Great spirits have always encountered violent opposition from mediocre minds.
— Albert Einstein
They laughed at Einstein. They laughed at the Wright Brothers. But they also laughed at Bozo the Clown.
— Carl Sagan
Everything at the Membrane Domain
Great spirits have always encountered violent opposition from mediocre minds.
— Albert Einstein
They laughed at Einstein. They laughed at the Wright Brothers. But they also laughed at Bozo the Clown.
— Carl Sagan
Put your brain in gear before starting your mouth in motion.
There’s a lesson that I need to remember
When everything is falling apart
In life, just like in loving
There’s such a thing as trying to hard
You’ve gotta sing
Like you don’t need the money
Love like you’ll never get hurt
You’ve gotta dance
Like nobody’s watching
It’s gotta come from the heart
If you want it to work.
— Kathy Mattea
If God had meant for us to be naked, we would have been born that way.
— author unknown
Research, n:
Consider Columbus:
He didn’t know where he was going.
When he got there he didn’t know where he was.
When he got back he didn’t know where he had been.
And he did it all on someone else’s money.
Adhere to your own act, and congratulate yourself if you have done something strange and extravagant, and broken the monotony of a decorous age.
— Ralph Waldo Emerson
It has been said that man is a rational animal. All my life
I have been searching for evidence which could support this.
— Bertrand Russell
Man has always assumed that he is more intelligent than dolphins because he has achieved so much — the wheel, New York, wars and so on — while all the dolphins had ever done was muck about in the water having a good time. But, conversely, the dolphins had always believed that they were far more intelligent than man — for precisely the same reasons.
— D. Adams, “Hitchhiker’s Guide to the Galaxy”
Murphy’s Law, that brash proletarian restatement of Godel’s Theorem.
— Thomas Pynchon, “Gravity’s Rainbow”
Gödel’s incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The two results are widely, but not universally, interpreted as showing that Hilbert’s program to find a complete and consistent set of axioms for all mathematics is impossible, giving a negative answer to Hilbert’s second problem.
The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an “effective procedure” (e.g., a computer program, but it could be any sort of algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that such a system cannot demonstrate its own consistency.