What is it with cats and cardboard boxes? Anecdotal evidence suggests it's not just our Bess who has a mysterious fondness for tight cardboard spaces (if over 1600 catbox photos on Flickr are anything to go by). If there's a box to be occupied, she'll choose it over other accommodation options (fur-lined basket, radiator cradle, lap. etc.). In searching Google I learned that even Schrödinger's cat was placed in a box and that boxes make "unglamorous" kitty toys, but find myself no closer to the truth. You know The Question—it's like a splinter in your mind. Is there a relationship between the size of the cat and preferred box size?
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Bess in an Amazon box
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I could provide a similar photograph of John's cat, Unit, in a cardboard paint-tray. So, I relate to this photograph of Bess.
As for your question, here's my answer based on Unit's favourite choices:
Box must have a maximum of 1cm chin resting space on one side, remaining 3 sides must be exactly the measurements of said cat.
And this could lead on to other box related questions, such as:
Why, no matter how fantastically flash your present may be, a toddler only ever seems to get maximum enjoyment out of the scruffy old cardboard box you wrapped it in??
Unit? Now that is a good cat name! So you've observed the same phenomenon in toddlers? Interesting... maybe it's a "mammal thing" then? The cardboard box could represent a Freudian desire to return to the womb. I wondered (in the case of cats anyway) if it had anything to do with the thermal properties of cardboard, but that's a much less interesting theory ;-)
I just came across this little YouTube moment and had to share.
Warning: it has hideous music.
But, it does go somewhere towards validating the "return to the womb" theory you have expressed. ;)
LOL. Me thinks these kitties have been watching too much Doctor Who: they're convinced this box is the TARDIS.