RootsTech 2015

Some people eat, sleep and chew gum, I do genealogy and write...

Wednesday, August 27, 2014

The Limits of Accuracy


In quantum mechanics, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle known as complementary variables, such as position x and momentum p, can be known simultaneously. This is sometimes referred to as the Heisenberg principle, but it was formally derived by Earle Hesse Kennard and Hermann Wey. See Wikipedia: Uncertainty principle.

In 1931, Kurt Gödel proved two theorems of mathematical logic. Quoting from Wikipedia: Gödel's incompleteness theorems,
The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" (e.g., a computer program, but it could be any sort of algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that such a system cannot demonstrate its own consistency.
One of the most influential books I have ever read discusses the application of the Heisenberg principle and the incompleteness theorem of Kurt Gödel. The book is Hofstadter, Douglas R. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Basic Books, 1979.

These mathematical principles were "discovered" and changed mathematics in a fundamental way. So, you say, here we go again, how can this possibly have anything to do with genealogy? Well, humor me. Here is what I have to say on the subject of certainty. In essence both principles boil down to the statement that some measurements can never be precise and some systems cannot ever be proved completely without resorting to proofs outside of the system. These limitations were not known until quite recently. Now, I am not saying that genealogy is very much like mathematics, but there are several concepts that suggest similarities.

It has only been quite recently that a large mass of genealogical data has been created in centralized repositories and made reasonably available. Historically, genealogists had to focus their efforts entirely on a smattering of records scattered pretty uniformly all over the world. Those large centralized data accumulations, such as the libraries of the Genealogical Society of Utah (i.e. the Family History Library in Salt Lake City, Utah), the New England Historic Genealogical Society and others were only accessible if you had the time and the resources to travel to the library itself. Now today, most of these scattered collections still exist, but technological changes have made untold millions of records accessible for free or for a moderate cost. For example, even with the advent of microfilmed records, obtaining access to the microfilm could be a slow and inefficient process. You could only guess from the microfilm's catalog description if it might contain information about your ancestors and it was very disappointing to order a film, wait until it appeared and then find that it had no useful information.

Most recently, advancing technology has resolved some of the microfilm issues by making the images available in digital format online. But the changes being wrought by technology are more basic than just increasing genealogical record availability. The vast accumulations of genealogical source records and online family tree entries are pointing out some ultimate limitations on accuracy and completeness. Ultimately, these physical limitations of the system will be the most significant barriers to genealogical research.

The effect of the accumulation of massive genealogical data concentrated online and available to huge numbers of people who, previously, would never of had such access is starting to reveal the fundamental limitations in the overall system. The most evident of these limitations is the level of accuracy of the overall system. Researchers are becoming painfully aware of the inconsistencies and contradictions contained in the accumulation of records. You can rail against the inconsistency, but as we accumulate more and more sources and records, the fact that there are such inconsistencies becomes more and more apparent. For example, it my knowledge of my ancestors was limited to one source, perhaps a surname book or a pedigree chart from a relative, I had one version of my ancestral history. Today, we can have hundreds or even thousands of versions. It is not just the compiled family tree records that are at fault, the very documents we refer to as sources are inconsistent and vague. There are few days that go by that I do not hear the complaints about the inaccuracy of the system.

What is less apparent is that there is an ultimate limit to our accuracy. No matter how careful we are and no matter how experienced, we will encounter inconsistency. We will be forced to choose between different dates, places and even different people. It is not that the records are unreliable, it is just that we now have access to multiple versions of the same types of records and multiple records that were either previously unavailable or impossible to obtain. Even if we resort to the time honored "proof statement," in many more cases we will be forced to admit that the conflicting evidence cannot be reconciled. We have found our own genealogical uncertainty principle, the limit of our ability to prove our ancestry.

But there is an even deeper issue. That is that genealogy, as such, is incapable of even defining itself. This is similar, in some ways, to the limits imposed by the theorems postulated by Kurt Gödel. By analogy, genealogy can never be completely defined or complete. In saying this, I am expressing a physical certainty. There will always be more records, but the search for absolute proof will never be complete. We cannot even come up with an adequate definition of "genealogy," much less come to a universal agreement as to what constitutes an adequate proof.

We can wring our collective hands over these limitations but they are physically imposed by the system we have collectively created. Genealogy will always be uncertain and incomplete. 


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