The obvious place to start is with the fundamental assertion of the book Origin and Destiny of the Earth's Magnetic Field by Thomas G. Barnes, I.C.R. Technical Monograph No. 4, copyright July, 1973, by the
Institute for Creation Research. Barnes earned an A.B. degree in physics from Hardin-Simmons College, that the Earth's magnetic field is exponentially decaying. If this turns out to be untrue, or unsupportable, then Barnes' entire thesis is immediately nullified. So the next most obvious thing to do at this point is to present the reader with the data. These data, which follow in my table 2, are taken from Barnes (pages 33 & 61). Barnes in turn credits the ESSA report of McDonald & Gunst [
5] as his source. I once saw a copy of that report, but am not able to find it now. I presume that Barnes can copy, and that the data are as given in [
5]. In any case, these are the data that Barnes presents in defence of his own thesis, so the enterprising reader can examine the data as they see fit, in order to gauge compliance with the exponential decay hypothesis. Multiple values for one year indicate separate determinations, reported in separate original references. Those references are given by Barnes, but I have omitted them here.
Table 2
Dipole Magnetic Moment Data
From Barnes Pages 33 & 61 Year Dipole Moment
(× 1022 amp-meter2)1835 8.5581845 8.4881880 8.3631880 8.3361885 8.3471885 8.3751905 8.2911915 8.2251922 8.1651925 8.1491935 8.0881942.58.0091945 8.0651945 8.0101945 8.0661945 8.0901955 8.0351955 8.0671958.58.0381959 8.0861960 8.0531960 8.0371960 8.0251965 8.0131965 8.017Before we go any farther, the attentive reader should have already spotted at least one problem. This table does not show any experimental uncertainties associated with any of the data points. This is the manner in which Barnes presents the data, and nowhere in his book is the subject of experimental uncertainty mentioned at all. I have not seen the McDonald & Gunst paper in preparing this article, so I cannot say whether or not they presented the data without uncertainties as well, but if they did, then their own argument suffers from the omission just as Barnes' argument does here.
From these data Barnes has determined that the Earth's magnetic field is decaying exponentially. Throughout his book, whenever he mentions this exponential decay, he points the reader to section II-D, page 36 to view the justification. On that page of his book, he justifies the exponential decay conclusion as follows, the emphasis is mine. B0, as referred to by Barnes, is the equatorial magnetic field strength, which is included in his tables, but omitted from mine.
"When values of the magnetic moment, M, in table 1 are plotted against time, t, on semi-log coordinate paper, the points lie approximately on a straight line, as one would expect for an exponential decay of the Earth's magnetic moment. This is also true, of course, for a plot of B0 against t. We therefore assume that the decay is exponential and write ... "
This, of course, is no justification at all. Barnes simply assumed that the decay was exponential. However, later in the book, at the beginning of section IV, page 52, Barnes makes a slightly more heroic attempt to justify the exponential decay theory as follows:
"All data were processed on a CDC3100 electronic computer. A least square exponential fit was employed to evaluate the time constant. As a separate check it was noted that the variability was smaller for this exponential fit than for a straight line fit, as one would expect from the exponential solutions obtained from Maxwell's equations."
In these two passages we see the full and entire text of the justification for deriving an exponential decay from the tabulated data. Anyone reading this who has had experience with numerical approximations, data curve fitting, and etc. should be able to recognize at once that the argument is very poor. First, it should be obvious that one cannot perform an unweighted fit, completely ignoring any experimental uncertainties. The early data from the mid 1800's, which are derived from experimental methods that are far less accurate and precise than modern methods, necessarily have much larger uncertainties associated with them, and should be weighted accordingly in any attempt to fit the data to a curve. Second, Barnes' reference to the "variability" of the exponential versus straight line fit is highly ambiguous. Is "variability" supposed to mean "variance"? If the variance of the fit is greater than the experimental uncertainties, then the line and exponential cannot be distinguished, in fact, one from the other. And what does "smaller" mean? Was the difference in variance between the two fits (if that is what "variability" means) significant or not? These kinds of curve fitting exercises are fraught with peril, and relying on the difference in variance between fits, where it is obvious that in fact either an exponential or a straight line will produce a "good" fit, is an exceptionally unreliable procedure.
Even without a plot, just by looking at the data tabulated above, the reader should be able to see that the moment values since 1935 appear essentially flat around a value of about 8.047 +/- 0.029, while the data prior to 1935 show a clear downward trend. One could easily argue that two straight lines fit the data better than one, and even better than one exponential (this is an exercise that I have not undertaken, but the motivated reader is welcome to see if my intuition is trustworthy). That fact alone will easily explain why a single exponential will fit the data better than a single straight line, as the slight curve of the exponential can better approximate the kink in the data. These considerations make it extremely difficult to use the data alone as an a-priori justification for any particular curve fit over another. In fact, one could over interpret the data even to the extent of claiming that the field was in decay until about 1935, when it then stopped decaying.