithmetic sequence, the nth term of which is predicted by:
4. a_n=5+9(n-1)
5. a_n=9n-4 (equivalently)
Since the earth is the third planet, then n=3 yeilds:
9(3)-4=27-4=23
As it so happens, 23 is the 9th prime number, and represents the earth. We write, from 5:
6. 23=9x-4
7. 27=9x
8. 9x-27=0
We equate equation 8 with equation 3:
9x-27=x^2-x-1
to find the intersection of 9/5 and the golden ratio at earth orbit, and get:
9. x^2-10x+26=0
Equation 9 can be solved with quadratic equation and has the solutions, (5+i),(5-i)
These are two complex numbers with real parts 5 and 5, and imaginary parts sqrt(-1) and sqrt(-1). They are vectors whose sum are:
(5,1)+(5,-1)=(10,0)
and whose points are separated by:
|(5+i)-(5-i)|=2i
with a modulus of sqrt(5^2+1^2)=sqrt(26)
This generates the triangle with height 5 and base 2i or complex number 5+2i.
The Mandelbrot set is the iteration of a function of complex numbers that generates the fractal given by:
F(z)=z^2+c
If the seed is zero and c is our 5+2i
Then F(0)=(0)^2+5+2i=5+2i
And F(5+2i)=(5+2i)(5+2i)+5+2i=
26+22i
We have generated our 22 cards of the tarot, and our four in that 26-22=4, from 9/5 and the golden ratio.
Furthermore 22=> 2+2=4 and 26=>6-2=4
We have generated four, three times as well, and 3 times four is twelve. Twelve is the most divisible number for its size. It has been Raphael’s suggestion that we express all in a simple truth. This might be a start. Also, 22+26=48 and 48/4=12
