Spend this holiday season with Hilbert’s Paradox of the Grand Hotel (and other tales of the precious customer)

19th century German mathematician David Hilbert described the concept of infinity this way: first, you must picture a hotel so vast, so overwhelming that it has an infinite number of guest rooms. This hotel is not only large, it is also full, with every guest room occupied. One evening, a sojourner enters the lobby, seeking a room in this hotel with absolutely no vacancy. Despite being sold out, the traveler gets a room, since the hotel is not limited by any finite number of accommodations. So the guest in room 1 is moved to room 2, the guest in room 2 is moved to room 3, and so forth, ad infinitum. The newcomer is put into room 1. The hotel can repeat this procedure any number of times whenever new clients happen to show up.

Would that this were so for retailers—a steady line of customers snaking out the door, waiting to come in, every section packed, every aisle occupied, a hub of activity 24/7/365, one shopper after another after another with no end in sight.

While this isn’t real, we’ve often observed sales associates who believe that customers are an endless resource. Like it’s no big deal if they don’t sell customer 1, because a customer 2 will be right behind. There’s always one more and one more after that. Take this incident at Best Buy, in which an employee told a customer, without checking, that a hard drive was out of stock. When he ordered the same item online for in-store pickup, less than an hour later, it was miraculously available. Or this customer service fiasco at Men’s Wearhouse, in which a saleswoman insulted a customer with lines like “I don’t know why you’re here,” and “I can’t help you now.” Even in the best of times, it’s foolish not to treat every single customer as if they are critical to the success of the store—because they are. And to do otherwise in this economy, it’s deadly. If enough customers are lured away, whether it’s by lower prices or better service, stores that treat customers as expendable will find themselves on the road to oblivion.