noun
epis·​te·​mol·​o·​gy | \ i-ˌpi-stə-ˈmä-lə-jē  \

: the study or a theory of the nature and grounds of knowledge especially with reference to its limits and validity
— Merriam-Webster

Here’s my take on epistemology. Or, more specifically, a subset of epistemology; I’m not so much going to address how we know truth, or even what is truth, so much as I am what is the arena of truth?

I should preface this discussion by saying that I am a white, American, middle-class cis-hetero man; I have background in both STEM (as will probably become obvious) and theology, the latter as mediated through a Jesuit college.

Anyway, epistemology. Let’s start with the universe, because why not:

For now, we will say that the universe contains matter and energy in time and space.  We will put on the mantelpiece the question of whether the universe contains anything else.

Statements we make about the universe have the property of truth.  That is, they may be true or false.  I can say, “This rock is in my hand,” and I may be telling the truth or I may be lying or I may be mistaken, but no matter what that statement will be true, or it will be false, or partly true and partly false.  We can always ask, of a statement made about the universe, “Is that true?”  (We may not always be able to find the answer, but we can always ask the question.)

Now, as residents of the universe, we want to understand it.  One of the ways we want to understand it is to know what might happen in the future, or what happened in the past, or what might be happening far away.

Here’s how we go about doing that: we create two mental constructs.  The first construct is a system:

Systems contain entities and rules for manipulating entities.  Euclidean geometry is an example of a system; it contains entities such as points, lines, and planes, and rules such as, “The interior angles of a triangle add up to 180°.”  Another example of a system would be Joseph Campbell’s Hero’s Journey; in this case the entities include the hero and the mentor, and an example of a rule is that the hero cannot ultimately refuse the call to adventure.

Whatever the system, it is a construct of abstractions.  As such, statements made about the system cannot properly be true or false; rather, statements about a system have the property of consistency.  A statement may be consistent with the rest of the system, or inconsistent with it.  For example, in Euclidean geometry, the statement that the sides of a right triangle are related by the Pythagorean Theorem is consistent with the system; the statement that five points always lie on the same plane is not consistent.

This is important.  While we can say true or false things about the universe, anything we say within the context of an abstract system like this can only be evaluated from within that same context; and therefore cannot be true or false in the same sense that, “This rock is in my hand” can be.  We could just as well construct a system within which it is consistent to say that five points always lie on the same plane.

But a system by itself – whether geometric or mythical – is no more than mental exercise.  It has no relationship to anything in the universe.  To provide that relationship, we create our second mental construct, a mapping:

A mapping is simply a scheme for translating things in the universe to entities in the system and vice versa.  Thus, a chunk of granite may become a point mass; a series of positions in time and space may become a velocity; and so on.

The mapping creates a relationship between the universe and the system.  Together, the system and the mapping constitute a model, which is fundamentally a means for making predictions.

Making a prediction follows these steps:

• Map objects in the universe to entities in the system
• Manipulate the entities according to the rules of the system
• Map the entities back into objects

Thus, if I’m pondering the question, “What will happen if I throw this rock?” I can use the mapping to produce a point mass, a force vector, gravity, air resistance, and so on within the system of Newtonian physics; then I use the equations of motion within the system to manipulate those entities; then I map the resulting trajectory back into real-world objects, and I get my answer:  “It should land next to that bush over there.”

Models have the property of utility.  That is, the predictions that a model generates are more or less useful in knowing what will happen in the universe.  Just as with systems, it is a category error to try to describe a model as true or false.

Thus, if I’m trying to predict the position of celestial bodies, I can use the model of Ptolemaic epicycles; or I can use the model of Newtonian mechanics; or I can use the model of Einsteinian relativistic corrections to Newtonian mechanics.  All of these models will “work” in the sense that they will produce predictions, and in fact they will all produce predictions that are sufficiently accurate for many purposes when compared to the actual positions of actual celestial bodies.  The Ptolemaic model is generally less accurate and harder to use than the Newtonian or Einsteinian models; but that doesn’t make it false, it just makes it less useful.

The insight which I consider important from this view of epistemology is precisely this distinction:

• Statements about the universe – and only statements about the universe – have the property of truth.
• Statements made within the context of a system have the property of consistency.
• Models – the combination of a system and a mapping – have the property of utility.

A great deal of philosophical confusion arises directly from making category errors about these different things.

For instance, if someone poses the question, “Is it true that the earth rotates around the sun?” most people would immediately answer, “Yes, that is true; everyone knows that.”  But I have seen a cunning professor drive a class into serious confusion by pressing them on this point – how do you know that?  What does it really mean that the earth “rotates around” the sun?  Didn’t Galileo teach us that all motions are relative to each other?

In fact, the statement, “The earth rotates around the sun,” is neither true nor false, because while it sounds like a statement about the universe, it really isn’t.  Although “the earth” and “the sun” are certainly things that are in the universe, “rotates around” is a statement that belongs to the system of Newtonian mechanics.  (And even within that system, it’s more complicated than that.)  In fact, “the earth rotates around the sun” is a model, and so the correct question to ask is, “Is it a useful model?”  And the answer turns out to be that, if you’re plotting the motions of the planets, or planning a rocket trajectory, then yes, it is extremely useful to model the earth as rotating around the sun.  On the other hand, if you’re standing on the surface of the earth enjoying a sunset, you can argue that it’s marginally more useful, or at least more convenient, to use the model that the sun is sinking below the horizon.  Neither is true, nor false; just useful in different contexts.

So: remember to check what your statements are statements about, and avoid epistemological category errors.

Now, at this point, a reader could easily be forgiven for thinking that I’m using a very positivist definition of “truth,” restricted only to material or measurable things. That’s not actually what I’m doing, although the examples I’ve used so far do fit that mold.

What I’m trying to do is to draw a circle and say, “This is the circle within which true things live,” and then to invite the question of what belongs in that circle.

In fact, the reader may recall that way back at the very beginning we put a question up on the mantelpiece – namely, this very question of whether the universe, and by extension the arena of truth, can properly be said to contain anything besides matter and energy in time and space.  Let’s take that question off the mantel and examine it a little bit.

The reason this is important becomes immediately apparent when we ask, “What about concepts like beauty, or goodness?  Where do they live?”  That is, is beauty a thing in the universe, or is it only an entity within a system?

In the former case, we can say things about beauty that are essentially true – however nuanced and complicated that truth may be.  In the latter, we can only evaluate beauty in a way that is consistent with the rest of whatever system we’re using; and the person next to us may be using a completely different system.

This may not seem quite so fraught when we’re talking about beauty; most people are at least somewhat comfortable with the idea that beauty is in the eye of the beholder.  But the question becomes much more pointed when we start talking about goodness – or rightness, or ethics, or however you want to phrase that concept.  Can an ethical statement be in any sense true?  Or can it merely be consistent with other ethical statements within the context of a given system?

As one might expect, I have thoughts on that topic; but they are beyond the scope of this post.  Perhaps we’ll return to that later.  But I do think that it is helpful to realize that the question of whether there is anything in ethics that can be considered universal, or in any way not completely subjective, is tantamount to asking whether goodness is a thing that actually exists in the universe in the same way that a rock exists.

[This is something I posted on my old Livejournal a few years ago; I happened to be thinking of it the other day, and it seemed worth reposting.]

[Originally posted Sept 2010]

On the way home from work the other day, I was idly thinking about soteriology, as one does.

Soteriology, for those of you who didn’t choose to spend a bunch of time in theology school, is the “theology of salvation.” In Christian theology, it is specifically the theology of how we are saved, and what we are saved from, by Jesus Christ.

Back in 1931 a guy named Gustaf Aulén published a book in which he argued that traditional theories of soteriology could be broadly divided into three categories: “Christus Victor” theories, in which humanity was oppressed by sin, death, and/or the devil, and Christ by his death and resurrection had defeated those enemies; “satisfaction” theories, in which humanity owes a debt or penalty to God and Jesus becomes human in order to pay it on our behalf; and “moral influence” theories, in which Jesus’ life and particularly his submission to a painful and shameful death is God’s ultimate example of a selfless and self-sacrificing life.

I was thinking about this, and reflecting on how it seemed that each of these theories emphasized certain aspects of Jesus’ existence over others. Satisfaction theory, for example, hinges on the Incarnation (Jesus had to be human in order to pay the debt for humanity’s sake, and he had to be God in order to be able to pay a debt so great) and the Crucifixion (the moment at which the debt was paid.) Jesus’ life and ministry, and the Resurrection, are not completely ignored in this theory, but they are definitely of secondary importance. Moral influence theory, on the other hand, emphasizes Jesus’ life and his death; in this case, the Incarnation and the Resurrection are secondary. Christus Victor puts the primary weight on the Crucifixion and the Resurrection.

At this point the Techer in me pointed out that it appears we have four possible aspects of Jesus’ existence, namely:

The Incarnation — by classical Christian theology, this is the means by which Jesus Christ came to be simultaneously fully human and fully God. (Two natures in one person, if you want to use the neo-Platonic language that the Council of Chalcedon used to explain this apparent paradox.)

Life and Ministry — Jesus’ teachings, his parables, his miracles, the example of how he lived and acted; everything he said and everything he did during his life.

The Crucifixion — the way in which Jesus died.

The Resurrection — the way in which Jesus rose to new life on the third day.

Out of these four aspects, then, each of the soteriologies mentioned above highlights two, and largely ignores two others. Does this mean — I pondered to myself — that we can use this to create a schema for soteriological theories based on which two of these four aspects they emphasize? And if we can, is it useful to do so?

Well, I don’t know if it’s useful, but I’m intrigued to see if it’s possible. Elementary combinatorics tells us that if we take four aspects and choose two at a time, there are six possible results; so we can start by simply enumerating them:

Aspect of Jesus’ Existence				Resulting Soteriology
Incarnation	Life & Ministry	Crucifixion	Resurrection
		X	X	Christus Victor
X		X		Satisfaction/Atonement
	X	X		Moral Influence
	X		X	“Narrative Christus Victor“
X	X			Divinization
X			X	???

Let’s take these in order.

Christus Victor: emphasizes Crucifixion and Resurrection

One of Aulén’s models, alluded to above. variations on this were common in the early centuries of the church; by dying and rising again, Christ is victorious over the forces that have oppressed humanity since the Fall. This model often includes the “Harrowing of Hell,” the idea that during the three days that Jesus was dead, he was rampaging through Hell and busting out all of the virtuous dead — who, since there was no salvation before Jesus, had perforce gone to Hell regardless of their virtue. This is the model that fans of The Golden Bough are likely to gravitate to, because it embodies the same kind of “the king must die so that the crops will grow” thinking.

One instance of the Christus Victor model — one which was current around Anselm’s time, and revulsion at which led him to come up with the satisfaction idea; see below — went like this: Because of the Fall, Satan owned the souls of all humans by legal right. God offered Satan a bargain: the soul of Jesus in exchange for everyone else. Satan eagerly accepted, but was foiled when Jesus was raised on the third day. If this sounds familiar, it may be because it was also the model that C. S. Lewis used in The Lion, the Witch, and the Wardrobe.

Satisfaction/Atonement: emphasizes Incarnation and Crucifixion

The second of Aulén’s models. Anselm of Canterbury, as noted above, found the version of Christus Victor theory circulating at his time revolting: partly because it suggested that Satan had legal rights that God had to respect, but mostly because it made God a cheater. Anselm wrote a book called Cur Deus Homo — loosely, “Why Jesus Became Human” — in which he proposed an alternate theory: the sins of humanity since the Fall were an affront to the honor of God. (Anselm was writing around 1000 CE, so he had a medieval idea of Creation as a medieval kingdom, with God of course as the monarch; sins of the subjects impugn the honor of the king.) This affront demanded satisfaction; but all of humanity together would be unable to render a satisfaction large enough to be sufficient.

Therefore, God devised the plan of the Incarnation: Jesus would be both fully human, and therefore able to offer satisfaction on behalf of humanity, and fully God, and therefore the satisfaction would be sufficient. The Crucifixion was the manner in which satisfaction was offered, and God’s honor restored.

In time, particularly around the Reformation, this model evolved: rather than a king’s court, it became a legal court, and sin was a crime against the justice of God rather than an affront to God’s honor. Jesus came to pay the penalty for humanity’s crimes, rather than to offer satisfaction. Still, it was fundamentally the same concept. Strictly speaking, this version is known as penal substitutionary atonement, and it is normative in many, many Protestant churches — so much so that many people are convinced that it is the only understanding the church has ever had (it isn’t) and that it is explicitly stated in the Bible (it isn’t, although there are passages in Paul you can read this way if you come at them with that preconception.)

Moral Influence: emphasizes Life & Ministry and Crucifixion

The third of Aulén’s models, and one associated primarily with Peter Abelard (1079-1142). Abelard was a rock star in the medieval academy; a prodigy who blew away his teachers with his dialectic. He famously had an affair with a young woman named Héloïse, which ended abruptly when her uncle had Abelard castrated. He retired to a monastery, where he continued his philosophical and theological work somewhat out of the public eye.

In this view, Christ’s life was intended to demonstrate God’s all-encompassing love for humanity; so great that he would even give up his life and suffer a torturous and shameful death for our sake. This example is intended to influence humanity to strive to emulate it; the “action” of salvation, therefore, is directed not so much at God (as in satisfaction theory) or towards evil forces (as in Christus Victor theory) but rather at humanity itself.

This model is favored in parts of the liberal wing of Christianity. In some cases (not all, by any means) it goes so far as to regard the Incarnation and the Resurrection as mythical, in which case Jesus becomes a great teacher but otherwise a normal human being.

“Narrative Christus Victor”: emphasizes Life & Ministry and Resurrection

The term “Narrative Christus Victor” is taken from a book called The Nonviolent Atonement, by Mennonite theologian J. Denny Weaver. Weaver is concerned by the violence he finds in the classical Christus Victor and satisfaction theories; he develops a soteriology in which Jesus’ entire ministry is based on themes on non-violence. In this model, the Crucifixion is not part of the divine plan; it is rather the response of violent humanity to the perfect example of non-violence, Jesus. The Resurrection is God’s absolute vindication of Jesus’ life, and the ultimate demonstration that non-violence can triumph over violence without resorting to violence itself.

Weaver’s view is not, I think, a very widespread one — for one thing, most Christian sects are less focused on non-violence than the Mennonites are — but it was the example that came to mind that favors Life & Ministry in common with Resurrection.

Divinization: emphasizes Incarnation and Life & Ministry

The second-century Church Father Irenaeus believed that the purpose of Christ’s coming was to imbue human life with divinity. Since Christ was both human and God, as Jesus lived through the various stages and experiences of human life they would become sanctified and made divine. Jesus was born; therefore birth is shot through with a divine spark. Jesus was a child, therefore childhood is made divine. And so on, up to and including human death; but in Irenaeus’ view, this was merely the culmination of a human life.

This model never really caught on, although it does seem to resurface every now and again.

???: emphasizes Incarnation and Resurrection

Here I’m stuck; I can’t think of a soteriology that emphasizes the Incarnation and the Resurrection, but isn’t much interested in the ministry or Crucifixion. It seems as though such a model would be largely focused on the Kingdom of God and the new life that everyone would inherit then; you could pick up on Paul’s language out Christ’s Resurrection as the first-fruits of the Kingdom, and Christ as the new Adam; but you’d have to step over the parts of Paul that emphasize having to die (to self, to sin, to your previous life) in order to get there. I can’t recall having seen that exact combination, but that doesn’t mean that someone hasn’t done it.

So there it is. Not exactly a great discovery, but an interesting exercise nonetheless. What do you all think?

[After I posted the original post, a comment pointed out that, of the four aspects listed above, “Life & Ministry” and “Crucifixion” are “ordinary” in the sense of not being miraculous; while “Incarnation” and “Resurrection” are explicitly supernatural. This helps explain why the Moral Influence soteriology, which emphasizes only the mundane elements, tends to be favored by the more secular-minded; whereas the missing soteriology, which would emphasize only the miraculous elements, would have difficulty relating to the mundane world of human experience. I think that’s a very useful addition to this analysis.]

I watched Terminator Genisys the other day (only two and some years after it came out, so yeah, I’m behind) and, while I liked it quite a lot, it did make me think about portrayals of time travel in movies and books, and how most of them are nonsense.

One of many egregious examples that comes to mind is Back to the Future, where Marty McFly is on-stage trying desperately to preserve his own personal timeline, and watching members of his family gradually fade out of a photo as things go sideways. There is no coherent model of time travel by which that scenario makes a lick of sense.

So here are some models that I think do make sense, or at least are self-consistent given the initial assumption that time travel is a thing.  And I should perhaps stress that I’m speaking here of models of fictional time travel — I have no opinion on the possibilities or nature of real time travel — and my only criteria is self-consistency; that is, a model that does not contradict itself or result in nonsensical conditions.

That being said, the underlying assertion I’m going to make is this:

The timeline cannot change.

Whatever the overall shape of the timeline — linear, branching, a helix of semi-precious stones — that shape must be static.

This is because when you’re looking at the timeline from outside, you are ipso facto outside time itself, and change is impossible unless you are inside time. Change, by definition, means that something is different from one moment to the next moment; no moments, no change.

This means that we rule out from the start any idea of “changing history.”  The Back to the Future scenario is not self-consistent, nor is that one Red Dwarf episode where they change the past and as a result their timeline begins to dissolve around them.  (Not that Red Dwarf ever prioritized consistency over comedy.)  Also that Bradbury story about stepping on a butterfly.  Also also the “grandfather paradox” and all its variations.

Does this mean that we have to give up all fictional time travel, or that we can’t have stories about what happens when you go back in time and try to kill Hitler?  Not at all.  We certainly can have those stories; we just need to be careful about it.

So given our principle that we can only deal with static timeline structures, what are some of the models that do work?  And how close can we come to classic time travel tropes without giving up self-consistency?

Let’s start with the simplest model: a single timeline, moving linearly from past to future.  Here’s what that looks like:

Within this timeline is depicted the personal timeline of a single person; let’s call her Timothea the time traveler (although she’s not time traveling in Figure 1.) Also on this timeline is a critical event; for the sake of example, we’ll say that a laboratory experiment intended to produce a cure for cancer went horribly wrong and instead turned 95% of all humans into zombies. The world timeline is colored red after this event to indicate that it is a bad future.

Now let’s look at what happens when we add time travel to this model.

After the critical event, Timothea finds or invents a time machine, and travels back in time in an effort to avert the catastrophe. Her personal timeline jumps back to a point in the world timeline before the critical lab experiment, and continues from that point forward, in parallel with her previous timeline (“previous” by her own personal experience.)  In between the time that she arrives in her time machine, and the time she departs, there are two Timothea’s — or more accurately, her personal timeline is running in parallel with itself (these sections of her timeline are designed T₁ and T₂ — for Timothea 1 and Timothea 2 — on the figure.)

In this model, try as she might, Timothea is unable to avert the catastrophe. Whatever happened the “first” time (by her own timeline, in the section T₁) happens exactly the same way the “second” time (again, by her own timeline, in the section T₂.)

(In fact, she might find that her attempts to avert the catastrophe are precisely what caused it. This is possible for dramatic irony, but not required by the model.)

Further, let’s say that Timothea, being a careful and methodical sort, decides to do research on the events just before and after the critical point in time. And for the sake of argument, let’s say that she has access to complete video recordings of all relevant events.

At point “R” (for Research) in her personal timeline, then, Timothea looks at recordings of two past points in time, marked as t₀ and t₁. At time t₀, Timothea sees her past self at point A on her own timeline, doing things that she remembers herself doing. The same applies at time t₁, at point B on her personal timeline.

She also sees her future self (“future” based on her own timeline, in that she has not yet experienced those points) at points C (t₀) and D (t₁) doing things that she doesn’t remember because she hasn’t done them yet.  In fact, she may remember, from points A and B, seeing her future self do those things at points C and D.  (It depends on whether, after the time travel journey, Timothea [T₂] decides to keep herself hidden from her past self [T₁].  For the sake of simplicity, we’ll assume from this point on that Timothea always reveals herself to her past self.  Of course in this model that means that Timothea [T₁] is surprised to see her twin suddenly suddenly appear in front of her just before a routine laboratory experiment.)

After she time travels, at times t₀ and t₁, she may try to do something different than what she has seen herself doing. She will not be able to. She will, inevitably, do exactly the things she saw herself doing, no matter how she tries to change anything. She will have the experience of predestination — of knowing the future but being unable to do anything other than what she knows will happen.

This is a simple and self-consistent model for time travel, but it really only makes for one kind of story, and not a particularly satisfying one:  the story of futility and unavoidable destiny.

Let’s look at another model: a timeline that branches at critical events.

This timeline starts the same way as before, but when it reaches the critical point, the world timeline branches. In one branch, branch α (alpha), the experiment goes wrong and brings about the zombie apocalypse. In the other branch, branch β (beta), the experiment succeeds and all cancer is cured forever. This branch is colored green to indicate that it is a “good” future.

When the world timeline branches, everything in the timeline also branches, including Timothea’s personal timeline. So at the critical point, Timothea’s timeline forks into Timothea-alpha (T_α, in the “bad” branch) and Timothea-beta (T_β, in the “good” branch.)  Timothea-alpha has to battle to survive hordes of zombies; Timothea-beta is enjoying a cancer-free world.

Now let’s add time travel to this model.

Here, after the fork, Timothea alpha-1 (T_α1) decides to travel back in time to try to avert the zombie apocalypse.  She appears shortly before the critical lab experiment, surprising her past self.  When her personal timeline arrives at the critical point the second time, it — like everything else — forks again, meaning that Timothea’s timeline is now doubled in both branches of the world timeline.

Let’s look at the experience of each of the four Timotheas.

Timothea alpha-1 (T_α1) is our time traveler.  She remembers points A and B in her past, and when she does research at point R, she observes her future self at points D and E (as well as remembering witnessing D and E when she experienced A and B.)

Timothea alpha-2 (T_α2) traveled back in time, attempted to avert the catastrophe, and failed.  She remembers points A, B, R, D, and E, in that order.  Furthermore, she experienced predestination at both t₀ and t₁ — she was unable to do anything other than what she had seen herself doing.  In fact, her experience is indistinguishable from that of Timothea (T₂) in the previous model.

Timothea beta-1 (T_β1) has never time-traveled.  She remembers points A and C only.  Her experience is that her twin suddenly appeared in front of her, warned her of a potential catastrophe, and together they were able to avert it.  She’s happily living in the good branch of the timeline.

Timothea beta-2 (T_β2) has time-traveled and, so far as she can tell from her own experience, has changed history.  She remembers points A, B, R, D, and F, in that order; meaning she remembers the zombie timeline but is now living in the cancer-is-cured world.  She experienced predestination at time t₀, but not at time t₁ — at t₁ her research showed point E but she experienced point F.

It’s important to note, however, that despite what both Timothea-betas think, they have not actually changed history.  The zombie apocalypse branch of the timeline still exists; The T_βs are simply experiencing a more congenial branch.

This model is definitely closer to some of the standard time-travel tropes, but in fact we can do better while still maintaining self-consistency. To do so, we have to make two assumptions:

1) In addition to forking at critical points, the timeline also forks whenever a time traveler arrives from the future.

2) The personal timeline of the time traveler continues in only one of the resulting branches.

(Are we allowed to make these assumptions? We’re dealing with fiction; we can make any assumptions we like so long as the results are self-consistent.)

The diagram for this looks complicated at first glance, but bear with me.

The timeline begins the same way at the others. It forks first at the point when Timothea’s time machine arrives from the future, into branches alpha and beta.  At the moment of forking, the only difference between the two branches is that branch alpha contains only one instance of Timothea’s timeline, while branch beta contains two.  Timothea’s original timeline (prior to any time travel) forks into the two branches as Timothea alpha (T_α) and Timothea beta-1 (T_β1). The timeline of the Timothea that time-traveled continues, per our assumption, only in branch beta, as Timothea beta-2 (T_β2).

The critical lab experiment occurs in both the alpha and beta branches (although details may be slightly different) and causes both branches to fork again, each one into a “bad” branch (zombie apocalypse) and a “good” branch (cancer cured forever) although again details will be somewhat different. These are branches gamma (γ), delta (δ), epsilon (ε), and zeta (ζ).

Note also that unlike the previous models, Timothea’s timeline is not doubled back upon itself in the alpha/gamma/delta subtree.  Let’s look at the Timotheas in that subtree:

Timothea alpha (T_α) does not see her time-traveling twin suddenly appear in front of her; she has no forewarning that anything bad may be about to happen.  Her timeline continues up to the critical lab experiment, when it forks into Timothea gamma and Timothea delta.

Timothea gamma (T_γ) is our time traveler.  Her timeline (up to that point) is A-B-C-R.  When she does research at point R, she sees no evidence of time travel in the past, at any of points t₀ (A), t₁ (B), or t₂ (C).  Depending on how she thinks time travel works, she might explain this by saying that her time journey “hasn’t happened yet”; but in fact the correct explanation is that everything her future self will do is in a different branch of the world timeline.

Timothea delta (T_δ) is the only Timothea whose timeline is completely untroubled by time travel.  Her timeline is A-B-D.  So far as she is concerned, the lab experiment worked beautifully, cancer was cured, and everything is as it should be.

Now let’s look at the more complicated subtree, beta/epsilon/zeta, which contains the timeline of time-traveling Timothea, continuing from T_γ.

Timothea beta-1 (T_β1) is startled when, whilst preparing for the lab experiment she hopes will cure cancer, her identical twin suddenly appears and claims she’s come from the future to avert a terrible catastrophe.

Timothea beta-2 (T_β1) is the timeline of Timothea gamma as it continues after her time journey.  She appears in front of her past self, warns her of the impending apocalypse, and together they begin planning to “change” the outcome.  At time t₁, this Timothea remembers point B on her past timeline, but experiences point H, and sees her past self experiencing point E — she sees that things are already different than what she remembers, even though they haven’t gotten to the critical point yet.

At the moment of the critical experiment, the timeline forks and both Timothea’s timelines fork as well, into Timotheas epsilon 1 and 2 (T_ε1 and T_ε2) in the “bad” branch, and Timotheas zeta 1 and 2 (T_ζ1 and T_ζ2) in the “good” branch.

Timothea epsilon-1 (T_ε1) has never time-traveled, but she saw her future self appear and warn her, and together they attempted to avoid the catastrophe and failed.  Her timeline is A-E-F.

Timothea epsilon-2 (T_ε2) traveled back in time, warned her past self, tried to avoid the catastrophe, and failed.  Her timeline is A-B-C-R-H-I.  However, her experience is much different than time-traveling Timothea (T₂) from the first model, or Timothea alpha-2 (T_α2) from the second model; she has experienced a different timeline from the moment she stepped out of her time machine.  She never experienced predestination.  As far as her experience shows, she did “change history,” just not enough.

Timothea zeta-1 (T_ζ1) has never time-traveled; she saw her future self appear and warn her of the catastrophe, and together the worked successfully to avert it.  Her timeline is A-E-G.

Timothea zeta-2 (T_ζ2) traveled back in time, warned her past self, tried to avoid the catastrophe, and succeeded.  Her timeline is A-B-C-R-H-J.  She never experienced predestination, and as far as she knows her time journey was a complete success; she “changed history.”

Of course neither of the Timothea zeta twins changed history; they’re just living in a fork of their timelines that is in a better branch of the world timeline.

See how this model, while remaining consistent according to the basic principle — the timeline cannot change — still supports many of the classic time-travel tropes.  If you write about Timothea zeta-2, her story looks like a good old-fashioned time-travel yarn, complete with past selves and history changing and a happy ending.  The only difference is that all those other branches are still there; nothing any Timothea does affects that, because — say it with me — the timeline cannot change.

This model also unravels the hoary “grandfather paradox” and all its variations. If you travel back in time and kill your grandfather before he can have children (for whatever reason that course of action seems good to you) no paradox results and the universe does not disappear in a puff of logic; in the branch of the timeline in which the murder took place, it’s true that “you” will never be born, but the you that committed the murder came from a different branch. Diagramming this is left as an exercise for the student.

Another interesting exercise would be to use this model to diagram the various Terminator timelines.  Of course the critical point in those timelines is Judgement Day — Skynet either does or does not come online and start a nuclear war.  However, one of the Terminators in Genisys remarks that certain events like Judgement Day “want to happen” — which means that the “good” outcome of any crisis point in the Terminator branching futures only means that there will be another crisis point later on.  There would be many “bad” Judgement Day branches, some starting later than others, and one timeline where Judgement Day keeps getting averted over and over again.

I’ll leave actually drawing that out to someone better acquainted with the franchise than I am.

However,  I think this model provides a way of writing about time travel that still lets authors do most of the things they want to do, but doesn’t do it at the expense of paradox or nonsensical outcomes.

What do you all think?