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Partially correct. For sure a lot of it is getting attention, but they do care about the warmth. I've walked in to my office plenty of times to see my cat sitting on my laptop when I haven't even been in there for hours. She will even find the laptop and lay on it when it's in random places around the house. Reproduced with three different cats over the yeras. The warmth is definitely a cat magnet.
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Noticed that in my absence, cats hang where I spend the most of my time when present. If for a few days I only come home to sleep I'll usually find them on my bed. If I work at my desk for a week, then the next days they'll be found on my chair. And so on.. A somewhat reliable habit indicator.
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When my cats want warmth, they go on top of my desktop tower (or on my lap under the keyboard tray). If they're at the level of my desk, they're almost definitely angling for attention.
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sometimes its scent too.
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I'm not sure if this is enough for demanding cats, but I used to type with a small dog bed directly in front of me and my keyboard behind it, so that I'd work typing with my arms around my elderly chihuahua every day. She seemed to like it a lot, and she basically had my attention every time she stirred.

I also felt that it was probably good for me for her to break my flow and demand my attention every now and then. It helped remind me to get up and stretch and be human better than I otherwise would have done.

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I have a keyboard tray and a desk with two monitors. Both of my cats love to stand on the space in the desk of whatever monitor I happen to be focusing on more (preferably blocking as much of it as possible from my view). They know exactly what they're doing.
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i came across a manuscript once that had a bunch of inky paw prints across a page. the scribe clearly tried to blot one of them, merely smudging it, then decided to let the rest be. it was in a very beautiful hand, and the full page must've taken hours to write. that scribe's exasperation echoes through the ages. i wish i could find that MS again.

to be fair, the page was probably arranged in a nice sunny spot at the time of the incident.

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