Ah, yes, that weasel word, “could.”
With all this discussion of what could happen, does anybody consider that one result could be absolutely nothing? That a tiny event in the past might not be magnified (butterfly effect) but reduced to insignificance?
Then what would we call it?
Jebus people, have none of you seen any of the Back to the Future films?
Yeah, but Doc was greatly exaggerating when he thought that running into your past self would result in a galactic (or at least solar-system sized) matter / antimatter spacetime continuum explosion!!!
I see. And then the bear, having not eaten the fish on schedule, doesn’t… um… do what bears do in the woods on schedule. This lack of bear plop fails to fertilize one tiny little hemp seed that, due to a unique genetic make-up, would have produced a plant containing 20% to 30% more cannabinoids than the others. This tiny seed founders and expires.
Flash forward into the future and Bam - no Mary Jane.
Ok, so there’s no pot, big deal - The Grateful Dead and Phish just had to have a little more talent is all. A few stoners never became stoners, whoo hoo, big change. But consider the effect marijuana has had on our culture, on our language. Thanks to that one tiny organism dying, there would be no Straight Dope and thus no SDMB.
Oh the humanity.
But if that tiny creature died, then the food that it would have otherwise eaten will now be available for another tiny creature who would otherwise have died of starvation. Unfortunately its demise was delayed only long enough to be eaten by a fish. Or not, but unlikely that something as robust as a fish would have died as a result of missing one bite of food.
“For want of a nail, the war was lost.” I doubt it.
Well at least one person gets it 
It was a very tiny fish
I think inherent to the river view is some underlying fatalistic/intelligent design/IPU outlook. That is, the course of the river is set and dominates any small-scale interferences because the watercourse is guided by the banks and bed.
While I don’t necessarily agree that each and every butterfly is special, and crunching one a million years ago will necessarily result in bad television movies, I don’t think time/nature has some sort of compensating mechanism. That is, if you step on a bug that is somehow connected to the rise of Rome, some other coincidence won’t come along to compensate and preserve dear Romulus—the wolf never would have shown up.
On the other hand, if your theory is that the number of factors giving rise to Rome is so vast that annihilating one of them will have no noticeable factors, then I tend to agree. However, this strikes me as recasting the original idea in an unfair manner. Granted, I can’t speak for the actual original (who gets credit for it, anyway? I thought the story was Bradbury, but don’t know if that’s correct of if it predates him), but the warnings were not to interfere with the past because it may have vast consequences—things are so complex there’s no way to tell. This is different from all acts will have such consequences, as a quick trip to Frogstar will surely tell.
Back to the Rome example, yes, it is comprised of a myriad of factors, and removing any one of them may not be noticeable. But if there were a pair of twins, or a great writer who gave a burgeoning tribe a central myth to cling to, there are remote factors that could, if removed or altered, poof away said factors such that Rome would be unrecognizable. A ‘river’ theory suggests that nature/fate/et al would compensate. Nothing wrong with that, mind you, if that’s your intent.
Let’s try this in Mundane Pointless Stuff I Must Share instead of General Questions. Don’t get up, I’ll move it for you.
Gfactor
General Questions Moderator
The further back you go, the more drastic the changes will be. Any minute changes to the time of conception will radically change the genetic makeup of any pregnancy. And any change at all to the timeline, including just the mere existence of a new person for a brief moment will likely completely change the history of weather starting about two weeks later. Extrapolate from there - how important is the genetic makeup of specific people to major historic events. How important are particular weather patterns to major historical events?
Do you mean “will be” or “may be”?
One change in my genetic makeup and I have red hair instead of brown, another change and I have boobs and a vagina instead of moobs and their appropriate accompanyment.
One change in history and Romulus is raised by a pack of water buffalo, another change and Rome builds pyramids while Cairo invents gunpowder.
I think it boils down to a perception of scale. A tiny fish could doom us all but the accidental destruction of a continent could barely affect the weather. The only way I can wrap my mind around the dissonance of scale is to apply Schodenger - the effects will be both insignificant and cataclysmic at the same time, only the observation of the effects defines them (but even that changes the outcome).
The weather is a chaotic system, which means that it’s extremely sensitive to initial conditions. This is why we can’t predict the weather more than a few days in advance. No matter how many measuring stations we have and how accurate we make them there are alway tiny little fluctuations and eddies that we can’t measure and that will eventually turn into global effects.
In a true chaotic system ANY change to the initial conditions will eventually have a global effect. So it’s not a matter of the time traveller accidentally killing the wrong butterfly. Every butterfly is “the wrong butterfly”. In fact even if the time travel just spends his time sitting quietly in the middle of the Sahara Desert the tiny temperature and air flow fluctuations he introduces will eventually (over the course of several months) completely change the weather for the entire globe.
I wonder if incredulity at that was a factor that led to the OP. Do the basic precepts of chaos theory state that something will have such effects or that it can have such effects? Say I travel back in time and, two minutes before eruption, I take a dump in Pompeii. Or, for that matter, on the rim of Vesuvius. Say I pop back a few thousand years and piss right into a hurricane. Will these have global effects? Say I play fetch with my dog in the Yucatan Peninsula ten minutes, hours, days, weeks, years, decades, or millennia before the big smoosh—which will have a global effect, which will be overwritten? Or do I have chaos theory wrong, and each will have a global effect, but on the what, an atomic scale? At what point does the effect become so small as to be negligible?
So yes, randomly stomping on butterflies is a bad idea for a time traveler, but some river-like events may nullify the effects of such brutality.
In a true chaotic system small changes NEVER become negligible.
Now since the weather is a real-world system and not a mathematical abstraction we can’t be absolutely certain that its behavior doesn’t become more stable at some extremely small scale. However, given that the same laws of fluid dynamics that are used to model large weather systems can also be used to model very tiny volumes of liquid or gas it’s reasonable to assume that the weather behaves chaotically even on the scale of fractions of an inch.
The river metaphor is comparable to the idea of a “strange attractor”. Many chaotic systems converge on a bounded set of possible configurations. You can’t predict what state they will evolve into, but there are certain states that are impossible for them to reach. For example, a butterfly can’t cause a hurricane at the north pole no matter how much it flaps its wings. When you step in a river you can’t make it jump its banks, but you will completely change the flow pattern far downstream.
Will be. Weather and sperm selection are chaotic systems which mean that extremely small changes in initial conditions will have drastic effects on the final outcome. In the case of weather, I’d say that any change at all on the planet will completely change the history of weather from two weeks on (excepting general patterns like seasons of course). In the case of sperm, probably a difference of one second in the time of ejaculation will result in the child being almost as different as a sibling (the genes from the mother will be the same but the father’s contribution will be completely different including possibly the gender determination) as well as the possibility of course of no fertilization - or of fertilization in cases where originally there wasn’t any.
It’s not a matter of the child’s genes changing as it is of the sperm being a completely different one which means that 50% of the genes (the father’s contribution) will be a different set.
One change in history and Romulus is raised by a pack of water buffalo, another change and Rome builds pyramids while Cairo invents gunpowder.
Weather will definitely be affected by any small change. Again, how much effect this has on history depends on how much you think history is affected by weather patterns and the particular genetic makeup, gender or existence of certain people. It will also likely be changed most by other events that had small probabilities of occurring but major impacts. And of course, the further away from an event you get, the more small changes will combine to gradually change things down the line.
It’s this little bit right here I’m struggling with. Sure, one tiny change and a whole different sperm fertilizes the egg with a whole different set of genes. But that set is from the same source, the original genic information that wrote itself onto the sperm is the same. Unless I missed something with that whole Friar Mendahl [sp] and his peas in high school biology class then the changes may occur, or they may not. They may be as varied as different sex or they may be as simple as male pattern baldness. Either way, if the source of the information is the same I may or may not come out the same or similar but at worst I will be my brother or sister (actually the chances are exact that I will be my brother or sister).
The same with the global events. I think Rhythmdvl made an excellent point with the Pompeii example. I find it hard to believe that, if I timed my time trip just right and popped into a shack in Washington at exactly the right moment, suprised the occupant with a cheerfull “Hi-ya Howie, how ya doin’?”, take a quick piss on the duvet, shout out “By the way, duck.” and pop out just milliseconds before the Mt. St. Helen’s eruption that my presence would have any effect what so ever.