It is to some extent paradoxical that humans, finite beings, have been capable of conceiving the idea of the infinite and, furthermore, developing it with noteworthy sophistication. To the simple opposition between what is consumed and the never-ending have been added religious, philosophical and mathematical expressions with that same idea, and in all cases with a level of complexity that, even now, several years and even centuries since having been formulated, can still be difficult to comprehend.

Such is somewhat the case with the “Paradox of the Grand Hotel,” thought up by David Hilbert in 1924 based on a simple idea: How would a hotel function that had an infinite number of rooms, and what problems could it face?

As we can see, the premise is sufficiently playful and as a result it is logical that it has found notable adaptations, such as that produced recently by Jeff Dekofsky for Ted.com, the site for the spreading of knowledge. There, among the ‘Lessons Worth Sharing’ is this video which explains what happens when a traveler arrives at that hotel in search of a room, or a bus filled with an infinite number of passengers, or an infinite series of buses with an infinite number of passengers. The incredible thing is that for all of those guests the concierge has a room available.

The exercise is extremely educational and, above all, stimulating, as it invites us to fantasize about our own idea of the infinite.

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It is to some extent paradoxical that humans, finite beings, have been capable of conceiving the idea of the infinite and, furthermore, developing it with noteworthy sophistication. To the simple opposition between what is consumed and the never-ending have been added religious, philosophical and mathematical expressions with that same idea, and in all cases with a level of complexity that, even now, several years and even centuries since having been formulated, can still be difficult to comprehend.

Such is somewhat the case with the “Paradox of the Grand Hotel,” thought up by David Hilbert in 1924 based on a simple idea: How would a hotel function that had an infinite number of rooms, and what problems could it face?

As we can see, the premise is sufficiently playful and as a result it is logical that it has found notable adaptations, such as that produced recently by Jeff Dekofsky for Ted.com, the site for the spreading of knowledge. There, among the ‘Lessons Worth Sharing’ is this video which explains what happens when a traveler arrives at that hotel in search of a room, or a bus filled with an infinite number of passengers, or an infinite series of buses with an infinite number of passengers. The incredible thing is that for all of those guests the concierge has a room available.

The exercise is extremely educational and, above all, stimulating, as it invites us to fantasize about our own idea of the infinite.

.

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