Circular Reflections

 
The Queen in Lewis Carroll's Alice in Wonderland recommended that Alice get more practice at believing impossible things. And when she admonished Alice to think carefully before speaking, Alice indignantly replied: "How can I know what I think till I see what I say?"

Exercises to illustrate eigenbehaviour?

Take an urn containing one white and one black ball. Draw one ball from the urn at random and, whatever its colour, replace it and add another ball of the same colour to the urn. Observe that the percentage of, say, black balls in the urn will reach a particular value and stay there. After an initial period of fluctuation, the ratio will settle to a stable value; another time you do it, it will arrive at a different stable value. 

Writing out the number in full (e.g. thirteen), complete the following sentence - accurately.
This sentence has ______ letters.
There are two correct answers and one of them is thirty three.

About the Liar Paradox:

Ever since Epimenides the Cretan said:
"Hark! All Cretans are liars"
There have been poets and authors I've read
with self-referential desires
The version of Willard Van Orman Quine is
frequently used as a model
But Hofstadter's heart is rather where mine is
Bach and Escher and Godel

Disobey this command.
On both sides it says: The statement on the other side is false
This sentence contains exactly threee erors.
I am the meaning of this sentence.
Due to circumstances beyond my control, I am master of my fate and captain of my soul
What would life be, without me?

Oscar Wilde said:
The only way to get rid of temptation is to yield to it.
One should not carry moderation to extremes.
Koestler cites the following:
Psychoanalysis is the disease for which it pretends to be the cure.
Philosophy is the systematic abuse of a terminology specially invented for that purpose.

Constant change is here to stay.
To change takes time yet you can do it immediately.

Western science is gravely addicted to certainty yet the science of physics has undermined this position completely.
The most strictly accurate science could be the least honest because it ignores the paradox.
We impose our explanations onto animal behaviour which form models for sociobiology and then argue that, because animals do it, it must be a part of us as well.
We can be in deepest communion when in deepest solitude, but lonely in a crowd. When we are most comfortable with ourselves we are most comfortable with the world at large. When not in touch with ourselves, we are out of touch with the larger world as well. When I speak personally I speak most generally.

Every end is a new beginning
Every failure is something learned 
Every loss gives a chance at winning 
Unrequited means truly yearned

Every tumble leads to rising 
Every hurt has need to heal 
Every grief yields sympathising 
Every pain shows that you feel

Difficulties are debentures 
Problems are a challenge really 
Even mishaps are adventures 
Setbacks show the path more clearly

Every wrong is a cause worth righting 
Each mistake is a chance success 
Every miss improves the sighting 
And every more is also less

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Nothing is the other half of something
Black is just the other half of white
Nowhere is the converse side of somewhere
Dark is just the other half of light

Personal is the flip of universal
Cocky is the other half of coy
Thinking is the reasoned half of feeling
Sorrow the unwelcome half of joy

Going is the other half of staying
Planning's the preceding half of done
Working is the other half of playing
Moping is the nether half of fun

Singleness goes back to back with many
Plenty is reciprocal to none
Particular is like and not like any
Zero is the other half of one

Taking is the other half of giving
Despair is the other half of hope
Dying is the other half of living
Copes well who dares to say I cannot cope

Dependency is just not living freely
Control is the flip side of submitting
Limpid is the other half of steely
Given up is linked to unremitting

Asking is the other half of telling
Saying shares a thought with 'keeping mum'
Sulking is the other half of yelling
Gone is the antithesis of come

Doing is the other half of being
Spoken co-exists with nothing said
Blindness is the other half of seeing
Living cannot be unlinked from dead