The Pinocchio Dilemma

We have all heard of the original Pinocchio paradox.

Just to jog your memory, consider Pinocchio,
a being who's nose significantly grows only when he lies,
saying "My nose will grow now".



If he is telling the truth, his nose will grow. But his nose is only suppose to grow if he is telling a lie. So he must be telling a lie!

If he is telling a lie, his nose will not grow. But when ever he tells lies his nose must grow.

"A contradiction!" explains Kurt Gödel.







Now here is a spin from that little paradox. Consider this:
Pinocchio says "my nose will grow in the future".

Let me rephrase that:

Person P has the following properties:

• Tells lie -> nose grows
• ~(Tells lie) -> ~(nose grows)

Are you with me so far? By the way, the "~" symbol means "not" in case you got confused.
OK going on...

At time t=0, person P announces the statement "my nose will grow in the future".
The statement "my nose will grow in the future" is isomorphic to "I will lie in the future".
And the statement "I will lie in the future" is isomorphic to "I will lie at t>0".

So if his nose does grow in the future he told the truth.
But if his nose does not grow in the future he told a lie.
Makes sense so far, right?

If person P has free will, he has the choice to either tell the truth or tell a lie at any given time in the future.

case 1: for t>0, P chooses to NEVER LIE again.
Therefore his statement at t=0, "I will lie in the future" is false!
Therefore his nose will grow at t=0.

case 2: for t>0, P chooses to LIE.
His statement at t=0, "I will lie in the future" was true!
Therefore his nose will remain normal and not grow at t=0.

Here is the exciting part:

If person P's nose grows OR doesn't grow then there is no such thing as free will!
What? Yea you heard right!
It's because we assumed free will exists for person P so the future must be uncertain. But as soon as we know the property of P's nose at t=0, we have determined whether P will lie or not.


For P, if free will exists then the past can be changed. Why? Because if he never lies, then his past-self's nose (from t=0) will grow. Thus his present nose will also grow. Huh? Did his nose just grew from not lying? That's not possible; his nose grew from not lying! A Contradiction! Free will is impossible for person P.



Poor Pinocchio.

Collatz Conjecture

Collatz Conjecture is a 72 year old unsolved conjecture about numbers. You can learn more from wikipedia.

My prediction: It will be proven within the next year. (August 9, 2009 - 2010)