Frog Choruses Sing Out a Song of Creation

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My last name, Rana, is Sanskrit in origin, referring to someone who descends from the Thar Ghar aristocracy. Living in Southern California means I don’t often meet Urdu-speaking people who would appreciate the regal heritage connected to my family name. But I do meet a lot of Spanish speakers. And when I introduce myself, I often see raised eyebrows and smiles.

In Spanish, Rana means frog.

My family has learned to embrace our family’s namesake. In fact, when our kids were little, my wife affectionately referred to our five children as ranitas—little frogs.


Image: Five Ranitas. Image credit: Shutterstock

Our feelings about these cute and colorful amphibians aside, frogs are remarkable creatures. They engage in some fascinating behaviors. Take courtship, as an example. In many frog species, the males croak to attract the attention of females, with each frog species displaying its own distinct call.

Male frogs croak by filling their vocal sacs with air. This allows them to amplify their croaks for up to a mile away. Oftentimes, male frogs in the same vicinity will all croak together, forming a chorus.


Image: Male Frog Croaking to Attract a Female. Image credit: Shutterstock

As it turns out, female frogs aren’t the only ones who respond to frog croaks.

A research team from Japan has spent a lot of time listening to and analyzing frog choruses with the hopes of understanding the mathematical structure of the sounds that frogs collectively make when they call out to females. Once they had the mathematical model in hand, the researchers discovered that they could use it to improve the efficiency of wireless data transfer systems.1

This work serves as one more example of scientists and engineers applying insights from biology to drive technology advances and breakthroughs. This approach to technology development (called biomimetics and bioinspiration)—exemplified by the impressive work of the Japanese researchers—has significance that extends beyond engineering. It can be used to make the case that a Creator must have played a role in the design and history of life by marshaling support for two distinct arguments for God’s existence:

Frog Choruses: A Cacophony or a Symphony?

Anyone who has spent time near a pond at night certainly knows the ruckus that an army of male frogs can make when each of them is vying for the attention of females.

All the male frogs living near the pond want to attract females to the same breeding site, but, in doing so, each individual also wants to attract females to his specific territory. Field observations indicate that, instead of engaging in a croaking free-for-all (with neighboring frogs trying to outperform one another), the army of frogs engages in a carefully orchestrated acoustical presentation. As a result, male frogs avoid call overlap with neighboring males on a short timescale, while synchronizing their croaks with the other frogs to produce a chorus on a longer timescale.

The frogs avoid call overlap by alternating between silence and croaking, coordinating with neighboring frogs so that when one frog rests, another croaks. This alternating back-and-forth makes it possible for each individual frog to be heard amid the chorus, and it also results in a symphonic chorus of frog croaks.

The Mathematical Structure of Frog Choruses

To dissect the mathematical structure of frog choruses, the research team placed three male Japanese tree frogs into individual mesh cages that were set along a straight line, with a two-foot separation between each cage. The researchers recorded the frog’s croaks using microphones placed by each cage.

They observed that all three frogs alternated their calls, forming a triphasic synchronization. One frog croaked continuously for a brief period of time and then would rest, while the other two frogs took their turn croaking and resting. The researchers determined that the rest breaks for the frogs were important because of the amount of energy it takes the frogs to produce a call.

All three frogs would synchronize the start and stop of their calls to produce a chorus followed by a period of silence. They discovered that the time between choruses varied quite a bit, without rhyme or reason, and was typically much longer than the chorus time. On the other hand, the croaking of each individual lasted for a predictable time duration that was followed immediately by the croaking of a neighboring frog.

By analyzing the acoustical data, the researchers developed a mathematical model to describe the croaking of individual frogs and the collective behavior of the frogs when they belted out a chorus of calls. Their model consisted of both deterministic and stochastic components.

Use of Frog Choruses for Managing Data Traffic

The researchers realized that the mathematical model they developed could be applied to control wireless sensor networks, such as those that make up the internet of things. These networks entail an array of sensor nodes that transmit data packets, delivering them to a gateway node by multi-hop communication, with data packets transmitted from sensor to sensor until it reaches the gate. During transmission, it is critical for the system to avoid the collision of data packets. It is also critical to regulate the overall energy consumption of the system, to avoid wasting valuable energy resources.


Image: The Internet of Things Made Up of Wireless Sensors. Image credit: Shutterstock

Through simulation studies, the Japanese team demonstrated that the mathematical model inspired by frog choruses averted the collision of data packets in a wireless sensor array, maximized network connectivity, and enhanced efficiency of the array by minimizing power consumption. The researchers conclude, “This study highlights the unique dynamics of frog choruses over multiple time scales and also provides a novel bio-inspired technology.”2

As important as this work may be for inspiring new technologies, as a Christian, I find its real significance in the theological arena.

Frog Choruses and the Argument from Beauty

The grandeur of nature touches the very core of who we are—if we take the time to let it. But, as the work by the Japanese researchers demonstrates, the grandeur we see all around us in nature isn’t confined to what we perceive with our immediate senses. It exists in the underlying mathematical structure of nature. It is nothing short of amazing to think that such exquisite organization and orchestration characterizes frog choruses, so much so that it can inspire sophisticated data management techniques.

From my vantage point, the beauty and mathematical elegance of nature points to the reality of a Creator.

If God created the universe, then it is reasonable to expect it to be a beautiful universe, one that displays an even deeper underlying beauty in the mathematical structure that defines the universe itself and phenomena within the universe. Yet if the universe came into existence through mechanism alone, there isn’t any real reason to think it would display beauty. In other words, the beauty in the world around us signifies the divine.

Furthermore, if the universe originated through uncaused physical mechanisms, there is no reason to think that humans would possess an appreciation for beauty.

A quick survey of the scientific and popular literature highlights the challenge that the origin of our aesthetic sense creates for the evolutionary paradigm.3 Plainly put: evolutionary biologists have no real explanation for the origin of our aesthetic sense. To be clear, evolutionary biologists have posited explanations to account for the genesis of our capacity to appreciate beauty. But after examining these ideas, we walk away with the strong sense that they are not much more than “just-so stories,” lacking any real evidential support.

On the other hand, if human beings are made in God’s image, as Scripture teaches, we should be able to discern and appreciate the universe’s beauty, made by our Creator to reveal his glory and majesty.

Frog Choruses and the Converse Watchmaker Argument

The idea that biological designs—such as the courting behavior of male frogs—can inspire engineering and technology advances is also highly provocative for other reasons. First, it highlights just how remarkable and elegant the designs found throughout the living realm actually are.

I think that the elegance of these designs points to a Creator’s handiwork. It also makes possible a new argument for God’s existence—one I have named the converse Watchmaker argument. (For a detailed discussion, see my essay titled “The Inspirational Design of DNA” in the book Building Bridges.)

The argument can be stated like this:

  • If biological designs are the work of a Creator, then these systems should be so well-designed that they can serve as engineering models for inspiring the development of new technologies.
  • Indeed, this scenario plays out in the engineering discipline of biomimetics.
  • Therefore, it becomes reasonable to think that biological designs are the work of a Creator.

In fact, I will go one step further. Biomimetics and bioinspiration logically arise out of a creation model approach to biology. That designs in nature can be used to inspire engineering makes sense only if these designs arose from an intelligent Mind.

In fact, I will go one step further. Biomimetics and bioinspiration logically arise out of a creation model approach to biology. That designs in nature can be used to inspire engineering makes sense only if these designs arose from an intelligent Mind. The mathematical structure of frog choruses is yet another example of such bioinspiration.

Frogs really are amazing—and regal—creatures. Listening to a frog chorus can connect us to the beauty of the world around us. And it will one day help all of our electronic devices to connect together. And that’s certainly something to sing about.


  1. Ikkyu Aihara et al., “Mathematical Modelling and Application of Frog Choruses As an Autonomous Distributed Communication System,” Royal Society Open Science 6, no. 1 (January 2, 2019): 181117, doi:10.1098/rsos.181117.
  2. Aihara et al., “Mathematical Modelling and Application.”
  3. For example, see Ferris Jabr, “How Beauty is Making Scientists Rethink Evolution,” The New York Times Magazine, January 9, 2019,

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Fatty Acids Are Beautiful



Who says that fictions onely and false hair
Become a verse? Is there in truth no beauty?
Is all good structure in a winding stair?
May no lines passe, except they do their dutie
Not to a true, but painted chair?

George Herbert, “Jordan (I)”

I doubt the typical person would ever think fatty acids are a thing of beauty. In fact, most people try to do everything they can to avoid them—at least in their diets. But, as a biochemist who specializes in lipids (a class of biomolecules that includes fatty acids) and cell membranes, I am fascinated by these molecules—and by the biochemical and cellular structures they form.

I know, I know—I’m a science geek. But for me, the chemical structures and the physicochemical properties of lipids are as beautiful as an evening sunset. As an expert, I thought I knew most of what there is to know about fatty acids, so I was surprised to learn that researchers from Germany recently uncovered an elegant mathematical relationship that explains the structural makeup of fatty acids.From my vantage point, this newly revealed mathematical structure boggles my mind, providing new evidence for a Creator’s role in bringing life into existence.

Fatty Acids

To first approximation, fatty acids are relatively simple compounds, consisting of a carboxylic acid head group and a long-chain hydrocarbon tail.


Structure of two typical fatty acids
Image credit: Edgar181/Wikimedia Commons

Despite their structural simplicity, a bewildering number of fatty acid species exist. For example, the hydrocarbon chain of fatty acids can vary in length from 1 carbon atom to over 30. One or more double bonds can occur at varying positions along the chain, and the double bonds can be either cis or trans in geometry. The hydrocarbon tails can be branched and can be modified by carbonyl groups and by hydroxyl substituents at varying points along the chain. As the hydrocarbon chains become longer, the number of possible structural variants increases dramatically.

How Many Fatty Acids Exist in Nature?

This question takes on an urgency today because advances in analytical techniques now make it possible for researchers to identify and quantify the vast number of lipid species found in biological systems, birthing the discipline of lipidomics. Investigators are interested in understanding how lipid compositions vary spatially and temporally in biological systems and how these compositions change in response to altered physiological conditions and pathologies.

To process and make sense of the vast amount of data generated in lipidomics studies, biochemists need to have some understanding of the number of lipid species that are theoretically possible. Recently, researchers from Friedrich Schiller University in Germany took on this challenge—at least, in part—by attempting to calculate the number of chemical species that exist for fatty acids varying in size from 1 to 30 atoms.

Fatty Acids and Fibonacci Numbers

To accomplish this objective, the German researchers developed mathematical equations that relate the number of carbon atoms in fatty acids to the number of structural variants (isomers). They discovered that this relationship conforms to the Fibonacci series, with the number of possible fatty acid species increasing by a factor of 1.618—the golden mean—for each carbon atom added to the fatty acid. Though not immediately evident when first examining the wide array of fatty acids found in nature, deeper analysis reveals that a beautiful yet simple mathematical structure underlies the seemingly incomprehensible structural diversity of these biomolecules.

This discovery indicates it is unlikely that the fatty acid compositions found in nature reflect the haphazard outcome of an undirected, historically contingent evolutionary history, as many biochemists are prone to think. Instead, the fatty acids found throughout the biological realm appear to be fundamentally dictated by the tenets of nature. It is provocative to me that the fatty acid diversity produced by the laws of nature is precisely the isomers needed to for life to be possible—a fitness to purpose, if you will.

Understanding this mathematical relationship and knowing the theoretical number of fatty acid species will certainly aid biochemists working in lipidomics. But for me, the real significance of these results lies in the philosophical and theological arenas.

The Mathematical Beauty of Fatty Acids

The golden mean occurs throughout nature, describing the spiral patterns found in snail shells and the flowers and leaves of plants, as examples, highlighting the pervasiveness of mathematical structures and patterns that describe many aspects of the world in which we live.

But there is more. As it turns out, we perceive the golden mean to be a thing of beauty. In fact, architects and artists often make use of the golden mean in their work because of its deeply aesthetic qualities.

Everywhere we look in nature—whether the spiral arms of galaxies, the shell of a snail, or the petals of a flower—we see a grandeur so great that we are often moved to our very core. This grandeur is not confined to the elements of nature we perceive with our senses; it also exists in the underlying mathematical structure of nature, such the widespread occurrence of the Fibonacci sequence and the golden mean. And it is remarkable that this beautiful mathematical structure even extends to the relationship between the number of carbon atoms in a fatty acid and the number of isomers.

As a Christian, nature’s beauty—including the elegance exemplified by the mathematically dictated composition of fatty acids—prompts me to worship the Creator. But this beauty also points to the reality of God’s existence and supports the biblical view of humanity. If God created the universe, then it is reasonable to expect it to be a beautiful universe. Yet, if the universe came into existence through mechanism alone, there is no reason to think it would display beauty. In other words, the beauty in the world around us signifies the Divine.

Furthermore, if the universe originated through uncaused physical mechanisms, there is no reason to think that humans would possess an aesthetic sense. But if human beings are made in God’s image, as Scripture teaches, we should be able to discern and appreciate the universe’s beauty, made by our Creator to reveal his glory and majesty.

Resources to Dig Deeper


  1. Stefan Schuster, Maximilian Fichtner, and Severin Sasso, “Use of Fibonacci Numbers in Lipidomics—Enumerating Various Classes of Fatty Acids,” Scientific Reports 7 (January 2017): 39821, doi:10.1038/srep39821.
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Whale Vocal Displays Make Beautiful Case for a Creator



There is the sea, vast and spacious,
teeming with creatures beyond number—
living things both large and small.
There the ships go to and fro,
and Leviathan, which you formed to frolic there.

—Psalm 104:25–26


A few weeks ago, I did something I always wanted to do. I listened to the uncut, live version of the Allman Brothers’ Mountain Jam from beginning to end. Thirty-four minutes in length, this song appears on The Allman Brothers’ live At Fillmore East album. Though The Allman Brothers are among my favorite groups, I have never had the time and motivation to listen to this song in its entirety. I like listening to jam bands, but a thirty-four-minute song . . . in any case, a cross-country flight finally afforded me the opportunity to give my undivided attention to this jam band masterpiece. What an incredible display of musicianship!

Humpback Whale Acoustical Displays

Rockers aren’t the only ones who can get a bit carried away when performing a song. Humpback whales are notorious for their jam-band-like acoustical displays. These creatures produce elaborate patterns of sounds that researchers dub songs. The whale songs can last for up to 30 minutes, and some whales will repeatedly perform the same song for up to 24 hours.

Humpback whale songs display a complex hierarchical organization. The most basic element of the song consists of a single sound, called a unit. These creatures combine units together to form phrases. In turn, they combine phrases to form themes. Finally, they combine themes to form a song, with each theme connected by transitional phrasing.

Researchers aren’t certain why humpback whales engage in these complex acoustical displays. Only the males sing. Perhaps their singing establishes dominance within the group. Most researchers think that the males sing to attract females. (Even for whales, the musicians get the girls.)

Humpback whales in the same area perform the same song. But, their songs continually evolve. Researchers refer to the complete transformation of one whale song into another as a revolution. As the songs evolve, each member of the group learns the new variant. When one group of humpback whales encounters another group, the two groups exchange songs. This exchange accelerates the song revolution. As a result of this encounter, members of both groups develop and learn a new song.

How Do Humpback Whales Learn Songs?

Researchers from the UK and Australia wanted to understand how humpback whales learn new songs.1 Their query is part of a bigger question: How do animals transmit culture—learned information and behaviors—to other members of the group and to the next generation?

To answer this question, the research team recorded 9,300 acoustical displays over the course of two complete song revolutions for the humpback whales of the South Pacific. Among these recordings, they discovered hybrid songs—vocal displays comprised of bits and pieces of both the old and the new songs. They concluded that these hybrids songs captured the transition from one song to the next.

These song hybrids consisted of phrases and themes from the old and new songs spliced together. The structure of hybrid songs indicated to the research team that humpback whales must learn songs in the same way that humans learn languages, by learning bits and piecing them together.

Rock on!

The Creator’s Artistry

Sometimes, as Christian apologists, we tend to think of God solely as an Engineer who creates with only one specific purpose or function in mind. But, the insights researchers have gained into the vocal displays of the humpback whales reminds me that the God I worship is also a Divine Artist—a God who creates for his enjoyment.

Scripture supports this idea. Psalm 104:25 states that God formed the leviathan (which in this passage seems to refer to whales) on day five to frolic in the vast, spacious seas. In other words, God created the great sea mammals for no other purpose than to play!

Artistry and engineering are not mutually exclusive. Engineers often design cars and buildings to be both functionally efficient and aesthetically pleasing. But sometimes, as humans, we create for no other reason than for our pleasure and for others to enjoy and be moved by our work.

Nature’s Beauty and God’s Existence

The humpback whale exemplifies the remarkable beauty of the natural world. Everywhere we look in nature—whether the night sky, the oceans, the rain forests, the deserts, even the microscopic world—we see a grandeur so great that we are often moved to our very core.

Watching a humpback whale breach or hearing a recording of its vocal displays is more than sufficient to produce in us that sense of awe and wonder. And yet, our wonder and amazement only grow as we study these creatures using sophisticated scientific techniques.

For Christians, nature’s beauty prompts us to worship the Creator. But it also points to the reality of God’s existence and supports the biblical view of humanity.

As philosopher Richard Swinburne argues, “If God creates a universe, as a good workman, he will create a beautiful universe. On the other hand, if the universe came into existence without being created by God, there is no reason to suppose that it would be a beautiful universe.”2 In other words, the beauty in the world around us signifies the Divine.

But, as human beings, why do we perceive beauty in the world? In response to this question, Swinburne asserts, “There is certainly no particular reason why, if the universe originated uncaused, psycho-physical laws…would bring about aesthetic sensibilities in humans.”3 But, if human beings are made in God’s image, as Scripture teaches, we should be able to discern and appreciate the universe’s beauty, made by our Creator to reveal his glory and majesty.

In short, the humpback whales’ acoustical displays—a jam band masterpiece—sing of the Creator’s existence and his artistry.



  1. Ellen C. Garland et al., “Song Hybridization Events during Revolutionary Song Change Provide Insights into Cultural Transmission in Humpback Whales,” Proceedings of the National Academy of Sciences USA 114 (July 25, 2017): 7822–29, doi:10.1073/pnas.1621072114.
  2. Richard Swinburne, The Existence of God, 2nd ed. (New York: Oxford University Press, 2004), 190–91.
  3. Swinburne, Existence of God, 190–91.
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