GSA members only
Discussion of GSA Time Unit Conventions
The Case for Abandonment of Dual Units for Ages and Durations of Time
The IUPAC-IUGS Joint Task Group on Isotopes in Geosciences (TGIG) has recommended the use of a single unit of time which does not intrinsically distinguish between age, as used particularly in the Earth Sciences, and time intervals. The motivation for this recommendation was to bring Earth and Planetary Sciences’ usage of time units into consistency and accord with the Sisteme International (SI) and thereby achieve a more seamless compatibility with other physical sciences. The issue rose to our attention when the three nuclear chemists serving on the TGIG expressed confusion over inconsistent use of time units during our evaluation of radioisotopic decay constants.
The most straightforward issue is that of consistency- multiple units are in common usage, such as Myr and Ma, that are intended to convey exactly the same concept. The need for standardization is obvious and, we assume, uncontroversial.
Regarding the apparently more controversial issue of “absolute” (e.g. Ma) versus differential ( e.g., m.y.) time, both the general use of the SI units and the TGIG’s rationale are quite simple. The second is a duration, and all multiples of the second are intervals. The annus (a) is a derived unit, defined in terms of the second, and is used throughout the scientific world. There is no question that time intervals may be expressed in a, ka, Ma, Ga, etc. What is debated here is the validity of an ad hoc unit to distinguish between “absolute” time and time intervals.
It must be acknowledged that units for any physical quantity in the SI should obey a distributive law such that xm − ym = (x−y)m. We don’t use different units for absolute temperatures versus temperature differences, for example. Everyone would presumably agree that a magma at 1000 K is 100 K hotter than one at 900 K, because 1000 K − 900 K = (1000 − 900) K = 100 K. Chemists, physicists and geologists alike have all managed to live with using the same unit for absolute and differential values. The same rule, of course, applies to distances: if the Triassic/Jurassic boundary is 700 m down a borehole, and the Jurassic/Cretaceous boundary is 500 m down the same borehole, we would all agree that the two boundaries are 200 m apart in that borehole. By the same token, the duration of the Jurassic Period is given by the difference in ages between these two boundaries, and is therefore (as defined by GTS 2004) equal to: 199.6 Ma − 145.5 Ma = 54.1 Ma.
The main objection to our recommendation is embodied in the notion that, for example, the age difference between 264 Ma and 255 Ma (two Permian ages) cannot be called 9 Ma because “A stratigrapher knows that t=9 Ma means Miocene!” (L. Edwards, written communication, 22 June 2009). The logic of this perceived need for dual units can only be grasped if one ignores both the SI and the ability of language to convey clarity. For example, we cite from a NASA website: “On May 4 the spacecraft executed its second trajectory correction maneuver. Burning its rocket engine for 95 seconds, the spacecraft speed was changed by 18.2 km/h”. Obviously, NASA didn’t mean that the spacecraft slowed to the speed of a bicycle, and this is clearly communicated with the use of “by” rather than “to” in the last sentence.
Part of the zeal for maintaining distinct time units may stem from a perception that there is a fundamental difference between absolute and differential time. In fact, there is not- absolute time, as historically represented in GSA journals by ka, Ma, and Ga (meaning thousands, millions, and billions of years ago) have an implicit time datum built into them, which is generally “the present” or in the case of ages determined by radiocarbon, the calendar year 1950 CE. Unfortunately, “the present” is not well-defined, but nonetheless any radioisotopic age is determined relative to the time of isotopic measurement, and the span of less than a century over which such measurements have been made to date is negligible for most radioisotopic systems. Regardless of whether ambiguity in meaning of “the present” is significant, the fact remains that even such “absolute” ages are inherently relative to a datum-whether or not that datum is explicitly defined.
Proponents of dual time units argue that the a priori distinction between time differences and “absolute” time (or age) is a matter of convenience, without which literary precision would suffer. We are convinced on the other hand of the inconvenience of an abnormal status, whereby dual time units should be unmatched by dual length or mass units, noting that scientists in other disciplines have expressed themselves heretofore just fine without dual units for length, mass, temperature or other fundamental quantities that are just as important to them as time is to us geoscientists.
A resolution of this debate may lie in our proposed addendum to the definition of the derived unit annus (a), which is to benchmark the annus definition in terms of seconds to the calendar year 2000.0. This would place the annus and its mulipliers ka, Ma and Ga on comparable status with the Kelvin or Celsius temperature scales, both of which have defined reference points. Thus for example −10 ka would mean 10,009 years (i.e., 10.009 ka) prior to the writing of these words. There is no need maintain dual units under this or any other definition.
Paul R. Renne
Director, Berkeley Geochronology Center and Professor in Residence, Dept. of Earth and Planetary Science, University of California, Berkeley
Igor M. Villa
Professor of Geochronology, Institute for Geology, University of Bern
The Case Against
CONVENTIONS AND SYMBOLS FOR GEOLOGICAL TIME
The Council of the Geological Society of America (GSA) has decided wisely to seek advice from the society’s membership as it reconsiders conventions and symbols for geological time for use in GSA publications. The content of arguments offered will likely carry more weight than the number of responses favoring any particular view. Broad engagement is nonetheless encouraged in order to sustain the claim that the membership has been appropriately represented.
The outcome is also important. Once a decision has been made, any convention will be subject to future amendment only insofar as this is needed to maintain consistency with the standards of such international bodies as the International Union of Geological Sciences (IUGS) and the International Bureau of Weights and Measures (BIPM) – the organization responsible for the International System of Units (SI). At the same time, GSA has both an opportunity and a responsibility to provide thoughtful advice.
The central issue for GSA relates to conventions for communicating Earth science. Conventions are a matter of choice, not discovery, and they ought to reflect the varied preferences and needs of the diverse constituencies involved. While it is useful to establish rules that apply as far as possible across the sciences — and SI provides a mechanism for accomplishing that — it is also the case that each scientific discipline inevitably develops its own culture. Earth science and astronomy, for example, are distinctive because they involve large physical and temporal scales and an important historical dimension. For geologists, time is more than the x-axis for the output of some laboratory experiment. It is the context in which we understand our planet’s evolution, make comparisons between geohistorical data of many different types, and relate events at one location with those at another.
The practice of carefully distinguishing events and dates in geological history from unconstrained spans of time has proven vital for communication among Earth scientists for more than thirty years, and it ought to be preserved (North American Commission on Stratigraphic Nomenclature, 1983, 2005; Salvador, 1994; Aubry et al., in press). According to this convention, ‘90 Ma’ and ‘100 Ma’ refer to specific datums in the Cretaceous Period. The 10 million year interval between those datums is not written as ‘10 Ma’ because that invites immediate confusion with a different moment in time, in the Miocene Epoch. Geohistorical dates and durations of geological time are also governed by different sign conventions. Time’s arrow points towards the future. Yet an event at 100 Ma took place before one at 90 Ma.
A different view has been articulated in the draft recommendations of a joint International Union of Pure and Applied Chemistry (IUPAC)-IUGS task group on Isotope Data In Geosciences (Holden et al., manuscript in review). According to these authors, an age is no more than the time difference between “now” and an event in the past, and it is equivalent conceptually to the time difference between two events in the past. Adherence to SI, it is argued, requires units to follow algebraic rules such as the distributive law. e.g., 100 Ma − 90 Ma = (100 − 90) Ma = 10 Ma. Adoption of ‘a’ (‘annus’), ka, Ma and Ga as symbols for years and thousands, millions and billions of years, and in reference to both durations of time and dates, will bring GSA into compliance with SI and permit the abandonment of such ad hoc abbreviations as k.y., M.y., m.y. and G.y. (among many).
My own view is that the IUPAC-IUGS task group is for the most part intent on fixing a problem that does not exist, and that their recommendations, if accepted, will constitute an unwelcome step backwards for communication among Earth scientists. The SI unit for time is the second (s). So whatever conventions are finally adopted, and unless that includes measuring geological time in seconds, GSA’s ‘compliance’ with SI will be not much affected. It is permissible under SI rules to make use of non-SI units when there is a “particular scientific advantage” in so doing (BIPM, 2006, p. 123). And given the absence of agreement on how precisely a year ought to be defined, a very good case can be made for clarifying that with what is known formally as a ‘non-SI unit accepted for use with the SI’ (BIPM, 2006, p. 123). Even then, however, SI rules do not apply to events in Earth history (the ka, Ma and Ga of current usage) in the manner supposed by the IUPAC-IUGS task group for a very simple reason: they are not physical quantities even if they are expressed in multiples of years. Nor is it necessary or advisable, in formulating a non-SI unit for use with SI, to adopt the symbols ka, Ma and Ga.
A simple analogy provided by Aubry et al. (in press) may help. Consider five exits on a highway, named for kilometer posts 1, 6, 13, 18 and 23. The distance between Exit 1 and Exit 18 is 17 km; it is not 17 exits or even 17 km-posts. Time durations are homologous to geographic distances, while geological dates are homologous to exits and km-posts. Exit 18 can be at only a single location along the highway, just as 18 Ma represents a specific moment in the Miocene Epoch. In contrast, there is a literal infinity of 17 km-long intervals between Exit 1 and Exit 23, just as there is an infinity of 17 million-year-long intervals between the beginning and end of the Miocene. The distributive law of algebra does not apply to either exits or events in Earth history.
The IUPAC-IUGS task group offers a counter example on the “use of absolute and relative SI units.” “It is rarely denied,” they state towards the end of their manuscript, “that the depth difference between 100 m and 200 m below ground level in a borehole is 100 m.” This is true, and it is a fine example of SI usage. It is also specious because depth in a borehole hardly carries the same significance as geohistorical events. Moreover, it is necessary in borehole data to specify the depth with respect to a datum (the ground surface, the sea floor, the kelly bushing, etc.). The unit ‘mbsf’ (meters below seafloor) used by the Integrated Ocean Drilling Program exemplifies why, even in this case, it is useful to employ a modified unit for specific depths.
While the symbol ‘a’ (‘annus’, and its derivatives) has been used for years and multiples of years by various organizations and journals in the manner proposed by the IUPAC-IUGS task group, and by astronomers, chemists and physicists as well as Earth scientists, that usage has been far from monolithic (see Aubry et al., in press for a review). The appropriate procedure for resolving a conflict in the choice of symbols will be for IUGS to engage IUPAC, the International Union of Pure and Applied Physics (IUPAP), the International Astronomical Union (IAU), the International Organization for Standardization (ISO), and so forth. It is premature for GSA or IUGS to anticipate the outcome of such discussions.
The proposed formalization of a, ka, Ma, Ga, etc. as symbols for a non-SI unit for use with SI is also problematic because it conflicts with the uniqueness that is characteristic of SI. The SI-approved prefix for 1015 is peta (P). While half lives as long as 1015 years are rarely of concern (the hafnium isotope 174Hf provides an example), the symbol Pa is already reserved for a unit of pressure and stress (pascal). In comparison, ages not governed by SI and five orders of magnitude greater than the age of the Universe are not of concern to anyone.
I agree very much with one of the IUPAC-IUGS task group recommendations: the welter of internally inconsistent abbreviations for spans of geological time needs to be rationalized. The symbols recommended by Aubry et al. (in press) for this purpose are yr, kyr, Myr and Gyr using standard SI prefixes for 103 (k), 106 (M) and 109 (G) years (yr). The abbreviations m.y. and b.y. can be defended for millions and billions of years as correct English, with periods denoting the foreshortening of the words millions, billions and years. In this case, m is specifically not an SI prefix (milli). However, k.y., M.y. and G.y., though formatted in a similar way, are poor choices because k, M and G are SI prefixes. So periods are not required. The difficulty with y, ky, My and Gy is that Gy is already a symbol for an SI derived unit for absorbed energy (gray), where Gy stands for J/kg or m2 s−2 (BIPM, 2006, p. 118). If Gy is not available for billions of years, on the basis of priority, then for reasons of consistency My, ky and y ought not to be used either. The symbol my is incorrect because in the absence of periods it implies 10−3 years, and not the intended 106 years.
In summary, GSA should continue to distinguish geohistorical dates (in ka, Ma and Ga) from spans of time (for which other abbreviations or symbols are needed). I have no strong opinion on the use of ‘a’ for a date in years. That strikes me as an appropriate symbol from the standpoint of consistency. However, the reference (zero) needs to be carefully specified, as is currently the case with BP (before present). The radiocarbon, cosmogenic isotope and archaeological communities are among those with a vested interest in such details. As a matter of editorial policy, GSA may choose in the near term to use whatever abbreviations the Publications Committee prefers for intervals of time. The symbols yr, kyr, Myr and Gyr are recommended here, in the absence of any obvious conflict. Formal establishment of a non-SI unit for use with SI in Earth science (and astronomy) is a worthy goal, but one that will require the engagement of diverse scientific communities under the umbrella of IUGS, IAU and other interested international organizations if a true consensus is to emerge on the choice of appropriate units.
Helpful email exchanges with Marie-Pierre Aubry, William Berggren, Lucy Edwards, Brian Pratt, Paul Renne, John Van Couvering and Igor Villa are gratefully acknowledged. The in press manuscript by Aubry et al. may be downloaded from the following website: www.ldeo.columbia.edu/~ncb/Selected_Articles_all.html
Aubry, M.-P., Van Couvering, J.A., Christie-Blick, N., Landing, E., Pratt, B.R., Owen, D.E., and Ferrusquía, I.-V., Terminology of geological time: Establishment of a community standard: Stratigraphy, in press.
Bureau International des Poids et Mesures (BIPM), 2006, Le Système International d’Unités — The International System of Units (SI): Paris, Stedi Media, 8th edition, 180 p.
Holden, N.E., Bonardi, M.L., De Bièvre, P., Renne, P.R., and Villa, I.M., Recommendation for a common definition and use of the year as a derived unit of time: Pure and Applied Chemistry, manuscript in review.
North American Commission on Stratigraphic Nomenclature, 1983, North American Stratigraphic Code: American Association of Petroleum Geologists Bulletin, v. 67, p. 841-875.
North American Commission on Stratigraphic Nomenclature, 2005, North American Stratigraphic Code: American Association of Petroleum Geologists Bulletin, v. 89, p. 1547-1591.
Salvador, A., ed., 1994, International Stratigraphic Guide. A guide to stratigraphic classification, terminology, and procedure: International Union of Geological Sciences and Geological Society of America, second edition, 214 p.
Department of Earth and Environmental Sciences and Lamont-Doherty Earth Observatory of Columbia University, Palisades, New York 10964-8000, USA