One of the more pathetic examples of bad math from the creationist camp is an argument based on the
claim that the sun is shrinking. This argument has been [thoroughly
debunked](http://www.talkorigins.org/indexcc/CE/CE310.html) by other folks, so I haven’t bothered to
add my two cents here at GM/BM. I hadn’t heard anyone mention this old canard until
recently, when a reader wrote to me to ask if I could comment on it. I *hate* to disappoint
my readers, and this is *such* a great example of flaming bad math, so I figured what the heck. So hang on to your hats, here it comes!
There are a lot of [different](http://www.answersingenesis.org/creation/v11/i2/sun.asp) [variants](http://www.evcforum.net/cgi-bin/dm.cgi?action=msg&f=2&t=138&m=1) of [this](http://www.creationism.org/ackerman/AckermanYoungWorldChap06.htm) [argument](http://www.icr.org/index.php?module=articles&action=view&ID=165) out there. There are two main forms of this argument; there’s one version that focuses on extrapolating measurements of
the sun, and the more complicated one that adds in an explanation of the shrinkage and tries
to use neutrino measurements as a support. I was going to cover both in this post, but it was getting way two long, so in this post, I’m going to stick to the first naive argument, and then in my next post, I’ll cover the second.
So, let’s take a look at an example of the measurement argument. Here’s one
from that paragon of good science, the [Institute for Creation Research](http://www.icr.org/index.php?module=articles&action=view&ID=165), titled “The Sun in Shrinking”. This is very typical of the naive measurement argument: it doesn’t worry about the *cause* of the alleged shrinkage of the sun, but instead just focuses on estimating a rate of shrinkage, and using that to create a bound on the age of the earth.
>Does the size of the sun change over the years? Recently, “John A. Eddy (Harvard -Smithsonian Center
>for Astrophysics and High Altitude Observatory in Boulder) and Aram A. Boornazian (a mathematician
>with S. Ross and Co. in Boston) have found evidence that the sun has been contracting about 0.1% per
>century…corresponding to a shrinkage rate of about 5 feet per hour.”1 The diameter of the sun is
>close to one million miles, so that this shrinkage of the sun goes unnoticed over hundreds or even
>thousands of years. There is no cause for alarm for us or for any of our descendants for centuries
>to come because the sun shrinks so slowly. Yet the sun does actually appear to shrink. The data Eddy
>and Boornazian examined spanned a 400-year period of solar observation, so that this shrinkage of
>the sun, though small, is apparently continual.
>What does the shrinkage of the sun have to do with creation and evolution? The sun was larger in the
>past than it is now by 0.1% per century. A creationist, who may believe that the world was created
>approximately 6 thousand years ago, has very little to worry about. The sun would have been only 6%
>larger at creation than it is now. However, if the rate of change of the solar radius remained
>constant, 100 thousand years ago the sun would be twice the size it is now. One could hardly imagine
>that any life could exist under such altered conditions. Yet 100 thousand years is a minute amount
>of time when dealing with evolutionary time scales.2
>How far back in the past must one go to have a sun so large that its surface touches the surface of
>the earth? The solar radius changes at 2.5 feet per hour, half the 5 feet per hour change of the
>solar diameter. The distance from the sun to the earth is 93 million miles, and there are 5,280 feet
>in one mile. Assuming (by uniformitarian-type reasoning) that the rate of shrinkage has not changed
>with time, then the surface of the sun would touch the surface of the earth at a time in the past
>equal to t = (93,000,000 miles) (5,280 ft/mile) (2.5 ft/hr) (24 hr/da) (365 day/yr)
>or approximately 20 million B.C. However, the time scales required for organic evolution range from
>500 million years to 2,000 million years.3 It is amazing that all of this evolutionary development,
>except the last 20 million years, took place on a planet that was inside the sun. By 20 million
>B.C., all of evolution had occurred except the final stage, the evolution of the primate into man.
>One must remember that the 20 million year B.C. date is the extreme limit on the time scale for the
>earth’s existence. The time at which the earth first emerged from the shrinking sun is 20 million
>B.C. A more reasonable limit is the 100 thousand year B.C. limit set by the time at which the size
>of the sun should have been double its present size.
>A further word of explanation is needed about the assumption that the rate of shrinkage of the sun
>is constant over 100 thousand years or over 20 million years. The shrinkage rate centuries ago would
>be determined by the balance of solar forces. Since the potential energy of a homogeneous spherical
>sun varies inversely with the solar radius, the rate of shrinkage would have been greater in the
>past than it is now. The time at which the sun was twice its present size is less than 100 thousand
>B.C. The time at which the surface of the sun would touch the earth is much less than 20 million
>B.C. Therefore, the assumption of a constant shrinkage rate is a conservative assumption.
A good summary of this argument would be: *Measurements show the sun’s radius growing smaller at a rate of 2.5 feet per hour. If we extrapolate from that rate of contraction in the most conservative way, we find that the earth would have been inside the sun no more than 20 million years ago. Therefore, all of the arguments about geology and biology that talk about hundred-million-year timescales must be wrong, because the earth can’t possibly be more 20 million years old.*
There’s a whole lot wrong with this argument.
First of all, it’s based on lousy data. Numerous careful analyses of measurements of the sun show a basic periodicity about the sun’s size – a periodicity of about 80 years. We’ve got about 400 years of measurements of the sun; but those older than about 150 years are *highly* questionable in their accuracy. Even if we focused on the last 150 years, the accuracy of the earlier measurements are much less precise than the more recent ones. There’s so much noise in the the data that it’s very difficult to draw too much of a conclusion.
The original versions of the shrinking sun argument relied on less than 100 years of data – if you take the most precise group of measurements, spanning the last fifty years, you can see a nice declining trend – because you’ve selected the data from the downside of the cycle. It’s a standard
bad math trick: select the data that matches your conclusion, and then say that the data you selected proves your conclusion.
When scientists studying the sun did more careful detailed analysis, and showed that the size of the sun actually varies in a cyclic way, the creationists tried to refine the argument. Using the 400 year data, they try to make the case that while there is a cyclic pattern, the cycle is superimposed on a longer-term linear trend.
That’s where things get a little bit interesting. If you accept the idea that the data from the last 400 years is accurate enough to be able to precisely recognize trends, what you get *does* look like a *very small* decrease. The question is: what does that mean? Is it reasonable to suppose that it’s
part of a basically monotonic decreasing trend?
And the answer is: I don’t know.
You see, the bare measurements of something like this just aren’t enough. Given the kind of data we have, you can do curve-fitting to it in any number of ways: you can fit a sine curve to it, or a line, or a logarithmic curve, or a curve asymptotic to a line at a minimum size… Any of those
possibilities *can* fit the data. You need to propose an explanation, and show *what* that explanation predicts, and then see how well the predictions match the measurements.
Let me demonstrate what I mean. Suppose we had data that produced the curve in the image below.
Looking at that data, you could quite reasonably suppose that the curve was roughly a sine curve superimposed on that line. Looks like a pretty good match. Now let’s zoom out a bit. Here’s the same curve and the same line, only we can see a wider range of it.
Not such a good match, but you can’t quite be sure; it could still be a short-period sine curve superimposed on a long-period sine curve superimposed on the line, but it looks a lot less likely.
Let’s zoom out again.
Same curve, same line, but now the line looks like a positively *awful* match. Now, here’s how I
generated the curve.
It’s the sum of the three sine curves – the very short period/low amplitude green (y=sin(50x)/8), the medium period/medium amplitude gold (y=sin(4x)), and the long period/high amplitude red (y=2sin(2x)).
If you don’t have an *explanation* of the data that explains *why* it makes sense for a particular
curve fitting to make sense, then just arbitrarily picking a linear regression because it *looks* right is really bad math.
Based on what we know about the sun, it’s most likely to be a combination of cyclic phenomena. The reason say that is that we’ve observed multiple periodic phenomena about the sun: there’s a periodic variation in the size of the sun; periodic [variations in the brightness of the sun](http://www.nature.com/nature/journal/v360/n6405/abs/360653a0.html); and periodic variations in sunspot activity. And many of those are two-part periodic variations; both the brightness and sunspot variations have a short cycle superimposed on a longer cycle. Given that all of the phenomena that we’ve observed about the sun appear to be periodic, and often multi-periodic, the most reasonable guess without more information is that the size variation (if it isn’t simply an artifact of measurement) is part of a cyclic pattern of some type. To claim that it’s part of a *linear* cycle because a relatively short period of observation produces an apparent very low-slope linear reduction – with *no* reason for why a linear pattern makes sense – is silly, sloppy, and frankly, dumb.
So, is the sun shrinking? According to all of the data we have, examined carefully with good math, the answer is *almost certainly not*. There’s some noise in the data that makes it less than 100% certain, but I wouldn’t recommend gambling against it. When you add in the *other* data we have, such as the shape and stability of the orbits of the planets in the solar system, the geological records of earth, and the correlation between *known* solar patterns and geological records, it becomes *absolutely* certain that while there may be some variation in the size of the sun, it’s *nothing* like the constant linear decrease in size required by the creationist argument.