If it is beyond our abilities to determine the exact string compactification des

Question

If it is beyond our abilities to determine the exact string compactification describing our universe, is it not wrong to call the compactification unobservable? Only things which are experimentally observable, possibly with the aid of theoretical interpolations, and can make experimentally verifiable predictions count as science. Within the realm of physics, are we forbidden to ask which string compactification describes our universe? Must we stick to the effective field theory if we wish to remain physicists and not philosophers?

Explanation / Answer

There is an real life analogy that provides a nice answer to this question

In 1999 Lord Monckton marketed a toy called the "Eternity Puzzle". It was a tiling problem with 209 pieces. He thought it was sufficiently complex that nobody would solve it even with a very powerful computer, so he offered

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