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Rudy #6. Time As A Divergent Series

As I mentioned in an earlier post, I've always been repelled by the notion of the multiversal world of branching time--a cosmos in which no decision matters, as you also do the opposite in some other branch of time.

Rather than feeling that the other paths are real, we in fact have an emotional, experiential sense that the bad, unchosen paths are in fact shriveling away to the left and the right. If we didn't feel this way, why would we sweat our big choices?

I'd like to see a story in which the unchosen paths really are withering away. Or, if not withering, being somehow backed away from.

So for the purposes of an SF story I'm thinking of, I'll propose that there really is only one truly existing path through the branching thicket of possible worlds. The others are juiceless abstractions. But I do want a sense of someone feeling out the best paths as in Phil Dick's vintage precog story, "The Golden Man."

My gimmick might be to suppose that our path is not a striaght line. It has kinks in it, stubs. Our cosmic world line does very commonly grow a stub out a few seconds (or longer) past a given branch point. But then it backs up and goes into the main branch. There's a continuous line of time but it sometimes reverses its direction a bit and then starts forward on a new tack.

Suppose these reversals of time are very common. In fact they're all but ubiquitous, as rapid as the flickering flow of thought. I think of the physicist John Wheeler's remark that electrons are waves because they need to "sniff out the best path."

People don't notice the reversals. When the time flow kinks and makes a U-turn, those moving along the timeline experience events as running backwards. Like a rewind. But they don't notice. The memories get erased. If you play a movie backwards, it's not like the people on the screen start saying, "Hey, we're going backwards."

In order to have a story, we'd need that our character does learn to notice. How?

Not quite sure. Suppose this guy has learned to view his memories as in some sense real. And he develops a 4D spacetime consciousness so as to be present at each instant of his life. And he manages to get so in tune with the universe as a whole that he (falsely) begins to imagine that he's influencing the reversals, the U-turns. Like a gambler on a roll who starts falsely imagining he's influencing the dice with telekinesis.

Some others have the rare power to notice time's reversals as well. And our hero meets a woman with this power, and they are fellow travelers for a while. Watching the reversals happen. Timefreaks. Not entirely sure if they are or are not causing the U-turns. Discussing this.

In writing about time adventures, I'd prefer not to bring in the tar-baby of second-order time. I'd like to see just one bright, folded time line that's etched upon a time fan. So I don't want my characters actually to be changing the shape of the line, because then we're looking at a second-order time in which the man's and the woman's long world-snakes of a time-bodies are kinking and writhing. They feel like this is happening. But actually they're wrong.

So what's the story's kicker? Let's say something bad happens to our hero. He's about to die in a really gnarly and horrible accident. And he decides that his life for the last few hours or months has been on a bad path. There's an element of romantic conflict with his woman friend as well. And now he wishes he could roll back the universe before he dies. And then at the last second there's a U-turn in time.

It's a little like the Jorge Luis Borges story, "The Secret Miracle," where the passage of time pauses for this guy who's about to be executed by a firing squad, that is, the guy perceives time as stopping so he can think things over before the end. But nobody else notices.

In our story, when our hero hits the U-turn, our hero imagines that he or some cosmic power has gotten hold of the whole universe and put it into reverse just before he was about to get creamed. And for awhile it's better for him than for the guy in the Borges story, as he's off doing new stuff.

But now, with universe onto a new path, something worse happens. Our hero meets up with his lost woman friend, and, oh no, now she's about to die horribly. He makes another huge effort of the will, and experiences another temporal U-turn and maybe then he goes into a branch where things get even worser. There seems to be no happy path on the time fan of possibilities. The world was as good as possible before he hit that one lifesaving U-turn. And now, without exactly willing this, he ends up at that point again. And he meets his death. It's a little like that Ambrose Bierce story, "An Occurrence at Owl Creek Bridge."

The one upside is that, in this (final?) version of the guy's timeline, the woman lives.

Right before he dies he realizes that there never was any second-order time at all, no meta-time. He was just sniffing along a repeatedly folded back section of the immutable cosmic timeline, and was only imagining that he was causing the U-turns.

Haunting possibility--the timeline is fractal, like a space-filling curve, endlessly going back and forth, so that there never is a stone-cold final version of your life--as more and more of the timeline is taken into account, you undergo an infinite number of fate-flips. Like trying to sum the divergent series:
1 - 1 + 1 - 1 + 1 - 1 + ...



Why not go with a SF version of Cramer's Transactional Interpretation, with the other end being the "future you".


Not a bad idea, Dirk, I'll have to ponder if that would be a good fit.

I wrote about Cramer's Transactional interpretation in my nonfiction tome THE LIFEBOX, THE SEASHELL, AND THE SOUL. I compare it to a reversible cellular automaton.

If I'm not mistaken (although I often am), I think you can find a sample PDF chunk of the LIFEBOX tome online at Look in the physics chapter, and search for "Bruegel."


I've occasionally wondered whether a direct apprehension of the future might be an answer to the problem of Free Will. It would certainly introduce a feedback that would make the process non-linear and inherently unpredictable.


I'd also like to pitch the limited-branching fantasy Chronoplex that I made up for a time travel story, The Ghosts of Deep Time. The idea is that Earth's history is a tree, with bifurcations at the major mass extinctions (mostly because the extinction event covers up the chaos of the bifurcation). What limits the number of bifurcations is what I called chi (dark energy) and spirit (dark matter). They are conserved in the six-dimensional ylem that we mistakenly perceive as the four-dimensional universe. Matter and energy are not conserved, and they can bifurcate infinitely. Conversely, dark matter and dark energy are halved with each bifurcation. If there's not sufficient chi and spirit around, life is impossible (insert handwavium about how chi and spirit mediate the quantum aspects of electron transport chains and similar).

Time travel in this world is easy, because it's performed by beings that live on the surface of Earth's history tree, that can be paid to lift us out at one point and insert us at another. What is a tree without its symbionts? Time travelers are what also cause the history tree to bifurcate.

The Chronoplex has an innate propensity to bifurcate and fuse, which is why things we lose sometimes mysteriously turn up again in places we've already looked, and why eyewitnesses normally tell differing versions of events. Really. If you don't impose strict observational protocols with many replicates, people really do experience reality a bit differently. The History Service normally uses localized bifurcations to catch time traveling criminals. The get caught in a small, closed side branch, that branch evanesces, and so does the problem.

Why bifurcations? The galaxy is "alive," and planets with intelligent beings are the way it reproduces itself (I'm not sure what gender a galaxy takes, anyway). Ultimately, intelligent beings have this innate drive to generate black holes on their planets (usually expressed as a consumerist culture trying to become fully four-dimensional through time travel), and these black holes go on to grow other galaxies. Since planets that produce intelligent species are rare, the galaxy arranges for these planets' histories to bifurcate (just like the flowering inflorescence on a tree), so as to make as many baby singularities as possible. Most of these singularities will be consumed or evaporate, but a very few grow into a new galaxy, especially after merging with other singularities from other planets... Think of it as cultural syngamy, mediated by post-singulitarian black holes.

Now obviously, some humans (and the other intelligences on Earth's Chronoplex) don't relish the thought of caught in a singularity as the proper end to history. These dissenters are the ones who settle throughout the four billion years of deep time. These settlers ultimately make the bifurcating chronoplex possible, mostly because they fight over how much chi and spirit should go to their downtime ancestors at each major bifurcation (see mass extinction, cause of).

Living with such loopy causality takes some getting used to (as does writing stories in it), but it's possible.

And to answer your question, no I'm not cynical about people's place in the natural order. Not at all. Why do you ask?


Dirk, Rudy...

I tried using Cramer's transactional thingy in my Nulapeiron books (starting with Paradox) to justify the existence of Oracles who really could see the future (therefore no altering of any envisioned future events). It gave me, to my satisfaction, confidence in the concept of a definite future.

I didn't find it convincing in terms of information flowing against the normal arrow of time. What I used instead was a conjecture due to Hawking, Sakharov and Gold, that the thermodynamic arrow of time is linked to the cosmic arrow of time - that the future always lies in the direction in which the cosmos is bigger.

The implication is that, by producing small volumes of collapsing spacetime, you get time going the other way...

Hey, it's only fiction!

Regardless of how you get the reversals, how about tying in the ability to perceive the reversal with neutral kaon-antikaon decay, which is time-asymmetric?


There's actually been a lot of thought put into this topic by the various Remote Viewing programs, esp RVing future events. One important lesson is apparently the need to "close the loop" and provide a self fulfilling prophecy (if possible). This is often applied to RVing information from ones future self as part of the program.


Multiverses – as the one remaining get-out clause for backwards time travel – is a somewhat lazy device for sf writers. And some prominent physicists (such as Roger Penrose) have doubts about the many-worlds interpretation (who also theorizes that when the matter universe breaks down into only energy there is no context for time, effectively no temporal process – so it could be the beginning again). If the multiverse theory is correct then these universes are beyond our observational horizon.

I like the idea of life flipping back without ending – like an eternal causality loop. Each time the protagonist has their memory erased, or the memories themselves are simply unmade (as with time). Anyone looking for a simple story-title to express this idea may be out of luck...


There is only one problem with assuming that time is dimension in which we are moving in one direction or another. Time cannot change by definition. Why? Simply because a changing time implies a rate of change in time, which would have to be given as dt/dt. That is nonsense, of course.

The unchanging nature of time is the reason that nothing can move in Einstein's spacetime (surprise!) and that Sir Karl Popper compared Einstein to Parmenides and called spacetime "Einstein's block universe in which nothing happens". Source: "Conjectures and Refutation". Look it up.

Any talk of parallel universes branching off at every instant of time is silliness. Worse, it is deceptive and unproductive because it brainwashes generations of young people into believing in a lie. To call it 'science' is to add insult to injury.


Meanwhile QM says exactly the opposite. Which is why either QM or GR or both are wrong


So deja vu in this scenario might be considered as rare instances when a brain does "store" an event and time that backtracks and then moves forward on the same or a close trajectory brings the observer back to the event?

What I'm not clear about is how the protagonists can even hope to experience the huge combinatorial explosion of possible alternative events, unless those alternatives are only a short time in the future, or are you saying that the number of possible branches is not infinite?


Hmm, interesting.

This reminds me of several rather confusing short stories of the 60s, but more recently (Tuesday November 1st, 2011) I came across a guest strip by Mike Holmes in the "Superhero Girl" series by Faith Erin Hicks.

Little Marty has a really cute power, yes?

Of course, that's just one way of expressing the concept visually. You could also make a painting of a plant growing in zero gravity.


Surely if precog was effective intelligence would never have developed?


Dirk @ 9 Erm - we NEED a solution to the "renormalisation problem".

And "wrong" for certain values of wrong, as Pterry would say!


Your series sums to 1/2 (as I'm sure you know).

And lovely post... great idea, if bleak.


Analytic continuation, I assume you're joking when you say that series sums to 1/2. Check your local calculus book! Divergent means there's no unassaailable way to assign a sum.

(1 - 1 ) + (1 - 1) + (1 - 1) + ... is "obviously" 0. 1 + (-1 + 1) + (-1 + 1) + (-1 + 1) + ... is "obviously" 1.

Philosophers of science discuss a similar process as the "Thompson lamp" which has an on/off push button. Using a Zeno speedup you push the button alef-null times in a second, that is, at 1/2 second at 3/4 second at 7/8 second and so on. After a second is the lamp on or off?


"After a second is the lamp on or off?"



Come on, Louis Savain, what are you so dire and cranky about today? We're talking about IDEAS FOR AN SF STORY, man, not about RELIGIOUS DOGMA. This is supposed to be fun, okay? The free play of ideas.

A few days ago you had a comment that interested me, and I was wondering if you have a source, or even better, a link for it: "The idea is that there is a tree of knowledge (hierarchical memory) and that only one branch of the tree is active at any one time."


Dear Rudy,

Not joking. There are lots of ways to sum divergent series, and there is probably even a Wikipedia article on it.

The most intuitive here is that you can sum a geometric series 1 + x + x^2 + ... and get 1/(1-x); the sum converges if the absolute value of x is less than 1. But the function 1/(1-x) only has a pole at x =1, so you can think of its value for any other x as being the sum of the series.

Take x = -1, and you get 1/2 as the sum of your series. You can also see this as the average of the sequence of partial sums; thats another way of summing the series.

Anywho, back to work

PS Read White Light as a teenager, at the same time as trying (and failing) to read Cohen's Set Theory & the Continuum Hypothesis. Your books had a lot more sex in it... (Been an itinerant fan ever since).


Your philosophy thought experiment reminds me of the Hitchhikers Guide to the Galaxy (also devoured in my teenage years, along with Hardy's Divergent Series, come to think of it).

The philosophers, arguing at the launch of 'Deep Thought', the second greatest computer in all time and space...

"What's the point of us staying up all night, arguing if there is -- or is not --- a god, if your machine comes and gives us his telephone number the next morning?"

(the satirical reflections on London pundit life escaped me at that time...)


It fascinates me how the question of interpreting quantum physics so often reduces to arguments over esthetics, and how often the same principles are used by all sides of the argument. Poor William of Occam's name gets taken in vain by everyone, because everyone has a different idea of which notions are simple and which are not.

Now Rudy finds Everett-Wheeler repellent because to him it means that none of our decisions matter. I don't happen to agree that it does mean that (and I'll go into that another time perhaps), so I find it more tolerable. But that doesn't mean I think it's necessarily the right answer. I don't have any idea of what is right, though like all the rest of us I have some idea of which interpretations I don't like: Copenhagen bothers me, because it says that there isn't any ground to physical existence, that at small scales it's just card tricks all the way down. And the DeBroglie-Bohm Pilot Wave model, while it is far less mystical than most of the interpretations, has always struck me as somewhat of a kludge.

It's interesting, though, that this subject raises such strong emotions. I've known people to raise their voices and pound on the furniture for emphasis when debating it. And there's sure a lot of vehemence here. For my part, I know I don't understand enough of the subject to have a meaningful opinion on the basis of physical theory, and I know that the universe doesn't give a damn what I think, so the only thing I really care deeply about in this context, is that I'd like to live long enough to see at the least the beginnings of resolution of the question. I'm curious, damnit!

And, of course, in this discussion we're just talking about the McGuffin for Rudy's story, so for the sake of argument there is only one world, and Rucker is its author.


Alex, there aren't necessarily an infinite number of branches, unless the universe is infinite in space-time. If it's finite then there are a finite number of decision nodes and therefore branches leaving them. Of course that finite number is just humongous.


Turns out we're both "right," analytic continuation.

See the Wikipedia article on this famous series, called Grandi's series.

As I recall, it may have been Grandi himself who said the series showed how the Creator was able to make something out of nothing! Merely a phase shift, you understand.

Glad to hear you're a fan of WHITE LIGHT.


Just a brief note, that any type of infinite multiverse has all the free will problems of the MWI.


Track down the play and DVD of Copenhagen by Michael Frayn for a great example of worldines mixing together and cascading out reality.

Your model #2, With Reverses, is the right one. Each person is moving forward and resetting their worldline all the time. What you see around you is the result of those wordlines interacting with each other.

  • A person buys a plane ticket a month before his flight. He sees a great deal and the flight fits his schedule. The day arrives, he boards the flight, it is full, halfway through it crashes killing everyone onboard. The after event report blames it on faulty maintenance; some bolts failed.

The death echoes back down his worldline to when he is buying the ticket. He sees a great deal that leaves an hour later so that he has more time to get through security. Why rush. The day of the flight comes, and the flight before him crashes, luckily it was only half full. The after event report blames it on faulty maintenance; some bolts failed.

Each person who boarded that first flight faced branch points. Each death echoed back down their worldline. Some people made different choices. Those worldlines occurred multiple times, with different people choosing to take the flight or not.

At one point the mechanic who failed to catch the cracks in the bolts that failed, killing everyone, called in sick the day of the inspection and his relief technician caught the problem, replaced the bolts, and no crash occurred.

All those people who were involved have a memory of events in the form of a palimpsest of memories layered over memories. They dismiss that odd memory of dying on the flight as a mere daydream.

  • This is why no two people can agree on actual events. And the greater the number who were involved/interacting with the event increases the number of different accounts of an event. Each person lived through wave after wave of worldline resets.

This happens all the time, everyday, with everybody. What we call the worldline is the result of the wave resets that wash through each other.


Thanks, Allynh, well said. It's nice to hear from a commenter who gets what I'm talking about and agrees with me!

Your words make my idea more vivid to me than before. This is the kind of comment that makes it worthwhile for me to take the psychic risk of posting ideas for unwritten stories...


Life as treesearch...


You're welcome. There are many examples in fiction that fit this model.

It is all based on the fact that time is not linear, because there is a fuzz to Now. There is no such thing as an absolute Now. Now exists as a region of Now(past) and Now(future).

That's how the play Copenhagen works. It shows Heisenberg's Uncertainty Principle and Schroedinger's Wave function in action, along with the Observer Effect as it cascades reality into existence.

Basically, Consciousness is a wave function that exists on each worldline, like the sound that exists on a violin string.

To have a sound on a violin string, the string must be bound between two points. Consciousness is a result of the worldline vibrating, pinned between two points: birth and death. As with sound on the violin string, consciousness bounces back and forth between birth and death, thus consciousness is aware at some deep level of the whole worldline. The only reason that the worldline is not clear to consciousness is that the end point, death, constantly changes based on the wave of changes from resets.

Visualize the Now(past/future) as a bead that travels up the worldline. As that bead of Now(past/future) moves up the worldline it constantly overlaps itself; that is how information travels the length of the worldline. The path that the bead of Now(past/future) forms on the worldline is a tube that is consciousness itself, constantly changing in length.

  • Just as the violin string makes a primary tone with many layers of harmonics, consciousness is the main tone, the subconscious is the underlying harmonics.

Look at the comicbook/movie Watchmen. Dr. Manhattan could see the whole of his worldline, past and future, as long as he did nothing to change that worldline. He was trapped in doing and saying everything that he already knew, because if he changed anything, the future would vanish in a blur of all possible futures. He was only freed at the end when he chose to make choices. The tachyon radiation didn't create the static, stoping him from seeing beyond the bombs detonating, his worldline was blasted into noise because he took a branch point, he made a choice. He chose free will.

Look at Slaughter House 5. The Tralfamadorians saw time as locked, the same as Dr. Manhattan. They knew that the universe would be destroyed by them. The Tralfamadorians existed only in that locked worldline. They could exist forever living between those points of birth and death. They knew that at some point, after living endless subjective years, that they could stop the accident from happening, at which point they would cease to exist. They were a standing wave that would vanish, the universe moving on without them. They existed only as long as they stayed deterministic and abandoned free will, for a time.

These are some of the implication of this model.

  • Time is not linear.

  • Free will is absolute, as long as you make choices.

  • The subconscious is aware of an ever shifting future and past, but the conscious can't see any one future clearly, except in rare moments.

  • Every psychic makes accurate predictions of worldlines that they Observe, but those predictions are not destiny and may not occur.

  • Choices/insights that you make today can resonate back along your worldline changing past choices, changing the Now.

How many times have you talked to family and friends about past events only to discover that no one agrees about what actually happened. It is not about memories being bad it's that the past ain't what it used to be.

How many times have you learned something and suddenly everything changes. Now you know why. HA!


That raises an interesting question- a plane full of people crashes and they all die. Why did that happen?


I refer you to the Alanis Morissette song, Ironic. HA!


I think I have read stories where lines that are close rejoin the first in time. Well, its just fiction, so why not.


I think we're a very long way from dealing with free will in physics no matter which quantum interpretation you choose. For one thing, we need a definition of free will that everyone can agree on to have some sort of physical meaning. Determinism is easy to define, but free will isn't the opposite of determinism, that would be randomness. Free will is something else, but defining it without resorting to dualism is hard.


brucecohenpdx Really? I agree that the "classical" definition of so-called "free will" is dead, if only because of what we know about things like flocking behaviour, decisions (except they are not) being made before they are made. Etc .... No, you don't have to go down the dualism road, either. Because that heads straight into mystical/religious untrue claptrap-areas again. I just suggest that: 1] it's COMPLICATED 2] there are truly random events going on (unless you have a handle on the underlying order, and we don't) 3] even with all the available information, you have to simultaneously model ALLL the electronic.chemical events occurring in someone's brain to fathom the eventual result - which means instant upload, and no-one's ecpecting that any time real soon now. 4] oddly enough, a true quantum-approach, where you are dealing with particles, rather than the defeatist mysticism of collapsing ... (ahem, oops) might be a clearer line to follow.


Rudy, sorry about raining on your fine parade. In the end, the truth is always stranger than fiction.

The tree of knowledge and branch hypothesis is my own. There are actually two trees and two branches if you count both the left and right hemispheres.

However, I don't think you would like how I came up with this hypothesis. This is why I gave no link. Look up the metaphorical two olive trees and the so-called Branch in the book of Zechariah.

See? I told you you wouldn't like it.


we in fact have an emotional, experiential sense that the bad, unchosen paths are in fact shriveling away to the left and the right. If we didn't feel this way, why would we sweat our big choices?

I have to deal with the consequences in this branch, the unchosen paths are the responsibility of my duplicates that I will never have to account for myself to.


Before you've made the choice, you and your duplicates are still the same: the branch in question has not yet forked.


" Free will is something else, but defining it without resorting to dualism is hard."

Resorting to dualism does not help at all. If it did it would be a huge plus in favor of dualism.



Seems to ignore the notion that one can accurately record and review the past via video and other recording technology (we ARE ourselves a recording technology, as anyone with a scar or children etc. will attest to).

I see no space for free will in reality at all. Making a random epiphenomenal choice is not free will.


@bellingham: Stipulated, but how would the consideration of the pre-choice unity bear on the expected consequences of the decision? I can't expect to be less dead next week because my decision to do something more dangerous tomorrow is also a decision to do something less dangerous tomorrow.


OK. Two ideas. Not incompatible with each other.

The first is that the timeline variants are more like sunspots than a binary tree. The frequency and duration vary with some complex but partially predicatble way. Recently there has been an unusally long branch that snapped back and this unusally intense snap-back made the sensitive hero notice, and then start to notice the more minor snap-backs. This gives the interesting possibilities of their having been major historical snap-backs which many people noticed, creating myths of atlantis etc which was an alternate technological future which un-happened etc. The obvious painful twist is that all time is ultimately a branch and will snap back to another course. The deepest bits of the tree from our hero's noticing the effect (or his/her birth) is only a few years. Life is meaningless and all actions will be rendered irrelivant.

Another idea is that time moves differently in differnet parts of the universe, perhaps due to gravity, velocity etc. (which it does, but my physics is rusty). This means that sometimes our local time may get ahead of itself and go in a direction not actually compatible with where the rest of the galaxy or universes time is going, and that's got more inertia so the local time gets pulled back and in a new direction, like pulling a sheet over a very bumpy surface (very loose analogy). Basically the idea that areas of space have temporal inertia and that the higher inertia will "win" pulling other spatial/timelines back on themselves. Perhaps the Hero can discover a way to give the future he's in more inertia so it can pull the universe behind it or rip iteslf free. Presumably so he/she can get the girl/macguffin. Or alternatively, to cancel the inertia to undo time to the point of some crisis, eg. the death of loved one etc. but if I was writing that it would be tempting to have them unravel the entirity of time by accident.

A good friend of mine (also a Comp Sci) had a dream where you could pass information back in time in very controlled ways (maybe a single bit from a theoretical timeline), which meant you could solve O(N) problems in log(N) time because each sub timeline could also use the tech to send one bit back to say if it was the correct or false path etc. In his dream, Apple released a device which would alert you if in 5 minutes time your heartrate spiked or stopped...

(I'm also a fan, I once emailed you to ask what we should do with the laser pointer we'd purchased, on the advice of the cyberpunk handbook, and you suggested it's excellent fun using them to start gang wars)


Allynh, on second thought I don't quite agree with your model after all. It was just your elegant prose that won me over.

My issue is that I want to write this time-branch story WITHOUT invoking a second-order time in which the world's timeline is changing. I want there to be a FIXED timeline as I show in my second figure, and I'm talking about on person's experience of this line given that he, unlike others, is able to notice the reverals.

Other points. Thinking in terms of a changeable future, I used to wonder about the plane crash thing myself. Did everyone on the plane at some level "want" to die? I don't like this idea so much, it's akin to blaming peole who get lethal diseases. I think this is a human tendency---someone has something horrible happen to them, and a part of us wants to say, "Well they were asking for it, and I'm not asking for it, so it could NEVER happen to me."

I notice a few people mentioning free will. By way of opening a fresh can of worms, I might point out that the problem has been solved, to my satisfaction, by Stephen Wolfram's analysis in A NEW KIND OF SCIENCE. I go into this in THE LIFEBOX, THE SEASHELL, AND THE SOUL.

The idea is pretty simple: the world may well be deterministic, that is, the future follows invariably from our present. We have an ILLUSION of free will because we are, even in principle, unable to PREDICT (form computation theoretical reasons) the future.

The big new insight from CS that isn't so well known is that many computer-like processes are, although deterministic, unpredictable---that is, there's no O(log(N)) method to predict the state of hte system after N steps. And improved tech isn't going to change this. It's a fundamental aspect of computational systems.


There's something that bugs me about an Everett-Wheeler multiverse, which is what it does to the conservation of energy and mass.

Assuming that a universe is splitting and multiplying an infinite number of times each second (first approximation of the number of quantum interactions), what does that monstrous proliferation of mass and energy do to whatever hyperspace all these splits are occupying? From the hypothetical outside, it would look like an exponentially monstrosity.

Is anything conserved? Or are the laws of thermodynamics illusions that result from us being stuck on the inside?

Of course, some clever SF writer could link a proliferating multiverse with the dark energy that's accelerating cosmic inflation, but there's probably some reason the cosmologists wouldn't buy it.


There are hints that the sum total of energy and information in an infinite multiverse sums to zero. In our universe the energy probably sums close to zero, as gravitational energy is negative. However, our universe is also very low entropy.


What are the x axes?


The core question is: what causes a universe line to be "snipped". Why is the hero (and his girlfriend) important, so much so that the universe will rewrite itself to save his life- while the millions of people dying in Africa don't get a rewrite? Why do avoidable bad things- wars, pogroms, murders, rapes, etc.- still happen, in a universe that rewrites itself?

Imagine that there is a gigantic computer somewhere, and our universe, the universe we see all around us, is just a simulation running in this computer. Now, the computing resources this computer has is enormous, by our standards- it doesn't think doing 10^100 computations is hard- but the computing resources are still finite. This computer is then doing an A* search on all possible time lines of our universe.

In this scenario, what happens when a given timeline encounters a paradox? A paradox presents itself as a point in time at which point the amount of computation needed to determine the next state of the universe is infinite- the computation doesn't converge. While the computational resources of the universe simulator are huge, they're not infinite- that timeline literally ends right there, it is impossible for it to experience another quanta of time.

In this scenario, we're not living in the best (according to our definition) of all possible worlds, but instead just a stable (paradox-free, computationally tractable) universe. It's okay for bad things to happen, so long as they don't lead to paradoxes (sorry, Africa). We may also rule out "uninteresting" universes- universes that collapsed into a black hole milliseconds after the big bang, for instance. Or universes where the lambda force so overwhelmed gravitation that the universe is, for all purposes, empty of matter.

Note that only certain types of paradox are a problem. There are two types of "paradox" here- self-cancelling, and self-reinforcing. Self-cancelling paradoxes map vaguely onto the statgement "the statement is false"- if they happen, the conclusion is that they can not happen, if they don't happen, then they do. If you go back in time and shoot your grandfather, you don't exist to go back in time to shoot your grandfather.

The other type of paradox, self-reinforcing, maps to the statment "this statement is true". If you go back in time to warn yourself to be careful crossing the street to not get hit by a bus, you're likely to be careful crossing the street, and thus not hit by the bus, and thus around to go back in time to warn yourself. Note that this sort of paradox does not stop the universe-line, as it does not take infinite computational power to calculate the next state.

Indeed, if you're in this sort of self-reinforcing paradox, attempting to get out of it immediately converts into the universe-ending self-cancelling form. Say that you think "screw my future self- not only am I not going to be careful crossing the street, I'm going to throw myself in front of that bus!"

So, this is what is special about our hero- he is in a self-reinforcing paradox. Say, sometime in the future he invents time travel, and travels back in time to save his grandfather's life. If he dies, he doesn't save his grandfather's life, so should never have existed- universe ends. If his girlfriend dies, the depression that causes means he doesn't have the important thought that lets him invent time travel. And so on.


If you really want an example of how the multiverse may rewrite itself (subjectively), then google "quantum suicide". It's a question of what finite subset of an infinite vista the mind chooses to look upon. Only by looking does it exist. Where it does not look, it does not exist.


Watch Copenhagen and you will see that we are talking about the same thing.

There is no fixed worldline, that violates the Copenhagen Interpretation, but that doesn't mean you can't have a character that is absolutely aware of all the changes.

Consider that most people can't remember passed last Tuesday, yet there are some people who do remember their whole life, in detail. There was a 60 Minutes episode about The Gift of Endless Memory. Look on YouTube for Endless Memory part 1 and part 2.

Marilu Henner has random access to her memory, organized by date. Many others have that endless memory, but only have serial access.

Your character would remember his entire worldline, being aware of the resets because he has endless memory.

Look at The Lathe of Heaven. George Orr remembers every change, every reset, while the people around him have no clue.

"George tells Heather that the "real world" had been destroyed in a nuclear war in April 1998. George dreamed it back into existence as he lay dying in the ruins. He doubts the reality of what now exists, hence his fear of Haber's efforts to improve it."

You probably know a number of people who remember everything, and are always correcting the people around them. They are dead annoying. No one with limited memory wants to deal with someone who remembers everything. After a time, the person with endless memory learns to just keep silent. Trust me, it's easier that way.

As to people still dying in accidents, etc...

I refer you to the Alanis Morissette song, Ironic. HA!


So if you don't like the multiverse because decisions don't matter, aren't you running into the same problem here?

If the protagonist cannot change the future, then none of his decisions matter, either. Why is that more appealing?

Not criticizing, just curious.


Dirk and Greg,

Sorry, I was unclear; I'm not advocating a dualist explanation. I find dualism unacceptable for a lot of reasons; no need to go into them now. But materialist approaches don't seem to leave room for free will, whatever it really is. What it's not, IMO, is stochastic; neither classic chaos nor quantum indeterminacy contain any will, not matter how free they may be. For there to be free will, I think there have to be possible alternate choices, and there has to be some mechanism whereby a choice is made.

This applies to your story, Rudy, because if the outcomes are fixed, there's no free will. That's implicit in saying that the hero only gets to perceive alternatives; he doesn't get to choose them. But if we are talking about quantum outcomes here then perhaps his perceptions work something like the Feynman sum-over-histories model: all alternative outcomes add something to the outcome that is measured. Those alternates are parallel, not serial, and they merge back into the final measurement, so there aren't multiple worlds. Suppose our hero does experience the outcomes in parallel, but being human, he can't experience them that way, so his memories of the experiences are sequentialized by the workings of his nervous system. An important question for the plot of the story is what order he remembers them in; if you assume that it's random, then you can use whatever works for a particular event in the story.


This reminds me of a short story I read recently but can't remember the author (Doctorow?). Boy meets girl and both can see the future (and both know the other can) but they see it in different ways. The boy sees only one fixed path. He knows what is going to happen and it is unchangeable. Consequently he is fairly fatalistic and gets depressed. The girl sees many possible futures and has at least some small control over which actually happens. Both know when they meet about how the relationship will end - with a big argument and recriminations. The girl keeps hoping she can change it and the boy getting more and more depressed (hence making the prediction self-fulfilling). I won't add spoilers for the end :-)


In Lathe of Heaven and in Next, the movie version of The Golden Man, they were conscious of their actions. The reality is that the unconscious is the communication channel that carries the information on the worldline. The unconscious is not good at transmitting numbers or words, i.e. specifics. Thus you have people still get on the plane and die.

Next time you are asleep and dreaming, try to read something or see a number, you will find it hard to do, and impossible to write down later when you wake. That's the fuzziness of the unconscious communication channel.

If you look at Next you have the best example of what a conscious person could do, especially when he is working his way through the warehouse and having all the versions of himself die, finding the safe path.

Go through your day, making choices, feeling your way forward, actually seeing all the other options that you did not take, all the branches trimmed. Now look at everyone else doing the same thing on an unconscious level, with all those worldlines interacting, cascading out reality, and you will get an idea of the model.

Be prepared to be dizzy when you do that. HA!


I find RR's reference to Wolfram interesting I'm going to look that up, just in case .....


My opinion of the many worlds theory is, if the thought of it doesn't lead to pants shitting terror, you're not thinking it through.


It's an interesting idea, but as laid out, it's a pretty unsatisfying conclusion!

"And in the end, I was wrong."

Perhaps discovering that before the end would allow you to create a sense of impending doom, and then a faux-happy ending which gets undone in the epilogue.

Or the Director's Cut.


Rudy, I suggest you check out the alterna-physics of Finland's Matti Pitkänen, as chronicled daily on his blog at He was one of the first people in the world to have a theory of branes (late 1970s), then he was shut out by the Scandinavian physics establishment, and he went on to invent an incredibly detailed ontology and cosmology, which includes quantum biology, some parapsychology, and jumps between alternative possible histories. You could spend weeks reading his life's work, which is full of dense mathematical prose. He might be the most visionary Nordic thinker since Emmanuel Swedenborg. :-)


There's a movie that was made not so long ago with a similar premise - - wherein the protagonist has the ability to change the past while remembering the original timeline. It doesn't go well for them.


Wrote this up yesterday, then decided not to post, but what the heck.

People don't notice the reversals. When the time flow kinks and makes a U-turn, those moving along the timeline experience events as running backwards. Like a rewind. But they don't notice. The memories get erased. If you play a movie backwards, it's not like the people on the screen start saying, "Hey, we're going backwards."

In order to have a story, we'd need that our character does learn to notice. How?

What if we do notice. What we call Deja vu? Suppose that the time reversals take you back to a specific point. You can remember that moment, but nothing that came after, allowing you to make different choices.

Now, what is there to keep you from making the same, presumably wrong, decisions? Preferably something non-deistic; Aliens, or 'The Future protecting itself'--though I think that's been done.

Or, what if people compare notes and notice that their moments of deja vu occurred at the same moment--leading them to realize that the time reversal was universal?


"unchosen paths are in fact shriveling away to the left and the right."

Sounds like some form of "Mean reversion".

The emotive/psychological feels are probably side-effects to this - reaction of our minds/bodies to a "natural" effect.


RR @ 40

re: Wolfram Just got round to looking him up. pp 750-2 in the hardback - "computational irreducibility", and the subsequent notes on pp.1132-37

I hate to agree, but I think you and Wolfram are correct. Wonder how long it will take these ideas to penetrate the religious believers' skulls? ( I would guess never, actully )


"Wonder how long it will take these ideas to penetrate the religious believers' skulls?"

When they do there will be a whole new type of religion emerging


Unfortunately, the cult leaders and self-help gurus seem to be quite adept at picking up persuasive lines of patter from popular science books and news articles. "Quantum" has been one of their favorite buzz words for a generation now, probably because of the way "consciousness" was used by some physicists early on. The fact that most physicists have moved on to seeing measurement as a physical process rather than an unexplained semi-mystical phenomenon hasn't even slowed the gurus down.


It falls far short of a religion though. I hope to remedy the situation :-)


That's how L. Ron Hubbard got into the biz: he started with Dianetics, which was billed as psychological self-help, then started Scientology as an add-on, and turned it into a religion for the tax-breaks and the opacity.


Bruce: you may want to note that LRH's "religion" is on a list of terms that will get any comment held for manual inspection before publication.


You mean Sceintology?


Well, that particular niche is overfilled, and has been since around 1980. A new approach is needed - a bit more "open source".


Err, but maybe 'Open Source' is somewhat contrary to the spirit of the whole thing, IMHO 'religion', 'faith', 'magick' etc. are quite intertwined with some strange parts of our brains.

First of, I guess many a well-meaning godless underestimates the role of 'cognitive dissonance', e.g. absurd articles of faith are more costly for various metrics of costs, e.g. ridicule, thus believers rationalize these costs by declaring them precious, see 'credo quia absurda est' and 'the spit of the unbelievers is the seed of faith', err, somewhat free from the more sanguine remarks about the martyrs. Incidentally, one of the first mentions of the concept of CD was in the context of a, err, New Religious Movement, somewhat related to the example of misguided fandom with the rabid lawyers...

OTOH, I guess the fact that invisible skydaddys somewhat hack our primate drive to take it from behind with the alpha male is not detrimental to the Darwinian fitness of the world explaining systems that deal with this shit, even if the skydaddy in question is Great Comrade Stalin and the system in question is the late and unlamented DIAMAT. And historically, becoming the alpha male had a certain correlation with becoming a paranoid quasi-sociopath, where the thesis of 'paranoid and sociopathic tendencies being adaptive in certain circumstances' and the antithesis that 'paranoia is not really paranoia if everybody is really after you' yield a synthesis that 'being top dog is not that indicative of your mental and physical health', but then, even without the strange notions of materialism Lenin et al. adhered to, dialectics is somewhat neurotoxic.

Still, maybe many people prefer something like an elevated subordinate status to the fun of being the One in the Matrix.

As a sideline, telling people you're the big skydaddy himself is not that much accepted behaviour in Christian and Islamic societies, but still, there are other roles you could play in your own private little eschatology that are somewhat more survival friendly, e.g. telling a Christian you're Jesus makes for extreme reactions, telling him you're Simon Petrus is somewhat more level; and since we're talking about organized religions, they form somewhat of a hierarchy. But since these are extraordinary claims, few people make them, except when, well extraordinary circumstances require extraordinary explanations, and so those roles might be your brain's best explanation when several of your causation and salience modules play samba, e.g. you have a florid psychosis. It might be interesting to do interviews with your local schizophrenics, manics and psychotically depressed, with regards to who chooses what narrative. Of course, you had to control for catholic saints that might appeal to people in a psychosis, e.g. St. Antonius

but still, count the people who are St. Antonius tempted, the people who are Jesus tempted or, for contrast, some minor saint tempted, some demon tempted (not that unheard of in cases of psychotic depression, e.g. in 'Devils of Loudon' by Huxley) and, for completeness, temptation with correct identification of own person. Of course, there are other factors at work, e.g. affective symptoms and severity of cognitive decline, but still, my guess is there is going to be a tendency to identify with the minor saints and not the big ones. Which might mean even psychotics try to keep some plausibility by keeping somewhat 'level' to minimize cognitive dissonance, though then maybe we should see a correlation between cognitive performance in the theory testing domain and assumed persona when controlling for affective symptoms. Or people have somewhat of a tendency to shy away from being boss. Err, sorry, just some ramblings.

Then, IMHO both 'religions' and 'magick' tap into our tendency to see patterns in somewhat random data and to deduce causation from correlation, where the resulting theories give a sense of control, either with pure knowledge, with seers and like, or ways of hacking causation, with rituals. Fun is, when you look at the history of ideas, somewhat wobble theories like psychoanalysis etc. might explain more than clearer theories, they might be more immune to falsification, they might require more attention and thus be more salient etc.

To cut a long story short, maybe the elaborate BDSM games many religions play are not a bug but a feature to reach a certain headspace.

As for religions and therapeutic system, err, IMHO the lawyer cult is just a typical religion, though that goes to the detriment of the latter, not to the benefit of the former. To be specific, religious movements using therapeutic techniques to recruit followers

and medical practices that only work for those of true faith (read Acts of Apostles 19.12 and have fun with interpretation) are older than the (Christian) Bible. But then, looking at Hellenistic and Roman times and contemporary New Religious Movements, sex life etc. is always fun. Just see ROME.

As a last note, let's hope nobody ever puts the Japanese to the apocryphs:

Simon Petrus and Simon Magus in a levitation duel in the air, can't wait to see the Mecha (or Hentai?) version...


I think you have a rather naive view of religion. Religion is primarily a social system, secondarily a political one with theology trailing way behind. The actual belief only matters to a minority, and of that minority very few will be able to argue theological points. The belief is to religion what the flag is to nationalism. The real action is elsewhere.

It is the "elsewhere" and it's reinforcement that needs the focus.


(Bit late to the party, but someone might still read this)

What this immediately brought to mind for me is the film Lola Rennt (a.k.k Run Lola Run). In it the titular Lola lives through several versions of the same day until she reaches a version with a "happy ending", for her and her boyfriend at least. IIRC, she does not retain knowledge of the previous runs, but it is implied that the "rewinding" is an act of will on her part when events reach an intolerable point.

You also get to see snapshots (literally presented a series of photos) of the future lives of people she interacts with; as with her, their future lives are drastically altered by a small change in circumstance.

There is also Groundhog Day, where the main character retains memory of the previous branches/loops, and its short film predecessor 12:01pm (I'm sure you can find on YouTube).


I think you have a rather naive view of religion.

Might be, might not be.

Problem is, we have had this all before, big chunks of the Reformation were actually trials at 'Open Source Christianity' or styled themselves that way, with groups like Unitarian Universalists

quite akin to some of the goals of 'Open Source religion'. Also note the ideas about 'Priesthood of all believers'.

But then, some of the groups that practice universal priesthood today are far from what you'd call an OSR:

And while one might argue about the notion of Roman Catholicism as necessarily more 'closed source' than Protestant Churches (imagine someone like Stephen Colbert

coming from one of the latter) there are people who move closer to the RCC or even convert for exactly these reasons.

BTW, note that most Catholics I know view converts to Catholicism for reasons other than shagging a Catholic, vide Mel Brooks, with some, err, let's just say Walter Sobchak from 'Big Lebowski' is not an exclusively Jewish phenomenon.

Religion is primarily a social system,

True. And meaningless. Anything humans do is a social system, even if the system in question has only one member. And given that many religions are quite close to animism, AKA ascribing social intentions etc. to non-human actors, that is even more like saying an ocean is quite a lot of salty water, though not every mass of salty water is an ocean, vide Caspian Sea.

with theology trailing way behind.

Err, it's more complicated than that; Even in 'true' sciences like physics personal preferences and social factors play in, vide the scepticism some people here had about the multiversum theory, since it belittles everything we do. Of course, that is in the context of ironic science, but still, you get this quite often in degrees. What's special in science is that eventually you have a negative or positive feedback loop by experiments, successful applications etc., while in theology, the only feedback is sociological in nature. E.g. for the more cynical inclined of us, it's right because it feels good, the Catholic doctrine of Purgatory (praying for people in hell makes little sense) and the Ontological Proof of God by Anselm of Canterbury (sounds eerily familiar for somebody who spent some time with adolescent dopeheads) are examples. So well, when you come to theology, that is not religion without social system, it is a veritable social system, again like everything else people do.

OTOH, even if theology is mostly a sociological phenomenon, humans have a tendency to keep things logical. I guess Christian slaveholders were quite positive about some interpretations of Pre-Adamism,

but there were serious problems with lining it up with the rest of theology. So sometimes theology matters in social terms.

If you want to elaborate, go to the Marxists and talk about 'Überbau' and how it interacts with modes of production.

Remember, after about 2 years, get a life.

The actual belief only matters to a minority, and of that minority very few will be able to argue theological points.

Again, I'm afraid it's more complicated than that.

First of, before one buys into the notion of a general dumb population, let's remember about 50% of the population (somewhat more, taking the Flynn effect into consideration) have an IQ over 100, so


At least, most of our elitist pseudo-intellectuals take their car to an able mechanic and not to an economist, lawyer or media guy. And to be nitpicking, this IQ of 100 seems to be way more then some theologicians of the past. g

(Oh, and this one doesn't go for mobs, you know intelligence of a mob is equal to intelligence of dumbest member of mob. Divided by number of members of mob.)

That said, of course there is a difference between, err, intelligence and knowledge, where I agree testing some believers on the latter might be, err, fun. Though you'd have to differentiate somewhat. Thing is, most theological questions don't matter to most members, they don't even matter to theologicians, because nobody has thought about them. Others are not important to most, just like most physics don't care if it's Kopenhagen or Bohm. With those, some might argue about it in a playful way, e.g. when reenacting some of the scholastic debates, and then, there are some people to whom it's deadly serious business.

And I guess those questions are not going to be of similar importance to everyone, when you look at the different interpretations of e.g. Evangelicalism,

So, well, it's not going to be black or white, not even grey, e.g. some care more than others, it's more like yellow, green and blue, for some, religion means, just as for the Old Romans, fulfilling certain social roles, for some, it means seperation from 'the sinfull world', etc.

The belief is to religion what the flag is to nationalism. The real action is elsewhere.

Excuse me, but in Germany, the flag you're under is not that unimportant...

The kind of religious experiences that get's mainly fostered by, say, Christian beliefs is going to be different from the one that you get from, say, Theraveda Buddhism.

Speaking about Christianity, it'd be naive to think a belief system like e.g. Gnosticism'd have no impact on religious practice.

Of course, you can get experiences similar to Buddhism in Christianity, e.g. with certain lineages of ascetism, and in Buddhism, there is Mahayana, which is the one most Christians think of when they speak admirable of 'Buddhism'. Still, the interactions of, err, original teachings, interpretations etc. is somewhat more complex then you think. E.g.

It is the "elsewhere" and it's reinforcement that needs the focus.

might boil down to a minimization of the social community aspects of religion, a certain interest in solitary spiritual practices and, possibly, a certain esotericism. In short, the opposite of what others think 'Open Source Religion' is about.



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