Um exemplo com uma prova matemática fabulosa desempenhando o papel que sua informação em um pedaço de papel jogou:
On the other hand, we have to consider the idea of a consistent causal loop. While equally thought-provoking, this theoretical model of time travel is paradox free. According to physicist Paul Davies, such a loop might play out like this: A math professor travels into the future and steals a groundbreaking math theorem. The professor then gives the theorem to a promising student. Then, that promising student grows up to be the very person from whom the professor stole the theorem to begin with.
De Como funciona o tempo de viagem , de Kevin Bonsor e Robert Lamb
Heinlein, na história "Por seus bootstraps" também ilustrou esse tipo de causal loop em um aviso "sem causa" ou "auto-causado" que dá voltas no tempo . A partir dos Paradoxos da Viagem no Tempo do site www.fresian.com:
A paradox of time travel arises in relation to this story. The narrator does indeed set himself up "by his bootstraps" -- his present and future selves all interact with each other to produce the events. The paradoxical nature of this comes down to the case of a notebook that was provided to the narrator by the older man in the future. It contained a vocabulary of the language that was spoken by people in the future. The narrator learns the language and, as the book wears out over the years, copies it over into a notebook he had fetched from the present. This notebook, as it happens, is the very one he, as the older man, then provides to his other self. He is therefore the same person who both learns the knowledge from the notebook and put the knowledge into the notebook in the first place. The vocabulary as a certain list of items arranged in a certain way was thus complied by no one whatsoever. The knowledge exists in a closed temporal loop and is in an important sense uncaused or uncreated. The narrator himself notes that there is something peculiar about this.
Existe, é claro, uma página da Wikipedia dedicada aos paradoxos das viagens no tempo , e um deles é o causal loop paradox, ou como também é conhecido o paradoxo de predestinação :
A predestination paradox (also called causal loop, causality loop, and, less frequently, closed loop or closed time loop) is a paradox of time travel that is often used as a convention in science fiction. A temporal causality loop is an event whereby a specific moment in time repeats itself continually inside an independent fragment of time. The paradox occurs when a time traveler is caught in a loop of events that "predestines" or "predates" him or her to travel back in time.
No seu exemplo, a informação no papel é o viajante predestinado.
De fato, há uma página da Wikipédia dedicada à ficção apresentando laços causais temporais (embora algumas das histórias desta lista são sobre esses laços causais, algumas das histórias listadas ali se direcionam para a profecia auto-realizável).