The Decay of c-decay

by Robert P. J. Day

Copyright © 1997-2003

[Article: 1997]

[Links updated: July 22, 2003]

[Originally appeared in the OASIS Newsletter, 385 Main Street, Beaverton, Ontario, Canada L0K 1A0]

he above quote is, to my knowledge, the first salvo by Australian creationist Barry Setterfield regarding his hypothesis of "c-decay," the notion of the decreasing speed of light that has been used for years as evidence for a young universe. Setterfield's hypothesis, while initially embraced by the majority of the creationist community, received heavy criticism from the scientific establishment for several years since its introduction in 1981, and was finally rejected by the creationists themselves after it became such a major embarrassment that even the San Diego-based Institute for Creation Research rejected it (Acts and Facts , May 1988, G. Aardsma).

While the creationist camp would have us believe that the theory of c-decay represented a viable scientific alternative to uniformity, and collapsed only under recent, more intense scrutiny, the thrust of this article is to show that the theory was riddled with massive flaws and glaring contradictions from the very start, and was kept alive as long as it was solely by wishful thinking and grotesque deception on the part of its supporters (a sort of Australian Paluxy River, if you will).

The initial hint of trouble in Setterfield's work is found in his very first article, from which the quote above is extracted. In addition to Setterfield's reference to "an act of creation only 6-7000 years ago," he states that one of his goals is to reconcile "the observational problems of astronomy and Genesis creation ...". Setterfield's religious motivation is now clear, and if his revised figure for the age of the universe just happens to match the now-discredited chronology of Bishop Ussher (about 6,000 years), it would probably not be a coincidence.

As Setterfield states, "The basic postulate of this article is that light has slowed down exponentially since the time of creation," making it clear that he intends to show not only a decay in the value of c, but an exponential decay.

After supplying all of 41 selected data points representing measurements of c since 1675, Setterfield claims to have found the one and only curve that adequately fits these particular points and that must represent the behavior of the value of c. In Setterfield's precise words (words that will come back to haunt him), "There was only one curve tried which fitted the data points exactly and reproduced all of the observed features. Its general form is a log sine curve, with a logarithmic vertical axis...". Note Setterfield's insistence on a unique curve to explain the data, and the fact that this curve reproduced all of the "observed" features; these claims become of major import later.

With his "unique" solution for the curve-fitting problem in hand, Setterfield concludes that the date of origin equals that at which the value of c, as represented by the curve, goes to infinity. To no one's surprise, this date is given as "4040 B.C. +/- 20 years... the time of creation/fall." It is here that Setterfield's case descends into absurdities.

Realizing that a simple way to check his work would be to analyze the value of c during the last 20 or 30 years (when highly accurate values became available), Setterfield introduces "the cutoff date beyond which there is a zero rate of change," and confidently states that, "From these observations it would seem that beyond 1960 the speed of light had reached its minimum value and was constant thereafter," thereby denying anyone the chance to perform their own modern, more accurate measurements.

In order to justify such a convenient property for his unique curve, and knowing full well the objections such a claim would produce, Setterfield says, "This conclusion raises the obvious difficulty as to how one verifies a process which has occurred in the past but is not occurring in the present. To answer this, we would point out that the curve is solely dependent on actual observations ...," again emphasizing the dependence on observed values, and observed values alone.

The above rather questionable mathematical machinations are almost acceptable, in view of Setterfield's next unbelievable act. Having used some rather dubious analysis to determine the "unique" curve that must fit the data, Setterfield then describes the curve as "virtually asymptotic, but a very good estimate of the actual initial value is given by the curve at one to one and a half days from its origin."

What Setterfield has done here is to decide that the value of c does not follow his "virtually asymptotic" curve all the way back to infinity at the time of creation, but that it levels off at T-plus-one-day or so, for no apparent reason and in blatant violation of his insistence on "observed values." But Setterfield is not finished yet.

He then proposes that this value does not just remain constant from time zero for the first day and a half until it encounters his magic curve, but stays fixed for several days thereafter, extending past the curve. As justification for this proposal, Setterfield abandons science entirely and descends fully into Christian apologetics, stating, "I will assume that this value held from the time of creation until the time of the fall, as in my opinion the Creator would not have allowed it to decay during His initial work." Given Setterfield's hypothesis that the speed of light begins significantly below the curve, then extends beyond and above the curve, one wonders what the purpose of the curve is in the first place.

The question of why Setterfield is so anxious to mutilate his solution as described above is answered in the next paragraph, "Integration over the curve shows that the initial problem of light travelling millions of light years in only 6000 years, is solved ... The total distance travelled ... would be about 12 x 10⁹ light years." Again in violation of his insistence on satisfying only the observed values, Setterfield now requires that the area under the curve represent an approximation to the commonly-accepted age of the universe, another contrived property that he will later use to reject alternate curves that fit his particular data at least as well as his own solution.

It is not hard to see that Setterfield is capable of producing almost any area under the curve he wishes, by choosing a time during the first "creation" week to produce his constant value for the week; in his case, the arbitrary choice of one and a half days after creation produces the value he needs.

The final blow to Setterfield's credibility is his statistical analysis of the results, given in Appendix 3, in which he discards 3 of the 41 data points shown in an earlier table, and claims a coefficient of determination r² of "1 to nine significant figures, indicating a near perfect fit to the data" (emphasis added). As anyone with even the most basic knowledge of analysis will know (and as Setterfield will later learn the hard way), a coefficient of determination of 1 can only be realized if the data points lie precisely on the curve in question, yet Setterfield shows a pathetic ignorance of this fact by following the above claim with, "All told, 17 values were above the curve and 21 below, the r² value indicating a perfectly balanced distribution of the cluster of points as well as close proximity to the curve."

In fact, as Setterfield openly admits, not a single data point of the 38 considered lay on the curve, yet this does not prevent him from claiming a perfect correlation.

The reaction to the many howlers listed above from Setterfield's initial article was depressingly predictable; creationists fell over themselves praising the work, while the scientific community practically wet themselves in hysterical laughter, then proceeded to give Setterfield's research the shellacking it so royally deserved.

A letter to the editor in the very next issue of the journal asked, "Have statistical tests [e.g., X²] been applied to the fit of the data to the postulated curve of decrease in the velocity of light? If so, with what result?" Assuming that the X² value mentioned is actually the statistical "chi-squared" measure, the question is actually rather meaningless.

Rather than recognizing this, Setterfield responds that, "X² is the same as r² in the article," which it most certainly is not. Setterfield then emphasizes the same statistical nonsense contained in the original article with, "This r² is the 'Co-efficient of Determination' which tells how accurately the proposed curve fits the data. If the fit is perfect the value of r² is 1.000000000," which is of course utter rubbish since not a single point actually lay on the curve.

Setterfield provides some unintentional hilarity by adding, somewhat gratuitously, "The DEC 10 computer at Flinders University decided that the published curve had an r² value of 1.000 to nine significant figures. I am therefore satisfied that the postulated curve fits the observed data beyond any doubt."

As a doctoral student in computer science, I must admit to some amusement regarding the image of a computer "deciding" what the correct answer is when this answer is so obviously wrong. Perhaps it really is the computer's fault after all. Bad computer, baaaaaaad computer. (As a side note, the other half of the page containing the above describes the genetic variation in dogs as "devolution, a downward trend in efficiency," and concludes that, "The fall affected dogs and man. [ Romans 8:20-21]" One has to wonder whether the poor dogs should be held responsible for original sin. But I digress. Onward.)

After several critical letters to the editor regarding Setterfield's work, stressing particularly the suspicion of carefully selected data, Setterfield was finally forced into some damage control. In vol. 5, no. 3, Setterfield's article, part two (b) has the revealing subtitle, "Using all measurements of c."

Having taken quite a pounding until then regarding his statistical analysis, Setterfield begins by defining his 'Co-efficient of Determination,' r², and its relation to the standard correlation coefficient. He follows this up by again (correctly) explaining the significance of an r² value of 1, but finally twigs to the many objections by adding, "It was subsequently noticed that [the r² value] had been obtained at an incorrect point in the computer programme, and a check gave the value as r² = 0.99+ which appeared in the International Edition."

(This value, unfortunately for Setterfield, turns out to be wrong as well. In a later publication of the same journal, Setterfield again revises his value of r² downward to 0.986 based on, of all things, correspondence from readers who calculated it for themselves. In all, five different values for r² were published.)

At this point, one might almost give Setterfield the benefit of the doubt and accuse him only of gross incompetence and mathematical illiteracy, but the saga does not end just yet. A cursory examination of Setterfield's data on which his curve is based reveals that the exact formula for the curve is heavily dependent on two values from the 17th and 18th century, and it behooves us to ask just how much confidence we can place in values this old, or whether Setterfield has even recorded the values properly.

The very first value in his table, dated 1675, is credited to Romer and is listed as 301,300 plus or minus 200 km/sec. According to Setterfield, "'Sky and Telescope' June '73 45:353 gave Romer's 1675 value after reworking a selection of his data. The result was 0.5% above the current value i.e. 301,300. Froome & Essen placed it higher. The minimum value was used." The first question is how, given two conflicting values, Setterfield could arbitrarily choose between them, or whether he should choose either of them. The next issue is considerably more serious.

The referenced article in Sky and Telescope is actually a short summary of a full article by Goldstein, Trasco and Ogburn in the Feb. 1973 issue of The Astronomical Journal.

Why Setterfield chose not to refer to the original article is unclear, but there is little doubt that this is extremely unprofessional behaviour, although this is insignificant compared to what one finds upon reading the original article. After considerable mathematical analysis, the three authors conclude, "... we estimate that the difference between light travel time three hundred years ago and today's value is less than 0.5%" (emphasis added). In fact, the authors plot a set of residuals against light travel time and state, "The best fit occurs at zero where the light travel time is identical to the currently accepted value value," completely contradicting the value in Setterfield's table. In short, the 1675 value is completely fictitious and is based on deliberate misrepresentation.

Precisely this accusation was made by a Mr. R. Holt in a letter to the editor in the vol. 1, 1984 issue of the creationist journal EN Tech. J. (apparently an abbreviation for Ex Nihilo Technical Journal, although every effort is made to conceal this). Holt minced no words and described the 1675 value as "not only erroneous, but entirely unsupported by his references and contrary to the actual data." Setterfield's response was that the reference "... was not a direct use of the Goldstein et al result." If this is true, what was the point of using an indirect reference to the article in the first place, if not to use its results?

Setterfield further justifies the value with, "What was done was to take the Froome and Essen value of 303,000 km/sec with its error margin of 2,000 km/sec and the error limit of the Goldstein et al re-working of 1,500 km/sec above the present value and reconcile the two authorities by taking the common ground of 301,000." Ignoring the fact that the original value is listed as 301,300, and not 301,000, this method clearly has no value whatever, and completely avoids the fact that the Goldstein conclusion is that the value of c has not changed. How the Goldstein paper can be used in support of a value of c 0.5% higher than the current value is a total mystery, and testifies to Setterfield's lack of integrity in his research.

There is little doubt that the above glaring flaws and outright dishonesty on Setterfield's part would cause the immediate rejection of his material by any reputable and well-refereed journal, and it seems unnecessary to continue the dissection. There is, however, one final issue that deserves some mention.

Although the final blame for the early work must rest ultimately with Setterfield, it seems that the editors of the Australian creationist journal Ex Nihilo are not without fault as they seem to be just as capable of misrepresentation as the authors of the articles they publish. A rather blatant example of this is found in vol. 6, no. 4 of the journal, on a page entitled "on what's being said about Barry Setterfield's work on the Speed of Light."

Amidst glowing reviews from noted creationists such as Thomas Barnes, Walter Brown and Setterfield's collaborator Trevor Norman, there are two testimonials from Dr. Barry Tapp and Dr. Peter Cadusch, both faculty members at institutes of technology in Australia. While the quotes attributed to them appear to represent positive support for Setterfield's work, inspection of the original letters to the editors show that they are based on a ludicrous misrepresentation of both individuals.

Tapp is quoted as stating that, "The values of c determined between 1870 and 1940 do show a definite decay patterning." In fact, Tapp's exact words were, "The values for 'c' determined between 1870 and 1940 do however appear to show a definite 'decay' patterning." It is already unconscionable that the editors cannot seem to faithfully reproduce a single line of text.

The case of Cadusch is far more serious. Cadusch is quoted as saying, "Despite extensive reworking and analysis, these determinations [of c prior to 1940] cannot be harmonised with today's values." The accuracy of this quote is so poor, it is laughable. Cadusch's actual words, as given on p. 81 of that issue, are, "The sudden change of measured c after the war has already been commented on, and current feeling seems to be that, despite extensive reworking and re-analysis, pre-war determinations are now mainly of historical interest."