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Temporal Anomalies

Main Page
Discussing Time Travel Theory
Miscellany
Conversation
Other Films
Perpetual Barbecue
About the Author
Contact the Author

See also entries under the
Temporal Anomalies/Time Travel
category of the
mark Joseph "young"
web log
elsewhere on this site.

Quick Jumps

The Letter
Woman on the Plane
Static Time in 12 Monkeys
Reply
Answers to 12 Monkeys Issues
The Grandfather Paradox
Illuminating the Theory
What Happens to Marty

Conversation
Not Letters

Conversation
Chuck Buckley's Time Travel Problem:
  First Response

Chuck Buckley's Time Travel Problem:
  Second Response

Chuck Buckley's Time Travel Problem:
  Third Response

Chuck Buckley's Time Travel Problem:
  Fourth Response

Vazor's Time Travel Questions:
  First Response


Conversation
Letters

Doctor TOC, 12 Monkeys Fixed Timeline
Doctor TOC, Woman on Plane
JKrapf007, Evil Dead 2 Not a Remake
Nathro, Evil Dead 2 a Sequel
JKrapf007, Travel Before Your Birth
Nathro, More About Evil Dead
Sauce96, Terminator and Star Trek
Sauce96, Presenting an Original Story
Sauce96, Defending Paradox
Muhammed, A Line from 12 Monkeys
Holger Thiemann, 12 Monkeys Fixed Time
Chad Hadsell, Local Infinity Loops
Chad Hadsell, Time an Abstraction
Holger Thiemann, Testing the Theory
Chad Hadsell, Travel to the Future
Chad Hadsell, Erasing Future Self
Holger Thiemann, Temporal Duplicates
Gecko, 12 Monkeys Analysis Incorrect
Jason Seiler, 12 Monkeys Static Time
Jason Seiler, Metaphysics Class Links
Etienne Rouette, Woman on Plane
Matthew Potts, Woman on Plane
Bart, Parallel Universe Theory
Bart, Clarification

Movies Analyzed
in order examined

Terminator
    Addendum to Terminator
    Terminator 3:  Rise of the Machines
    Terminator Recap
    Terminator Salvation
    Terminator Genisys
Back To The Future
Back To The Future II
Back To The Future III
Millennium
Star Trek Introduction
    Star Trek IV: The Voyage Home
    Star Trek: Generations
    Star Trek: First Contact
    Star Trek (2009)
12 Monkeys
    Addendum to 12 Monkeys
Flight Of The Navigator
  Flight Of The Navigator Addendum
Army of Darkness
Lost In Space
Peggy Sue Got Married
Bill & Ted's Excellent Adventure
Bill & Ted's Bogus Journey
Frequency
Planet of the Apes
Kate and Leopold
Somewhere In Time
The Time Machine
Minority Report
Happy Accidents
The Final Countdown
Donnie Darko
  S. Darko
Harry Potter and
    the Prisoner of Azkaban

Deja Vu
Primer
    Primer Questions
Bender's Big Score
Popular Christmas Movies
The Butterfly Effect
  The Butterfly Effect 2
  The Butterfly Effect 3:  Revelations
The Last Mimzy
The Lake House
The Time Traveler's Wife
The Hot Tub Time Machine
Premonition
Los Cronocrimines a.k.a. TimeCrimes
Timeline
A Sound of Thundrer
Next
Frequently Asked Questions
    About Time Travel

Source Code
Warlock
Blackadder Back & Forth
Watchmen
Teenage Mutant Ninja Turtles III
11 Minutes Ago
Men in Black III
La Jetée
Triangle
Midnight in Paris
Meet the Robinsons
Looper
H. G. Wells' The Time Machine
The Jacket
Safety Not Guaranteed
The Philadelphia Experiment
  The Philadelphia Experiment II
Time After Time
TimeCop
About Time
Free Birds
X-Men:  Days of Future Past
Edge of Tomorrow
Mr. Peabody & Sherman
Predestination
Project Almanac
41
Time Lapse

Copyright Information

The temporal anomaly terminology used here is drawn from Appendix 11:  Temporal Anomalies of Multiverser from Valdron Inc, and is illustrated on the home page of this web site.  This site is part of M. J. Young Net.

Books by the Author.

Temporal Anomalies in Time Travel Movies
unravels
A Letter from Doctor TOC:
The Woman on the Plane

A good reply often stimulates another good letter.  Chris decided to follow the subject further on several fronts.

Pattern

Mark,

  Thanks for the reply. I must admit I wasn't expecting such a response of such epic proportions, but I'm pleased and grateful that you could take the time to get back to me so quickly.

  The "Reverend" is genuine, as I'm an ordained minister. The "Doctor" was originally a nickname, but now refers to my doctorate in metaphysics.

  Thanks for clarifying your explanation of your theories about "12 Monkeys". There is one point which you raised which I interpret differently.

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Woman on the Plane

  You wrote:  "One is that the woman who appears to be one of the chief scientists through the majority of the film is in fact introduced to us as an insurance somebody, possibly a salesperson, so we hardly expect them to fully understand either what they have said or what they have done."

  The chief scientist appears on the plane at the end of the movie, and is the same apparent age as when we saw her in the future. Part of Cole's mission is to obtain a pure sample of the virus (before it mutated) for the scientists to study in the future, which is why he was eating spiders (that he was doing this before the virus had been released is an indication of his confusion at the time). I interpret her appearence at this point to mean that she was sent back as a backup, to obtain an unmutated sample in case Cole failed in his primary objective. Hence the comment about "insurance" (a wry joke rather than her actual job). Since it's been a while since I saw the film she may have turned up earlier, but I don't recall it.

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Static Time in 12 Monkeys

  While I agree with the majority of your thoughts about the nature of time, I think that "12 Monkeys" is a poor example to use to illustrate your point, since the whole point of the film is that history cannot be changed, and it strives hard to show this.  I agree that the provision of a gun to Cole at the end of the movie showed that the scientists weren't 100% positive that history was inflexible, but it was a purely human action. In a similar situation, who would not try to change things, no matter how much they "knew" that things would happen as they always had? If they proved themselves wrong, they won by having their terrible future wiped out. And if they were right, they were in no worse a situation than before.

  You wrote:  "it is clear that whether or not they believe the past can be changed, they are trying to change it.  The changes they intend are extremely small (at least in the beginning), but they do seem to expand as the movie progresses.  They are injecting someone from the future into the past; and they are trying to cause someone in the past to send information from the past to the future.  However, I understand their perspective:  they would have us believe that there is a single time line, and that all of the events which happen on it are fixed."

  I'm not sure I can agree with this. Cole is merely trying to get a pure sample of the pure virus back to the scientists in the future. They gave him the phone number because they already hade the information he is going to provide on the tape, and therefore they knew he would call them to fulfill that loop. The passage of information from past to future is no more paradoxical than archaeology. Since they already know Cole went/is going to go back in time, history is not changed. I have to assume that since Cole is an adult of reasonable intelligence when he is first sent back, and he is briefed by scientists who are at least smart enough to build a time machine, the information he has as to whether history can be altered or not is correct (how they would ever know this is another matter entirely).

  you wrote: "I gave a lot of consideration to the static timeline theory of time; however, there are plausible time travel events (many covered in films) which cannot be possible under that theory."

  True, but in this case the film is entirely consistent with its own stated temporal mechanics.

  "The classic puzzle of the man becoming his own grandfather,"

  Always fun, but genetically impossible.

  "With the static timeline theory, we must either presume that time travel is utterly impossible and always will be (which might be the case, but does not make good fiction), or that Providence is so deeply involved in controling events that our entire science and perception of the universe is illusory."

  Which is what the movie was trying to say. It's not a view I subscribe to, but it was the core of the film, so it seems a little redundant to attach a convoluted (though brilliantly reasoned) explanation of events to it.

  "That said, let me suggest that perhaps those in the future didn't mean that you could not change the past at all, and that the movie may not have intended for us to believe this.  Consider this scenario. <scenario snipped>"

  Hmmm. So they might have been saying "you can't change history sucessfully_" rather than "you can't change history, period".

  Interesting.

  I've always been intrigued by the often-used literary mechanism of having those "pastwards" of a historical change remaining unchanged by it. This would mean that in the scenario snipped above, James Cole could travel back in time, discover the man responsible for the release of the virus, kill him, and live out the rest of his life in the 1990's, neatly avaoiding the possibility of unravelling his own existance through his own actions. Poul Anderson's classic "Time Patrol" used this approach, allowing that the traveller would then be a man without a past, who had apparently appeared out of nowhere fully grown and with a past that no-one else would ever experience. While it's patently absurd, it is no more laughable than some of the deep strangeness that occurs at the quantum level all the time. A problem of this theory is that it must logically lead to duplicate travellers, should the traveller ever return home. The scenario runs like this: James hops onto a timebike and jumps back to kill the psycho lab assistant. He then jumps forward to his home time, only to meet with James Cole 2. James Cole 2 grew up in a world with no virus and never jumped back in time, and is surprised to meet his balder, more mentally divergent twin.

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The Theory of These Pages

  "The timeline theory I developed while working on Multiverser explains how all of these stories are possible, what brings them about, and what consequences flow from them.  It is deterministic in a limited sense, in that it suggests that whatever someone does at a given instant is what they would do at that given moment in any history in which events causative of that action are unchanged.  Thus if the pass Larry makes at Ginny causes Ginny to slap Larry across the face in a world in which Ted Kennedy is Senator from Massachussetts, that same pass will get the same slap in a world in which Bob Schwartz is Senator from Massachussetts, assuming that who the Senator from Massachussetts is has no effect on either Larry or Ginny.

  "But there is another sense in which the past cannot be changed which is intrinsic to my theory.  It is commonly suggested in time travel movies that if the past is changed by a time traveler, the time traveler will know what it was before he changed it.  I find this doubtful in the extreme.  As you will note in my analysis of Back to the Future (Part I), Although there is a Marty McFly who grew up under the roof of the George and Loraine McFly who met when her father hit him with the car, that Marty's history has ceased to exist when he returns to the future.  He is replaced by the Marty McFly who grew up in the home of George McFly, science fiction author, and knows nothing of that other Marty.  If subsequent to the time travel event history is able to continue (not always possible), the only past known to anyone is the last past created."

  In your timeline theory, what actually happens to the original Marty? Does he cease to exist as soon as he catches up with his point of origin? What is the mechanism for this? This also begs the question why the original Marty doesn't change in New Marty (tm) immediately after he gets George and Lorraine together.

  I'm sorry to bat questions at you like this, but without more info on your version of temporal mechanics, I have no other recourse. I hope you don't think I'm attempting to knock holes in your reasong either. I'm just fascinated and want to know more.

...

  "I hope I haven't bored you with my complicated reply (and I hope it's coherent--I was fighting to stay awake when I began it, and am too tired to proofread it now)."

  It's a damn sight more coherent than I usually am, and no, you haven't bored me at all. I love debating possible temporal mechanics with people, and it's always nice to "meet" someone who doesn't glaze over and start to nod after a few logical twists :D

Thanks again for your thoughtful reply, Mark. All the best with Multiverser.

Chris

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Reply

Chris--

  I'm glad for the opportunity to correspond with someone able to keep pace with me.  I often quote (more to myself than to others) C. S. Lewis quoting Augustine, "I am one of those who by writing profits, and by profiting writes."  It's good to have my thinking challenged; it makes me think.

  As to the length of my reply, I do tend to write extended epistles.  I've managed to contribute over a hundred pages on various subjects to the web to date, and am still going, so a long letter is a small thing.  I try to answer mail when I get it, because if I put it off, it's much harder to get back to it.

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Answers to 12 Monkeys Issues

  I like your joke about the woman being in "insurance"; unfortunately it was my impression that she was much older in the future scenes than on the airplane.  However, I don't currently have access to the tape, and can't verify that.  It would be a logical next step for them to have taken, given all that had happened to that point, and makes a satisfying conclusion to the film, but I can't confirm or refute it.  Also, it does create an additional time trip, an additional anomaly, which is probably another N-jump.

  I'm not at all sure either that the movie intends to show that history cannot be changed, or that it is a poor example for me to use.  Remember that Cole was in second grade when his education ended.  Were I preparing a person with a second grade education--even an adult so limited--for a time trip, I might prefer to tell him that he can't change the past, rather than attempting to explain why he mustn't do so.  Providing the gun for Cole is a mistake.  If they are right about time, then he cannot change it, and providing the gun cannot help.  But if they are wrong, then I am right, and if I am right, Cole can change the past by killing the lab assistant.  However, if he does so, he eliminates the future from which he has come, and the reason for having done so--therefore he will not come back in time and kill the lab assistant.  If my theories of time are correct, they have everything at stake, for their success will destroy the time line.

  If you read my page on Millennium, you know how skeptical I am of the idea of traveling back in time without changing anything.  However, I confess that I expressed myself poorly in regard to the notion of transmitting information from the past to the future.  You are of course right that information moving from the past to the future is not different than archaelogy; and it is not the information moving that direction which matters.  However, Cole and his handlers intend for him to make multiple changes to the past in the name of obtaining information.  Consider them.

  Cole is attempting to recover not information about a virus, but the virus itself.  The virus is made of genetically-coded self-replicating matter; that means that we are intending to remove from the past both a small quantity of matter itself (which will vanish entirely from the universe for perhaps thirty years), and one of the pattern replicating organisms.  There will be less virus in the world because of this action.

  He swallows the spider.  This is a larger quantity of matter removed from the universe, and an organism which would have continued to have offspring which will now never be born.  We think that if you kill a human you will change the past, but if you kill an animal, you will not.  That's anthropocentric reasoning.  The fact is that if you step into the past, you have changed it.  Killing a spider or killing a human, or just breathing and sweating, you create a new history.  The difference is that if you kill a human, you might change the gene pool of humanity sufficiently that you compromise your own existence; if you kill a spider, you have a much lower probability of doing so.  However, even without the example of the whales in Star Trek IV:  The Voyage Home, it is possible that the destruction of one creature could result in a change in the population such that an ecological alteration occurs impacting on the human condition.  We change the past whenever we enter it from the future; what matters is that we take care not to change it in a way which impacts our ability to change it.

  The phone number is not completely explained.  The suggestion is that someone from the future came back and set up a voice mail account.  This is a change in history--the commitment of resources in the past to different uses.  That phone number would have been issued to someone else were it not taken by the voice mail account; the memory chips which record the digital messages would have been used to record other messages.  Now, it's possible that they did not set up this account, but merely identified a little-used account on a digital service which would survive; this is less invasive of the past, but still commits resources in the past to serve the future, making them unavailable in the past.  Even if we knew as a fact that those circuits had contained no information at all before we recorded our messages, the fact that they now contain information we put there which would not be there were it not for our invasion of the past is a real change in the past.

  But the movie does make a good example, as their own single-timeline theory does not explain even their own story as well as my theory--and their theory also does not explain anomalies which are plausible and explained by my theory easily enough.  The classic puzzle of the man becoming his own grandfather seems absurd to anyone locked into a single timeline theory; but I can explain it, as well as similar problems such as the object which is given by the future owner to the past owner, and stories in which characters in the past take actions inspired by their own futures.

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The Grandfather Paradox

ADDITIONAL TEXT

  I wasn't going to do the grandfather of himself example--in my mind, it is in some ways the jewel of the temporal anomalies material in Multiverser--but it shows how the theories work.  I use as an example a nearly forgotten movie I saw on television years ago, in which a man received a medallion from his father which had belonged to his grandmother.  She had gotten it from his grandfather, and come to San Francisco looking for him, where she became matriarch of their family.  He accidentally goes back in time, meets a woman and becomes involved in a passionate affair.  He is rescued by friends from the future, and she pulls the medallion from him, going to California to seek him, the father of the child she now carries, who will be his father.  My immediate reaction, based on the single timeline theory, was that it was absurd and impossible; yet it has a simple plausibility to it:  if men have free will and can move through time, they can do this.  I found the answer in the theories I developed for a multiple timeline approach.

  The answer to this kind of problem begins with the observation that we have come into the story in the middle.  (As someone has said, all of science amounts to the statement "Humpty Dumpty is falling"--we don't know how it began.)  Follow my timeline carefully; this shows more than any other example why I feel that either time travel is not possible, or time will follow my theory.

  There is an original A-B timeline in which grandmother meets stranger.  Stranger gives her a medallion, and becomes the father of her child; this child becomes the father of traveler.  The medallion passes from grandmother to father to traveler.  Then traveler stumbles back into time, initiating the C-D timeline.  He meets grandmother, and interferes with her meeting with stranger; he fathers her child, and she takes the medallion from him.  There are now two medallions.  The one which is passed from grandmother to traveler in this segment is older; it has been through this timeline before.  The other one is still in the possession of stranger, who will pass it on to someone else.  Grandmother's medallion is a temporal duplicate caught in the anomaly, and only exists from the moment traveler reaches the past to the moment he leaves the future.  A simple N-jump is created, and the future sees only that a medallion moves from grandmother to traveler to grandmother; it sees a separate medallion which moves from stranger to someone else.

  But what of the genetic problem?  This is the best example of the sawtooth snap (illustrated on the main page) that I have.  At the end of the A-B timeline, father's genetic makeup is half grandmother, half stranger, and traveler's genetic makeup is half mother, quarter grandmother, quarter stranger.  At the beginning of the C-D timeline, traveler replaces stranger, and the genome changes.  Father is now 62.5% grandmother, 12.5% stranger, and 25% mother, and traveler is 31.25% grandmother, 62.5% mother, and 6.25% stranger.  Thus at point D, the traveler who goes back in time is a different person, and creates the E-F timeline, different because he is different, in which the genetics shift further.

  The theoretical limit is that father will eventually be 2/3 grandmother and 1/3 mother, and that traveler would have the reverse proportions; however, two things should be obvious.  First, anyone whose entire DNA comes from grandmother and mother is a girl, and cannot become his own grandfather; this reversal of gender will happen before the complete genetic switch has occurred, increasing in probability with each loop.  Note that by the tenth segment, stranger's DNA accounts for about one one hundred thousandth of one percent in traveler; long before that the gender will have reversed.  Second, as the DNA shifts, the character will change in other ways.  He will look different, act differently.  Having different strengths and talents, he will pursue different interests--as will his father before him.  Perhaps father will no longer appeal to mother, or traveler will not be attracted to grandmother.  Or perhaps traveler will not be in a position to go back in time.  The time will come on which the cycle is broken.  In this case, traveler will eventually not interfere with stranger and grandmother, and we are returned to the original timeline in which grandmother and stranger beget father.  The cycle resets, as it were, to the A-B timeline, and repeats itself perpetually.  We have a sawtooth snap with an infinity loop ending; time never gets beyond these events.

  One of the beauties of the system I use is that it can solve puzzles like this; things which seem possible in a sequential action logic are possible, even if they involve actions in the future undermining themselves in the past.  The damage to the time line can be horrendous; but there is no reason to think that men who have learned to destroy matter and dissipate energy would be unable to destroy space and time also.

  It is possible that the movie is trying to say that time is fixed in this odd way--much like Lewis' chess game at the end of The Great Divorce, the ends are known from the beginning, and every move written in stone, so the sequence in which they appear to occur to us is not relevant.  I am not certain they were saying that; but even if they were, the fact that my "convoluted explanation of events" (and no offense taken) can explain their story on its own terms, and do so without taking away the ability of individuals to make choices which affect events or otherwise lock us into the deterministic views of history which are so antithetical to our feelings about life, shows that perhaps time works as I suggest, instead of as they suggest, even when they define the events of the story.

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Illuminating the Theory

  Regrettably, I have not had the opportunity to read Poul Anderson's Time Patrol.  However, I would agree with your assessment--he seems to be thinking along much the same line as I.  And is it truly absurd?  You live in a town with many other people, probably none of whom grew up where you did.  Why is it necessary that they should have grown up WHEN you did?  Some did not--you identify them by whether they are older or younger than you.  But if time is at all like space, it should be possible to live in one time, and then move to another.  As to the temporal duplicate problem, I don't see this as problematic either.  If I met myself, I might not know it was me; and the older self seeing me would know me, but need not say so.  But your scenario is the basic infinity loop.  The virus was released, and James hops on his time bike, goes back to before the virus was released.  A time trip has two critical points:  the point in time from which the traveler leaves, and the point at which he arrives.  For convenience, we identify the point in the timeline at which he will arrive as point A in the original timeline; if traveler is here, it is because he lived then (like the young James Cole).  The theory maintains that before anyone can go into the past, the past must pass without them.  Point B is the point from which the traveler leaves.  When he reaches point A, his arrival intrinsically changes history--he is now there, whereas he was not there before--so we have an altered timeline, identified as point C:  exactly the same instant as point A, but changed by traveler's presence.  There are indeed two travelers in this time line--the young Cole and the old Cole were both in the airport.  Both may exist until point D, which is point B, but at the end of the timeline in which traveler has changed things.  Now at point D the critical questions revolve around whether the Cole for whom the C-D timeline is the only history he knows will choose to make the same trip back in time, and whether he is the same person as the Cole who made the trip at point B.  If both of those things are true, then the C-D timeline is preserved:  the younger Cole will go back in time and do what his older counterpart did, so the future continues with the C-D timeline as its history.  We call this an N-jump, because if drawn with the past below in looks like a letter N (see the index page for the illustration).  If the younger Cole does not make the trip, then the C-D timeline fails, and we revert to the A-B timeline, setting up the original Cole to make the original trip, creating the infinity loop, because the A-B segment causes the C-D segment, but the C-D segment causes the A-B segment.  On the other hand, if the younger Cole at point D does go back in time, but is not the same Cole, he creates point E, the beginning of the sawtooth snap, as his character and actions will create a slightly different history.  The analysis continues in the same way at the end of this segment (point F) and any succeeding segments, until eventually the line stabilizes into a resolved history (in which the same Cole makes the same trip), or errors into an infinity loop (in which the trip is prevented).

  There are other events which can cause the various anomalies, but in essence these are the three anomalies which explain everything.  But during the segment which represents the time jumped by the trip, the existence of temporal duplicates of some sort is a certainty, even if it is only physical matter which is so duplicated.

  Now you know most of what you would get about time travel from the game, except how to make it work in the game.

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What Happens to Marty

  What happens to the original Marty McFly?  I suppose this is in one sense the glitch in the system, although I don't see it as such.  When anyone goes back in time, at that instant (the instant from which they leave) their timeline ceases to exist; this is logically necessary, because they have erased the history upon which that timeline is based.  There is no further future for the George McFly who never knew Calvin Klein.  Marty's arrival in the past has created a new timeline, and the old timeline is entirely forgotten.  Of course, no one in 1955 except Marty knows that such a timeline ever existed; and Marty could stay here until 1985 fully aware of that information, because he lived it; but when he returns to the future, the timeline he left is gone.  He comes back to a timeline which he has already changed.  Now if time were to continue from here into the future, this Marty would remember the other timeline.  But he sees himself go back in time--and because that is a different Marty McFly--not merely a temporal duplicate who is identical, but a temporal duplicate whose divergent history has made him a different person--that trip creates the E-F timeline.  At that instant, the timeline which this original Marty created has also ended; that Marty will never reach Doc.  I think, however, that the Marty who just went back in time will throw himself into the relationship of his parents, and create a history not much different from that of the C-D timeline.  If so, then the Marty who leaves at the end of that segment is the same person, and will do the same things in the past; and upon returning, that Marty will go directly to Doc.  The other Marty's don't exist independently; they cease to exist because time ends in the universe in which they are.  It's a bit like asking what happens to the characters in a movie after the film ends--nothing happens to them; they cease to exist because there are no more frames in which they can have life.  But they don't die.  They just lose who they were, becoming the people with the alternate history in the other timeline.

  As to the other Marty becoming the new Marty upon getting his parents together, that's an interesting concept.  However, I would need a mechanic to explain how his memories changed.  He is the only person who ever had any memory of the other timeline.  But more to the point, why should his memory and identity change at the moment he gets them together?  If the events of this timeline will change who he was when he left the future for the past, isn't it the case that from the perspective of the time from which he left, all of those events are already the past, even if any of them are still the future for him now?  It is the problem of the photographs and newspaper articles:  if the actions of Marty in the past are going to change those papers, won't they have already changed the instant he enters the past, reflecting the changes which he will have made by the time those papers are printed?  I find it more reasonable to suggest that that which comes from the future recalls the alternate history (and Back to the Future is very inconsistent about this question--if Doc is locked up as insane, why doesn't the Delorean vanish?), but in the alternative, if actions done in the past will change that which comes from the future, it is a fait accompli at the moment they arrive in the past.  (That's a difficult concept--did I get it across alright?)

  I will briefly note the irony that I should have chosen the state of your current residence for my illustration.  I actually have been picking on Boston in my temporal anomalies stuff, as the place you could go to and be gone for years just as if you'd left time altogether.

  Thanks for your letter.  I enjoy the challenge of dealing with these problems.  Every time I tackle one of these films, I realize that something happened temporally that I didn't catch when I first watched it; and the time lines aren't usually what I thought they were at first.  Your questions are similarly challenging:  did I get it right?  or did I miss something?

  I look forward to your next challenging missive.

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