Science in Christian Perspective



Information Theory and Biblical Inerrancy

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From: PSCF 39 (September 1987): 168-170.

"Biblical inerrancy?" an acquaintance of mine once scoffed. "For ancient documents of which numerous copies now exist with thousands of textual variations? From the scientific viewpoint, the very concept is absurd!"

But the speaker was not a scientist, and he was wrong. Even more interesting-perhaps even surprising to many Christians-the fact that he was wrong can be demonstrated on the basis of the modern, rigorous science of information theory. Join me for a few minutes on a logical journey that examines the concept of biblical inerrancy' from this point of view.

We begin by asking the question of whether information can ever be inerrantly transmitted from a sender to a recipient, and if so, under what conditions? An immediate and fairly obvious answer is: "Yes, in the absence of noise whose magnitude and character interfere with the transmission of the message." When such noise is present, however, errors result.

Consider an example. Frank and John are attending a football game with three other friends. During the game, Frank goes to the refreshment stand about a hundred feet away from their seats to get a hot dog. While he is there, John calls to him from his seat, asking him to bring some refreshments for himself and the other three men. He then proceeds to shout the items and quantities that each man wants. This is a classic case of the attempted transmission of information in the presence of disruptive noise. John is the Sender, Frank is the Recipient, and the hundred feet of space between them in the football stadium is the channel of transmission, filled with noise coming from the public address system and the thousands of other spectators in the stadium-noise whose magnitude is equal to, or greater than, the amplitude of John's shouts in Frank's ears. Small wonder if Frank comes back with the wrong items.

A similar situation exists in the attempted transmission of information by radio signals over great distances, especially between space vehicles and earth stations. The relatively low-power signals travelling thousands or millions of miles between the transmitter and receiver are just as vulnerable to disruption by the incessant electromagnetic noise that pervades space and the earth's atmosphere as a human voice trying to shout to someone a hundred feet away over the din of a crowded football stadium. Inevitably, the recipient receives a distorted sequence of message elements from that which was emitted by the sender/ transmitter.

Is inerrancy of transmission still possible under such difficult conditions? Surprisingly, the answer is: Yes! This remarkable fact was mathematically demonstrated in 1948 in what is known as "Shannon's theorem," enunciated by Dr. Claude E. Shannon of Bell Laboratories in New Jersey. It states essentially that if the amount and character of the noise in a given channel are known, then a system of encoding can be devised which, when utilized, will make possible virtually error-free transmission of information between originator and recipient .2 Techniques based on this theorem are now commonplace in the encoding and transmission of information in a variety of applications, particularly between space vehicles and earth stations. They guarantee essentially inerrant transmission via relatively low-power signals over vast distances, in spite of the presence of noise whose magnitude and character would otherwise make such inerrant transmission impossible.

One interesting consequence of this theorem is that inerrancy does not demand that the sequence of signals received by the recipient be identical to the sequence emitted by the sender. In the simplest kind of example, suppose the sender emitted a sequence of 100 binary digits containing information about the magnetic field vector, at a certain time, at a certain point in space between the earth and the planet Jupiter. It is possible that the sequence of digits received by the earth station may differ from that emitted by the space vehicle at several points, and yet the information contained in that message would be inerrantly received, providing the information was properly encoded prior to transmission (and decoded following reception).' It is even possible that earth stations at widely-separated locations on the globe would receive sequences of digits differing from each other at several points, as well as from the distant transmitter, and yet each recipient would receive the information inerrantly. In other words, here we have inerrancy in spite of textual variations, within the rigorous mathematical framework of modern information theory.

The logic of Shannon's theorem is independent of the mode of communication in question. It applies in principle to all methods by which information can be transmitted from sender to recipient (s)'-whether by electromagnetic waves propagated through space or by successive copies of written documents propagated through human history-which brings us to the Bible.

The Bible, by its own witness, consists of an ensemble of messages emitted by its originator, God, into the noisy channel of human history. Clearly, its divine Originator knew the character and magnitude of the noise in the channel of transmission when He composed the messages in the ensemble. Equally clearly, He would have no difficulty encoding the information in this ensemble of messages in such a way that it could be inerrantly received by every intended recipient, in spite of the effects of the noise upon its individual message elements-that is, in spite of scribal errors, editorial or redactional emendations, or any other occurrences that would cause the text viewed by the recipient to differ in some ways from the text originally committed to the channel of transmission. Indeed, two or more recipients possessing texts differing from one another at various points could still inerrantly receive the same information, because these variations would not nullify the error-free character of the transmission.

An interesting consequence of this is that it demands verbal inspiration of the original documents, even though we need not possess verbally-inerrant copies of those documents today. In order to achieve error-free transmission of information, God must have encoded the original documents in the form that would accomplish His purpose, rather than leaving that form up to the unguided control of the human authors, before committing them to the channel of human history. This does not, however, imply that He must have obliterated the humanity of the human authors in the process, or reduced them to the status of mere dictating machines. Being omnipotent and omniscient, He surely had access to ways of guiding the human authors to produce documents encoded in conformity with His purposes, while still allowing them to retain and express their full humanity in the process.

The thesis of this paper, then, is simply this: the existence of a finite amount of textual corruption in the biblical documents as we possess them today does not, by itself, rule out the possibility of its originally encoded information being communicated inerrantly to its readers, in a way analogous to that in which information about magnetic fields (and other data) at different points in the solar system is routinely communicated inerrantly to scientists here on earth-in spite of the "textual corruption," due to electromagnetic noise, of the signals carrying that information between space vehicles and the earth. In other words, to return to the phrase used in the first paragraph of this article, the idea of biblical inerrancy is not, from the scientific viewpoint, absurd. On the contrary, it is quite reasonable.

One result of this thesis is to suggest a viable alternative to the doctrine of the Bible's inerrancy as consisting of inerrancy in the autographs (original manuscripts) only. George Mavrodes, in his article "Science and the Infallibility of the Bible" in the September 1967 issue of JASA, coins the term "A- Infallibility" to denote this formulation, and demonstrates by logical analysis that it leads to the conclusion that "the reliability of the science of textual criticism places a limit on the reliability of any information now derivable from the Bible."' If, however, the type of inerrancy that the Bible possesses is not "A-Infallibility," but rather the type which is described in the present paper, which we might abbreviate as "I-Inerrancy" or Informational Inerrancy, then the reliability of the information now derivable from the Bible is not limited by the science of textual criticism .6

This new view of biblical inerrancy (1, at least, have not seen it proposed anywhere else) will obviously not resolve all difficulties connected with the interpretation of the Bible. It may serve as a starting point for further new and fruitful explorations into the way God speaks to us through it.

Most of all, I hope that it may contribute to a recognition among Christians that the concept of biblical inerrancy is not something about which we, in our modern, scientific age, are forced to equivocate or hedge, as if it were akin to some sort of medieval superstition or a product of ignorance and naivet6 regarding the science of communication. This is not to claim that information theory can be used to "prove" biblical inerrancy. Because of the unique character of the data involved compared to usual scientific categories, the question of such proof lies far outside the bounds of scientific disciplines. It is only for us to recognize that the idea of such inerrancy is, in the light of modern communication theory, not only wholly plausible and achievable, but already a practical reality in a number of fields of human endeavor. Surely there is no absurdity in ascribing to God a feat which, far from being logically impossible, is now routinely accomplished by human beings (though on a more modest scale) over and over again.


1. Beneath much of the debate over the "inerrancy" of the Bible, one senses a lack of agreement over what really is the definition of that term. I would advocate its definition simply as accuracy. Data that is accurate is ipso facto data that is not in error, i.e., "inerrant." I am aware that others may feel that this definition does not adequately express some aspects of the traditional concept of biblical inerrancy. I believe, however, that it adequately conveys the meaning of that concept as found in the Scriptures themselves.

2. C. Shannon, The Mathematical Theory of Communication (Chicago: University of Illinois Press, 1949), pp. 70-72. As is often the case when a highly technical subject is presented in general language, there is some over-simplification in this statement of Shannon's theorem, which does not, however, nullify the implications drawn from it in this article. The theorem is true with qualifications related to such things as the entropy of the source, the capacity of the channel, the amplitude of the noise, and the power of the signal carrying the information. Also, the frequency of errors cannot be reduced completely to zero, but it can be reduced to a negligible, essentially infinitesimal, magnitude.

3. Readers may wonder what kind of encoding method could accomplish this. Basically, it is achieved through redundancy, i.e., using more symbols than the minimum necessary to express the information, Frequently, the additional digits function as parity checks, i.e., specifying whether the sum of a block of digits was odd or even. For an example of such encoding, see Shannon, op. cit., p. 80. In addition to the book by Shannon, cited in the previous footnote, this subject is well-presented for the interested general reader in J.R. Pierce, Symbols, Signals and Noise (New York: Harper, 1961), chapter VIII.

It is interesting, although beyond the scope of the present paper, to conjecture how the Bible as we now possess it might give evidence of being the product of such encoding methods. Certainly it is filled with redundancy: Deuteronomy duplicates much of the contents of Exodus, Leviticus and Numbers, and I and II Chronicles duplicate much of I and II Kings. There is much duplication of contents among the first three Gospels, and even some when they are compared with the Fourth Gospel. There is redundancy in the Psalms, the Proverbs, and the New Testament Epistles. The question of whether there is something in the Bible that functions in a manner analogous to parity-checking is more speculative.

A significant consequence of this is that proper decoding of the information requires processing of the entire ensemble of code-elements in order to receive the full benefit of the effect of the redundancy. If some of the code-elements of the received message are omitted or ignored during the decoding process, inerrancy is lost. This implies that the information contained in the Bible can only be inerrantly decoded if one processes the contents of the entire Bible, and not just part of it. Drawing conclusions from a consideration of only part of the Bible has certainly been one of the major causes of error during the two-millenium history of Christianity. It is significant that Psalm 119:160 says, "The sum of Thy Word is truth."

4. Warren Weaver says in the introductory essay to Shannon's previously cited book: "This is a theory so general that one does not need to say what kinds of symbols are being considered-whether written letters or words, or musical notes, or spoken words, or symphonic music, or pictures. The theory is deep enough so that the relationships it reveals indiscriminately apply to these and to all other forms of communication." (Shannon, op. cit.7 p. 25.)

5. George I. Mavrodes, "Science and the Infallibility of the Bible," Journal of the American Scientific Affiliation, Vol. 19, No. 3, Sept. 1967, pp. 90-92.

6. It is recognized that there is another problem still to be dealt with, namely, the character and integrity of the decoding process by which information is actually derived from the ensemble of message-elements. In other words, errors may still be introduced into the information actually derived from the Bible, but if they are the fault is to be traced to the decoding processes that we are using to derive the information, not to the character of the biblical texts themselves. The same kind of errors would result, for example, if the computers here on earth were incorrectly programmed to process the signals received from distant space vehicles.