Go out into the world - The Tempest?

Solution 1:

According to the Michael Coveney, a theater critic writing in the Wednesday 29 August 2012| Independent, Sir Ian McKellan lost his script and improvised.

Theatre critic's view: Sir Ian McKellen improvises as Miranda floats past during the Paralympics opening ceremony

But he'd lost his script, so he improvised a modern imprecation, telling his daughter, Miranda, floating by in a flying wheelchair, to "go out into the world…and shine your light on to the beautiful diversity of humanity".

It was literate, but it wasn't Shakespeare. And – sorry to be a party-pooper at the friendly games – it was, well, a bit banal.

Sir Ian remained in long shot and didn't act remotely sonorous, which was something. Perhaps he was in a sulk: Prospero's lines had been nicked, after all, at last month's opening ceremony by Ken Branagh.

The article contains a great picture of Sir Ian, and goes on to describe Stephen Hawking commanding Miranda to "be curious".

I didn't find the origin of the expression "go out into the world", but "the world is your oyster" was coined by Shakespeare in "The Merry Wives of Windsor". See What is the meaning and origin of the common phrase "the world is your oyster"?

Solution 2:

It's possible that, having lost his script, Sir Ian subconciously recalled lines heard in his youth:

Go forth into the world in peace;
be of good courage;
hold fast to that which is good;
render to no one evil for evil;
strengthen the fainthearted; support the weak;
help the afflicted; honour all men;
love and serve the Lord,
rejoicing in the power of the Holy Spirit;

Unfortunately the adaptation from 1 Thessalonians 5 is anonymous, although a blog post attributes it originally to American Episcopalians in the 1890s. Even though that benediction was not officially adopted at the time, it was taken up by Presbyterians of a similar ilk to his own family connections.