Thursday, March 18, 2021

Almost Everything You Do Causes Almost Everything

Suppose I raise my right hand. As a result, light reflects off that hand differently than it otherwise would have. Of the many, many photons flying speedily away, a portion of them will escape Earth's atmosphere into interstellar space. Let's follow one of these photons.

The photon will eventually interact with something -- a hydrogen atom, a chunk of interstellar dust, a star, the surface of a planet. Something. Let's call that something a system. The photon might be absorbed, reflected, or refracted. (If the photon passes through a system without changing or being changed in any way, ignore that system and just keep following the photon.) If it interacts with a system, it will change the system, maybe increasing its energy if it's absorbed or altering the trajectory of another particle if it's reflected or refracted. Consequently, the system will behave differently over time. The system will, for example, emit, reflect, refract, or gravitationally bend another photon differently than it otherwise would have. Choose one such successor photon, heading off now on Trajectory A instead of Trajectory B or no trajectory.

This successor photon will in turn perturb another system, generating another successor photon traveling along another trajectory that it would not otherwise have taken. In this way, we can imagine a series of successor photons, one after the next, perturbing one system after another after another. Let's call this series of photons and perturbances a ripple.

Might some ripples be infinite? I see three ways in which they could fail to be.

First, the universe might have finite duration or after a finite period of time it might settle into some unfluctuating state that fails to contain systems capable of perturbation by photons. However, there is no particular reason to think so. Even after the "heat death" of the universe into thin, boring chaos, there should still be occasional fluctuations by freak chance, giving rise to systems with which a photon might interact -- some fluctations even large enough, with extremely minuscule but still finite probility, to birth whole new usually solitary and usually very widely spaced post-heat-death star systems. (This follows from standard physical theory as I understand it, though of course it is disputable and highly speculative. If there are nucleations of Big Bangs in ways that are sensitive to small variations in initial conditions, that could also work.)

Second, successor photons could have ever-decreasing expected energy, gaining longer and longer wavelengths on average, until eventually one is so low energy that it could not be expected to perturb any system even given infinite time. Again, there is no particular reason to think this is true, even if considerations of entropy suggest that successor photons should tend toward decreasing energy. Also, such an expected decrease in energy can be at least partly and possibly wholly counteracted by specifying that each successor should be the highest energy photon reflected, refracted, emitted, or gravitationally bent differently from the perturbed system within some finite timeframe, such as a million years.

Third, some photons might be absorbed by some systems without perturbing those systems in a way that has any effect on future photons, thus ending the ripple. Once again, this appears unlikely on standard physical theory. Even a photon that strikes a black hole will slightly increase the black hole's mass, which should slightly alter how the black hole bends the light around it. And even if photons occasionally do vanish without a trace, such rare events could presumably be cancelled in expectation by always choosing two successor photons, leading to 2^n successors per ripple after n interactions, minus a small proportion of vanished ones.

It is thus not terribly implausible, I hope you'll agree, to suppose that when I raise my hand now -- and I have just done it -- I launch successions of photons rippling infinitely through the universe, perturbing an infinite series of systems. If the universe is infinite, this conclusion is perhaps more natural and physically plausible than its negation (though see here for an alternative view).

Such infinitudes generate weirdness. With infinitude to play with, we can wait for any event of finite probability, no matter how tiny that finite probability is, and eventually it will occur. A successor photon from my hand-raising just now will eventually hit a system it will perturb in such a way that a person will live who otherwise would have died. Long after the heat death of the universe, a freak star system will fluctuate into existence containing a radio telescope which my successor photon hits, causing a bit of information to appear on a sensitive device. This bit of information pushes the device over the threshold needed to trigger an alert to a waiting scientist, who now pauses to study that device rather than send the email she was working on. Because she didn't send the email, a certain fateful hiking trip was postponed and the scientist does not fall to her death, which she would have done but for my ripple. However vastly improbable all this is, one thing stacked on another on another, there is no reason to think it less than finitely probable. Thus, given the assumptions above, it will occur. I saved her! I raise my glass and take a celebratory sip.

Of course, there is another scientist I killed. There are wars I started and peaces I precipitated. There are great acts of heroism I enabled, children I brought into existence, plagues I caused, great works of poetry that would never have been written but for my intervention, and so on. It would be bizarre to think I deserve any credit or blame for all of this. But if the goodness or badness of my actions is measured by their positive or negative effects (as standard consequentialist ethics would have it), it's a good bet that the utility of every action I do is ꝏ + -ꝏ.



My Boltzmann Continuants (Jun 6, 2013).

How Everything You Do Might Have Huge Cosmic Significance (Nov 29, 2016).

And Part 4 of A Theory of Jerks and Other Philosophical Misadventures.

[image source, cropped]


Anonymous said...

This is great. But just a note about your invocation of probabilities and inevitabilities. For no finite universe (in time or space) must an event of nonzero probability ever occur. All we can try to say, under some assumptions of independence, etc., is that the odds of it *not* occurring may be very small. And if we have an infinite universe, probabilities can start to behave in unexpected ways (cf. infinite lotteries). Things don't work quite as simply as "probability x infinity = inevitability."

But there's a larger problem, which is that we don't know at this point in our understanding of the relevant science whether the sample space of possible events in our universe is compact or not. If the sample space is noncompact (roughly speaking, unbounded), then there can be large regions of that sample space that are never visited, no matter how long we wait.

Eric Schwitzgebel said...

Thanks for this helpful comment, Anon! If I wanted to state this more rigorously with respect to the probabilistic assumptions, do you have a source you'd recommend I look at? Although I didn't get into it in the post, the way I'm thinking about it is finite collections of particles (say galaxy-sized), which we care about within finite error tolerances (say a millionth of a Planck length), the configuration spaces of statistical mechanics and quantum mechanics, and Poincare recurrence.

Anonymous said...

Different Anonymous Guy:

Another mistake frequently made when speaking about probabilities is the whole "infinite monkey's ... Shakespeare" thing. I say it like this:

There are infinite real numbers between 1 and 2. You could go on for infinity simply listing them. Nowhere though in that set will you ever see 7.

Infinite doesn't mean "contains everything" it means endless, boundless, goes on forever, etc.... Those monkey's could just repeat gobbledygook forever.

chinaphil said...

Yeah, as with the guys above, I wanted to say, infinite space/time does not mean infinite possibilities. Specifically, some events may in fact have zero probability of occurring, but we can't know that in advance.
Another issue would be to do with noise and diminishing signals. At a given distance away from an event, it would become impossible to detect that event either because there is too much intervening noise (e.g. random quantum events in space) or because the effect of the event, attenuated over the surface of its event-cone shell now falls below detectable levels. That would effectively break the chain of causation.
A third breaker in causal chains is quantum randomness. If a photon hits an atom, there is a probability that it will cause an electron to jump orbits, and a probability that it won't. To the extent that I understand it, it's genuine randomness hard-coded into the universe. You cannot ascribe the outcome to the incoming causes.
And a final one is people or other conscious beings. If consciousness means anything, it almost certainly means that the actions of people are not merely the mechanistic results of inputs to them. So it doesn't matter how much I provoke you, the fact that you bash me over the head cannot be caused by my input; it must be caused by you.

P.D. Magnus said...

You begin by saying, "Of the many, many photons flying speedily away, a portion of them will escape Earth's atmosphere into interstellar space. Let's follow one of these photons." Have you done a back of the envelope calculation on this? I honestly don't have a hunch about this one way or another.

George Gantz said...

I'd suggest we stick with the finite. If there was a big bang, it was finite and the ensuing universe must be also. Moreover, quantum physics has shown time and space are not continuous, but quantized and therefore finite. Thankfully! Anything beyond that is unprovable speculation, and speculations about the infinite are fraught with impossibilities. In my book, infinities are in the God zone.

Given a finite universe, your meditation about the traveling photons is interesting. One Unitarian minister once framed it this way: It is quite plausible (although difficult to calculate), that the communion wine you consume contains at least one molecule that was in the body of Jesus. I put it another way during one induced ecstatic experience fifty years ago: "Everything is Everything." So I wonder now - is nothing something?

SelfAwarePatterns said...

The flip side of this is everything that happens here is influenced by ~13.8 billion years of converging causal factors. (Assuming nothing bleeds through the big bang from whatever might have existed before it.) It makes hand wringing about free will seem misplaced.

It seems like if the universe continues expanding, eventually we end up with a situation where every elementary particle is in its own Hubble volume (maybe in 10^10^100 years or something). With nothing to interact with, it seems like the wave function of that particle would be smeared out over the entire volume. Your hand raise might still be imprinted on many of those wave functions, but it seems hard to see them propagating after that. (Not that 10^10^100 years isn't a very good run :-) )

Tyler said...

This is related to "longtermism"

Most of the predictable effects of our actions are on the distant future, so we should take the actions with the most positive effect on the distant future:

Given roughly the reasoning in the OP, if we accept the doing/allowing distinction we should do as little as possible:

Arnold said...

'Standard consequentialist ethics as positive, negative, neutral'....
...and nature is movement and change, shades of light and dark ...

Then the moral object too, is a particle before us...
...without time or space as a consequence...

Great stuff..

Eric Schwitzgebel said...

Thanks for the continuing comments, folks!

Anon 04:55 & chinaphil: Although it's possible that the monkeys would always create the same proper subset of plays, that's not what would be predicted by standard physical theory as I understand it. But yes, you're right that infinite -> everything is too fast. There are some other assumptions needed, which I left implicit and probably should have specified more clearly!

Chinaphil: (1) See above. (2) Right, only finite probability events. (3) If the photon is absorbed, then it would be a violation of conservation of energy if the system did not in some way become higher energy and then, presumably, act differently than it otherwise would have. If some proportion of systems absorb the photon without being perturbed, however, that's built into my third ripple stopper and shouldn't mess things up if it's << 50% of the time. (4) On consciousness: I'm not sure I'd agree, but even if so, again as long as << 50% of the system perturbances are of suitably stubborn conscious beings, the ripple should continue.

PD: I'm not aware off the top of my head of the percentage, but geostationary satellites can pick up pretty good detail despite being above almost all of Earth's atmosphere and photons are plentiful. Even if (as seems unlikely) not a single photon escapes, we can start the ripple within the atmosphere if we like.

George: Ah, but why not explore the consequences of infinitude also? There's certainly no consensus that the universe is finite. If infinitude is weird and in the "God zone" -- well, who will think about such matters if not weirdo philosophers like us?

SelfAware: Both your points seem right to me, but your second point assumes an unfluctuating post-heat-death universe. That's certainly a possibility, but mainstream physical theory, as I understand it, predicts fluctuations.

Tyler: Yes, those are interesting connections. One person's modus ponens is another's modus tollens, though!

Arnold: Thanks!

Ezra said...

Your signal combined with other independent signals (from everything else' photons) quickly loses its informational value. You see this both in thermodynamic ensembles and in encryption.

Theoretically, you can reverse out the constituents, but the easiest way to treat the outcome is just as some of statistical noise. I don't think you can call it "causation" anymore.

Eric Schwitzgebel said...

Thanks for the comment, Ezra. As I see it, there are two separable issues.

One is whether the decrease in informational value makes any of the claims in my post false if they are interpreted as claims about counterfactuals or what-would-happen-if. I don't see how (pending some more specific counterargument). But for that photon off my hand, that scientist would have died hiking, for example.

The other issue is whether the truth of those counterfactuals is sufficient to warrant saying that my hand's motion "caused" the survival of the scientist. I interpret this as a terminological issue about the word "cause". I favor a liberal terminology, but I don't object too strongly to more conservative constraints on what ought to count as a "cause" and think the substance of the view remains the same, regardless of that terminological dispute. Yes?

Ezra said...

I suppose I'm using a narrower definition of causation.

Previously I didn't see your post about the Cosmic Butterfly Effect, which is an interesting idea. I'm not sure I 100% believe in it (mainly because the universe is so sparse vis-a-vis the atmosphere on earth), but I'm not 0% on that either.

It seems like your argument is if you believe in the Cosmic Butterfly Effect, then everything that happens or not-happens _could_ counterfactually be caused by your doing or not-doing some minor thing. That's seems a natural consequence of the definition of a chaotic system, where some slight change in initial conditions can result in some arbitrary big change in the outcome.

I suppose that's true in a way. Although I would still question how often a theoretically chaotic system is in practice that chaotic. Maybe only 1 out gazillion butterfly flaps actually have that big an effect, in which case, most ripples still cancel themselves out and you don't have to subtract infinity from infinity in summing up your consequences most of the time.

Why do you think "almost everything" you do would have such wide effects?

Eric Schwitzgebel said...

Right, the difference between that previous post and the current post is that in the current post I was trying *not* to assume a that the universe is a chaotic system in that specific sense, but instead trying only to trace out the effects of a single, non-chaotic photon on the assumption of infinite time and arbitrarily large post-heat-death fluctuations.

NC said...

Interesting. I'm currently working on a scifi novel project. There's a scene this reminded me of from my novel. A protagonist who was once a math and phil major is on a hike and meets a astrophysicists who believes in infinite multiverses. He also is suffering great depression because he concludes that this entails none of our actions matter because nothing can contribute to the total goodness or badness of the cosmos since it's infinite. He loses the will to live. My protagonists cures him of his depression by telling him of surreal numbers and addition under the surreal infinite numbers.

Yohan said...

The photon could perturb a dissipative system that is in a deep attractor basin, in which case the system will very quickly return to its stable state, and it will be "as if" the photon did nothing, since such a system is memoryless. Most living things have quasi-stable states, a single photon perturbing a whole "system" is a very rare occurrence.

Going further, you can think about what Robert Batterman calls "asymptotic freedom" and what Robert Laughlin called "insensitivity to miscroscopics". Many systems have robust invariance to pertubations. In some sense this is why they are "systems".

Also, as others have pointed out, the probability calculations may not always give you an appreciable expectation. (You can only define probabilities over infinite spaces by positing a restricted/asymmetrical density, so even the tiny probability cannot be constant over all spacetime, and will generally shrink to almost-zero over time.) You may have seen those "age of the universe" style arguments in physics and computer science. Some probabilities are small enough that the expectation is less than one event for the entire known age of the universe.

Eric Schwitzgebel said...

Yohan, yes presumably events like saving the hiker will be much less frequent than the entire known age of the universe. We're talking about minuscule probabilities but *infinite* time. At least that's the setup I'm working with in this post.

Arnold said...

Do finite/infinite together provide a space a place a object a (moral) standard...
...regarding is just a measurement, but okay, in science and philosophy, if confused with location or non-location events...thanks, "Is The "Many-Worlds" Interpretation Of Quantum Mechanics Viable"

JS said...

Suppose you're right. Doesn't that mean (from a consequentialist viewpoint) nothing we do matters? Murdering someone is no worse than giving them a cupcake - since, in the grand scheme, each event causes everything.

Patrick S. O'Donnell said...

More modestly (ontologically speaking) or analogically, is the so-called butterfly effect relevant here? Perhaps someone has mentioned this but I missed it.