DK. Flipping the Mattress
We consider the ways in which we might preserve a mattress. Every six months, as we all know, you should rotate or flip your mattress so that it wears out evenly. Is there a simple, easy to follow procedure for ensuring that the mattress cycles through all four possible orientations?
(This is really a lead-in for a discussion about Group Theory.)
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DavidAnderson said,
February 3, 2008 at 11:00 am
At first blush, since you’re not displacing the mattress in space, all you can do in 3D is spin it around an axis – either around the head-to-foot centerline, around the left-to-right centerline, or around the floor to ceiling centerline. Since the axes are orthogonal and you want a “single” instruction to run every six months, you’re out of luck for just a repeatable, no-state instruction.
If you can add a piece of state information, however, you can do it just fine. For instance, say you flip the mattress on midsummer and midwinter. If you rotate around the head-to-foot centerline in midwinter (the long dimension since nights are at their longest) and around the left to right centerline in midsummer (the short dimension since nights are shortest) you end up getting all for orientations in a two-year cycle.
so, algorithmically speaking:
at each solstice,
if mights are longer than days,
flip along the long axis
else
flip along the short axis.
You don’t have to keep the state attached to the bed, you pick it up from the time of year. And if you live south of the equator, you invert the process.
If you live on the equator, you’re most likely sleeping in a hammock enjoying the weather, so you don’t need to flip anything. :)
– Dave
jlundell said,
February 4, 2008 at 11:22 pm
There’s a simpler solution than the mark-the-head one you mentioned on the program, in which there’s no need to remember the order of operations. Effectively you make it a Z4 group.
Mark any corner. When it’s time to cycle the mattress, notice which corner is marked, and do whatever it takes to move the mark clockwise by one corner. This will be a flip, either the long way or the short way (or a rotate and flip, doesn’t matter).
You do have to remember that you’re rotating clockwise, and not widdershins, but that’s easy enough, since the whole matter is a function of time.
Now, if the mattress happens to be square….
mjplatt said,
February 29, 2008 at 12:55 pm
As a housewife who never remembers to turn the mattress, and its too heavy anyway, surely the simplest solution is to label the 4 corners ( as above, 2 on each side) 1,2,3,and 4. After an even number you flip the mattress! that way you don’t have to remember anything, because it won’t take long to realise you need to flip the mattress when you can’t find the next number on the side showing!