Vacancy at the Grand Hotel

One of the most famous thought experiments in modern intellectual history is the Infinite Hotel Paradox. Introduced in 1924 by a German mathematician, David Hilbert, it posits the Grand Hotel, which has an infinite number of rooms, all occupied. However, someone arrives and asks for a room. To accommodate him, the manager moves each guest over one room: the guest in room 1 goes to room 2, the guest in room 2 to room 3, and on . . . into infinity.

Word gets out about a hotel that always has a vacancy, and a bus pulls up with an infinite number of people who need a room. Knowing his math, the manager has each occupant go to the room number double his own: the guest in room 1 goes to room 2, room 2 to room 4, room 3 to room 6, and on and on . . .. His move will free up an infinite amount of odd-numbered rooms for the new guests (though going from room 684,250 to 1,368,500 might take some time).

But this leads to the paradox. If an infinite number of occupied rooms already existed, how do you add one more, much less an infinite number more? The only logical option? Infinity must come in different sizes.

After all, an infinite amount of whole numbers exist: 1, 2, 3, 4, 5, 6 . . . But there are also infinitely many even whole numbers, 2, 4, 6, 8 . . . But how could what’s only part (half, in fact) of the whole have the same number as the whole? It’s like me eating half the M&Ms in a bag, but having the same amount left over, as if I had eaten none.

Not quite. Because however big my bag of M&Ms, it contains only a finite number of goodies, and infinity is a radically different reality than finitude. It would seem fitting to say that there’s a quantitative difference between the finite and the infinite (after all, we’re dealing with numbers here), but it is not. As the above examples show, it is a qualitative difference.

This leads to my point. “Eternal life,” wrote Ellen White, “is an infinite gift. This places it outside the possibility of our earning it, because it is infinite.”

Infinity isn’t just lots of finite stuff, which is why our every effort to earn eternal life must fail. All our selfless works, all our encouraging words, all our pure motives, added up, multiplied, raised to the tenth (or hundredth) power, whatever, are always and only finite. And because “eternal life is an infinite gift,” you can no more earn it than you can count to infinity.

And who alone could bestow the “infinite gift” of eternal life except a God who not only is infinite and eternal, but who transcends them too? The Lord, to offer infinity and eternity, must be beyond both. Jesus said, “In my Father’s house are many rooms” (John 14:2, ESV). Maybe not infinitely many rooms, as in the Grand Hotel, but room enough—with every charge, tax, and amenity paid, fully and in advance, by the “infinite gift,” the blood of Jesus.

* Ellen G. White, Faith and Works (Nashville: Southern Pub. Assn., 1979), p. 27.