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L: Lifetimes of Civilizations
N = N* fs fGHZ fp ft nH fl fJ f�fEufm fi fcL /T L: lifetime of a communicative civilization T: age of the Galaxy L/T: the fraction of the age of the Galaxy during which the civilization is able to communicate.
The Last Term
T is known. T ~ 1010 years. The age of the universe is 13.7 Gyr. The oldest stars in our Galaxy are about 13 Gyr old (but are metal-poor). The stars that make up the disk of the galaxy are younger than about 10 Gyr. The Sun is 4.5 Gyr old. The Sun has a 10 Gyr main sequence lifetime
T
L is not known. L for humanity is about 150 years (so far). A typical species survives 106 years. The Earth becomes uninhabitable in 109 years. How long will we (or our successors) last?
L
What Affects L?
External Influences • Asteroid Impacts • Nearby supernova • Gamma-ray burst • Habitable zone evolution • Alien invasion
What Affects L?
Internal Influences • Tectonics
What Affects L?
Civilizations self-destruct • Military technologies become more
lethal • Nuclear weapons • Biological weapons
What Affects L?
Inadvertent destruction • Self-induced climate change • Over-reliance on technology • Reliance on monocultures
What Affects L?
Natural causes • Carrying capacity • Depletion of resources • Human And Natural DYnamics model
HANDY model Human and Nature Dynamics (HANDY): Modeling Inequality and Use of Resources in the Collapse or Sustainability of Societies
Ecological Economics, 2014, 101, 90–102 Motesharrei, S., Rivas, J., & Kalnay, E.
Predator-Prey Relation
HANDY model
• Humans as predators • Nature as prey Parameters: • Population
– Elites – Commoners
• Natural resources • Accumulated wealth
HANDY Equations • Δxc = βcxc – αcxc
• ΔxE = βExE – αExE
• Δy = γy(λ – y) - δxcy • Δw = δxcy - Cc – CE
• βc = βE : birth rate • αc, αE : death rate • δ : depletion per worker
• y : natural resources: regeneration, depletion • w: wealth = production – consumption • C: consumption
– Cc = sxc
– CE = κsxE • κ: ratio of elite to commoner salary
HANDY Equations • Birth rate same for commoners and elites
• Death rate differs, depends on wealth
• Consumption depends on wealth – Commoners consumption ceases when wealth
falls below threshold – Elites consumption ceases when wealth falls
below threshold/κ
Handy Solutions
• Vary parameters to find equilibria • Look for maximum carrying capacity
HANDY Conclusions
Stable equilibria exist for • xE = 0 (no elites)
• κ = 1 (no income inequality)
• Slow growth
HANDY Conclusions
No equilibria exist for • κ >> 1 (large inequality)
• Rapid growth
xE = 0
xE = 0
xE = 0
xE = 0
κ = 1 (equitable salaries)
κ = 1 (equitable salaries)
κ = 1 (equitable salaries)
κ = 1 (equitable salaries)
κ = 100 (inequitable salaries)
κ = 100 (inequitable salaries)
κ =10
Fate of Human Societies
Most societies have failed within a few hundred years
Fate of Western Civilization (?) • Overpopulation • Anthropogenic climate change • Resource depletion
– Water – Soil – Oil – Uranium/thorium – Rare-earths – Lithium
What Affects L?
Societal factors • Decrease in curiosity? • Turning inwards?
Lessons from the Anthropocene
• There have been 5 major extinctions • These are attributed to
– Tectonic events – Asteroid impacts – Both induce climate change
• They usually occur over millenia • A sixth extinction is in progress
Relevance
• Once species become intelligent (fi) they are no longer mere participants
• An intelligent species can determine its own destiny.
• All the rules pertinent to evolution change.
Geological Timespans: Eons • Hadean
– Ends ~4 Gya with indirect evidence for life (kerogens)
• Archean – Ends ~2.5 Gya with first O2 catastrophe
• Proterozoic – Ends ~0.54 Gya with first animal fossils
Hadean, Archean, Proterozoic comprise the PreCambrian • Phanerozoic
– now
Geological Timespans: Eras
Phanerozoic – Paleozoic
• Formation of Pangea ~ 250Mya • The Permian/Triassic extinction
– Mesozoic • Era of the dinosaurs • Ends with the KT event ~66 Mya • Periods: Triassic, Jurassic, Cretaceous
– Cenozoic
Geological Timespans: Periods
Cenozoic Era • Paleogene
– ends with ice ages @ 23Mya • Neogene
– ends 2.58 Mya • Quaternary
Geological Timespans: Epochs
Quaternary period • Pleistocene
– Ends 11,000 years ago – Extinction of many large mammals – Attributed to asteroid impact – Human impact?
• Holocene – Begins with Older/Younger Dryas climate
changes
The Anthropocene Epoch
That epoch when human beings affect the Earth’s ecosystems • Start about
– 1945? (artificial radioactive isotopes) – 1850 CE? (industrial revolution) – 8000 BCE? (agriculture)
• Synonymous with the Holocene?
Recap: Evolutionary Mechanisms
• In a stable ecosystem, predators and prey are in equilibrium
• Most species are not extremely motile • Oceans and mountain ranges are
significant barriers • Evolution proceeds in small isolated
populations
Have Humans Upset the Balance?
• We are the predators • Humans are extremely motile • Oceans and mountain ranges are no
longer significant barriers • There are no small isolated populations
of humans
Invasive Species
• Transported to new ecosystem • Out of equilibrium with the ecosystem • Some fail to thrive • Some thrive in absence of natural prey
• If the number of invasive species is small, ecosystem can rebalance
Humans as an Invasive Species
• Homo Heidelbergensis ~ 1.8 Mya • Homo Sapiens “Out of Africa” ~ 75,000 ya • Technology permitted adaptation to wide
range of climates • Populated entire Old World by ~30,000 ya • Populated entire New World by ~15,000 ya • Populated Polynesia by 900 CE
Humans as an Invasive Species
Carried useful and not-so-useful species • Beasts of burden • Cattle • Edible plants
• Rats • Human parasites
Humans as an Invasive Species
Two effects: • Direct impact on the environment • Indirect impact on the environment
Direct Impact: Extinction of Large Mammals
• Large animals have few natural enemies
• Most large animals have a reproduction strategy of few young infrequently
• Hunting, combined with environmental stresses, can explain extinction of large mammals ~ 10,000 years ago
• Did not occur in Africa
Indirect Impact: Removal of geographic barriers
Pangea Pangea: Confluence of all continents into one super-continent ~300 – 200 Mya
Pangea and the P-T Extinction • Removal of ocean barriers • Species can migrate freely • Climate affected by continental distribution
• Pangea formation defines Paleozoic-Mesozoic border
• Related to Deccan Traps/global warming/ocean acidification
• Permian-Triassic Extinction event was the largest – 96% of marine species – 70% of terrestrial species – 57% of families; 83% of genera
Parallels with Today
Increase in invasive species from: • Rapid intercontinental travel • Trade in exotic species
Extinction leads to drops in bio-diversity
Agriculture
• Affects ecosystems and the atmosphere – reflects more sunlight than forests – produces more CO2 than forests – No Carbon sequestration – Reduces bio-diversity
L
Will humans survive the Anthropocene? • We are part of an ecosystem • The ecosystem is changing rapidly Technology to the rescue?
Overpopulation Earth has a carrying capacity • We need sufficient
– Fresh water – Food
• We need space for plants and animals
Carrying Capacity is unknown • Estimates range 4 - 16 billion
7.7 billion humans are alive today
Human Population Growth
Why the Population is Growing
http://www.eoearth.org/view/article/153596/
How Long Until the Earth is Full?
Exponential Growth
• Y=tX, X>1
The Meaning of Exponential Growth
• A constant percentage increase per time – e.g, a 2% population growth is exponential.
• The doubling time is 70 divided by the percentage growth (70 ~ 100 ln(2) = 69.3)
The Meaning of Exponential Growth
• In a doubling time, Y doubles • 5% annual interest means your money
doubles in 70/5 = 14 years • A crime rate that doubles in 10 years is
growing at 7% per year • A population that grows at 2% per year
doubles in size in 35 years
The Meaning of Exponential Growth
• Consider a test tube with one bacterium. • The size of a bacterium is ~1 µm (10-4 cm) • Volume of the bacterium ~ 10-12 cm3 • The bacterium divides every 30 minutes. • The volume of the test tube is 40 cm3. • You can fit 4x1013 bacteria in the test tube • How long until the test tube is full?
The Meaning of Exponential Growth
• Doubling time is 30 minutes • % growth = 70/30 =2.3% per minute • There is room for 40/10-12 = 4 x 1013 bacteria in the
test tube. • When is the test tube full of bacteria? • After ln(3 x 1013)/ln(2) doubling times • After 44 doubling times, there are 2x1013 bacteria
• In another 30 minutes the test tube is full.
The Meaning of Exponential Growth
• There are now 7.7 billion people on Earth • Population growth is about 1.08% per year (down from 2% in 1960s and 1.14% in 2016)
• The surface area of Earth is about 4.5x1014 m2 • About 25% of the Earth is land. • Each person has, in principle, about 15,000 sq m
The Meaning of Exponential Growth
• Define the Earth as full when each person has 1 sq m.
• That requires 15,000 times the present population, or about 1014 people on Earth.
• Current doubling time is 70/1.07 = 65 years • At the current rate, that will take 14 doubling
times, or 910 years!
The Meaning of Exponential Growth
Suppose we cap Earth at its current population, and start colonizing extrasolar planets. • Assume one Earth-like planet per star • We fill the galaxy (4x1011 stars) in 36 doubling
times.
That’s only 2300 years!
L
• L ~ 150 years.
• How much longer will we go?
1.5 x 10-8 < L/T < 0.5
L/T
1.5 x 10-8 < L/T < 0.5
L/T
N > 1 requires L/T > 2 x 10-3, or L > 20 million years Let’s be optimistic. Set L/T = 0.3 L = 300 million years
N = N* fs fGHZ fp ft nH fl fJ f�fEufm fi fc L/T • N* = 4 x 1011 • fs = 0.2 • fGHZ = 0.002 • fp = 1.0 • ft = 0.9 • nH = 4 • fl = 1.0 • fJ = 0.5 • f� = 0.01 • fEu = 0.2 • fm = 0.1 • fi = 0.5 • fc= 0.1 • L/T = 0.03 N = 42
N
But …
Uncertainties in the values are generally more important than the exact values
N = N* fs fGHZ fp ft nH fl fJ f�fEufm fi fc L/T • N* = 4 x 1011 ± 25% • fs = 0.2 ± 0.1 • fGHZ = 0.002 +0.01, -0.001 • fp = 1.0 ± 0.2 • ft = 0.9 +0.1, -0.5 • nH = 4 ±3 • fl = 1.0 +0, -0.99 • fJ = 0.5 +0.3,-0.5 • f� = 0.01 +0.1, -0.01 • fEu = 0.2 +0.8, -0.2 • fm = 0.1 +0.9, -0.1 • fi = 0.5 +0.5, -0.45 • fc= 0.1 +0.7, -0.3 • L/T = 0.03 (10-6 –> 0.5) N = 42 (from 1 [us] to 4x1010)
N
N* fs fGHZ fp ft nH fl fJ f�fEufm fi fc L/T = 42 Answers between 1 and 4 x 1010 acceptable with justification (YMMV)
The Final Answer ?
