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Just to warn the average reader this is probably going to read a lot like science fiction. I don't really expect anyone to believe any of this, but at the same time I cannot completely disregard my observations because there is enough supporting evidence that I have come across during my lifetime to make this theory plausible. Bear in mind I used the words "theory" and "plausible".
For a moment, consider the idea that time is not merely linear, travelling from point A to point B, but rather turns as a steady spiral, much like the coil of a spring or the shell of a snail. Unlike the diagram presented here, showing the various geological eras of Earth's history in a steadily rising and outward spiral - our "linear" time travels inward, reaching a finite "end point" beyond which nothing continues. This point could be considered the end of time, the point which Meat Loaf cannot wait to reach after scoring.
Now, imagine if you will, that humanity has realized the end of time is imminent, and the advance of technology has reached a point where it can not only conclusively prove that there will be an end of time, it can also measure how much time is left before the end. With such technology comes additional technology providing humanity with the means to travel through time via the fourth dimension, which permits crossing the bands of each loop in the time spiral. These crossing "windows" would need to be similar to the "windows" the NASA space shuttle uses to reenter Earth's atmosphere and return to the planet's surface. So it would not necessarily be possible for a time traveller to access any point in history at will, but rather only certain timelines that aligned with the one they currently occupied.
Knowing that time is about to end, and possessing the technology to travel backwards through time, humanity might choose to survive the coming armageddon by taking advantage of their time travel technology and jumping into the past. Thus surviving their doom, they would also (with great probability) introduce a schism into the time line, branching off from the original with potentially catastrophic results.
Anyone who has seen the film Back to the Future Part II should be familiar with the concept of alternate timelines. By travelling back in time and changing the course of history by interfering with a series of events as they played out, subsequent events will then change. This idea was previously introduced by the short story A Sound of Thunder by Ray Bradbury, where a time travelller inadvertently steps on and kills a butterfly during a hunt to kill a Tyrranosaurus Rex, and in so doing returns to a completely different timeline than the one he had left.
Should a significant number of humans (significant being more than two or three) travel to a point of time in the distant past permanently, or even should they travel to different points along the timeline, there would be an unbelievably different series of events that would unfold from that point forward. There would also be a significant increase in human population upon the planet, because I highly doubt that these time travelling humans would choose to sterilize themselves in order to reduce their impact upon the timeline. Humans are way too ego-centric to make such a decision for themselves.
However, I am a great believer in fate. As a great believer in fate I would state that certain events in the history of humankind upon the face of planet Earth are bound to repeat themselves, even in these alternate timelines. Therefore I would propose that as this new timeline created by the time travellers approaches its own end, a new group (and significantly larger number) of time travellers would choose to avoid their fate by travelling back in time. Due to this repeat event, the original problem (of a markedly different timeline being created by the time travellers) would be compounded by the new batch of time travellers, alongside perhaps some or all of the original time travellers from before who are now replicating themselves along this third newly created time line.
Before this gets far too messy to comprehend let me sum up:
Earth⍺ (Earth alpha, or original Earth timeline) approaches the "End of Time" and → human time travellers "cheat Death" by escaping to the past, which then creates → Earth¹ (first alternate timeline) with greater population than Earth⍺ and a completely different series of events of history, but still approaches the "End of Time" resulting in → more human time travellers who "cheat Death" by escaping to the past, including some or all of the original time travellers from Earth⍺ which creates → Earth² (second alternate timeline) with a greater population than Earth¹ including duplicate humans as a result of time travellers from Earth⍺ also present in the Earth² timeline. The Earth² timeline also approaches the "End of Time" resulting in → even more human time travellers who "cheat Death" by escaping to the past, including some or all of the original time travellers from Earth⍺ and Earth¹ which creates → Earth³ (third alternate timeline) with a greater population than Earth² including duplicate and potentially triplicate humans from the Earth⍺ and Earth¹ timelines respectively. And so on, and so forth, potentially to infinity.
Does your head hurt yet? If not, keep reading.
Does string theory, or the theory of multiple dimensions start to make a bit more sense now? It should. Each variation of these events can be simply explained by time travelling. Certain people and places will exist in multiple timelines, but not in all. Certain events will take place in multiple timelines, but not in the same way, and not with the same results, with the exception of the "End of Time". Also, unless these time travellers are able to return to their original timeline in order to warn their brethren of the mistake they are about to make by embarking upon their journey, there is no way to prevent history from repeating itself, in the future.
Okay, that last sentence made my head hurt, but it's the best I can do with this limited vocabularly called English.
One congruency that I can assume exists across all timelines would be the Georgia Guidestones. These mysterious stones appeared in Elbert County, Geogia, upon the request of a mysterious uknown person by the apparent pseudonym of R.C. Christian.
Most tellingly, in eight different languages the stones state the following:
Maintain humanity under 500,000,000 in perpetual balance with nature.
Guide reproduction wisely — improving fitness and diversity.
Unite humanity with a living new language.
Rule passion — faith — tradition — and all things with tempered reason.
Protect people and nations with fair laws and just courts.
Let all nations rule internally resolving external disputes in a world court.
Avoid petty laws and useless officials.
Balance personal rights with social duties.
Prize truth — beauty — love — seeking harmony with the infinite.
Be not a cancer on the earth — Leave room for nature — Leave room for nature.
Assuming I were a time traveller and wished to avoid repeating my mistakes, yet I was unable to pass the message to the source of the problem, because that source was far into the future, this is the best possible idea I can think of - create a monument that will hopefully survive intact to reach the future in order to warn time travellers of their folly.