# Shrinking Sun (Part 1)

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.
>OBSERVATIONS
>
>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.
>
>INTERPRETATION
>
>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.

## 0 thoughts on “Shrinking Sun (Part 1)”

1. Canuckistani

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.

Well, yes and no. It depends what you want to use the curve fit for. Empirical models are usually okay for interpolation and for limited extrapolation near the edges of the data set, but should never be used for extrapolation well beyond the range of the data. Such extrapolations do indeed need to be justified by require a theoretical model. So the criticism of these creationist arguments should be slightly narrower that the quote above suggests.
Shorter me: the problem isn’t picking a nice fitting curve, but rather for using the fit for extrapolation instead of interpolation.
(Incidentally, good Bayesian nonparametric fitting methods automatically demonstrate the loss of precision outside the range of the data — the posterior distribution of the fitted function relaxes back into the prior distribution in regions with no data.)

2. Brent

Wow. Usually the bad math you debunk at least sort of SEEMS to have a veneer of legitimacy upon a cursory reading, but this takes the cake!
BTW, are your second and third sine-wave graphics switched?

3. Z. Sesqui

In the formula that you gave from the item you quoted, did you leave out a ‘/’ between the 5280 ft/mile and 2.5 ft/hour? Otherwise units don’t work out. (You get ft^2 / year instead of years.)
A typo doesn’t change anything in your analysis….

4. CS

From Answers in Genesis:Stephenson . . . calculated as a decrease of 0.16 ± 0.14 second of arc per century. This, Stephenson again suggested, was essentially a null result–the sun was not shrinking on a long-term basis, its diameter merely oscillating at regular intervals of about 80 years.
. . . .
But this is not ‘essentially a null result’. More precisely worded, Stephenson’s conclusion should have been that the sun’s diameter is decreasing at a rate somewhere between 0.02 and 0.30 seconds of arc per century, a rate not incompatible with Gilliland’s suggested almost 0.2 second of arc per century.

I’m surprised you haven’t mentioned this. About the only time an error level is actually given in these arguments for a shrinking sun, it is then completely misinterpreted. They are suggesting the true value must fall within one standard deviation (+/-0.14) of the measurement (0.16), so zero is ruled out. For careful experiments, the true value should be outside of one standard deviation from the measured value about 1/3 of the time. If any scientist were to use the “more precise wording” suggested above, that would (and should) be the end of their career.

5. gg

It’s worth mentioning that from a physics point of view, the ‘shrinking sun’ would be somewhat of an idiotic argument. Even if one could conclusively prove that the sun has had a linear shrinkage over some stretch of the Earth’s history, it is a highly nonlinear physical system and without understanding the underlying physics, it would be absurd to apply ‘uniformitarian-type reasoning’ to extrapolate.

6. MiguelB

The time at which the earth first emerged from the shrinking sun…

I find this amusing. So they believe the earth actually existed inside the sun, rotated around it once a year, and then it basically “popped out” of the sun?

7. Mark C. Chu-Carroll

gg:
Of course you’re right. There are a lot of basic statistical methodology errors in the shrinking sun crap, and the standard deviation/margin of error issue is a good one. I just thought that the post was getting long, and that I should focus on just one or two problems. I find the whole crappy linear regression stuff to be the most amusing and novel error, so I focused on that.

8. Mark C. Chu-Carroll

MiguelB:
I don’t think that they believe that the earth popped out of the sun. I think that they’re trying to use that as a strict upper bound. They believe that the earth and the sun are much younger than 20 million years, and so the earth would never have actually been inside the sun.

9. Mark C. Chu-Carroll

Brent:
Yes, thanks, good catch. Interesting error actually; I made all of the images using a screen capture program; then grabbed them and ran them through a format converter. I accidentally did the format conversion out of order, and so the filenames were wrong :-). So when I was saving the files, since I saved the second zoomout first, it was named “curves-zoomout-one”, and the first zoomout was named “curves-zoomout-two”. I didn’t look at the images when I was pasting them into the post, just at the filenames.
That’s what happens when you’re going too fast!

I’m amazed that YEC:ers doesn’t try to make more of a stinker, since one of the reasons we use the null hypothesis of gravitation balanced by radiation pressure from fusion is the population model of stellar evolution ( http://en.wikipedia.org/wiki/Hertzsprung-Russell_Diagram , http://en.wikipedia.org/wiki/Stellar_evolution ). But perhaps that is too close for comfort.
Of course, the other reason is the detailed kinetic models, which are constantly revised, as in the solar neotrino problem and its solution that the next post promises to be about. I’m reminded about the old lithium discrepancy in bigbang nucleosynthesis where a paper this year was explaining the seeming lack in stars in an improved stellar model with includes production and depletion from fusion reactions. Any alternative model would have a lot of evidence to explain.
The body heat observation was a new one for me. Assuming it was statistically verified, and disregarding the possibility of changes in habits, habitation and infections, I would say that it is a nice indication of a possible evolutionary change. Evolution has been ongoing in humans into recent periods so it is another good null hypothesis. 😉

11. gg

MarkCC: “I just thought that the post was getting long, and that I should focus on just one or two problems.”
Sorry; I hope I didn’t inadvertantly impugn your critical thinking skills, which wasn’t my intent! I come from a physics background, so the first thing that jumped out at me was the bizarreness of the assumptions on physical grounds. For you, the bizarre math jumped out more.
It seems to me that science types of pretty much any field could tag team this creationist argument into the ground from a variety of angles. Any geophysicists/ earth scientists want to tag in?

12. jarvisjd

Could these guys have been involved in the “math” that says “social security will be bankrupt in 43 years!” Linear extrapolation in highly nonlinear systems over periods longer than the characteristic time of the system… I love it 🙂

13. Gerald Squelart

And I’m pretty sure that if we were in a growing phase, they would happilly use the data to show that the sun would have been a dot some millions of years ago, proving that the Earth or life couldn’t be that old, therefore it must be 6000 years old. 😛

14. Zombie

The missing neutrino problem isn’t that much of a problem any more; experiments in SuperKamiokande and Sudbury Neutrino Observatory have pretty much established the oscillation explanation for the depletion of solar neutrinos.
The kook explanation that fusion wasn’t happening never held water even with a neutrino deficit, because there were solar neutrinos detected, only at a lower rate (about half) than expected.
Incidentally SuperK deals with neutrinos produced by cosmic rays in the atmosphere. Those cosmic rays are known to consist of atomic nuclei where the distribution of elements agrees very well with standard models of stellar nucleosynthesis, which incorporates the whole fusion process. Cosmic rays are one direct measurement of the elemental composition of the universe, and that measurement is consistent with the stellar fusion model.
There’s just so much wrong with these guys…

15. Olly

Question: Have any of you actually experienced the joy of life? You can waste your short lives arguing about equations and formula but the fact of it all is that God designed us all amazingly well at some time in the past (exactly when really doesn’t matter) He designed us with the ability to think, feel, see and love so we can appreciate all the pleasures life has to offer, not to spend our lives argueing over sums! No I don’t go to church, I just used my common sense to determine that the evolution theory just doesn’t hold up at all. There are no half changed humans or other creatures for that matter and they would never have survived the change process.
Anyway guys, take some time out and enjoy what life has to offer – Stop, relax and marvel at nature. It is proof enough of a designer our brains are not capable of comprehending… just like infinaty.

16. Mark C. Chu-Carroll

Olly:
Your “common sense” tells you that evolution doesn’t work. That leads me to two questions.
The first: Does that make it acceptable to then deliberately lie in order to convince others to agree with you?
Second: Do you always accept everything your common sense tells you? Common sense would say that there’s no way that
the earth is spinning around an axis and zooming through space at tremendous speed! Do you really think that?

17. Jonathan Vos Post

Common sense is not common.
Common sense changes when you study and actually understand science.
Common sense changes when you study and actually understand mathematics.
Common sense changes when you study and actually understand computer programming.
To the extent that God is a Physicist (as Einstein and Hawking sometimes suggest) then one should learn more Physics, to better appreciate God.
To the extent that God is a Mathematician, as Plato and Erdos and others have argued, and Blake illustrated (God as a Geometer and/or Engineer), then one should study Mathematics to better appreciate God’s handiwork.
To the extent that God is a computer programmer, then one should become a good programmer, and be able to understand the issue of our trying to determine what the Operating System of reality is, and trying to hack it.
Also, to be able to understand the argument that Spinoza put forth that all matter, energy, time and space are within the mind of God. Films such as “The Matrix” and “The 13th Floor” popularize the metaphysical theory that we humans are merely simulations.
I was the first to publish a scientific article on the likeliehood that we were indeed simulated by positron-electron entities at least a googol years from what humans think is the present, in the magazine Quantum. Years later, Nick Bostrom got great publicity by rediscovering my argument, and claiming that he was the first to publish.
To the extent that God is a practcal joker, it is good to read early theologians who spoke of “hilaritas” as an aspect of godhead.
Anyway, my wife and my son both have more common sense than me. That’s why they don’t spend much time blogging.

18. David Marjanović

stellar evolution

Actually, that’s a misnomer because no descent is involved, only modification. Stars don’t reproduce.

19. Joe Schmo

I find it amuzing that the same people refuting evidence that the sun is shrinking because “we only have 80 yrs of data and that certainly doesn’t conclude that the sun is permanently shrinking” are the same who espouse that the earth is definitely billions of years old because of carbon/uranium dating. This same dating has no clue what happens to half lives after 100 yrs or more. You can’t swear by one extrapolation and deny the other on the basis that it helps your case. Especially when recently dead items are tested to be thousands of years old, there’s reason to question it’s validity. I’m not swearing by sun size theory proving a timeline, just addressing a convenient lack of consistency in the arguments.

20. Xanthir, FCD

Our sun is the only one that we can measure with the necessary accuracy. We have a sample size of one, which is never a good thing to try and extrapolate from. In addition, the sun is a gigantic, highly complex ball of gas, photons, and magnetic fields, the exact dynamics of which are not understood.
Radiation and half-lives, upon which things such as carbon-dating are based, are observed and used all the time, however. We have thousands, if not millions, of instances where half-lives are involved and that come out correctly. We understand the physics underlying them. They’re not difficult (anymore). Extrapolating there is simple and well-founded.

21. Doug

What I find amazing it that someone with so much mathematical knowledge is so blinded by foolishness (Psalm 53:1)that they don’t see the obvious signs of creation.
What is the probability that we all evolved from nothing? The atom is so complicated, for it to have spun off of some massive explosion (although there was nothing to explode, so explain that as well) is beyond mathematical probability. Not only that, but the same explosion created billions of unique fingerprints, the feathers of a peacock, color, etc., the list goes on for which no mathematician, good or bad, can put a number to.
At what rate are we now evolving or has evolution suddenly come to a halt? When will the next generation of man come out?
I can much more believe that the sun is shrinking than I can believe that we’re evolving from nothing.

22. Mark C. Chu-Carroll

Re #28:
It’s very simple. Take the radius of the earth’s orbit, re. Take the radius of the sun, rs.
Now, the distance between the earth’s orbit, and the surface of the sun: (re – rs).
What the “shrinking sun” argument does is it creates an approximation, saying that the sun is shrinking at a constant rate of 2.5 feet per hour. Divide
the distance between the surface of the sun and the earths orbit (in feet) by 2.5, and you get a sloppy approximation of when, if the sun is shrinking, the sun’s surface would have been where earth is currently orbiting.
You can do a similar trick using the 0.1% – but it’s harder to write in HTML. But it’s simple algebra, following exactly the same lines as the above.

23. arrowriver

I have a friend that basically opened my eyes to the shrinking of the sun. He’s a creationist and I need to prove his theory of the earth being only 6000 years old wrong because I am just that stubborn. Sadly, he’s almost as stubborn as I am. So thanks to you I have a good reason to prove him wrong! Thank you soooo much!

24. Ray

Romans 1:18,19,20,21 Pretty well sums it up for some of us uneducated,old folks that have seen “proven facts” change every decade or so.