Do Pólya's constants prove my cat will come home eventually?
February 5, 2011 7:01 AM   Subscribe

We have lost a cat. Ignoring obstacles like trees, roads and houses, I am assuming he has gone on a random walk. Me and my fiancée have been out every night since he left, also walking randomly, hoping to find him. But I know a random walk in two dimensions always returns to the origin eventually, so are we actually any better off searching for him than just staying at home?

We have already done two weeks of nightly searching, having checked under every bush in the town, in case he was injured or dead. We have put up dozens of posters, knocked on hundreds of doors, and called all the relevant authorities, vets and homes. The only thing we have left to do is search - but it's becoming increasingly demoralizing and I'm doubting whether it's doing any good at all. We are trying to convince ourselves it's time to let go. Is the above a sound enough reason to give up searching?

It seems to me like two points walking randomly should meet each other with exactly the same probability as one random walk hitting the origin - as you may, without loss of generality, take the location of the second point to be the origin, with respect to which the first point is still a random walk.

This is all assuming he really has gone on a random walk, rather than cycling between a small number of feeding spots. But without any knowledge or clues of where he is, it's all we have to go on.

Probability isn't my strongest suit, so it would be good if somebody could confirm whether or not I'm talking nonsense.
posted by hoverboards don't work on water to Science & Nature (20 answers total) 1 user marked this as a favorite
Walk in ever increasing circles. Cats rarely stray more than a quarter mile from home.

When we lost our cat for an extended period of time, it turned out that she was in the next yard and was unable to jump the fence to get back into our yard.
posted by tel3path at 7:10 AM on February 5, 2011

Unless there's some obstacle keeping them from doing so, cats generally know how to find their way home. I would say that at least one of you should stick around the house to let the cat in if it shows up.
posted by amro at 7:16 AM on February 5, 2011 [2 favorites]

Have you asked neighbors to check little-used outbuildings, storage rooms, etc? We once had a cat missing for a couple of days and it turned out he'd gotten into a storage room off our carport.
posted by Mavri at 7:32 AM on February 5, 2011 [1 favorite]

I'm sorry your cat is missing, but I don't think your theory about how to find him has any validity at all. Even if we accept your premise that he started walking randomly, there's no reason to suppose that he is still walking randomly. Just as you were surely not walking randomly while you were searching for him (humans do random badly, and since you ended up at home at the end of your walk, we know it wasn't random), there may be many things that have captured his attention. I would go door to door on nearby blocks asking about him.
posted by OmieWise at 7:32 AM on February 5, 2011 [3 favorites]

Two weeks is a little long, sorry to hear that. Ours ran off once, pissed because the neigbor was feeding her during our vacation, and (I guess) because there was some further disturbance through thunderstorms and heavy rain - she returned on the day of our return. But that was after one week.

A little depending on the kind of area you're in, visiting the potential accident hotspots may replace the walk in circles. You could also check on Google earth whether there are cat-trappy enclosures, gardens, swimming pools, whatnots close by. But other than that, one can only wait. As amro says, if they want to and are able to, cats know how to return.
posted by Namlit at 7:35 AM on February 5, 2011

Oh yeah and what Mavri says; absolutely. Start by checking your attic (if any). Stupid cat that used to visit my grandmother once got locked up up there for more than a week, didn't make a sound. We found her by accident.
posted by Namlit at 7:37 AM on February 5, 2011

Check out the Recovery Tips: Lost Cat Behavior on the Missing Pet Partnership website. House cats are often very close to home. Also great tips about signage and how to tag your car.
posted by Agatha at 8:09 AM on February 5, 2011 [3 favorites]

Check garages and under porches. My cat has been stuck in garages for up to a week before. I only found him by walking through the neighborhood screaming his name (his little tiny meow alerted me of his location).
posted by PhoBWanKenobi at 8:15 AM on February 5, 2011 [1 favorite]

Yes, thirding Mavri. We lost a cat once during the Blizzard of '78 — he got out, apparently went into our next-door neighbors' garage. They closed the door, then didn't go to the garage for days because of the storm. He had a nice big voice, though, so when I went out looking for him I heard him howling and got the garage open enough.

Wander around your neighborhood, get near garages, call his name. If you've had recent snow, he could just be stuck somewhere.
posted by clone boulevard at 8:42 AM on February 5, 2011

Yeah, another data point for suggesting looking close by for things the cat might be stuck in, ours got stuck in next door's shed for a couiple of nights for his longest stay away from home.
posted by biffa at 8:47 AM on February 5, 2011

If it's cold where you are right now, someone may have taken in your cat to keep him safe from the elements. If he's friendly to strangers, he might be quite happy about this, and if they don't let him out, you'd be none the wiser.

He could have roamed beyond the area in which you put up posters, so they'd think it was just a cat who got dumped or lost. (Did he have a collar or a microchip?)

Anecdata: We took in a small, friendly cat who turned up at our back door, starving. We had her for about ten days before we took her to the vet and found out she was microchipped and had been missing from her home (several streets from ours) for almost three weeks.

And one of our other cats was missing for almost a week and turned up scrawny and smelling like an oil slick. We figured he must have been trapped in someone's garage. He has a pitifully small meow, so it's likely that nobody heard him until they finally opened the door.
posted by vickyverky at 10:07 AM on February 5, 2011

I'm going to echo what's been said a lot upthread. Every time I've had a cat go missing (especially a housecat) they were somewhere very close by, either inside my apartment, or trapped in a basement or something. Did you recently move or have some other kind of household upheaval? My cat loves to hide for days whenvever there's any kind of big change to her routine, and won't budge until she's accepted her new reality.
I know you won't feel better until you find him, but the last time my cat went missing, I spent days in a search similar to yours, thinking the worst. It turns out she had found a way to get into my ceiling and was hiding out there to protest a recent move! I lived in a ground floor apartment and apparently there was a gap between my ceiling and the floor of the apartment above. She finally came out to eat, and I took the opportunity to seal off all the gap entryways.
You could maybe look for holes in the backs of closets and things like that. Cats can really squeeze. Best of luck to you.
posted by swingbraid at 10:28 AM on February 5, 2011

I've had two friends who have found pet cats that were missing for a while, one for several weeks, and a third friend who had a cat that wandered far from home chronically. The far-wandering cat was very bold and friendly with strangers, who frequently assumed he was lost. Friend got calls from people all over the area---"Is this your cat? He just came right into our kitchen, he looks hungry." If your cat is a wanderer, and somehow lost his collar, someone may be keeping inside thinking they're protecting him.

The cat that was found after several weeks was finally found to be locked up in the crawlspace of a house a few streets over that had just been put up for sale. A work crew probably inadvertently locked him up, and the house was empty, so no one knew. My friends found him by going on one last walk around the neighborhood on a quiet Sunday afternoon and calling for him. He answered, and my friend heard him and broke him free. Any empty buildings or construction in your neighborhood?

You don't mention moving, but another friend lost his cat several weeks after he moved into a new neighborhood. He finally drove to the old house, and his cat popped her head out of the shrubs and greeted him like he was the one who was lost. Friend was amazed cat had gone as far as she did, after as many weeks at the new house. She did this a couple more times, but then he always knew where to look.

You don't mention anything about your situation at home, but if anything had changed--new pet, house guests staying over, cat bed moved, your cat might just be upset and wandering off in reaction, or hunkering down like swingbraid says. But in that case it's more likely that your cat is alive and out there, but still might need a little human help to get home.
posted by tula at 10:58 AM on February 5, 2011

My cat that went missing was trapped under my neighbour's porch, where she got snowed in (for almost a month! She got out when the snow melted a little, because she refuses to meow, so we didn't ever hear her crying). Another cat that was missing (but for less time, just three days) came back with a broken leg. Other cats have been fed by neighbours regularly. I would bet that your cat is stuck somewhere -- a garage, a shed, etc -- or been taken in as a stray/discarded pet.

Walk around -- a 2 block radius is almost certainly far enough -- put up flyers/things in mailboxes -- and call for the cat. If your cat is not a complete idiot like mine, your cat will call out when it hears your voice.
posted by jeather at 11:28 AM on February 5, 2011

I've had cats decide to take a random, unsanctioned walk in the great outdoors, and then decide they don't like the great, wide open, and promptly go into hiding. But they knew where home was, and I "caught" them by leaving food outside the door and watching it carefully - especially during sundown and sunrise hours.

Alternately, you could get one of those humane traps from an animal shelter, and put food in that. Leave it overnight, and you may very well find your cat in the morning, extremely ticked off at being trapped in a cage. (If it's winter where you live, put the cage somewhere sheltered, obviously, or watch it continuously. You don't want your cat trapped inside the cage and cold.)

I'm thinking good thoughts for your cat's return. >^..^<
posted by MexicanYenta at 2:41 PM on February 5, 2011

Sorry about your cat.

The good news, from my 30+ years experience with felines: even in the newest of locations, a cat will always, somehow, miraculously, find her way home. Given that the freedom (and life force) is there to return.

When my bengal escaped after I'd moved into my new home in a very rural area of Washington, I was certain she was lost forever, as she didn't 'know' the area we were in at all. But, sure enough, two days later she was home and acted like nothing at all was the matter. Of course she was hungry. She ate and then took a long nap.
posted by zenpop at 3:37 PM on February 5, 2011

Um, I think your random walk idea is quite silly. But if it any reassurance, we had a cat who would disappear for a month at a time and come back (very happy to see us, too).
posted by schroedinger at 5:41 PM on February 5, 2011

Probability theorist here. While I'm pretty sure your cat's not going on a random walk (I'm not a cat theorist, though), if he were going on a random walk, you wouldn't improve your chance of finding him by engaging in your own random walk, assuming some things about when you and the cat make your respective moves and what the initial displacement is between the two of you. Basically, you can think of your difference vector as itself performing a random walk with possible steps of 2 units in each direction. If the initial vector is of the right parity away from 0, the random walk is just as recurrent as the ordinary 2-dimensional walk your cat is on, so you'll intersect with probability 1. However, the expected time for either random walk to return to 0 is infinite, I'm afraid.

Anyway, I'm sorry about your cat, and I hope you find him. At least you don't have a lost bird.
posted by albrecht at 6:10 PM on February 5, 2011

It seems to me like two points walking randomly should meet each other with exactly the same probability as one random walk hitting the origin - as you may, without loss of generality, take the location of the second point to be the origin, with respect to which the first point is still a random walk.

It is true that you can swap the origin and walker but to conclude that this means that if BOTH the origin AND the walker are moving they will meet with the same probability is a non sequitor.
posted by DU at 4:47 AM on February 7, 2011

Do you have a local animal shelter? I worked at a county shelter and we received over 500 stray cats a month (either brought in by animal control or citizens who had found them). Our legal obligation was to keep them for 3 days if they had no ID, or 5 days if they had a tag or microchip. After that they would be evaluated for adoption. So if you haven't been doing so, you should check your shelter every three days for as long as you feel the need (they will have you fill out a lost report as well, and try to match your cat with ones that come in). We had people find their cats over two months after they went missing, and sometimes even after they were put up on the adoption floor. Good luck!
posted by Delfena at 9:22 AM on February 7, 2011

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