Orthodox science is confident that the Earth originated 4.56 billion years ago. Though the age is not offered with an invitation to treat it with some caution, we should keep in mind that the planet has no birth certificate, and any precise figure is, inevitably, a theory- dependent inference, not a fact. Reasonable though the logic may appear in isolation, the theory behind the logic should be tested. If a coroner performs an autopsy and deduces from the bone tissue that the corpse is of a woman in her 70s whereas her outward appearance suggests she died in her teens, we may suspect that there is something wrong with his dating method. Common sense must be allowed to play a role.

To date a rock we must identify something in it that has changed over time at a regular rate. This is what radioisotope dating does. Certain elements are radioactive: they emit particles and decay into elements whose atomic number is thereby reduced. Though we cannot predict exactly when a particular atom will emit a particle, overall the decay takes place at a statistically constant rate, and if we can deduce what the parent-daughter ratio was at the time the rock crystallised, we can calculate how much time must have elapsed to account for the ratio now. Obviously the method applies only to rocks that contain the products of radioactive decay and are not derived from other rocks, i.e. they formed direct from the mantle in the course of igneous activity.

It also applies only if the rate of radioactive decay has always been the same. But can we be sure that it has been? Suppose the pattern was one where the rate gradually decreased, until the rate of decrease tailed off to zero. Would we be able to distinguish between these different possibilities? Since the currently measured value of the decay rate (or half-life) of an element has no theoretical basis, we need to be able to test the method against the primary evidence. It needs a ‘reality check’, much as the conclusion of our imaginary coroner needed a reality check. Unfortunately, this is never attempted. If a geological sequence suggests that it built up more rapidly than present-day decay rates suggest, the dating method itself is not questioned. Instead, the assumption – whether or not there is direct evidence for this – is that there were long intervals within the sequence which left no geological record. The reasoning is essentially circular.

Since the age of the Earth is a scientific question, neither religious dogma (”the Bible requires a short timespan”) nor atheistic dogma (”evolution requires a long timespan”) should be allowed to impose an answer that the primary evidence does not support. We advise the same approach as we recommend when considering to what extent organisms have evolved. If the fossil record shows species descending from other species by innumerable fine gradations and all converging upon a common ancestor, that is the conclusion we should draw. If it shows only limited evolution, we should not pretend that it shows something else. Science is not, in principle, about imposing on the evidence interpretations that make up for its not showing what we hoped for.

Anyone interested in the age of the Earth should endeavour to take responsibility for the question himself, and form some independent view. Below are a few thoughts that may help.

Milankovitch cycles

While there may be no independent check on radioisotope dating in relation to the entire span of Earth history, this is not quite true if we consider just the Mesozoic and Cenozoic. Here it has become increasingly common to compare the results of the method with the time the Earth takes to complete certain astronomical cycles. Such cycles are thought to affect the Earth’s climate and to be capable of being reflected in geological sequences. Thus, if a cyclical pattern of deposition can be matched with an astronomical cycle and the length of the cycle can be quantified, the geologist can calculate how long the whole sequence took to form. In principle it becomes possible, working back from the present, to link all such sequences into a master sequence, and to compare this astronomical timescale with the timescale based on half-lives.

The shortest astronomical cycles are the day, month, and year. In the case of the year, the cycle is defined by the seasons. Because the Earth’s axis is at an angle relative to its orbit round the Sun, a hemisphere experiences summer when it is tilted towards the Sun and winter when it is tilted away. Three other cycles also affect the intensity of the seasons.

The Earth’s tilt – known as its obliquity – is currently 23.5 degrees. It has been decreasing at a rate of 1.19 metres per century and is believed to oscillate between a minimum of 22.1 degrees and a maximum of 24.5 degrees, with a complete cycle calculated to take 41,000 years. The greater the tilt, the greater the difference between summer and winter.

The shape of the Earth’s orbit round the Sun also varies, from a near-perfect circle to an ellipse. This pattern of change – the eccentricity cycle – extends over 98,000 years. When the orbit is markedly elliptical, summers which coincide with the shortest distance between the Sun and the Earth will be warmer than those which coincide with the longest distance.

Finally, there is the phenomenon known as precession, where the elliptical orbit of the Earth turns around itself, and the Earth’s axis wobbles around itself, like the axis of a spinning top. Precession of the Earth’s orbit increases the seasonal contrast in one hemisphere while decreasing it in the other. At this present stage in the cycle the Earth is closest to the Sun when the northern hemisphere is in winter, so northern winters are less cold and summers less warm. Precession of the Earth’s axis (thought to be caused by the pull of the Moon and the Sun on the equatorial bulge) causes a corresponding shift in the celestial poles. These days the North Star is in the constellation Ursa Minor, but 5,000 years ago the North Star was in the constellation Draco. The precession cycle varies between 19,000 and 23,000 years.

The three cycles of precession, obliquity and eccentricity are known as Milankovitch cycles, after the scientist who proposed that these long-term variations have an appreciable effect on climate. Milutin Milankovitch published his theory in 1941, but it was not until the 1980s that geologists began applying it to sedimentary sequences. These seemed to bear him out. Where deposits were stratified in couplets and sedimentation seemed to have been fairly continuous, one couplet could often be interpreted as indicating a warm climate, the other a cool climate.

A good example are the couplets seen in chalk sequences. Chalk consists predominantly of detritus from calcareous warm-water algae known as coccolithophores. Although from a distance it can look like a monotonous mass of white or grey, on closer inspection chalk invariably proves to be bedded. In some places, beds of relatively pure chalk alternate with beds of marl – chalk mixed with clay. In others, the alternation is between beds that are compact and densely burrowed and beds that that are not so compact or densely burrowed. Often the tops of the upper beds are marked by nodules of flint.

The interpretation given to the chalk-marl couplets is that they reflect the precession cycle, with the chalk accumulating when the climate was warmer and the marl accumulating when the climate was colder. Clay, a product of erosion, eroded from the land more quickly when the climate was wetter, as is usually the case with colder climates. Oscillations in oxygen isotope ratios (δ¹⁸O) appear to confirm the interpretation, since they are an index of temperature and trace a similar pattern. Climate change thus provides an explanation for the very occurrence of bedding in chalk.

If the Milankovitch theory is correct, such cyclicity can be used to test the radioisotope timescale. For example, if radioisotope dating attributes 3 million years to a sequence and the precession cycle during the period was 20,000 years, the sequence would be predicted to comprise 150 such couplets. Substantially more or fewer than 150 would be evidence that the timescale was in error. In practice, however, the two approaches rarely give the same result, and sometimes even approximate agreement is achieved only on the premise that the couplets reflect obliquity rather than precession. On the other hand, some studies have claimed to detect cyclicity corresponding to all three Milankovitch cycles. In such instances the smallest cycle is visible as repeating couplets and the larger cycles as ‘bundles’ of couplets – a bundle of four or five couplets being seen as evidence of the eccentricity cycle. Thus, in relation to the Biancone Formation, in the Alps, Mayer and Appel (1999) report:

Cycle periods of 45 cm, 80 cm and 180 cm likely correspond to dominant precession, obliquity and eccentricity cycles. Owing to the inaccuracy of the Cretaceous time scale, periods cannot be matched exactly, but cycle ratios are extremely close to expected ratios so that Milankovitch climate cycles could be positively identified in this Early Cretaceous section.

Since the two methods of dating do not agree, and the radioisotope-dated timescale is not as precise as might be supposed (Gradstein & Ogg 2004), it is the latter which is judged to be inaccurate. Milankovitch cycles offer higher resolution, down to 20,000 years instead of uncertainties of a million years or more, and consequently geochronologists are now using them to ‘tune’ the radioisotope timescale. The latest timescale published (Gradstein et al. 2004) tunes radioisotope dates back to the Miocene. Portions of the Triassic, Jurassic, Cretaceous and Palaeocene have also been tuned, although, being discontinuous, these have yet to be tied to the present.

Astronomical tuning is a rash move, for if the only criterion for determining whether a sedimentary sequence reflects Milankovitch cycles is the degree of closeness to the radioisotope timescale, there is no independent control on either method. The Milankovitch interpretation is validated by producing a result approximately consistent with the radioisotope dates available, and the radioisotope timescale is then adjusted to it. The reasoning is again circular.

If the danger is not clear enough from the Biancone Formation, it is well illustrated by the debate over a succession in the western Dolomites, where 470 metres encompass around 600 bedding cycles. According to Preto and Hinnov (2003), it was possible, once allowance was made for variable rates of sedimentation, to detect signals relating to both precession and eccentricity:

All of the principal periodicities related to the precession index and eccentricity, calculated for 220 Ma [middle Triassic], are present: P1 (21.9 ky); P2 (17.8 ky); E1 (400 ky), E2 (95 ky), and E3 (125 ky), along with a peak at a frequency double that of the precession, which is a predicted feature of orbitally forced insolation at the equator. Components possibly related to Earth’s obliquity at ca. 35 ky and ca. 46 ky are present as well.

(P1 and P2 designate the different precession cycles, E1-E3 the different eccentricity cycles, ‘Ma’ is millions of years ago and ‘ky’ is a thousand years.) The succession preserved ‘the oldest pristine Milankovitch signature yet observed in the geologic record’. Other geologists rejected the interpretation, however, finding that radioisotope ages from interbedded volcanic-ash layers indicated a very much shorter interval. So it seems the procedures involved in analysing cyclical bedding can generate Milankovitch-like periodicities (once calibrated to the radioisotope timescale) that are nothing of the sort: the appearance of a close fit with the astronomical cycles may be illusory.

There may also be mathematical grounds for thinking so. Mensur Omerbashich (2006) has questioned the entire validity of the procedures which result in claims that bedding cycles reflect multiple kinds of Milankovitch cycle. In the case he analysed, the alleged 99% confidence level was ‘mostly meaningless in the context of total-information quality’, owing to prior editing of the data and failure to distinguish between signal and noise.

Discrepancies between the two timescales, some relatively minor, some major, can be documented many times over (e.g. Hilgen & Langereis 1989, Karner & Muller 2000, cf Ehrlich 2007). In order to save the theory, it has even been suggested that obliquity can dominate in one locality and precession, over the same interval, in another (Krijgsman et al. 2004). Like radioisotope dating, Milankovitch theory is an example of a scientific paradigm (Kuhn 1962), an all-embracing explanation which provides the framework within which ‘normal science’ can operate but which is not itself tested or questioned. Problems are identified and solved, so far as possible, within its terms. Anomalies with the potential to undermine the paradigm are put to one side, ascribed to errors in the data, or accommodated by modifying the paradigm, but faith in the paradigm itself remains strong. Thus, science can be both critically questioning in the domain where normal science takes place and unquestioning at the fundamental level where the thing at stake is its world-view and the sense of belonging to a brotherhood of common values and beliefs.

An alternative to Milankovitch

That said, the phenomenon of cyclical bedding is real, and if it is not a reflection of Milankovitch cycles, it must be the reflection of some other cycle. Chalk bed sequences – which provide some striking illustrations – can be traced for hundreds of miles; in one instance they can be traced from outcrop to outcrop over more than one and half thousand miles (Gale et al. 1999). They demand climatic explanations that apply on a global rather than regional scale.

Suppose, then, that the warm-cool cycle of each couplet was of summer and winter rather than precession – that we were looking at the deposit of one year rather than twenty thousand. Figure 1 (from Gale et al.) illustrates a characteristic series of chalk-marl couplets from the Cenomanian part of the Upper Cretaceous. The grey-scale fluctuations track the proportion of clay in the chalk, from 5-15% in the light-coloured beds to 10-30% in the darker beds. The top of each cycle is an omission surface, where sedimentation ceased for a time and animals made burrows. Although burrowing (‘bioturbation’) is reported to be pervasive throughout the succession, in the chalk it appears to be intensive only downward from the omission surface. Most of the marl beds are totally bioturbated, suggesting that the marl was a more oxygenated or nutrient-rich environment for deposit-feeders than the chalk. This is also evidenced by the lack of significant bioturbation from the marl into the chalk.

Dense bioturbation can commonly occur over a few months, and the detail of the fabric points to short time-spans. The walls of later generations of burrows are more sharply defined than earlier ones, indicating an initially high water content followed by dewatering and compaction (Jablonski & Bottjer 1983). The low level of activity in the lower part of the chalk beds is even less compatible with thousands of years being allocated to that part of the cycle. The coincidence of intense burrowing at the top with the virtual cessation of sedimentation suggests that bioturbation did not occur lower down in the bed because the rate of sedimentation was too high.

Figure 2 shows the δ¹⁸O profile of three chalk-marl couplets in the ‘white cliffs’ between the English towns of Dover and Folkestone, also of Cenomanian age. The zig-zag pattern follows that of the greyness scale (Fig. 1), and since low oxygen isotope ratios in sea-floor oozes correlate with warm sea-surface temperatures, and vice versa, explaining this as the effect of summer and winter does not seem unreasonable. The same pattern may be seen in the shells of individual organisms. A study of the tropical bottom-dwelling foram Cyclobirculina, for example, which has a lifespan of one year, recorded a variation in δ¹⁸O ratio from -0.5 in the summer to +1.5 in the winter (Wefer & Berger 1980 and Figure 3). Growth rate increased with age, peaking in the spring. Similar patterns have been detected in other kinds of carbonate-secreting organism, both from the past (Purton & Brasier, 1999) and from the present (e.g. Dunbar & Wellington 1981, Hickson et al. 1999).

Since coccolithophores are much smaller than forams and have a lifespan of only days or weeks, the ooze composed of their remains would reflect the annual oscillation collectively, not individually. They are more prevalent in the chalk than the marl and are thought to represent productivity blooms (Leary et al. 1989). The chalks are dominated by microplankton that lived close to the surface, the marls by microplankton that lived in deep water or on the sea bottom. Temperatures rose steeply in the course of marl deposition, peaked near the base of the chalk beds, then fell less steeply (Fig. 2). Fossil escape burrows have been reported from some bases (Leary et al. 1989), indicating that the rate of deposition in the lower part of the chalk beds was sometimes extremely high. This would also account for the relatively sharp transition from marl to chalk, and for the chalk being rather purer nearer the base than nearer the top (Fig. 1). The overall difference in composition between chalk and marl would be due to higher rates of planktonic productivity during early summer.

In modern settings the rate of coccolith flux to the seafloor has also been observed to vary seasonally. Around the Canary Islands sedimentation peaks in February/March following phytoplankton blooms in the winter (Sprengel et al. 2002). In the Arabian Sea the settling rate peaks in January and declines to very low levels in the months of August to November (Andruleit et al. 2004). Thus the hiatus in sedimentation at the top of the chalk beds is directly comparable to the virtual cessation of coccolith flux in these settings from late summer to late autumn.

Similar patterns characterise the chalks that formed later in the Cretaceous, during the Maastrichtian. As with outcrops onshore, cores extracted from the Dan Field in the North Sea showed metre-scale cycles, but here the alternation was between chalk that consisted of porous, mostly unburrowed sediment and chalk, higher up, that was compact and intensively burrowed (Scholle et al. 1998); in the lower part of the cycle the sediment retained its primary laminated structure. There was little bioturbation other than the vertical escape burrows of animals momentarily buried by dumps of sedimentary snow. Along with the high porosity this obviously indicated a rapid rate of sedimentation. Further up, the rate slowed, allowing organisms that burrowed regularly for a living to destroy the laminae. Calcite cementation began to harden the seafloor, enhancing burrow preservation, but insufficient time elapsed prior to the resumption of heavy sedimentation for true hardgrounds to form.

In the Central Graben of the North Sea the chalk cycles are of non-bioturbated, mainly laminated beds and slightly thicker bioturbated beds (Damholt & Surlyk 2004). The laminated beds consist of alternating millimetre-thick, graded, high-porosity laminae and non-graded, low-porosity laminae. The graded laminae are thought to have been deposited from small-volume turbidity currents and suspension clouds, the non-graded laminae from a rain of pelleted coccoliths produced directly from the plankton. In either case, only the briefest of timescales is required – minutes in the case of the graded laminae, hours in the case of the ungraded laminae. The bioturbated beds imply longer timescales, perhaps a few months in total followed by negligible sedimentation and then the commencement of the next cycle.

Are sedimentation rates of one cycle per year credible?

According to radioisotope dating, the Cretaceous period lasted 80 million years – a stretch of time that, accustomed though we are to such figures, is beyond our ability to imagine. The figure is based, however, on data extraneous to the sedimentary properties of the rocks themselves, and those properties can therefore provide a test of the timescale. As we have seen, in the case of chalk sequences, the sedimentary properties do not agree with ages of this magnitude. To put it another way, if we were to consider the primary evidence on its own merits, we would have no grounds for inferring the miniscule rates of sedimentation that the radioisotope timescale imposes.

A typical chalk-marl couplet has a thickness of around 50 cm, sometimes less. Before compaction the thickness might have been double that, around 100 cm. Averaged over 20,000 years, this gives a sedimentation rate of 0.05 mm, or half a hair’s breadth, per year. That too is difficult to imagine. By contrast, if the couplets were annual, the sedimentation rate would have averaged 2.7 mm per day. During productivity blooms the rate would have been higher – sufficient, as we have seen, to bury organisms alive; at other times lower.

Measurements of modern sedimentation rates tend to be expressed in milligrams per square centimetre. With solid chalk having a density of around 2,500 mg (= 2.5 g) per cc, the uncompacted density would be about 1,250 mg per cc. Thus, if chalk-marl couplets represented 20,000 years, the sedimentation rate would be 6.25 mg per year or 0.017 mg per day; if the couplets represented one year, the rate would be 125 g per year, or 340 mg per day. Modern rates vary according to the same factors that ancient rates vary, but are closer to the former than to the latter. For example, Broerse et al. (2000) reported a carbonate flux of 2.2 mg per cc per year, which is even lower than that calculated for the Cenomanian.

However, modern rates do not provide a meaningful comparison. The escape burrows and the generally low level of bioturbation suggest that the chalk formed rapidly, mostly during plankton blooms that were much more frequent than in modern times. In normal modern conditions the export of carbonate to the seafloor is limited by a negative feedback loop, where low productivity is accompanied by low settling velocity, which results in high rates of consumption by animal grazers and high rates of chemical dissolution. In bloom conditions, by contrast, not only does the rate of production increase by orders of magnitude but faecal-pellet clumping leads to greatly increased settling velocity, with consequently low rates of consumption by grazers and low rates of dissolution (Wal et al. 1995). Coccolithophores, it should be noted, are ‘the most productive calcifying organisms on earth’ and can reach a density during blooms of some 115 million per litre. The great chalk formations bear witness to the exceptional ‘hypercalcifying activity of the coccolithophorids’ (Aubry 2005).

The main factors governing the dissolution of calcium carbonate are temperature, acidity and pressure. Calcium carbonate dissolves more readily where the water is colder, more acidic and deeper. Acidity decreases with increasing temperature because warm water holds less carbon dioxide and thus less carbonic acid. In the warm, shallow seas of the Cretaceous, where the chalks were laid down, the conditions for calcium carbonate precipitation seem to have been optimal. Not only were the seas warm because they were shallow (most of Britain, for example, was inundated at this time), but the global climate itself was exceptionally warm (Huber et al. 2002).

Another point about the Cretaceous is that the ratio of magnesium to calcium in seawater was much lower than in modern seas. High levels of Mg have been found to inhibit growth rates. In experiments involving three species of coccolithophore in low-Mg seawater all showed dramatic increases in population growth rates; two of the species reproduced at rates approximately triple those observed in modern seawater (Stanley et al. 2005). The species dominating Cenomanian chalks are unlikely to have been less responsive. The ubiquitous Watznaueria barnesae, for example, is thought to have been highly prolific (Lees et al. 2005). Although the data are less clear, the same seems to have been true of Biscutum constans (or ellipticum).

Thus several lines of evidence additional to the purely sedimentary evidence support the inference that the Chalk was deposited rapidly compared to modern rates of deposition:

• The Chalk consists mostly of the remains of coccolithophores, which in the right conditions can reproduce at a prodigious rate.
• The warmth and shallowness of the waters where the coccoliths accumulated meant that a much smaller percentage of platelets shed by the coccolithophores dissolved before they reached the bottom.
• The low Mg/Ca ratio of Cretaceous seawater favoured coccolithophore reproduction.
• Some of the coccolithophore species that dominated chalk assemblages are known to have been prolific examples of their kind.

The role of faster plate tectonics

Coccolithophore blooms can occur only if there is a sufficient supply of inorganic nutrients, calcium ions and dissolved carbonate. Once the supply is exhausted the blooms will cease, and they will not have the potential to recur until the minerals are replenished. Thus in the context of sedimentation rates of around 1 metre per year the final question to consider is how the minerals could be replenished that quickly.

Whereas modern seas are relatively poor in calcium, brines from the Cretaceous have high Ca/Na ratios and low Mg/Ca ratios, indicating that seawater was relatively rich in calcium. Seawater chemistry is controlled primarily by the flux of hydrothermal brine from mid-ocean ridges, and Cretaceous seas were rich in calcium and certain other minerals because rates of ocean crust production were higher then (Hardie 1996).

On the assumption of unchanging rates of radioactive decay, the rate of ocean crust production in the Middle Cretaceous is estimated to have been almost twice the modern rate, declining progressively thereafter to present-day values. In terms of seafloor spreading the rates are tiny, of the order of centimetres per year. On the other hand, if radioactive decay was higher in the past, enhanced radioactivity would have had the effect of speeding up geological processes, including activity at the mid-ocean ridges. The flux of hydrothermal brine into the ocean would then also have been higher. Large quantities of mineral nutrients would have been released directly into global current systems, and large amounts of carbon dioxide would have been transferred from the crust to the ocean surface indirectly, via the atmosphere. As is well known, the oceans are a major sink of carbon dioxide, on a par with tropical forests.

Clearly the minerals removed from the oceans by coccolithophore blooms would have been quickly replenished in these circumstances. The chalk deposits – along with levels of atmospheric carbon dioxide ten times higher than now (Royer et al 2004) – can therefore be seen as indirect evidence of elevated plate-tectonic activity under the oceans.

Conclusions

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