Causality: The Path Forking Problem


forkingIt seems to me that humans don’t assess cause and effect very well; we had to invent the scientific method as a way of teasing out which causes of a particular effect are the important ones. That’s a comforting illusion for us, but causality is not a chain of events and causes, it’s more like a lattice-work stretching backward in time to the Big Bang. In practical terms, it doesn’t make much sense for us to answer “Why did the chicken cross the road?” with “The Big Bang” even though it’s true: we search for something we can pin it on immediately.

We look around and see the coyote stalking the chicken and say “That’s why the chicken crossed the road!” while simplifying cause and effect down to a single sequence, in fact there were intertwined causal meshes that put the coyote there, intertwined causal meshes that put the chicken there, and intertwined causal meshes that put the road there for the coyote to chase the chicken across. Our world would be too complicated for us to cope with, so we simplify the more tenuous chains out of the picture. But if we think about it, we have to acknowledge that everything in the scenario is a necessary precondition for the scenario happening at all: there first had to be domestic chickens, or was it eggs?

When we simplify our view of cause and effect, we also create a side-effect that I call The Path-Forking Problem: it’s our tendency to look at a simplified view of a particular situation’s causes, then imagine that if we could change just one thing, the outcomes would otherwise be the same. I think it’s this simplification that’s at the root of time-travel stories: we imagine going back in time and changing a single cause, then let the clock run forward again and in all other respects everything works out the same way. But it won’t! When we go back to the fork in the path, and decide we’re going to take the other fork we assume we’ll toddle cheerfully down the other path, just like we did on this one, except – I don’t know – there won’t be a hungry mountain-lion on the other path like there is on this one. The path forking problem manifests itself in our thought, “If only I had taken the other path!” or “If I could go back in time and kill Hitler!”

Back in 1999 I had a chance to sell the company I had started, for a sizeable sum. The company that wanted to buy mine got bought by IBM for a very large sum, 3 months after I turned their offer down. So I would occasionally imagine that if I’d accepted the offer, I’d be exactly the same as I am now, except that my investment portfolio would have 6 or 7 more zeroes on the right-hand side of the total. But of course that’s an illusion: I might have taken the deal and been dead a year later, after wrapping a sports car around a tree. It’s not even possible to assign a likelihood to either of those paths, because there are infinities of things that never happened, that I can’t assign any likelihood to because I can’t imagine them all.

When I started to think about this, I realized that second-guessing your actions is an action, too – one which irrevocably changes the situation. That time it took for you to think, “I wonder if I should have taken the other path?” may be the time it takes for the mountain-lion to leap. Because all of the causes of an effect are necessary for it to have happened, the slightest change to any of them destroys the entire mesh of events that get us there. Stephen Jay Gould explains this in his book “Wonderful Life“: it appears that Pikaia Gracilens was a common ancestor of everything that has a spine; if something had even slightly altered the life-outcomes of some of them, the entire history of life on Earth would be unimaginably different. We don’t get to say “there might not be humans” and imagine that there still might be coyotes (or chickens) crossing roads. Or roads at all.

When this started to sink in for me I realized that every apparent decision – even the most insignificant – is irrevocable and utterly life-changing. One of my father’s friends was a heavy smoker and I told him “Mr Rose you should stop smoking” (I was about 14) and he told me that when he was on watch in Bastogne one night in December, 1944, he ducked his head to light a cigarette and a German bullet went by just where his head had been a fraction of a second before. But again the path-forking problem rears its head: perhaps if he hadn’t been a smoker, he wouldn’t have even ended up in that part of Europe at that time at all.* The infinity of possible futures expands out immediately from every point in the web of causes and effects and speculating about them is attempting to imagine an infinity of possibilities.

Then, I sort of felt like I understood what “living in the moment” means. We’re trapped like flies in amber in these webs of cause and effect. There is no “maybe” or “I wish” there’s only what is. What wasn’t doesn’t matter. What could have been isn’t even an illusion, it’s not meaningful enough to be an illusion: it’s a side-effect of our imagination, which is a mechanism we use to conjure possible futures so that we can convince ourselves that we choose between them.

Often, when we discuss “Free Will” there’s a dichotomy between determinism and “freedom” – the ability to decide which path we go down and the outcome of that decision. When I used to debate free will, I’d go back and forth on that balance, but now I understand that it’s uncontrollable incomprehensible randomness down one path, and random uncontrolled incomprehensibleness down the other; it just doesn’t matter. Free will compatibilists like Daniel Dennet make a big deal out of our “choice” while (Dennet, at least) accepting that the “choice” is largely illusory, its the future-predicting engine of our imagination running backwards and pretending it can understand and pick between possible pasts.

The chicken is free to imagine all the possible reasons it crossed the road, and the infinite options. I remember a comment by Richard Rosen on USENET back in the 80’s:

Anything is possible, but only a few things actually happen.

We’re machines that program themselves to think they can predict the future. Sometimes we even get it right. But usually that’s when the possible futures are fairly tightly controlled by physical law: if you jump out of an airplane, you are almost certainly going to go downward.**

divider2

(* He did die of lung cancer. But 40 years later than 1944.)

(**I always interpreted the surreal scene with the alien spacecraft in Monty Python’s “Life of Brian” as a particularly pythonesque commentary on our belief we can predict the likely effect of our actions)

Comments

  1. says

    I wrote:
    I realized that every apparent decision

    That’s why I question the idea of “decision”: when we think about decisions, we’re flattening the vast mesh of causality down to some little chain that we’ve arbitrarily ordered. If there’s free will in all of that mess, I’m damned if it’s anything worth having, especially because by the time we start thinking about our future decisions, we’re already in the future.

  2. sonofrojblake says

    Why was Mr. Rose smoking while on watch?

    Best time to spark up a fag is when all the Ruperts are in their pits.

  3. felicis says

    And yet we are still able to successfully plan out courses of action that turn out roughly like we thought.

    “we imagine going back in time and changing a single cause, then let the clock run forward again and in all other respects everything works out the same way. But it won’t! ”

    Well – it kind of will. In the short term – I expect because it takes time for the changes to propagate through the system. We can make predictions of various events and (on a gross scale) assign rough probabilities to them. We can make contingent plans that will turn out (for the most part) roughly as we expected, even if some of the details are different. And some of those details have a smaller impact than others. It’s easy to point out a single example of a single detail that leads to a large change – but he quits smoking and isn’t there at all? While possible, it is also possible that it would have no effect on where he was at all and he would have died (and so the conversation wouldn’t have happened and you would pick a different example to demonstrate your point).

    We can perform experiments in which we change one major factor and look for differences in the outcome and get consistent results. While, ultimately, you are correct about there being a web of causality, I think you are overestimating how sensitive this web is to changes.

  4. consciousness razor says

    I think it’s this simplification that’s at the root of time-travel stories: we imagine going back in time and changing a single cause, then let the clock run forward again and in all other respects everything works out the same way. But it won’t!

    Well, why won’t it? You seem to be assuming other stuff will certainly change, because we can’t control (or even know about) that other stuff changing. Which is correct, but that doesn’t imply anything about what would happen if you did “change a single cause.” The trouble here isn’t “incomprehensible randomness” down paths, but that we never change a single thing but always lots of things.

    Let’s imagine you don’t go back in time and don’t do anything. There are just two worlds. There is no physical interaction which at any time makes them different, nothing is causing one to be different from the other, or anything of the sort. They just are different. The difference is precisely and only that this electron is here in world #1, and it is a meter away from that location in world #2. Again, nothing interacted with anything, such that the electron was physically moved from where it is one of the worlds to its place in the other. Don’t imagine that, and don’t imagine that you did anything or could do anything about it, or that anything else did it for you. Those are just two worlds, which are otherwise identical in every respect, because that single electron’s location is the only difference.

    If the worlds are deterministic, that will be the only thing that implies they have a different history. They will have had to be different in the past if they will be in that pair of states in the present which I described, they’re different in the present, and they will be different in the future, for that reason and that reason alone.

    It’s fairly obvious that, when people are thinking about causation, they’re not thinking about anything like that (or if they are thinking it, they’re mistaken). Your time traveler will be interacting with stuff (all sorts of stuff they don’t want to interact with or don’t know about, besides Hitler who they wanted to kill) the moment they exit their time machine. If this kind of time traveler is merely visible, light reflects off of them or is absorbed, and that is very rapidly causing a mind-numbing amount of shit to happen everywhere around them.

    So, going back in time, walking up to him, and “causing Hitler to die” somehow would in any realistic and comprehensive account of the events involve causing more stuff to happen besides Hitler’s death. Lots and lots and lots more, most of which isn’t the slightest bit interesting to you (or so you think). So sure, who knows what all of the consequences of that will be? You don’t and nobody does. If the world’s deterministic, then the world “knows” what it will do (literally, of course, it just does it and knows nothing), which isn’t actually helpful to you.

    But if you did only do “one cause” at some time, then why wouldn’t you only need to keep track of how that has an effect on future events, since by hypothesis you didn’t cause anything else to be different? Of course, whether or not you cause that one thing, you’d also need to know everything else about the world other than that to make any use out of this information, which you’re never in a position to know. But it doesn’t look there’s any additional problem to pinpoint here, so long as you did have that kind of information. You’re just ignorant about it.

  5. Jean says

    I think we do more than flatten a mesh of causality when we talk of decisions. We imply at least some sort of duality. If we assume we are purely physical entities, which I do, then the decision you take (or don’t take) was the only one you could have taken.

  6. says

    Jean@#7:
    If we assume we are purely physical entities, which I do, then the decision you take (or don’t take) was the only one you could have taken.

    I agree with that.

    I’m a sort of a free will compatibilist in the weakest sense, though: I believe we have free will, but it’s an illusion. I have 3D vision, too, but that’s also an illusion. I believe sounds and sight are synchronized but that’s also an illusion. The stereotypical dualism-based free will – yeah, that’s not even an illusion, it’s just incoherent mouth noises.

  7. Jean says

    Speaking of illusions, I wonder how much our perception of time directionality is due to the directionality of the chemical processes involved in our consciousness. I don’t have enough knowledge of quantum mechanics to know if I’m completely off base but it seems to me that our every day concept of time is an illusion. And that also have an impact on causality.

  8. Pierce R. Butler says

    In any such discussion, I find it convenient to say

    If things were different, things would be different.

    This seems fairly effective at both killing the conversational topic and preventing it from returning. YMMV.

  9. says

    It is verifiable that much of our perception of continuous time is an illusion. See “stopped clock illusion” and also see what Apollo Robbins has to say about human attention. Not only is much of our perception an illusion, much of what we believe is true ABOUT our perception is also illusion.

    In truth, it looks a lot like we dip in and out of reality taking little bits here and there in a sort of predictable but wildly incomplete fashion. Then our brain makes up a fake movie for us to enjoy, and crudely paints in the bits that it can’t work out.

    Back to the original subject, I think Marcus has internalized too much of Primer to really be good for him ;)

  10. says

    felicis@#5:
    And yet we are still able to successfully plan out courses of action that turn out roughly like we thought.

    It’s amazing, isn’t it?

    It seems to me that the time-span (thus the number of other events taking place) between what we assign as “cause” and what we observe as “effect” has a lot to do with it. If I hold a ball, and drop it, it immediately falls. Aha! Science! If I decide as a teenager that I want to become a professional computer programmer, and I do, it’s … a bit harder to assign cause and effect – there we’re talking about broad trends that have a lot of other things impinging on them one way or another.

    When it comes to cause and effect in science I am always reminded of Feynman’s description of mouse experiments* – what scientists do when they set up an experiment is try to enumerate and isolate away all of the other causes for an effect. Scientists try to crush the latticework of cause and effect down into a single line – and it’s really hard to do that. Yet our brains and perceptions do it constantly: I turn the key in my car and it starts! But that’s a great oversimplification.

    I expect because it takes time for the changes to propagate through the system.

    I guess the speed of light’s got some hand in that, as an absolute lower limit. But there are always going to be broad historical trends that are going to (maybe?) fulfill themselves regardless of a single individual’s contribution. Hari Seldon’s historical predictions in The Foundation series always seemed like such a neat idea – yet when we think (as we do) of Hitler as a pivotal historical figure, we’re adopting the opposite idea: events move based on key individuals that catalyze them, not so much on broad trends like German militarism and the economic effects of the Versailles Treaty.

    The bigger the system and the longer the time between measures, the more likely a small change in a cause will result in a massive change in the effects. Hm. No that sounds right but (back to my earlier posting on this topic) it only makes sense because of our scale. Since the moment it began to form, Sol’s end-state was predictable, and therefore so was/is humanity’s history on Earth. There is no change to a cause that any human could make that would alter that effect in the slightest.

    While, ultimately, you are correct about there being a web of causality, I think you are overestimating how sensitive this web is to changes.

    Yeah. And I picked examples at a human scale; I think that’s our instinct. “Scale” in that context, I am not sure what I mean: it’s the size of effects and the rate of change as well as the duration of time. (I hesitate to push “Post Comment” on this because I realize that “size of effects” is begging my own question)

    (* Feynman really did not like psychology very much. I found his descriptions of psychology’s stupidities to be particularly amusing, since the psych department I graduated from was particularly fond of rat-running experiments)

  11. says

    consciousness razor@#6:
    The trouble here isn’t “incomprehensible randomness” down paths, but that we never change a single thing but always lots of things.

    Good point. I’m regretting invoking randomness, and wishing I had just stuck with “incomprehensible” – the last time I raised this topic in a thread someone made a very good argument that it’s not that this stuff is random, but rather that it’s incomprehensible because there are too many details at varying scales and our human brains tend to pick a scale that works for the occasion, and to stick with it.

    At the scale of The Battle Of the Bulge it’s very unlikely that Mr Rose’s decision to light up could have resulted in a German victory. I can only say “very unlikely” because of the strategic situation – if you asked me for a more precise estimate I couldn’t honestly give one. So, yeah, I’m not saying that if he hadn’t lit up, the allies might have lost WWII. That effect would be too large.

    [two worlds, one electron example]
    It’s fairly obvious that, when people are thinking about causation, they’re not thinking about anything like that.
    […]
    So, going back in time, walking up to him, and “causing Hitler to die” somehow would in any realistic and comprehensive account of the events involve causing more stuff to happen besides Hitler’s death.

    Yes.
    I forget which sci-fi story involved time-travellers going back to hunt a T-rex that was marked for death (due some sort of an accident) and deemed safe to kill a tiny little bit early. Of course one of the hunters stepped on a bug, too, and everything changed.

    But if you did only do “one cause” at some time, then why wouldn’t you only need to keep track of how that has an effect on future events, since by hypothesis you didn’t cause anything else to be different? Of course, whether or not you cause that one thing, you’d also need to know everything else about the world other than that to make any use out of this information, which you’re never in a position to know. But it doesn’t look there’s any additional problem to pinpoint here, so long as you did have that kind of information. You’re just ignorant about it.

    I agree with that. When you talk about
    ” you’d also need to know everything else about the world other than that to make any use out of this information” that’s the elusive (illusive?) “scale” of the cause and its effect. You do change the whole world.

    It doesn’t seem to go much beyond the world, though. Is that because planets are fairly self-contained by distance and gravity and vacuum?? I can see arguing that an event in WWII might change things that happen on Mars. What if Mr Rose’s grandsomething would have been Mars’ first explorer? I can’t see how his cigarette could change things happening at Sagittarius A*, though. Incomprehensibly small, perhaps.

  12. says

    Jean@#11:
    Speaking of illusions, I wonder how much our perception of time directionality is due to the directionality of the chemical processes involved in our consciousness.

    Last time this came up, Owlmirror recommended Sean Carroll’s “The Big Picture” talk. It’s interesting – Carroll appears to be arguing, if I understand him correctly, that entropy is what gives us our awareness of time’s passage.

  13. sonofrojblake says

    @Marcus Ranum, 15:
    The story is Ray Bradbury’s “A Sound of Thunder”.

    Interesting you should bring it up. If I recall correctly, the tourists leave a future world where there’s time travel on the day after an election, having been happy at the success of a sane, progressive, identifiably leftist candidate. The idiot hunter steps of the path, crushes a butterfly, and the tour guide gives him the causality spiel. They return to their point of origin, and the tech greeting them observes that it’s a good job that that pinko fag commie subversive wimp didn’t get elected (I’m paraphrasing), and that instead the strong, identifiably right-wing demagogue was successful instead. And at that point, the tour guide shoots the tourist. Which is the eponymous “sound of thunder”.

    I’m guessing someone stood on a butterfly.

  14. Rob Grigjanis says

    Marcus @16:

    entropy is what gives us our awareness of time’s passage

    Entropy changes define the “direction” of time. Clocks actually provide a good example of this. Roughly speaking, entropy change at constant temperature is the energy dissipated divided by the temperature. So, the gravitational potential energy of sand in the upper part of an hourglass is dissipated as the sand falls to the bottom. Likewise for the energy stored in a spring or a pendulum; it dissipates with operation. So the entropy of clock plus its immediate environment is increasing as long as the clock operates. Of course, “immediate environment” expands rather drastically for sun dials ;-)

  15. consciousness razor says

    Marcus:

    When you talk about
    ” you’d also need to know everything else about the world other than that to make any use out of this information” that’s the elusive (illusive?) “scale” of the cause and its effect.

    I would say a little bit elusive. It may not be what it seems to some people, so it’s an illusion (to them) in that sense, but I don’t exactly take an anti-realist line about causation. I’m a realist about most things, I suppose.

    But I’m a best-systems sort of Humean. What we see and know is just one damned thing after another. This, then that — this, then that. That’s basically all there is. However, we do notice patterns or regularities in those damned things, which are useful for understanding the world which contains them.

    So, physical laws (and concepts like causation, etc.) can be valid, true, factual statements about what happens, not extra things which govern or necessitate what happens. They are our pithy, informative summaries of what there is, in languages we can understand and use, which describe things just as any other particular fact does. There’s no metaphysical distinction to make between a fact which is lawlike or not lawlike. It’s just a matter of deciding what we need the most to make our systems for comprehending the facts. The “best” systems, people generally agree, are the ones which are the shortest and most informative about the most stuff, and maybe if we’re lucky they may do a few other things for us too, like being represented with nice pretty equations or whatever you like.

    It’s not a good system if you need every fact about everything in the entire universe. That’s not short, you can’t use it, nothing will every cause you to get all of those, and that’s not really informative in the way that you would like it to be even if you could have it.

    But that seems to be what is required if you’re going to remove all of these doubts and worries and such that you’re thinking about…. Maybe the thing to say is that you shouldn’t be so worried about it, because while it’s not even close to the whole story and can allow for errors/fallacies/confusion/etc. (if not used very carefully), concepts like causation aren’t really so bad when you look at it from that perspective. They’re doing a whole lot of fairly efficient explanatory work for us, which we aren’t otherwise equipped to do at all. It’s not something to be scared of or skeptical about — it’s a bargain.

    You do change the whole world.

    Or you don’t change anything. I don’t know…. What changes when “you” do something? Are you sure it wasn’t going to do that anyway? You’re part of this deterministic world, so the assumption goes, which doesn’t ever change what it was always going to do. You’re not a closed system either, so it’s hard to define very precisely what you’re referring to when you talk about “you changing stuff.”

    If literally the whole world/planet/whatever changes when you act, that’s clearly a violation of special relativity…. You’re not entangled with all of it, so quantum nonlocality couldn’t give you that either, however consistent it is with SR. Did you mean to keep within the speed limit on how this change propagates through spacetime, or is it something that can’t propagate? I guess I should assume the former, but it’s not obvious what you had in mind.

    I mean, if the world isn’t changing course in some sense, like I alluded to above, then that’s not something that propagates, in which maybe you could be thinking of something like selecting an entirely different universe with a different past, etc….

    It doesn’t seem to go much beyond the world, though. Is that because planets are fairly self-contained by distance and gravity and vacuum??

    Well, electromagnetism (including of course light) and gravity keep having effects, apparently to arbitrarily large distances. However, they’re inverse-square laws, so the effects become more and more neglible with larger distances.

    I can see arguing that an event in WWII might change things that happen on Mars. What if Mr Rose’s grandsomething would have been Mars’ first explorer? I can’t see how his cigarette could change things happening at Sagittarius A*, though. Incomprehensibly small, perhaps.

    Sure, some photons from Earth reached Mars very quickly. That has to be right, if any photon is headed in the right direction. Tiny gravitational changes would propagate outward at the same rate. Sagittarius A* would have to wait some tens of thousands of years though.

    It’s interesting – Carroll appears to be arguing, if I understand him correctly, that entropy is what gives us our awareness of time’s passage.

    He’s not one to say time is an “illusion” though. He’s in the “time is real” camp, but not necessarily in the “time is fundamental” camp. It corresponds with the entropy gradient, and the question is really how that can be explained or if it can be explained.

    Rob:

    Likewise for the energy stored in a spring or a pendulum; it dissipates with operation.

    The strange thing is that people have no trouble getting that it will work better if it’s not dissipating so much. You don’t need all of that heat/sound/whatever, which seems not to be helping it keep time. But you can’t get rid of it entirely, or else it wouldn’t work as that kind of clock.

  16. consciousness razor says

    Sure, some photons from Earth reached Mars very quickly. That has to be right, if any photon is headed in the right direction.

    Well, they could all scatter in the atmosphere or something else, thanks to EM obviously, but the basic point remains the same.

Leave a Reply