# Vacation Memories 2: Baggage

I’m back home from my brief travels, and I returned to find the latest outbreak of quantum woo infection, followed immediately by a heap of silliness about anthropic twaddle.

“Too soon,” I thought. “I need to go back on vacation.”

So, instead of complaining at great length about things I’ve already complained about, I’ll just share one quick observation and then head out into the outside world, shopping for art supplies.

Yesterday, I flew into Boston. In my laptop I carried a hardback of Lois Lowry‘s The Giver (1993) and, to recapture a more innocent time, Feynman and Weinberg’s Elementary Particles and the Laws of Physics (1987). In between reading these two, I happened to glance at the pamphlet-type thing which the airline clerk had given me to hold my boarding passes in. Here’s the puzzling part, under the “Free Baggage Allowance” heading:

Carry-on Baggage is limited to one piece per passenger, plus a personal item such as a purse, briefcase or laptop computer. The carry-on cannot exceed 51 inches (11″ × 14″ × 26″) and must fit under the seat or in an overhead compartment.

Why are the three linear dimensions added? The frame device the airline positions at each gate for testing whether or not your carry-on will fit rejects your baggage if any dimension exceeds the threshold set. Your baggage is deemed invalid even if the total volume is less than 11″ × 14″ × 26″ = 4004 in3 (just try carrying on something long and skinny). The longest diagonal of an 11″ × 14″ × 26″ box is

$\sqrt{14^2 + 26^2} \approx 29.5$

inches long. So, you can have a carry-on item the sum of whose edge lengths is, say, thirty-one inches, and which won’t fit the actual airline restrictions no matter how you try to wedge it in sideways. The sum of the height, width and depth is a meaningless number.

## 4 thoughts on “Vacation Memories 2: Baggage”

1. Joshua Zucker says:

It’s not quite as stupid as you might think.

http://www.dhl-usa.com/IntlSvcs/dimweight/dimweight.asp?nav=Inttools/DimWeiCal

shows that DHL uses cubic units to measure density, and charges you (by weight) as though your package has a certain minimum density, or they charge you for the actual weight, whichever is larger.

But they have a bizarre little section on length and girth at the bottom — why?

Well, things like this discussion
http://www.ups.com/content/us/en/resources/prepare/dim_weight.html
show that you will pay a surcharge based on length + girth of your package being too large. Why is length + girth a sensible measure? length is the longest side, so the formula is
length + 2*width + 2*height …
crazy stuff.

2. Anonymous says:

The sum of the height, width and depth is a meaningless number.

It’s actually the mean width of the box (as in Hadwiger’s theorem). This is the natural continuation of the sequence “volume, surface area, ?”, and it’s as mathematically meaningful as volume or surface area is.

Of course, I agree with you that it’s a stupid measurement to use for this rule.