Quotes
#24
Posted 24 January 2009 - 09:37 PM
crazy4laptops said:
this is a mind teaser--
what is the beginning of eternity, the end of time and space, the beginning of every end and the end of every place?
what is the beginning of eternity, the end of time and space, the beginning of every end and the end of every place?
To see the world in a grain of sand,
and a heaven in a wild flower;
Hold infinity in the palm of your hand,
and eternity in an hour.
~ William Blake, with italics to emphasize the Fibonacci significance
Divine Proportion
The Divine Proportion, also called the Golden Ratio, and has been designated by the 21st letter of the Greek alphabet, PHI φ (21 is, of course, a Fibonacci number). PHI is an irrational number created by the successive convergents of numerators and denominators following the Fibonacci sequence. To demonstrate this, take any Fibonacci number and divide it by the previous Fibonacci number. For example, 377 / 233 » 1.61803. The further you go in the Fibonacci series with this method, the closer you approach the Divine Proportion, which is equal to
PHI (φ) =( √5 + 1 ) / 2
Being an irrational number, it extends far beyond 1.618033988749894...but is often approximated at 1.618. The ratios of successive Fibonacci numbers tend toward PHI, so PHI is the limit of the sequence 2/3, 3/5, 5/8, 8/13, etc. These ratios approach, but never equal PHI. Mathematicians measure how "irrational" a number is by seeing how quickly the differences between these fractions and PHI shrink toward zero. It so happens that they shrink more slowly for PHI than for any other irrational number. This is why number theorists say that PHI is the "most irrational number." Two fascinating properties of PHI are seen in its reciprocal and its square:
1 / φ = φ - 1 or 0.618...
φ² = φ + 1 or 2.618...
Remember that multiplication is really a special form of addition, and PHI represents a coinciding of the processes of addition and multiplication. What was a linear accumulation suddenly becomes a square (φ+1 = φ²), and there is a leap of growth. In the plant, the simple additive growth in the stem suddenly erupts into a flower. When such a moment occurs in the context of spiritual development, it is called enlightenment. In our brains, the additive accumulation of data suddenly blossoms into a genuine understanding. There is a development from points to lines to planes, and finally, to volume. This is demonstrated by simultaneously adding and multiplying in the mathematical equation:
φ + φ² = φ³ = φ x φ²
~ Luca Paciol revealed in De Divina Proportione
#29
Posted 25 January 2009 - 10:04 AM
The only constant is change. ~ Confucius
It is the absence that defines the presence. ~ Yin Yang
Opposites Attract. (Well it's obvious, electricity, magnetism, gravity... universal law)
Persist and it resists. ~ Lao Tzu
The softest things in the world overcome the hardest things in the world. ~ Lao Tzu
The words of truth are always paradoxical. ~ Lao Tzu
To the mind that is still, the whole universe surrenders. ~ Lao Tzu
To realize that you do not understand is a virtue; Not to realize that you do not understand is a defect. ~ Lao Tzu
Truthful words are not beautiful; beautiful words are not truthful. Good words are not persuasive; persuasive words are not good. ~ Lao Tzu
When I let go of what I am, I become what I might be. ~ Lao Tzu
When you are content to be simply yourself and don't compare or compete, everybody will respect you. ~ Lao Tzu
To lead people walk behind them. ~ Lao Tzu
To see things in the seed, that is genius. ~ Lao Tzu
It is the absence that defines the presence. ~ Yin Yang
Opposites Attract. (Well it's obvious, electricity, magnetism, gravity... universal law)
Persist and it resists. ~ Lao Tzu
The softest things in the world overcome the hardest things in the world. ~ Lao Tzu
The words of truth are always paradoxical. ~ Lao Tzu
To the mind that is still, the whole universe surrenders. ~ Lao Tzu
To realize that you do not understand is a virtue; Not to realize that you do not understand is a defect. ~ Lao Tzu
Truthful words are not beautiful; beautiful words are not truthful. Good words are not persuasive; persuasive words are not good. ~ Lao Tzu
When I let go of what I am, I become what I might be. ~ Lao Tzu
When you are content to be simply yourself and don't compare or compete, everybody will respect you. ~ Lao Tzu
To lead people walk behind them. ~ Lao Tzu
To see things in the seed, that is genius. ~ Lao Tzu
#30
Posted 25 January 2009 - 10:17 AM
crazy4laptops said:
this is a mind teaser--
what is the beginning of eternity, the end of time and space, the beginning of every end and the end of every place?
what is the beginning of eternity, the end of time and space, the beginning of every end and the end of every place?
Although I provided an esoteric answer already, I can't find a simple one... Yet.
I'm such a nerd.
If you can't explain it simply, you don't understand it well enough.
~ Albert Einstein
#32
Posted 25 January 2009 - 07:16 PM
crazy4laptops said:
the answer is from a more literal perspective--- it is the letter E
I am amazed at the simplicity, thus the elegance of your brain twister! Good one! Thank you, I spent a few good moments thinking on this, and it was all FUN!
I am humbled, and true to my name, a tard...
All truths are easy to understand once they are discovered; the point is to discover them.
~ Galileo Galilei
All things being equal, the simplest explanation is usually the best one.
~ Occam's Razor
#36
Posted 26 January 2009 - 07:25 AM
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