The Cause-Effect Nullifier, conceived by Fred Blau, is a theoretical device that resolves cycles in a dependency graph. For example, let's say you lock your keys in your car. Well, you need your keys to get into the car to get your keys. So you'd invoke the CEN, which would let you use your keys to open the door so you could get them in the first place. Here are some other examples of its use:
But the coolest use of the CEN has to be the proof of P=NP. Since every NP-complete problem can be reduced to any other, solving one (in polynomial time) solves them all (in polynomial time). See the circular dependency here, eh?
There's also the reflexive use of the CEN: using the CEN to procure a CEN. What we do is first use the CEN (we don't have it yet) to locate the Universal Locator, then use the Locator to locate the CEN we needed to begin with. Then we can use the CEN again to make it so that we don't need the CEN to use it in the first place.
Of course there's the problem that the Locator will only locate things that exist. To bypass this, we have the thing-out-of-nowhere machine, which is yet another theoretical device that brings into existence anything you name, so long as it can exist (we don't want to create any square circles, for example). So now the thing-out-of-nowhere machine doesn't have to exist, because we can invoke the CEN (which also may not exist) so that the thing-out-of-nowhere machine creates the first instance of itself, then we can thing-out-of-nowhere the CEN we needed in the first place, invoking the CEN to resolve that circular dependency of using the CEN before we have it. Then we can locate the Locator and do all sorts of crazy stuff. Note that the thing-out-of nowhere machine doesn't have to tell you where it created the thing, because you can always just use the Locator.
I have yet to come up with a proof of the impossibility of the existence of any of the above theoretical devices. Such a proof would deny the existence of all of the other devices, because of the interdependencies... or would it?