Finally, a concise infographic to help keep you from getting trapped next to the guy who smells like shoes and only wants to talk about the size of his investments, if you know what he means. Designer Alex Cornell of Firespotter Labs lays out the optimal seating location across a sampling of tables sizes and arrangement.
Though we may quibble about his assumptions and methodology, he has indeed divined the basic rules that will prevent you from being boxed out of enjoyable conversation at a meal. He also has noted that acquiring the optimal seat without raising suspicion is also important.
You might want to print this out to review in the car before entering a restaurant, because trying to refer to the chart while picking seating almost certainly will tip your hand. As he notes in the "8 Person Rectangle" arrangement, timing is the key in the more difficult seating arrangements. Arriving at the table too late or too early could utterly hose you in seat choice. Too early and someone might ask you to move to accommodate his or her significant other. Too late and you're going to end up stuck at the end talking to yourself and drinking too much wine.
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Of course, this infographic is just a general guide and convenient visual reference for the socially awkward who still have nightmares about trying to arrange their place in a grade-school line so they can sit next to their crush at assembly. More serious social situation may call for the deployment of actual math and maybe a little game theory to derive an optimal seating location. The situation becomes even more complicated when you're trying to create optimal seating for an entire group, perhaps for a wedding. A suggested methodology employing algebraic matrices was presented in the Annals of Improbable Research and, if you can understand the math, is actually pretty slick.
The classic problem of seating at weddings is getting everyone seated at a table with at least a few people they know. Doing this all by hand, as anyone who has ever planned a wedding knows, is less than fun and extremely time-consuming. However if you can apply to numerical values how many people any given guest knows, you can plug that into some math, which will spit out table assignments ensuring that dates are kept together and you don't form one awkward table of total strangers. It might even be possible to assign additional values to account for things like "Mutual friends who are both invited but are now divorced and probably don't need to be at the same table."
Or you know, you could just find a seat at the table and make the best of it. Like humans have been doing since before recorded history.