Print Friendly, PDF & Email

The Mouse to Elephant Curve – Dinner with Rev’d Thomas Robert Malthus – In Case you are Wondering, Nero killed Saint Peter and Paul.

The Mouse to Elephant Curve

We learn a lot of secrets when we scale things. Scientists have observed scaling in nature and helped us unravel some mysteries embedded in nature via some pretty neat allometric laws. Exempli grati, the Kleiber’s rule or what you might know as ¾ rule: it states that the metabolic rate of an animal is proportional to the mass of the body raised to the power of three-quarter.

qo~ M3/4

Now, that is important.

Metabolic rate is indicative of how much energy you need to survive.  And if you happen to visit Mikumi National Park in Tanzania, ask the zoo keeper for the average weight of a Male African bush Elephant, she will say something like 6,000kg (~13,000lbs), now, compare that, for example, with a very healthy Etruscan shrew mouse which weighs – on average – 2g (~0.004lbs)

Your intuition will tell you that an elephant would need something like a million times more energy to survive compared to our shrew mouse. That is, if you by any chance, plot a graph of this with metabolic rate on the vertical axis and body mass of animal on the horizontal axis (logarithm scale), what we are talking about here is a linear or a super-linear scaling (slope >= 1).

Surprisingly, after doing this comparison with several mammals, what Max Kleiber found was a sub-linear scaling (check graph below) This simply means: as the body mass of an animal increases, even though an increased energy level is required, they tend to use it more efficiently, thereby reducing total energy needed (sublinear economy of scale). The curve has been dubbed the mouse to the elephant curve.


When things scale, our intuition suffers.

The original graph of body size versus metabolic rate hand-drawn by Max Kleiber

(Photo Credit)

Dinner with Revd. Thomas Robert Malthus

In the 1798 book, an essay on the principle of population by the 32-year-old Thomas Malthus, a population economist, argued that since it appears the world population will be growing at an exponential rate and food production from sedentary farming will only increase linearly. The world will end up in deep misery and hunger, forcing human to a subsistence economy – hunting, gathering, garbage picking, social paratism, artisan fishing, transhumance, that kind of thing. The last time I checked the history books Malthus was no prophet.

To quote Malthus directly:

“Famine seems to be the last, the most dreadful resource of nature. The power of population is so superior to the power of the earth to produce subsistence for man that premature death must in some shape or other visit the human race.”

Thomas Malthus (John Linnell)

(Photo Credit)

Rev’d Malthus’s dooms day was about a century into the future, little did he know I will writing about scaling in 2017 while battling with a chicken soup as I ride along.

And here is where Malthus missed it, our grandmothers knew this very well: Necessity is the mother of invention.  He saw humans primarily as a liability not as a potential asset. When I talk about assets, I talk about the agricultural revolution, the industrial revolution, and the green revolution.

And what happens when we scale human population (to Malthus’s dismay)?

“Between 1900 and 2000, the global population quadrupled, from 1.6 to 6.1 billion, [while] grain production quintupled, from 400 million to 1.9 billion tons.”

Prof. Geoffrey West of the Santa Fe Institute has showed us that, to paraphrase, if you home city is 15 times bigger than mine, innovation in my city will be less than 15 times smaller than yours, that is innovation scales superlinearly.



When things scale, some scientists go burst! **

In addition, cultures do scale at least with reverence to this soviet joke: “One Englishman makes a gentleman, two make a bet and three, a parliament. One Frenchman, makes a lady’s man, two makes a duel, three a Paris commune…”

In Case you are Wondering, Nero killed Saint Peter and Paul.

Scaling does not apply only in biology, cultures or cities as we will see very soon. It is an important detector of character. That is, to answer the question: how does human character scales with changes in social status?

To answer this question, it will be worthwhile to go back in history and revisit mortals that were afforded some of the greatest power on earth – the Roman emperors!

Nero was a popular emperor in the Julio-Claudia dynasty, and he had a very busy reign over the ancient Romans – he started off by killing his own brother, Britannicus with the aid of his in-house toxicologist Gaul Locusta.

Locusta later got some sort of medal for her accomplishment including lands outside Rome. Nero power drunkenness was not something that will soon assuage, so he continued –  in  A.D. 59, he killed his mother, Agrippina. Agrippina was a powerful woman in the roman empire, she was a wife of an emperor (Claudius), sister to another (Caligula, a no less brutal emperor) and mother to one (Nero, himself). But this doesn’t stop Nero from matricide.

Still, he continues – around 62AD after impregnating a very beautiful woman the daughter of Titus Ollius, Poppaea Sabina, Nero took one step further and divorced and later killed his wife, Octavia.  Even Seneca, his praecipuus caritate, could not stop him.

Without boring the reader with more horror stories (and there is still much, much more), let me wrap this up – Nero was brutal, extremely brutal!

And one wonders, is this not the position, the philosopher-king Marcus Aurelius held about a century later in 161 AD? An intellectual emperor, his book – meditations, is one that will easily stun any mortal (I read it for the first-time last summer, and I still regularly return to it). And, he is not just the talking type, he gracefully eats his own cooking and I am sure Emperor Marcus will not have attempted to eat in any Roman restaurant whose chef have decided to eat elsewhere.

Even though he was plagued by poor health his entire life and had to endure the death of about four children. He preserved the empire.

Cassius Dio, the classic historian, like most people was Marcus’s Fan:

“ [Marcus] did not meet with the good fortune that he deserved, for he was not strong in body and was involved in a multitude of troubles throughout practically his entire reign. But for my part, I admire him all the more for this very reason, that amid unusual and extraordinary difficulties he both survived himself and preserved the empire”.

Did I mentioned that at some point when the empire finance was crumbling due to strains from incessant wars, that Marcus sold his imperial properties in the forum of Trojan so he can pay his soldiers? forgive me if I have not. He did.

And I will quickly add: Nero did the exact opposite, at least if we go by the account of Suetonius. On July 18 the year 64, Nero was believed to have started the great fire of Rome, to clear some land space for his palatial complex, the Domus Aurea. He sings and plays his lyre while Rome burnt. In the aftermath, he organized the first Roman empire persecution of Christians, blaming the fire on the Christians. The persecution, some believed, lead to the death of Saint Peter and Paul.

Torches of Nero

(Photo Credit)

And to rewind back to his early teenage years, you might have mistaken Nero for some altar boy living down the street, or probably someone with an extremely strong interest in the Jesuit clan.

And I bet Seneca (Nero’s chief of staff) could have stick his neck in support of Nero’s integrity. (After all, why will the philosopher leave Corsica).

You only need read what Seneca wrote in De Clementia in 65, assuring people that Nero could only get better, effectively a recommendation letter: “That which is undergirded by truth, and grows out of solid ground, becomes better and greater with the passage of time”, referring to his boss.

While there are no power laws for this type of scaling, no slope, no graphs. All you need remember is the truth proclaimed by (again) our grandmothers – never trust the humility of a penniless man.

And to conclude, when things scale, some folks might end up dead.


** I must admit that I share Rev’d Malthus sentiments, we live unsustainably, it might just be a matter of time. Kapish?


<i> An Essay on the Principle of Population, Thomas Malthus, 1798.

<ii> Will the Earth Ever Fill Up? Adam Kucharski, 2015. Nautilus Magazine.

<iii> Marcus Aurelius, Wikipedia.

<iv> Dying everyday: Seneca at the Court of Nero, James Romm, 2014.

<v> Urban Friction, Geoffrey West, 2012. The Economist.

<vi> Body size and metabolic rate, Max Kleiber, 1947. Physiological Reviews. 27 (4): 511–541.

ShareShare on Facebook0Share on Google+0Tweet about this on TwitterShare on LinkedIn0

Leave a Reply

Your email address will not be published. Required fields are marked *