On 10 February Will Steffen and I published a new paper, the Anthropocene Equation, in the academic journal the Anthropocene Review.

1. The Anthropocene equation
The rate of change of the Earth system in the late Quaternary
under the influence of Anthropogenic pressures
Owen Gaffney

2. “H. sapiens is the prime driver of change on Earth.”
“Humans now rival the great forces of nature.”
Can we formalize such statements?

3. The paper The Anthropocene equation (10 February, Gaffney Steffen, Anthropocene
Review) proposes it is possible to mathematically formalise the Anthropocene in
terms of the rate of change of the Earth system.
This provides an unequivocal statement about the current state of the Earth
system.
Astronomical and geophysical forces approach zero compared with anthropogenic
influence on the rate of change of the Earth system.
Moreover, the force exerted has pushed the Earth system beyond the interglacial
envelope.

5. HJ Schellnhuber Nature, 1999

6. Rate of change of the Earth system
E is Earth
T is time

7. Internal dynamics
eg. evolution of
cyanobacteria
4 billion years
- Since evolution of Earth’s biosphere
Astronomical forces
Gravitational effects, sun’s output
Geophysical forces
(tectonics, ocean circulation)
After ‘Earth System Analysis and the second Copernican revolution’, Schellnhuber, Nature 1999
The rate of change of the Earth system is a function of astronomical and geophysical forces
and internal dynamics, often driven by these forces.

8. Holocene: last 7000 years
Earth entered the Holocene 11,700 years ago. This epoch has been characterized by a relatively stable
Earth system in terms of climate, biodiversity and biogeochemical cycling. The rate of change of the
Earth system has remained around zero, certainly if we use the last 7000 years as a baseline. Ice sheets
have been stable. Global average temperature has very gradually fallen at a rate of about 0.1°C/century.
This stability has contributed to the emergence of agriculture and civilization.
≈ 0

9. , H )
In recent centuries…a force awakens
(The Late Holocene in the Late Quaternary period)
After ‘Earth System Analysis and the second Copernican revolution’, Schellnhuber, Nature 1999
H=Anthropogenic
forcings, largely
industrialized societies

10. The Great Acceleration since the 1950s
Steffen, Broadgate, Deutsch, Gaffney, Ludvig 2015. Image Globaia.

11. Last 200 years….
≠ 0
…particularly pronounced in last 40 years

12. Rate of change of the Earth system today (last 40 years)
Temperature In last 40 years temperature rising 170 times the background rate
Carbon cycle Rate of carbon emissions highest in at least 66 million years
and 120ppm above Holocene baseline
Nitrogen cycle Most significant change in rate in 2.5 billion years
Ocean Rate unparalleled in possibly 300 million years
acidification
Biodiversity Extinction rates 10-100 times the background rate
Humans have now modified the structure and functioning of the biosphere to such an extent
that the Anthropocene may mark the beginning of a third stage in the evolution of Earth’s
biosphere following the microbial stage from ~3.5 billion years ago and the metazoan from
~650 million years ago.
NOAA 2016, Canfield et 2020, Hönisch et al 2012, Cui et al 2011, Zeebe et al 2016 Williams et al., 2015. see Gaffney & Steffen for full references.

13. The Anthropocene equation, Gaffney & Steffen, Anthropocene Review 2017
Currently, the ratio of A:H, G:H and I:H tends towards zero
Anthropocene equation
A, G, I forcings are currently orders of magnitude smaller than H

15. Earth has exited the interglacial envelope
The Anthropocene equation, Gaffney & Steffen, Anthropocene Review 2017
E is Earth system
H is industrialised societies
A is astronomical forcings
G is geophysical forcings
I is internal dynamics

16. Honoured! but not quite right….

17. Perhaps closer to the Drake equation

18. The search for extraterrestrial intelligence
The Drake equation calculates the probability of finding intelligent life in the universe
The continuity criterion

19. It is reasonable to expect an
intelligent planetary civilisation would
maintain the homeostasis
of its home planet’s biosphere in a
manner conducive to the civilisation’s
long-term survival.
After David Grinspoon, Earth in Human Hands
The continuity criterion
Homeostasis: the tendency towards a relatively stable equilibrium between interdependent
elements, especially as maintained by physiological processes, through positive and negative
feedbacks. In terms of the Earth system, homeostasis often refers to regulation in a habitable
state rather than optimum state for a particular organism.

20. Is there intelligent life here?
The search for terrestrial intelligence

21. The New Yorker 2015
The continuity criterion
It is reasonable to suggest, an
intelligent civilisation would
maintain the homeostasis of its
home planet’s biosphere.
This phenomenon has yet to emerge
on Earth.
Indeed, the rate of change
is accelerating.
It could slow in two ways:
civilisation collapses or civilisation
works out how to manage the
coupled Earth-world system.

22. The probability of finding intelligent life on
Earth is inversely proportional to the rate of
change of the Earth system.
Stockton and Gaffney
The New Yorker 2015
P(Itc)=c.(dE/dt) -1
Search for terrestrial intelligence
Itc = Intelligent technological civilisation
c = constant
What is the probability of a technological
civilisation surviving long enough to learn
to control the long-term future of Earth’s
biosphere?

23. The New Yorker 2015
The continuity criterion
OK, here’s the stretch goal. With a
little more effort, this generation
could achieve the most remarkable
feat in human history.
We now need development that
stores carbon not emits it, enhances
biodiversity not destroys it and
purifies water, air and soils, not
pollutes them.
NO PRESSURE.

24. First signs of intelligent life
emerging
• The Ozone hole is stabilising and predicted to make a full recovery by
2100
• The world has reached peak child: the average number of children per
woman on Earth is now 2.5
• Global emissions growth of carbon dioxide from fossil fuels has stalled
for three years running during economic growth (2014, 2015, 2016)

25. Summary in 3 tweets
The #anthropocene equation. 4 billion years: D🌎/d🕑 = f(☀️🌌🌋). Last
40 years: d🌍/d🕑=f(✈️🚢🌆🚜) @owengaffney
Search for terrestrial intelligence
P(Intelligent technological civilisation) = c*(d🌍/d🕑)^-1 @owengaffney
#seti #sti
With a little more effort, this generation could achieve the most
remarkable feat in human history, says @owengaffney #win
#anthropocene

26. The Anthropocene equation
The rate of change of the Earth system in the late Quaternary
under the influence of Anthropogenic pressures
Owen Gaffney
The search for intelligent life on Earth