We have made a complete study of the information on the Indo European peoples that can be derived from the languages.

As part of this study we have examined the time aspects; here we present a summary of this portion of our study.

Ours is an assessment of the probable date at which the original Indo Europeans started to spread throughout the rest of the world. These people are designated as "Proto Indo European", a term which we abbreviate as "PIE". As an integral part of this analysis we make a new, more precise assessment of the rate of change of Indo European languages.

Our analysis is far more comprehensive, thorough, and accurate than any previous analysis of this type. Specifically, we use a unique new methodology, improve the mathematical accuracy by using far larger vocabulary than has ever been used before, and for the first time we include all applicable Indo European vocabularies – ancient and modern.

Our method of estimating when the presumed single Proto Indo European people began to spread over the worlds is very simple – we assume that we know a sufficient number of the words in the original vocabulary and then calculate what fraction of these words is found at a specific later date. We can then "extrapolate backwards" to find out at what time 100% of the words would have existed. This approach makes the assumption that this "dispersal" occurred over a reasonably short time (relative to the rather long timescale involved) and was not excessively protracted. It also assumes that the later languages were cleanly derived from the Proto language and not muddled up with tongues from other sources.

To do this we must have a number of vocabularies in various languagesand they must be of known dates. It is beneficial to have information spread over as long a span of time as possible so that we have a long "baseline" for the back extrapolation.

One of the most striking achievements of linguists over the past 200 years has been the reconstruction of the "original" language of the Indo Europeans. We should note that not all linguists agree that there was an actual "language" which was spoken by a single group of people who split into many different languages. To the writer this seems to be obviously fallacious since all known languages have a common vocabulary and grammatical structure. But this is not an argument that we need enter into since, as we shall see, the consistency of our results is an empirical justification for the real, past, existence of an original language. The readers may make their own judgment on this point.

Whether Proto Indo European actually existed as an entity or not there is no dispute that it is possible to derive the vocabulary and form of an older language from later languages. Although precise reconstruction may well require extensive linguistic knowledge the principles involved are simple; if two or more later languages have similar sounding names and/or grammars then the older form must have been similar to these. Comparison of the forms and experience (for example, from earlier documents) in how words change can make this a quite precise process if enough information is available. And, more so in Indo European than any other language group, there is a vast amount of information to work with.

Although the analysis may be complex and time-consuming, in practice it can be simple. A simple but excellent example of the process is to look at the names for numbers up to ten, and the names for different family members. We shall not need to go into these aspects of the study ourselves since there are excellent sources for the proto-language, PIE.

There are comprehensive studies of the etymology of PIE. One of the most respected is the German-language work of Julius Pokorny entitled "Indogermanische Etymologisches Worterbuch" published in 1949. An English-language publication of the same date is "A Dictionary of Selected Synonyms in the Principal Indo-European Languages" by Carl Darling Buck. Both of these give detailed discussions of the words that are used to reconstruct PIE roots and are well worth study. But a more concise English source which gives the actual form of the PIE word as well as the words from which it is deduced is readily available as an appendix written by Calvert Watkins in "The American Heritage Dictionary of the English Language", published by Houghton Mifflin Company in 1969. This was revised and re-issued as a separate book in 1985.

The Watkins study is our source for Proto Indo European words.

Glottochronology is the name given to "dating" languages by looking at changes between earlier and later vocabularies. For example, this could be by studying differences between Anglo-Saxon and modern Germanic languages or between Latin and French, Italian, and Spanish.

This ponderous word gives an appearance of unjustified precision and certainty to a simple and imprecise but useful concept. Basically it rests upon the simple and obvious fact that languages change over time and that they change more and more as time passes. But the extreme advocates of the concept seem regard the concept as absolute and worthy of intense mathematical study while the detractors appear to believe that it is of no value whatsoever. And there seem to be few linguists who recognize that there is a middle ground between the two equally unjustified extreme views.

The concept originated with an anthropologist, Morris Swadesh, who appears to have had a very clear understanding of its value and limitations. But the intensity of arguments between his followers and his detractors appears to have obscured the facts.

In brief, the extreme advocates appear to believe that language change is strictly statistical and that rigorous mathematical statistical techniques may be applied. Unfortunately, many of these proponents clearly lack understanding of elementary facts of statistics, and, for example, they may present analyses that give the impression of great mathematical precision which simply does not exist. This is demonstrated by the presentation of numbers to a completely unjustified level of apparent precision (the number of significant numbers given is too great). Such studies are, to some extent, self-defeating since they tend to be disregarded by others even though they may contain useful information. On the other hand, the extreme nay-sayers choose not to open their minds to the fact that this procedure, when used sensibly, offers some additional guidance in the assessment of language changes.

Commonsense should prevail. This is an empirical means of adding to knowledge of languages that should neither be rejected out of hand or accepted as gospel truth.

The principle behind glottochronology is the simple assumption that the rate of change of the form of words is constant. In other words, if, for example, half (of any other fraction) is found to change in a certain period of time then the same fraction will change in the same additional time.

The reader will have recognized that the deliberate choice of "half" has introduced the well-known term of "half-life" which has entered the popular terminology since nuclear matters and radioactivity have become so prominent in public commentary. This term is strictly applicable only to those circumstances that are completely random, that is "statistical" in nature, and it is not a simple matter to ensure that this is true even when we are dealing with the inanimate, physical world. Even when measuring, say, the decay of radioactive atoms, there are likely non-random aspects that may have to do with inadvertent bias in measuring instruments, and there is also some inevitable human aspect. One nice demonstration of this is the realization that early measurements of radioactivity in which an experimenter actually saw flashes of light did not allow for the fact that the observer blinked; apparently we do not normally realize that we are blinking all the time our eyes are open.

When we then take into account that we do not (as far as I am aware) really know why some words change and others do not, the human element is clearly of some, unknown, significance.

We shall return to some of these points later, but we must reiterate that we cannot assume that language change is truly random, and our understanding is empirical and whose validity must either be proven or left with some (unknown) ambiguity. This empirical "proof" is a prominent part of our study.

The next point is the very important one that "more is better". If we have 100 examples the percentage error is 10 times poorer that if we have 10,000 examples, and 100 times poorer than if we have 1,000,000. The mathematical description is "uncertainty" which can have tricky mathematical aspects when seeking for precise descriptions, but the fundamental basis is that the uncertainty is related to the ratio of the "square root" of a number to the number itself. And this ratio goes down (the accuracy improves) as the number increases.

But Swadesh, the originator of the method, chose to compile a list of only 200 words that he suggested as a practical number for anthropologists to handle. This is a small number indeed for any significant accuracy and even current opinion surveys, which are usually now reported with an some indication of uncertainty, commonly use 1000 interviews. To compound the problem, Swadesh later dropped the number to just 100 and this is the list that most investigators use.

The basic point here is that there is a large uncertainty by the standards of most experimental sciences, and that this is seldom pointed out to the reader (and, one suspects, may not even be appreciated by the author).

But we should not be too critical of the practice since adoption of Swadesh’s list has introduced a welcome uniformity in looking at word lists world wide.

Unfortunately Swadesh also added an aspect that , in the writer’s opinion, has cast glottochronology in a false light - in constructing his list he apparently selected items that he thought were particularly suitable for this purpose.

There are two aspects. First, the criteria he used are unclear, but there are obviously implications that the choice of specific words is very important. The implication that "some pigs are more equal than others", is a huge assumption which is apparently unchallenged, and is not only almost impossible to prove and, in some cases, is actually untrue. Second, this has apparently led to the belief that only linguists can select words that should be used for dating; this has created a false impression regarding their role. The readers can decide for themselves whether two words in different languages are "the same", and, in the writer’s opinion, reasonable persons will have no problems in agreeing almost all of the time. And, most importantly, the small statistical sample always means that the results are imprecise to the extent that inclusion or exclusion of a few words is of little or no importance. Nevertheless, we have addressed both of these questions in our study.

The PIE wordlist that we use was taken entirely from Watkins’ study discussed above. To address the problem of statistical accuracy we have selected almost 900 PIE words as our initial list, a potential improvement in accuracy of a factor of nine compared to a 100-word list. Second, we have divided our chosen words into different categories to see if the choice affects the results.

The words included about 300 names for parts of the human body, for features of the natural landscape, for various objects that might be present in the home and community, and for divisions of the day and the year. In addition we have added generic names for plants and animals and for plant and animal products. We then added about 500 verbs that describe functions and actions of the body and actions connected with domestic, agricultural, and social activities. In all cases these names were chosen to be independent of the location of the people and their way of life. Finally we included about 100 descriptive words such as colors and "tall" and "heavy".

The total number was about 900 including cases where there was more than one PIE name for a given object, function, or attribute. This listing raised the issue of how to identify the number of cases where a PIE name had survived in a later language. In the 250 cases there was only one PIE name and it was simple to decide if one of these could be found in a later language. But in the other 650 examples there are several PIE names and perhaps several names in the later language, for example, in English. In these cases the number of possible matches is determined by the smallest number of names in either PIE or the later language.

In deciding if a PIE name had survived we have followed the guidance of our other language studies which conclude that this is essentially a question of matching the consonants in both words. Experience shows that the particular choice of vowel makes little difference to the pronunciation of a word; the fact that some languages, such as ancient Egyptian, did not have any means of writing the vowel is support for this judgment. On the lighter side we may speculate that this fact may have been behind the definition attributed to Voltaire that etymology is a science where "the consonants count for little and the vowels for nothing".

We have been able to calculate survival percentages for languages at eight different times, from modern (1950 AD) to 1390 BC. We will discuss the modern data last.

The oldest is Mycenaean Greek, a vocabulary that is found in excavations at Knossos in Crete. The date is well established but the vocabulary is very limited since it consists of listings of items held in storage at Knossos.

The next is Old Persian which is found on triumphal inscriptions, mostly from the texts of Darius on a cliff above an ancient caravan route. The date is well known but a vocabulary which commemorates a king’s victories tends to be quite limited.

Following this in age is Homeric Greek. Here the vocabulary is essentially that of Homer but not that at time when his works originated but the date from which the available manuscripts were written. This is quite ambiguous and may lie between about 150 BC and 550 BC. We have simply taken the central point of 350 BC in this long span of time.

The other data are better established.

The documents that contributed the vocabulary of Latin are well known and most date from between 180 BC and 120 AD; we take the midpoint of 30 AD as the date. And since the vocabulary is extensive this is one of the most accurate data points available.

Next comes Gothic which is both fairly extensive an well dated since it comes entirely from the Bible written in 370 AD to convert the heathen Goths to Christianity.

Old English and Middle English are taken respectively from Anglo Saxon texts of 900 AD and the works of Chaucer and others of about 1360 AD as given in Stratman’s dictionary of Middle English.

This brings us to modern languages which present us with a surfeit of languages and some difficulty. Here, of course, we have a vast amount of information so that there is no question of good statistical accuracy. We have looked at twenty-three languages in the European groups of Germanic, Baltic, Slavic, Greek, Romance, and Celtic and four Indian languages. Greek is only represented by the single language, but within each of the other six groups there is statistical consistency in the fraction of surviving PIE names.

However, although all the results for all the others are statistically consistent with each other, both Celtic and Indian show appreciably lower fractions of PIE survivors. If the modern data are taken as a whole they show a survival fraction of 10.5%, but if Celtic and Indian are excluded this rises to 12.6% (both with uncertainties of about 0.5%). The differences are not huge but larger than we might have expected. We speculate that this may reflect an over emphasis on some languages in the original PIE list and this is a salutary reminder of possible pitfalls in glottochronology. We have chosen to exclude the Celtic and Indian data in favor of the average of the other, internally consistent, data; this gives an average figure of 12.4% as the most reliable value.

The results of our analysis are given in the following table.

The table given above shows exactly what we would expect – the percentage of PIE survivors increases as we go back in time. And, again as we expect, the "error" increases when we have fewer numbers to work with. We need to explain a little about the "error" and why we have placed the name in quotes – it is not an error in the sense most people would expect but a statistical measure called a "standard deviation". We will not go into details since statistics is an area that many people find confusing) but need to point out that the "error" is not a rigid limit. There is a two-out-of-three chance that, if much more precise results were somehow derived, the answer would lie within the upper and lower bounds obtained by adding and subtracting the standard deviation to the "central" quoted value. But there is a one-in-three chance that it could lie outside it.

But a table of this sort is a poor way to grasp what these results mean; for this we need a figure of some sort, and this is best presented as the graph shown below.

This graph shows the dates on a horizontal or "x" axis, and the percentages on the vertical "y" axis; and the dates are shown as bars where the standard deviation "error" has been added and subtracted from the central value. As noted above, there is a 2/3 chance that a more precise measure would lie in this range and a 1/3 change that it would lie outside it. The reader with mathematical expertise will note that we have not assigned an uncertainty to the dates even though they are not perfectly known. This is because the main uncertainty lies in the number of survivors not in the dates.

Tthe graph will look strange to many people since the dates are evenly spaced but the percentages are "scrunched up" as one goes to the higher values. This is because this is a "logarithmic" vertical scale which allows for the assumption that equal fractions (not, for example, equal numbers) of survivors disappear in a given time. The virtue of this logarithmic presentation is that the measures would lie on a straight line if the assumption is true.

Indeed, the separate measures lie very nicely on a straight line given the statistical uncertainties involved. The heavy line is the "best fit" as determined by a mathematical technique called "weighted least squares". This is a well-known technique which allows for the fact that some points are more accurate than others, and, as can be seen, the line emphasizes the most accurate point where the bars are smaller. We suggest that the reader should not be concerned by the mathematical detail, and in fact a simple line drawn "by eye" would look just about the same. We have also drawn two lighter lines that show the fits within the top and bottom of the error bars.

Some readers may be disturbed by the fact that the oldest measure droops below the line but please be assured that there is no statistical significance in this. Indeed, about one-third of "one standard deviation" points should

lie off a best-fit line and results that show more perfect fits should be viewed with some concern.

Now we can look at the implications of this graph.

The foremost points stem from the fact that consistency of the numerical data vindicates the assumptions that have been made. These are as follows.

1. It is legitimate to examine how the reconstructed Proto Indo European vocabulary changed with time. By inference, a true Proto Indo European people indeed existed.
2. As far as we can tell, different portions of the PIE vocabulary changed in the same way; there is no evidence that the selection of names for glottochronology is limited to a specially selected list, for example, that of Swadesh.
3. A well-justified dispersal date of 4700 BC with and uncertainty of 400 years has been derived. This is significantly earlier than conjectured by archeologists and this could have significant implications. This point is discussed in detail in our full report.
4. The half-life of 2240 years derived by our method is significantly different from that implied by the 1953 study of Lees widely used by anthropologists and others since that time. The review by Gudchinsky used a survival rate of 80.5% over 1000 years which corresponds to a half life of about 3200 years. Our figure of 2240 years corresponds to a 1000 year survival of 73.2%. The difference could have significant implications in some instances.

We believe that our study has been very satisfactory as regards the consistency and accuracy of our analysis of Indo European languages and the status of Proto Indo European. We suggest that the results of our analysis should be used rather than older, less complete, studies when considering Indo European languages.

However, we urge that reader should note that our work has only been "proven" for Indo European, and that caution should be used with other language groups. We believe that the older assessments of the rate of decay are not particularly convincing since they (as noted by Gudchinsky) are based largely on Indo European but give different results from ours, but this in itself should not mean that our numbers should simply substituted for them.

A new, comprehensive analysis of all languages would be interesting, but this may not been very productive since there are very few instances outside Indo European where the basic data are available. To state the obvious, any analysis without two dateable vocabularies is impossible, and these are few and far between if they exist at all; and a minimum of three cases would seem to be necessary to justify the work involved.

Also, the virtues of not changing a practice without clear evidence of being able to improve the situation should not be minimized. Staying with the older data (except for Indo European) seems sensible. This does not mean that every analysis should not state clearly what data are being assumed and there is simply no excuse for not recognizing statistical limits and particularly for not over-stating the accuracy of the results.

Finally, although we believe that this methodology has virtues, we should note that we believe that there is clear evidence for the non-applicabilty of glottochronology for some languages groups. For example, some unpublished work of the author in Athapaskan clearly shows essentially no decay of an appreciable fraction of words, but there are changes in other words.

In brief, glottochronology studies are worth applying but only within limits and with care. It is not simply statistical and any extensive use and detailed application requires empirical justification.

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