No room at the Hilbert Grand Hotel

David Hilbert posed a thought experiment in which you have a fully-occupied hotel with an infinite number of rooms, but you may still accomodate an additional guest. Actually, you may accomodate an infinite number of additional guests. (Here is the explanation, if you are interested.)

This seems to me to be strikingly similar to the thought non-IT people have of their CIO’s to do list. “Sure, my CIO is 100% busy, but he/she can always take on an additional task.” The contention seems to be that the lowest priority task will be lowered one spot, the second lowest will be lowered one spot, and so on until all tasks have been pushed down one spot, and then there is room at the top of the to do list.

Hilbert’s paradox seems to resolve itself because the finite set of guests fit in an infinite set of rooms, so in my example, that would mean that the CIO’s to do list is really not 100% full. Unfortunately, the other way to resolve this is to discover that the number of rooms/to do list slots is actually not infinite, thus adding another guest necessitates walking someone to another hotel or adding another to do item necessitates dropping something from the list.

CIO’s, the next time you are asking to add something to your full to do list, try saying “There is no room at the Hilbert Grand Hotel.” Let me know how that works for you…

Leave a comment

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.