From the Narrow Desert

When Hamlet says, "We defy augury," modern readers are likely to understand this in terms of such familiar expressions as to defy comprehension and take it to mean, "Whatever is predicted of us, we can ignore the prediction and do otherwise." In fact, Hamlet's meaning is very nearly the opposite: We ignore omens that would allow us to predict and prevent future events, because all is fated and the future cannot be changed.

The naïve reader is liable to make a similar mistake in interpreting Jesus' famously cryptic statement to Simon Peter: "The cock shall not call out till thou hast denied me thrice." Thinking of such expressions as when pigs fly or when hell freezes over, the reader is likely to understand Jesus as saying, "You will certainly never deny me."

There are multiple obvious problems with this reading, though. What can thrice mean, for instance? That Peter might deny Jesus once or twice but that three times was unthinkable? And isn't the whole construction backwards? We say, "That won't happen until pigs fly," not, "Pigs won't fly until that happens."

As it happens, there is very strong textual evidence that what Jesus meant was, "You will certainly deny me, this very night." As strange as it may seem, multiple ancient authorities attribute to the "cock" (ἀλέκτωρ) a distinctive cry or "crow," sometimes represented as kukuriku or some similar onomatopoeia, and apparently cocks used to "crow" with such regularity that farmers used to use them as a sort of natural alarm clock, rising "at cockcrow" -- that is, at dawn. Thus, Jesus almost certainly meant, "You will deny me thrice before daybreak."

What to make, then, of the fact that Peter apparently never did deny Jesus, not even once, but stood with him when all the other disciples had abandoned him and was crucified alongside him? And how to reconcile the whole story with the very obvious fact that the cock has no call and is in fact proverbial for its silence?

Secular scholars will explain it away, of course. Jesus simply made a mistake, they will say, and his prophecy did not come true. And the ἀλέκτωρ that is represented in the New Testament, the Homeric Hymns, Pindar's Odes, and elsewhere as "crowing" loudly and regularly must have been some other species than the silent barnyard fowl we know today.

The faithful, however, can recognize the very strong evidence that the biblical ἀλέκτωρ is none other than our familiar cock or rooster, that this very animal used to give a distinctive call every day at dawn, and that all this "crowing" abruptly and miraculously ceased when Peter -- in the naïve, not the Shakespearean sense -- defied augury.

For every house is builded by some man; but he that built all things is God.

-- Hebrews 3:4

All the world's a stage,
And all the men and women merely players

-- Shakespeare, As You Like It

According to the Epistle to the Hebrews, every house is built by a human builder or builders, and every house is also built by God. Everything that exists and everything that happens, even when it seems to be (and is, at one level) the work of human actors or blind natural forces, is also something for which we can and should thank God. In my 2018 post "Shining Buddha problems" (written before I was a Christian), I make various attempts at understanding this idea, arriving in the end at what I call the "literary approach."

In trying to come up with some way of conceptualizing such an idea, I keep coming back to the metaphor of a book, which is why I’ve dubbed this the "literary approach." Everything that happens in a work of narrative fiction can be explained on two different levels. Assuming the story makes sense, every event therein will have a cause within the world of the story and can be fully explained on that level without reference to the author -- but from a "higher" point of view, that of the larger world within which the story-world is contained, every detail of the story is without exception the work of the author.

I go on to discuss how this metaphor can be used to conceptualize the idea of a "meaningful coincidence" -- or the coincidence which at another level is no coincidence at all. 

Take, for example, the storm on the heath in the third act of King Lear -- a perfect example of a meaningful coincidence. Viewed from within the story, the raging storm is a natural meteorological event caused by the mechanical unfolding of the mindless laws of physics, and the fact that it coincides so nicely with Lear’s psychological rage, and with the impending descent of Britain into political chaos, is just that: a coincidence. There is no within-story causal connection between the storm and what it mirrors -- and if there were -- if, say, Shakespeare had portrayed the gods specially arranging the storm for the purpose of providing a meteorological counterpoint to Lear’s psychological state -- that would be aesthetically objectionable . . . . But from a point of view that transcends the story itself, we can see that Shakespeare clearly arranged the coincidence on purpose and that we are therefore justified in considering it meaningful.

Even in King Lear, though, it seems that there are real coincidences -- truly meaningless coincidences, intended neither by the characters nor by the author. When Kent says, "the poor distressed Lear's i' the town; who sometime, in his better tune, remembers," only a person with a particularly strange way of thinking would notice the name Israel spelled backwards and connect it with Judges 2, where Israel is "greatly distressed" because, while they do sometimes in their better tune remember the Lord and serve him, they keep backsliding into idolatry. Surely no such message was intended either by Kent or by the Bard -- nor, if I may presume so to speculate, by God himself -- and yet there it is. There are so very many possible connections one could notice, it seems impossible that they could all be intended, all meaningful, all not-really-coincidental.

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In a comment on my post "No escape from coincidence," Bruce Charlton also proposes a literary analogy, even choosing the same author as an illustration.

Since this world is being-created by God, it is coherent at a spiritual level. Some of this coherence is important for salvation or theosis, which is the purpose of creation. These are the synchronicities.

But some of the coherence is an unintended by-product of the sheer fact of coherence of creation.

An analogy might be a good Shakespeare play - which has that coherence to it which is a product of deliberate authorial intention (coming via the author's mind); but there are other coherences (or 'symbolisms') which may be discovered by the scholar - and which are unintended products of the fact that this is a play, written by one Man, and was written so that it held-together.

If we look, there are many cross-correlated aspects of a play that are secondary to the nature of the thing, the fact of its coherence as a work of art.

I don't think this quite gets us to "no coincidences." There are just so many different things that could be connected, and so many different ways of connecting them, that it just seems inevitable that connections should arise "by chance," without reflecting either intention or "the sheer fact of coherence." Of course, this is a bit of a metaphysical assumption, and it's not as if there's any control group to compare things to. I mean, the world created by God is all we know, so we can't exactly look at an incoherent world that wasn't created and see if it differs from the real world in terms of the presence or absence of coincidences.

Using the literary analogy, though, let us look at what I would consider to be a truly meaningless coincidence in a coherent literary work by a single author. Our earlier "Lear's i' the town" example will not serve, because it is a coincidence between something in the text and something outside of it. If the text represents the created world, though, all coincidences must be within the text, without reference to anything outside it. (Obviously, any apparent coincidences we can observe in this world will be between various features of this created world, not between the world and something outside of it.) No Shakespearean example comes to mind, so let's take one from the Book of Mormon instead. 

Remember, to be carnally-minded is death, and to be spiritually-minded is life eternal. . . . I know that the words of truth are hard against all uncleanness; but the righteous fear them not, for they love the truth and are not shaken (2 Nephi 9:39-40).

It is an old Sunday-school standby among Mormons that "spiritually-minded is life eternal" (a slight modification of a phrase from Romans 8:6) forms the acronym SMILE -- and this is juxtaposed in the text with the implication that the words of truth would make the unclean frown but the righteous smile. (A biblical equivalent would be Matthew 7:7, where the first letters of the three clauses spell out ASK.) The word smile is also found in the BoM, so this counts as a proper within-"world" coincidence.

Now I am reasonably certain that this is not an intentionally created feature of the text. Obviously the Nephite authors writing in Egyptian could not have had English acronyms in mind, and while Joseph Smith could in principle have chosen this particular wording for its acronym potential, I see no evidence of that in the text. (Wouldn't he have paired it with something like "the flesh-regarding ones will never see life"?)

Here's another sentence, taken from a BBC article (qv), that coincidentally includes a series of words that form the acronym SMILE: "Although they had a tough time, none of our volunteers had to put up with the wide range of lethal microbes that killed so many in London's East End in the mid-Victorian period."

I would say that this differs from the 2 Nephi SMILE in that the coincidence does not seem in any way appropriate, intelligible, or meaningful. No one would say, "What a coincidence!" if you pointed it out. It doesn't even really count as a coincidence -- by which I mean it's not what people have in mind when they say "There are no coincidences."

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Anthony Hopkins has a name that resembles ant-honey and thus suggests hymenopterid insects, and the poster for the movie he is most famous for, The Silence of the Lambs, also features an insect, though one of a different order. Note also how Mark Antony (source of the English name Anthony) fell in love with a woman whose name resembles Coleoptera, another non-hymenopterid order of insects, and was co-triumvir with Lepidus -- Lepidoptera, of course, being the very order of insects to appear on the movie poster for Silence of the Lambs! What are the odds? The movie is about someone called Buffalo Bill who skins people. Buffalo is by far the biggest city in New York that ends with the letter O, and Anthony Hopkins's first name ends with ONY. Buffalo is called the Nickel City. and both Nickel and Hob (whence Hopkins) were formerly used as names for goblins. Hob, is a diminutive in which the initial letter of the original name (Robert) changes, and one of the few other English diminutives with this property is Bill, so Hob suggests both Buffalo and Bill. After the Hob element comes kins, which is just an anagram of skin -- so "Buffalo Bill skins" is right there in his name. We might also note that only two of the characters in this movie bear the title "doctor," and that both of them are played by actors named Philip Anthony H. who go by Anthony rather than Philip: Sir Philip Anthony Hopkins, and Philip Anthony Mair Heald. Sir and Mair are also equivalent because of the similar meanings of the Latin roots (senior, "the elder," and maior, "the greater") from which they derive. I could go on and on like this, and I've never even seen the damn movie! I picked Hopkins at random and just started writing.

These are junk coincidences, pseudo-coincidences, the kind of thing you'd find in "King-Kill/33" or Finnegans Wake (Downard and Joyce, sad James and happy James). Is anyone really prepared to maintain that they are all meaningful, all not-really-coincidences, all put there by God on purpose?

Anything as complex as the universe -- or even just as complex as Finnegans Wake -- is inevitably going to include billions and billions of coincidences above and beyond those intended by its creator -- yes, even by an omnipotent and omniscient Creator. It's statistically inevitable.

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But this literary analogy has led us astray. Who noticed that "Lear's i' the town" contains the name Israel spelled backwards? I did -- I, one of the readers of King Lear. But if all the world is a stage -- if the "literary work" we are considering is the universe itself -- then we are not readers or spectators but characters -- all the men and women merely players.

As someone who exists outside the world of King Lear, I can notice coincidental patterns in it that were never intended by the author -- truly coincidental patterns which must inevitably exist as a matter of statistical necessity. If a character in the play is made to notice a "coincidence" within the world of that play, though -- well that noticing was deliberately written into the script by the author, and we can therefore be absolutely certain that it is not really a coincidence at all but an intentionally designed and potentially meaningful feature of the text. If this universe was truly created by a divine Author, and all that happens in it was scripted by him -- if we poor players are not in any sense co-creators but simply follow a preordained script as we strut and fret our hour upon the stage -- then there would still be coincidences in the universe, but we characters could never notice any of them. "There are no coincidences," while technically false, would still be practically true for us. Noticing something and wondering if it was "just a coincidence," we could confidently reason, "No, nothing we notice is ever a coincidence, for we are characters in a play. Everything we notice, we notice by the grace of the author, and that means that it is not a coincidence but an intentional and meaningful feature of the play."

This is what I mean by the title of this post: "No coincidences" implies a single-author creation. It implies that everything in this universe, including everything we ourselves do and say and think, is fated, "scripted" by God. It means we have no free will but only a simulation thereof -- just as Hamlet seems to deliberate and vacillate and finally make a decision, but in fact every detail of everything he says and does is really decided by Shakespeare.

But we do have free will, and this means that coincidences -- true coincidences -- are inevitable. If I write a novel in which Bob and Alice meet by chance in a coffee shop, the meeting does not really happen by chance at all, because "Bob's decision" and "Alice's decision" are in fact made by me, the author, and I deliberately made them to coincide. In a world with real free will, though, Bob can freely choose to go to the coffee shop at a particular time, Alice can independently make a similar decision -- and these two decisions, being the work of two different free agents, would be causally unconnected in deepest possible sense and as true a coincidence as it is possible to imagine.

I think this is perhaps the metaphysical foundation of my delight in coincidences, my insistence that they are coincidences, and my resistance to the idea that "there are no coincidences." A coincidence as such may be meaningless, but in a deeper sense it is an indicator that we live in a world that has coincidences -- an open-ended world, co-created by many truly independent free agents. It is a reminder that free will is real, and as such its very meaninglessness reveals the meaningfulness of our existence.

In a recent post, Bruce Charlton asks "Can the past be changed?" -- and answers, "Obviously not," going on to pronounce the contrary opinion "demonic." Since I have been guilty of entertaining a version of this doctrine from the pit of hell (see this post), I thought I would revisit the idea.

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The first matter of business is to establish exactly what is meant by change. As a simple example of a change, consider my marital status, which changed in the latter part of 2010. Prior to that date, I was not married; after that date, I was and am. That's what change means: that a given proposition ("William James Tychonievich is married") is/was/will be true at some points in time and false at others.

We can represent this change graphically by means of a colored line. The dimension represented by the line is "time," with the past to the left and the future to the right, and the color of any given point on the line represents my marital status at that point in time (blue for single, gold for married). Below is a portion of such a timeline, covering the years from 2009 to 2020.

Now, we have already established that my marriage in 2010 constitutes an example of a change, and our timeline above locates that change to the left of the present moment -- that is, in the past. Is this, then, what we mean by "changing the past? Obviously not -- but why not, and what do we mean?

Well, the natural answer is something like this: The change in question occurred in 2010 -- which means that at that time, 2010 was not in the past but was the present year. If what happened in 2010 were to change now, that would be what we mean by "changing the past." But this introduces a distinction between 2010-in-2010 and 2010-now which cannot be represented on a one-dimensional timeline. Such time designations require two coordinates -- (2010, 2010), (2010, 2019) -- which means our simple timeline must be expanded into a two-dimensional "timeplane" of the type pioneered by J. W. Dunne and discussed in my post "The present now will later be past."

The title of that post, taken from the Bob Dylan Song "The Times They Are a-Changin'," was chosen because, while it seems very obviously true, it implicitly assumes a two-dimensional model of time. A simple timeline, like Fig. 2 above, can represent past, present, and future, but not the idea that "the present now will later be past." The very phrase "will later be past" describes the same state of affairs as being future in one sense and past in another -- which requires a rectangular coordinate system comprising two perpendicular timelines.

Fig. 3

Now I know from experience -- my own included -- that this is point at which readers' eyes start to glaze over, but I'm afraid there's just no avoiding these diagrams. I can only ask for the reader's patience and do my best to explain. The color of each point on the timeplane in Fig. 3 represents a proposition regarding my marital status: The hue represents the content of the proposition (blue for single, gold for married), and the tint represents its tense (pure colors for past, light colors for future). Each point is located in two different temporal dimensions: The x-axis ("object time") represents the time the proposition refers to, and the y-axis ("meta-time") represent the time at which the proposition is true.

I've marked two (arbitrarily selected) regions on the plane "A" and "B," respectively, in order to use them as examples. They represent the following meta-propositions:

A: In 2010, the proposition "WJT will be married in 2012" was true.

B: In 2014, the proposition "WJT was married in 2012" was true. 

For completeness, we really ought to indicate the tense of the meta-proposition as well. Fig. 4, below, is so modified as to express this. Solid colors (such as were used in Fig. 3) represent meta-past, and stippling represents meta-future.

Fig. 4

The region marked "C" in Fig. 4 represents the following meta-proposition:

In 2020, the proposition "WJT was married in 2011" will be true.

The "was" in the object proposition is indicated by the use of a pure color as opposed to a tint, and the "will be" of the meta-proposition is indicated by stippling.

The red dot in Fig. 4 marks the place where the true present may be found. (Or at least, this was true when I wrote it, about a third of the way through the year 2019.) When we say, "2019 is the present year," the word "present" corresponds to the diagonal line separating pure colors from tints, and the present-tense verb "is" corresponds to the horizontal line separating solid colors from stippling. The intersection of those two lines, marked with the red dot, is "the present now." Dylan's statement that "the present now will later be past" means that if we start at the red dot ("the present now") and move vertically down into the stippled region ("will later be"), we find a pure color ("past") rather than a tint.

Take a minute to digest that. I want to be sure the meaning of these timeplane diagrams is clear before proceeding.

Now look back at the region marked "A" in Fig. 3 and the meta-proposition to which it corresponds: "In 2010, the proposition 'WJT will be married in 2012' was [already] true." And consider this: If I were to extend my timeplane diagram to cover a wider range of past times, there would be a region on that diagram corresponding to the meta-proposition "In 4000 BC, the proposition 'WJT will be married in 2012' was already true." This is fatalism, of the unassailable variety spelled out by Richard Taylor (whose argument I discuss here) -- unassailable because it does not depend on the doctrine of causal determinism. From the mere assumption that all possible statements about the future are (already) either true or false, and that their truth-value cannot change, it follows that all is fated, that whatever happens is inevitable.

 To escape Taylorian fatalism, it is necessary to believe that we can change the future -- an idea which is common enough in naive discourse, and which our two-dimensional timeplane allows us to model. Let us modify our diagram, then. Instead of assuming (as Fig. 4 does) that my getting married in late 2010 is something that was always going to happen, something that was already written in the book of fate hundreds of years before my birth, or as far back as you care to imagine -- instead of assuming that, let's assume instead that I wasn't going to get married on that date, not until I actually made the decision to do so. Let's assume that my decision, rather than being just another step in the inevitable unfolding of fate, actually decided something, literally changed the future. And let's further assume (as seems reasonable) that this future-altering decision was made some months before the actual event of the marriage.

Fig. 5

The black dot on the timeplane in Fig. 5 represents the moment I exercised my agency and made the fateful decision (which, I need hardly mention, is entirely different from a fated decision, the latter being a contradiction in terms and no decision at all).

The diagonal line that passes through the black and red dots, and divides the pure colors on the left from the tints on the right, represents the timeline of my life as I experience it, as a succession of object-time "presents." The horizontal line that passes through the red dot, and divides the solid colors from the stippling, represents the meta-time present. (The object-time present is a point; the meta-time present is a line.) The intersection of these two lines divides the plane into four quadrants, representing (clockwise from the upper left), what had happened (solid pure colors), what was going to happen (solid tints), what will be going to happen (stippled tints), and what will have happened (stippled pure colors).

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The diagonal line -- my life as I experience it -- is exactly the same in Fig. 4 (where the future is fated) and in Fig. 5 (where it can change). It would appear, then, that there can be no empirical evidence for the one model or the other, no possible experience that would be more consistent with the one than with the other. Choosing one over the other would be a metaphysical assumption, not a conclusion from evidence.

However, that may not be entirely true. There is considerable evidence (see J. W. Dunne's Experiment with Time for starters) that, while the attention is generally confined to the point-present represented by the red dot, it can sometimes extend to other regions of the linear meta-time present, especially during dreams or similar states of relaxed or diffuse attention. In such states, we have access to the object-time future (precognition) and past (retrocognition) -- at least as they exist at the meta-time present. Under Taylorian fatalism (as diagrammed in Fig. 4), the content of object time does not vary across meta-time; the only meta-time change is that of tense (as the future becomes the past), so whatever future events are perceived through genuine Dunnean precognition will infallibly come to pass when the future times in question become present. There would be no possibility of seeing the future and then changing your behavior as a result of what you see, with the result that the foreseen event is averted. This is precisely what fatalism -- of the sort seen in the Greek myths, for example -- means. Cassandra's prophetic warnings are ignored and have no power to prevent the events they foretell. The prophecies regarding Oedipus are not ignored, but the very attempt to thwart them leads to their fulfillment. Either way, fate ineluctably plays out.

In the model where the future can be changed (as diagrammed in Fig. 5), even true precognitions need not necessarily come true. For example, look back at Fig. 5 and imagine that in 2009 (in both object time and meta-time -- that is, at a point on the diagonal line) I had a precognitive vision of 2011. Since such a vision would be of object-time 2011 at meta-time 2009, I would see myself as still single at that date. However, by the time object-time 2011 becomes the meta-time present, it will already have changed, so that the 2011 I experience will be different from the 2011 I foresaw. Nonetheless, what I foresaw was true. (If that seems like a contradiction, consider this analogy. I turn on the TV to the weather channel and discover that it is sunny in Taipei. I then get in my car, drive to Taipei, and upon my arrival find that it is raining. But what I saw on TV was true.) Instances of true precognition that do not come true would be evidence that the future can be changed.

The problem, of course, is that, if a vision or premonition does not come true, there would seem to be no grounds for considering it genuinely precognitive. For example, once in my late teens, at a time when I had no plans to go overseas, I had a very vivid and detailed dream in which I was about 30 and living in Vietnam. I'm 40 now and have never set foot in that particular country. It's possible that my Vietnam dream was genuinely precognitive, revealing what was (at that time) going to happen in the future, but that the future it foretold has since changed because of choices I or others have made. It could also be considered a garbled precognition of what in fact came to pass. (I do live in Asia and have for most of my adult life.) But there's no good reason to believe that, and the simplest explanation is that it was just a dream and not precognitive at all. Certainly such a dream cannot constitute evidence that the future can be changed. Is such evidence possible?

Consider the premise of the Final Destination series of horror movies. The protagonist has a sudden vision of a series of events leading up to all his friends dying horribly in a freak accident. When the foreseen events begin to play out in real life, he panics and manages to prevent his friends from getting on the doomed plane or roller coaster or whatever. Then the freak accident occurs as foreseen, except that his friends are not among those killed by it. Later they all go on to die horribly anyway, in different freak accidents, because "you can't cheat death," but that's not germane to my point here, which is that the originally premonition is clearly a true one even though it does not come to pass exactly as foreseen. When people act on a precognitive warning so that the foreseen event does not happen, but subsequent events make it abundantly clear that it would have happened had they not taken action, that is evidence that the future can be changed.

Such evidence in fact exists. The literature on precognition is full of Final Destination type stories (minus the post-accident bit where everyone dies horribly anyway). Someone has a premonition of being in a plane crash, they cancel their tickets, and then the flight they would have been on crashes. That kind of thing.

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What about changing the past? Well, it's a bizarre idea, so our illustrative example will be a little bizarre as well. I must ask the reader to suspend disbelief, ignoring for the moment the question of whether or not such things can really happen. Our question is what it would mean for the past to change, and, supposing it did change, whether there could be any empirical evidence of that change.

Suppose that "originally" I chose not to get married in 2010. Years later, in 2015, I looked back on that choice with regret and said to myself, "I wish I'd married that girl when I had the chance!" A passing genie happened to hear my remark and granted the wish. From that moment, it suddenly became true that I had gotten married in 2010. We can represent this hypothetical story graphically as below, in Fig. 6.

Fig. 6

The black dot on the plane in Fig. 6 indicates the moment at which my wish was granted. Notice that, when the past changes, the present and future change as well, since chains of cause-and-effect run horizontally from left to right across the diagram (i.e., causation is an object-time phenomenon).

Remember that the diagonal line dividing the pure colors from the tints represents my life as I actually experience it, as a succession of presents -- and notice that in the world depicted by Fig. 6, I never actually experience my own wedding or the first several years of my married life. I go directly from being a bachelor to having been married for nearly five years! Surely such an obvious discontinuity in my experience could not possibly go unnoticed, and surely the fact that people's lives don't include such discontinuities is evidence that the past cannot change -- right?

Well, not exactly. Remember that causation is an object-time phenomenon. When object-time 2010 changed in meta-time 2015, all subsequent points in object time also changed as a result of the causal effects of that 2010 wedding. For example, if photos were taken at the wedding, those photos will (after the granting of my wish) still be there in 2015 and after. But if the creation of photos is one of the effects of the wedding, the creation of memories in the minds of the participants is another. If my memories of the past are understood to be effects of those past events in the ordinary sense of that word (i.e., one of the effects of a given past event is an alteration in the state of my brain, which alteration persists through time and constitutes my memory of that event), then my memories at any given point in my life will be of what preceded that point horizontally (i.e., in object time), not diagonally along the line of my actual experience. If the past cannot be changed, the difference is immaterial, since the content of the horizontal and diagonal pasts will be identical. If it can be changed, then as soon as the change has happened, the content of my "original" past is inaccessible to me. When, at the moment marked with the black dot, I suddenly transform from a bachelor into someone who has been married for five years, my memories change as well. I would have no memory of ever having chosen not to get married in 2010, nor of regretting my choice and having my wish granted by a genie. My memory would tell me that I had "always" gotten married in 2010, and all observable effects in the present would also be consistent with that. No evidence that the past had changed would be possible.

What about retrocognition -- "paranormal" direct access to the past, corresponding to precognition and different from ordinary memory? Would that give us access to the "original" past, before it had changed? No, because like precognition, it represents an expansion of attention from the point-present to the linear present of meta-time (represented in the figures by the horizontal line passing through the red dot).

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I had originally planned to discuss the so-called "Mandela Effect" -- the phenomenon of memories that don't match documented history (such as many people's memories of Nelson Mandela having died in prison, or of the Berenstain bears being called the Berenstein Bears) -- as possibly representing memories of the past before it was changed, but our two-dimensional time model has no way of accounting for such "memories" (except to say that they are simply errors). That will require us to venture into the even-more-confusing domain of meta-meta-time -- and, this post already being quite long enough, I think I will reserve that discussion (and a discussion of the moral significance of changeable vs. unchangeable pasts, as raised by Bruce Charlton) for the sequel.