The Decay of C-Decay
by Robert P.J. Day
[Originally appeared in the OASIS Newsletter, 385 Main Street, Beaverton,
Ontario, Canada L0K 1A0]
"If you propose that the universe and all in it is the product of an act of
creation only 6-7000 years ago, many people ask - "How is it that objects
millions of light years away can be seen? Surely such light would take
millions of years to reach us." [B. Setterfield, "The Velocity of Light and
the Age of the Universe, Part 1," Ex Nihilo, vol. 4, no. 1, 1981]
The 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 ,
June 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 his novel h of "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
After supplying all of 41 selected data points representing
measurements of csince 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
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
Realizing that a simple way to check his work would be to analyze
the value of cduring 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
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 10^9 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
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,
r^2, 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 r^2 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. X^2] 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 X^2 value mentioned is actually the statistical
"chi-squared" measure, the question is actually rather meaningless.
Rather than recognizing this, Setterfield responds that, "X^2 is the same
as r^2 in the article," which it most certainly is not. Setterfield then
emphasizes the same statistical nonsense contained in the original article
with, "This r^2 is the 'Co-efficient of Determination' which tells how
accurately the proposed curve fits the data. If the fit is perfect the
value of r^2 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 r^2 value of 1.000 to nine significant figures. I am
therefore satisfied that the postulated curve fits the observed data beyond
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
Having taken quite a pounding until then regarding his statistical
analysis, Setterfield begins by defining his 'Co-efficient of
Determination,' r^2, and its relation to the standard correlation
coefficient. He follows this up by again (correctly) explaining the
significance of an r^2 value of 1, but finally twigs to the many objections
by adding, "It was subsequently noticed that [the r^2 value] had been
obtained at an incorrect point in the computer programme, and a check
gave the value as r^2 = 0.99+ which appeared in the International
(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 r^2 downward to 0.986 based on, of all things,
correspondence from readers who calculated it for themselves. In all, five
different values for r^2 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
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
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 re-working and re-analysis, pre-war determinations are now
mainly of historical interest."
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