There is a short list of time travel stories that are mentioned when the subject arises, and on it is a short story about someone who travels back to the time of the dinosaurs, steps on a butterfly, and returns to find that he has significantly changed history.  Some of those who read it also know that it is entitled A Sound of Thunder, or that it was written by Ray Bradbury.  Some, too, know that it was the basis for a movie of the same name released in 2005.

Bradbury is well known for collections of short stories--S is for Space, The Illustrated Man, even The Martian Chronicles were all such collections loosely connected by a thematic concept.  This story was in the 1952 collection R is for Rocket, but is also the most republished science fiction short story known.  However, the movie is so loosely based on the book as to be nearly unrecognizable; further, the movie introduces several concepts that are faulty, which cannot be laid to Bradbury's blame as they were not in the original version.  As always, this analysis is of the movie.

It begins with a time travel team comprised of five professional time travelers and two paying clients walking on a forcefield path inches above the ground in a cretaceous swamp.  They are here to kill an allosaurus, one of the deadliest predators known.  The professionals have done this before, and everything is arranged to ensure that it goes exactly as intended, that the right beast is killed at the right moment, and nothing else is changed.  It is obvious that even the impromptu speeches are well-rehearsed to give the clients the feeling that they took great risk and should be proud of their kill.

The festivities are interrupted by the protest of Doctor Sonia Rand, whose work made time travel possible and who believes that what they are doing is dangerous; but the wealthy owner of Time Safari, Inc., is able to defuse the tension.  The time travel team leader Doctor Travis Ryer, however, takes the time to learn from Rand why she is concerned, and explain their precautions.

The next trip does not go well.  An equipment malfunction disables the rifles, and it is necessary for Ryer to distract the beast while getting the clients to safety and having the team technician, Marcus Payne, fix one of the guns.  They return to the future, and Ryer insists that better precautions will be necessary.  However, it is too late--within twenty-four hours, the world is changing, and as "time waves", ripples of change emanating from an unidentified alteration in the past, reach the present, the changes become more drastic--first climate, then vegetation, then the appearance of dangerous new creatures and the collapse of artificial infrastructure.  Ryer and Rand lead the Time Safari people in a race to identify and repair the damage before the final time wave undoes the evolution of humanity itself. They encounter several problems in attempting this, but the future Ryer manages to communicate to holo recorder Jennifer "Jen" Krase that she must give the recording to the version of him contemporary with her, and to no one else, so that he can take the necessary steps to prevent danger in the future.

The film is riddled with problems, but it also raises important issues, so an examination of some of the details is warranted.

The time travel company takes many precautions to prevent temporal disaster.  These prove to be inadequate ultimately, but do illustrate the dangers of time travel remarkably well.

Three "Rules of Time Jumping" are stated.  The second and third are clarifications of the first, which is Never change anything in the past.  That includes Don't leave anything behind and Don't bring anything back, but goes beyond that.  The precautions are impressive.

The time travelers are innoculated before departure.  Given the other precautions, this is redundant.  All travelers wear environmental containment suits, so that they breath air they bring from the future and return their exhalations to the future; all sweat perspired and any microorganisms which might be traveling with them are contained within the suit.  As they enter the time machine, they pass through a spray and array of lights which presumably clean and decontaminate the exterior of the suits as well.  Once in the past, they walk on a forcefield path suspended above the ground, such that they do not leave so much as footprints in the grass and the impact of their steps will not cause vibrations.

The hunters are strictly instructed that they may only kill the one creature identified as the target, a dinosaur about to perish apart from their intervention as it becomes stuck in bog mud and then buried in ash from an erupting volcano five minutes after their arrival.  As an added precaution, the gauss rifles of the members of the party are equipped with radio-operated safeties such that they will not fire until the team leader fires his own.  The guns are laser-targeted to ensure accuracy, and the projectiles are frozen nitrogen bullets which will disintegrate completely within two minutes of leaving the weapon, leaving no traces of solid projectiles behind.

Yet for all this care, they are changing the past in ways they would have preferred to avoid; they have not fully considered the matter.

First, they are seen.  We know this, because they attract the attention of the allosaurus.  That means they are absorbing and reflecting photons which would have struck other objects in the original history.  Second, they are physically present, and so their presence and their movements are changing the flow of air around them in small ways.  They are also interfering with total energy in their environment--possibly absorbing light and heat, possibly radiating heat, since it is unlikely that the suits are already the same external temperature as the air or that they reflect the entire electromagnetic spectrum.  The guns, though, are the most problematic.  It is not explained how they manage to keep nitrogen in a solid state, but they must contain a refrigeration system, which means they are venting heat to the outside somehow.  They are also using energy, and so creating waste heat, to propel the projectiles.  Mitigating this, the bullets themselves are unnaturally cold, and so are drawing energy from the environment as they return to gaseous form.

Further, those bullets rip holes in the body of the beast, a body which otherwise would have remained sealed inside an intact dermal layer.  That provides access for different organisms in the decay process, and potentially alters the balance of life on that level.  This is exactly the kind of concern expressed in the flim, that killing one bee can result in a change in the number of flowers which are the food supply for some other creature.

Still, while they have not reached zero tolerance and are indeed altering the past, the film gets high marks for recognizing the dangers of time travel and having the time travelers address them so meticulously.  Further, the nature of their failure is instructive.

The chaos theory notion of the "butterfly effect" did not get its name from this story, but it well might have done.

We do not know how many times the professionals on this team have made this trip, but on this occasion they have a problem.  Liquid nitrogen had dripped onto the primary weapon, shorting out the firing mechanism safety signal such that none of the weapons would function.  Ryer tells the clients, a nervous family man named Mr. Ted Eckles and a wealthy businessman named Mr. Middleton, to run back to the time portal, which after a moment they do.  Payne attempts to repair the weapon while Ryer distracts the dinosaur, aided by Krase.  The other two professionals in the group, medical doctor Lucas and government observer (from the Department of Temporal Regulation) Clay Derris also fall back, but lose sight of their clients.  No one knows that Middleton misstepped, his right foot crushing a butterfly in the mud which clings to the sole of his boot.  We are given to understand that either the death of this butterfly or the removal of its tiny body from the cretaceous era completely alters the evolutionary history of the earth.

The theory is sound, but it is a bit improbable.  Certainly it is reasonable to suppose that the untimely death of a single creature can so alter the genetic distribution in the species as to completely change the future.  The problem is in the particulars, that is, whether the death of this specific butterfly could have had that impact.

The flaw lies in the expectation that this butterfly would have survived the imminent volcanic eruption so as to contribute to the ecology in some other way even five minutes later.  We know that the volcano erupts five minutes after the arrival of the team, and we know that on this occasion they are still fleeing the scene when it does so.  We could perhaps time how long it takes for the leading edge of the destruction, a destructive force so potent it would have killed the allosaurus had they not already done so, to travel from the distantly viewed volcano to the landing site, but it is certainly under a minute.  It is also more than a minute between their arrival and the moment they discover that the guns do not work, and even then Middleton and Eckles do not flee immediately.  Given the velocity and potency of the destructive wave, it seems nearly as certain that the butterfly would have been killed and buried in the debris as it is that the allosaurus would have been.  The added mass of the traveling team was less than two grams, and while we can argue that the spent nitrogen bullets must have decreased their total mass slightly, we also have to account for the mass of the mud in which the butterfly was trapped.  That tiny amount of organic material buried in that volcanic sediment could not have been missed by anything, but merely increased the amount of petroleum in the resulting oil field by a few unrecoverable drops.  To think that the butterfly might have escaped stretches credibility past the breaking point.

This is not saying that it is impossible for the elimination of a single butterfly from the ecosystem to have drastic long-term consequences.  It is only saying that the removal of this butterfly would not have done so.  If it were still there to be trampled by our fleeing Middleton, it was killed and buried in the blast.  It is an important consideration in time travel generally, but not in this particular case.  The story fails on that point.

However, there are more serious problems ahead.

We are given to understand that the time travel team has done this before.  They have many times taken paying clients to the past and given them the opportunity to kill an allosaurus who was about to become trapped in bog mud and finished by an erupting volcano.

That is, they have already on previous trips killed this allosaurus.

We get that impression on the first trip we see, as Ryer carefully tracks the movements of the beast waiting for the moment to let Mr. Wallenbeck and his daughter attack.  It is quite obvious on the second observed trip, as the same allosaurus makes the same movements in the same swamp.  They are hunting the same allosaur.

There is no inherent reason why a professional time travel team taking the Wallenbecks from one weekend in the spring of 2055 to a precise time and place in the cretaceous period to shoot an allosaurus could not the next weekend take Middleton and Eckles to the exact same time and place to shoot the same allosaurus.  The problem is, when the Middleton expedition arrives, the Wallenback expedition should also be arriving, along with every other group of hunters ever taken to kill that same allosaur.

You might escape this problem by making this not time travel but a specific form of parallel dimension theory in which every trip from future to past takes you to a different universe, and in which those other universes have all diverged sufficiently from ours that no one is traveling from them to the past in other universes (or travelers from ours would encounter travelers from those other universes).  However, were that the case, the changes made by killing the butterfly would not have happened in our universe, and when Ryer traveled to the past to prevent the disaster he, too, would have been in yet another universe, not the one in which any of the time travelers had arrived.  You can't get this story from parallel dimensions.  In fact, you can't get this story from any theory of time.

The death of the allosaurus is thus constantly changing.  On the first trip, whoever was in that first group shot and killed the dinosaur.  Then with the second trip, members of both groups shot the allosaurus, increasing the number of wounds it took and making it more difficult to know who killed it.  By the time Middleton and Eckles are facing the beast, there are perhaps hundreds of other hunters firing at it, and the fact that their weapons fail is moot, because we already know that the Wallenbecks killed the beast now attacking them, so the allosaurus already died at this moment.

The movie needed the hunt always to target the same creature at the same moment, because it was the only way Ryer and his team could recognize that they arrived too late in the next trip.  It is, however, an unresolvable impossibility.  If Ryer kills the dinosaur on the Middleton expedition, it was not killed on the Wallenbeck expedition; if Wallenbeck killed it, it dies of Wallenbeck's bullet before Ryer can fix his gun.

In order to give Ryer and Rand the opportunity to repair the damage done to the past, the movie suggests that the effects of changes move through time like ripples from a stone tossed in a pond, changing the future in increasingly significant waves.  There are a lot of problems with these waves; the first is their movement.

It apparently takes twenty-four hours for the second wave to hit the city; when it does, it is visible as a distortion moving toward them, and felt as a kinetic impact on some objects but not others (passing through walls and windows without cracking them, but pushing vehicles and people).  This raises problems concerning how it moves.  Since these are not the first changes (the plants changed), the first wave probably took twelve hours to cross sixty-five million years.

It is thus moving at slightly more than one and a half millennia per second.  In the ten seconds between Ryer seeing it and it impacting him, it traveled forward (from 2055) to the year 17101.  Yet if it moves outward spatially at one mile per second, given an earth diameter roughly eight thousand miles, it takes half an hour for the wave to engulf it--in which time the leading edge temporally will be approaching the year three million.  So for most of three million years the wave will have impacted only part of the planet.  This leads to untenable conclusions:  in the next second, the wave will not have covered as much of the earth as it did in the last previous.

Even if we are much more generous in our estimates, the wave itself is a paradoxical impossibility as presented.  We might make it reasonable if it moves spatially at the speed of light (as most of those who hold to such a theory suggest), but then you could not see it coming--you would get an "optic boom" as all the light from it and it arrived simultaneously.  In that case, the entire earth would change in four hundredths of a second, and the leading edge would only have reached 2120, so the disparity is not so significant.

However, there is a more fundamental question:  how can a change propagate through time at a rate other than either the speed of time or instantly?

If the change happens "at the speed of time", then in essence we are "outrunning" it--we are sixty-five million years ahead of the change, and for every second that the change moves forward through history we move forward a second, maintaining our lead.  This creates the absurdity that our present always exists as it is despite the fact that our past has been altered entirely.  The fossil record might be altered, some cretaceous and later fossil remains might vanish, and eventually our discoveries concerning early man might disappear, but by then we would be so far in the future that they probably would have crumbled to dust anyway.  Future time trips to the past would discover a different past from the one we expected, because the past would be changing but the present would still be built on the original lost past.  It wreaks havoc with cause and effect, because the chain of events which brought us where we are will have ceased ever to have existed, and yet we will continue to build a future.  It would be something like being on the top block of a Jenga® tower when the bottom level is removed, and having enough time to stack additional blocks upward before the block on which we're standing falls, so that we never fall because we are always stacking a new block atop a block that has not yet fallen.  This absurdity would not make a good story for the movie, because no one would ever know the past was changing.

In the alternative, we could accept that when the time travelers reach the future, the sixty-five million years that they cross has already been completely changed and they arrive in the world that results from those changes.  This would not make a good story for the movie, because no one would know that the past had changed (it is the past they've always known) and if humanity was undone by the change, our travelers were not human when they departed.

That leads to more problems, to be addressed.  For the present, we must accept that for some completely inexplicable reason the changes made to history reach the future in waves that are completely illogical--yet despite this illogic, Dr. Rand is able to predict when they will arrive with some accuracy.

The first wave of change arrives overnight after the fateful trip, but it is not obvious.  There is an abrupt climatic shift, with balmy weather in November.

It is certainly the case that fauna and particularly flora impact atmospheric conditions.  Natural forest fires control the oxygen/carbon dioxide balance in the atmosphere within a very narrow range (between the levels at which a fire won't start and one won't extinguish).  We are all too acutely aware of the impact greenhouse gases have on temperature.  However, on a geologic scale climate is controled primarily by geology.  Plate tectonics drive up mountains uncovering calcium-rich rock which dissolves in the slightly acidic rain created by carbon gases washing out of the air, removing carbon from the air and burying it on the bottom of the ocean.  This drives global temperatures down.  Continental drift redirects ocean currents which redistribute equatorial solar energy.  Volcanic eruptions and violent ground shakes add dusts and gases to the atmosphere.

At the end of the cretaceous period there was a meteor impact which is believed to be the cause of the extinction of all larger animals.  There have been several glacial ages since then, and some theorize that the earth would now be well into a new glacial age were it not for man's interference.  Certainly the proliferation of trees can be a factor in global climate.  However, the suggestion that any change in the evolutionary chain of life would have sufficient impact on climate to create semi-tropical conditions in higher latitudes is very difficult to support.  The factors that matter to climate are outside the realm of evolution.  No number of butterflies or their impact on the world will have greater effect on climate than the astronomical and geological activity of meteorite impacts, continental drift, mountain upthrusts, and volcanic eruptions; nor will any life form change any of those events.

The other problem with the climate change, though, is that anyone would be surprised by it.

At one point Dr. Rand comments concerning the plant life that it has had sixty-five million years since the change was initiated to evolve to its present form.  That, though, means that whatever the shape of the world today, it must be that shape which follows from yesterday.  If the world is so warm that there are no polar ice caps, it must have been so warm all year, and in fact for the entire lifetimes of everyone presently alive.  It makes no sense to suggest that the condition of the world abruptly changed today because of a change in the cretaceous era.  Rather, that change in the cretaceous era altered the condition of the world through the time that man appeared and through the entire history of humanity.  That is not to say that it has been warm the entire time, but that whatever the present state of the world climate it is exactly what humans expect based on having grown up in the new version of the world.

Looked at from the other end, even if we accept the ripple concept, before the change reached today it reached yesterday, and before it reached yesterday it reached last week, and before it reached last week it reached the day I was born.  Thus all my memories of the past have already formed in the world this has become.  Although today might be different from what it was before the butterfly was killed, that is not a temporal concept but a metaphysical one, and I have never known the world in which the butterfly lived because I was born in the world in which it was killed.  It all seems perfectly normal to me.

This echoes problems in Frequency, in which a number of events in the past had abrupt effects in the future, including a broken radio, a burned table, and the loss of a man's arm.  It does not withstand scrutiny.

In examining the supposed impact the death of the butterfly had on the climate of the world, we noted also the more general incongruity, that if the world changed in the cretaceous period, by the time the change reaches us in 2055 it has already reached us every year prior to that, so we are familiar with the world as it became, and ignorant of any reality that might have been.  As the next wave hits, another incongruity rides on it.

Dr. Rand comments about one massive tree that it was never there before; it is one of many plants that are already destroying the buildings.  Yet it is not at all hinted that there is a new breed of tree that sprouts from sapling to sequoia in mere minutes.  The tree is massive because it has been growing for generations.  And here we have our problem.  If the tree has been growing for generations, it was there yesterday; and if there were also people yesterday, they were aware of the tree and the hazard it posed to the building.  Why did no one fell the tree when it was becoming a problem?  Why did no one prune it to keep it contained?  Indeed, why did anyone ever build buildings that would be vulnerable to plants that could not be controlled, if that is the situation?

This problem is most evident when the last wave hits and Dr. Rand is replaced by some sort of amphibious biped sitting in the lab by the particle accelerator.  If the change has meant that all humans are these amphibious creatures, who built the lab?  Who had the knowledge to create particle accelerators?  Indeed, why is that amphibious creature sitting in this building?  We know why Dr. Rand came here, but that was because Dr. Rand was a human a few minutes before, trying to do something only a human would attempt.  This creature that replaces Dr. Rand must have existed somewhere yesterday, and it is beyond belief to suggest that it was working together with Dr. Ryer to return to the cretaceous period to prevent the change in history which caused it to exist.

The image of the world changing a bit at a time is nonsense.  Further, the film treats it inconsistently.  When the Middleton party changes the future, it creates ripples that move forward through time, altering the climate and changing the course of evolution, such that we see the buildings collapsing as the new version of nature overwhelms them, and watch our human heroes one by one killed by creatures that did not exist.  Yet by the time Ryer makes his trip, all of that is the history of his world.  He travels to the past and changes the future again.  Note that he does not really prevent it from being changed; he changes it to something similar to what it was.  (There never "before" was a history of the world in which Middleton almost stepped off the path and was prevented.)  Yet if that is so, then to be consistent he must set up a new set of waves which interact and interfere with the previous set, such that the future of the world will be in some sort of fluctuation pattern between two realities.  The first set of changes had already propagated through the entire future.  The lab is overgrown with plant life and overrun by monsters.  Ryer is changing that; he is again changing future history, just as Middleton did.  The changes he makes should propagate through time the same way as those he is attempting to undo.

In fact, Dr. Ryer's entire mission is nonsense.  That we will consider next time.

Last time we noted that because the changes must propagate through history, either humans have been alive during that time to fight against the changes, or they were never alive and never built the buildings that are now being destroyed by the new creatures.  Yet there is another problem which makes the entire story of fixing the past nonsense.

One second after Dr. Ryer leaves from the future to travel back supposedly to prevent the changes, the last time wave hits and Dr. Rand ceases to be human.  Yet if we think it through, we must realize that Dr. Rand ceases ever to have been human.  She was not human a moment before; she was not human a day before; she was not human the day that Ryer led Middleton and Eckles into the past to kill a butterfly.

And on that same day that she was not human, Middleton and Eckles were not human, either.  Neither were Ryer, Payne, Krase, or any of the other people who built Time Safari, Inc.  No humans ever existed, and no humans built any of these things.

That also means that no humans ever traveled to the past.

Unless we are going to embrace the popular understanding of Niven's Law, we are forced to conclude that no humans ever arrived in the past, either.  If it were possible for Ryer to leave a day or two later and arrive at that moment in the past, there would be no hunting party emerging from a time portal, because humans never came to be.

This puts us into a classic infinity loop, based on a grandfather paradox on a vast scale:  Middleton has killed the ancestor of his entire race (not the butterfly itself, but some creature whose future existence was dependent upon some action the butterfly has yet to perform).  He cannot make the trip because he does not exist; yet if he does not make the trip he does not undo his existence.  Our two alternate histories span sixty-five million years, from some specific moment in the cretaceous period to November, 2055.

Thus all the events of the movie after the return of the Middleton party never happen.  The Middleton party itself is returning to a time that does not exist, and so passes out of existence even as it undoes its own existence.  Ryer never has a chance to fix anything, and time is destroyed.

Unfortunately, the movie still offers more disasters.

When Dr. Ryer is explaining their precautions to Dr. Rand, he explains that the beast they hunt is about to die anyway, and specifically that it becomes trapped in a bog and then buried by the lava of a volcanic eruption.

How does he know this?

Obviously, someone scouted the past looking for such a target, and presumably identified this allosaurus, noting the nature of its death.  Of course that someone must have escaped before confirming the death of the monster, because the impact of that volcanic eruption would have killed any living creature in the area (including that butterfly).  But we can allow the benefit of the doubt, that the scout could tell the dinosaur, not having an available time portal, was not about to escape.  There is, however, a much more significant problem.  Watch what happens as temporal anomalies interact.

Scout travels from perhaps April 2055 to target time A1 sixty-five million years ago.  He probably arrives a few days before our allosaurus dies, because it's going to take time to find the perfect victim, but eventually he sees what he needs and records what the company must know.  He returns to April, 2055.  Now let us suppose that our first team of hunters, Mutt and Jeff led by Dr. Ryer, travel from May 2055 to target time A2, watch that allosaur approach the swamp, and shoot him with their nitrogen bullets, based on the information in the report Scout gave the company in April.  Wait, what just happened?  We'll have to get technical for a moment.

At point A1, there is an allosaur hunting near the swamp.  He dies in the swamp, and sixty-five million years pass to point B1, in April 2055 when Scout travels to the past.  He targets point A1, but since his arrival changes history he initiates a different history, beginning at point C1 (the same time as A1 but with a different history of the world).  He makes a record of events and leaps to the future.  While he is leaping to the future, sixty-five million years pass, and he has been careful enough not to impact anything significant, so at point D1--the same moment as B1 except that it follows from that history in which he was in the past--his doppelganger makes the same trip, observes the same history, and makes the same return.  We have a benign N-jump.

Point A2 was determined from that information, and so in May 2055 at point B2 Ryer leads Mutt and Jeff to the past, hitting point C2 (again, the time of point A2 altered by his arrival).  They shoot and kill the allosaurus and flee to the time portal, aiming for point D2.

The problem is, Scout is already there at C2.  He arrived at C1 some time earlier, and is tracking this creature to determine whether it is a viable target.  While he watches, another portal opens and a team emerges, kills the creature he is stalking, and rushes out to avoid the volcano.  Scout also must avoid the volcano, so he also leaves, but arrives before them at D1 to give his report.  What does he know?  He knows that the allosaurus he thought might be a good target was targeted by a company hunting team, and that it was shot and vanished into the mud before being buried by the volcano.  He does not know how it would have died, and cannot include that in his report.  Thus when Ryer is preparing to leave before point D2, this Ryer does not know what happened to the allosaurus--he only knows that Scout reports that the Mutt and Jeff team killed it.  Thus this is a different Ryer, and he creates point E2, the third variation of history in this anomaly, which is a sawtooth snap.

It's not a disaster.  Scout will now see Ryer kill the allosaurus in the EF2 timeline, and will give the same report.  But it means that no one in the company knows how the allosaurus would have died; the observation of that original death has been erased and now never happened.  So Ryer can't tell Rand anything more than that he trusts the system, that somehow this target passed the test before they erased what originally happened to it.

It is of course not possible for there to be a trip after the Middleton-Eckles disaster, because time has been destroyed.  However, the filmmakers obviously did not realize this and so have such trips.  First, Misters Zong and Chang make the same trip to kill the same allosaurus, but they arrive too late.

This is the first hint something is wrong, and Ryer is certain it is related to the Middleton trip--a safe bet, since that was the last prior trip and the only one that did not go according to plan.  That sets up the rest of the movie; but the questions we have are why the computer, TAMI, sent them to the wrong moment, and how this anomaly resolves.

The latter question is rather simple.  This plays as all previous trips to the past, minus the complication of other travelers being present.  They appear to have arrived at just about the time they ought to be leaving; the allosaurus is already dead, and the volcano is erupting.

It is interesting that the allosaurus appears to be lying in the exact position in which Ryer left it after killing it in the Middleton trip.  There are three plausible explanations for this.  It could be simply that the producers were too cheap to design a second set with pieces of a simulated dead dinosaur protruding from the swamp water, and thought no one would notice.  It could be that against all probability the allosaurus that was shot after a deadly dance with time travelers landed in the exact same position as it would have landed had there been no such dance and/or no such time travelers.  Most probably, though, it is in the same position because the Zong-Chang party arrived within seconds of the Middleton-Eckles party departure:  they are looking at the dinosaur Ryer just killed moments before.

TAMI insists that the calculations are correct, and that the party was sent to the correct moment.  The team blames a software glitch and begins seeking the problem.  Then having concluded that something was changed, they attempt to send Ryer back again to repair it.  He lands in the American Midwest, where a hunting party of Native Americans on horseback apparently leaps over him and his path while galloping across the plain.  (Since horses were not indigenous to the Americas but were brought by early European settlers, this is not earlier than the sixteenth century.)  The explanation of this failed trip introduces the notion that Ryer cannot travel to the right moment because the waves distort time and prevent him from reaching it.  Since the solution intended to overcome this problem works, it is reasonable to suppose that they correctly identified the problem.

That also suggests that the reason the Zong-Chang party could not reach the allosaurus hunt is that they, too, were blocked by the waves.  It is odd that the waves kept them mere minutes from the target time, but kept Ryer many millennia from it not long thereafter.  However, by now we recognize that we cannot expect logical consistency from this film, and thus this must be the intended reason.

Ryer's midwest trip also would resolve to an N-jump.  He was seen, and those who saw him slightly altered their course and the amount of energy their beasts used (leaping over the forcefield walkway), but this is unlikely to have done more than introduce the story of the strange man in golden clothes standing on the invisible path, which while it will be an interesting fireside story probably won't change the future.

This aspect of the waves, though, presents another problem.

The reason the Zong-Chang party arrived minutes late was the same reason that Ryer's next trip took him to the near-modern American midwest:  once the waves of change were moving forward through time, they prevented travelers from traveling back to the point of change.  Dr. Rand proposes a possible solution, by which TAMI will calculate a trip to a year prior to the change, and then in calculating the return trip will include a stop perhaps a minute before the change occurs.  The theory is that since Ryer is targeting a moment further in the past than the change event, the waves will not interfere with his trip, and then when he approaches the moment of change coming forward from the past he will not have to cross them.

It is difficult to find any explanation for why this would work.  That is, the challenge is figuring out what the waves do that cause travelers to arrive so much later than the targeted time that they would not do to the same travelers traveling through the same history but targeting an earlier time.

The waves are, after all, analogized to ripples in a pond.  Thus we envision the time traveler as a boat, but as the boat attempts to move through the water toward the past a wave presses it back.  At the very least, it makes calculating how much force is needed to get the boat past the waves very difficult.  But then, if that's the case, those same ripples would impede any travel to the past which had to cross them.  It would be no easier nor more reliable to target an earlier time, because you would still have to cross the same ripples.

So perhaps the analogy is wrong.  The waves are different.  The reason the Zong-Chang party arrives moments after the dinosaur died is that a traveler aiming for a specific moment that has created a ripple can go as far as the ripple emanating from that moment, and that was as far as the ripple had traveled overnight.  Then within the next few hours it leaps ahead, hitting the present, and the one which is following it gets into the sixteenth or seventeenth century by the time Ryer makes his trip, and catches him there.  Obviously the temporal velocity of the ripple would have to be increasing exponentially (which means that by the time it reaches 2055 it is moving much faster than we calculated).  This, though, would mean that the problem could be solved by targeting a moment slightly before or slightly after the original moment.  But then, in some sense TAMI is already targeting an earlier moment.  The Middleton-Eckles party had been in the past at least two minutes before Middleton stepped on the butterfly, and it was not their arrival in the past that created the supposed wave but the premature death of the butterfly.  Therefore if TAMI can successfully target a time prior to the moment of the disaster, she should be able to hit the time she usually targets, because the disaster occurred minutes later.  If she cannot target that time, there is no reason to think she can target a moment a year earlier and then bring Ryer back to that time.

It seems no understanding of the wave creates a logical reason for it to prevent Ryer from traveling to the moment the Middleton party arrives but does not prevent him from traveling to an earlier time.  The explanation fails; the problem could not happen that way.

Hidden under all this talk about the wave moving through time making changes is a more fundamental problem.  As we noted, despite the many precautions Time Safari Inc takes, they are making changes to history.  They are deflecting photons which are perceived by creatures in the past; changing airflow and energy levels; puncturing the dermal layers of the prey's body; transporting small quantities of nitrogen from the future to the past.  The changes they make are minimal, but they are changing the past.  It is foolish to pretend otherwise.

Yet when Middleton changes the past by killing the butterfly, waves of change pass through the future, crashing into physical objects as they alter the universe.

What we have here is a distinction made between "minimal" and "meaningful" changes.  That is, a "meaningful" change causes a visible wave to pass through time, but a change that is not "meaningful" does not.  The complication is, how does the universe know the difference?  At the moment the change happens, it cannot even be recognized as a change at all--for the universe to know that the altered path of photons or the death of the butterfly is a "change", it must know what would have happened otherwise.  It is difficult to explain the concept of a wave of change occurring without this aspect that it occurs when what would have happened does not happen as it did in the original history.  Yet if what triggers the wave is that somethng changed, a wave should occur whenever anything changes.  Every trip to the past should trigger waves.

This is awkward, because obviously they do not.  Granted, a change that is minimal will not have the severe consequences, altering climate and speciation drastically.  But it remains the case that the waves can be seen and can be felt, and even if all they are changing is the total amount of nitrogen in the atmosphere, we ought to be able to see and feel the waves.

Perhaps, though, a minimal wave peters out.  If it's only a bit of nitrogen, a scattering of light, and a slight localized temperature change, perhaps the waves created will be so weak that they will fade within a few years.  This is contrary to what we observe, as the waves appear to become stronger as they advance through time, but it is a poorly understood and explained idea so it may be that we have it wrong.  Yet that leaves the other problem.  If the wave emanating from Middleton's change made it impossible for Ryer to travel to the moment of Middleton's arrival, then it would seem that smaller waves ought also have the same effect, such that once the scout has changed the world by scouting no one should be able to travel through those waves to reach the moment the scout was there.  All trips make changes, therefore all trips generate waves, no matter how small; and if waves prevent time travelers from reaching the point from which the waves emanate, no time traveler can ever visit a location previously visited by another traveler.

The distinction of a "meaningful" change to history is not one that history itself can understand; it must generate waves for every change if it does so for any change.  The waves must have the same qualities even if they are making what to humans seem insignificant changes.  Waves should have been a common experience by the time the serious ones arrived.

There is, though, another problem with them.

We touched on this problem with waves already:  if the wave of change is moving from the past to the future, by the time it reaches the present it has already changed the past, and everyone in the present knows it.  However, there is a more fundamental problem, and that is that by the time the wave reaches us in the future, it has already reached us in the past, and we must already know that.

This is most apparent when Ryer encounters the plains Indians, sometime in the sixteenth to eighteenth century.  He perceives the timewave crossing approaching, and flees to the future to warn everyone that there is another coming.  He barely has time to say so before it arrives, but we know that it already hit the sixteenth century before it was here.  That means before it hit 2055, it hit 2054; and before it hit 2054 it hit 2053.  More complicating, before it hit November, it hit October; and before it hit the 31st it hit the 30th; and before it hit 1:00 it hit 12:00.  Everyone alive has seen a time wave before this moment, but more tellingly everyone has seen a time wave in every minute of every day of his life, all the way back to sixty-five million years ago.  An object or force which travels through time at faster than the speed of time must exist in every second of the history through which it passes.  "Engulfed in time wave" is thus the normal reality, and has been since the first time wave was generated.

This is not how such timewaves are envisioned by those who embrace them, but ultimately they do not make sense unless you ignore obvious facts about them.  Just as Hartdeggen's time machine must be visible to everyone in every second through which it passes, so, too, the time wave must be visible in every square inch of space in every instant in time, because in some sense which we can only call "eventually" it will pass through every point in space and time, and once it does so it will be as if it always had done so.

Again we find that the wave does not make sense.  If it exists at all, it is ubiquitous.

To put things in sequence, we considered the problem of the scout, and its interaction with the first hunting journey; and we considered the problem created by hunting the same allosaurus multiple times.  It also should be obvious that the Middleton-Eckles trip creates an inescapable infinity loop via a grandfather paradox.  The notion of change arriving in waves was weighed and found wanting, and so the story has collapsed rather completely.

However, we still have one more trip to examine.  Dr. Sonia Rand and Dr. Travis Ryer have struggled through the second half of the movie to find out what changed and attempt to prevent it, and now at the last possible second (well, that's a movie trope) he departs.  He intends to interact with a previous trip, to undo the disaster by preventing it from happening, and to make his doppelganger aware of what occurred.

As it says somewhere in Multiverser, sometimes the successful intended actions of time travelers are catastrophic.  This is one of those.  As a word of advice for time travelers, if you are able to return to any future, do not attempt to return to the past to fix something, because that is a recipe for disaster.

If we begin with the assumption that somehow Middleton did not cause an infinity loop, and thus that humans continue to exist and to create time machines and have cretaceous hunting safaris, but that the changes are somehow still catastrophic (well, we have to have the trip or there is nothing to which to return), that somehow this resulted in an N-jump, allowing time to continue, we now have a new anomaly in which Ryer 2 leaves from what we will call point B2 to intercept the Middleton party, who left from B1.  Ryer 2 cannot travel to that moment directly, so he travels past it and bounces back, stopping on the return trip.  Thus C2 is perhaps a year before C1, but Ryer 2 hops forward to a time close enough to C1 to do what he intends.  He communicates with Krase concerning the video, which he wants given to Ryer 1 and no one else, which includes the fact that he is there.  He then prevents Middleton from stepping off the path.

This raises issues concerning how the time machine works.  The part about it using a particle accelerator isn't important; what matters is the question of how time travelers who travel to the past return to the future.  In stories like Happy Accidents, Terminator, and Bender's Big Score, the simple answer is that they don't; time travel is one way.  The best solutions to two-way time travel are found when the travelers take the power of time travel with them, as in The Time Machine, Bill and Ted's Excellent Adventure, Back to the Future, and in a different way The Time Traveler's Wife.  But when the time machine in the future has to bring people back from the past, as in Millennium and Timeline, you wind up with the problem we saw in the latter of those, in which all of time must pass before the machine in the future can recall the travelers from the past.

It is not, however, at all clear how this machine works.  It may be that a device is placed inside the particle accelerator which is powered by it, enabling it to travel to the past, generate the force field walkway, and return.  In that case, things are not so bad.  However, it appears rather that the machine stays in the future, and a doorway opens to the past through which the travelers pass.  The doorway must remain open a preset duration, and so be maintained in an instant in the future--that is, the machine opens a portal to a range of time covering five minutes, and the travelers emerge at the early end and depart from the late end.  That does not appear to be how it works, though, leaving the mystery of whether this machine does something possible.

It raises another problem as well.

The last reported trip gives us another problem with the nature of the time travel.  It suggests that Ryer will make one trip back to a year before the critical moment, and then on the return trip stop for a few seconds in the time of the disaster.  It also suggests that he will only have a few seconds to solve the problem, because such a trip will use up most of the energy--whatever that means.  Pseudo-rational explanations in science fiction and fantasy are good, but there ought to be some kind of consistency within the same story, and that seems to be lacking here.

On every previously observed trip, a hole opens in the air with a forcefield walkway extending from it, and the party walks out of the hole and down the path.  When they are finished, they walk--or sometimes run--back to the hole, and it closes behind them, and then they are returned to the future, somehow.

This last time it is different.  We see no hole in the air.  Ryer appears on the forcefield path created by the other time trip.  Then when he has accomplished what he came to do, he simply vanishes, as if he were never there.  The others return to the hole in the air and thence to the future.  This Ryer we never see again (a problem for next time).

The suggestion is made that he is going to run out of energy within a few seconds of arriving at that point, and that this is why he vanishes.  That then suggests that it would require a continuous expenditure of energy to keep any object in the past that came from the future.  It also suggests that such objects are charged as part of the time travel process, and thus that when the battery is dead the traveler can no longer stay in the past.

Why, then, worry about bullets?  That is, a lot of effort is made to ensure that nothing is left in the past, including using frozen nitrogen projectiles and making it one of the Rules of Time Jumping.  If it requires energy to keep anything in the past, then the bullets will, like Ryer, vanish once they have exhausted the energy that keeps them there.  It becomes inherently impossible to leave anything in the past, because it won't stay there.

Obviously, their concern arises from the certainty that objects left in the past will stay there; if so, then Ryer, too, will stay in the past if he does not return by means of whatever is carrying him through time.  But the time machine appears to open a portal, and instead of returning through his portal he simply vanishes.

We might suppose that since he is doing this entirely differently, it is an entirely different experience, that somehow the portal only existed at the distal end a year in the past and here he is simply pausing on his journey to the future, appearing for a moment before continuing that trip.  That would be strange, but since we have no idea how it works it is not beyond all credibility to suppose that it works differently if you make a pit stop on the return trip.

It is possible in the alternative that at that moment Ryer ceases to exist; but in that case he should have ceased ever to have existed--that is, to have existed as that version of himself in that time and place.  That's the problem for our final article.

Even a beginning student of temporal theory will recognize that, under replacement theory, the final trip made by Dr. Ryer must cause an infinity loop.  But let me make it clear.

Ryer leads the Middleton-Eckles trip.  We're ignoring the fact that this itself creates an infinity loop, because that would be the end of the movie.  Instead, the team determines that something happened, and they find out what, and then perhaps a couple days later Ryer again travels back to the same moment, and prevents Middleton from stepping off the path and killing the butterfly.

That having been done, the Ryer who is leading the Middleton-Eckles group returns to the future, where nothing goes wrong.  Krase gives him the hologram, as the other Ryer directed, and he takes it to Rand, and together they work to get Time Safari Inc. closed.  However, now there is no butterfly, there are no waves of change, and we have no urgent effort to send Ryer to the past to prevent what now never happened.

Thus Ryer does not leave to prevent Middleton from stepping off the path.

As an aside, note that even were he to do so, no one would think to send him to a year earlier and have him stop on the return trip to overcome the ripples, because now according to the film's treatment there are no ripples.  The fact that the change to the past of preventing Middleton from stepping off the path must be as great as the change that occurred when he did is again something that is ignored, because for some reason the filmmakers think that we're putting things "right" and therefore undoing sixty-five million years of altered history is not the same kind of drastic shock as undoing sixty-five million years of original history.  But we are to accept that there are no ripples so there would be no reason to avoid them.

Back on point, there is also no reason to send Ryer back to prevent the disaster.  Of course, from one level of thinking there is every reason to do so, because if he does not make that trip he will never arrive in the past, and if he never arrives Middleton will step off the path, kill the butterfly, and send everything back to the way it was.  Yet not only will Ryer and Rand not think to send Ryer back to do what he needs to do, Time Safari Inc. will have no reason to let them do so, and will not be kindly disposed to them when they announce that there was a disaster and they have the proof.

It might be suggested that this end of Ryer's existence is why he vanishes from the path:  having eliminated the need for him to make the trip, he eliminates the fact that he made it, and he vanishes.  The problem is, he has not caused himself to cease to exist, but to cease ever to have existed, and that means that he was not there a moment before, either.  People will not vanish in such circumstances.  History will rewrite itself such that they were never there--and if he was never there, he did not save history.

And if he did not save history, he did what we see in the movie, and then he was there.

Ray Bradbury's story is not perfect, but this disaster of a movie is not his fault.  He deserves our sympathy.