Sawmidass (C24),
Thanks for letting me know of your reply by e-mail. Otherwise I would have missed your reply.
You quote me and say,
For the second question, I would appreciate it if you did look closely at it. :slightly_smiling_face:
Can you clarify the questions you are asking about? I don’t know which questions each number refers too, and you’ve been a patient interlocure. I want to be sure I answer fairly and on point.
The numbering of the questions came from my C20, paragraph 2, where there were 4 major questions I raised. The second question was,
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?
I hope that clarifies the question involved. You may want to do a careful read of my paper that was originally referenced ( https://scientifictheology.us/wp-content/uploads/2020/12/IsochronDating.pdf ). It is free on the internet.
On question 3 you comment,
I don’t think isochron dating requires homogeneity at *all* scales, does it? Rather, by *other* means, a well mixed geological formation (which might be large or small) that would have cooled at the same time are identified. It is only from that context that it is valid to compute an isochron.
It appears that you do not really understand the assumptions that are required to be fulfilled for a valid isochron date. I will try to explain the fundamentals of isochron dating, so that you can see those assumptions for yourself.
The general principles of radiometric dating are that one measures parent isotope (P), daughter isotope (D), and (usually someone else measures) the decay constant k (lambda is usually used but I’m too lazy to figure out how to put in Greek letters). If one allows Po (my imitation of P subscript 0) to represent the amount of P at time zero, the general formula is,
P = Po exp(-kt) = (P + D) exp(-kt),
or with some rearrangement,
t = ln((P + D) / P) / k
(these are standard formulas).
In some systems, say, potassium-argon dating, it is assumed that the daughter argon all is driven off when the rock is heated (time To), and so the D is simply the measured Ar-40, and the potassium is simply the measured K-40. (Actually one has to correct for the branching ratio, and for absorption of argon from the air, and the total potassium is measured rather than the K-40, and the assumption that all the argon is driven off may not be accurate, but let’s not open that can of worms.) But for several systems, including rubidium-strontium dating, samarium-neodymium dating, and uranium-lead dating (two different kinds–U-238-Pb-204 and U-235-Pb-207), it simply is not believable that the daughter element is all lost at time To, and so one must figure out another way to account for residual daughter element in the original melt (magma, lava, whatever) that would otherwise throw off our calculations.
So what is done is the assumption is made that, for example, in rubidium-strontium dating, the strontium isotopes are homogenized throughout the melt, to incredible accuracy (the ratio of Sr-87 to Sr-86 when measured might vary, say, between 0.690 and 0.760 for an older rock, with the baseline needing to be flattened to ~1 part in 100 to ~1 part in 1000 in order to give a reliable isochron line–see the original line, labeled t0, on the illustration at the top of this page, that is completely horizontal). If one does not have an initially constant ratio of Sr-87 to Sr-86, one cannot get an accurate age.
You say (C24),
I don’t think isochron dating requires homogeneity at *all* scales, does it?
Technically it only requires homogeneity at all *measured* scales. There is no substitute for homogeneity (however it happens) if one wants an accurate date.
This is not just my opinion. Mebus A. Geyh and Helmut Schleicher, authors of Absolute Dating Methods (Berlin: Springer-Verlag, 1990), say on pages 12-13,
For example, there are indications that the condition of isotopic homogeniety of a magmatic body at time t0, prerequisite for isochron dating of magmatic rock, is not always fulfilled. But for the Rb/Sr system, for example, initial heterogeniety would place the determination of a whole-rock isochron age in doubt, if not make it impossible.
You say,
The issue of a two-component mixture may be a confounder that can’t be ruled out merely because the samples fall in a line. However, it seems that in many cases we have multiple different isotopes producing the same age for the same set of samples (Isn’t that right?).
I do know that in some cases the dates are close enough to be statistically indistinguishable. What I do not know is what proportion of dates fulfill those requirements. I know of several examples where the dates are not close to each other, and even some where concordant dates are generally rejected as erroneous. I can share this evidence if you wish, but this is, of course, anecdotal evidence. What I would like to see is a study where the tests are done "blindly" and all the results are published, sort of like what one would do in a good study in medicine.
You say,
As I understand it, isochron dating is usually not wildly out of line with other dating methods, and has been validated. It generally gives a concordant date, with far more precision.
I am not quite as confident as you, and would love to see the data behind your understanding.
You say,
@PaulGiem, wouldn’t it require fine tuning of the two component mixtures to get the SAME date predicted from DIFFERENT isochrons across the SAME set of samples? Likewise, if the isochron dates matched dates by other non-isochron methods, wouldn’t the composition of the two components have to be fine tuned?
One of the points of the paper I originally wrote was precisely to ask what kind of fine tuning it would take to get different isochron dates to match if the isochron dates were really produced by mixing lines. You, or perhaps one of your friends, might read the paper and critique it carefully but fairly, and could do all of us a favor.
You say,
(If you disagree, can you produce any math that shows that mixing lines would produce the same date independent of decay rate and starting composition? I don’t think that’s the case.)
That's precisely what I was doing in the paper. I was offering what I believed were testable hypotheses, and was hoping someone with the requisite expertise (and funds) could test them. If everyone waits long enough, I may test them myself.
I appreciate your comments, and look forward to further comments.