Time Travellers Diaries are confusion.
You might read a Diary linearly from the first to the last of a month in a year. Only later does it occur to you that actual sequence of events was 1, 3, 5, 7, 9, 11, 13... not 1, 2, 3, 4, 5, 6,... - the key with time travellers is discovering the monotonic function that describes their sequence of time stamps. A monotonic function is one where the line of the graph never crosses. A straight line is a monotonic function. A string of spaghetti is, when dry, a monotonic function but when cooked it can be a knot, a tangle, a non-monotonic function. Which is not a guarantee that cooked spaghetti is non-monotonic.
You really do need your wits about you to work out how to read a Time Traveller's Diary.
The Grandparent Paradox, in time travel, is where you travel back in time to become the parent of your parent. It can transform the monotonic function of a Time Traveller's personal time line into a knot. Where the beams are crossed. Where things get tangled. The Grandparent Paradox has variations that include killing your grandparents thereby ceasing to exist and so not travelling back in time to kill your grandparents therefore existing therefore travelling back... ...it is questionable if this is really just an infinite repetion or an actual logical paradox. Regardless of the logical analysis, there is an idea that is important: you can see a potential paradox by simply listing out the dates the Time Traveller visited in the order that the Time Traveller visited them. The Time Traveller's time line is the uncooked spaghetti, the dates visited, in the order visited, are the cooked spaghetti. Which means that the grisly technical details of monotonic functions being everywhere continuous or, everywhere differentiable, or any one of a number of concepts in higher mathematics are not absolutely needed. You can simply contemplate the order of events in a diary.
Which leads to a very interesting variation on the Prisoners' Dilemma.
Two time travellers are imprisoned in solitary confinement with no means of communicating with the other. This can happen when there is a knot in the spaghetti and one Traveller is in the Future of the other Traveller in their own time line. Since time lines are independent, both travellers can be in the Future and so unable to communicate with the other.
A third Time Traveller, lack sufficient information to oblige the pair to admit a hideous act, but they have enough oblige them to admit to a less hideous act. Say mugging as against murder. Simultaneously, the Third Time Traveller offers the One Time Traveller and the Other Time Traveller a bargain. Each betray the other by testifying that the other committed the murder, or to cooperate with the other by remaining silent. The possible outcomes are:
- If One and Other each betray the other, each of them remain in their space time positions for two years.
- If One betrays the Other but the Other remains silent, One will be set free and the Other will in their space time position for three years.
- If One remains silent but The Other betrays the One, The One will remain in their space time position for three years. and the Other will be set free.
- If One and The Other both remain silent, both will remain in their space time positions for one year.
If there are Three Time Travellers then the two of their numbers can be obliged to participate in a Prisoners' Dilemma. Which, coupled with the possibilities of the Grandparent Paradox makes for an interesting problem. Especially if the Murder Of A Grandparent is taken to be the Forging Of A Block on a Blockchain Ledger that subsequently forks.
Paradoxes are something that plague both the Time Traveller and the Cryptographer.
The trick is to be imprisoned in time for only the year. Which means cooperating. Which means having a Zero Knowledge Proof method for communicating that you wish to cooperate across space time.
September 23 1987.
