## Is there anyway this statement can be summed up in a mathematical formula [closed]

Imagine you have created (nanobot) fabricator. The nanobot's core function is to collect the data of every subatomic particles position, movement and all other necessary information about them. Becoming omniscient, they have the fundamental knowledge to predicting every single event from that point onward. If the deterministic view is correct.

I meet up with your omniscient (nanobot) fabricator, I ask them a simple question . (Though they may already know the question.) The question is what hand will I raise ? The conditions are this, you must tell me before I make the decision, also what ever hand you choice I will choice the opposite.

Sorry for the dull question, this will be my first and last question here.

The above post is suppose to be taken hypothetically as it's impossible in the real world theoretically or not. Most of you maybe aware this is similar to Kurt Godel's incompleteness theorem and maybe I'm wrong in thinking this does apply to the above post exactly I've just always wanted to have the above statement in a mathematical form if that's even possible.

Thanks you very much.

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MO is not really for these kinds of questions; this is more philosophical than mathematical, if anything. – Qiaochu Yuan Aug 15 2010 at 17:28
But if there is a mathematical answer to the question, it would seem to be Tarski's theorem on the non-definability of truth, which asserts in a precise way that no mathematical universe admits a first-order definition of its own truth function. Tarski's proof proceeds via a liar-paradox-like contradiction resembling the situation of you and your nanobot fabricators. See en.wikipedia.org/wiki/Tarski's_undefinability_theorem – Joel David Hamkins Aug 15 2010 at 23:11