Browsing articles in "exponential function"

Feedback Loops, why fossil fuels are financial candy

Nov 3, 2011   //   by 1000arms   //   Blog, exponential function, renewable energy  //  No Comments

One of my favorite thought experiments involves the oil industry.

Supply Side Feedback Loop:  Even though fossil fuels are a finite trust fund of stored up solar energy, unlike most other resources, when harvested, it provides energy to harvest more of itself.  Fossil energy is one big positive feedback loop.  Estimates suggest that its energy return on investment (EROI) is a 5:1 ratio.  That is, it takes 1 unit of energy to pull up 5 units, for a net of 4 units.  One can pay back the first unit and combust those 4 harvested units to mine 20 new units. The oil industry has exponential growth written all over it.  This densely-rich fuel source is a no-brainer for any business person.

Demand Side Feedback Loop:  Mining oil, has many co-products.  The most valuable are for synthesis of organic compounds – the long carbon-chains in fossil resources are a chemical engineer’s wet dream. Then there is jet fuel, and diesel fuel and petroleum.  It’s a long list, including a processing ‘waste product’ we now call tar.  So Ford invents the business plan to get every person a car.  The cars start driving, slowly, on bumpy roads.  As more cars drive slowly on bumpy roads, a co-product of petroleum starts to amass – tar.  So some resourceful supply chain engineer says, Wo-ah, lets make asphalt.  We essentially landfill this asphalt on our highways resulting in smoother driving and better gas mileage bc the friction has gone down. In these more pleasant conditions, citizens drive faster to more places and longer distances.  We learn the American cliche of “Freedom” and “Power” and “Speed”. Every doubling of speed results in a quadroupling in air resistance which lowers gas mileage.  Citizens use more fuel, and generate more tar, creating more roads to drive more miles.

Now here’s the kicker.  I’m no economist, but applying the supply and demand charts to oil just screams cash cow.  First, there is an increase in supply (remember, oil is internally accountable to itself, it is the source of energy to mine more of itself, generating oodles of cheap energy), which society relentlessly entertains itself with.  This results in an increase in demand.  Sure the price fluctuates, but an oil baron doesn’t care, bc implicitly the oil company already has a 5:1 return on investment just within the system of fuel extraction, say nothing of mark up.  Cheap or expensive to the end-user, the company is in the clear.  Now, add scarcity, or the perception of scarcity to a society that has grown dependent on oil (to boil the water, get kids to school, power the computer, cool the refrigerator, run the A/C, and light the bathroom).  The oil company doesn’t care, bc the demand is so high, scarcity makes the price go up and they’ll mine until it’s no longer profitable and the trust fund runs out.  They’re going to milk that cow until it’s bone dry.

Sure, alternative energy can’t compete w cheap oil; oil is trust-fund privilege and renewable energy is blue collar hard work.  So how do we convert over to a more efficient energy-society with renewable fuels?  Like any venture, we invest in it.

Brain Spores- the advantage of 7 billion people

Nov 2, 2011   //   by 1000arms   //   Blog, exponential function, think tank  //  No Comments

So, the world turned 7 billion.  Anxiety for a finite planet? or a hot bed of brain spores.

I’m terribly fond of mushrooms for all kinds of reasons.  For example, a mushroom in Oregon may be the world’s largest single organism.  “This 2,400-acre (9.7 km2) site in eastern Oregon had a contiguous growth of mycelium before logging roads cut through it. Estimated at 2,200 years old, this one fungus has killed the forest above it several times over, and in so doing has built deeper soil layers that allow the growth of ever-larger stands of trees.” —Paul Stamets, Mycelium Running

Mushrooms don’t have seeds; mushrooms drop spores.  The dispersed spores land like birdshot on a field of resources.  Then the spores look for each other and connect by hyphae.  Like any node (spore) and edge (hyphae) configuration, as the nodes connect edges, the ability to extract and allocate resources across the field increases as the network becomes more connected.

Today is Day of the Dead – and mushrooms know how to dance on the grave.  That is, mushrooms thrive by working the reciprocal relationship of exponential growth with exponential depletion.  Mushrooms understand and thrive on a steady state economy.  What is so exquisite about this mycelial mat, is that the mushroom mat can kill and eat a tree that is floundering in a shady area and move those resources to feed another tree in a brightly lit area.  That is, the system gleans and allocates from across a large landscape for the success of the overall system.

R Williams estimates the human brain has about 100 billion (1011) neurons and 100 trillion (1014) synapses.  Multiply that by 7 billion brains; we have a force of nature.

While our collective population is a force of nature currently pushing toward the limits of our finite system in myriad ways (e.g. exponential increase in energy use causes exponential depletion of oil reserves which is directly related to exponential increases in atmospheric greenhouse gases thus exponentially increasing heat retained from the sun and disappearing ice pack reserves…), we are a reflective species.  In the same way we can learn how the exponential function is a way to access resources, it is also the means by which we can understand that growth is predicated on depletion in a closed system.  Geometrical cause and effect.  We can begin to change our focus of vitality based on the abstract monetary system of economic growth to one of steady-state ecological stewardship of our material home.  Economics and Ecology both come from the Greek oikos “house, dwelling place, habitation”.

What I’m trying to talk about here is how each and everyone of us is a witness of the state of our home.  Embodied within the global citizenry are perspectives, ideas, and solutions to global problems to redefine these status quo behaviors and inform sustainable solutions. This think tank project liberates, combines and sequentially layers ideas from people who might be geographically remote to each other to generate solutions that impact the global ecosystem.  By releasing these ideas, we will have a greater capacity to respond to our rapidly changing environments.  We can harness the power of the exponential to redefine civic action.

Let’s mat together.

Flat world -> Round world -> Finite world w 7 Billion people

Oct 15, 2011   //   by 1000arms   //   Blog, exponential function, sustainability  //  No Comments

Throughout history, we have come upon ideas that are difficult to integrate.  It’s normal.  Think of when we thought the earth was the center of the Universe.  It was a completely reasonable idea based on our immediate senses.  Or that the world was flat – also a reasonable hypothesis.  Or that the world ended at some edge of some ocean – just bottomed out like the edge of our bed!  Or that the earth was round, a very reasonable hypothesis.  Following this hypothesis, explorers from the flat world were rewarded with gigantic landmasses of unmined natural resources – ‘the new world’.  So while we don’t have to worry about sailing off the face of the earth at some unknown (but infinitely far) edge, we now have to worry about its finite surface area.  The possibilities implicit in finding the new world, also defined some basic physical limits.

And like our predecessors who tried to integrate sensory perception w abstract thought to conceptualize a round earth when for all intents and purposes it was flat, I recognize it is difficult to think about a finite earth when I can buy asparagus in NYC for $2/lb in October.

As a biologist, I often struggle w economic structure (asparagus in October for $2/lb, really?!); economists (generally) think of material resources as just subservient materials to the agency of humans rather than being the very intimate and mineral cycling of what we call humanity.  But Herman Daly is an economist I actually like.  In his “Beyond Growth”, he sees the disgruntled logic when an infinite economic growth paradigm is placed in the context of the Laws of Thermodynamics.  I’m going to quote at length from the first chapter of his book that set up the notion of a steady state economy:

“The growth advocates are left w one basic argument:  resource and environmental limits have not halted growth in the past and therefore will not do so in the future…

Earl Cook offered some insightful criticism of this faith in limitless ingenuity in one of his last articles (1982).  The appeal of the limitless ingenuity argument, he contended, lies not in the scientific grounding of its premises nor the cogency of its logic, but rather in the fact that:

‘the concepts of limits to growth threatens vested interests and power structures; even worse, it threatens value structures in which lives have been invested… Abandonment of belief in perpetual motion was a major step toward recognition of the the true human condition.  It is significant that “mainstream” economists never abandoned that belief and do not accept the relevance to the economic process of the Second Law of Thermodynamics; their position as high priest of the market economy would become untenable did they do so.’

Indeed it would.  Therefore, much ingenuity is devoted to ‘proving’ that ingenuity is unlimited.  Julian Simon, George Gilder, Herman Kahn, and Ronald Reagan trumpeted this theme above all others.  Every technical accomplishment, no matter how ultimately insignificant, is celebrated as one more victory in an infinite series of future victories of technology over nature.  The Greeks called this hubris. “

Daly ends this section by quoting from Cook again “without the enormous amount of work done by nature in concentrating flows of energy and stocks of resources, human ingenuity would be onanistic.  What does it matter that human ingenuity may be limitless, when matter and energy are governed by other rules than is information (Cook, 1982, p194).

So as we enter this magnificent period of the internet of ideas on a materially finite world, I am reminded of a book I read by Barbara Novak titled “Nature and Culture; American Landscape and Painting”.

America has become wealthy for many reasons.  In my mind, entering a pristine landscape and discovering oil catapulted the American dream for the various ex-patriots that arrived in ‘the new world’.  But that dream was predicated on growth by increased access to unspoiled resources.  America was rich in natural resources.  So incredible economic growth was totally possible (in that context).  What I like about Barbara Novak’s book, is that she notes the transition of styles of landscape paintings of the 1800s that I think reflect an important transition in thinking about nature.  There developed a tension between the pristine quality of the untouched land and the opportunity for mobilizing unexploited material wealth.  Artists went on dangerous expeditions to capture and record the virgin landscape and then they documented the transformation of that virgin landscape.  Landscape images ranged from untamed wilds of nature, to wilderness mysteries, to gardens of eden, to utilitarian topographic maps,  to pastoral narratives, to pre-industrial documentation.  What kind of landscape paintings do we have today?

In the 1800s, people on a crammed and overpopulated European continent, moved to an underpopulated and materially rich continent.  Growth! Unless we get to the moon and can grow our carrots there, there is no place to expand this growth paradigm as we currently understand it.  Given that I accept I live on a finite round earth, receiving a finite amount of sunlight daily, yet thriving on a trust fund of fossil energy, striving for a sustainable world is a real concept – an hypothesis that seems worthy of serious thought and meaningful exploration – not to be reduced to cynicism about how people appropriate the word ‘sustainable’.

We are not the center of the universe.  We do not live on a flat planet.  We live on a finite planet.  And on Halloween 2011,  world population is projected to hit 7 billion, each of us with varied demands on this finite surface, but 7 billion, none-the-less.  Trick or Treat.

Number Sense & how we unlearn the intuition of a log scale

Aug 29, 2011   //   by 1000arms   //   exponential function, links, poetics, theory  //  No Comments

My favorite science/wonder reporting is a WNYC program called RadioLab.

One episode called Innate Numbers discusses how children in our culture are trained out of an intuitive and innate understanding of the logarithmic scale and into integers and linear thinking.  This is based on research and speculation by Stanislas Dehaene who wrote The Number Sense and Susan Carey.

Mirror Image

Aug 29, 2011   //   by 1000arms   //   exponential function, poetics, theory  //  No Comments

The thing I love about the exponential function is that it always has a mirror image.  For example, exponential growth in human population, would have many images that mirrored it such as exponential loss in square feet per person.  Now perhaps this is one of those tautological redundancies that I’m prone to, but I’m not so sure.  It has more to do with layered causes and effects in a complex and dynamic system.  So for example, exponential growth in fossil fuel use relates to exponential depletion of fossil reserves storing carbon in the deep earth, which relates to the exponential increase in gaseous CO2 to the atmosphere.  Really, we could come up with all kinds of chains of events that integrate to tell something about our deeply interrelated world.  The point here, is the exponential has momentum and as that momentum builds, one can start looking for the causal impacts resulting from that momentum.

A graph of the exponential function is a map of growth and decay.  In general, an exponential pattern can go unnoticed for generations before the culminating impact of its sequential doublings becomes observable.  The exponential function is the summative outcome of ‘normal’ behavior – what our parents did, what our neighborhoods are doing, what our children will do (unless something changes this pattern of behavior).  Climate change, population growth, AIDS, and consumption are status quo problems of exponential nature.  The change seems imperceptible in day-to-day life until it reaches a critical level when the culminating force of the doublings becomes abundantly clear.  The exponential function is self-similar change (1, 2, 4, 8, 16 or the reverse).  As one element grows, implicitly another recedes; the exponential function has a mirror image.

A good way to illustrate the exponential function is with the story of the poor boy who returns a lost princess to the king.  When asked by the king for any gift in trade, the boy only asks for a grain of rice, to doubled across each square of a chessboard (64 doublings).  The king knowing he has eight million bundles of grain (with one trillion grains per bundle) exclaims: That is all you want for returning my daughter?

But by the end of the simple doubling (1, 2, 4, 8, 16) across 63 squares, the poor boy has the king’s wealth in rice.  For the first 55 squares, the king is beaming because this request has barely made a dent in his stores.  By the 61st square, the king still has ¾ of his grain but by the 63rd square, the king is completely broke and encourages marriage between his daughter and the boy since he can no longer fulfill his end of the deal nor feed his daughter.  By simple doubling, the king experienced exponential loss of his finite resources and the boy exponential gain.

The ‘fact’ of the exponential function is that there is relatively little time to respond when the curve becomes noticeable.  In the example above, the simple doubling pattern can go for more than 55 generations, before the exponential function begins to be observable in the graph of the king’s rice.  Just two doublings from being broke, the king still has 75% of his resources.  This doubling is exponential growth coupled to exponential depletion of available resources.  When the resources are no longer sufficient, the king gives way to the boy.

The exponential function makes for a very simple graph – it is easy to name when you see it.  So easy, that the pound-in-your-heart implication embedded in the graph is lost and it is simply named:  ‘Oh, that is exponential’.  To most, it is a factual word without cultural embodiment.  It is a word lacking a literalization to bring it forth from the abstract.  What is the implication of ‘giving’ cultural meaning to ‘made’ abstract facts?  How do we culturally qualify the quantified?  There are nearly 7 billion people, each standing on his/her changing two foot square of earth with his/her own perspective on what is going on.

Meanwhile, the contemporary economic system thrives on infinite growth.  Infinite growth would be possible if we lived in an infinite world, but we don’t.  In ecology, the term carrying capacity is used to define the maximum population of a given organism that a particular environment or habitat can sustain (this includes biological and technological limits).

Awareness of the consequences of exponential growth is not recent.  In fact, Darwin cites the exponential function in the context of natural selection in the Origin of Species: ‘There is no exception to the rule that every organic being naturally increases at so high a rate, that, if not destroyed, the earth would soon be covered by the progeny of a single pair’.    And yet, modern civilization has not come to terms with the social, cultural, and political significance of the exponential function:  that our normal behavior will be changed with or without our thinking consent, with or without our ability to use the information embodied in the multiple expressions of the exponential function.

The doubling of a population mirrors the doubling of resource depletion which mirrors a doubling of waste products or pollution.  As a species advances on the ecosystem creating a network of chemical synthesis, spreading out from the originator, it both exponentially grows in number and simultaneously depletes it resource base.  The mirror informs us too.

jlw29aug11 tho much of this text came from JVC.2008.7(3).309-334.