Limits vs. Hard Limits

I found the following pages (links below) about physical and logical
limits. The author posits that true limits are frequently and
practically the result of knowledge systems themselves. My take on
his argument is that even where true limits exist (Godel, Penrose,
Turing) the limits in our own notational, logical and processing
systems prevent us from ever experiencing the true innate limits in a
system.

My guess is that Godel's incompleteness limit and Turing's halting
problem, and even Penrose's arguments about self same limits imposed
by the false mapping of one computing or mapping system onto a domain
with its own (incompatible) processing system. Again, these logic
and processing system miss-mappings may present false limits that are
fundamentally different from any true limits that may exist, and
importantly, one might mistake the false limits for the real one(s).

Interestingly, Turing's process halting proofs prove that all of his other work on computing system equivalence may never be conclusively
applied to a given process (as it is impossible to say whether or not
a given process is computable (will not halt) and his equivalence law
depends on a process being computable.

The work of most theorists depends on the notion that the universe is
computable, is Turing complete, is not a member of the group of
programs that will halt. Even more problematic is the work of theorists who attempt to build ad hoc simulations of the most causal layers of the universe, of its origin, in which case both the simulation and what it simulates must both be Turing complete and not a member of the set of halting programs.

My mind is whirling around all of these issues. Plus, I am noodleing around the notion that the lowest levels of hierarchies of influence
cones (more later) necessarily share commonalities (even become
equivalent) at their lowest or most causal point. If that is indeed
the case, then there is a reason that I am seeing such parallels
between GUTs, information science, thermodynamics, linguistics,
bioinformatics, genetics, genomics, evolution, and AI. The other
less appealing possibility is that these apparent similarities
between the base of all domains is a byproduct of the ignorance that
is a natural byproduct of exploring an edge of what is known.

http://www.fortunecity.com/emachines/e11/86/crashbar.html
http://www.fortunecity.com/emachines/e11/86/loglimit.html

Note: The author of these linked pages is JOHN L. CASTI a professor
at the Technical University of Vienna and at the Santa Fe Institute.

Productivity at Base

I have an economic question or two. Why is monetary policy
positioned at the apex of control in our nation's economic
hierarchy? Why is the Fed Board Chairman the go-to lifeguard and man-
on-the-mountain-guru for our entire economy? Failing a lowering of
the prime lending rate or the fed rate, we don't seem to know how to
intervene or plan the economy such that moments of panic necessitate
these quick fixes (that only harm the economy in the long run). And
this makes me confused about everything I have learned and everything
that makes sense about economic theory. In academic circles, there
seems to be a general acceptance of what might be called the standard
model of economic science. From what I have read, serious scientists
of economies almost always agree that productivity alone sits at base
of all influencers at play in any economic system. Ultimately, this
means that other factors weigh in more on the side of effect and that
productivity is THE factor that more often than not is more causal
than any other factor effecting economies. Modelers of economic
systems, like modelers of global climate, implement countless
mathematic dynamics seeking mathematic descriptions that can robustly
mirror and follow the arch of actual economies under actual natural
pressures over time. In these models, the ones that can achieve some
success aping real economies at global scales... productivity rises
to the top of every influence hierarchy. So what is productivity?
How is it different from other metrics of economic influence like
spending, commodity, resource, stock, currency, and geopolitical
trade markets, saving rates, inflation, jobless rate, secondary
education rate, incarceration rate, capital investment rates, basic
research spending, infrastructure amortization, how indeed is it
different from large scale economic measures like GDP itself?

The concept backing the term productivity is a more complex than
other common economic measures. Like evolution it is obvious that it
is central to and at base of the inverted influence pyramid... but
like evolution, it seems also to be a moving target... like the
shadow of a person walking east in the evening, it is right there, it
has a finite length, yet one never catches or completely possesses
it. Wow that is a metaphor out of control. Actually, a moving
target is just what you would expect in a dynamic system that feeds
on it's tail, that is different tomorrow because of what happens
today. And, like evolution, productivity defines the propensity of
today's systems to maximize the effectiveness of tomorrow's systems.

The problem with Fed Rate finagling and other Monetary Policy
doodling is that, like lifeguards flinging life rings, is to public
and to immediate, to much of a band aid, to much after the fact, and
we soon forget that the very use of such stop-gap measures is usually
a good indication of deeper ills, ills that can not be truly fixed
with heroics (with all the screaming and running around, and with all
of the cowboy heroics and wasn't that close brow wiping and back
slapping afterwards, who is going to remember the importance of
swimming lessons and civic behavior, and safe pool design?). Here
come the bank chairman calling out for a quick fed fix (read subsidy,
read absolute disincentive to act responsibly or to care about the
health of the economy) and the here comes the Fed Chairman on his
white horse again to provide a temporary high level fix to what is by
definition always the result of deep low-level wows. And here we
are, the public, by practical necessity (our busy lives) ignorant of
the subtile complexities that make up the grand causal stack that is
the economy, anxiously anticipating a quick fix, so that we can go
back to our blissfully simple understanding of the economic world
around us.

I frequently use the term hierarchy of influence to remind myself and
others that every complex system is an assembly of parts arranged by
hard natural law into an influence tree where some parts have greater
influence on change than others do. On the bottom of this tree
influence tree are the things that cause other things, as you move up
the tree you find things that are more caused by or are the effect of
other more influential things below them. Cause and effect are very
very different. This is the important concept to get. Consider a
simple system, a steel bolt laying on a concrete floor with a magnate
laying on a bench a few feet away. The prime influencer in this
system is gravity. If you move that magnate closer to that bolt, the
influence hierarchy will at some point flip when the attractive force
from the magnate is stronger than the gravitational force between the
bolt and the earth. At all times one must remember, both forces are
at play, it is just their relative influence that changes. The
physical and behavioral state of all systems at any given moment are
simply the sum of all influences at play within them. And these
influences are not equal. If your goal was to move that bolt, it
would be ridiculous to spend much energy worrying about the
orientation of that magnate on the bench. Yes, spinning the magnate
does have some (miniscule) measurable effect on the system... on the
bolt, but there are other potential influencing factors that will
have far greater effect on the system (moving that magnate within a
few inches of the bolt for instance). Same goes for the economy of
course. If you were given the task of defining the indispensable
factors that would absolutely have to be present in a healthy,
growing, regionally and globally competitive economy, prime rates and
cash fluidity would probably not enter the picture until many more
profound factors were taken care of (resource availability, trained
and knowledgeable labor base, save and stable living conditions that
promote individual well being, transportation and communication
infrastructure, physical and virtual markets (where to buy and sell
things), ownership protection, ready availability of credit for
capital expenses, etc. It is when the existence, availability or
balance of these systems fail, that stop gap measures like currency
and lending rate control become necessary.

The Biggest Why

Here is my attempt to explain my self and my work.

My goal is to contribute ideas, knowledge, tools and infrastructure
that will help humans understand and exploit the most pervasive and
powerful structures, processes and agents of change... towards
accelerative increases in productivity. I see this as the only
process that matters. To the extent that we stay attentive to the
process that is change, productivity increases apace. But what is
this process and how can I claim to know that it is THE process?

I began this exploration as a 9 year old one afternoon while walking
home from school. That was the day I decided to spend my life
looking for a truth or set of truths that sat at base beneath all
other truths, that informed and gave shape to all processes, a truth
that was independent of domain, that was true and formed the shape of
all things and all processes. I also made a promise to myself that I
would reject any of the theories I came upon or created if even one
small measurement conflicted or even worse, if my theory called into
question any other empirically verified theory. In short, I would
accept ideas only if they were in complete agreement with everything
else that was known to be true (verified by measurement). Over the
next 10 years I worked several theoretical epochs to this abortion
point where my stringent test of data agreement was violated.
Because the truth I was looking for had to be independent of domain,
because it had to be as true and as primary to particle physics as it
was to quantum electrodynamics as it was to the Krebs Cycle it was to
atmospheric dynamics as it was to galaxy and super galaxy evolution,
as it was to market fluctuation, and cultural evolution. etc., I was
forced to look to meta patterns and meta dynamics. Thanks to the
good people who independently discovered thermodynamics and
information theory, two sets of identical math that show the
absolute equivalence of structure and energy, two theoretical
frameworks that describe the parameters and limits that govern change
in any system, I had a solid scaffolding or armature with which to
give definitive structure to the more bio-centric theories of change
outlined by Darwin. I began to from a mash-up theory of change in
any domain, rooted in evolutionary theory and informed by
thermodynamics/information theory.

We are familiar with these ideas in the pedestrian; in business and
economics we collectively call the result, productivity. In
evolution this is the elusive arrow of time, this is that wily
fitness that determines whether a bit of DNA will be more or less
represented in future branching of the tree of life, this is why any
tomorrow is qualitatively different than and dependent on any today.
At base my work is founded on the theory that complexity increases
over time in small regions of larger systems (or THE system) simply
because complexity gets energy and structure to degrade towards heat
and random distribution faster than without complexity. This
degradation of order over time is domain independent and drives all
change. Most of the random accumulations that result are simpler
than the order from which they precipitate, most of these byproducts
of action are unstable and short lived. Once in a great great while,
a novel structure falls out with the other detris of action, and even
rarer, this novel structure is both stable and generative... causes
its own out-fall of debris. This is the process of evolution. This
is the reason it happens. If degradation of order is the most
universal of processes, then it is the base pressure behind change,
it is the why of evolution. With this knowledge we can know
important things about all process. That no action happens except
the process that takes the least energy. That competition between
structures is competition to degrade energy and structure faster and
more completely. That structures that are more fit by these
standards will inform the structure of the future of complexity more
than structures and processes that are less fit. That fitness is in
fact a measure of a system's ability to create structures of even
greater fitness over time. That this metric is a property or the
property of value to the universe (or any universe). That this
metric represents a moving target, an n-hard problem, a solution
built of terms from its previous state, is by its very nature not
deterministic. The end-state is knowable; heat-death. The process
is knowable; optimization of structures that maximize the production
of sustained entropy. But the exact most optimal solution at any
given time is unknowable and additive. Understanding this process
should yield growing efficiencies can never result in the perfect
solution.

As I said before, I am interested in domain independent truths. One
of the conceptual tools I use is what I call hierarchies of
influence. A hierarchy of influence is a cline stretched from pure
cause to pure effect. It assumes that some parts of a system are
more cause and some are more effect. I like to think of these
hierarchies of influence as inverted cones where one will find the
most fundamental influencers near the bottom point and the derivative
cause agents above them. In fact, real systems are more than
probably not so suited to simple diagrammatical organization... but
it works for me to think this way. I'm sure many people will say
that their work will eventually sit as THE primary causal agent at
the base of the most universal influence hierarchy cone. I almost
agree. I agree that some theory will eventually explain, even
ferment, all theories above it. A GUT theory! For this universe
anyway. And this is why I posit a tangential influence cone. One
that is abstracted to the point that it has to be true no matter what
self consistent set of physics your universe is derived from.

Patterns that Enchant vs. Patterns that Matter

A fractal is a special kind of crystal. Before I go into this, I
will attempt a very high level definition of the concept crystal.

Crystals are patterned aggregates (accumulations) of similar parts.
These parts come together over time and assume structures that are
notable principally because they assume shapes that are repetitive at
any scale. Crystal parts do not necessarily look like the final
crystal, in fact it is rare that they do. If the crystal's shape is
a cone, when you hit it with a hammer the shards that result will
most probably not be cone shaped. Think of a crystal as a hollow box
and then think of the shape a brick or tile would have to have so
that if it was repeated over and over it would form layer after layer
of concentric skins or shells... and that will be one of the possible
part shapes for a crystal of that shape. This is true while the
crystal is growing, at each stage it is a cone, a cone that grows
into a bigger cone. Of course the parts themselves can be made of
other smaller sub-parts, (atoms, molecules, etc.) that are not
themselves shaped like the crystal or its parts. The shape a crystal
takes is dependent on inherent energetic and structural properties of
its component parts and the conditions present during each stage of
its development or growth. Another way to say this is that under
different environmental conditions the same sub-parts will self
organize into different shapes or crystals. This is why carbon finds
so many crystalline forms in nature (graphite, diamonds, and the far
more exotic Bucky Balls, and Bucky Tubes).

In simplest terms, if the crystal's parts are shaped like cubes...
the crystal that grows of these parts will naturally tend towards
larger and larger cubes. Pyramid parts will most likely be some
slightly imperfect three dimensional rhomboid shape which when
allowed to aggregate slowly in large numbers yield larger and larger
pyramids made up of concentric skins like the layers of an onion or a
self-stacking Russian doll. Of course you can build odd shaped
things from a cube... but the shape that will occur most often (cause
it takes less energy for these parts to fall into this shape) will be
a shape the mimics the shape of the original part. But sometimes the
conditions in the environment will influence which types of
aggregates will form... with which resulting shape. The graphite in
your pencil, a diamond, coal, and exotic materials like the carbon
fibers used in tennis rackets and fighter jet wings, and the even
weirder Bucky Balls or Bucky Tubes (little molecules shaped like
geodesic spheres or tubes and named after the systems scientist and
inventor Buckminster Fuller... all of these things are crystals made
of the carbon atom under various common and uncommon (extreme)
environmental conditions. Are carbon atoms shaped like cubes or
balls or tubes or strands? No. But a small variability in the
number (and orbit) of the negatively charged electrons that orbit a
carbon nucleus (positively charged) is all that is necessary to cause
accumulations of similar atoms into one of these many crystal
shapes. Be cautioned here, the conditions surrounding a bunch of
potentially crystal building parts plays a huge role over the growth
of a crystal. Under the wrong conditions, a crystal will never form.

Unlike the strict chemical or mineral shiny things that generally
come to mind, the term crystal, at a more abstract level, can
describe a looser category of patterned accumulations, even
behaviors. Mountains, for instance can be thought of as a type of
crystal. At the scale of a mountain, it really doesn't matter
whether it is made of silica rocks or basaltic rocks, if you get a
mountain's worth of rocks and stack them up, the resulting shape will
always be mountain like, a squashed pyramid or cone shaped thing.
Given earth amounts of gravity, a mountain is the shape a whole lot
of rocks takes. Now if you had the same mountain amount of mass but
instead of rocks the mass consisted of large slippery-smooth ball
bearings, it would be improbable that a mountain would ever result.
Try and stack them and their slipperiness makes them act more like a
fluid, flowing down and outward until there is nothing but a sea or
lake of little balls. It is some combination of the downward force
of gravity and the grittiness and irregularity of rock-like things
that makes mountains or mountain shaped things happen. This is why I
think it is funny when people are in such awe of the Egyptian
pyramids. Sure it took a lot of work to cut the rock from its
source, ship and stack it, but the shape is exactly the only shape
you could stack that much sandstone (the Pharos tried other shapes...
they all failed, crumbled, and don't exist except as much flatter and
less defined pyramids or mounds). Now if that same quantity of stone
had been formed into a sphere, then even I might be inclined to
believe in ancient astronauts. Planets are a spherical crystal that
results when gravity at huge planetary scales absolutely overcomes
the stickiness of any possible chemical or aggregate parts. When a
system is so large that mountains are the parts, even a mountain like
Everest becomes inconsequential to the dominant crystal, the sphere.

With an even looser definition of the concept crystal, one can
include the behavior of atmospheres... of weather. Once again we
start with a whole mess of self similar parts, in this case, the
molecules that make up air and sea. As these parts interact within
the context of energy applied by the sun, patterns arise at various
scales. Wind, clouds, fog, storms, thermals, precipitation, tornados,
hurricanes, jet streams, ocean currents, etc. Unlike the spacial
patterns of mineral crystals and mountains, most weather systems also
show their patterns as temporal cycles repeating over time, even if
these patterns sometimes also have a spatial component (often a
spiral or hexagonal rod).

Building bricks can also be thought of as crystals or crystal causing
parts. If you don't have any cement to glue them together you end up
with certain shaped buildings... add some grout and you can end up
with other shapes that generally mimic the original block or brick.

What makes this true, that the aggregate crystal retains the shape of
its component parts, is that the crystal is the most stable
relationships for these parts to find themselves in... it would take
more energy to get them to assume non-crystal like shapes... the
crystal is the natural or least-energy arrangement. Statistically,
the overall structural and energy state of the parts, insures that
the crystal will most often result. At the sweet spot (in scale),
where the dominant force or condition that builds parts into crystal
shapes neither overwhelms the structural integrity of the parts nor
is itself overwhelmed by another force or condition, crystals will
continue to grow and maintain their own integrity. At this in-system
scale, the more parts, the more likely the result will be crystals,
lots of crystals, and crystals that approach the perfect shape
defined by that particular crystal's growth pattern.

A more accurate categorization of crystals would be by how
autonomously they come into existence (morphological vs.
developmental). Developmental crystals would be crystals in the
traditional sense... those that develop purely as a result of the
forces innate to the crystal materials themselves. On the other end
of the scale are morphological crystals; those that have crystal like
shapes, but which got that way because of external processes or
machinery. A snails shell is morphological. Quartz is developmental.
DNA is morphological. Salt is developmental.

Now that we have an understanding of crystals, their shape and why
they are likely to have that shape at all stages of their growth...
we begin to see that the really interesting thing about crystals is
that they aren't very interesting at all. Here's what I mean. A
crystal of any size can be described by a very short statement... x
number of bricks... where the brick is like y... and is arranged in
pattern z. Doesn't matter if the diamond is microscopic or the size
of a house... the same little sentence or equation will describe
both. And the description in both cases will be exact and complete.

Compare a crystal to the text in this essay. The arrangement of
characters, words, sentences, paragraphs, etc. is not repeating in
any kind of readily apparent pattern. Even if I was to write a
condensed version of this essay... it would not be an exact
description of the original. This essay is not pretty or elegant or
shiny... will not illicit any kind of emotional outpouring... but
it's information content is much more rich than the biggest diamond.
Unfortunately... we humans are drawn to the kinds of simplicity
represented by crystals... like crows to shiny objects. I suspect we
are attracted to the profound simplicity of crystals precisely
because the rest of nature is in fact so profoundly complex. Perhaps
the attraction to this kind of simplicity reveals a deeper mechanism
of pattern finding at work deep within our big brains. But the truly
interesting (information rich) things around us describe patterns
much too complex to resonate emotionally with the same simple pattern
matching parts of brains. As a consequence, we have a tendency to
value the simple and ignore the complex and truly amazing. Why?
Because the emotional part of our brains... the old parts that have
not really changed sense we crawled out of the ooze... are very
simple... can only see simple patterns. And the very new complex
parts of our brains... the parts that can write and read things as
complex as language and its content... these parts do not directly
control emotions. Sad. The other reason we struggle with complex
patterns is because they are so much harder to see against a
background of true noise or randomness. Arrange text by blindly
picking from a box of letter blocks and you will approach the look of
actual text. Same goes for the arrangement of base pairs that make
up the ladder at the middle of DNA's famed double helix. It is
taking researchers around the world millions of man hours just to
begin to tease pattern and meaning from the seaming randomness in the
long arrangement (three billion pairs) of the four little proteins
adenine, thymine, guanine, and cytosine in the human DNA within each
of our cells. The exact why behind the truth that is the similarity
between any particular statement written in any particular language
and a random arrangement of the symbols of that language of the same
length is beyond the scope of this essay but it is worth looking into
(I will examine this critical point in a later post to this blog).

Fractals are a family of complex crystals. Fractals result in
organic shapes that are more like living things. Examples are the
branching of trees, the shape of a cauliflower bunch, a rocky
coastline. One of the characteristics of a fractal is that the
repetitive patterns are the same at any scale. If you look at the
edge of the cauliflower you have cut in half... then zoom in to one
small region of that edge... you will find that the pattern is
identical in both large and small scales. Of course this is the same
with regular crystals. But the organic shapes in fractals seem too
complex to repeat, so we are surprised.

Though they look more complex than grains of table salt, fractals
share the same descriptive characteristic... a fractal of any size
can be described by one simple sentence (equation). Size does not
change the small number of bits it takes to describe a fractal.

Fractals illicit an even stronger shiny object response in us (than
their more common rock crystals brothers and sisters). The slight
added complexity surprises us... we are amazed that living plants and
eroded landscapes could be described by simple mathematic
equations... so fractals do for nerds what a quartz crystal hanging
in the window does for new-age healers and unicorn loving romantics.

Humans are humans. We were emotion processors long before we were
reason and logic processors. We carry all of this emotional
processing machinery forward, tucked under our much much newer
ability to reason. Not only that, the emotion processing part of our
brain is in charge, at base, in the center of everything we think and
do. Because of this we seem to be most reverent to the things that
deserve it the least. It's the classic old mind / new world
mismatch. This little essay... the meaning encoded within it... is
millions maybe billions of times more complex than any fractal. But
we are in general stupid to this kind of beauty. Sad.

Technically, all solids are crystals (or in the case of a mixed up
rock like granite, all solids are made of mixed up areas of different
kinds of crystals).

Except when they aren't. Some rock-hard things that don't move or
squish or pour or compress... are not technically solids. Glass is a
liquid! Even in its

It is just so viscous (thick) that you can't see it flow. A old
window in an old house will be thicker at the bottom than at the
top... over the years, it has flowed very very slowly as it reacts to
the gravity of the earth. Crystals resist flow because their
molecules don't slip past each other (as in a liquid)... they are
locked into each other more like puzzle pieces (each atom shares
electrons with other atoms in the matrix). Some rocks that form in
volcanic eruptions (obsidian... the stuff of Indian arrow heads) are
like black glass (though not as pure) and like glass this stuff is
technically considered to be a liquid not a crystal.

Most substances are liquids when they are hot... and form crystals as
they cool beyond a certain temperature (their freezing point).
Remember that temperature is just a measure of how violently the
molecules in a thing are jerking around. The atoms or molecules of
hot things won't settle down long enough to freeze into crystal
lattices. Most substances get smaller when they freeze, dropping
down into a crystal lattice means getting tighter with your molecular
or atomic neighbors. Except water! The crystal lattice that water
forms, ice, takes up more space than it did as liquid. Which by the
way is a really good thing... it is why ice forms on the tops of
lakes (it is bigger... less dense... then the water it used to be...
thus lighter... so it floats on top). That keeps fish and everything
else alive by insulating the rest of the water from the much colder
air above it. Water is freaky in all the right ways.

Anyway...

Substances that are much more much more complex than rocks, metal,
ice, and glass... like the stuff life makes... bones, cell walls,
muscle fibers, wood, sea shells, brains, chlorophyll, proteins,
hormones... these things are nano-constructed by living things one
molecule at a time by molecular machines (RNA, proteins and the like)
acting from the outside. Compare this to things that self construct
(by virtue of their own internal properties)... these tend to form
crystals. Things that are constructed from the outside by bigger
stronger more energetic machines... can force parts into less energy-
perfect shapes... can force unnatural combinations... mashed-up into
any manor of crazy information-rich constructs that have complex
behaviors and interactions with the stuff around them.

Crystals don't do much! Why? Because all of their parts are already
in the most stable relationship they can be to the parts next to
them. That is what things acting on their own power do. That is the
only thing things acting on their own power can do. But complex
systems are complex because they have been forced into un-natural,
less stable, and as a result, more reactive orientations.

This is an important concept... so pay attention here (your guru is
saying things that few people really understand the importance of)...

Life has learned to build (or facilitate the natural building) of
crystals where stability is needed... and to build non-crystals where
reactions are appropriate.

Look at a snail. The shell is crystal like... repetitive, simple,
geometric... stable and non-reactive (dead)... that is the point...
the snail uses its shell for protection and structure. Inside the
shell, you will find all of the non-crystal stuff... information
rich... built to react all day long in very complex chemical dances
that extract energy from the surroundings, store that energy in
awkward configurations that can be relied upon to do it all over
again the next day, and get rid of waste products. The most
interesting chemical in the body... DNA... has properties of both!
It's structure (the famous double helix) is highly crystalline... but
the rungs that are strung between the winding bands... where all of
the genetic information is written... is highly reactive. Very
cool! Just think how fucked things would get in a hurry if the
crystal part didn't absolutely protect the genetic information or if
the information part couldn't easily read it's pattern out to RNA (so
it could make all of the stuff that makes us... well... alive).

Crystals are repetitive, information poor, stable, and ultimately
dead. Life stuff is complex and non-repetitive. And this is why
scientists shy away from new age (and old age) theories that try to
fit complex biology, personality, or social behavior into simple
shape and crystal-based theories like hexagons or pentagons or twelve
sided horoscopes. Nice try old brain! But things as simple as
crystals are never going to be good abstractions of the truly amazing
complexity of life and culture and behavior (and the smell of sex).

Oh, I almost forgot. The difference between fractals and regular
crystals is really kind of simple. Of course simple little
differences can make all of the difference in the world (our DNA is
less than 2 percent different than that of a Chimpanzee... less than
twenty percent different than that of a tree). The statements that
describe both crystals and fractals are not really equations like 2
+4=6 which can be computed in one pass. Crystal equations are
algorithmic... meaning they must be calculated over and over again
(so the thing can grow). What sets fractals apart as a class of
crystals is that part of the equation or algorithm demands and uses
the answer from the previous calculation of the same equation. There
is a feed-back loop in the calculation of the thing... and because of
this... a fractal is technically not solvable... goes on forever.
Actually that is the same with most crystals... they just grow and
grow and grow as long as the building blocks are available and the
environment is suitable for the necessary reactions. Of course there
are always exceptions, some crystals are self limiting... they grow
like the surface of of a ball and end up running into themselves on
the other side. But with fractals... this inward facing,
masturbatorial, feedback-loop will keep building detail at smaller
and smaller scales... so it never runs out of space... so if you
start your fractal from only one point you will never get a full
fractal built... just a more and more detailed section of one.
Nature solves this problem by calculating every part of a fractal in
parallel... starting the calculation (the reaction) from many many
points at the same time (in nature everything is the computer and the
computer is everything). In a man-made computer we are forced to do
one thing at a time... one thing after the other... in one long train
of calculations... so we have to insert artificial limits into the
algorithm... you know... do this inward loopy thing only 100 times
then move on to the next large-scale section... repeat.

That Was The Free Energy That Was

Went to see that movie "There Will Be Blood" (written and directed by
Paul Thomas Anderson and staring Daniel Day Lewis. It is an
adaptation of the Upton Sinclair book "Oil!". Funny because the
Lewis character is from Fon Du Lac, Wisconsin (ten miles from my
father's birth town) and the movie takes place in the hills just east
of Santa Maria, CA (where I was born). But other than that, there
isn't anything funny about the movie at all.

This is a good story to cap off our short little 100 year obsession
with oil (written 70 years ago!). Puts our naive habituation to
(almost) free energy and the god-like feeling of omnipotence, or at
the very least, endless hope into perspective. As a result we have
been living with a false since of security resulting from this almost
free energy and the simple fact that nothing before us has had the
wits or tenacity to tap into all of this conveniently stored, highly
concentrated, solar energy, tucked away as it has been, untouched
while it accumulated for the past few hundred million years.

Three hundred million years of accidentally stored solar energy!
Then we humans burn through it in just a few decades. That feat would
be impressive if it weren't for the rather sobering fact that there
really isn't anything to replace it, nothing at all waiting in the
wings to take it's place at the base of this giant churning machine
of progress we have come to know as "is". The great achievement,
success and yes, progress we have produced this last century is based
entirely on this ready-to-burn source of abundant and highly
concentrated energy. Without coal, oil and gas we could never have
done what we have done. Never. As obvious as this is, people really
don't get it, we don't experience our own recent history as a history
of easy energy driving every progress we have achieved. Yet it was
and is. Yes we have worked hard to drill it, tap it, pump it, refine
it, ship it, and build devices that burn it to productive ends... but
all of that work of extraction or use is but nothing in comparison to
the wealth of energy trapped into every drop of it.

And what of the sun's energy? What of the constant stream of
energetic photons arriving each and every moment, free of charge?
There is roughly 4 orders of magnitude more energy arriving from the
sun than we humans currently use... that is ten thousand times as
much solar energy hitting this earth every year than all of the
energy we humans consume. At first glance, that would seem like a
hopeful figure. But how much of that yearly budget of solar energy
is truly available for the taking? Meaning, how much of the solar
budget is excess, is not necessary for the continued healthy stable
running of basic global processes like the atmosphere, the oceans,
the plant and animal biosphere, the water cycle, wind, ocean
currents, the jet streams, etc. We are not used to thinking in these
terms. We are not used to the fact that the daily doings of human
culture now legitimately compete with systems as vast as ocean
currents and hurricanes. So lets ask this question because it needs
to be asked... how much of the earth's daily solar energy budget can
we divert into power lines and into the batteries of our cars and
trucks, and the machines of our collective industries without forever
disturbing the atmospheric and bio systems upon which everything we
do is interdependent? I don't have an answer to this question. I
don't know where to look. I don't know how one would set up a
simulation or metric to measure this percentage of "excess" energy or
biosphere leeway.

One thing is certain, we are just now beginning to become aware of
the sensitivity of our planet's heat budget. We are not a closed
system. But it looks like this planet is better at capturing energy
than it is at releasing it. As space craft engineers are well aware,
getting rid of heat in a vacuum is a difficult process. Earth is a
space craft, sits in the vacuum of space in the exact same way. As
we all now know, carbon accumulating in the upper atmosphere (from
human burning of fossil fuels) has begun to effect colossally large
systems like ocean temperatures and polar ice sheets. Wouldn't it be
presumptuous to assume that man-made solar energy collectors would
not have a profound effect on our global solar powered natural
systems? Taking sunlight that would otherwise be absorbed as heat,
used by plants (to strip water into its component oxygen an hydrogen,
build complex carbon chains from that hydrogen and the carbon dioxide
in the air), or bounce back into space, would necessarily effect this
balance of heat even more. When we collect the sun's rays and
convert them into electricity, we trap a percentage of energy that
would otherwise be reflected into space, or absorbed into natural
heat or bio-cycles. When we ship our electricity by wire we loose
between 20 and 50 percent of it to friction in the wire... that is
heat. When we use what electricity makes it to the end of the wire
to power a machine, we are usually even less efficient.

If Boltzman, Carnot, Boyle, Hooke, Joule, Thomson's, von Guericke,
and others are right (and there is evidence that they are more right
than anyone else has ever been... that their discoveries sit at base
under and inform the behavior and makeup of all other physical
processes in every domain) then their laws of thermodynamics make it
clear that energy captured eventually has to be released as heat and
that is that. The question then becomes not one of energy type, but
energy source: is the energy already here on earth, or is it getting
into our system from the sun (or somewhere else). If it is already
here, already in-system, then it will shift energy around, could
accelerate local heating (or in the case of not using a resource that
is already here... cooling), but won't ultimately add to Earth's heat
budget. But when we capture solar energy that would otherwise have
not stayed here, solar energy that misses the earth or that bounces
off, then we do increase the amount of energy in-system and thus the
amount of heat that will ultimately precipitate... heat that will
either drive the earth's temperature up or have to be exported into
space.

Do man-made solar collectors collect energy than would otherwise be
reflected into space? If they are doing a better job of capturing
the sun's energy than what ever they cover up or replace, then the
answer is "yes". If the answer is "yes", then any such use of solar
energy will increase the rate of global warming. It is that
simple. The next question is: is more or less heat accumulated
through the capture and use of solar energy than by the burning of
fossil fuels? Which is the better of the two evils? A similar
comparison must be made between these and other energy sources like
nuclear and solar energy's cousins, wind, ocean currents, and waves,
and then there is the moon's tidal pull, and the earth's internal
geothermal heat. Other deeply sober measurements must be made and
understood... what is the net heat signature if an acre of land that
was grassland (ice field, ocean, mountain, desert, jungle, forest)
as compared with the same acre covered by photovoltaic cells?

Of course other energy sources contribute to global warming as well.
In-system or not. When we take fossil fuels out of the ground and
convert their "potential" energy into actual energy, we activate that
total heat signature and move it rapidly out of the realm of some-day
and towards it's ultimate resting state as heat. Both rapid
oxidation (burning the stuff) and more gentlemanly conversions like
the the pseudo-alchemy that charms electricity in fuel cells excite
the rapid aging of energy towards heat. Before these forced
conversions, energy trapped for millions of years will become plain
old run of the mill heat within seconds, minutes or, at best, days.

So, we have discussed the inevitability of the energy-to-heat process
that results in any energy use. We have looked at the earth as a
heat-trap positioned as it is in an almost perfect thermos that is
the vacuum of space. Now let's refocus our discussion on the other
side of energy use inevitability... the lockstep growth in evolution
that binds increases in complexity with increases in energy use. It
is obvious that we humans continue to desire, find and use more and
more energy. Until now we have found (in oil) a ready supply to meet
this increasing demand. Now what?

Even if we were to use all of the (excess?) solar energy streaming
down on this little planet (that not used by the plants and the
oceans and the atmosphere) we could still just barely supply the
energy needed now, this year, the energy needed by a planet where
only 1/30th of the population uses energy at first world levels. In
the next few decades, the energy demands of the 3 percent of us that
are rich enough now to use oil will be mirrored in the other 97
percent of the world's population. That means that the world will
collectively demand about 30 times the energy that we are currently
using. And that figure assumes a freeze on the amount energy per
person per year to what we use in the west today! A freeze in energy
use has never happened before so it would be naive to assume it will
happen now. The pattern so far is to double (per person) energy
demand each twenty years or so. Given this unadjusted historically
proven growth curve, the global appetite for energy should quickly
rise to about 900 times as great as today. How will we meet this
demand?

There is no science available today that can come close to answering
this question, meeting this demand! People talk of the potential of
nuclear but nuclear represents a paltry single digit percentage of
current global energy production. If nuclear was to replace oil in
the next few decades we would have to build over 10,000 times more
reactors than are on line today. We don't have access to 10,000
times more plutonium. This is a hard limit. It is true that nuclear
power plants convert only a sliver of the energy Einstein's little
equation (E=mC2) allows, but other even more fundamental
thermodynamic laws insert ridged upper limits under most realistic
situations. It is possible that some new Manhattan Project will do
for the strong force what the weak force did for the A-bomb, but
containment of such a quantum reaction might actually demand or be
the cause of a new universe (more later). Suffice it to say, we can
probably expect percentage increases in energy production
efficiency... but we will squeeze these last few drops from the well
of potential while our global economic engine demands instead fold
increases in energy supply.

So, if energy demand rises geometrically (and I have seen no science
saying it won't), and if energy supply continues to fall (or
stagnate) do to natural limits imposed by resource depletion, what
will happen? This is the big question. This is the civilization
ending question.

My parents like to say that when I was a kid I wouldn't believe that
we were out of ice cream; that I said "I want to see the all gone!"

How much shock of the all gone will civilization be able to stand?
What happens when everything we equate with modern life becomes
impossible? What happens when humans have to take a giant step
backwards in the span of one generation. I think this scenario is
unprecedented in human history. We are simply not used to not moving
forward... to giving up what we are used to... our kids having less
than we have. Yet I can think of nothing interrupting this
depressing inevitability. Nothing is standing in the wings as
replacement of geologically stored hydrocarbons... to replace oil.
Nothing!

Oil is why we only have less than 3 percent of our population
involved in food production. Oil is why we have trains, cars, ships,
and airplanes. There is nothing like oil. There is no other
substance that we can put into the tanks of our transportation
machines. The defiance department spent a lot of money in the 50's
and early 60's trying to do for airplanes what nuclear reactors did
for submarines and destroyers. Of course this didn't work, the
shielding necessary to protect the rest of the plane and it's
passengers from radiation and heat (lead) are far to heavy to use in
a flying machine. Same goes for cars and tractors of course. This
is why I am always talking about passing the evolution baton to that
which will come after biology.

Humans are smart, but not smart enough to do what needs to be done in
the next 30 years. This planet is now in need of a thing or things
thousands of times smarter (more alive) than humans. It might be
true, it might be possible, if we had 300 years to react, for humans
to come to a solution, but we don't, we don't have much more than 2
decades to figure this out. I truly hope I am wrong. I truly hope
there is a technological solution, a political solution, a policy and
cultural solution, but I am not able to bet my own energy in this
direction of hope. The odds are to slim. The science is not there.
Reality points to limits where exponential growth is demanded.
People who care point optimistically towards conservation and
efficiency. These efforts must continue, they must be taken all the
way to their maximum potential. But they won't be enough. Worse,
we must ask some sober questions about the collective human psyche
when our world becomes increasingly uncompromising in its inability
to satisfy our demands.

How do people react when resources shrink instead of grow? This is
new psychological territory. We have always lived within limits. But
we have never lived within increasing limits. What does increasing
limits do to our already child like temperaments and intolerance's
towards not getting what we want? We knew we could easily rebuild
the fallen twin towers, yet we still choose a course of destructive
reaction that has almost brought the world's economy to it's knees.
What will we do, what will the common human reaction be, in a similar
situation where we know we can't rebuild? Anyway, for today we are
fine (at least we are a few years away from the impending obviousness
of the energy wall we face).

Please visit the following Wikipedia section on global energy use and
supply (excellent summery of our situation):

http://en.wikipedia.org/wiki/World_energy_resources_and_consumption