Population calamities in seemingly empty environments 8 feb 2013a

Real-world
population calamities

in

seemingly “empty” environments?

THREE classicalreal-world examples of population calamities in
environments that remain 99.998% unoccupied

2/1000ths of 1%
occupied

THREE classical real-world examples of population calamities in
environments that remain 99.998% unoccupied

2/1000ths of 1%
occupied

Real-world population-environment calamities, die-offs, and mass mortalities in „too-late‟ /
„vast open-space‟ / „almost entirely empty‟ conditions as depicted in this image

Look at the tiny
2/1000ths of 1% dot
in this image

and imagine the most intelligent
possible individuals
residing there

Which, if any, members of
such a population could be
convinced that their population
faced a calamitous
population-environment
die-off and collapse

when such vast amounts
of „open-space ‟ appear to
remain seemingly available?

We are covering this because
it has possible implications for us

The “Open-Space” Delusion
There is a widely-held misperception within much of society that
human population growth and overpopulation cannot become
truly serious so long as “vast amounts of open space”
appear to remain theoretically-available

These seemingly innate
or intuitive
“open-space”
suppositions can be
exceptionally dangerous

because they tempt us into
complacency

This presentation outlines THREE separate, classical,
and catastrophic real-world population outcomes (and die-offs)
at tiny fractions of one percent thresholds

suppositions
assesses such

mathematically
This presentation

“vast open-space”

Supporting mathematics for the three classical examples
that we use is outlined in the presentation‟s addenda

Imagine a real-world
population of organisms
surrounded by „vast
2/1000ths
of one percent amounts of open-space‟

in surroundings
For the population in the above tiny
that remain 99.998%
white dot, the moment in time unoccupied
depicted here was already “too-late”
and which, visually-
speaking, appears to remain

almost entirely empty

Imagine, then, a population
whose combined bodies
2/1000ths (or cells)
of one percent physically-occupy an area
equal to the tiny white
dot in this image

which constitutes
2/1000ths of one percent

of the
red rectangle in
which it resides

Too-late conditions?

Notice that it would be
nearly impossible for even the
brightest scholars and leaders
of such a population 2/1000ths
of one percent
to realize that the population-
environment conditions
depicted here

are ALREADY “too-late”

And that at this point in time,
both they and members
of their population

will have already
waited TOO-LONG Too-late conditions?

This presentation will review three classical real-world
examples of population-environment calamities

in environments that remain 99.998% unoccupied
and which appear to remain ALMOST ENTIRELY EMPTY

In all three classical examples, the populations involved
experienced 99%-plus die-offs and/or other mass mortalities

even as their combined bodies (or cells) physically-occupied
roughly 2/1000ths of one percent of the surroundings that appeared
to remain theoretically-available to them

We will see that for all three examples
that we cover, the 2/1000ths of 1%
conditions denoted by the tiny
2/1000ths white dot in this image
of one percent

already constitute
too-late
conditions,

and at the point in time depicted here, for
all three real-world populations it will
already be too late,

and they will have already
waited too-long
Too-late conditions?

This presentation is a courtesy of
The Wecskaop Project

What Every Citizen Should Know About Our Planet
Copyright 2012, The Wecskaop Project.
All rights reserved.


It is entirely free for use by
scientists, students, and
educators anywhere in the world.

What Every Citizen Should Know About Our Planet

Biospherics Literacy 101
(Five PowerPoints / Five Days)

There are five PowerPoints in this
open-courseware collection

Biospherics Literacy 101
(Five PowerPoints / Five Days)

1 – World Population and Core Demo-
graphics – An Introductory
Overview

2 – Ecological Services and
Biospheric Machinery

3 – Real-world population-environ-
ment calamities in seemingly
„empty‟ environments?

4 – Earth‟s Thin Films - Thin Surface layers of
Atmosphere, Oceans, and Seas

5 – Exponential and Non-linear Growth in Population Systems

This presentation is about

 Climb-and-collapse outcomes in real-world
population systems

 Population calamities in seemingly “vast
open-space” environments

 Population explosions that induce calamity
by their secretion of wastes

 U.N. human population projections to the
end of this century

and 2/1000ths of 1%

This presentation is also about Climb-and-collapse

 Climb and collapse outcomes really happen
and we are not immune

 Collapse routinely occurs in environments that
visually appear to be almost entirely empty

 Collapse with 99% mortality is a biological reality

 We are not immune to collapse, and compared to
any other animals or dinoflagellates that have
ever lived, we are behaving very badly

 Three real-world examples of calamity in tiny
fractions of 1% “vast open-space” conditions

 Plus , two classical real-world climb-and-collapse
examples in separate mammalian populations

This presentation is also about

We are covering this because it has possible implications for us
 Our release of wastes, which shows a disquieting
similarity with population explosions of red-tide
dinoflagellates

 Dinoflagellate red-tides as quintessential
examples of population explosions that induce
calamity by the release of wastes

 The fact that calamities can arise from wastes
eradication, and damage

(as opposed to “running-out-of” things)

This presentation is also about

 Our own trajectory which may well be far worse
than outbreaks of dinoflagellate red-tide because
we supplement our biological and metabolic
wastes with a daily, and growing worldwide on-
slaughts of industrial and societal wastes

 While outbreaks of dinoflagellate red-tide can be
categorized as localized events, our own species
exerts impacts that are global in extent

visually-appear to be almost entirely empty

 Earth‟s atmosphere and seas as onion-skin-thin
and superficial surface films

Population
calamities
in seemingly
„empty‟
environments:

Example one -
Three Dinoflagellate red-tides
classical
real-world
examples

The dot in this image reflects one of
nature‟s quintessential real-world
population-environment calamities:

an outbreak of
Dinoflagellate red-tide

The dot in this image denotes
2/1000ths of 1% of its rectangle

In two OTHER classical studies
we will see that the organisms
involved have also already

waited
too long
Supporting mathematics is posted in
presentation appendices

and have already passed a
critical population-environment
tipping-point

so that the white dot in these
images depicts conditions that
are already

TOO LATE

One-celled marine organisms
called dinoflagellates

constitute one of
nature‟s quintessential
examples of

population explosions that
induce calamity by

their production
Red-tide of wastes
Dinoflagellates

Bushaw-Newton, K.L. and Sellner, K.G. 1999. Harmful Algal Blooms
IN: NOAA‟s State of the Coast Report, Silver Spring, MD.

red-tide

in 1997-1998
dinoflagellate

21 million fish
For example, a

killed an estimated
along the coast of Texas

Other individual outbreaks have

Bushaw-Newton, K.L. and Sellner, K.G. 1999. Harmful Algal Blooms
resulted in the deaths

IN: NOAA‟s State of the Coast Report, Silver Spring, MD.
of an estimated 150 tons
of fish as well as

manatees and
other marine organisms

One species of dinoflagellate
known for such outbreaks is
Karenia brevis

Real-world population explosions
of Karenia brevis manage to inflict
such population disasters even as
their populations of 1,000,000 cells
per liter physically-occupy

less than 2/1000 ths
of one percent

of seemingly "vast amounts of
open-space" that appear to
remain theoretically available

Recall, then, the tiny
white dot in this image

which depicts in a
mathematically-correct way

2/1000ths of 1%

of the rectangle in
which it resides

In other words, the population-
explosions of dinoflagellates in
red-tide outbreaks
produce

calamities

in environments that

Supporting mathematics is set forth in our appendices
visually-appear to remain

Look again at the
2/1000ths of 1% dot
in this image

and imagine the most intelligent
possible individuals
residing there

Which, if any, members of
such a population could be
convinced that their own species
faced a calamitous
environmental threshold

when such vast amounts of
open-space appear
to remain seemingly available?

In other words, they undergo
and induce

calamities

by their production and
release of wastes

in environments that
visually-appear to be


This set of conditions
would seem to be
worth noting, perhaps,

since our own species
appears to exhibit

an extraordinarily similar
pattern of behavior

Unlike red-tide dinoflagellates,
however, our own species
does not confine itself

to releasing

only
our biological and
metabolic wastes into our
surroundings

Instead, each day,
on a worldwide basis, we
supplement
our biological wastes,

in a way that is
unprecedented
in the history of life on earth,

with billions of tons of
societal and industrial wastes

so that we may be embarked upon a
trajectory that is not only

worse
than that of
red-tide dinoflagellates

but may be multiple orders of
magnitude worse, at that

This, of course, is not to necessarily
suggest a direct applicability

of dinoflagellate impacts and
trajectories

to humanity‟s own global
trajectories and impacts today

However, the fact that dinoflagellate
populations can induce calamity

by their production
and release of wastes

even when seemingly
“vast amounts of open-space”
appear to remain
theoretically-available

would seem to be worth noting

since our own species appears to exhibit an extraordinarily
similar pattern of behavior

It is also worth noting that while
K. brevis cells release only their

biological, cellular, and
metabolic wastes
into their surroundings,

our own species
supplements
its biological wastes with daily,
worldwide, and ever-increasing

avalanches of industrial
and societal wastes

No other animals do this,

and

no other animals in
the history of
the earth

have EVER done this

No other animals do this,

and

no other animals in
the history of
the earth

have EVER done this

And we are doing so on a global scale in less
than a single human lifetime

so that our own species
may, perhaps,
be on a trajectory
that is not only

Worse

than that of an outbreak
of red-tide
dinoflagellates,

but may be multiple orders of magnitude
worse at that

Also, outbreaks of red-tide, while
catastrophic, are at least
relatively localized events

While our own population
explosion, however, encompasses the
entire earth’s biosphere

as do the damages, wastes, impacts, and
eradications that we inflict

But we are
smarter

than a population
of mindless one-celled
dinoflagellates

aren‟t we?

Of course we are smarter than dinoflagellates, aren‟t we?

Dinoflagellates, for  Nor ways to pollute earth‟s
example, have not devised waters and drain aquifers and
eradicate water bodies like the
 Bulldozers, chain saws, tools, Aral Sea
and machines to quickly
eradicate entire forests, throughout the entire world
all at the same time
 Long-lines, radar, and GPS to
catch entire schools of fish, in less than a
single human lifetime
 Automobiles, coal mines, and
power plants to pump green-
house gases into the atmosphere

Of course we are smarter than dinoflagellates, aren‟t we?

Dinoflagellates, for  Nor ways to pollute earth‟s
example, have not devised waters and drain aquifers and
eradicate water bodies like the
 Bulldozers, chain saws, tools, Aral Sea
and machines to quickly
eradicate entire forests, throughout the entire world
all at the same time
 Long-lines, radar, and GPS to
catch entire schools of fish, in less than a
single human lifetime
 Automobiles, coal mines, and
power plants to pump green-
house gases into the atmosphere
Which means that we are
smarter, right?

In other words, our ingenuity and technologies not only allow
us to not only produce far more wastes more quickly
than cells of red-tide dinoflagellates

but they also allow us to multiply and amplify
our individual and collective impacts,
damage, and eradications

more quickly, completely, and efficiently
than any other animals that have ever lived

In other words, our ingenuity and technologies not only allow
us to not only produce far more wastes more quickly
than cells of red-tide dinoflagellates

but they also allow us to multiply and amplify
our individual and collective impacts,
damage, and eradications

more quickly, completely, and efficiently
than any other animals that have ever lived

and to do so on a global scale
in less than a single human lifetime

All of which may not necessarily
qualify as especially “smart,” right?

Two classical examples
Real-world Climb-and-collapse

appendices ONE and TWO

We are covering this
because
it has possible
implications for us

Scheffer, V.B., 1951. The rise and fall of a reindeer
herd, Scientific Monthly 73:356-362

Scheffer, 1951
population studies of reindeer herds
First, note these two classic Climb-and-collapse

Klein, 1968

Klein, D.R., 1968. The Introduction, Increase, and Crash of Reindeer on
St. Matthew Island. Journal of Wildlife Management 32: 350-367.

Notice that each reindeer herd exhibited a classic

Climb-and-collapse
population
curve

Scheffer, 1951 Klein, 1968

In each case, an initial period of
exponential growth was followed by a

99%-plus die-off

Scheffer, 1951 Klein, 1968

Secondly we note that each reindeer population
physically-occupied

roughly 2/1000ths of 1%

of surroundings that, visually-speaking, appeared to remain
theoretically-available to them at the time of the collapse

So that both classical die-offs BEGAN (and proceeded) in
environments that visually appeared to remain


approximately 99.998% EMPTY

So that both classic die-offs BEGAN (and proceeded) in environments
that visually appeared to remain almost entirely empty

Compare these two graphs

Below: Note the reindeer rocketing
upward before their 99% die-off

Right: Human population growth
8000 BC to present
(and now rocketing upward?)

Compare these two graphs

Which upward trajectory is
more pronounced and more extreme?

Do you see any
disquieting similarities?

More disquieting still, the real-world
numbers that actually emerge
could turn out to be

very much larger

than the medium-
fertility U.N. estimates

If worldwide fertility levels

Billions 7, 8, 9, 10, 11, 12, 13, 14, and 15 are based
average just

on U.N. high- fertility projections to 2100
½ child per woman higher

than the U.N.‟s medium-
fertility projections,

we will find ourselves
on-track toward

15.8 billion by 2100

Even the most intelligent, thoughtful,
and educated members of a highly-
intelligent species living in such
“vast open-space” conditions

would find it difficult (if not
impossible) to imagine
either the degree or
the proximity
of the too-late population-
environment dangers and
calamities

that are about to
overtake them

when so much surrounding open-
space appears to remain seemingly-
available

Yet, all three of the classical examples
used in this presentation, for instance,

show quite powerfully that if the
scholars and leaders of any of these
three populations were to
WAIT

until the conditions depicted in
the image shown here develop

at this point, they would have
already waited

Too-long

In 1911 in the V. B. Scheffer study,
25 reindeer were introduced to
41 square mile St. Paul Island, Alaska

Scheffer, 1951

by 1938, their population peaked
at more than 2000 reindeer – yet

by 1950 only eight remained

At their peak population of more
than 2000 reindeer (shown here)

their combined bodies
physically-occupied roughly
2/1000ths of 1%
of the island
upon which they lived

And then they underwent a

99% - plus die-off
Scheffer, V.B., 1951. The rise and fall of a reindeer

even as, taken together, their
herd, Scientific Monthly 73:356-362

combined bodies physically-
occupied only a tiny

Scheffer, 1951
fraction of one percent

of their seemingly-available
environment

In 1944, 29 reindeer were introduced
to 128 square mile
St. Matthew Island, Alaska

Klein, 1968

by 1963, their population peaked
at more than 6000 reindeer
and fell to 42 remaining in 1964

At their peak population of more than
6000 reindeer (shown here)

their combined bodies
physically-occupied about
2/1000ths of 1%
of the island
upon which they lived

Klein, 1968

And then they underwent a

99% - plus die-off

even as, taken together, their
combined bodies physically-
occupied only a tiny

fraction of one percent
Klein, 1968

of their seemingly-available
environment

Notice therefore that both herds underwent a

99% - plus die-off

even as their combined bodies
physically-occupied a tiny

fraction
of one percent

of the “vast quantities of open-
space” that seemed to remain roughly 2/1000ths of 1%
theoretically-available

In nature, this really does happen, and
this presentation cites actual examples
in four entirely independent settings

 Twice in reindeer herds (mammals),
AND

 In outbreaks of red-tide in unicellular
marine organisms,
AND

 Apparently to the early human
inhabitants of Easter Island
(which we include in our appendices)

Also disquieting, the real-world
worldwide human population
numbers that actually emerge
could turn out to be

very
much larger

than the
medium-fertility U.N.
estimates shown here

Six-fold life-extensions have already been

Unexpected advances in

would result in healthy, active 500-year-olds
achieved in laboratory organisms

And an equivalent extension in humans
life-extension or unexpected
declines in mortality

or if worldwide fertility levels
stall or turn out to be just

½ child per woman
higher
than the U.N.‟s
“medium-fertility” estimates

15.8
billion
headed toward

(as shown in this graph)
We could find ourselves

by the end of this century

Even tiny fractional such extensions in humans would toss
current U.N. population projections right out the window

Notice that these graphs
are quintessential
examples of J-curves

(one of the most dangerous
types of graphs in the world)

and since earth‟s
planetary carrying
capacity for a
modern industrialized
humanity is on
the order of
TWO billion or less

And since we are now
beyond seven billion and
may be headed toward
10, 11, 12, 13, 14, or 15.8
billion this century

and since each one of
our billions is
a truly enormous
number (see appendix)

Policymakers, academia, and the
world‟s rising generations of
„Under-20s‟ should accord
emergency-scale attention to
these numbers

Key Ideas so far

There is a widely-held misperception within our societies that
human population growth and overpopulation cannot be truly
serious so long as “vast amounts of open space”
appear to remain theoretically-available

Part two– Key Ideas

Supporting mathematics is posted
in appendices ONE AND TWO
 Real-world examples of Climb-and-collapse in population systems

 Collapse can and does occur in environments that appear to be
almost entirely empty (.. less than 2/1000ths of one percent ..)

 Real-world examples of 99% - plus die-offs
 A graph of human population growth over the past two centuries
appears to be both more pronounced and more extreme than those
seen in either of the cited reindeer examples

Given the current demographic
challenge that these numbers
represent

(and with up to our 10th to 15th
billions on-track to arrive
by the end of this century)

One would hope that we are collectively smarter than
a mindless population of one-celled dinoflagellates

that routinely show themselves
capable of calamity while less than 2/1000ths of 1% of the
occupying volume in which the population
sample resides

Invoking sobriety, however,
we may actually be following
a trajectory that has a
worrisome similarity to that
of the dinoflagellates

because our own species, like the red-tide dinoflagellates of marine
habitats, releases chemical wastes and toxins into our surroundings

Worse still, from at least one point of
view, however, we may actually be on a
trajectory that is worse than that
of the dinoflagellates

and multiple orders of
magnitude worse at that

for each dinoflagellate cell releases ONLY its
metabolic and biological wastes into its surroundings

In our own case, however, we
release not only our biological and
metabolic wastes

but also an unprecedented daily
avalanche of societal and industrial
wastes that are worldwide
in scope

and amplified by our
ever-growing numbers
and increasing industrialization

Reviewing Several Key Ideas

1 Dinoflagellate red-tides are quintessential examples of population
calamities arising from the release of wastes

2 Dinoflagellate red-tide calamities, however, arise from their release of
cellular and metabolic wastes into their surroundings

3 Because our own species also releases wastes into its surroundings,
we may be following a trajectory that is provocatively similar to that
of an outbreak of dinoflagellate red-tide

Reviewing Several Key Ideas

4 Except, of course, our own species supplements its biological and
cellular wastes with a daily worldwide avalanche of industrial and
societal wastes

5 (A behavior that no other animals on earth exhibit – and has
never previously happened in the entire history of the earth)

. 6 And lastly, while deadly outbreaks of dinoflagellate red-tide are
localized events, our own population outbreak is a
worldwide phenomenon and worldwide in its effects

Part Four

No other animals do this

Photos courtesy of life.nbii.gov: fox = Mosesso; Others - Hermann

species other than our own
Envision an individual animal of any

Photos courtesy of life.nbii.gov: fox = Mosesso; Others - Hermann

In virtually all of these cases, each organism‟s daily pollution of its
environment is limited to daily production of its bodily wastes

No population explosions of
red-tide dinoflagellates

(which poison their environments by the
wastes that they release)

have EVER supplemented their cellular
and biological wastes
with a daily worldwide avalanche
of industrial and societal wastes
the way that we do

No other animal species
supplements
its cellular and biological wastes

with a planet-wide and ever-
increasing avalanche of
industrial and societal wastes
the way that we do

And then there are also the enormous
additional levels of eradication,
degradation and sheer levels of

PHYSICAL DAMAGE

that we are inflicting everywhere
upon the ONLY planetary life-support machinery

so far known to exist anywhere in the universe

No other organisms
in the entire history
of the earth have

EVER
supplemented

their cellular and
biological wastes

the way that we do

And these behaviors are NOT a minimal or incidental
footnote to the biology of our species

Instead, they are one of our most distinctive
and all-encompassing characteristics

Summaries and Key
Concepts

We are dangerously misled by our
prevailing “open-space” suppositions

2/1000 ths of one percent

for it is a misperception to presume that human population growth and
overpopulation cannot be truly serious so long as “vast amounts of
open space” remain

This presentation has
also been about Climb-and-collapse

 Climb and collapse outcomes really happen
and we are not immune

visually appear to be almost entirely empty

 Collapse with 99% mortality is a biological reality

 We are not immune to collapse, and compared to
any other animals or dinoflagellates that have
ever lived, we are behaving very badly

 Three real-world examples of calamity in tiny
fractions of 1% “vast open-space” conditions

 Plus , two classical real-world climb-and-collapse
examples in separate mammalian populations

This presentation has also been about

We are covering this because it has possible implications for us
 Our release of wastes, which shows a disquieting
similarity with population explosions of red-tide
dinoflagellates

 Dinoflagellate red-tides as quintessential
examples of population explosions that induce
calamity by the release of wastes

 The fact that calamities can arise from wastes
eradication, and damage

(as opposed to “running-out-of” things)

This presentation has also been about

 Our own trajectory which may well be far worse
than outbreaks of dinoflagellate red-tide because
we supplement our biological and metabolic
wastes with a daily, and growing worldwide on-
slaughts of industrial and societal wastes

 While outbreaks of dinoflagellate red-tide can be
categorized as localized events, our own species
exerts impacts that are global in extent

visually-appear to be almost entirely empty

 Earth‟s atmosphere and seas as onion-skin-thin
and superficial surface films

In addition, the “running-out-of” suppositions
that traditionally seem to govern our thinking

such as “running-out-of” space, food,
oil, resources, or anything else

may not be the first or only factors
that threaten us

and such suppositions may lead us to an inaccurate
assessment of our current status or impending danger

Finally, we are the only animals that
do this, or that have ever done this

and we are doing so on a worldwide
scale so that we are not a localized
phenomenon

and our behaviors in this respects are not a minimal
or incidental footnote to the biology of our species

but are instead one of our most distinguishing
and all-encompassing characteristics

Lastly, but not least,
there are these
two graphs
of our demographics

which are very
much like

J-curves on steroids

First, five additional billions in
less than one human lifetime
since 1930

with the potential arrivals of billions
numbers 10, 11, 12, 13, 14, and 15
(and 800 million more after that)
due by the end of this century

on a planet whose biospheric machinery was already being
damaged at levels of five billion and six billion in 1987 and 1999

and whose planetary carrying capacity for a modern,
industrialized humanity is on the order of two billion or less

also
remembering the
levels of

sheer physical damage
and eradication

that we inflict all
around the world

Appendices
and supporting mathematics

Supporting Math – Red-tides
Severe red-tide conditions are common when Karen- In other words, one million dinoflagellate cells in a
ia brevis populations reach concentrations ranging 1000 cm3 sample still have approximately
between 100,000 to 1,000,000 or more cells per liter. 999.986 875 cm3 of unoccupied volume that would
Secondly, approximate dimensions of a typical K. appear to remain theoretically-available to them.
brevis cell:
Percentage Unoccupied
(1) Volume of 1 liter = 1000 cm3
Therefore, the percentage unoccupied equals
(2) Approximate dimensions of a typical K. brevis:
(999.986 875 cm3) divided by (1000) so that about
99.998 672 percent of the sample‟s total volume
L: ~30 um (= 0.03 mm) **
remains unoccupied … 99.998%
W: ~ 0.035 mm (“a little wider than it is long") *
D: ~ 10 – 15 um deep (10 um = 0.010 mm;
This means that such Karenia populations manage
15 um = 0.015mm), (so average = ~ .0125 mm)
to routinely visit calamity upon themselves and the
** Nierenberg, personal communication, 2008 environment in which they reside, even as all the
** Bushaw-Newton, K.L. and Sellner, K.G. 1999. cells taken together physically-occupy less than
Harmful Algal Blooms; NOAA 2/1000ths of 1% of the total volume that appears to
** Floridamarine.org, 2008 remain seemingly-available.
Using the above:
Thus, (100%) – (99.998 687 %) = (0.001 313 %),
Volume of a typical cell of K. brevis = (L) x (W) x (D) = or less than 2/1000ths of 1% of the volume that ap-
(0.03) (0.035) (0.0125) = ~ 0.000 013 125 mm3 pears to remain theoretically-available.

Thus one million Karenia brevis cells occupy ap- Thus, even though the K. brevis cells occupy a
proximately (1,000,000) x (0.000 013 125 mm3) = volumetrically-insignificant portion of the "open-
13.125 mm3, or about 0.013 125 cm3 occupied. space" that visually appears to remain almost
entirely “empty,” they manage, by their combined
Since 1 liter = 1000 cm3, subtracting 0.013 125 cm3 overpopulation and production of invisible and
(volume occupied) leaves (1000) minus (0.013 125 ) calamitous wastes, to catastrophically-alter and visit
or about 999.986 875 cm3 unoccupied utter calamity upon their home environment which
visually appears to remain almost entirely empty

Supporting Math
The image shown left depicts the physical amount of
space that constitutes two one-thousandths of one
percent. Note that the dot in the image denotes two
one-thousandths of one percent of the dark rectangle.

The step-by-step mathematics outlined below permits
preparation of a two-dimensional illustration like the
one shown here that visually depicts the proportional
amount of area occupied by two one-thousandths of
2/1000ths of one percent.
one percent
(1) Use imaging software to open a rectangle 500
pixels high by 350 pixels wide = 175,000 square
pixels (Here: wine-red rectangle)
(2) Thus, one percent of this area = (175,000) x (.01)
equals 1750 square pixels
(3) In addition, 1/1000ths of one percent = (1750)
times (.001) equals1.750 square pixels
(4) And two1000ths of one percent = (1750) x (.002)
equals 3.5 square pixels
(5) Calculating the square root of 3.5 square pixels
equals 1.87 pixels, so that a square of (1.87 pix-
els) by (1.87 pixels) equals 3.5 square pixels

Real-world population calamities Thus beginning with a rectangle of 500 x 350 pixels,
in nearly “empty” environments a small square of 1.87 pixels by 1.87 pixels (length
times width) would visually depict a physical region
of two one-thousandths of one percent.

Supporting Math – Reindeer of St. Paul Island
Concerning V. B. Scheffer‟s classic reindeer climb- that the bodies of the entire herd of 2000 animals
and-collapse study on St. Paul Island, Alaska, our would physically-occupy a total of 2470 m2.
estimate that the reindeer of St. Paul Island, Alaska
physically-occupied approximately 2/1000ths of 1% of Since the area of St. Paul Island, Alaska is about
the island‟s total area at the time of collapse is 106,000,000 m2 (about 41 square miles), we next
derived as follows. subtract the 2470 m2 that are physically-occupied by
the entire herd from the total area of the island, so
L: Assume an average reindeer is approximately that (106,000,000 m2) minus (2470 m2) roughly
190 cm long equates to a total “unoccupied” area of about
Female reindeer ~ 180 cm long; males ~ 200 cm 105,997,530 m2 that would visually appear to re-
plus non-adults, etc., so average = ~190 cm main seemingly-available.
W: Assume that the width of an average reindeer
is approximately 65 cm wide Lastly, dividing the island‟s total unoccupied space
(105,997,530 m2 ) by the total area of the island
Girth will vary with time of year; food, pregnant . . . (106,000,000 m2) equates to the percentage of total
females, and non-adults, so assume = ~ 65 cm
unoccupied space at the time of the peak reindeer
population, which was 0.999 976 or 99.998%.
Thus the area physically-occupied by an average
member of the population would equate to about
Notice then that the collapse (and 99% die-off) of
(190 cm) x (65 cm) or about 12,350 cm2 each
the St. Paul Island reindeer population began at a
time when 99.998% of the island‟s total area ap-
Given a peak reindeer population of slightly more
peared to remain theoretically-available, so that the
than 2000 animals, (2000) x (12,350 cm2) equates to
herd‟s maximum population, along with its collapse
a total physically-occupied area by all the reindeer of
and catastrophic 99% die-off all took place and pro-
the herd combined of approximately 24,700,000 cm2
ceeded to near annihilation in a surrounding en-
vironment that visually appeared to remain
One square meter = 10,000 cm2, so that dividing
24,700,000 cm2 by 10,000 equates to 2470 square almost entirely empty.
meters physically-occupied by the entire herd, so

Supporting Math – Reindeer of St. Matthew Island
We can apply the same approach to D.R. Klein‟s of the entire reindeer herd on St. Matthew Island
classic reindeer climb-and-collapse study on St. would physically-occupy a total area of 7410 m2
Matthew Island, Alaska (1968). Our estimate that
Since the total area of St. Matthew Island, Alaska
the reindeer of St. Matthew Island physically-occu-
is about 331,520 km2 (which equates to about 128
pied approximately 2/1000ths of 1% of the island‟s
square miles), then expressed as m2, the island‟s
total area at the time of collapse is derived as follows.
total area equates to about 331,520,000 m2 .
L: Assume an average reindeer is approximately Next, we subtract the 7410 m2 that are physically-
190 cm long occupied by the entire herd from the total square
Females ~ 180 cm long; males ~ 200 cm long plus. . .
meters of the island so that (331,520,000 m2) minus
non-adults, etc. thus, thus averaging circa 190 cm
(7410 m2) equates to a total “unoccupied” area of
W: Assume that the width of an average reindeer approximately 331,512,590 m2.
is approximately 65 cm wide
Lastly, dividing the island‟s total unoccupied space
Girth will vary with time of year; food, pregnant . . .
(331,512,590 m2) by the total area of the island
females, non-adults, etc., thus, roughly 65 cm
(331,520,000 m2 ) gives the percentage of total
unoccupied space on the island at the time of the
Thus the area physically-occupied by an average
maximum reindeer population, which was 0.999 978
member of the population would equal (190 cm) x
or 99.998%. Notice then that the collapse and
(65 cm) or approximately 12,350 cm2 each
99% die-off of the St. Matthew Island reindeer
population began at a time when 99.998% of the
Given a peak reindeer population of St. Matthew isl-
island‟s total area visually-appeared to remain
and (1963) of slightly more than 6000 animals, (6000)
seemingly-available, so that the herd‟s maximum
times (12,350) equates to a total physically-occupied
area of approximately 74,100,000 cm2 population, along with its collapse and catastrophic
99% die-off all took place and proceeded to near
annihilation in a surrounding environment that
One square meter = 10,000 cm2, so that dividing
visually appeared to remain
74,100,000 cm2 by 10,000 equates to about 7410 m2
which means that taken together, the peak population almost entirely empty.

Easter Island?
We assess Easter Island‟s historic climb-and-collapse human population data as outlined in Jared
Diamond‟s book, Collapse – How Societies Choose to Fail or Succeed (Viking, 2005) as follows:

Area of the island = approximately 170 km2 (about 66 square miles) or about 170,939,215 square meters.

Assuming a mid-range peak human population of approximately 15,000, and that the average individual in
the population physically-occupied approximately one square meter (standing), the combined area physic-
ally-occupied by all 15,000 individuals combined would equal approximately 15,000 square meters.

Therefore, given an island of approximately 170,939,215 square meters, if we subtract the approximately
15,000 square meters physically-occupied by all 15,000 human inhabitants combined, we are left with a
remainder of approximately 170,924,215 square meters of “unoccupied” “open-space” that would visually-
appear to remain seemingly-available.

Next, dividing the total “unoccupied” area (170,924,215 m2) by the island‟s total area of 170,939,212 m2,
equates to an island that is 0.999912 unoccupied, or 99.991% empty.

Thus we see that the mathematics suggests that a mid-range peak Easter Island human population reached
its peak and began its collapse even as “vast amounts of open-space” appeared to remain seemingly avail-
able and its inhabitants seemed to be living in an environment that was almost entirely empty.

Thus we see still another natural experiment that ended in collapse, this time involving a human society.
Note, however, that the similarity of our situation and that of the peak population of Easter Island is not
perfect, for the humans on Easter Island constituted a pre-industrial society that could kill its birds and

Easter Island?

most of its seabirds, deforest its surroundings, and
overexploit its resources.

Our own numbers, however, are both far greater, and
our individual harmful impacts may have 50 or 100s
or even1000s of times the impact of a single pre-
industrialized individual.

Also unlike us, the island‟s pre-industrial society
was a localized society that could not generate
billions of tons of CO2 and industrial wastes, de-
grade and eradicate natural systems and plunder
resources from all parts of the planet.

In addition, they had no automobile exhausts, chlor-
ofluorocarbons, logging concessions, mechanized
fishing fleets, fossil fuels, nuclear and industrial
wastes, and investment portfolios with which to
simultaneously assault every corner of our planet.

Yes, we did notice the close agreement between the view of our planet itself.
2/1000ths of 1% that turned up in the assessment of
dinoflagellate red-tides and the 2/1000ths of 1% figures Because we are, as individual creatures, such small
that turned up independently in both of the mammalian beings compared to our planet, we tend to imagine,
climb-and-collapse reindeer studies that we cite. again erroneously, that the earth's atmosphere and
seas are so immense that they must be relatively
immune to the industrial and societal insults that we
Also, yes. We mathematically analyzed only the four
inflict.
cases cited, and were as surprised as anyone at the
degree of agreement in all four results, strongly sug- In mathematical and planetary terms, however, both
gesting that our natural, instinctive, or intuitive "open- earth's atmosphere and its seas are extraordinarily thin
space" suppositions may be causing us to seriously and superficial surface films. Mathematically speaking,
underestimate the proximity, extent, and degree of for example, 99.94% of our planet consists of its crust,
danger that our present numbers may portend. mantle, and its molten interior and the thin layer of
water that we refer to as an ocean exists only as an
(And using an estimated peak population of preindus- inexpressibly thin and precarious surface film that is
trial humans on Easter Island, as reported by Jared just 6/100ths of 1% as thick as the earth itself.
Diamond in his book Collapse, of 15,000 - 30,000,
analysis produces another tiny fractional portion of To illustrate this depth to scale on a model globe, we
1%.) (And a typical, modern industrialized human would need a layer of water just 12/1000ths of an inch
has 50-100-1000s of times the impact of a single deep to proportionately represent the depth of earth's
pre-industrialized individual.) oceans. If we were to wipe a wet paper towel across
a 40-cm globe, the film it leaves behind would be too
In addition, the dangerous and widely-shared "vast deep to properly characterize the depth of earth's
open-space" suppositions that we have addressed in oceans.
this presentation also extend to our widely-shared

After What Every Citizen Should Know About Our Planet; Anson, 2011; Marine Biology and Ocean
Science, Anson, 1996; and Planet Ocean, International Oceanographic Foundation, 1977.

In nature, population calamities in
environments that visually
appear to be
ALMOST COMPLETELY EMPTY

are common enough to be
disquieting and may
have something to tell us about
ourselves


It is entirely free for non-commercial use
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What Every Citizen Should Know
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