Sands of Time

What do Quasars, Corals, and Rocks have in common?

The question may seem odd. Many happy coincidences from seemingly unrelated fields have led to scientific breakthroughs in the recent past. They have helped solve puzzles that broaden our understanding of nature. One fascinating story involves quasars, deep-sea corals, and ancient rocks! First, it requires understanding long time-horizon phenomena unfolding in epistemic contrast to what humans can comprehend with our quirks, beliefs, and all.

Human Quirks

House of Mirrors at the Garden of Unearthly Delights: Photo Credits to Jesse Neill

Perception Is Not Reality

Objective reality is how the universe is. Perception is our subjective experience of it — how it seems. This distance separating perception and reality is a curious fact explicable both by nature and nurture. Natural selection, in part, has selected us for the express outcome of survival and gene propagation.

Genes aside, objective reality gets distorted by our senses, wetware (the brain), emotions, prior experience and knowledge, and hard-wired biases. It’s as if we are stuck in a house of mirrors in the carnival of life. If the lens of perception distorts reality, how can we comprehend its true nature? Science and reasoning provide the means! Objective reality is stranger than we can suppose. Extending our senses using scientific apparatus allows us to probe deeper into reality, however queer it may seem.

Beyond Our Senses

Radio-frequency (RF) sensors and tags in retail stores prevent theft. Sonograms (fetal ultrasound images) provide expectant couples much joy and a sense of well being of the unborn. Powerful telescopes allow us to scan the electromagnetic spectrum and understand the cosmos. Neuralink has the potential to be a game-changer for paraplegia. These are a few examples of scientific instruments that extend our senses beyond our limited capacity.

Long Arc of Change

Mundanely, we perceive natural patterns as relatively stable and immutable. Consider the twenty-four-hour cycle or the seasonal year. They seem quite regular and repetitive that we organize our lives around them. But beneath this veneer of constancy lurks the profound reality of change — especially of the slow variety. Nobody has witnessed the time-lapse images of the Colorado River sculpting the Grand Canyon. Or the growth of the giant sequoia trees of the Redwood National Forest. The former known to have occurred over millions of years and the latter, several thousand — to say nothing of climate change exacerbated by ongoing human activity over the last century.

Scientific Pursuit

Viscerally, we are ill-equipped to experience changes that occur over a long time horizon. We are intuitively crippled to grasp their glacial pace. Innumerable human life spans strung end-to-end are fleeting compared to geological time. Consequently, we tend to be dismissive of changes that occurred in our geological past. Or deeply discount the consequences of present actions that could affect posterity. Despite human frailty, scientists must overcome personal idiosyncrasies and persevere, armed with extended senses and reasoning. The endeavor is piecing the clues together — telltale marks of changing phenomena etched into rocks of the earth and into the cosmos itself. Amazingly, impermanence underpinning change has left wreckage buried by the sands of time. How can it go unnoticed by keen observers?


Two solitary horn corals fossilized in limestone from Cincinnati, Ohio. Image Credits: Paleontological Research Institution (PRI), Digital Atlas of Ancient Life

Steno’s Principle

When the lowest stratum was forming, none of the upper strata existed.

De Solido, Nicolaus Steno (1638–1686)

In the earth’s history of over four billion years, the oceans, continents, and mountain ranges have undergone gargantuan geological events, moving laterally as well as vertically. This movement has created a veritable jigsaw puzzle with pieces of fossils and layers of rock strata jumbled across many continents. In a given layer, if the same type of rock housing the same fossil-type appears in different places, they are considered to be the same age. Common sense dictates that deeper layers must have existed before the shallower layers. It’s a statement of the Principle of Superposition — which is a fundamental, recurring theme in geology, physics, and engineering. In stratigraphy, it’s also known as Steno’s First Principle, in honor of Danish geologist Nicolaus Steno. Since then, geologists and paleontologists have painstakingly pieced the puzzle together by ordering specimens of rock strata and fossils in space (deep to shallow) and time (older to newer).

Portrait of Nicolaus Steno as bishop: Source Wikipedia

A sign of his time, Steno, even as he continued his pioneering work, took a vow of poverty and became a catholic priest. He proselytized Protestants into Catholicism and died eventually of emaciation. The juxtaposition of irrational personal beliefs and rational inquiry has been a perplexing, recurring topic of human psychology. He got inducted into sainthood in 1988, three hundred years after his passing.

Built-In Clocks

How can we date rock strata, either relative to each other or by determining their absolute age?

Uranium-238 decays into Thorium, emitting a helium nucleus (alpha decay)

Uranium is the heaviest, naturally occurring element in nature. It remains a mystery how Uranium ended up in the earth’s mantle, continental, and oceanic crusts. Uranium-238 (U-238) is a primordial nuclide, i.e., it predates the earth’s existence. It is radioactive with a half-life of a whopping 4.468 billion years! Uranium-235 (U-235) is another, with a half-life of ~704 million years. Their decay chain terminates, culminating in stable Lead (Pb-206) daughter-isotope, by a cascade of chain reactions with the emission of radiation. Carbon-14 is not primordial and has a half-life of about 5370 years. These exponentially slow decay processes occurring in rock strata act as built-in clocks.

Figure 1: Image Source: Fig 17.2, p. 131, A. N. Strahler, Science and Earth History

Follow the diagram (Figure 1). The two curves plotted are a relative number of atoms (U-238, Pb-206) vs. half-life of U-238. After one half-life, only half (F = 50%) of the parent isotope (U-238) remains. The other half would have transformed into Lead (Pb-206), the daughter isotope. Looking at Table 1 below, this would take 4468 million years, longer than the earth and our entire solar system itself! After ten half-lives, the traces of the parent isotope would be negligibly tiny. The column shaded in green (F = 65% for U-235) is salient because all primordial nuclides have half-lives exceeding 437 million years, and also a tenth of the estimated age of our solar system. It’s a significant fact because these nuclides are also found elsewhere in our universe.

Table 1: Fraction remaining after millions of years (Ma). 65% of U-235 (and 35% of Pb-206) will remain after 437 Ma. Similarly, 50% of U-238 (and 50% of Pb-206) will remain after 4468 Ma!

Radiometric Dating

Isotopic age determinations on rocks of known stratigraphic age define an absolute time scale for earth history.

— J. Laurence Kulp, Geologic Time Scale, Science Magazine, 1961

At the heart of radiometric isotopic dating lies a significant claim — of knowing the absolute age of a specimen. It is only natural to be skeptical of this claim. Can we trust the absolute age? Let’s explore the three assumptions underlying this technique:

  1. The original number of unstable atoms is known.
  2. The rate of isotopic decay is constant
  3. All daughter atoms of the stable Pb-206 are results of the decay

Take ten half-lives. The fraction of parent isotope remaining is negligibly small (F = 1/2¹⁰ = 0.1% ) and is generally accepted to be non-existent (zero). If we know the number of atoms of Pb-206 isotope in a sample, we can deduce the original number in its parent. All primordial nuclides have half-lives greater than 437 million years, when 65% U-235 isotope would have decayed (green shaded column in Table 1). Decay rates of primordial nuclides also confirm the age of the solar system, and our Milky Way galaxy, lending credence to this assumption.

Assumption #2 is justified by our understanding of nuclear physics. The strong-nuclear force is the strongest of the four (electromagnetic, strong-nuclear, weak-nuclear, and gravity). It governs atomic interactions responsible for decay rates at even the highest temperatures and pressures found on earth’s crust, mantle, and volcanic rocks.

Assumption #3 is justified by cross-checking several different parent-daughter pairs. They give concordant (similar) ages for a given rock or mineral.

Thermal ionization mass spectrometer used in radiometric dating: Source

This technique has long since matured, widely established today, bolstered by various mitigating factors to reduce bias, reduce the problem of nuclide loss, remove contamination of parent and daughter isotopes, improve measurement precision and accuracy, and isochron dating methods. Around 1950, when this technique was still in its infancy, critics included young-Earth creationists and opponents of evolution. The nub of the issue, in any new line of inquiry, can be summed using a word — Credence.

Rock Sandwich

Radiometric dating of rocks is applicable for molten rocks such as igneous, and volcanic varieties, containing traces amounts of radioactive parent isotopes and their stable counterparts. But how can we date fossils that are not usually found in igneous rocks, but in sedimentary rocks? By looking for layers of igneous rock or volcanic ash that sandwich the fossil layer above and below. Using radiometric dating of the surrounding layers, they can estimate the upper and lower age bounds of a fossil specimen. This is known as “bracketing” the age of the sedimentary rocks containing fossils.

Notwithstanding its success, wouldn’t it be convenient to calibrate the radiometric measurements with a complementary technique to verify its claims?

This is where our story dives under water, into the world of Corals!


Coral with Polyp. Image Credit: Marcelo Kato on Pixabay

Symbiotic Adaptation

Corals (singular, corallum) are marine organisms that are close relatives of jellyfish and sea anemones. They are an ancient symbiotic adaptation in the evolution of life. A hard coral (i.e., hermatypic or reef-building) attaches to the seafloor, but it’s not a plant. It is an animal that doesn’t move! Coral is a colony of thousands of carnivorous invertebrates called polyps. A polyp has a soft sac-like body and an opening for a mouth. At night, stinging tentacles surrounding its mouth sway and capture tiny organisms like zooplankton, small fish, and other prey. During the day, polyps form a symbiotic relationship with zooxanthellae (microscopic algae). The algae photosynthesize and provide energy to polyps in exchange for their excrement. For protection, polyps produce a hard, cup-shaped skeleton made of limestone (calcium carbonate) harvested from seawater. Corals form intricate patterns as a direct consequence of seasonal changes and persist after polyps die.

Coral Growth

Understanding coral growth requires us to focus on the symbiotic relationship of polyps with zooxanthellae (algae). Different species of coral grow at different rates. Their rate of growth depends on

  • water salinity, turbulence, and temperature
  • sunlight available for photosynthesis for algae to provide energy to their hosts, the polyps
  • availability of prey for polyps and how they can nourish their tenants, the algae.

Because of their sensitivity to temperature, salinity, and sunlight, corals show variations in density and have growth bands, similar to rings in tree trunks. Scientists like this fact because it helps them calibrate independent sources of data obtained for seasonal changes over extended periods in history. Indeed, there are time-lapse videos of coral growth that are fascinating to watch. Global climate change is a real threat to corals. The oceans absorb atmospheric carbon-di-oxide, causing acidification and killing off the algae. This delicate ecosystem is thrown off balance, resulting in coral bleaching.

Ancient Horn Coral

Of the five major extinction events our geological past, the Permian extinction, which occurred 300 million years ago, wiped out 95 percent of marine species. Horn corals (Heliophyllum Halli), named so because of their resemblance to a bull’s horn, were among those that went extinct. When alive, they were either solitary or colonial. They belong to the order Rugosa (ruga is Latin for wrinkled) because of their wrinkly outermost (epithecal) skeletal sheath with coarse and fine ridges (or growth bands).


“Oh,dinner at the White House. The wife will like that” — John W. Wells,

Quote Excerpt from A biographical memoir, National Academy of Sciences, by William R. Brice

Prof. John W. Wells (1907–1994) — Image Credit: NAP

Prof. John Wells was a brilliant paleontologist who dedicated his illustrious career studying corals, both living and fossilized. In the mid-1930s, paleontologists studying fossilized corals speculated that growth bands, like tree rings, were the result of seasonal temperature changes, nutrient supplies, and coral reproductive activity. There was very little evidence by way of experiments in living corals suggesting that was indeed the case. In 1961, causal reasons for their growth came under scrutiny by Prof. Wells, especially the fine-ridges on the horn coral. He remained unconvinced they were annual fluctuations because the fossil specimens were telling a different story, unnoticed by others. His ingenious contribution was to follow this line of inquiry leading to the crux of the problem. In his words:

“The ridges are parallel to the growing edge of the corallum and are tacitly accepted as growth increments… No one, however, seems to have concerned himself with their significance in growth time. They clearly indicate regular fluctuations in the rate of calcium carbonate secretion, but whether this is hourly, daily, monthly or yearly periodic reproductive activity is the problem.

Can the minute ridges point us in the direction of daily variations in growth?

The tantalizing evidence in support of daily coral growth requires a final detour in our story — Astronomy!

Earth’s Rotation

“Genius and science have burst the limits of space, and few observations, explained by just reasoning, have unveiled the mechanism of the universe. Would it not also be glorious for man to burst the limits of time, and, by a few observations, to ascertain the history of this world and the series of events which preceded the birth of the human race?”

Essay on the Theory of the Earth, Georges Cuvier (1769–1832)

Tidal Forces

Consider the earth — a giant blue marble. My initial reactions on first encountering this fact at school were bewilderment and mild skepticism.

  • Are we on the surface or inside?
  • Are we clinging to its outer surface?
  • If it spins, why do we not we feel it, or worse, get flung outward?
Earth Polychromatic Imaging Camera (EPIC) image of our earth. Image source: NASA

These and other questions are bound to arise naturally in any curious young observer. Nowadays, we have stunning earth images from NASA for satisfying our curiosity. The earth undergoes the following periodic motions relevant to this discussion:

  • rotation around its polar axis
  • orbital revolution around the sun

The earth spins around a polar axis that is tilted, a complete spin taking a day or twenty-four hours. A revolution in an elliptical orbit moseying around our sun has a period of one year or 365 days. Seasons are directly a consequence of the tilted axis.

Is the period of rotation, at twenty-four hours, always constant?

Who dares to pose this question, let alone dispute the accuracy of this fact? If you are a paleontologist or an astronomer or a geophysicist, this question is worth posing.

Astronomers, as early as 1952, knew and agreed that the period of revolution around the sun has been constant. But the period of rotation around its polar axis, not so much throughout the history of our home planet. But why is one constant, and the other, not? The same reason why any spinning object slows down and eventually stops spinning! Friction and dissipation of rotational energy. It’s one thing for a spinning figure skater to alter her rotational speed by extending her arms outward, away from her body or bringing it closer it, but yet another for the earth to slow down! But obey they both must, the law of conservation of angular momentum. Both must eventually stop spinning, albeit one outlasting the other. And both undergo friction and dissipate energy.

To understand why there is friction associated with the earth’s rotation, we should note that the earth is not physically rubbing against any object. It is wobbly like a washing machine with an unevenly distributed load in the tub around the agitator. The oceanic tidal forces due to the gravitational pull of the moon and movement in the core cause the earth to wobble and lose its rotational energy. If one teased out the cyclical variations in the earth’s rotational speed, the remainder is a gradual slow-down that has occurred over millions of years. Not that anyone living would notice such changes.

It slows down by approximately two seconds every hundred thousand years.

Happy Coincidence

Let’s pick up the story of fossil corals where we left off. Can there be a daily variation in the skeletal deposition? And what evidence supports it. It was starting to become clear based on physiological studies of living corals off Jamaican reefs (Thomas Goreau, 1959) that the calcium carbonate absorption varied significantly. This precipitous drop in coral formation by a factor ranging 50 to 100 in nightly darkness compared to sunlit day is a critical fact, indicating diurnal growth of the minute ridges.
Armed with this clue, John Wells set out to count the minute epithecal ridges on fossil horn coral. But he ended up with numbers greater than 365 (days in a calendar year) — between 385 and 410, but usually about 400.

But how could there have been 400 days in a year in the Earth’s geological past?

Image Source: Britannica, Devonian Geology

If the earth spun faster on its polar axis shrinking the diurnal day but orbited the sun at the same rate. How far back do we go to get four hundred days in a year?

  • We can do a simple calculation using the rate of two seconds per one hundred thousand years show that the earth’s day would have been shorter (~ 21.9 hr day) during the middle Devonian period (380–400 million years ago) when the horn corals were alive, lending credence to the astronomers’ claim gradual slowing down of the earth’s rotation over hundreds of millions of years!
  • Radiometric measurements (recall Fossil Sandwich) had placed the horn corals in middle Devonian geological period which is between 380–400 million years ago. It also went a step further in its claim of absolute age of the specimen. If Wells’ observations were correct, they would lend credence to this method and corals could be used in independently calibrating the radiometric measurements.

Wells’ seminal paper titled “Paleontological Evidence of the Rate of the Earth’s Rotation” in 1961 is arguably his most important contribution that expanded our horizon of knowledge to encompass astronomy, stratigraphy, geochronology, and isotopic radiometry. It not only provided independent verification of the absolute age of radiometric measurements, but also put the astronomical facts on firm ground. A happy coincidence indeed!


We are nearly six decades beyond John Wells’ groundbreaking contribution in 1961. How far have we extended our senses? Thanks to the computing revolution and extremely high precision global network of radio satellite arrays (antennas), we can measure minute (a few millimeters) movements of these antennae relative to each other using Quasars, a loosely knit acronym (quasi-stellar radio sources) — which are extremely bright, Active Galactic Nuclei (AGN) with a supermassive black hole at their center, surrounded by a gaseous accretion disk.

Early quasars (3C 48 and 3C 273) were discovered in the late 1950s, as a source of radio waves in all-sky radio surveys. Since then, over 3400 extra galactic radio sources are used to precisely measure the earth’s rotational variations using a technique called Very Long Baseline Interferometry (VLBI) with NASA’s space geodesy program.

VLBI observations of a quasar with three radio antennae. Image source

Quasars are motionless when viewed from the earth because they are located several billion light years away. These global network of antennae located at different stations around the world simultaneously observe a selected quasar, each station recording the time of arrival of the signal from the quasar with exquisite accuracy. This is done for a series of quasars during a typical twenty-four-hour session. These measurements are so accurate that the radio signal does not arrive at every station at exactly the same time. From the minuscule differences in arrival times, and geometry, scientists figure out the precise positions of the stations and calculate the earth’s rotation speed relative to the quasar positions.

Let’s get back to our original question. What do Quasars, Corals, and Rocks have in common? Change! Nature leaves an indelible imprint of impermanence on everything it owns, including humans. The humanity has progressed in science, despite its shortcomings, by using its extended senses and collective capacity for reasoning, and uncovered the telltale signs left behind by the sands of time. This inspiring story is one of many happy coincidences in the history of modern science.

Lives of great men all remind us 
We can make our lives sublime, 
And, departing, leave behind us 
Footprints on the sands of time

H. W. Longfellow


This piece was inspired by a paragraph in Prof. Jerry A. Coyne’s book titled “Why Evolution is True”. It kicked off a survey of John Wells’ and other related work. I had fun researching and deep diving into this topic.

  1. Variation of the Earth’s Rotation in Historical Time, Walter H. Munk, 1960
  2. Paleontological Evidence of the Rate of the Earth’s Rotation, John W. Wells, 1961
  3. The Ecology of Jamaican Coral Reefs I. Species Composition and Zonation, Thomas F. Goreau, 1959
  4. The Cosmic Origins of Uranium, 2016
  5. Radioactive Dating, Earth-Science, Australia
  6. Why Evolution is True, Jerry A. Coyne, 2010

©️ Venkat Kaushik 2020. All Rights Reserved.