There are some issues that are resolved through some brilliant insight which comes quickly, dramatically, and satisfyingly. These are issues that turn on some genuine problem which is accounted for through the discovery of some unknown or unnoticed point, or through some significant reorganization of the previous orthodoxy.

There are other issues that arise because of some general confusion. Their resolution is achieved only through a deliberate, mundane, and tedious process.

Such, unfortunately, is the nature of the task that confronts us in dealing with some of the questions which cloud much popular discussion of the compatibility of two methods of determining the age of the universe: the general (scientific) method, which yields a result of billions of years, and the traditional Torah method, which gives a result of less than 5,800 years at the time of this writing.

Our current understanding of the methodologies involved allows for a definitive resolution of the discrepancy between the results of these two methods. A word of caution is in order, since the remarks here do not resolve all aspects of the so-called conflict between the scientific and the Torah accounts of the history of the world. In particular, there are many (particular) events in the scientific account which are not included in the Torah one, at least in any obvious way. In a general way, these discrepancies can also be resolved, but that is not the topic of this essay. Here I will deal only with the problem of assigning a number to the age of the universe.

It is well known that a correct statement of a problem is often an important step toward its solution. The case at hand is no exception. The latter phrase, in particular the phrase "assigning a number," will prove the basis for the resolution, but obviously some elaboration is in order.

Though most of us experience few problems in use, the concept of time has proven to be awfully subtle and complex. There are really a few distinct ideas. A critique of one part of this complex, simultaneity, is central to Einstein's Theory of Special Relativity.

There have also been many deep discussions aimed at determining a physical basis for the irreversible aspect of the time ordering, that is, that in time, one can get from here to there but not back again.

These problems should not detain us here for we are concerned only with two aspects of time: the comparative (topological) measurement of time intervals, and the assignment of an origin. This will, it is hoped, become clear from the subsequent discussion.

When we set up a system to measure any quantifiable stuff, like disance, weight, or temperature, the procedure is to set up some reference standard and then to compare subsequent collections of the stuff to that standard. Such a process will tell us when we have an amount of stuff which is as much as our reference standard.

We will skip some intermediate steps and now assume that we have a full system of comparative measurement: that we can tell when we have as much as our reference standard, and also whether more or less than it, and how many times as much as that standard (two times as much, three times as much, one-half as much, and so on). As an example, we can consider the standard meter in Paris, which was long used as the reference standard for length. (There was an attempt to make it a "natural" standard by making it equal to one ten-millionth of the length of the arc from the equator to the North Pole, but that was rather accidental to the process from our perspective.) If we concluded that a particular wall was three meters long, that was tantamount to saying that the length of the wall was three times the length of the standard meter in Paris, that if one were to directly compare the two, three of those reference standards would occupy the same length as that wall.

In ordinary talk of measurement of spatial quantities such as length, few problems arise, since we can easily isolate several different quantities, compare them, and abstract the common factor (spatial extension).

We are not in the same happy position with respect to time. We cannot isolate chunks of it and abstract what is common to them. In fact, we cannot in any way directly experience a chunk of time at all. We experience time one instant after the other, in the present, but we are unable to aggregate these instants.

Thus it is necessary and worthwhile to clarify what it is that we are measuring when we measure time. It should become evident that in measuring time, we are really measuring the amount of global change.

When we set up a system for measuring time, we select a process which we believe proceeds at a regular rate. This is to say that we pick some process within which the amount of change is fixed across different equivalent time intervals. We then compare the amount of change in the reference process to the process to be measured and arrive at a result.

This may not be so obvious since we use a standardized unit for measuring time, the second. This makes it appear like any other measurement of stuff. However, if we use a standard wall clock in the US to measure a process, the basis for our saying that a particular process took three seconds is really that the electric current powering the clock we looked at reversed itself 360 times, while if we use a digital timepiece our basis is usually that a quartz crystal has vibrated 100,000 times (approximately). Our free use of "seconds" in both cases is the result of careful standardization. Someone reliable has carefully determined that 100,000 vibrations of a quartz crystal span the same amount of change as 360 current reversals do, in the standard American electrical system for most practical purposes. (In most of the world it is 300 current reversals since they use 50 hertz current unlike America which uses 60 hertz ac current.)

For a long time, the motions of heavenly bodies were the obvious standard of time measurement. There is no other natural process directly accessible to man that even approaches these motions in its regularity. Thus the celestial changes were the best choice for standard units of change, whether that choice was the day, the month, or the year. These standards are no longer used for many applications in modern technology, for various reasons, but they still form the basis for most of our personal measurements of time, that is, for most purposes which apply directly to our persons.

The important thing to remember is that when we say that some process took three seconds, what we are saying is that the amount of change in that thing is the same as the amount of change in three seconds worth of the standard. We are only comparing the amount of change in two process, and not in any way declaring something about the amount of some absolute entity which we call "time."

For convenience let us take the year to be the amount of time between recurrent appearances of the sun at either solstice, and the day as the amount of change subtended by two successive appearances of the sun at one of the horizons at one of the solstices. These are said to be definitions of convenience only because others could have been chosen. What is convenient about the ones we picked is that they are definite and familiar and that they are simple relative to some of the others -- but all are practically equivalent.

Now, when we say that something took ten years, what we mean is that the amount of change in that process is equivalent to the amount of change subtended by ten successive appearances of the sun at one of the solstices. As we have explained above, the term "day" would be applicable even if there is no sun present. Since in saying that something took one day what we are trying to do is to measure the amount of change--rather than merely to state that some event took place over the same time as our reference process--it makes sense to attempt to apply the term even when on sun is present.

As a result, we can evaluate the truth or falsity of the sentences at the beginning of the Bible that describe the events of the early days of creation (before there was a sun) as having taken place in one day. The somewhat surprising result is that they all turn out to be false, since the full description of the amounts of change which took place in the early days (and the later ones) is clearly far more than is subtended by successive appearances of the sun at the horizon.

Faced with this unsatisfactory result, we are forced to revise an unstated hypothesis, namely, that "day" is always an accurate translation for "yom," as it occurs in those Biblical sentences. The contradiction that we generated by assuming "day" as the translation for "yom" was generated at the level of pshat (the first, basic level of meaning), and we cannot thus be accused of a departure from the pshat of the text if we discard that hypothetical translation. Thus, we may grant that the events described in the Torah account of creation took many (perhaps billions of) days, though we insist on retaining the application of "yomim" in the original manner to the events described there. Scientific theories of the formation of the solar system, since they are merely backward extrapolations, yield only measurements of the amount of change which took place, and it would seem that anyone must agree that there are many, many years worth of change in those events. This in no way affects the accuracy of the Biblical account which is in terms of yomim rather than days. There is, however, the disturbing problem of the

Continues . . .