Talk:Radiocarbon dating/Archive 2

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[edit] Simplified archaeological sample age determination for laymen

New section deleted because:

  • The heading was confusing. Radiocarbon is used to date much more than archaeological samples, as said in the articles related to C-14. The reader would get the impression that the simplified method works only for archaeological samples.

The simplified calculations proposed have a granularity of one half-life, i.e. 5730 yrs. This gives the reader a false impression re the real precision of the method when seeing dates quoted with a +/- statistical error of, e.g., 100 yrs. BTW, such coarse method is described in the article about radiometric dating, see [1] Jclerman 01:38, 26 June 2006 (UTC)

I have written another trial version of the 'simplified calculation bit with perhaps a bit more explanation/derivation, see User:Vsmith/Dating calc - comments? The method gives the same dates (w/in about 0.1 yr) as the standard formulae that seems to intimidate some readers in the section Computations of ages and dates of this article. Vsmith 15:30, 26 June 2006 (UTC)

I looked at the method on your user page, but it seems like verbiage. Also, the formula is not that important, because you really have to calibrate the ages (via tree rings). You are probably right that the formula unnecesarily intimidates people though. Perhaps the discussion of the formula should be improved. Also, I like the example that you give at the end on your user page: 2 half lives * 5730 yrs/half life = 11460 yrs; this is easy to understand and should help people who have trouble with the formula.
—Daphne A 16:23, 26 June 2006 (UTC)
I also looked at Vsmith's proposal. I tried to shorten it but, in fact, I got it longer. I made some punctuation and other minor changes that migth be incorrect or unwanted... (It's at User:jclerman/Dating calc.) True, we do dendro calibration, but we need a raw date to input into the calibration curves, and the readers might want to know how do we get the number/date we input. Perhaps the table could have an extra row with the corresponding dates for each fraction, thus avoiding the mystery of the logs... Jclerman 23:27, 27 June 2006 (UTC)
Looks good. This is the way I introduce the concept to my beginning high school Chem 1 students as they haven't been exposed to rate laws and such and this is easier for them to grasp. I use base 10 logs for them as it's easier for them to grasp (most don't know what logs are) and with a brief intro they can use another button on their calculators :-). The example giving non-integer half lives is important as it is simply the most common real world outcome (I just picked a random fraction off the top of my head there). Probably should convert the table to a wiki table from the HTML one I made if it is a go. Cheers, Vsmith 02:01, 28 June 2006 (UTC)
Okay—my suggestion is that the new text replace, rather than supplement, the current explanation, except keeping the first sentence of the current explanation.
You said that "we need a raw date to input into the calibration curves". We need the raw 14C measurement, true, but we do not need to do the exponential calcuation. Rather, the raw 14C measurement can be directly compared with the raw 14C ages in tree rings (it is actually easier this way, because then the distributions are true Gaussian).
—Daphne A 04:19, 28 June 2006 (UTC)
Thanks to Vsmith and Daphne A for your useful comments. I'll be considering them when I make some minor edits to the sections in discussion. It will be later, probably overnight. Thanks again. Jclerman 17:41, 28 June 2006 (UTC)
My suggested Note, still rough, in progress, etc. is ready to be viewed at User:Jclerman/Dating calc.--Jclerman 16:18, 29 June 2006 (UTC)
Attn Vsmith: I wonder if you could put a webcam in your classroom. We would not only learn something, but we would avoid convoluted discussions ;-). I destroyed a little more your table, examples and text. See suggestions that I included between [] (I am not familiar with table editing, neither wiki or html). See also my comments below. And your non-integer n is a great idea. See my suggestion for an extra example with a larger n. --Jclerman 16:18, 29 June 2006 (UTC)
OK, I converted the table to wiki format with an online tool ([2] wow was that easy) and added the age (year) row. Also added one more column - just cause it would fit :-) Note, I removed the cell borders as it gives a "cleaner" look, but can set it back to one if preferred. The only problem I find with using the "easy" method is that my advanced chem students want to use it rather than the "book" rate constant eqn. - hey they learn :-) I try to have them also work with fractional values of n also, even had my adv students calculate how many C-14 atoms decay per second in an average human, one second is a very small fraction of 5730 years. Interesting result 'tho I can't say how accurate. Cheers, Vsmith 02:57, 30 June 2006 (UTC)
Attn Daphne A: I failed to understand your statement: We need the raw 14C measurement, true, but we do not need to do the exponential calcuation. Rather, the raw 14C measurement can be directly compared with the raw 14C ages in tree rings (it is actually easier this way, because then the distributions are true Gaussian). Can you please explain this method and give a reference to it?. Since to use calibration curves one needs to input a raw age or raw date value, I've expanded my current draft in progress to explain the experimental procedures to obtain such value before using a calibration curve. One of my problems was not to understand what do you mean by raw 14C measurement (activity?, age?). Other statement I couldn't parse is: the raw 14C ages in tree rings. How different is this from a calibration curve? I'll be glad to delete/edit/merge relevant statements in the article's Note as soon as I understand your method without the exponential. --Jclerman 16:18, 29 June 2006 (UTC)
To me, the proposed new text looks too complicated. Many people will not understand it; among those people that do, they could find out what they need from the article on Exponential decay (which is linked to from this article). I preferred your previous proposed text!—as a replacemnt for the current text.
As for the term "raw", I'd used this because that is what you had used. In any case, one problem with reporting radiocarbon ages is that they are not true Gaussian (for example, 15000±50 is usually considered to be Gaussian, but in fact it is log-Gaussian). As for tree rings, suppose that their (13C-normalized) activity levels are measured to be m1±s1,m2±s2,m3±s3,...,mk±sk; and suppose that we have a sample whose activity level is m0±s0; then it is clear that we can interpolate the tree-ring activity levels and calibrate the sample measurement directly against the interpolated curve. So we do not need to use exponentials.
—Daphne A 09:42, 1 July 2006 (UTC)
  • I don't think I've used the expression "raw C14 measurement" unless I was quoting you. Notice that I would not know what it means. I use "raw C14 date", "raw C14 age", "calibrated (calendrical) C14 date", "raw C14 (radio)activity", "net C14 (radio)activity", etc. Notice that only the "raw activity" is the result of a primary measurement. All other quantities are calculated.
The first time that the word "raw" was used was in your posting at 23:27 on June 27. I actually don't know what "raw" means in any context. Anyway, though, I think we might be better off letting this subject drop, and I will agree not to use "raw" anymore. —Daphne A 13:24, 8 July 2006 (UTC)
  • The "Note section" in the article and its current draft proposal are not intended to be a main section of the article. In fact, they grew up during six months of extensive exchanges with users from varied backgrounds. It still keeps growing in length due to the need to define the quantities we are using. Once we agree about what we all mean, it could be trimmed down.
  • I still do not understand how can you avoid the exponential to obtain a "calibrated (calendrical) date" from a "raw C14 age". To understand what you mean I need to know what is that you measure. what dendrochronological information you use, the physical measurements you perform and the ensuing data processing.
Okay, here's a simplified example. Measure the (13C-normalized) activity levels of tree rings from the years AD 500, 510, 520, 530, ..., 800. Also measure the (13C-normalized) activity level of the sample that you want to radiocarbon-date. Suppose that the sample has the same activity level as the tree rings from AD 700 (and a different activity level than all other measured tree rings). Then the sample must be from about AD 700. And if the sample has an activity level between the activity levels of rings from AD 700 and AD 710, then the sample is from sometime between those two dates. (There are details that I've left out here, but I hope the example illustrates the main idea okay.) —Daphne A 13:24, 8 July 2006 (UTC)
  • You might be referring to a new or unsourced method, which even if it could not be incorporated in the article (by Wikipedia policies) it would be valuable to explain within this discussion space for the benefit of radiocarbon researchers.

--Jclerman 19:06, 5 July 2006 (UTC)

This is the method that seems to be described—albeit briefly in the last paragraph—at http://www.informath.org/Basic14C.pdf (one of the External links for this article). There should be better sources. —Daphne A 13:24, 8 July 2006 (UTC)
To me it seems to be a simplification for teaching purposes, like the use of isotope abundances (in parts per trillion) rather than measurements on basis of the percent modern, as it is done. I am describing how it is done in the following. I fail to see the advantage in reconverting data from ages to activities, though. See below: --Jclerman 01:36, 11 July 2006 (UTC)
I agree that it seems to be for teaching purposes, rather than explaining how calibration programs actually work. Which is better for Wikipedia? (This is a serious question; I'm not really sure.)
Regarding what you wrote below, it mostly reads nice and clearly! The explanation for 13C could be clearer, I think. Also, the text does not account for AMS labs, which can use milligram amounts of carbon. And it is untrue that trees are from many latitudes: there is little equatorial, for example.
—Daphne A 11:46, 14 July 2006 (UTC)
Each simplification done for the sake of teaching later requires longer add-ons. It would be senseless to sample Equatorial treerings because most if not all species grown in such latitudes do not have annual rings since there are no marked seasonal variations and, anyhow, because the Equatorial masses of air are a mixture of Northern and Southern Hemisphere air. The article states clearly that corrections or normalizations for isotope fractionation have not been included (yet?). Where is the limit between an article and a how-to manual? Decontamination of samples for extraneous carbon has not been described either. My below discussion of calibration clearly refers to (radio)activity (detection)counting, thus AMS was not mentioned. Anyhow, when the collection of samples with potential dendrochronological+radiocarbon value was made, AMS had not yet been foreseen. --Jclerman 12:18, 14 July 2006 (UTC)
Yes, equatorial trees do not have annual rings—that was my point: it indicates that the proposed statement about "diverse latitudes" is misleading. Activity levels are determined by AMS. The paragraph about "grams of wood" seems to be irrelevant here and potentially misleading. Also, the part about "protected species" is new to me; are you refering to bristlecone pine? —Daphne A 07:00, 18 July 2006 (UTC)
1. "Diverse latitudes" is not misleading. Have you seen the list of the different localities, continents, elevations, in N and S Hemispheres from where tree sections were collected?
2. AMS is mass spectrometry, it does not measure activities. It counts atoms which have not yet disintegrated: it measures in units of "number of [undecayed] atoms" which are collected in a "cage" or "cup" whereto they are deflected. The earlier method of (radio)activity counting detects only the atoms at the moment they are disintegrating: thus it measures in units of "dpm" as registered in a "counter" (proportional or scintillation).
3. "Grams of wood" is neither irrelevant nor misleading. Lets the reader infer the non-trivial task of chiseling wood from a tree section to obtain suitable amounts of wood that were used for "points" on the calibration curves.
4. "Protected species" lets the reader infer that "tree rings don't grow on [free and easily available] trees". FYI, bristlecone pine is not the only such species used for calibration because it grows in very restricted localities. Calibration of the radiocarbon scale had to rely also on S Hemisphere and European trees.
--Jclerman 07:44, 18 July 2006 (UTC)
A non-specialist might well tend to think that "diverse latitudes" includes non-temperate latitudes. Activity levels can be determined from AMS measurements (think about it). What does it matter if conventional radiocarbon was used for most of the calibration measurements?—and I think that AMS was used for a few of the measurements that went into INTCAL04 (though I'm not certain). It is potentially misleading because without more discussion readers might think that grams are always necessary. Many of the trees used for calibration are readily-available oaks; I don't think that they are protected. The problem with the oaks was not that they were/are protected, but rather that they had died a long time ago and had to be retrieved from bogs, etc.
Maybe the root of our apparent disagreement is over how much detail should go into this article. My view is that too many details obscure the central points and leave readers more confused than enlightened. Possibly a compromise would be to include many more details even than you are suggesting, and put that in a separate article?—just an idea.
—Daphne A 09:31, 18 July 2006 (UTC)

[edit] About calibration

  • Radiocarbon dating analyses are destructive. This means that the wood of treering samples is combusted to produce carbon compounds (carbon dioxide, benzene, etc) whose [specific raw (uncorrected, unnormalized) radio]activity can be detected by counting its disintegrations per minute.
  • To attain the appropriate precision and accuracy, the determination of such raw activity requires grams of wood and weeks of counting its radioactive disintegrations.
  • The computation of the net specific activity of each sample requires extra weeks analyzing background ("dead" radiocarbon) and modern ("AD1950") standard samples, then to be normalized to a standard C13 value.
  • The raw radiocarbon ages are evaluated from the standardized specific net activities described above.
  • The series of treerings to be dendrochronologically & radiocarbon dated to be used to calibrate the radiocarbon dating scale were the result of decades of explorations begun in the early 1960s. Remote sites were explored at diverse latitudes and elevations, searching for unique rare, living and dead millennary trees to obtain suitable samples. They were mostly from protected species.
  • All the determinations of the radiocarbon activities described above have been cross-correlated and preserved as calibration curves (or tables). By definition a calibration curve has quantities of the same kind on both axis, namely calibrated dates (given as Calendar Years) on the horizontal axis and raw ages (given as Before Present years) on the vertical axis. See Example 1.
  • Should a conversion curve be preferred, rather than a calibration curve, the ages on the vertical axis can be converted to the original radiocarbon activities by a simple mathematical operation.
  • Any radiocarbon activity from a sample to be dated might match the radiocarbon activities of more than a single tree ring. In Example 1, the sample whose activity dated as 900BP old matches 5 different calendar dates which were obtained from 5 different dendrochronologically dated treerings.
Example 1.
Example 1.
  • In practice, things are complicated by the statistical uncertainties (a) of the curve itself, which is really a band, (b) the uncertainty distribution of the sample's activity, and (c) the non-monotonic character of the calibration band. Graphical examples covering the statistical uncertainties and their propagation are given here [3] and here [4].

--Jclerman 01:39, 11 July 2006 (UTC)