In order to do this convincingly, we must make the Discworld intrusions consistent, but even then we must address the convergence/ divergence problem, which is this. Would such a meddled-with world converge on to ours, demonstrating that history is stable, or would any tiny difference start a divergence that became wider and wider, proving history to be unstable?
Most people think the latter. Indeed, even the wildly imaginative physicists who believe that a new world history is created by each and every decision in this universe, spawning new universes in which the other choices were implemented, don't imagine that the histories converge. No, each universe goes its own way, spitting out new and divergent universes as it goes. The Trousers of Time are a tree: their legs can branch but never merge.
The Worlds of If stories were divided on this issue. Some had each tiny change in the past getting amplified, resulting in vast changes now: we've mentioned Bradbury's story where you trod on a butterfly in the far past, on a dinosaur hunt, and came back to find a fascist regime. Or the changes you made were all wiped out, because there was a gigantic all-powerful inertia-of-events Kismet that you couldn't change. However you tried to avoid your fate, that only made it more certain to happen. And some stories took a middle way; some things converged and others didn't.
This, we think, is the rational way to think about time travel and altering the past.
After all, we don't change the rules by which the past works. Gravity still operates, sodium chloride crystals are still cubical, people fall in and out of love, misers hoard and spendthrifts squander. What we change is what physicists call the `initial conditions'. We change the positions of a few of the pieces on the Great Chessboard of Life, The Universe and Everything, but we still keep to the rules of chess. That's how the wizards operated in The Science of Discworld II. They went back in time to remove the Elves from the game board; then they went back again to stop themselves making that mistake.
We are now ready to think about our question above: would the names of newspapers have changed if Abraham Lincoln had lived to a ripe old age?
Perhaps some of them would, because some cultures would have become rather different. Perhaps Quebec wouldn't have been French; perhaps New York would have been Dutch. But names like Daily Mail, Daily News and New York Times are so obvious, so appropriate, that even if the Roman Empire were still running things, the Latin equivalents would seem fitting. Someone would have invented flush toilets, and there would have been a steam engine time, when several people invented steam power. Some things in Western culture seem so likely, from toilet paper on up to (as soon as paper is invented) daily newspapers to plastics to artificial wood ... Technology seems to have a set of rules for its advancement, so that it seems rational to expect gramophones of some kind if people make music with musical instruments, then tape players when people get used to electricity and its possibilities for amplifi cation. Then from analogue to digital, to computers ... some things seem inevitable.
Perhaps this feeling is misleading, but it's silly to insist that absolutely everything in a slightly divergent future has to end up different.
Organic evolution has lessons for us here, and these lessons can instruct us about how likely various advances in animal organisation were. Innovations like insect wings, vertebrate jaws, photosynthesis, life coming out from the seas on to the land ... if we ran evolution on Earth again, would the same things happen? If we went back to the beginning of life on this planet, and killed it, would another system evolve and give us a whole different range of creatures, or would Earth remain lifeless? Or would we be unable to decide whether we'd done anything, because everything would be just the same the second time around?
If history `healed up', we wouldn't be able to tell if it was the second, or the hundredth, or the millionth time around - each time sooner or later producing a version of us, whose time machine goes back to The Origin. There would be a consistent time loop, as happened with the Elves in The Science of Discworld II. If life is `easy' to originate (and the evidence does look that way) then this isn't an exercise in going back and killing your grandfather, or if it is, your grandfather is a vampire and doesn't remain killed. If life is easy to invent, then preventing it happening once, or a million times, will make no difference in the long run. The same process that generated it will happen again.
Looking at the panorama of life on this planet, in time as well as space, we can see that there are two kinds of evolutionary innovation. Photosynthesis, flight, fur, sex, and jointed limbs have all arisen independently in several different lineages. Surely, like toilet paper, we would expect to see them again each time we ran life on Earth.
And, presumably, we'll see them on other aqueous planets when we explore our local region of the galaxy. Such evolutionary attractors are called `universals', in contrast to 'parochials': unlikely innovations that have happened only once in Earth's history.
The classic parochial is the curious suite of characters possessed by land vertebrates, because a particular species of Devonian fish succeeded in invading the land in our, real, history. Those fishes' descendants were amphibians, reptiles, birds, and mammals - including us. Jointed limbs are a universal innovation. The limbs of spiders, hydraulically operated, differ in detail from the limbs of mammals, and were presumably acquired via a different ancestor, perhaps an earlier arthropod proto-spider. The mammalian internal skeleton, with one bone at the body end, then two, then a wrist or ankle, then five lines of bones for fingers or toes, was an independent evolution of the same universal trick.
This highly unlikely combination now occurs in all land vertebrates (except most of the legless ones), because they are all descended from those fishes that came out of the water to colonise the land. Other parochials are feathers and teeth (of the kind that evolved from scales, which are what we have). And, especially, each of the special body-plans that characterise Earth's animals and plants: mammal, insect, rotifer, trilobite, squid, conifer, orchid ... None of these would appear again after a rerun of Earth's evolutionary history, nor would we find exact replicas on other aqueous planets.
We would expect much the same processes to occur, though, in a repeat run of Earth or on another similar world: an atmosphere far from chemical equilibrium as life forms pump up their chemistry using light; planktonic layers of the seas colonised by the larvae of sedentary animals; flying creatures of many kinds. Such ecosystems would also probably have `layers', a hierarchical structure, fundamentally similar to the ecosystems that have emerged in so many different circumstances on Earth. So there would be 'plantlike' creatures, a productive majority of the biomass (like Earth's grass or marine algae). These would be browsed by tiny animals (mites, grasshoppers) and by larger animals (rabbits, antelopes), with a few very large creatures (elephants, whales). Comparable evolutionary histories would lead to the same dramatic scenarios, but performed by different actors.
The central lesson is that although natural selection has a very varied base to work with (recombinations of ancient mutations, differently assorted in all those `waste' progeny), clear large-scale themes emerge. Marine predators, such as sharks, dolphins, and ichthyosaurs all have much the same shape as barracuda, because hydrodynamic efficiency dictates that streamlining will catch you more prey, more cheaply. Very different lineages of planktonic larvae all have long spines or other extensions of the body to restrain the tendency to fall or rise because their density differs from that of seawater, and most of them pump ions in or out to adjust their densities too. As soon as creatures acquire blood systems, other creatures - leeches, fleas, mosquitoes - develop puncture tools to exploit them, and tiny parasites exploit both the blood as food and the bloodsuckers as postal systems. Examples are malaria, sleeping-sickness, and leishmaniasis in humans, and lots of other parasitic diseases in reptiles, fishes, and octopuses.