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“If you really book it” meaning several miles a year. Nomadic hunter-gatherers wander hundreds of miles a year. If they kept on in one direction, they could cover the 10,000 miles or so from Alaska to Patagonia in less than 100 years. But I don’t think that’s how it went.
The hunter-gatherers known today walk hundreds of miles in big loops, almost always ending up back exactly where they started – but all the habitable land around them is already occupied, and they’d have to fight to move outside of their ancestral lands. The first ones in the Americas would always be finding new land, with animals who hadn’t learned to fear human hunters. They’d have looped back over the same territory for a few years, then moved their base towards a new area. Most bands would stop moving rather than cross a desert or other difficult area, but a few bands would want to see what was on the other side. If the most daring moved base-camp 100 miles every 5 years on the average, the Folsom-point culture would spread out all over North and South America in 500 years.
They’d be even faster if they were using boats to go down the sea coasts rather than just walking – even with a primitive boat made by stretching a bison hide over a wooden frame, you go faster with less effort and can bring more stuff with you. Humans in Eurasia and Africa were crossing rivers and settling islands over ten thousand years before the Folsom-point culture reached North America, so they probably did know how to make boats.
The odds against something like the Miller-Urey experiment going all the way to a self-reproducing organism in a few years in a laboratory vessel are almost infinite. But life didn’t originate in a laboratory vessel, it originated anywhere on Earth – or any similar planet. That “experiment” was running in millions of pools of impure water on each of trillions of planets over hundreds of millions of years. There were an almost infinite number of chances for that almost infinitely unlikely event to happen. And we only know about one planet of the trillions in our galaxy – one where it did happen.
Robert A. Heinlein somewhat subverted that idea in another 1950’s novel, A Door into Summer. Time travel was discovered in a secret government project, hoping to be able to collect armies from several decades into one big army when needed. It didn’t work out and they stopped the project and buried the invention. You could set the time change, but whether you went forward or past was random, and that was a law of nature. Before the project was closed down, a scientist named Leonard Vincent tried to use the machine to see the future 500 years from now. He went the other way, and is known as Leonardo da Vinci – a very frustrated guy, knowing how all sorts of stuff worked but unable to make the materials to make it work in the 1400’s.
It was used one more time. Heinlein’s protagonist had been betrayed by his business partner and his girlfriend, who together stole a billion-dollar invention and hustled him into cold sleep to wake up broke decades in the future. He got a job as an engineer and learned about the time machine when a co-worker who’d been involved got drunk. He broke into the government building and used the machine to go back in time and change things. (No revenge needed except leaving his betrayers to go broke.) He knew the machine would take him back, because he knew another self had been doing the things he would have.
Isaac Asimov explained that way back in 1955, in his novel The End of Eternity. There’s at least one other novel on the same theme, but I don’t remember the author or title.
Time travel is invented. It transforms the world. Someone doesn’t like the changes. They go back and sabotage the invention. Time travel is never invented. Repeat as many times as needed.
Not if there are bagpipers.