Paul Giem: Isochron Dating Rocks and Magma Mixing

@PaulGiem reached out to me discuss a thread on the forum from a while ago (Paul Giem: Isochron or mixing line?) that references his work ( The original conversation involved @Ignostic and @davidson.

Isochron Dating

To follow this conversation, you learn a bit isochron data, one advanced radiometric dating technique that geologist date rocks. This is a powerful method because requires fewer assumptions that other methods, and works by measuring a precise pattern (an upward sloping line) in several samples.


Basically the slope of the line corresponds to the age of the rocks. Several samples of rock are drawn, and that is what forms the line.

Mixing Can Produce Isochrons Independent of Age?

Giem’s idea is that mixing could produce a line in these plots, and it is notable that this is stated by Davis Young too.

Conceivably, straight lines on an isochron diagram could be generated simply by mixing two magmas in various proportions and allowing them to crystallize. If so, the resulting straight line would tell us nothing about the age of the rocks.

So his basic idea seems plausible. Davis goes on to point out the problems with this:

The vast majority of straight lines of an isochron plot, however, cannot be explained by simple
mixing for several reasons. We mention only two. For example, evidence of extensive magma mixing can generally be detected from variations in chemical composition of an igneous rock body as well as from field evidence. For most igneous rock bodies, however, field and chemical evidence of significant mixing of two or more magmas is lacking. In addition, the mixing hypothesis fails to account for the very wide range of values of Sr isotope ratios that have been observed on all isochron diagrams of igneous

That might be true, but it seems to be difficult to show that data to us in a way we can see it. I think an objection @Ignostic found was more directly visible:

From this discussion, I am still wondering how geologists constrain and quantify the uncertainty of dating from isochrons due to this mechanisms. Perhaps it doesn’t make space for a YEC earth, but it might mean that some of the confidences are overestimated. Perhaps.

Paul Giem’s Email

Today Paul sent me a very courteous email noting he had missed the discussion on this. I offered to create this protected thread for him to hash this out with informed and respectful scientists. Here are the key parts his email…

Perhaps what I consider the biggest misunderstanding of the paper in the comments was the implication that I was simply looking for a way out of accepting radiometric dates at face value, as in

“As far as the particular work of Giem goes, it represents one of myriad “just so” stories that essentially say “but what about THIS for undermining confidence in dating?””

That is a fair point, and I think we should hear him out.

As noted by Gunter Faure, mixing lines can (and 2-component mixing lines always do) precisely mimic isochrons, and as I mentioned in the paper, I don’t like the idea of people staring at each other across an unbridgeable chasm, with no testable way to resolve their differences. My model for flattening mixing lines simultaneously was not meant to simply say that there was a possible way to explain matching apparent isochrons, but rather to create a theoretical model for creating matching mixing lines so that we could test whether those apparent isochrons are really isochrons or are better explained as mixing lines. In other words, it was created to be tested.

I think that if we are to be good scientists, we cannot start with the assumption that short age, or long age, is correct for any given feature of nature. We may get there eventually, but as soon as we assume our conclusion, we have short-circuited the process. (That position makes me a heretic among some young life creationists.) I would appreciate criticism of the theory, or perhaps the testing of it on data, with confirmation or refutation of the theory that a particular suite of matching apparent isochrons can be explained by mixing lines.

That, it seems, is the goal of this thread. To be honest, I’m not even sure what Paul thinks about the age of the earth from this email. It is the sort of email I would expect from a secular scientist that was exploring the reliability of a particular method.

The Rules

This thread is protected. @Moderators will watch it more closely.

Disrespectful and uninformed posts will be deleted. Please engage with Paul respectfully and on topic, noting as well that he works a full time job and may be delayed in some answers.


For clarification, is the question

  1. How one would go about determining if a particular isochron was not a mixing curve?
  2. How one would go about determining, in general, if at least a subset of isochrons can’t be mixing curves, OR
  3. How would one determine if radioactive decay rates have been constant, such that radiometric dating is even possible?

I can address #3 reasonably well, and #2 with some ideas, but would have to defer to someone with expertise in isochron dating for #1.


One could try other dating methods. If they match the isochron date, that would suggest that it’s not a mixing curve. Try dating minerals that really don’t want to incorporate decay products of whatever chain you’re using.

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I’ll ask one of my faculty with expertise. Can’t promise an answer, but we shall see. (I am curious myself now.)

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I got a quick “short version” answer, which will provide teasers more than actual answers. Here it goes:

“It depends on the isotopes in question and the magmas themselves. Some are easier to identify time vs mixing. U-Pb is pretty easy to ID which is which. Rb-Sr is more difficult. Sm-Nd and Lu-Hf are either easy or difficult depending on the magmas in question. Mafic vs. felsic is pretty easy, felsic vs. intermediate is so-so. Even felsic vs. felsic is so-so. Mafic vs. intermediate and mafic vs. mafic gets more difficult. For all systems, if the two magmas in question are similar in age and composition, you can’t tell them apart. The wider the gap in age and composition of the magmas, the easier it is to tell them apart.”

If I learn more I will pass it on. Meanwhile, maybe someone with firsthand expertise will weigh in?

It sounds like part of what is going on is that the samples you measure need to be from an identifiably distinct source for isochrons to work. I don’t have the context to know how difficult that is.

It does seem that looking at multiple radiometric isochrons would help a lot. If they produce the same date, it would be hard to explain as mixing.

@davidson (Comment 2), the question starts out as
#1 How one would go about determining if a particular isochron was not a mixing curve? (I prefer mixing lines to mixing curves, as the mixing lines are in fact always straight lines, but whatever.)
and then moves on to
#2 How one would go about determining, in general, if at least a subset of isochrons can’t be mixing curves[?]
For #3, there would be very little testable evidence that could distinguish between the standard mode and accelerated decay (helium in uranium-bearing rocks being one of the few differences) and even this difference could be explained by either side, and although perhaps massive data could swamp one side, true believers on either side could always hang on. For that reason, in the paper, I explicitly assumed that the decay rate has remained constant, and that essentially precludes a young earth perspective (although not necessarily a young life perspective).

@John_Harshman (C3),
Would those other dating methods also be isochron methods? Or were you thinking about K-Ar (and/or Ar-Ar) dating?

@davidson (C5),
You’re right. More teasers than answers. “U-Pb is pretty easy to ID which is which.” How, exactly?

@swamidass (C6),
The paper outlined ways in which multiple matching “isochrons” could arise from mixing 2 magmas. Then it would not “be hard to explain as mixing.” However, then we could test to see whether evidence of magma mixing (e.g. mixing hyperbolae–see my paper) were present, and failure to find such evidence would be evidence against mixing lines. Also, as was noted by Davis Young (cited in the PDF you posted), some dating methods consistently date older than others. The mixing model predicts which dating methods should apparently date older in a mixing line process, and one can compare the predictions with the reality. We are definitely not wrapping things up. There is a lot of work ahead.


Welcome @PaulGiem.

Why would you expect mixing magma to produce the same slope for different isotope isochrons? I don’t think we would expect the same slope, so each isotope-isochron is an independent measure of age.


My #3 is addressing a much broader question, so no, the other methods are not isochrons. Methods for testing if radioactive decay was faster in the past include things like comparing the real-time measured spreading rate of the Pacific plate with calculated rates based on radiometric ages of the Hawaiian island chain and distances between islands/seamounts. If decay was faster in the past, the two values should not be the same, but they are. (Not going into much detail on this as it is off-topic from the primary intention for this thread.)


I wasn’t thinking about isochron methods, but they could be. Should different decay series have the same mixing line?


Would secular equilibrium be another way of determining historical decay rates?

My tentative answer is no, as secular equilibrium just means that enough time has passed within a system of interest for radioactive daughter isotopes to build up to the point where their own decay rate equals their production rate. It doesn’t tell us whether those rates were slower or faster some time in the past.
There are other ways of testing for constant decay rates. I have mentioned a paper before on this site that I wrote with Ken Wolgemuth that combined tree rings, lake varves, and carbon-14 to test competing conventional and young-earth claims about decay rates and the number of rings or sediment layers produced each year.


The biggest problem I have with the young-earth arguments about changing decay rates is the RATE project itself.

It was their own admission that increasing nuclear decay rates enough to squeeze the radiometric evidence into 6,000 years would have raised the Earth’s temperature to 22,000°C. It was also their own admission that no known thermodynamic process could have removed the excess heat fast enough to stop that happening.

When they themselves are making that kind of admission, pretty much everything else is window dressing. Faux isochrons due to mixing could be two a penny and it wouldn’t make any difference. It blows the case for a young earth right out of the water. It’s science fiction, it’s as simple as that.


@davidson (C9)
You are right about radioactive decay changes taking us in a completely different direction.
I am curious. The other two comments are regarding the dating methods, and so the quotes they start with make excellent sense. However, I am missing the relevance of your quote to your comment. Is there some kind of standardization of quotes from a previous post that led you to use this quote? Just trying to understand, since I’m new here.

@John_Harshman (C10) and @swamidass (C8),
The math for flattening a mixing line would be the same for any pair of isotopes (see my paper, pages 15 and 16, for one example). Differences between two isochron pairs would be primarily in the differences in half-life leading to differences of putative ages found (see my paper, pages 20 and 21), and fractional crystallization resulting in partial separation of elements might not (in fact, probably would not) be the same for two isochron pairs. However, it is not clear precisely what the differences in flattened isochrons should be.

There are two ways of testing this. First is to observe what happens during fractional crystallization of a magma, specifically noting which isotopes concentrate in particular portions of the magma, and then calculating what difference, if any, those fractional crystallizations would make for a pair of isochron vs mixing lines. The second is a more brute force approach. Simply pick a suite of rocks that everyone agrees is a mixing line (a few are listed in my paper, page 9, notes 9 and 10), and date it by more than one isochron method. If the methods agree on the age, that would argue that at least for this suite of rocks, matching dates do not mean true isochrons and therefore true ages. Other rocks with similar chemistry and geology would then be viewed with suspicion. On the other hand, if the calculated dates are different enough, it would lend credence to the idea that matching date lines, at least in this chemical and geological setting, really are isochrons and really do indicate time.

Should we use time, effort, and money doing such studies? That depends partly on whether we want evidence to answer the question, or whether we want two systems of thought to argue it out without that evidence and turn the question into more of a postmodern power struggle. Personally, I like the idea of evidence answering the question better.

For now I will ignore discussions of possible changes in decay rates, or even of a young earth. The question at hand relates to whether life on earth can be dated as old, not whether the earth itself is old.


Those would seem to be largely the same question, since life has been around for most of the earth’s existence. And we can probably determine the Phanerozoic to be a significant fraction of the earth’s age, whether or not we can decide that the fraction is 1/9.

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@John_Harshman (C15),

My point was not so much to determine the age of the earth, as to explore the reliability of isochron dating. A long involved discussion can be had about what part of the geologic record has evidence of life in it, and how much of that life had to be deposited in situ, but that would not change the question of whether isochron dating was reliable.

The fact of the matter is that the straight line of isochron dating is always mimicked by 2 component mixing lines, and it is important to be able to objectively tell them apart. In fact, it is even theoretically possible that a mixing line with apparent age (or even reverse age) could then age to give an apparent isochron line whose final slope was determined by a combination of mixing line physics and isochron aging.

Another question should be addressed. Is the original required homogenization of strontium (or other daughter and reference) isotopes believable from a physics point of view? Without this homogenization, to parts per thousand or so, a valid original isochron line with zero age (to start the clock properly) does not happen, and one should not get an accurate isochron age. See pages 13-15 of my paper for a discussion. This also raises interesting questions about the relationship between whole rock and mineral dating.

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I don’t think one could actually have such a discussion, but sure, it has little to do with the reliability of isochron dating. Still, that’s what I’m interested in. Old earth/young life has always been inexplicable to me, and I was wondering how anyone could justify such a claim.

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This facebook group is where to find out the answer: Young Biosphere Creation

@John_Harshman – YBC has a different take on Genesis, but I think you (or most) are unlikely to be satisfied with the justification and more than you are satisfied by YEC justifications. The big difference I find is a matter of tone; Bob and Wes (mods on that group) are friendly and very pleasant to chat with, even though we have very strong disagreements. Their attitudes are near polar opposites from stereotypical YEC, which is very refreshing.

Otherwise there is strong similarity to YEC, defending many YEC claims (Noah’s Flood, soft tissue in dinosaur fossils, etc.), but they don’t really like being called/compared to YEC. They see a greater distinction between YBC/YEC in a way that is not clear to me. For example, acknowledging Old Earth should make radiometric dating of rock layers a non-issue, but they do not accept radiometric dating as accurate when it comes to Flood Geology - in seeming contradiction to their acceptance of an Old Earth. I’ve tried to elicit their thoughts on this contradiction and the response was (paraphrasing), “This is what we believe.” They do not acknowledge some of their beliefs contradict physics even when pressed to do so, and I pressed as hard as I could in polite conversation.

(AND Bob, if you are reading this, you are a great guy, but you seem to be blind to your own contradictions. That’s OK, this is a matter of faith after all. :slight_smile:


The discussion that John_Harshman (C17) is most interested in, IIUC, seems to be the age of the earth. And that’s okay. Perhaps in another thread we can discuss this. One part of that discussion was alluded to by @swamidass (C18), and Dan_Eastwood (C19) is at least somewhat familiar with the YBC position (which appears to be roughly identical to the YLC position).

However, in this thread I hope we can stick to the subject that started the thread, the reliability of isochron dating. Is there any disagreement that isochron lines are mimicked by 2 component mixing lines? Is there something identifiably wrong with the assumptions or the math of my proposed explanation for how multiple “isochron lines” can be flattened to roughly the same degree? Is there evidence for or against the proposition that batholiths mix their strontium (or lead or whatever) isotopes to better than one part in 100, in some cases one part in 1000, when they are emplaced? That initial mixing of daughter and reference isotopes would seem to be required for an isochron line to start at zero age. Has anyone tested to see whether lines which everyone grants must be mixing lines also have apparent matching “isochron ages”? What are the data? Do we need more data, and if so of what kind?