Mr. Koshkin consistently refers to the theory on this site as The Spreadsheet Theory.  He cannot be faulted for this, as for years the site has promoted a theory without giving it a name.  It has only been within the past year or so that I have begun referring to it as The Replacement Theory, and I am not even certain I have used the term in any page on the site.  Thus Mr. Koshkin could not be faulted for not knowing that I had named the theory something else, and it does not in one sense matter what he calls it.  He is addressing the theory I present and defend on this site.

At the same time, the fact that he has used this name is problematic, because it appears to me to indicate a fundamental misunderstanding of the theory itself.

Clearly he took the name from one page in the Theory section, entitled The Spreadsheet Illustration of Temporal Anomalies.  That page attempts to illustrate concepts of time travel from a perspective in which time is taken as a static dimension, something which exists through which we move.  Much as a road exists and we drive from one end to the other, but the road has always existed and we could in theory teleport from one end to the other, so too time is treated as fully existing from beginning to end, and time travel as hopping from point to point along that road.  The spreadsheet illustration is not the basis for the theory nor a completely adequate explanation of it.  It is what it purports to be:  an illustration, a metaphor to help some people understand aspects of the theory that are confusing.  For some people, the illustration is very helpful, as they understand this notion of history being fully formed; for others, it is yet the more confusing, as for them time is something living and moving.  Whether time is the one or the other does not matter, because the replacement theory can be understood either way.  Koshkin, though, appears to take the spreadsheet illustration as the theory itself, and so rejects the theory based on his understanding of the illustration.  The impact is not total; his critique is still quite insightful.  It does, however, suffer some from this incongruity.

Koshkin writes, "One problem is that this account is incompatible with relativity.  Let us analyze the situation from the point of view of a distant observer far removed from the place where the time machine is activated.  It would take light a significant time to travel from that point to the observer and nothing can travel faster than light."  He is not the first to suggest this as a problem with the theory, and it is difficult for me to explain this; but Koshkin is also a mathmatician, so perhaps I can explain it differently.

I am not speaking of an effect which spreads outward from a point to impact every object in the universe.  I am speaking of something which in one sense does not affect any object in the universe.  There is no "sudden death", as he puts it.  All this theory says is that when you reach the moment from which a time traveler moves to the past, the next moment for the entire universe is a moment in the past.

I can think of two imperfect ways to illustrate this; they will have to suffice.

One can begin to understand this through the notion of clock arithmetic.  Everyone knows that eleven plus three is fourteen, but that if you add three hours to eleven o'clock you get two o'clock.  The number system is such that it loops, such that the number after twelve is one.  What a time travel event does is change the number line itself, such that the instant after midnight January 1st 2010 is midnight January 1st 2000, what we would call ten years earlier.  It does not actually change the universe at all; it simply changes the number line along which the universe is moving.  Since that temporal number line exists as an independent dimension, its physical distance from the point at which the time travel event occurs is 0; since it is not a spatial dimension, limitations on the speed at which change can move through space are irrelevant to it.  It is not where the change occurs but when it occurs that is impacted.

Alternately, anyone who played early video games will understand the concept of "screen wrap".  I have written a number of articles in my Game Ideas Unlimited series at Gaming Outpost in which this concept has been explored.  In essence, in early versions of games like Tank it was possible to fire a missle or even drive a tank off one side of a screen and have it appear on the other side.  For video game designers this was a simple solution to the problem of edges.  In the programming it was a simple matter to instruct the system that when the X or Y coordinate reached its maximum value plus one, it was reset to zero, and when it reached negative one it was reset to its maximum value.  What time travel does is create that edge, that boundary on the universe, setting the maximum value for time, and changing the programming such that the next number is whatever the destination value is of the time traveler.  Thus once that boundary has been set, everything that crosses that line emerges in the past, but as it was at that moment in the past.

Thus I think that objections based on the speed of light carrying information throughout the universe miss the point entirely.  No information need move through space at all; it need only touch the non-spatial temporal dimension.

Mr. Koshkin then suggests that the notion that one individual could change the entire universe is "absurd", and that it would require "infinite energy" to do so.  Since, as already mentioned, we are not really changing anything inside the universe, but only the temporal track along which the universe moves, we cannot guess how much energy might be required.  However, his answer seems at least as absurd as my own.

It seems more plausible that your description applies to time traveler’s worldline only.  For him there is no future after 2030, for him the history ends and rewinds, but the rest of the universe continues merrily on its way, just without the time traveler.

He addresses this more fully later, but the solution seems absurd.

Put simply, the kind of multiverse which Mr. Koshkin proposes here could not be entertained seriously.  It suggests that I did change the universe, but only really succeeded in creating my own private version thereof.  He objects that my scenario requires a tremendous amount of energy, but the creation of an entire duplicate universe would require that all the matter and energy in the current universe be consumed to create all the matter and energy in the new universe, and that without any loss in the process.

What is really being proposed here is a kind of divergent dimension theory, that a time traveler creates a new version of history without impacting the old one at all.  I have already shown the flaws in such a theory; such concepts are not time travel but dimension travel.  I cannot have my own personal universe.  Even if there are dimensions we cannot perceive, there is ultimately only the one universe, or at least as far as we can determine that is the case.  If there is another, it is completely unlike this one; and it is certainly beyond any power we will ever control to create another universe on any scale remotely comparable to this one.

Mr. Koshkin attacks in passing one of the most difficult and critical points in the theory, and that is that it maintains both complete free will and complete determinism.  Many readers balk at this, quite apart from the rest of the theory, and I have addressed it uncounted times in e-mail and kept promising myself I would put an answer on the web someday when I had time.  It appears that time has come today, as the old song once said.

He writes:

I do not see why after 2nd, 3rd or 17th run along the C-D timeline the traveler will do exactly (or even ’mostly’) the same thing as the 1st time.  As you yourself say when criticizing the fixed timeline theory, this goes against ’even the most conservative understanding of free will’.

It is certainly a fair question, and we would all like to believe that the nature of our "free will" is such that we really could do anything we chose to do, and that we really could choose to do otherwise.  I am persuaded, however, that this is not the case.  I have a number of examples which I have used to illustrate this, but I usually begin with my shoes.

Each day I get dressed in my office.  My office has moved since I first started answering these questions, but it is still in my home (which has also moved) and I still dress there.  Each night I remove my shoes and drop them into a space where I will find them the next day, and the next day that is where they are.

At one time the space was such that one shoe was always atop the other, and I noticed that in the morning I would don the top shoe first.  There was nothing preventing me from donning the bottom shoe first, but I never did.  Something in my psychological makeup--call it laziness, if you like--caused me to select the top shoe first, every time.

Certainly I could have selected the bottom shoe, and I was free to do so, in every sense that mattered.  I could don whichever shoe I preferred.  Had I thought about it, had I wanted to change my routine, I could have pulled the bottom shoe from beneath and donned it.  Yet even here, the point remains.  It would have required that I think about it and that it mattered to me.  Since it never mattered, I did automatically what came naturally.

Yet what if it mattered?  Had I stopped and thought about it, would this not mean that I might choose either shoe?  In fact, it would not; when it matters, that is when my "freedom" is most determined.  Suppose instead of which shoe to don first, my question is whether to steal some money left on a table or countertop.  At that point, even if were to I steal it on impulse, the forces that are involved become much more complex.  My moral sense takes one position, my needs and greeds take another, my fear of being caught becomes involved, and whether over several minutes or in a flash of decision, those factors come to a balance and I make my choice.

In both cases, whatever I choose to do is exactly what I have freely chosen to do; and in both cases, whatever I choose to do is completely determined by the psychological factors within me that have brought me to that choice.

This means that if we could rewind and completely erase everything that has happened to me up to the moment of that choice, and then replay it without changing any of the psychological factors, as if it were the first time, I would make exactly the same choice the first time as I did the first time.

Certainly if I face the same choice again, I could choose to do otherwise; but the point of the theory is that I am not facing the same choice "again".  Because time has been erased, I have never faced this choice before, and am facing it for the first time; and because I am exactly the same person I was in the previous pass through time, the exact same person is making the exact same choice based on the exact same factors and influences.  The result is that he will do exactly the same thing.

I have occasionally had the opportunity to play chess with a very brilliant chess player, my good friend the Reverend David D. Oldham.  I am not a brilliant chess player, but an adequate one; he defeats me simply, and I learn almost nothing from my losses.  I have learned, however, that David knows how to manipulate me on the board.  He can make a move and know to a very high degree of probability what move I will make in response.  (He sometimes fails because he assumes I am a better player than I am, so I make moves that are not as smart as the ones he had intended for me; that, though, does not matter to the point.)  My responses, thus, are completely predictable, given sufficient knowledge about me.  If you knew me well enough, you would know how to persuade me to lend or give you money, how to induce me to change my clothes, how to tempt me into questionable conduct, and what you could not by any means get me to do.  My actions, even my well-considered actions, are responses, reactions, to conditions and events around me, and given sufficient information they are completely predictable.

That they are completely predictable means that as free as I am to choose whatever I choose, what I choose is also completely determined by who I am.  In one sense I can do whatever I choose; in another, I can do nothing other than what I in fact choose.  I am totally free and completely limited at the same time.

What, though, if I rebel against these restrictions?  What if I break out of my bonds and do something completely irrational?  This, too, is part of the psychological framework that controls my choices.  I chose to do what I thought unreasonable, what I thought I would never do, precisely because my psychology at that moment goaded me into doing something different.  And that, too, would be predictable, given sufficient information about what is happening inside me; it merely requires much more information.  Yet it, too, is determined.

I maintain that this internal determinism controls everything we do, from such autonomic functions as our heartbeats and breathing to whether we fall in love to whether we pull the trigger to fire the bullet that kills Joseph Stalin.  I maintain that we are completely free in our choices, because we will choose to do exactly what we determine to do, and that at the same time our choices are fully predictable.  Further, because these actions are fully predictable, they are fully determined, and no matter how many times the exact same person goes through the exact same events for the first time, as long as it is always the first time and he is the exact same person, he will, completely of his own free choice, do exactly the same thing.

Mr. Koshkin returns to the notion of free will and determinism later, in discussing Supertime, where he writes:

Spreadsheet theory assumes (I think) that the past stays frozen until being reactivated after a time jump. It is not clear what to think about the future. If it is already ’there’ we have a grand illusion of living, while simply retracing predestined events. Then time travelers, and they only, would have a singular ability to break this chain of predestinations.

To my mind, the difference between the future and the past is that we do not know the future, because we have not yet experienced it.  It is completely true that we by our choices will impact the form of that future; it is equally true that we by our choices have impacted the form of the past.  This does not mean that our choices are predestined or predetermined; it means that our experience of them occurs in time.  From a metaphysical (or if you like, "supertime") perspective, we have already made all the choices we will ever make within time; some of those choices are behind our present point and some are ahead.  All are just as flexible as they are fixed, that is, any of them could have been made otherwise, and all of them were already known and completed.

If, theoretically, I could travel to 1955, and observe my own life without in any way interfering or being detected, I would observe myself making choices, completely freely, many of which I as observer would remember having made, and so would know to a certainty what I as the observed would choose.  My knowledge of his choices does not in any way constrain his choices; he chooses as freely as I did when I made those same choices.  Yet his choices are determined and certain.  In the same way, if a future version of me were to come back from 2035 (assuming I live so long) and similarly observe my actions now, he would recall having made many of the choices I am now making, and know how I chose and what consequences flowed from those choices and what choices I faced next week.  That does not constrain my choice in the least; it merely means that all of my freely-made decisions have already been recorded for the entire expanse of my life, but my consciousness exists at a single point along that timeline, recalling all that precedes and anticipating all that antecedes that point of consciousness.  Arguably, my consciousness, too, exists at every point along my lifetime; I experience it moment by moment.  The choices I will make tomorrow I have in some sense already made, completely freely.  Tomorrow I will in making those choices discover what it is that I completely freely chose.

This is difficult for many of my readers.  Yet perhaps I can analogize it to a simple game of chess.  Let us suppose that I sacrifice my knight to capture David's queen.  David then says, "I knew you would do that," and three moves later has me in checkmate.  In what sense was my choice to sacrifice the knight not freely made?  I cannot now change it, but that does not mean I was forced to do it.  Further, the fact that David (whom as I mentioned is an extremely good chess player) predicted that I would make that move does not mean the move was predestined.  The difficult step is here:  if time is a dimension, then the future exists as surely as the past, and even before I had experienced making the decision to sacrifice the knight, that decision and its consequences already existed in the future.

This is not predestination, as demonstrated by the very concept of the replacement theory.  If somehow before I sacrificed the knight I received a message from the future warning me that by sacrificing the knight I would lose the game in three moves, I could take that information into account in making the decision what to do next.  That, though, simply means that the data available to me has changed, and I am freely choosing based on different information.  The fact that I can change the past demonstrates that my choices, and everyone else's, are perfectly free despite the fact that they are already made and awaiting our experience of them.

This is entirely different from the problem posed in the Granfather Paradox, of whether I can choose to do one thing or another.  To say that it would not be possible for some specific person to decide to kill his grandfather is one thing; to say that it would not be possible for anyone ever to decide to do this is quite another.  Free will means that we can choose the things we would choose.  It does not mean we necessarily could have chosen otherwise, from the perspective of who we are, but only that we could have chosen otherwise from the perspective of universal possibilities.  I do not believe it would be possible for me to choose to kill a grocery store clerk; that does not mean no one could ever choose to do so.

I admit at this point to being out of my depth.  Mr. Koshkin works in the realm of mathematical physics; I work in the realms of metaphysics and theology.  He asserts that at the quantum level there are genuinely random events, and that these will result in slight changes to the timeline in each iteration, forcing all such anomalies to become sawtooth snaps.  If he is correct, I concur:  genuine randomness at the quantum level would mean a single time travel event would result in infinitely varying histories of the universe, an eternal sawtooth snap.  It is a very unfortunate end of the world, but it is a logical conclusion from the theory, given true randomness in any aspect.

For most of my readers, some discussion of the concept of true randomness will be necessary to follow the logic from here.

We speak of certain things being random when we mean more precisely that they are unpredictable; further, we mean that they are unpredictable by us.  A good example of this is the throw of dice in a game.  We can predict the statistically most and least probable totals, based on an assumption of randomness; but any physicist will admit that the throw of dice is not true randomness.  Were one able to track the starting position of the dice, the movement and force of the hand or cup, the trajectory, and the elasticity of all the surfaces, one could calculate which way the dice would land quite precisely.  What makes such throws seem random to us is that we cannot possibly gather that information and perform those calculations, let alone control them adequately to get a desired outcome.

So, too, with chaos theory we do not have genuine randomness.  We are told that the flap of a single butterfly's wings in the Amazon Delta can be the deciding factor in whether there is a hurricane in the Carribean Sea, and thus that it is impossible to account for all the causes and their effects in predicting weather; but the fact that the hurricane is dependent on whether or not that butterfly flaps its wings shows that this is all part of specific causal chains, that the hurricane is an effect of a combination of causes, even if we cannot identify all those causes.

What is argued in quantum physics is that there are some quantum events, notably the decay of an unstable atomic nucleus, which do not have causes, in the sense that we cannot know when they will happen not because we have insufficient information but because the event itself is genuinely random.  I am told that there is a proof of this, a proof that demonstrates that there cannot be a cause of this moment of atomic decay, that there cannot be a trigger event.  That makes atomic decay a truly random event, which in theory could happen at a different moment in a repeated version of history.

I have also corresponded with physicists who do not believe this.  Their position is certainly comprehensible, and I would think it defensible.  They maintain that there is a difference between not knowing the immediate cause of an event and knowing that there is no immediate cause.  That is, just as we cannot trace the hurricane back to the flap of the butterfly's wings, it may be that atomic decay is triggered by some cause thus far indetectible to us.  To say that there is no cause merely because we do not know the cause is arrogant.

I cannot settle the debate here; I do not know even what kind of mathmatical arguments might be able to prove that there is no cause of an event.  Perhaps Mr. Koshkin is familiar with those proofs and is persuaded by them; perhaps it is only that he has been told that these events are genuinely random and has accepted on faith that those who told him were correct.  I can assert that the matter is not settled even among physicists, and as long as it is not settled all that we can say is that if time travel proves to be possible (which as I say in the opening page of this site is not a position to which I am committed--only that I wish to explore what would happen if it were), and if quantum events are truly random, then Mr. Koshkin's prediction of an infinitely cycling sawtooth snap from any and every time travel event (of which there then would logically in all probability be only one) is inescapable.  If either of the premises are false, though--and each of them might be--then this is not a fatal argument.  Time travel could be possible under the replacement theory if time travel is possible and quantum events are unpredictable but not random.

Mr. Koshkin summarizes what he thinks of my theory thus:

Perhaps the spreadsheet analogy illustrates too much too well.  The reason a spreadsheet can change all the values instantly is that it is run by a central processor that has direct access to each cell.  It can precalculate all the values along the sequence and then enter them simultaneously.  I find this instantaneous causality that enacts changes in sequence to be the most obscure part of the theory.  The only way I can imagine this working on spacetime is through a central processor of its own, an Invisible Hand, omnipresent and omnipotent, transcendent and eternal, that has direct access to its every point.  In other words, God makes the changes.

In fairness, I believe in God; but my theory is not in any way dependent upon His intervention to make it work.  I am in fact surprised that Mr. Koshkin has this specific problem, because the notion of a computerized spreadsheet program is already a step away from the point of the illustration, and that point is the mathematics of the system which the spreadsheet represents.

Let us take a simple equation for an example, but one with variables.  We'll take A+B+C=D.  Now let us give these variables meaning.  A will be the number of apples on the shelf, B the number of bananas, C the number of cantalopes, and I wish I had a nice mnemonic name for D, but it will have to be pieces of fruit.  If we have 5 apples, 8 bananas, and 3 cantalopes, we have 5+8+3=16.  We calculate this by starting with 5, adding 8 to get 13, then adding 3 to get 16.  Our spreadsheet program does exactly the same thing, but it does it faster.

What Mr. Koshkin is thinking, though, is patently false given this example.  If we take away two of the bananas, we now have 5+6+3, and we can add 5+6=11, 11+3=14.  By Mr. Koshkin's reasoning, we cannot have 14 pieces of fruit until we have done the math.  The point is, though, that absent those two bananas we actually do have 14 pieces of fruit; the part that is absent is that we do not yet know it, because we haven't done the math.

In the same way, the spreadsheet illustration is intended to show how when one variable in history is changed, all the variables dependent upon that one variable are also changed, instantly.  I remember working with Lotus 1-2-3 on computers with what must have been 286 processors, and you would enter the numbers and click the command to do the processing, and sometimes have to do the processing again because some of the equations had not been completed on the first pass.  It has been a long time since I have had a computer so slow and an equation so complex that the rendering was not instantaneous, and modern spreadsheets rely on processing power sufficient to make the updates on the fly, as it were, as the numbers are entered.  I chose to use the computer spreadsheet to illustrate the matter because for most of my readers, that would show an instantaneous change in all the results, while on reflection they would realize that that change had to occur in sequence.

Mr. Koshkin, though, is actually too clever for the illustration.  He recognizes that the seemingly instantaneous rendering of all the corrected numbers is a function of the central processor choosing to do this in that way, and in the process overlooks the much more fundamental fact--that once we have changed the number of bananas, we have changed the total number of pieces of fruit, and the result is already altered instantly even though we do not know what the result is.  Mr. Koshkin, please forget all about the spreadsheet illustration.  It has caused you to completely misunderstand what it was trying to illustrate.  For you, time makes more sense as a moving transport than as a static dimension.  The spreadsheet illustration does not work for you.

There has been so much in Mr. Koshkin's critique that I neglected to examine his problem with the "universal now".  In brief, he maintains that

In relativity there is only here-and-now for each observer, but there is no universal here and certainly no universal now.

This is a mistake that students of relativity make concerning their own theory.  They understand how time dilation impacts various objects in the universe such that elapsed time for each object will differ; they then draw the incorrect conclusion that there is no uniform "now" because of that.  Hopefully I can illustrate how this is mistaken.  To do so, I will have to give what is undoubtedly a very elementary explanation of time dilation.

Let us suppose that we launch a spaceship toward a point in space which is five light years distant.  Our spacehip is able to travel at an enormously quick speed, half the speed of light; thus it will reach its destination in what is for us ten years.  Let us suppose that by some miraculous future technology this ship is able to accelerate to that velocity instantaneously and upon reaching the destination turn on a dime and return at the same rate.  It will return to us in what for us is twenty years.  They have raced a beam of light and lost, but got there in only twice the time it took the beam of light to do so.

For those on the ship, though, their perception of that beam of light must be that it is moving at the speed of light.  Just as we perceive it as moving one hundred eighty-six miles every thousandth of a second, they too must see it moving at the same speed.  The beam of light cannot travel at two different speeds, and the distance cannot change, so what changes is the length of the second.  For those on the ship, half a second elapses for every second of ours, and in that half second they perceive the light beam as moving ninety-three thousand miles (as they have covered the other ninety-three thousand themselves).  Then the beam continues another light second relative to us and another half a light second relative to them, the second half of their second ticks, and they experience one second to our two.  The result is that they cover the distance in half the time, returning to earth in what they have experienced--not exactly subjectively, but objectively and really as measured by any device or process we know--as ten years.

Thus were we to launch this ship in 3000, by earth-based chronometers it would reach its destination in 3010 and return to us in 3020, but by ship-based chronometers it would reach its destination in 3005 and be back in 3010.

However, even though time is moving at different rates in these distinct locations, for any given now in either location there is a corresponding now in the other.  When the ship returns to the earth, it does not return in 3020 for the people on earth and 3010 for the people on the ship--two different times.  It returns at exactly one moment which the people on the earth call 3020 and those on the ship call 3010.  Further, at the moment the ship arrived at its destination, even though no one on earth would know that it had happened successfully until light arrived five years later, it was perfectly reasonable for people on earth in 3010 to say, "They have arrived now."  Now has meaning throughout the universe.  The very fact that it has meaning is what makes it possible for us to say that the light from a distant star originated fifty or a hundred or ten thousand years ago, because when it was now for us ten thousand years ago it was also now for that star, and however many years the star has experienced since then, it has been ten thousand for us.

Nowhere in the replacement theory is this concept rejected.  It is only that in describing the effects of the theory, local time is used.  That is, we say that all time moves from 2010 to 2000, but what that means is that all of time moves from that now which is locally identified as 2010 to that now which is locally identified as 2000.  It does not mean that everything in the universe goes back in time ten years by its reckoning; it means that everything in the universe goes back however far it is by its reckoning to that moment that was now ten years ago at the target destination by the local reckoning.

A planet is like an orange in some ways.  I can slice the peel of an orange from stem to bottom, and do so again in another location, and so remove a bit of the peel.  Solar light creates lines similar to those cuts across the surface of the earth as the earth rotates.  The distance between a specific pair of those lines in Nome, Alaska, is a lot shorter than the distance between the same pair in Honolulu, Hawaii; yet we do not have any trouble speaking of the movement of sunrise from one meridian to the next.  In that case movement of the same object at the same speed for the same time results in different distances covered.  In the case of time, it is measured lengths of time between the end points which are different; the end points are still the same.

When we speak of the state of the universe now, that has meaning.  When we ask what is happening on Mars or at Alpha Centauri or in the Andromeda Galaxy now, that has meaning.  Time might be moving at a different rate in those places, but that does not prevent a time traveler from moving from one universal now to another, nor does it prevent the entire universe from displaying the other now as it was then.

Certainly there are many things about relativity which I do not understand, but I do understand that the astronauts do not return to earth twice.  When they parted, it was now; when they returned it was now.  Now in both instances was the same moment for both, even though the temporal distances between those nows was different for them.  It makes sense that there was a now when the astronauts reached their destination, at which moment there was a matching now on earth.  They experience a different length of time, but they exist in the same now.

Before addressing Mr. Koshkin's proposed alternate theory, I need to address one point he raises in passing while expressing it.

But if the metaphysical goal is to have causally consistent timestreams only, it is subverted anyway by the time traveler himself.  He pops up out of nowhere, he acts on causes inexplicable in the new history, he is the old history inserted into the new one, he is the uncaused cause.  Thus, old and new histories co-exist even in the spreadsheet theory, except the old history is entirely concentrated in the person of the time traveler.  He singularly remembers the old future and acts on causes derived from it.

That does not describe the norm for the replacement theory; it misunderstands a fundamental principle of it.

It is stated quite repeatedly in describing N-jumps that they will occur when, and only when, the traveler leaving from point D (the future end of the altered history) is exactly the same in every pertinent way as the traveler leaving from point B (the future end of the original timeline).  "Every pertinent way" would include the traveler's memories and knowledge.  Thus there are three ways in which this condition can occur:

1. If arriving in the past, the traveler's impact is sufficiently minimal that nothing he has changed will ever touch the life of his now younger self, then the version of himself which will leave from that future will not have been altered.  That means that there will have been changes to history, but the traveler's knowledge will not be different.  How much change is too much we cannot easily guess, and it will depend on many factors.  If, for example, the time machine is designed to displace the traveler spatially as well as temporally, and our traveler lands on Triton a hundred years ago and does nothing that would be noticed by our own observers, his ability to change the universe without affecting himself is fairly broad.  If he lands in the same room ten minutes before his departure, it may be very difficult to isolate his alternate self from any knowledge or suspicion of this.  Yet what matters is not that the universe did not change, but that the change did not in any way affect the traveler or the trip.
2. Given that that scenario may be somewhat improbable, the next best hope is stabilization of a short sawtooth snap.  That is, as suggested in the analysis of Back to the Future Part I, the original traveler might have altered his own life significantly, but as he ceases to exist and is replaced by an altered version of himself, that altered version might succeed in creating his own history, becoming the supporting cause of the world he knows.  This has the appearance of Uncaused Cause of fixed time theory stories, but resolves them by extrapolating an original now erased history which provided the original cause, that cause replaced by the new cause.  While this is yet more improbable, it is not impossible.  Simply recognizing that the formation of the future he knows depends on him could be sufficient to ensure that it occurs.
3. In a variation of the first option, it could be possible to isolate the time traveler sufficiently that he is not exposed to the events he is altering.  For this, perhaps an example is needed.

I am fond of the television series Seven Days, despite its flaws.  Having given it much thought, I have decided that there is a way for a government agency to run such a program without creating the infinity loops that show appears to create week after week.

The program would require four separate teams:  the research team, the time travel team, the response team, and the coordinating team.  The most critical aspect of this is that the time travel team is in complete isolation at all times.  Any member of that team that visits the outside world is quarantined for seven days (the maximum possible jump to the past) before being returned to sequestration.  All incoming communications and media are delayed by a similar time.  No one in that unit knows anything that has happened over the most recent week.

When a disaster occurs, the research team immediately gathers all the information available, and delivers it, in a data format that can be protected, copied, and carried easily, to the coordinating team.  The coordinating team copies this material to a durable medium, something like a compact disk, and delivers it to the time travel team.  The two teams have no contact but for the delivery of the disk; the time travel team thus does not know whether this is the first time through this history or the thirtieth, but they know only what is on the disk.  They in turn send their courier back seven days to deliver that same disk to the coordinating team.  The coordinating team copies that data and gives the original to the response team, which takes the suggested action to prevent the disaster.  The coordinating team also takes the copy of the research--identical even to the fact that this will be the top disk in their bin, the same disk they used in the previous history--and delivers it at the same second to the time travel team.  At this point, no one on the time travel team knows that the disaster has been averted, so they take the same actions they took in the previous history, delivering the data to the coordinating team, who also does not know that this has all happened "before" and delivers it in turn to the response team.  The response team has exactly the same information under exactly the same conditions, and so takes exactly the same actions, with exactly the same outcome.  The coordinating team again forwards an original copy of the data to the time travel team, and history is now fully self-supporting.  We have an N-jump termination.

All of which is to say that the time traveler in the timeline that marks the final, stable history of the world knows nothing about any previous history of the world but what he has learned from his predecessor or deduced from such data as apparent uncaused causes.  This time traveler has no first-hand knowledge of the original history; that version of him was erased along with everything else in that universe, replaced by the version of himself originating from the universe that remains.

Mr. Koshkin moves from his critique of his understanding of the replacement theory to developing his own theory, which he dubs Supertime.  That theory has some similarities to the concept of two-dimensional time which I explore in the page Toward Two-Dimensional Time, and so it must be said in fairness to both of us that at the time Mr. Koshkin was preparing his treatise I was writing mine, and that the original form of my article, A Draft:  Toward Two-Dimensional Time, appeared on Gaming Outpost mere days before his first letter appeared in my inbox, but he was not aware of that article.  Thus the similarities are not exactly coincidental, but are due to parallel independent consideration of some of the same difficulties suggested by time travel.

Mr. Koshkin subsequently read that article at Gaming Outpost and commented on it there, and I responded there to his comments.  Those comments are relevant to this discussion, but not precisely on point.

It is at this point, though, that I shift from explaining and defending the replacement theory, to presenting what I see as the essential flaws of the supertime theory.  This would ordinarily, I expect, lead to extended discussion, were it being done by e-mail, as Mr. Koshkin would answer my objections either by explicating or by modifying his theory; to some degree it is regretable that that discussion cannot occur here for the benefit of the general readership.  However, the length of Mr. Koshkin's combination critique and presentation as well as the format in which he originally sent it (as a paper in PDF, not as an e-mail) have made this the best format in which to respond, and in the process perhaps curtailed some of the discussion.  I welcome anyone who wishes to discuss the matter to e-mail me or to post at Gaming Outpost's official Multiverser forum; I cannot speak for Mr. Koshkin's availability or involvement.

I appreciate the fact that Mr. Koshkin sees his concept of supertime incipient in the replacement theory; indeed, there is a sense in which history existed "before" the time travel event, and in that sense there is some metaphysical reality to what I consider the erased universe.  It is the more obvious in the explorations of two-dimensional time, where I use the phrase "lateral time" in much the same sense.  However, what appears to me to distinguish the supertime theory from either of those is the insistence that the original history of the universe still not only exists but continues, that the departure of the time traveler from any point along that original history is nothing other than his disappearance from that universe and subsequent appearance in another.

This, to my mind, makes this a variant of parallel or divergent universe theory.  It suffers from most of the same flaws considered in The Two Brothers:  Why Parallel Dimension Theory Is Not Time Travel.  Mr. Koshkin does not deny this, but embraces it as inherent in his theory, and suggests that time travel develops progressively across lateral time--the last experiment in each universe fails, but succeeds in the next universe, leading to a next experiment in that universe.  This is not impossible, and it will be admitted that in those branching universes time travel will continue to be explored at least until something like our two brothers paradox or a grandfather paradox disrupts the entire concept.

What is more problematic for me is not so much that history will be created beyond the time traveler's departure, but that the arrival of the time traveler at some point in the past begins to create the new history from that point, moving at the speed of time.  This bothers me because it means that time travel to the future is and will always be inherently impossible, even as a return from the past, except in the most peculiar of conceptions.

The first of those conceptions is the simple leaps to the future made in such stories as (most famously) Buck Rogers, where the time traveler is in suspended animation, frozen in time, as it were, not aging or decaying or experiencing the effects of time at all, for the duration.  This is not really time travel, but it does have a similar effect, as the traveler arrives in the future without experiencing the intervening time.  Perhaps the most significant aspect of this concept is that it is not reversible; one cannot go back to the starting point by a similar process.  That is not fatal, but it does illumine the point that this is not really time travel.  In any case, under the supertime theory any traveler wishing to travel to the future must in essence wait for the future to arrive.  It does not yet exist, and will not exist until it has been created, moment by moment, from the actions in the present.  This is true even if the traveler came from an existing future; that is the future of a different history, and not the future of this history.

The second concept of travel "to the future" that is possible on this version of time is that the time traveler can travel to the present in that other timeline.  Here Koshin is a bit unclear.  It seems on one hand that that history still exists as a separate dimension; it also seems that the part of that future that is still future from the perspective of the time traveler's position in the past is the future of this dimension, existing in the old form until altered by the progression of events moving from the present.  Thus it might be that someone who jumped from 1985 to 1955, changed the world, and then jumped back to 1985, would find that the world was unchanged, and if he stayed with time as it moved forward from 1985 it would be as if he had not changed anything--but if he traveled from 1995 to 1965, he would find time changing around him, consequent of his acts in 1955, the wave of change having moved ten years in the ten years since he initiated it.

It seems to me, then, that Mr. Koshkin's "supertime" requires three temporal dimensions.

Time is the medium within which we understand and perceive change.  Ordinary linear time requires that we accept change moving in one direction, as we move from past to future.  Fixed time theory also maintains a single linear dimension of time, but allows that causes and effects might not be in sequence along it, as the perception of time is not the reality.  Parallel and divergent time requires two dimensions, in that each alternate history lies alongside an original; it is possible in divergent dimension theory to make changes moving in this lateral dimension.  As Mr. Koshkin observes, replacement theory also has some sense of a second dimension of time, in that there is change from one history to the next, even though only one dimension is perceived and there is only one linear history of the universe.

However, the way supertime theory works, there is linear time, a coherent history from past to present which is being created into the future; and there is lateral time, as universes branch from an arrival point much as in divergent dimension theory, but there is a third axis:  at the moment of the branching, the future history of this new universe already exists as identical to the future history of the universe from which the time traveler originated, but as linear history forms the new timeline that future history is changed to conform to the new version of time.  This is not an easy image to grasp, but consider it thus.  If our time traveler goes from 2010 to 2000, the history of the new world is the new history at 2000, but is still the old history at 2001; it takes a year of movement for 2001 to become the new history, but 2002 is still the old history; it again takes another year for 2002 to become the new history, and still 2003 is the old history.  Second by second, the history of the new timeline is being replaced; second by second the complete history of the universe is changing.  That change, though, must occur atop the existing timeline, neither in linear time (because in the base universe the future does not yet exist, and linear time is the medium which creates it) nor in lateral time (because lateral time is the creation of new universes themselves) but overlaying this, the medium within which the future history of a secondary universe changes from what it was to what it is becoming.

Further, because of Mr. Koshkin's commitment to true randomness at the quantum level, it must also be the case that all histories of all worlds are constantly undergoing this process, becoming different in unexpected ways.  We have constantly multiplying universes, because history keeps changing, but the original history remains.  More surprisingly, no two such universes will ever be alike, perhaps not in our age remotely similar, because instant by instant billions of random quantum events are happening throughout the universe, and thus the universe is splitting into billions to the power of billions of different universes.  These quantum events do impact the larger world, in releasing subatomic particles which can destabilize other nuclei, mutate cells, or conceivably alter thought processes.  The universe we passed through yesterday is already unrecognizably different from that which we remember, because in supertime it is constantly in flux.  We cannot easily travel to our own past, because our own past has been replaced a billion times by altered versions.  What we mean by time travel is genuinely impossible.  The past as we knew it does not exist; we would arrive somewhen else.

I have sometimes been criticized for failing to retain the law of conservation of matter and energy; I have always answered that this law is maintained in the replacement theory:  all matter and energy are reconfigured to a position they held elsewhere on the timeline, and that which constitutes the time traveler himself, an increase in matter at the point of his arrival, is simply displaced from the future, and so is balanced by a corresponding decrease in matter at the point of his departure.  It is not different from moving an object from one room to another:  the matter is in a different location along the temporal dimension, but its displacement will be corrected.  The divergent dimension theory is much more susceptible to this criticism, as it appears that the entire universe must be doubled each time someone travels to a point in the past.  Yet Mr. Koshkin's Supertime has the total matter and energy doubling innumerable times per second, as random events which could have been otherwise cause the universe to split.

Mr. Koshkin invokes Occam's Razor, the principle that the simplest explanation should always be preferred.  There are two problems with that principle.  One is that the simplest explanation is not always the correct one, particularly when we do not have all the possible data.  It is entirely possible that the truth is much more complicated than the simplest explanation allows.  The other is that perfectly reasonable intelligent individuals may reach very different conclusions concerning what is the simplest explanation of any given data set.  I will not say that Mr. Koshkin's supertime does not appear simpler to him than my replacement theory does to me; I will say, though, that invoking this three-dimensional time makes it appear much more complicated to me.