The Book
In fact, I agree wholeheartedly. Seeing time as fixed, and events as being in their place along that medium, actually works better for the theory. It solves a lot of the confusion about why certain events don't happen sooner. For example, why doesn't Marty McFly instantly vanish the moment he has undone his own existence by preventing his father from meeting his mother? If his entire universe was at that instant undone (as indeed we ultimately conclude it was), how can he still exist now, and yet not exist later?
I find that the easiest way to perceive this is by considering something of a computer spreadsheet program. This example will show how events can change instantly and yet not immediately; and it may help to display the nature of our three basic anomalies for those who are having difficulty grasping them in the context of rewind and replace.
If the reader is not familiar with the way spreadsheets work, I trust this will still be clear enough. Imagine opening a spreadsheet program--Excel is the common one for most computer users, although Lotus 1-2-3 is the one on which I first learned, I think. You see a gridwork of what are called cells, in numbered rows and lettered columns. Thus there is a block near the top left corner of the work area which is in the first row and the first column. The first column is designated A, and the first row is designated 1, so that block is known as A1. The block below it would be A2, and the block beside it would be B1
We will imagine that we've typed a value into A1. There is now a number there. What that number is does not matter at this point.
In A2, we're going to enter a formula. A formula is a mathematical equation which calculates the value for that cell. The beauty of a spreadsheet program is that you can use in a formula the value of any other cell, and that's what we're going to do. We're going to create a formula which makes the value of A2 dependent on the value of A1. For example, we could say that A2=A1+1. Now we know that if A1 is 1, then A2 will display as 2. Similarly, if A1 is 365, then A2 will be 366. The formula is not displayed; only the value is displayed.
We will do the same thing in A3, making it dependent on A2; and A4 will be dependent on A3, and on down the column, until we reach A100, which will be dependent on A99.
Now we'll come back to the top and enter a formula in B1 that is dependent on A100, that is, B1=A100-100, or something like that.
A moment ago we said that the value of A1 didn't matter; there is a sense in which that's still true. However, whatever you've imagined that value to be, now imagine that it changed. That is, let us suppose that the value of A1 was 1; erase that and type 2. What happens? With a good modern spreadsheet program and a decent computer, the value of B1 also changes. That is, if we suppose every cell from A2 through A100 is adding one to the previous value, such that A2 equals (A1+1=)2 and A100 equals (A99+1=)100, and then B1 equals A100-100, then when A1 showed 1, B1 showed 0; but when A1 showed 2, B1 showed 1.
It's important to note that this change was, in strictly theoretical terms, instantaneous. The instant the value of A1 changed, the value of B1 changed. It doesn't matter if you've got a slow computer or a slow program and you didn't see the change immediately; it doesn't matter if you're aware that there's an imperceptible delay for processing time; it doesn't matter if you've used very complicated formulae which slow the machine. At the instant A1 changed, B1 changed. B1 was no longer equal to 0; it was instantly equal to 1.
Yet it is equally important to note something else. We could say that B1 changed because A1 changed; but there is a stricter sense in which that is not true. B1 changed because A100 changed; A100 changed because A99 changed; A99 changed because A98 changed. Every step in the chain had to be altered before B1 could be altered. In a sense, it is absolutely true that B1 changed after A100 changed; yet that is not a temporal sense, it is merely a causal sense. When A1 changed, every item after A1 also changed. They changed in sequence, one after another; yet they did so instantly, without passage of time.
Time is like that, or at least it is so understood by many. If you were to change an event at point A1, it would immediately change an event at point B1. All those intervening moments would have been instantly altered. Yet they would have been altered in sequence, and it is a sequence we can only discover by moving through time.
Now, imagine that your fantasy computer is capable of something of which no computer is capable: imagine that you could make A1 dependent on B1 without causing an error. That is what time travel is like. Normally each moment in history is dependent for its "value" on the moment that preceded it in time. When someone, or something, travels from the future to the past, suddenly that moment's value is dependent on the value of a future event, one which is itself dependent on the value of the past event. Every time the value of A1 changes, the value of B1 must compensate; and every time the value of B1 compensates, the value of A1 changes.
Our three anomalies can each be illustrated from this.
In the example we've just described, after all the events presented, B1 always winds up equal to A1-1. If A1 is 1, B1 is 0. What happens if we make our formula in A1, A1=B1?
It should be evident that if A starts at 0, B1 will come to -1; but at that moment, A1 will change to -1, causing B1 to drop to -2, causing A1 to go to -2, B1 to -3, and spiraling downward, repeating the loop perpetually forever without ever repeating any of the data. Also, not only do these two numbers change, all the steps between them are undergoing similar changes. The entire line we've created cannot stabilize.
Let's expand our spreadsheet a bit. Let us suppose that B1 is the beginning of a new decade. B2 is the next event. Just as the value of A2 is dependent on the value of A1, so the value of B2 is dependent on the value of B1. What is the value of B1? Its value is in flux; it is constantly changing. B2 cannot have a value, because it cannot derive a value from B1. This is different from A1, which is situated in the chain such that, from its perspective, the value of B1 is momentarily stable. B1 only changes after (sequentially) A1 changes. B2 cannot proceed from B1 because it's outside the loop.
If you have not recognized it, this is the Sawtooth Snap. In this pristine mathematical environ, it is perpetual, never resolving to either N-jump or Infinity Loop. Although this is the simplest to create on a spreadsheet, it's a lot more complicated in reality. In reality, we're not only changing the values--sometimes we're also changing the formulae.
The next example is a bit tougher to set up. Let us suppose, however, that the starting value of A1 is 1 (as it was in our original example). Let us also suppose that through the wonders of math, the outcome of our loop is B1=-A1, that is, if A1 is one, B1 is negative one. Now, let A1 equal B1. What happens?
A1 started at 1, and resulted in B1 being -1. That, however, changed A1 to -1. Our contracted formula tells us that B1 must equal -(-1), which is of course equal to 1. Now A1 is back to 1, B1 to -1; A1 becomes -1 and B1 becomes 1.
We have not constructed the intermediate numbers this time; however, it's clear that however they're derived, they, too, are constantly changing. However, they're not changing in the same perpetually different manner as they were a moment ago. They are merely switching between two values, that which springs from A1=1 and that which springs from A1=-1.
It is also clear that once again our continuation in B2 is impossible, because we have no fixed value for B1.
This is of course an Infinity Loop. Although a bit tricky to create in the example, it proves to be the easiest to create in reality. The most common way it is created is that the value of A1 is alternately made dependent on or independent of B1; that's beyond the ability of the illustration, but clearly a hazard of reality.
This is hardest to imagine in the spreadsheet program, because of the involvement of math in the process. However, it can be demonstrated.
Let us suppose that we're back to our original formula, where A1 starts at 1 and B1 winds up being equal to A1-1. Now, let us insert in A1 the formula A1=B1+1. What is this result?
For the mathematically inclined, let me quickly suggest that if A1=B1+1 and B1=A1-1, then A1=(A1-1)+1; solve for A1 and we get A1=A1.
For those for whom that was more confusing than enlightening, what we've just done is create a string of formulae which result in A1 not changing. Whatever the initial value inserted in A1, when it is replaced by the formula it retains that value. Since it retains the value, all of the equations dependent on it also retain their values, including B1.
Since B1 is no longer changing to keep pace with A1, B2 has a stable value from which to proceed.
This illustrates the N-jump. Although the cause of the value at A1 has changed, the value itself has remained the same, and all the values springing from it are likewise preserved. Although this did not require much effort on our parts in the spreadsheet, it is a very difficult object to achieve in reality--and the only one truly desirable.
Before anyone writes to me about fault protections and overflow errors, let me again clarify that I understand these examples won't work on our computers. I just got those error messages yesterday, as I was making changes in a spreadsheet which, in the order I made them, resulted in reflexive references. Those of you who understand computer spreadsheet programs must accept that this is some sort of fantasy program that runs properly despite those errors.
It hopefully is clear that the theory of time presented in these pages is not dependent on an idea of time as in motion. Time can easily be perceived as the playing field against which these events occur. Events still occur in causal sequence, and it can be said that causally the effects are instantaneous. That does not alter the fact that we normally will encounter the changes temporally, because we have to arrive at Noon on Tuesday--or at Cell A25--before we know the value there.
It is also hoped that by seeing these three anomalies in this context will help some to understand how and why they do what they do.
It should also be explained again that this is an illustration; it is not the theory. The theory was developed and expounded for quite a number of years before this particularly illustration was devised. Don't fall into the error of thinking that because this particular illustration shows so much so well that it is the source of the ideas. It is a relatively late way of presenting the ideas.
As always, questions will be entertained by e-mail.
