To answer the OP directly: no, it’s not forbidden to wipe one’s behind on Sabbath.
To answer the others:
Martini Enfield:
As someone mentioned, “rest” on Sabbath doesn’t mean “relaxation.” It means “cessation of physical creative activity.” How is “creative activity” defined? The Torah mentions the prohibition in the context of the creation of the Tabernacle in the desert, so the Rabbis derive that any type of work that was necessary for the creation of the Tabernacle is forbidden on the Sabbath. Thirty-nine categories of work were identified by the Rabbis as prohibited by the Torah. Despite the fact that many objects exist today that the Rabbis could not possibly have anticipated, the essences of these categories of “work” are well-defined, and it can be determined whether new inventions make use of any of those forbidden categories. Light bulbs, pressing the buttons on elevators (though not specifically riding on them without taking any action), TVs, Computers and PlayStations all involve creating sparks of electricity, which falls within the halachic definition of fire, which is forbidden to create or maintain.
What activites are permitted? Plenty. For one thing, you mentioned a picnic…you can certainly have a picnic, as long as you’re within a halachically-valid private domain (note, this does not relate to ownership of the land, but to certain properties of a defined area). Take a walk. Read. Play board games without recording scores in writing. Bring the kids to a playground. Pray. Learn Torah, or other intellectually stimulating subjects. Are we so addicted to our electronic entertainments that we now feel incapable of resting without them?
And yes, have sex as well. Although it can lead to creation, it does not NECESSARILY lead to creation, and more importantly, it is not one of the categories of labor that was required for Tabernacle construction.
chappachula:
Destroying something is Rabbinically forbidden, but tearing a piece of toilet paper from a roll is worse…it is tearing something to size, which is a creative act.
The Chao Goes Mu:
That’s a gross oversimplification. One would not be allowed to put raw food in an oven in order for it to cook on the Sabbath, automatically timed or otherwise. This would only allow re-heating of already-cooked food, or further cooking of food that is already somewhat edible, and even within those actions, there are limits to what you’re allowed to do.
Mangetout:
If you’re talking about a regular proxy bid, I think that would be fine…if another bidder causes your bid to be raised, that’s not your action, and it wasn’t even an action you indirectly caused, as you didn’t know for sure that someone else would be bidding. If you’re taking about using one of those automatic “snipe” engines that places a bid at the last minute and that happens to be on the Sabbath, I don’t think that’s allowed.
panache and Johanna - re:sex, see above.