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Sure the world will be completely different, but in high likelihood it will be very similar.

To take your examples, the kid born might be completely different, but will likely receive a somewhat similar education that it would have so he won't be too different.

Wars that might have been avoided on one occasion might just have been delayed, (WW1 ferdinand assassination comes to mind).

In chaos theory, the space of possibilities is usually split up in different regions called basins that each converge towards around its own attractor point. But usually a small change isn't enough to make you change of basin. It only matter when you are close to the boundary, on the edge of chaos.

It's kind like re-rolling when playing D&D, you can get luckier and win the fight instead of losing it, but if you are not well prepared it won't matter in the long run.

At scale, the law of large numbers average effects out. In science-fiction the theme of order vs chaos is often evoked, because it's one of the most powerful tool for the underdog hero to turn the situation around. By definition the hero must choose the more risky side and chaotic situation that will give him his only chance to get out on top.

How can the world be "very similar" if it consists of an entirely different set of people within a relatively short time? Think about it, if not a single one of the politicians, inventors, scientists, or really any plain regular person would have existed. If any tiny change does not stay in complete isolation (which I don't think is physically possible), eventually the world will be entirely different. Even language will completely diverge.

> Think about it, if not a single one of the politicians, inventors, scientists, or really any plain regular person would have existed.

The world would look more-less the same.

We like to ascribe inventions to lone brilliant geniuses, but the truth is, inventions are made on schedule. Whenever the "time is right", all the necessary preconditions are met, someone makes the invention. Usually multiple people simultaneously, but we tend to credit the first one that manages to tell the world about it. In our timeline, relativity is attributed to Einstein, but if a time traveller killed him when he was a child, someone else would still have published more-less the same thing around 1905. Maybe some time later.

Similar things seem to apply to economies too. People predominantly follow incentives, and those don't tend to flip randomly.

So if you traveled back in time a hundred years and thrown a rock at a random squirrel, the world today might be populated by completely different set of actors, but the scene would be roughly the same.

The weather patterns, infrastructure, and economic constants are going to be nearly identical. Roll back the clock 2,000 years and you would still see major cities mostly at the same rivers and ports.

Major inventions often have several people making the same basic discovery at the same time. You can’t build heavier than air controlled flight without efficient engines. You can’t build efficient engines without high precision manufacturing. Which requires it’s own constraints etc.

Replay the last 30 years and Dell might not have been the mail/phone then internet order PC vender to become a household name. But, one of them would because several where trying and efficiency of scale is a major advantage.

PS: One if my favorite examples is in a high school science class I was messing around with a power supply and mechanical pencil lead. It ended up making a rather bright light, in a moment of wonder I realized I had become possibly the millionth person to discover a precursor light bulb. Well over a hundred years late by on measure but in terms of the 100,000’s of years history of humanity fairly close.

On the other hand, going to war (or not) could either accelerate or prevent major technological progress. And that depends on politics. So it seems like that's not all that predictable either?

I agree that there would probably still be major cities at the same rivers, but they would not be speaking any language you would recognize.

Also, it's not that hard to discover electric light if you have a fully working power supply already... just about any piece of conductive material that is too small to handle the current going through it will make some light of varying intensity, so that realization probably came very very quickly after the concept of electricity was born. (The hard part was then to make that light last.)

Different language but a similar diet at the list of domesticated plants and animals has not changed all that rapidly. Which means at least some aspects of culture would be similar.

As to light requiring a power supply that’s my point. Roll back 50 years to 1969 and they had integrated circuits, phones, radios, batteries, CCD, and networked computers. Without WWIII the odds seem high they would end up with highly capable cellphones with cameras, internet access, and reasonably familiar form factors due to human hands.

GPS being a free public system links to a specific aircraft being shot down. So that’s questionable, but we had early satellite navigation. Thus, the odds are good the military at least would have a similar system and if nothing else a paid for version via private companies seems likely.

Chaos theory uses the term strange attractors to these kinds of situations. Minor changes are generally going to end up in very similar situations.

Siblings born years apart can turn out to be similar to one another as adults, both in appearance and temperament, despite the fact that the parents have changed and learned in that time, and they grow up with a different peer group.

Someone born from the same batch of sperm, with parents at the same stage in their lives, is likely to be pretty similar.

There may be significant differences at the individual level e.g. a child of a different gender is born to a family with certain ideas about gender roles, or stillbirths/miscarriages/disabilities occur or fail to occur due to this falling branch, but in aggregate, the people of the next generation will be pretty similar to the ones who would have existed otherwise.

A lot of inventions get attributed to individual geniuses, but in many cases society was ripe for them, if Joseph Swan didn't exist, or became a ballet dancer instead, we would still have had electric light bulbs around the same time.

I am not just the product of my parents, but of the centuries of history of society leading up to now.

So in a few generations, you are right that all those small changes will result in all the people being different, society as a whole is likely to be fairly similar.

At the grand scheme of things level, most of the time, the world is very resilient. For example if a cosmic ray hits RAM and flips a bit, well we have correction codes, and it will be as if nothing ever happened, the error will be corrected and the change will lose all its oomph by being transformed into useless heat.

Even before error correcting codes we would have just got a crash and rebooted. This universe with a sightly angrier developer would still most likely be the same once he vented it out with a few swear words.

People once were looking for signs in the skies, and acting upon it to inject chaos into their lives, but random act of chances take time to make an impact whereas Order is effective and to the point.

Once the world has favored order over chaos, it builds itself to be resilient to small changes, it submit itself to the law of large numbers, and once it has mastered it, it submit itself to the rules it has chosen for himself.

That may be the great filter of Order to explain the Fermi Paradox. Order is so effective, that it can convince itself there is no Fermi Paradox using basic statistics, and march in order towards its own doom, because the doom is in the order itself. Hopefully once we storm area 51 in September, we will know for sure that aliens exist and that there is no reason to worry about Order being a great filter.

Take the problem from the other perspective, imagine you are given the opportunity to re-roll something in the world, but just one single thing locally to create a brand new universe, would you still choose to break a branch in a random forest ? Would you try to find a camel just before the last straw breaks its back, just to see the camel owner pick-up the fallen straw once again. At what point in time should you rollback for the world to be receptive to your divine intervention ?

In your example, a falling _might conceivably_ affect one person's conception. But even in that example, the odds are most likely that it doesn't.

Let's say 99 times out of 100, a delay of a few seconds doesn't impact whether one person is conceived.

There's a pretty big gulf to cross from that, to 'an entirely different set of people in one generation.'

> Let's say 99 times out of 100, a delay of a few seconds doesn't impact whether one person is conceived.

It does not? Isn't the person that comes out dependent on many many minuscule factors? Aren't all sperm cells, from the same person, different in genetic makeup? Aren't many outside factors influencing how exactly the genes will combine?

You assumed that the woman who was delayed would go on to conceive that night. I suggested that, generously, 99 times out of 100, the branch falling doesn't slow someone down and/or that person doesn't go on to conceive that very night.

So? You assume that with the end of the day, the person gets magically reset, and will next day behave exactly as without the change, without the slightest difference? Despite having arrived a few seconds later, had different conversations because of that, went to bed slightly differently, had more and more diverging thought trains...?

In a more physicalist sense, you are somehow assuming that all the state that exists in her brain and body in general, all the synapses, electricity pulses, cells etc. have a chance to get back to the same state that it would have been without the change. I think that's pretty much impossible.

In fact, if anything, things will be even much more different the next day, and the further you go into the future, imposing more and more differences onto her own environment, rippling out exponentially.

Even more generally, every particle is subject to the same, with or without people in the equation, bounded only by the Light Cone emanating from the change (due to light speed being the limit on everything, including information; https://en.wikipedia.org/wiki/Light_cone ).

I'm not saying it isn't ever possible, just that most of the time, whether you arrive at work at 8:00 or 8:01 doesn't have a meaningful knock-on effect in your life or anyone else's.

I have to concede on your conception argument -- that is legitimately fragile.

A man ejaculates around 200 million sperm. The tiniest change to either of the parents and a different sperm will be the on to fertilize. Then, you have a different person born.

It may be we have a warped or view of "similar" because it's so close to us -- how do we calibrate it?

As far as we know, no causation goes faster than light, so even if the "small change" was "an utter tide of total destruction of all matter", most of the observable universe can't be affected.

I've had the same thought before. In response to the question "if you go back to being a child knowing what you know now, what would you do?"

Being the eldest I thought I would immediately cry for my unborn siblings who are now just an unrealized possibility.

How could we estimate how resilient the timeline is to small changes? If no small animal had been in the vicinity of the falling tree, perhaps that event would be much more insulated from humans.

Think of it this way: if you take a single particle in the world changing course, when it eventually collides with another, it will be with a different particle that it would originally have collided with. Once that happens, two particles now have a different course. Eventually, it'll be four, then eight, and so on, until pretty much every particle's course is shifted. This global shift is almost certain to happen eventually, and relatively quickly.

At a macroscopic scale, though, that won't look like much at all. Air currents, temperature, and so on don't really depend on what specific microstate the atmosphere is in. It's like shifting every object in a room at random by a tenth of a millimeter, for all intents and purposes it doesn't change anything. Usually. From time to time, some microscopic details can snowball into macroscopic effects. Well, pretty much any small change anywhere in the world is going to shuffle all of these, everywhere in the world, a few years down the road.

This means that, perhaps counter-intuitively, the more time passes, the more likely a small change is to have an effect. First it will shift everything a tenth of a millimeter, but eventually one of these shifts will snowball into a one-millimeter shift... which will propagate everywhere, setting the stage for a ten-millimeter shift, and so on. You'd be unlikely to notice, though, because the proximal cause for a big change will almost always be a medium-sized change, not a tiny one. Furthermore, it could take a very long time for the effects to really ramp up: large scale natural processes are very robust. Still, if a process has any kind of sensitivity to noise, it's just a matter of time before it shifts.

One simple way it can snowball is by affecting who gets cancer due to some radiation being or not being absorbed.

I think it's a good question. Let's assume there is absolutely no animal nearby (tree branch makes a sound, slightly changing any animal's behavior, chain reaction...), and let's further assume that the tiny air currents generated in this scenario do not only not cause a tornado as in the original butterfly effect (which, frankly, is not very likely), but are "buffered" enough that they don't create any change perceptible to any human at all.

Then, overall, the makeup of the world is still different. Will this really never cause anyone to get a speck of dust in their eye that they otherwise wouldn't, flinching, preventing them from having the though "oh I have to buy milk" that they were about to have?

I don't know... maybe it's just that some changes are indeed so tiny and remote that it takes them a long long time to have an effect, but once an obvious effect is present, I guess we're back to everything changing again?

> let's further assume that the tiny air currents generated in this scenario do not only not cause a tornado as in the original butterfly effect (which, frankly, is not very likely)

You're underestimating the effect now. You only have to play about with a simple chaotic function and see how quickly the most infinitesimal change leads to utterly different results to appreciate that a butterfly flapping its wings sufficiently in advance literally alters the course of all subsequent tornados.

If your home had a 99% chance of making it through tornado season unscathed one year but for the flap of a butterfly's wings, then it may still have a 99% chance, however it would be a completely new role of the dice.

But you're assuming the world is a chaotic function. Don't confuse the ability to add up tiny changes with those changes having a meaningful impact.

You can dip your finger in a river and tell me how a bunch of molecules are displaced and then those molecules displace other molecules and so on in a way that wouldn't otherwise have happened. But for all intents and purposes, the river carries on in its original course as if nothing happened. It doesn't turn into a seething mass, it doesn't reverse course, it doesn't spiral off into infinity.

Sensitivity to initial conditions is relatively rare, and even most chaotic functions only get interesting around certain values.

The timeline should actually be hugely resilient to changes at smaller scales.

Consider the world in terms of large numbers of probability distributions.

When you combine distributions it's the variance and not the deviation that you add together.

I.e.: at larger scales the distribution of probabilistic variables tends toward the mean.

All that's left at smaller scales is quantum white noise.

I think all that resolves to is that average temperature, mass/energy ratio, and other macroscopic values will be (roughly) the same. It says nothing about whether the same people will exist or not. Consider that simply one person not existing, or simply not procreating, means that the entire tree of descendants below them won't exist.

Sure, they won't be exactly the same - but give it 20 generations and there won't be a significant difference.

The people will largely be genetically the same, the population and its distribution will be largely the same - they'll fit into the same ecological niche, they'll be inventing the same things and polluting the same rivers.

There is potential for the butterfly effect to do something - the right change to an unstable equilibrium certainly has the potential to trigger a cascade of events.

In general though, such events are highly improbable - and even dramatically cascading events will have their impacts dampened across time and space.

But a different tree of different people will exist in their place, and their contributions to the world are likely to be similar to the original peoples' too.

But are people objectively as importantly unique as we subjectively perceive them to be?

You could extend this further: what if we could "rewind" time, then just let things play back again. Would everything be exactly the same as it is now?

Would "random" particle interactions happen in the same way (making them decidedly not random)? Would the same branch fall at the same time, landing in the same place? Would every coin flip be the same? Would every single decision every human makes be the same?

Since rewinding time is entirely theoretical, and assuming physicalism, I guess that entirely depends on whether, in your thought experiment, you allow quantum interactions (those which are posited to be truly random) to play out the same way or not. If yes, yes, if not, not. 8)

Choas is kinda funny. When you have systems of a large number of non-linear things they tend to average out. A time traveler could be as little as a single particle and still re-shuffle the entire deck so to speak. But it's still the same deck of cards.

In the end you're still in nearly identical initial conditions. While the individuals will change, the whole of society will be extremely similar due to statistical mechanics. Susie being slightly more aggressive will be balanced out by Johnny being slightly less aggressive, etc... You may cause a new extrema event though like Johnny inventing a cheap nuclear bomb, or you may prevent one.

A good time traveler would be able to sit outside time and probe reality using tiny changes until they get the outcome they want. But at that point you are so powerful I can't imagine anyone would care. Maybe that's why we didn't all kill ourselves yet. Some time traveler poking at the timeline.

The short story "Anxiety is the Dizziness of Freedom" has an interesting take on this theme, where the many worlds interpretation of quantum mechanics is true, and a device lets people communicate with parallel realities. They start off with a difference of one quantum measurement but slowly diverge.

Well, go ahead and try it out. Have you and a friend leave slightly differently from your homes in San Francisco to go see another friend in San Jose. You leave ~ 10 mins from each other and you'll arrive ~ 10 mins from each other. You'll encounter similar traffic.

Go ahead and test the way your world works. The short term doesn't matter. It gets beaten by the weight of other stuff.

Absolutely, the butterfly effect renders all back in time plots fatally flawed. Never mind killing Hitler's grandfather or making sure your parents still meet, your very appearance in an earlier world, even for an instant, would guarantee that before long you and everyone else who would otherwise have been born afterwards would certainly never exist.

I saw a drama based on Steven King's 11/22/63. A guy goes back in time to save JFK from assassination. Spoiler: he saves JFK in the past and when he finds his way to the future the world is destroyed. Oops.

This presumes a variant of time travel that allows changes to make a difference. A many world interpretation would just mean branches (and you'd only see your changes if you manage to find a way to navigate to them); a fully deterministic model would imply you can't change anything and your time travel always had happened exactly the way it would happen, and whatever you think you achieved was consistent with history (wasn't really Hitlers grandfather after all for example); a strongly convergent model would see the effects mostly have relatively minor effects, and when they tip over and have bigger effects, those bigger effects still end up cancelling out over time.

We both don't know how time travel would work if it is possible, and don't know well enough what the odds are of any small change affecting large long time change.

E.g maybe if Hitler didn't come along, someone else would have.

And in fact, exploring those effects is often a major part of back in time plots.

Moorcocks 'Behold the man' for example have someone travel back in time to meet Jesus only to realise that the real Jesus was a mentally disabled man and that since he is the only one that knows the image of present day Jesus, the time traveler himself must always have been the person history knows as Jesus, presenting a deterministic idea of time, where paradoxes would be impossible, because time is in that world in effect just one more spatial dimension our perception moves across.

There are many such models that would allow for some time travel plots to be plausible all the time we have no idea how it actually works.

Of course all of them will probably look quite ridiculous and quaint if we ever figure out the real thing.

Not in Gargoyles

It depends on what theory of time travel we are talking about. If we have the multiverse theory, then you are just creating a new split in the possible timelines.

Other theories would say that your time travel has already been taken into account in the timeline, so anything you are doing to change the future will actually cause it to happen as it has already happened.