Universal Mathematics: The Spooky Uniformity of Life on Earth

Is all life on Earth bound together by mathematics?

GEOFFREY WEST: So I think it’s one of the more remarkable properties of life actually, but just taking mammals: that the largest mammal, the whale, is—in terms of measurable quantities of its physiology and its life history—is actually a scaled up version of the smallest mammal which is actually the shrew, but a mouse is very close to that.
And everything in between, that they are scaled version of one another and in a systematic predictable way to sort of 80 percent or 90 percent level. So the kinds of things that you might measure might be as mundane as the length of the aorta, which is the first tube coming out of your heart, or it could be something as sophisticated and complex as how long each one of these mammals, for example, is going to live or how long it takes to mature.

So all of these things scale in a very predictable way and they scale in a way that’s nonlinear. So even though it’s simple it’s highly nonlinear, and that can be expressed in the following way. 

So perhaps the most well known of these is the scaling of metabolic rate. And metabolic rate is maybe the most fundamental quantity of life because metabolic rate simply means how much energy or just how much food does an animal need to eat each day in order to stay alive. And everybody’s used to that and is familiar with that. It’s sort of roughly 2,000 food calories a day for a human being. So you can ask “what is that for different mammals?” and what you find is that they’re related to one another in a very simple way despite the fact that metabolism is maybe the most complex physical chemical process in the universe. It’s phenomenal because metabolism is taking essentially almost inorganic, something that’s inorganic an making it into life.

And so here’s this extraordinary complex process and yet it scales in a very simple way. And you can express it in English, it can be expressed quite precisely in a very simple mathematical equation but in English it’s—roughly speaking—that every time you double the size of an organism from say two grams to four grams or from 20 grams to 40 grams or 20 kilograms to 40 kilograms or whatever and just doubling anywhere. 

Instead of what you might naively expect—double the size, you double the number of cells roughly speaking; therefore, you would expect to double the amount of energy, the amount of metabolic energy you need to keep that organism alive because you have twice as many cells—Quite the contrary you don’t need twice as much. Systematically you only need roughly speaking 75 percent as much. So there’s this kind of systematic 25 percent, one-quarter “savings.”
And it turns out that anything else you measure as I mentioned a moment ago scales in a similar way with this sort of 25 percent role occurring in some interesting way. 

So, for example, if you take mammals: we have beating hearts, we have a circulatory system with a beating heart. So every time you double the size there’s a systematic decrease in heartrate as most people are familiar with. An elephant’s heart beats much slower than ours and ours beats much slower than a dog’s or a mouse’s, for example. And that also obeys this kind of quarter-power scaling, so in a very systematic way we see this repetitive nature.

And what is amazing about that is that each animal, each one of these animals—and by the way it’s not just true for animals, it’s also true of plants and trees—but each one of these organisms has evolved by natural selection, each subsystem has evolved evolutionary by natural selection, each cell type, each genome that comprises of the organism has its own unique history that ended up being this particular organism. So you might have expected, in fact, you would sort of think of that (and often colloquially we think of it) as some kind of random process, natural selection. 

And that you would therefore have expected, if you look at something like metabolic rate or length of aortas or whatever it is, lifespan—They would sort of be randomly distributed because they would simply represent or reflect the evolutionary history of that organism, or of the components of that organism. 

And quite the contrary, as I say, it’s not that. Somehow natural selection has been constrained by some underlying principles. And what I have spent quite a lot of time thinking about and developing a theoretical structure based on underlying principles and put into a mathematical framework for understanding where that regulatory comes from, and why it should be this number one-quarter. Where does that magic number fall—so to speak, arise? And the work that I did with some marvelous biology colleagues, Jim Brown and Brian Enquist, we developed this what I consider very elegant theory: that what these scaling laws are reflecting are, in fact, the generic universal mathematical physical properties of the multiple networks that make an organism viable and allow it to develop and grow and so on. And the ones we’re all familiar with, many of them like our circulatory system and our respiratory system. But our neural system is like that, it transmits information. But these are networks that have evolved to distribute energy from something macroscopic like a heart or a pool of blood down to deliver oxygen to the cells by going through a hierarchy called network delivering as I say oxygen, resources, metabolic energy to the cells.

And it is the universal properties, the universal mathematical properties of those networks that transcend the evolved design. So the same mathematical – now this is extremely important. It’s the same mathematical and physical principles applied to a mammal which has a beating heart as applied to a tree. And a mammal, you know, our circulatory system is a bunch of tubes like in your house the plumbing and the building that we’re sitting in. That’s our circulatory system. 

But a tree and a plant, they’re not like that. They’re a bunch of fiber bundles kind of joined together like electrical cables that spray out, and that’s what you see when you see a tree. In each branch there’s actually just these fibers transmitting, transporting fluid to the leaves and so on. And they don’t have beating hearts as we well know. And yet they satisfy the same mathematical principles, and those mathematical principles give rise to this quarter-power scaling in mammals but also in plants and trees. But also in fish and birds and crustacea (in principle) and insects and so on. That’s the idea.

So one of the nice things about this theory is that if you like it’s kind of a unified theory because it brings – since metabolism underlies, you know, pretty much the way we live, the way any organism lives because it is the way energy and resources are being supplied to cells and so forth.

Are we all connected? Mathematically, yes. It might seem like a stretch, but all living organisms on earth are connected by a unified theory. The more into the (metaphor alert) nuts and bolts of it all, the more science is finding just how connected we all are by way of energy and resources being supplied to cells—and by a methodology known as quarter scaling. The larger something is the longer it lives. Let's say there's a dog that is 500 times bigger than a mouse: in essence, we can then estimate that the dog's lifespan will be about 125 times greater than the mouse. An elephant's heart beats a lot slower than a human's heart, but our hearts beat slower than a mouse and a dogs. It's all interconnected!


Geoffrey West's most recent book is The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies.

7 most notorious and excessive Roman Emperors

These Roman Emperors were infamous for their debauchery and cruelty.

1876. Painted by Henryk Siemiradzki.
Politics & Current Affairs
  • Roman Emperors were known for their excesses and violent behavior.
  • From Caligula to Elagabalus, the emperors exercised total power in the service of their often-strange desires.
  • Most of these emperors met violent ends themselves.

We rightfully complain about many of our politicians and leaders today, but historically speaking, humanity has seen much worse. Arguably no set of rulers has been as debauched, ingenious in their cruelty, and prone to excess as the Roman Emperors.

While this list is certainly not exhaustive, here are seven Roman rulers who were perhaps the worst of the worst in what was one of the largest empires that ever existed, lasting for over a thousand years.

1. Caligula

Officially known as Gaius (Gaius Caesar Augustus Germanicus), Caligula was the third Roman Emperor, ruling from 37 to 41 AD. He acquired the nickname "Caligula" (meaning "little [soldier's] boot") from his father's soldiers during a campaign.

While recognized for some positive measures in the early days of his rule, he became famous throughout the ages as an absolutely insane emperor, who killed anyone when it pleased him, spent exorbitantly, was obsessed with perverse sex, and proclaimed himself to be a living god.

Caligula gives his horse Incitatus a drink during a banquet. Credit: An engraving by Persichini from a drawing by Pinelli, from "The History of the Roman Emperors" from Augustus to Constantine, by Jean Baptiste Louis Crevier. 1836.

Among his litany of misdeeds, according to the accounts of Caligula's contemporaries Philo of Alexandria and Seneca the Younger, he slept with whomever he wanted, brazenly taking other men's wives (even on their wedding nights) and publicly talking about it.

He also had an insatiable blood thirst, killing for mere amusement. Once, as reports historian Suetonius, when the bridge across the sea at Puteoli was being blessed, he had a number of spectators who were there to inspect it thrown off into the water. When some tried to cling to the ships' rudders, Caligula had them dislodged with hooks and oars so they would drown. On another occasion, he got so bored that he had his guards throw a whole section of the audience into the arena during the intermission so they would be eaten by wild beasts. He also allegedly executed two consuls who forgot his birthday.

Suetonius relayed further atrocities of the mad emperor's character, writing that Caligula "frequently had trials by torture held in his presence while he was eating or otherwise enjoying himself; and kept an expert headsman in readiness to decapitate the prisoners brought in from gaol." One particular form of torture associated with Caligula involved having people sawed in half.

He caused mass starvation and purposefully wasted money and resources, like making his troops stage fake battles just for theater. If that wasn't enough, he turned his palace into a brothel and was accused of incest with his sisters, Agrippina the Younger, Drusilla, and Livilla, whom he also prostituted to other men. Perhaps most famously, he was planning to appoint his favorite horse Incitatus a consul and went as far as making the horse into a priest.

In early 41 AD, Caligula was assassinated by a conspiracy of Praetorian Guard officers, senators, and other members of the court.

2. Nero

Fully named Nero Claudius Caesar, Nero ruled from 54 to 68 AD and was arguably an even worse madman than his uncle Caligula. He had his step-brother Britannicus killed, his wife Octavia executed, and his mother Agrippina stabbed and murdered. He personally kicked to death his lover Poppeaea while she was pregnant with his child — a horrific action the Roman historian Tacitus depicted as "a casual outburst of rage."

He spent exorbitantly and built a 100-foot-tall bronze statue of himself called the Colossus Neronis.

He is also remembered for being strangely obsessed with music. He sang and played the lyre, although it's not likely he really fiddled as Rome burned in what is a popular myth about this crazed tyrant. As misplaced retribution for the fire which burned down a sizable portion of Rome in the year 64, he executed scores of early Christians, some of them outfitted in animal skins and brutalized by dogs, with others burned at the stake.

He died by suicide.

Roman Emperor Nero in the burning ruins of Rome. July 64 AD.Credit: From an original painting by S.J. Ferris. (Photo by Kean Collection / Getty Images)

3. Commodus

Like some of his counterparts, Commodus (a.k.a. Lucius Aelius Aurelius Commodus) thought he was a god — in his case, a reincarnation of the Greek demigod Hercules. Ruling from 176 to 192 AD, he was also known for his debauched ways and strange stunts that seemed designed to affirm his divine status. Numerous statues around the empire showed him as Hercules, a warrior who fought both men and beasts. He fought hundreds of exotic animals in an arena like a gladiator, confusing and terrifying his subjects. Once, he killed 100 lions in a single day.

Emperor Commodus (Joaquin Phoenix) questions the loyalty of his sister Lucilla (Connie Nielsen) In Dreamworks Pictures' and Universal Pictures' Oscar-winning drama "Gladiator," directed by Ridley Scott.Credit: Photo By Getty Images

The burning desire to kill living creatures as a gladiator for the New Year's Day celebrations in 193 AD brought about his demise. After Commodus shot hundreds of animals with arrows and javelins every morning as part of the Plebeian Games leading up to New Year's, his fitness coach (aptly named Narcissus), choked the emperor to death in his bath.

4. Elagabalus

Officially named Marcus Aurelius Antoninus II, Elagabalus's nickname comes from his priesthood in the cult of the Syrian god Elagabal. Ruling as emperor from 218 to 222 AD, he was so devoted to the cult, which he tried to spread in Rome, that he had himself circumcised to prove his dedication. He further offended the religious sensitivities of his compatriots by essentially replacing the main Roman god Jupiter with Elagabal as the chief deity. In another nod to his convictions, he installed on Palatine Hill a cone-like fetish made of black stone as a symbol of the Syrian sun god Sol Invictus Elagabalus.

His sexual proclivities were also not well received at the time. He was likely transgender (wearing makeup and wigs), had five marriages, and was quite open about his male lovers. According to the Roman historian (and the emperor's contemporary) Cassius Dio, Elagabalus prostituted himself in brothels and taverns and was one of the first historical figures on record to be looking for sex reassignment surgery.

He was eventually murdered in 222 in an assassination plot engineered by his own grandmother Julia Maesa.

5. Vitellius

Emperor for just eight months, from April 19th to December 20th of the year 69 AD, Vitellius made some key administrative contributions to the empire but is ultimately remembered as a cruel glutton. He was described by Suetonius as overly fond of eating and drinking, to the point where he would eat at banquets four times a day while sending out the Roman navy to get him rare foods. He also had little social grace, inviting himself over to the houses of different noblemen to eat at their banquets, too.

Vitellius dragged through the streets of Rome.Credit: Georges Rochegrosse. 1883.

He was also quite vicious and reportedly either had his own mother starved to death or approved a poison with which she committed suicide.

Vitellius was ultimately murdered in brutal fashion by supporters of the rival emperor Vespasian, who dragged him through Rome's streets, then likely beheaded him and threw his body into the Tiber river. "Yet I was once your emperor," were supposedly his last words, wrote historian Cassius Dio.

6. Caracalla

Marcus Aurelius Antoninus I ruled Rome from 211 to 217 AD on his own (while previously co-ruling with his father Septimius Severus from 198). "Caracalla"' was his nickname, referencing a hooded coat from Gaul that he brought into Roman fashion.

He started off his rise to individual power by murdering his younger brother Geta, who was named co-heir by their father. Caracalla's bloodthirsty tyranny didn't stop there. He wiped out Geta's supporters and was known to execute any opponents to his or Roman rule. For instance, he slaughtered up to 20,000 citizens of Alexandria after a local theatrical satire dared to mock him.

Geta Dying in His Mother's Arms.Credit: Jacques Pajou (1766-1828)

One of the positive outcomes of his rule was the Edict of Caracalla, which gave Roman citizenship to all free men in the empire. He was also known for building gigantic baths.

Like others on this list, Caracalla met a brutal end, being assassinated by army officers, including the Praetorian prefect Opellius Macrinus, who installed himself as the next emperor.

7. Tiberius

As the second emperor, Tiberius (ruling from 42 BC to 16 AD) is known for a number of accomplishments, especially his military exploits. He was one of the Roman Empire's most successful generals, conquering Pannonia, Dalmatia, Raetia, and parts of Germania.

He was also remembered by his contemporaries as a rather sullen, perverse, and angry man. In the chapter on his life from The Lives of the Twelve Caesars by the historian Suetonius, Tiberius is said to have been disliked from an early age for his personality by even his family. Suetonius wrote that his mother Antonia often called him "an abortion of a man, that had been only begun, but never finished, by nature."

"Orgy of the Times of Tiberius on Capri".Painting by Henryk Siemiradzki. 1881.

Suetonius also paints a damning picture of Tiberius after he retreated from public life to the island of Capri. His years on the island would put Jeffrey Epstein to shame. A horrendous pedophile, Tiberius had a reputation for "depravities that one can hardly bear to tell or be told, let alone believe," Suetonius wrote, describing how "in Capri's woods and groves he arranged a number of nooks of venery where boys and girls got up as Pans and nymphs solicited outside bowers and grottoes: people openly called this 'the old goat's garden,' punning on the island's name."

There's much, much more — far too salacious and, frankly, disgusting to repeat here. For the intrepid or morbidly curious reader, here's a link for more information.

After he died, Tiberius was fittingly succeeded in emperorship by his grandnephew and adopted grandson Caligula.

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The ‘Lost Forty’: how a mapping error preserved an old-growth forest

A 19th-century surveying mistake kept lumberjacks away from what is now Minnesota's largest patch of old-growth trees.

Credit: U.S. Forest Service via Dan Alosso on Substack and licensed under CC-BY-SA
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Physicists push limits of Heisenberg Uncertainty Principle

New studies stretch the boundaries of physics, achieving quantum entanglement in larger systems.

Credit: Aalto University.
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