He proves by algebra that Hamlet's grandson is Shakespeare's grandfather and that he himself is the ghost of his own father.

The time is out of joint: O cursed spite,
That ever I was born to set it right!
*********Hamlet, act one, scene 5

What keeps Hamlet from acting? His father's ghost told him who did the killing. Why doesn't Hamlet take this information and exact revenge for his father's death? What's his problem?
Hamlet was born betwixt and between. The, ‘times were out of joint.’ The dying Age of Faith still lingers on as seen in the ghost of Hamlet’s father. But a new age was being born. And this new Age of Science could not be satisfied by the testimony of a ghost at midnight.
Hamlet played at being crazy. But if you are born in the middle of a paradigm shift, if you feel drawn towards both ideals you will feel crazy. You will always be neither fish nor fowl and you will never feel completely at home or welcomed by either ideal. The times will truly be out of joint.
The epistemological goal of the new age was the banishment of doubt and its replacement by certainly based on independently verifiable sensory experience. Thus Hamlet ended up constructing the crude experiment of putting on the play reminiscent of his father’s death and observing his uncle’s reaction. Hamlet was too much a man of his time to be able to feel comfortable with proceeding to action without satisfying the needs of the new scientific method.

crossposted at The Chinese Jar