Kirk Bertsche recently posted a review of the RATE project’s 14C investigations on the TheologyWeb site (http://www.theologyweb.com/campus/showthread.php?t=103916). His main conclusion is that the radiocarbon in fossil organisms which the RATE team documents from the peer-reviewed radiocarbon literature, together with the radiocarbon we measured in our own suites of coal and diamond samples, is, in his words, “nothing more than contamination.” Below the quoted article is a response by Dr. John Baumgardner.


There have been a number of mentions in various threads of the ICR RATE project and its conclusions about radiocarbon. I have finally looked into this in detail (read their reports, read most of their references, and spoken with the expert who measured the radiocarbon samples for them.) My conclusions are below. (This is slightly modified from a post I made on the ASA mailing list, http://www.calvin.edu/archive/asa/200710/0173.html)

Baumgardner1 claims to present experimental data showing that all biological material contains intrinsic radiocarbon, no matter how old it is claimed to be. He makes additional weaker claims that even non-biological carbonaceous material contains intrinsic radiocarbon. He presents two classes of data. Firstly, he re-analyzes radiocarbon AMS dates published in peer-reviewed scientific literature. Secondly, he presents results of samples which RATE has collected and sent to a leading radiocarbon AMS lab to be dated. In both cases, I am convinced that his “intrinsic radiocarbon” is nothing more than contamination.

Modern radiocarbon dating by AMS is a complex process with numerous opportunities for contamination. Taylor and Southon break the contamination into 7 general types, each of which can have multiple specific sources2. The largest contamination component is generally the conversion of the sample to graphite; this introduces a small amount of modern carbon (typically at least 1 microgram3). Thus a 1mg sample of infinitely old carbon would measure at least 0.1 pMC (percent modern carbon) before background subtraction. Earlier techniques and malfunctioning equipment contribute more contamination. (Baumgardner does not seem to understand this; he wants to treat the quoted background from one of the leading modern labs as a constant value applicable to all labs and to all historic measurements.)

Baumgardner’s first class of data is previously-published radiocarbon AMS dates which he has re-analyzed. He has divided the samples into two groups: Paleozoic geological samples, and Phanerozoic biological samples. He claims that the geological samples have a mean radiocarbon content of 0.06pMC and the biological have a content of 0.29 +/- 0.16 pMC1. But he fails to note that all of their geological samples are actually of geological graphite, so did not undergo the graphitization process which was required for the biological samples. In fact, two geological samples (entries 21 and 40 in his Table 1) were omitted from Baumgardner’s geological data histogram; these were identical to other geological graphite samples (entries 62 and 79 respectively) but were re-graphitized in the lab as controlled measurements of contamination from the graphitization process. These tests yielded characterizations of 0.25 and 0.14 pMC contamination from the graphitization process. Entry 10 in Baumgardner’s Table 1 compares radiocarbon AMS with the older radiocarbon decay counting, giving a roughly 0.4 pMC contamination level for AMS, mostly from graphitization. In fact, many of Baumgardner’s references include systematic tests for contamination, with the graphitization process typically adding from 0.1 to 0.7 pMC (highly dependent on sample size and procedure). It is quite clear that the differences he sees between geological and biological samples is simply the contamination introduced by the graphitization process. Further, the radiocarbon content of his selectively plotted geological samples of <0.1 pMC is in excellent agreement with the instrument backgrounds characterized in many of his references. Thus, the geological samples give no evidence of intrinsic radiocarbon.

Baumgardner’s second class of data consists of samples which the RATE team has collected and sent to be analyzed. This includes a set of 10 coal samples (0.25 +/- 0.11 pMC) and a number of diamond samples1. Both materials are problematic in general, and even more problematic in the specifics of the RATE samples.

The expert who prepared and measured the RATE samples is convinced that the RATE coal samples were contaminated in situ. Coal is “notorious” for contamination, due to uranium which is often in or near the coal (especially a problem for N. Australian coals), from humic acids which are almost always present, and from microbial growth. The best coal dates reportedly come from anthracites with glassy surfaces, which have given dates as old as 70k years, or about 0.02 pMC.

It is also possible that the coal samples were contaminated while in storage for an indeterminate time in a DOE geology lab refrigerator1. Geology labs often have elevated levels of radiocarbon due to tracer studies, neutron activation studies, and dust from uranium-bearing rocks. Carbon is highly mobile and contamination can spread through an entire lab and persist for decades4. (I have seen a badly contaminated sample which was traced to storage in a geology lab refrigerator.)

The diamond samples were difficult to graphitize, and apparently required some modifications to the normal procedure1. This likely increased the contamination. In addition, the samples themselves were reportedly pitted and appeared to have been subjected to previous analyses of some sort. Nevertheless, the 5 deep-mine diamond samples were only slightly above background levels (0.01 to 0.07 pMC after background subtraction), while the 7 alluvial samples ranged from 0.03 to 0.31 pMC after background subtraction. Subsequently, this lab has inserted diamond directly into an ion source, eliminating the graphitization process, and has measured much older dates (unpublished). Taylor and Southon have measured 0.005 to 0.03 pMC by the same technique, which they interpret as their instrument background2. This gives strong evidence that the RATE diamond samples were contaminated, either by previous testing or by graphitization.

Thus it is clear that the previous peer-reviewed radiocarbon AMS measurements can be explained by contamination, mostly in the graphitization process. The recent RATE coal samples were probably contaminated in situ, and the diamond samples were either contaminated in the graphitization process or by previous analyses. In any case, other coal and diamond samples have been measured at essentially the instrument background levels, giving no evidence for intrinsic radiocarbon. RATE’s claim that all carbonaceous material contains intrinsic radiocarbon is not supported by the data.

Kirk Bertsche—accelerator physicist, formerly at a leading radiocarbon AMS laboratory

References

  1. Baumgardner, Radioisotopes and the Age of the Earth, vol. II, ch. 8. Everything except the diamond data is contained in this earlier paper: http://www.globalflood.org/papers/2003ICCc14.html
  2. Taylor & Southon, NIM-B 259(2007)282ff.
  3. Kirner et al, Radiocarbon 37(1995)697ff; Brown & Southon, NIM-B 123(1997)208ff; Mueller & Muzikar, Radiocarbon 44(2002)591ff; Southon, NIM-B 259(2007)288ff.
  4. Zermeno et al, NIM-B 223-224(2004)293ff.

Learning to Trust

I just want to thank AIG for your faithfulness in standing on the authority of the Word of God. I am an American who has lived in the Philippines for over 11 years. I came accross your website in June 2006. I had been exposed to God’s Word for some of my life and felt that I believed upon what was in the Bible, but I eventually realized that my belief didn’t turn into trust and dependence. Growing up in American public schools I had just assumed evolution was a truth that couldn’t be denied, at least credibly. I thank God for using your ministry to open my eyes to the truth, which is God’s Word—John 17:17. Not only have I been saved from the destruction I deserve, I have been saved from the life I once lived and have dedicated it unto the Lord. I am now in my second semester at a fundamental Bible College in Metro Manila. I have seen how being able to defend my faith in God’s Word has brought such wonderful blessings not only to me and my family, but also those who can now do the same

—C.W., Philippines

Introducing the Truth

My husband is a chaplain in the U.S. Army and deployed to Iraq just before Thanksgiving. He shipped with him materials from AIG and consistently uses them to show soldiers the foundational answers found in Genesis. I am using your curriculum as well in the Chapel’s high school Sunday school class. We have been blessed to use your materials to introduce soldiers and families in locations around the world to the Creator God of the Universe. Thanks to you for your commitment to bring people back to the foundations of God's Word.

—T.V., U.S.

Taking the Message to the Streets

I just wanted to say thank-you for all the great updates on your website. I read them regulary and use the knowlege four times a month when we do street outreaches on the streets of London and “Speakers Corner” in Hyde Park. The information about “Lucy” has helped people on the streets [understand] the new findings of this ape and that we are not related to them at all. Your organisation is doing a great job with all the investigation and keeping up to date with all the latest evolutionary findings. So please be encouraged and continue the good work because slowly but surely, London is hearing the good news of Jesus Christ and AIG material is involved with reaching the people with the truth of creation and the flaws of evolution which regularly come up as questions. May God continue to bless you all and your ministry.

—P., England

Satisfying the Thirst

I thank God for you, and I also think it’s important for you guys to know how much I appreciate your staunch defense of Truth in the face of the World’s mockery. Not only do you do a remarkable job of proving that belief in our Creator is not illogical, but you also uphold the calling of our Lord to bring others to Him! It’s been so refreshing to see your professionally designed website full of logical, well-reasoned articles standing strong against the deceitful propaganda of those that would call themselves enemies of our Lord.

The true wisdom displayed on your website is like a cold drink of water to my parched brain in this World’s desert of closed-mindedness and anti-God agendas. It has been encouraging to read an AiG article as one of your wise authors makes folly the “wisdom” of those who call us fools. They testify to the existence of God when they even claim the existence of logic! May God bless you and give you increase.

—P.S., U.S.

By way of introduction to my response, let me point readers to a section entitled “Coping with Paradigm Conflict” in my chapter on 14C in the 2005 RATE book edited by Vardiman et al. [Editor’s note: Readers might also be interested inRadioisotopes and the Age of the Earth, Volume 1 (PDF).] In this section I provide some examples of how the radiocarbon community has dealt with the dilemma discovered soon after the accelerator mass spectrometry (AMS) method began to be applied to 14C analysis in the early 1980s. This dilemma is that samples they expect to be 14C-free because of their supposedly old age (>100,000 years according to the standard geological time scale), instead routinely display significant and reproducible 14C levels, typically two orders of magnitude or more above the threshold sensitivity of the AMS system.

This unexpected finding led immediately to a thorough evaluation of every aspect of sample processing in an attempt to identify what most investigators logically assumed to be the result of contamination in their procedures. This earnest search for the source or sources of contamination led to dozens of papers in the peer-reviewed radiocarbon literature on various aspects of AMS methods. For obvious reasons, most of these studies utilized samples that ought to have been 14C-free given their position in the geological record. Although some relatively minor sources of contamination were identified and fixed, the main part of the 14C signal remained, particularly in the case of samples such as coal, wood, bone, and shell from living organisms. This is the reason that 14C levels in biological samples from deep within the geological record are so thoroughly measured and documented in the open radiocarbon literature.

So how does the radiocarbon community deal with this state of affairs? Even to the casual observer, the presence of significant levels of 14C, which has a half-life of only 5,730 years, in biological samples that are supposed to be tens or hundreds of millions of year old cries out for explanation. First of all, researchers within the community have avoided publicizing the problem to outsiders. For the most part, they keep this state of affairs to themselves. And even among one another, they mostly act as if the issue does not exist. In addition, they have adopted some special terminology that prevents most outsiders from realizing the problem exists. One of these terms is in situ contamination. This term was invoked more than twenty years ago by Vogel et al. [1987] to account for the high level of internal 14C (0.44 percent modern carbon, or pMC) they established to be present in the anthracite coal they utilized in their study. When researchers employ this term, they generally mean that the 14C they are detecting was already inherent to the sample when it reached their laboratory. Just how it got there, they generally refuse to speculate. Their job is to measure the 14C in the sample. Just what the sample history may have happened to be before the sample reached their lab, they say, is not their concern.

Nevertheless, to keep this dilemma largely under wraps, most commercial labs apply a high “standard background” to the samples they process. For several labs, this standard background is about 0.8 pMC, corresponding to a radiocarbon age of 40,000 years. This standard background value is subtracted from the 14C value the lab actually measures in each sample. If the resulting 14C value is zero or less, the lab reports an ‘infinite’ radiocarbon age. Since vast majority of samples for materials that ought to be 14C-free, because of their location in the geological record, have values less than 0.8 pMC, this procedure saves the laboratory the awkward difficulty of explaining to a customer why a coal sample, for instance, has a non-zero level of 14C.

Although Bertsche styles himself as an “accelerator physicist, formerly at a leading radiocarbon AMS laboratory,” it is clear from his post that, as far as radiocarbon measurement procedures and issues are concerned, he is a novice. If he were truly an insider, he would be fully aware of the history I just outlined and that fossil material throughout the Phanerozoic record routinely displays 14C levels hundreds of times above the intrinsic AMS measurement threshold. This reality is what has generated the scores of papers over the past 25 years, mostly by researchers at the AMS facilities, seeking to understand this highly unexpected state of affairs. Samples truly more than 100,000 years old should have no detectable 14C. But in reality, biological specimens generally thought to be tens or hundreds of millions of years old consistently contain levels of 14C that at face value would indicate these organisms were alive only thousands of years ago, as I have just indicated.

If Bertsche had fully understood the very papers to which he refers, he would immediately realize that his first claim that laboratory contamination is responsible for the high 14C levels routinely measured in “old” biological samples is unsustainable. To highlight the issues he is failing to grasp, I point to the paper by Brown and Southon [1997] who state

Several “14C-free” background materials were used in obtaining these data: 1) Coal (supplied by Beta Analytic), 2) Calcite (TIRI sample F: Icelandic doublespar), 3) QL4766 wood (> 56.6 ka BP), 4) QL1428 wood (>55 ka BP), and 5) Yale Anthracite (YA-13; no measurable 14C activity). The latter three samples, and their 14C contents, were supplied by the Quaternary Isotope Laboratory, University of Washington (Stuiver, pers. comm., 1996). In our measurements there were no significant differences between the results obtained for these background materials, and the data from all these materials were used.

In Figure 2 these authors plot their own measurements for the 14C levels in what they describe as “14C-free” background materials for varying sample sizes. What a novice reader of the paper can easily miss is that the plot shows that these materials converge to a value of 0.25 pMC for larger sample sizes! The value should be zero for truly 14C-free material. The measured value is 14C some 450 times higher than the threshold for the AMS hardware. That is why the authors use quotation marks with the term “14C-free.” The AMS insiders understand the lingo. Bertsche apparently does not. (It is noteworthy that their value of 0.25 pMC, based on two coal samples, two wood samples, and a calcite, is almost identical to the mean value that the RATE team obtained for its suite of ten coal samples.)

Because of his shallow grasp of the issues, Bertsche throws out a number of “red-herrings.” He invokes the fact that over the years many AMS labs have established that their procedures routinely introduce tiny amounts of modern carbon (with today’s level of 14C), typically on the order of 1 µg, into the samples they process. This level of contamination becomes serious for tiny sample sizes, say, 1 mg or less, especially if the sample is old. On the other hand, 1 µg of contamination has negligible consequences when the sample size is on the order of 100 mg, as was the case for the samples we tested and reported. Bertsche fails to point out the very basic reality that AMS labs normally require a large enough sample such that this issue does not affect the precision of their measurement. For most of the 14C values reported in the peer-reviewed literature which I list in my chapter in the RATE book [Vardiman et al., 2005] the investigators had plenty of material available, and so, small sample size was just not an issue.

Bertsche also makes a “red-herring” of the choice of samples I selected from the peer-reviewed literature to include in the category of non-biological Precambrian. He complains that I excluded two graphite samples that had been oxidized to CO2 and then reduced to graphite again. I did this deliberately, since it was clear from the references that these samples had been reprocessed, and I was seeking to compare apples with apples to get as clear a picture as possible what the 14C level in non-biological Precambrian carbon might be. Surprisingly, he displays a serious lack of familiarity with the terms used to describe the geological timescale. Instead of Pre-Cambrian or perhaps Proterozoic, he substitutes the incorrect term Paleozoic.

Bertsche further reveals the shallowness of his understanding of AMS procedures and terminology by referring to the entire process of converting a sample to graphite as “graphitization.” Standard sample processing involves several steps: first, an acid-base-acid sequence of washing to remove possible surface contamination, then conversion of the carbon in the sample to CO2 (either by dissolving the sample in acid, if it is a carbonate, or by direct oxidation via combustion), and finally reduction of the resulting CO2 to graphite, usually as a graphite coating on iron or cobalt powder in the presence of hydrogen at about 600 °C. Only the last step in this overall process is referred to by people in the radiocarbon community as “graphitization.” The paper by Kirner et al. [1995], to which Bertsche refers, describes these sample processing steps in detail. Contamination can occur during any one of these steps, but the AMS labs have developed techniques for minimizing it and also for detecting when something has gone awry. None of the papers to which Bertsche refers identifies the final graphitization step as the main culprit as far as the overall sample processing contamination arising is concerned. Just why he uses the term graphitization in the peculiar manner he does is a mystery.

Moreover, Bertsche is simply incorrect when he then claims “the graphitization process typically add[s] from 0.1 to 0.7 pMC (highly dependent on sample size and procedure).” This is absurd. He cannot support such a claim from any peer-reviewed source. It is certainly not to be found in any of his references. In fact, the papers to which he refers all clearly refute such a notion except for atypical sample sizes. Hence, Bertsche’s statement that “the differences [Baumgardner] sees between geological and biological samples is simply the contamination introduced by the graphitization process” is flatly unsupportable. Dozens of papers in the peer-reviewed literature irrefutably demonstrate this, as I point out in my chapter in the RATE book. If Bertsche disagrees, let him clearly show why all these AMS specialists are wrong!

Bertsche produces still more “red-herrings” to create confusion about the RATE 14C measurements on its ten coal samples. First, he quotes the scientist who actually performed the AMS measurements to the effect that the coal samples “were contaminated in situ.” Again, one needs to understand what this terminology means to an AMS insider. To an AMS insider, “contaminated in situ” means simply that the 14C measured by the AMS system was intrinsic to the sample before it arrived at the laboratory; in other words, such 14C is not a result of laboratory procedures.

Bertsche then tosses out several possible ways the coal might have acquired its inventory of 14C in its natural setting. He first mentions the presence of uranium and alludes to northern Australian coals. Northern Australian coals? Just where, pray tell, might they be found? There are none of any significance in northern Australia. In regard to 14C production due to the presence of uranium in crustal environments, I treat that topic in detail in section 7 of my chapter and show the maximum plausible 14C production rate, given measured neutron fluxes in deep mines and measured reaction cross sections, is more than four orders of magnitude too small to account even for the small measured 14C levels in diamonds. This same analysis also applies to coal. Uranium concentrations in coal are typically less than those measured for granite, which is the setting for most of the diamonds we studied. (See the USGS fact sheet on uranium concentrations in coal and granite in the References.)

Next, incredibly, Bertsche proposes microbial growth as a source of 14C! Just what does Bertsche imagine such microbes to be eating if it is not the coal itself? It they are eating the coal, then how can the 14C levels within them be any different from that of the coal itself? It seems he’s grasping for straws here.

Next Bertsche resorts to speculating that our coal samples were contaminated while in storage “in a DOE geology lab refrigerator.” To me that smacks of a deliberate distortion of what I described in my chapter on pages 605–606 regarding the pedigree of the samples we acquired from the U. S. Department of Energy Coal Sample Bank at Pennsylvania State University. I emphasized the careful procedures applied in the collection and preservation of these samples. They were sealed under argon to preclude contamination from just moments after they were collected. For most of their lives these samples were sealed in argon in multi-laminate foil bags and refrigerated at 3 °C. Just why does Bertsche choose to engage in this sort of distortion? To me it suggests a significant level of desperation in the face of such obvious evidence for the presence of genuine intrinsic 14C in these samples.

Note that in attempting to explain the 14C in our coal samples as contamination outside the lab, Bertsche is undermining his earlier arguments that the nearly identical 14C levels reported for coal and wood by AMS research scientists in the peer-reviewed literature are readily attributable to contamination within the lab. So which is it? Bertsche cannot have it both ways. Indeed, the preponderance of papers, written by AMS specialists, show that the 14C levels routinely measured for coal and other fossilized organic remains are not the result of contamination within the lab. The RATE coal measurements merely serve to affirm this already well-established fact.

Finally, Bertsche seeks to dismiss the 14C we measured in diamonds also as contamination. He cites a 2007 paper by Taylor and Southon. The paper describes the techniques the authors recently applied to measure 14C levels in natural diamond. As part of the background of their paper, Taylor and Southon list six potential sources of contamination for samples analyzed in AMS laboratories. At the very top of their list is “1 Pseudo 14C-free sample: 14C is present in carboniferous material that should not contain 14C because of its geological age.” By placing this item first, they acknowledge what has long been known by AMS radiocarbon specialists: namely, that the vast majority of samples that ought to be completely 14C-free because of their geological context display 14C levels far beyond what can be accounted for by sources attributable to laboratory procedures or equipment design.

Indeed, they implicitly acknowledge this in the first paragraph of their introduction by mentioning 14C ages of 47.9 ka for a marble sample and 52.1 ka for a Pliocene wood sample, both far beyond the AMS 100,000-year detection limit they mention in their first sentence. It is astonishing that these authors never attribute this discrepancy to any one of the six possible explanations they list later in the article. In fact, they are completely silent as to just what the correct explanation might be. This silence is all the more noteworthy since the 14C level in the marble sample is 546 times the detection limit of their AMS system.

The main point of their paper is that by using diamonds and mounting them directly in the sample holder, they are able to exclude items 2 through 5 in their list of six potential sources of contamination. These items are 2 Combustion/acidification background, 3 Graphitization background, 4 Transfer (to the sample holder) background, and 5 Storage background. The last item in their list, 6 Instrument background, involves a “14C signal registering in the detector circuitry when 14C-ion [is] not present.” This item is routinely and reliably tested by running the system with no sample in the aluminum sample holder. This test is the basis for the value of the ultimate AMS detection limit, about 0.0005 pMC, corresponding to about 100,000 14C years. Therefore, by process of elimination, what these authors are measuring and reporting is their item (1), namely, 14C intrinsic to the diamonds! This is precisely what we claim for diamond samples we measured using the same technique.

Taylor and Southon report results from eight individual natural diamonds and from six separate fragments cut from a single diamond. The 14C values ranged from 0.005 to 0.021 pMC for the eight individual diamonds and 0.015 to 0.018 pMC for the six fragments, with typical uncertainties of ±0.001-0.002 pMC. Note that a value of 0.015 exceeds the AMS system background value by a factor of 30.

I certainly grant that one needs almost to be an AMS insider to be aware how routine it is to measure the sixth item in Taylor and Southon’s list, instrument background, and hence to realize that the 14C values they report represent intrinsic 14C in the diamonds themselves and not instrument background. It is therefore understandable why Bertsche comes away with an incorrect conclusion after reading their paper. This illustrates again, however, that he is not the expert in 14C dating that he makes himself out to be.

What about the RATE diamond measurements? Bertsche alludes to the fact that the RATE team also tested diamond by placing diamonds directly into the AMS sample holder. Our tests were done in 2006 after the RATE book was published in 2005. We obtained results quite similar to those reported by Taylor and Southon in 2007. Our ten diamond samples displayed 14C values between 0.008 and 0.022 pMC, with a mean value of 0.014 pMC. Certainly these 14C levels are much smaller than what we obtained for our coal samples; so, caution is obviously advisable in their interpretation. Nevertheless, unless one has a philosophical bias against such a possibility, the most plausible explanation, astonishing as it may be to some, is that natural diamond contains measurable and reproducible levels of intrinsic 14C.

In summary, Bertsche fails to make his case that the radiocarbon in fossil organisms described so frequently in the peer-reviewed radiocarbon literature, as well as the radiocarbon we document in our own coal and diamond samples, is “nothing more than contamination.” In light of this discussion, I urge him to take a fresh look at the issues involved, especially the rationale and techniques we used to reach our conclusions.

Help keep these daily articles coming. Support AiG.

Footnotes

  1. Brown, T. A. and J. R. Southon. 1997. Corrections for Contamination Background in AMS 14C Measurements. Nuclear Instruments and Methods in Physics Research B 123: 208–213.
  2. Kirner, D. L., R. E. Taylor, and J. R. Southon. 1995. Reduction in Backgrounds of Microsamples for AMS 14C Dating. Radiocarbon 37(2): 697–704.
  3. Radioactive Elements in Coal and Fly Ash: Abundance, Forms, and Environmental Significance. 1997. USGS Fact Sheet, FS-163-97 (http://greenwood.cr.usgs.gov/energy/factshts/163-97/FS-163-97.html)
  4. Taylor, R. E. and J. Southon. 2007. Use of Natural Diamonds to Monitor 14C AMS Instrument Backgrounds. Nuclear Instruments and Methods in Physics Research B 259: 282–287.
  5. Vardiman, L., A. A. Snelling, and E. F. Chaffin (eds.), Radioisotopes and the Age of the Earth: Results of a Young-Earth Creationist Research Initiative. 2005. El Cajon, CA: Institute for Creation Research and Chino Valley, AZ: Creation Research Society, Chino Valley. Chapter 8, 587–631. (An earlier version of this chapter was presented at the 2003 International Conference on Creationism, and this paper in PDF format may be downloaded at http://www.icr.org/pdf/research/RATE_ICC_Baumgardner.pdf.)
  6. Vogel, J. S., D. E. Nelson, and J. R. Southon. 1987. 14C Background Levels in an Accelerator Mass Spectrometry System. Radiocarbon 29(3): 323–333.