As a full time systems analyst
(doing database and applications development for nearly 30 years
now), you might wonder why I would go out of my way to take more than
a passing note of this development. It's important, certainly, as it
may have marked an impressive milestone in the annals of science, buy
why would a non-scientist want to attempt what is, hopefully, a
reasoned criticism of the effort as a whole?
Most everyone, of course, is quite
excited by the announcement. And this usually breaks down into
“another great leap for science”, or the “this proves there’s
no God,” groups. Hardly anyone, though, appears willing to go
against the tide of giddy acceptance here; to be the contrarian
asking questions about whether a larger view point might be in order;
a view point that would hope to raise several scientific and moral
issues.
That we’ve been burned before by
lack of caution ought to go without saying, but we are all subject to
AADS when it comes to history these days. Add to that the fact that
the principle proponents are physicists and you end up with a surge
of expectations more akin to a tsunami than a big tide. More than a
few of them have attained near Rock Star status after all, and they
work with the heavy cords of mathematics. How can you be a contrarian
in this context without sounding like some kind of flat-earth,
everything revolves around us, advocate?
I’m certainly no different,
having been wowed by both physicists and their power math for years.
Getting into your sixties, though, does wonders for the inner
curmudgeon. Getting older also seems to give one a renewed respect
for how virtually anything can cut in ways other than the obvious.
Especially with powerful tools do we tend to be blinded by their
general reliability; granting them a very subtle perceptual bias.
Which is why I can say, sadly, that there has been precious little
serious debate over the years on what is the bedrock of accelerated
particle research; namely the notion that intentionally smashing
abstracted affect amounts together is done with so little
consideration of possible negatives. And in that I would include
epistemological considerations; its potential negatives to both the
practical environmental around us, as well as the to the realm of
the empirical environment such smashing is done in.
Sure, there was the temporary
uproar, just before its initial powered testing, that the new Cern
accelerator might cause mini singularities, but this was quickly lost
within an argument of dueling interpretations of probabilities
already stipulated; an argument it's proponents had little chance of
winning. The problem was that they keep it too narrowly focused on
the probabilities themselves, which was a huge mistake. Not only were
they low, but that narrow focus turned it into a contest of who was
the more credible; and in that kind of fight it is hard to beat
established physicists who have already sold governments on a shiny
new toy.
That the announcement would also
bring out the “There Is No God” camp is as unsurprising as it is
depressing. Having something getting the unfortunate nickname of “God
Particle” certainly seems to be reason enough for simplistic
reflection to come to the conclusion that anything with God in its
name, that can, as well, be measured and replicated, must prove that
God doesn't exist. This is also why one might start down the road of
depression, but I have what I feel is a more important reason. And
that is the sorry state of affairs concerning the dichotomy between
reason and the need for transcendent explanation that exists in
humanity today.
I have to confess that this is
where the part time philosopher in me comes to the fore, as well as
where I must divulge my own pet ax; an ax that, fair warning, will
most definitely be ground before I am through here. I am, you see, a
proponent of a particular philosophy I'm sure you have never heard of
before. Not surprising as I am it's only devotee, as well as its
founder. I call it Cosmolosophy (pronounced Cos-Mo-Los-Ophy). I won't
weigh you down with all of what it proposes (I'm really not here to
proselytize so you can investigate more if you care to here),
save to say only these few primary propositions; namely that: a: we
desperately need a better balance between the rational and the need
for transcendent explanation, and b; that, if one can accept the
notion that the entirety is made up of Love and Mind, one can have
the foundation for this balance.
Depressing though the debate of
this announcement has been so far, there have been moments to cause
one hope. There has, for example, been much better insight into what
is actually being sought out here; at least in as much as how one
might label the thing. I refer to what I have always felt was a much
better nickname for the Higgs Boson; one that was probably proposed
incidentally, as well as some time ago; namely the Love particle (I
first heard it used in the Antonio Banderas/Sienna Guillory/Sam
Elliot movie “The Big Bang”). It's a better name, in my opinion,
because it alludes to something that ought to be quite obvious; that
what the physicists are attempting to encapsulate (or objectify) here
is what constitutes the “Elemental Embrace” (another proposition
from Cosmolosophy). What is missing, as far as the physicists are
concerned, is that little bit of extra humility that might get them
to better appreciate a couple of things; that not only are there
limits to what can be measured empirically, but that there are some
things one needs to be very careful about within the process of
deconstructing and analyzing.
What I'm talking about here is a
subset of a larger human paradox. On the one hand, we must question
and understand, for that is part of our purpose, but it is only one
part. There also needs to be humility and a sense of awe for we are
deeply connected to what we probe; as well as what we probe with. And
because we necessarily operate within the full range of human
frailties, we tamper with these deep connections at great risk; if
for no other reason than what we connect with, and how we connect,
are pivotal to what makes us human, and socially organized.. The
paradox of needing both deep connection, as well objectification,
though, parallels the dilemma of creation and existence itself; to be
of it and apart from it at the same time, knowing that knowing itself
represents manipulation of a relationship we are only beginning to
comprehend. And yet, despite this situation, these scientists presume
to be ready to objectify an interactive entity so huge in its micro
scale, as well as so fundamental, as to make suggestions of divinity,
and the power of creation, quite acceptable as selection criteria for
an alias.
Christianity, despite whatever
other flaws it might have, tried to at least give some hint as to how
encapsulation and creation are related; as evidenced by the fact that
their scriptural translations, over the centuries, have left us with
a bible that begins with “In
the beginning was the word...” (see this
for a few more) For them, unfortunately, there had to be an
ultimate, sentient purveyor of objectification. Unfortunate as well
that they seemed, at least in large part, not to see this ultimate as
a divine process, but more as an actual being; a being with plans,
desires, and emotions (which, paradoxically, would follow from a
purely analytical view of sentience; something that would require
objectification, and thus singular point of view, and thus ego.
Which, one supposes, might explain this inordinate need of admirers,
as opposed to individuals who simply behaved in a manner morally
consistent with her teachings. One might also lay the notion that you
cannot be spiritual, or a believer in faith, without her being
involved in some way, as a jealous protection of turf). In my view,
however, the salient point of what is being alluded to here is that
differentiating at this level might require god like powers of
discernment. Heady stuff to be sure but that is precisely why I have
been motivated to jump in here. I don't think that nearly enough of
us truly appreciates just how important all of this is. But enough of
preliminaries. Let us get started.
I have, of course, already alluded
to where I am coming from in this exercise. And I need to point out
at the start that this is where the systems analyst in me comes out;
particularly where it concerns complex systems. This is a big part of
why I question the basic assumptions inherent in smashing protons
together at ever higher energy levels. There are several issues that
just don't make sense to me. Allow me to list them for you.
- How you observe or measure a thing can determine how that thing manifests itself; as in measuring light quanta.
- A basic tenet of complex systems is that small inputs can have very large affects.
- There is no such thing as zero; which is just another way of stating that empiricism can ultimately only measure the limits of instrumental precision after certain levels of energy (or scales of micro-consideration) are attained; or stated even one more way: meaningful units of information rely on the fundamentals of boundary resolution within a given vector of association (or reality if you will), and the higher we go with energy levels the more we move away from those fundamentals.
Let me now delve into each of
these in greater detail so I can, hopefully, give you some
perspective on how they apply to my concerns towards these “basic
assumptions.”
The first one might seem self
evident at first glance, but I want to be as specific in how I see it
as I can be. And I have to start by separating out what is obviously
implied here, and what I see as a related issue.
Most people who do even casual
reading of things scientific know that, tested in one way light
appears to be a wave, while tested in another a discrete quanta. This
naturally suggests that physicists ought to be looking for a
fundamentally different means to test these predictive equations;
certainly no easy task by any stretch of the imagination. They could
also counter this proposal with the assertion that they are not doing
anything that nature isn't already doing; and if nature does it, how
could it be all that much different than what we are doing? Their
conclusions, therefore, ought to apply to nature.
The problem is the same as it has
always been for humankind when confronted with systems they cannot
possibly, in the beginning at least, grasp the full complexity of;
the crux of which is not having anywhere near all of the questions to
ask yet, let alone any of the really meaty answers. For example: if
they could measure particles accelerated by natural means, can they
blindly assume it would be the same as what occurs in that marvelous
piece of engineering at Cern ? Don’t you have to test a notion
before you can begin to accept its credibility? And wouldn’t
proceeding without such tests be an act of faith?
Related to this is the proposition
that the very act of observation changes a thing; more precisely
described by stating that observation resolves what is normally
considered a large range of possible states of energy, mass and
position; where in one sense the thing is all of the possibilities
simultaneously, and only has an existence as one of them upon
observation. As we move down into ever smaller scales of
consideration (which is to say ever more abstracted interactions in
relation to the nominal units of information transfer our reality
provides), with ever greater energies, our level of ignorance of what
constitutes the possible range of states increases by factors that
can only be guessed at (which is precisely what they must do in
coming up with sigma-level numbers). And the fact that the math might
be quite supportive, in one instance or another, at best only proves
that they might have modeled what happens in, for lack of a better
term, artificial accelerations.
It is also useful to remember what
actually generates the numbers they use in their elegant models. They
call them detectors and they are also marvelous pieces of
engineering; with a lot of thought put into making them do what they
need to do; with as much precision as materials and fabrication
knowledge can muster. These are clever people after all, and I do
hope you believe me when I say that I have only the greatest respect
for all of them. Even with that said, however, they are still human,
thankfully, and therefore only too prone to the same propensity
towards hubris that we all confront. And one can see this at work in
the way they conceptualize their detectors for outside consumption.
The following is a direct quote
from the European Organization for Nuclear Research web site (see
this):
“How a detector works:
The job of a particle detector is to record and visualize the
explosions of particles that result from the collisions at
accelerators. The information obtained on a particle’s speed, mass,
and electron charge help physicists to work out the identity of the
particle.
The work particle physicists do to identify a particle that has
passed through a detector is similar to the way someone would study
the tracks of footprints left by animals in mud or snow. In animal
prints, factors such as the size and shape of the marks, length of
stride, overall pattern, direction and depth of prints, can reveal
the type of animal that came past earlier. Particles leave tell-tale
signs in detectors in a similar manner for physicists to decipher…”
They go on to point out that they
use 3 types of sub-detector; as in:
- Tracking device which detects and reveals the path of a particle.
“Tracking
devices reveal the paths of electrically charged particles through
the trails they leave behind. There are similar every-day effects:
high-flying airplanes seem invisible, but in certain conditions you
can see the trails they make. In a similar way, when particles pass
through suitable substances the interaction of the passing particle
with the atoms of the substance itself can be revealed…”
- Calorimeter which stops, absorbs and measures the energy of a particle.
“A
calorimeter measures the energy lost by a particle that goes through
it. It is usually designed to entirely stop or ‘absorb’ most of
the particles coming from a collision, forcing them to deposit all of
their energy within the detector…”
- Particle identification detector which identifies the type of particle using various techniques.
“Two
methods of particle identification work by detecting radiation
emitted by charged particles:
- Cherenkov radiation: this light emitted when a charged particle travels faster than the speed of light through a given medium. The light is given off at specific angle according to the velocity of the particle. Combined with a measurement of the momentum of the particle the velocity can be used to determine the mass and hence to identify the particle.
- Transition radiation: this radiation is produced by a fast charged particle as it crosses the boundary between the two electrical insulators with different resistances to electric currents. The phenomenon is related to the energy of a particle and distinguishes different particle types.”
As impressive as all of this is,
do not forget that it relies on one very important starting
assumption: namely that, in the unbelievably compressed space-time
event represented by a collision of protons moving very close to the
speed of light, boundary resolution will occur exactly as it does in
nominal space-time; as well as to say that the interactive products
of such events will translate up to our nominal space-time with
little information lost: which is to invoke terms I am sure have
already caused considerable consternation in getting your head
around. Well, let’s step back a moment and try to help out in that
regard.
Some of the tenets in Cosmolosophy
parallel what is described in a thing physicists refer to as the
Anthropic principle (see these)
which, put simply, involves asking questions about how our presence
in the vast scheme of things does, and/or must, influence the way it
comes together. And one of the things that becomes quite prominent
within these questions is consideration of a very small set of
numbers (at least of few of which are key to defining the field of
effect that an interaction entity possesses) that are necessary for
the cosmos to allow life at all, much less sentient life. And for my
part the key point here is sentience itself.
I have always been fascinated by
the parallels between what a sentience organ must do to create a
self, and what a cosmos must do to have process be possible in the
first place. Basically they must both objectify a basis potential;
which is no more than to say that there must be discrete units to
provide differentiation (as well as to make information, and its
transfer, possible). It is precisely this differentiation that
provides the self with identity, and a point of view. And in that
there naturally arises a further fascination; which is that the very
nature of relativity requires a point of reference. As such
Cosmolosophy posits that the singularity that begins the whole mix of
what and when is really a vector of sentient association; a starting
point that allows any particular reality to have the various
essential differentiated units because, at that point only can their
nominal field boundaries be resolved. Love, of course, as expressed
by the notion of the “Elemental Embrace” is what keeps
interaction going. Cosmolosophy also posits that, just as Love cannot
be measured in its human expression, the elemental embrace, at
whatever scale of cosmological consideration, also cannot be
measured. This is definitely not to say, however, that it can’t be
hinted at, or suggested. Or that questioning minds should stop doing
what they were designed to do, for one of the most basic tenets of
Cosmolosophy is that the entirety is essentially one unimaginably
huge Question/Answer engine; some kind of recursive, self-programming
totality that uses the infinite array of associative vectors in a
process of accumulative reality ray tracing. Where, in every
iteration, the creation of the answer simply reformulates the engine
into a new question to be answered.
The essential point of
Cosmolosophy is that we are as necessary to the entirety as it is to
us. It needs us to consider it, view and appreciate it. Our mental
and physical constructs, in as much as they represent loving
structure, help keep the entirety, not to mention our little vector
of it, combining and exchanging in a like manner. These are all
notions that I take on faith because they not only make sense to me,
they feel right. I like to think of them as faith based extensions of
reasonable logic.
In any case, though, let’s get
back to our detectors. Let’s consider their analogies in light of
what I have described above.
At the beginning we were told to
think of detection in the context of “tracks left in mud or snow…”
I don’t want to suggest that this is literally how particle
physicists view what they do, but I do think its fair to assert that
they feel what they do is equivalent in its essence. And to keep with
that equivalence you have to maintain that the trace paths of
electrically charged particles have not lost anything of significance
from their source analogue; even though the electrons, nuclei, atoms
and molecules of what actually moves the beam of an oscilloscope, or
triggers some threshold counter, or gets sliced into billionth of a
second numerical representations, operate in a space-time frame of
reference that may well be qualitatively, and/or quanta-tatively,
different than that of the impact event itself. The simple fact of
the matter is that we can’t know what increasing levels of energy
might add in terms hidden complexity; precisely because those levels
alter not only the very things we depend on to translate something
meaningful back to us, but also alter the fabric which they are a
part of, and of which, it in turn is shaped by. It’s almost as if
we were depending on mud or snow to reveal the tracks of an entity
that walks inverted, well beneath the surface, stepping with plasma
bolts for feet. A creature that, with each step, changes not only
fundamental characteristics of the intervening material, but
fundamental aspects of the sphere that contains this material.
Changes for which we not only lack the speed to examine, let along
measure objectively, but for which we have no proper shovels. The
question is not so much that the mud or snow wouldn’t reveal
anything, but rather the degree to which one could rely on
extrapolations of these revelations; especially as the creature moved
deeper.
Let us now move on to the second
of my concerns: That, in complex systems, small inputs can have large
effects.
By now, I'm sure, everyone has
some inkling of this notion. Movies like “The Butterfly Effect”
have certainly moved the concept into popular culture. If one uses a
search engine on variations of the phrase above the info-ether will
come back with fascinating combinations of what complexity and
feedback circuits do in the whole range of human endeavor (I have
compiled a small list here).
And in many of these one sees the terms chaotic and non-linear.
Weather is chaotic and non-linear, and therefore predictions, based
on ever improving mathematical models, running on ever bigger
parallel processing machines, are still quite limited as to how far
out in time they can go. Social/economic systems even more so.
The first thing you must remember
about the quantum world is that everything is a tightly integrated
interaction. We used to think that there was some ultimate point of
granularity at which no further deconstruction of process could take
place; that one or another conceptual field of affect was its own bit
of irreducible amount. We have found, or at least think we have
found, that having these amounts run into each other with sufficient
intensity teases out even lower scale effect amounts. Affect amounts
whose interaction seems to create the larger amount we once thought
irreducible. And of course, the deeper an explorer might want to go,
the more energy they need to apply to the collision. It is just this
artificial application of energy to tightly integrated systems that
we should be concerned with. Just because effect amounts interact
energetically all the time (creating and destroying associated affect
amounts in abundance) in the natural scheme of things doesn't allow
an explorer to assume that an artificial injection would be
completely benign (in its differential to the non-artificial) to this
layer upon layer of tightly woven integration. Physicists own
understanding of probing tells them this (it is sentient choice,
after all, that decides what light is). In the natural scheme of
things interaction and the expansion of what and when go hand in
hand, following unimaginable matrices of cause and effect from the
original singularity. The act of probing, on the other hand, might be
input of another kind entirely. How can we know for sure? Has that
unimaginable cascade of cause and effect been pre-programmed to make
that artificial input possible? Was it expected and already factored
into all of that tight integration? Are they prepared to risk pretty
much anything imaginable on this assumption?
The really scary part here is
that, in our ignorance, we have so little with which to make reliable
calculations of probability. This is because, as already stated, the
higher the energies go, the more we introduce unknowable matrices of
non-linear interaction; with feed back circuits capable of who knows
what kind of power. And the thing is, that power might not manifest
itself in a self-evident time scales (the starting time of the effect
might not have any ordinary relationship with the impact event at
all). In fact, the power to time ratio might be an inverse
relationship; whereas the more powerful it is, the longer it takes to
become evident to us. The reverse of that might be the case instead,
for all anyone knows. Perhaps it applies to the macro-view of our
reality in one case, and the micro in the other. Again, who knows?
Perhaps in the micro-view it acts to distort associated affect
amounts; either positively or negatively. Perhaps in the macro-view
it distorts as well, but in an opposite fashion. Perhaps, without
realizing it, we are shaping our reality to fit the mathematical
models; all in a cosmic act of self-fulfilling manipulation
(violently disassociated entities in ever greater disconnection). One
is limited only by one's imagination here.
Be that as it may, though, the
real issue is why we would go forth so blindly in the first place.
Would we experiment in a like manner on the planet's atmosphere?
Blasting it with whatever kind of highly interactive input just to
try and understand it better? And now that we realize that this is
exactly what the industrial revolution, competitive consumption, and
monied prosperity have been doing, should we be all that excited
about finding new ways to continue the exercise; with even more
powerful blasts?
There is another aspect of “big
from small” that needs to be considered here as well and that is as
it pertains to the researchers themselves. This may seem an
over-reach at first glance, but I think it deserves sober reflection.
And that is the effect of what so many true believers have on the
results; just from the fact of their own frame of mind. There is no
double-blind kind of methodology in place here after all (not that
there necessarily could be), but even if there were, when you start
messing around with manipulation of the very fabric of existence,
with such large energies, creating what would otherwise be low
probability events (at least in the context of an idealized universe
expanding out and interacting without any sentient choice involved);
events directed by a common mental energy, who can truly know what
the relative probabilities might be
Controversial though it might be,
there is a great deal of effort in place to explore this very thing
(see this
for a brief list). Just to take one plausible track of conjecture,
one could certainly ask just how far quantum entanglement might be
extended. It might be subtle, what our massed thoughts can do, but at
ever smaller space-time points of reference, subtle might find just
the right cascade channel sets.
In any case, I think we've done
enough with “large effects from small inputs” for the time being.
I want to start on my third assertion now: That there is no such
thing as zero.
In one sense this is certainly not
true. I either have a positive integer value of whatever common place
object you might think of, or I don't. My living room might have x
number of family portraits, but a count of zero famous person
pictures. Quite simple. The quantum world is, as most of us have come
to understand, no where near so simple. In fact, things started
getting that way when relativity was first introduced. You might have
a zero velocity relative to the chair you are sitting in, but it's a
pretty sure bet it's non-zero relative to most of the rest of our
solar system.
I bring the assertion to our main
argument to reiterate two things. In a world where any interaction
can only be approximated in terms of other interactive
encapsulations, very little can have the various factors of its state
(position, mass, energy) expressed as XX.0. Scientists may say that
they have brought a volume of one or another material to absolute
zero, but that's only relative to a certain level of substantive
sub-structure; just as the precision of that measurement is relative
to the interactive sub-structure of the thing we probe with. The real
question is why should that be important.
We already hinted at the answer
when we stated that empiricism can ultimately only measure the limits
of instrumental precision after certain levels of energy (or scales
of micro-consideration) are attained; as well as stating that
meaningful units of information rely on the fundamentals of boundary
resolution within a given vector of association (or reality if you
will), and the higher we go with energy levels the more we move away
from those fundamentals. The physicists at Cern claim they have
measured something verifiably discrete beyond the randomness of any
noise that may have crept in from interactive translation to
interactive translation up the layers of scale. An affect amount as
equally fundamental to the nature of the fabric, and its ability to
differentiate encapsulated process, as the encapsulations we use to
probe with. And that they've done this with a level of distortion of
their own making so low that it approximates zero at the very least.
How can the rest of science take
this at face value? How can the physicists themselves prove anything
objectively here when they operate at the ragged edge of what is
object? How can they establish their precision with such confidence
when their very ability to be precise at the outset has to be
questioned? How can they assure us, with any real precision, that
what they are doing is benign in any case? And make no mistake dear
reader. As we have already discussed, even infinitesimally small,
non-zero variations of precision here could have very large effects.
I want to step back now make sure
that one thing is abundantly clear. I don't know for a fact if what
they are doing is dangerous or not. Just as its possible that they
are, it is also possible that they aren't. I just wish they would
stop for a while and start asking a lot more questions of themselves.
Have they truly exhausted all alternatives? Even if it might take a
while, wouldn't it be worth that wait so that a much more viable
space program could be built? A space program that might make truly
imaginative alternatives possible; launching probes several orders of
imaginative magnitude greater than what is possible now?
I know that a great deal in terms
of reputations, money spent, and livelihoods are on the line with
this. It is also no small thing to ask a person to stop doing what
they have probably devoted their lives to do. I would remind them,
however, that there may well be moral issues involved here that go
beyond any questions of direct physical harm. In fact, I have a
confession to make. It was not the possibility of physical harm that
first prompted the notion of speaking out to be suggested to me, but
rather one of what we risk in a spiritual nature.
As you might already have guessed,
I don't put much stock in the notion of deities. They have never made
much sense to me, and I don't expect that they ever will. I do
believe in spirit, though, and that there are interactions that
transcend ordinary objectification (how can you have faith in love,
or what is truly exchanged in an embrace, otherwise). As such I worry
a great deal about what we are already doing to ourselves with social
and economic structures that don't foster loving structure. The
fragmentation, abstraction and disassociation of everything that
makes us human that competitive consumption, and specialized
production have wrought, has done incalculable violence to our
spirit; just as they have done to the spirit of what is natural
around us. We thus live without any kind of balance (koyaanisqatsi
if you will), let alone much loving structure. Violence then becomes
an accepted way of life. Why then would we even think twice about
what is essentially a very violent, not to mention invasive, means of
probing the deepest aspects of our existence (or even why we would
want to objectify something so precious and wondrous in the first
place).
To objectify is, after all, to
separate ones self from direct connection with the matrix of process
that is existence. It is, as with creation itself, a form of
violence, for it destroys what was to create what can be. It is as
inevitable as it is necessary, but that is not to say that its excess
is benign. Any more than not being objective at all would be benign.
That's one of the points of striving for the ideal of loving
structure. It is deep connection and interaction in balance with
rational objectivity; living what you believe is the very nature of
existence itself.
The above having been said, I
would ask physicists if they have pondered very deeply at all on what
they risk. It's not just what we might do to the processes around us,
but what we would do to ourselves. Even if you did no physical harm,
and it were possible to objectify every last essential aspect of
existence, would you still be human at all? Would anything have
wonder or magic?
I would hope that all of us would
remember what Jeff Goldblum’s character in Jurasic Park said (just
before the wondrous new thing began to chomp unexpectedly): just
because you can (and allowing that curiosity is a part of our nature)
do a thing, doesn't necessarily mean you should. Knowledge, as well
as ideas, are sharp and multidimensional. They can cut in ways you
can never fully anticipate. I beg of you, please proceed with all due
care and humility. Your “Lab Rat” could encompass a great deal
more, or less, than you could possibly imagine.
http://www.marxist.com/science-old/chaostheory.html
http://en.wikipedia.org/wiki/Analog-to-digital_converter
http://en.wikipedia.org/wiki/Variety_(cybernetics)
http://en.wikipedia.org/wiki/Avalanche_effect
http://en.wikipedia.org/wiki/Nonlinear_system
effects&pf=p&sclient=psy-ab&oq=small+inputs+can+have+large+effects&gs_l=&pbx=1&bav=on.2,or.r_gc.r_pw.r_qf.,cf.osb&fp=ce19979f0aca28f&biw=1920&bih=923
effects&pf=p&sclient=psy-ab&oq=small+inputs+can+have+large+effects&gs_l=&pbx=1&bav=on.2,or.r_gc.r_pw.r_qf.,cf.osb&fp=ce19979f0aca28f&biw=1920&bih=923
http://transliteracies.english.ucsb.edu/images/flash_projects/word/
http://www.physics.sfsu.edu/~lwilliam/sota/anth/arguments.htm
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