Concrete - Abstract
Simple - Complex
One - Many
Low resolution - High resolution
In interpreting the world we're constantly faced with the decision of what level of resolution - or level of analysis - to use.
If we take it as a given that we're always missing something, then the question is, exactly how much can we miss before it becomes a problem? The answer, it seems, depends on context - in other words, what are our goals, and what level of analysis do they demand? In other words, what level of detail is appropriate to this situation?
Complexity can be seen as noise, or entropy. It is a breaking-apart into ever more detail. The more detail we see the truer our picture. In this sense, the best map of the territory is the territory itself. And yet, we need our maps, our simple representations.
Sometimes short-cuts - low resolution interpretations - are useful and appropriate. But sometimes they prevent us from seeing something vital.
What are we leaving out? And is it important?
As soon as we look into something - i.e. remove the lid, the capstone, and see what lurks inside or beneath - we find that we are much less able to make simple generalisations about it.
From the outside, from a distance, it is easy to characterise things - perhaps due in large part to the fact that we are largely ignorant to their inherent complexity. A distant view gives the comforting illusion of simplicity.
So, for instance, I can speculate about the various problems of the education system, or the problems with teachers, but were I to become a teacher myself, I would not, generally speaking, find it as easy to make the same sweeping pronouncements. The field would suddenly have become much more complex, and I may find myself pulling back from definitive statements; easing on the brake instead of the accelerator.
The more I experience of life, the more I realise this seems to apply to everything. It may even lie behind Conquests Third Law: Everyone is conservative about what he knows best.
This implies that any firm judgement or pronouncement is always made in ignorance - by overlooking complexity - and as such every judgement, every bold move, can be criticised by making reference to the many details that have been overlooked - to all those things that have necessarily been ignored in order to provide the illusion of solidity and to make the judgement firm.
Definitions do not contain any knowledge [...] they are simply shorthand labels introduced in order to cut a long story short.
[Jeremy Waldron]
Karl Popper: Critical Appraisals, p. 222
"Laziness."
What is "laziness"? Does "laziness" describe an element of reality, a "real" phenomenon? Does "laziness" actually exist?
"Laziness" is, amongst other things, an explanatory principle that we use to describe a category of behaviours.
From the endless profusion of reality - the continuum of events and things - we sketch out some borders, and tell ourselves that everything in between them will be referred to as "lazy." It is a handy fiction. Like all explanatory principles, laziness is a shortcut, a label we wheel out to stop us from having to dig any deeper, from spending any time. It is an adaptive invention that conserves energy, allowing us to get from A to B in the shortest possible time. If we can only cram so much information into our consciousness - concentrate on a finite amount of things - then our shortcuts allow us to get on with things, to get things done. They bypass the long route, because the long route is wasteful.
And so more often than not, we take the short one: "he is lazy." But if we use "lazy" then we should be aware that we are using a placeholder; that we are, in fact, marking something for further examination. The problem with a fiction like "lazy" is when it is literalised; when we begin to believe that the dragon really exists, and that it is embodied by this person, or that person.
When we look beneath "lazy" we begin to see a number of other things; more words rush in. We begin to see "preoccupied," "depressed," "afraid." We see these and much more. And then these words begin to crack and crumble, revealing further intricacies.
"Laziness" is not designed to hold reality, or to reflect it. Whilst pretending to describe reality, "laziness" actually works to keep us at arms length from it. The actuality that lies beneath "laziness" in an unexploded bomb: remove the lid - the label - and it detonates into a million pieces; a million fragments of reality - so many that we cannot hold them all, understand them all. They whirl around us, spinning us into a confusion. Perhaps then, it is best not to remove the lid, to look beneath "lazy."
But if we care about this person - this lazy so and so - then perhaps we owe them more than "lazy." Is "lazy" ever excusable? Maybe it just needs untethering from the reality that we hang around it, so that it can float up and take its rightful place, among all the other nebulous words.
Perhaps to use terms like "lazy" might just be plain ... lazy.
“I saw him every once in a while pass by, he was a very shy guy and tall, about 6ft 2in [1.88 metres]. He wasn’t very sporty, rather a little chubby,” said Stephan Baumanns, the 47-year-old owner of the Treemans bakery and coffee shop in the leafy Maxvorstadt neighbourhood.
“He seemed like a lazy guy. He had a job distributing a free newspaper, Münchener Wochenblatt, but I often saw him rather than deliver them, throw them all away into the garbage bin.”
''He seemed like a lazy guy': locals describe Munich shooter'
The choice is always the same. You can make your model more complex and more faithful to reality, or you can make it simpler and easier to handle.
Only the most naive scientist believes that the perfect model os the one that perfectly represents reality. Such a model would have the same drawbacks as a map as large and detailed as the city it represents, a map depicting every park, every street, every building, every tree, every pothole, every inhabitant, and every map.
Were such a map possible, its specificity would defeat its purpose: to generalise and abstract. Mapmakers highlight such features as their clients choose. Whatever their purpose, maps and models must simplify as much as they mimic the world.
[James Gleick]
Chaos, p. 278-9
Kinds, and sameness of kind -what colossally useful denkmittel for finding our way among the many!
The manyness might conceivably have been absolute. Experiences might have all been singulars, no one of them occurring twice. In such a world logic would have had no application; for kind and sameness of kind are logic's only instruments.
Once we know that whatever is of a kind is also of that kind's kind, we can travel through the universe as if with seven-league boots. Brutes surely never use these abstractions, and civilized men use them in most various amounts.
[William James]
'Pragmatism and Common Sense', Pragmatism and Other Writings, p. 80
[The historian] is back in his proper place when he takes us away from simple and absolute judgements and by returning to the historical context entangles everything up again.
The whole process of historical study is a movement towards historical research - it is to carry us from the general to the particular, from the abstract to the concrete, from the thesis that the Reformation led to liberty to an actual vision of all the chances and changes which brought about the modern world.
The volume and complexity of historical research are at the same time the result and the demonstration of the fact that the more we examine the way in which things happen, the more we are driven from the simple to the complex.
If history could be told in all its complexity and detail it would provide us with something as chaotic and baffling as life itself; but because it can be condensed there is nothing that cannot be made to seem simple, and the chaos acquires form by virtue of what we choose to omit.
There is a danger in all abridgments that acquire certainty by reason of what they omit, and so answer all questions more clearly than historical research is ever able to do.
Perhaps the greatest of all the lessons of history is this demonstration of the complexity of human change and the unpredictable character of the ultimate consequences of any given act or decision of men; and on the face of it this is a lesson that can only be learned in detail.
If history can do anything it is to remind us of those complications that undermine our certainties, and to show us that all our judgments are merely relative to time and circumstance.
So the last word of the historian is not some fine firm general statement; it is a piece of detailed research. It is a study of the complexity that underlies any generalisation that we can make [...] Indeed the historian is never more himself when he is searching his mind for a general statement that shall in itself give the hint of its own underlying complexity.
[Herbert Butterfield]
The Whig Interpretation of History, p. 69, 73-5, 97, 101-2
One of the main themes on which Taleb touches in The Black Swan, is "Platonification", or our tendency as humans to simplify.
We like to explain history by using general themes when, in fact, history is very complex and cannot be simplified into one theme and a few pages. We not only simplify history, but we also generalize problems and make simplifying forecasts. Our tendency to Platonify also leads us to depend on averages and to believe that the future will be average. We then miss the "Black Swans".
'The Black Swan, by Taleb'
When I wondered about the cause of the estuary die-off, an hypothesis may have jumped into your mind – climate change, the culprit du jour for nearly every environmental problem.
If we could identify one thing as THE cause, the solution would be so much more accessible.
As I was doing research for my book, I googled “effect of soil erosion on climate change,” and the first two pages of results showed the converse of my search – the effect of climate change on soil erosion. The same for biodiversity.
No doubt it is true that climate change exacerbates all kinds of environmental problems, but the rush to name a unitary cause to a complex problem should give us pause.
The pattern is familiar. Do you think the “fight against climate change,” which starts by identifying an enemy, CO2, will bring better results than the War on Terror, the War on Drugs, or the War on Poverty?
[Charles Eisenstein]
'Of Horseshoe Crabs and Empathy'
Innumerable kinds of causes and conditions are necessary to bring about [a person’s] action - social causes, educational causes, economic, political, climatic, nutritional, genetic, medical causes, besides the subjective and neural angles that we have noticed. Each of these sets of causes may partially explain the action. But none of them invalidates the others; there is room for them all.
The question which of them counts as the explanation in a given case depends entirely on our interests, on what we want to find out.
Current notions of determinism, however, allow specialists in any of these topics to feel that the whole logical space is theirs - that they alone possess the explanation. Thus we get the odd spectacle of many competing determinisms - genetic determinism, economic determinism, neurological determinism and so forth - where the claim seems to be that a single discipline has finally found the engine which runs all the other causes.
That is another trouble about current notions of determinism which needs to be sorted out. On large topics, this kind of tribal narrowness is always disastrous.
[Mary Midgley]
Science and Poetry, p.166
A very practical way to think about this is that when you’re presented with [a pattern], how easily can you summarise what you see?
If it’s just a uniform [pattern], you’re done. You have a quick description that gets you the complete specification of the pattern.
When we see things as complex, what’s really going on is that we, as human analysers of what we’re seeing, don’t get very far. We can’t [capture] the thing we’re seeing with some simple description. We’re just stuck with saying, ‘it is what it is’.
We may be able to give some ornate description of what’s there, but we don’t get to summarise everything in a sentence or two.
[Stephen Wolfram]
'Stephen Wolfram - What is Complexity in the Cosmos?'
[...] in the use of reason lies the eternal temptation to do with human data in experiment and argument what the child does with them in play: namely, to reduce them to a size and an order in which they seem manageable.
Thus human data are treated as if the human being were an animal, or a machine, or a statistical item. Much naive sense of power can be derived from the fact that, properly approached, the human being up to a point is all of these things, and under certain conditions can be reduced to being nothing but their facsimiles.
But the attempt to make man more exploitable by reducing him to a simpler model of himself cannot lead to an essentially human psychology.
[Erik H. Erikson]
Childhood and Society, p. 378
Society is composed of persons who cannot design, build, repair, or even operate most of the devices upon which their lives depend […]
In the complexity of this world people are confronted with extraordinary events and functions that are literally unintelligible to them. They are unable to give an adequate explanation of man-made phenomena in their immediate experience. They are unable to form a coherent, rational picture of the whole.
Under the circumstances, all persons do, and indeed must, accept a great number of things on faith […] Their way of understanding is basically religious, rather than scientific; only a small portion of one’s everyday experience in the technological society can be made scientific […]
The plight of members of the technological society can be compared to that of a newborn child. Much of the data that enters its sense does not form coherent wholes. There are many things the child cannot understand or, after it has learned to speak, cannot successfully explain to anyone […]
Citizens of the modern age in this respect are less fortunate than children. They never escape a fundamental bewilderment in the face of the complex world that their senses report. They are not able to organize all or even very much of this into sensible wholes […]
[Langdon Winner]
Autonomous Technology: Technics-Out-Of-Control
In the modeling of physics, a toy model is a deliberately simplistic model with many details removed so that it can be used to explain a mechanism concisely. It is also useful in a description of the fuller model.
In "toy" mathematical models, this is usually done by reducing or extending the number of dimensions or reducing the number of fields/variables or restricting them to a particular symmetric form.
In Macroeconomics modelling, are a class of models, some may be only loosely based on theory, others more explicitly so. But they have the same purpose. They allow for a quick first pass at some question, and present the essence of the answer from a more complicated model or from a class of models. For the researcher, they may come before writing a more elaborate model, or after, once the elaborate model has been worked out.
In "toy" physical descriptions, an analogous example of an everyday mechanism is often used for illustration.
'Toy model'
Wikipedia
Models have to reduce the complexity of the phenomena being described, they have to leave something out.
However, we have no way of predicting the importance of that which is not considered. In a non-linear world where we cannot track a clear causal chain, something that may appear to be unimportant now, may turn out to be vitally important later. Or vice versa, of course. Our models have to “frame” the problem in a certain way, and this framing will inevitably introduce distortions.
This is not an argument against the construction of models. We have no choice but to make models if we want to understand the world. It is just an argument that models of complex systems will always be flawed in principle, and that we have to acknowledge these limitations.
My conclusion is that it is impossible to have a perfect model of a complex system. This is not because of some inadequacy in our modelling techniques, but a result of the meaning of the notions “model” and “complex”. There will always be a gap between the two. This gap should serve as a creative impulse that continually challenges us to transform our models, not as a reason to give up.
[Paul Cilliers]
'Boundaries, Hierarchies and Networks in Complex Systems'
NNT (that is, me): Assume that a coin is fair, i.e, has an equal probability of coming up heads or tails when flipped. I flip it ninety-nine times and get heads each time. What are the odds of my getting tails on my next throw?
Dr. John: Trivial question. One half, of course, since you are assuming 50 percent odds for each and independence between draws.
NNT: What do you say, Tony?
Fat Tony: I’d say no more than 1 percent, of course.
NNT: Why so? I gave you the initial assumption of a fair coin, meaning that it was 50 percent either way.
Fat Tony: You are either full of crap or a pure sucker to buy that “50 pehcent” business. The coin gotta be loaded. It can’t be a fair game. (Translation: It is far more likely that your assumptions about the fairness are wrong than the coin delivering ninety-nine heads in ninety-nine throws.)
NNT: But Dr. John said 50 percent.
Fat Tony (whispering in my ear): I know these guys with the nerd examples from the bank days. They think way too slow. Any they are too commoditised. You can take them for a ride.
Dr. John thinks entirely within the box, the box that was given to him; Fat Tony, almost entirely outside the box.
To set the terminology straight, what I call “a nerd” here doesn’t have to look sloppy, unaesthetic, and sallow, and wear glasses and a portable computer on his belt as if it were an ostensible weapon. A nerd is simply someone who think exceedingly inside the box.
[Nassim Nicholas Taleb]
The Black Swan, p. 124-5
We can argue over which slice is more right…which once we’ve seen the undeniable partial rightness of each (from their own perspective), is of course just silly. Or we can hold that both are somehow true, despite being mutually exclusive descriptions of reality (from a 2D view)…and surrender to calling it paradox and give up on congruent understanding altogether.
Or we can take another reconciliatory approach and say that they are both partially true so we must find a middle path…which in this case, still embedded in 2D, looks like something half way between a circle and a rectangle… which comes out to be a kind of rounded-corner rectangle. Which is actually further from the reality than either the circle or the rectangle had been, since at least they were each true slices of the cylinder.
The problem of course is in the reductionism.
There is no 2D slice of a 3D object that gives a real sense of what it is. Neither is any 2D negotiation of slices going to yield something in 3D. The cylinder is not somewhere between the two reductionistic views: 50% circle, 50% rectangle… It is 100% of both descriptions…which are only mutually exclusive and paradoxical if they are trying to be reconciled in the same plane, which is the essential mistake. In the higher dimensional reality the object actually lives in, the simultaneous full truth of both partial descriptions is obvious and non-paradoxical…as is the seamless way they fit together as parts of a congruent whole.
The recognition of orthogonality…gives us the cylinder, recognizes both lower dimensional perspectives as 100% true from their limited vantage point, and forces the recognition that a congruent picture is possible but requires a fundamentally more complex kind of perspective.
Our perception of existential paradoxes often comes from exactly this kind of process: believing in false dichotomies through reducing reality to conceptual slices that are true but partial to the point of actually requiring a seemingly mutually exclusive perspective to explain the full phenomena.
[Daniel Schmachtenberger]
'Higher Dimensional Thinking, the End of Paradox, and a More Adequate Understanding of Reality'
Fuzzy intersections are the realm of apparent paradox. For instance, they easily yield the set of men who are both tall and short […] Of course it is really an intersection of men who are partly tall and partly short.
The contradiction arises from assuming crispness.
[Daniel McNeill & Paul Freiberger]
Fuzzy Logic, p.38
Think about a tree in an ecosystem - what is the value of that tree?
It’s providing a home for pollinators and birds, it’s stabilising topsoil, it’s symbiotic with the fungus and bacteria in the soil, it’s proving shade, it’s pulling out CO2 and producing oxygen, it’s proving food for animals. It might have millions of value-metrics as part of this complex ecosystem.
But then we cut it down to make it ten-thousand dollars worth of two-by-fours, and its value is ten-thousand dollars. And the two-by-fours [aren’t] sequestering CO2 and stabilising top soil - they are serving as a structural strut, as one really simple thing.
So we took this very complex thing and reduced the complexity of it radically, and made it a very simple thing. We downcycled it, because the metric we were seeking to optimise was dollars in my account.
How do I relate the value of an elephant tusk, or a person’s art, or a tree - these should not be fungible, these are fundamentally different things.
But I remove all of the information from them and all of the context [because] I want them to be simply exchangeable in terms of capital, so that I can maximise the ease of transaction. [This] is an extinctionary dynamic.
We’re taking complex value and turning it into simple value.
[Daniel Schmachtenberger]
'46: Daniel Schmachtenberger - Winning Humanity's Existential Game' (23:00)
Consider […] the case of families. How are families established? What constitutes membership in a particular family? […] even in the simplest cases the boundaries of families are far from clear: there isn’t always a definitive answer to the question whether two temporally distant individuals do or do not belong to the same family […]
In many cases this answer will depend on the purpose with which the question is asked and on what is at stake […]
[...] family connections are immensely more complex than our usual representations of family trees can ever suggest. When we appeal to family trees, we are concerned to trace, for particular reasons, an individual’s origin to a particular source though a particular path […]
[…] but a moment’s thought shows how crucial our “particular reasons” always are in such situations. On one occasion, for example, we may want to […] see how all the central characters of The Forsyte Chronicles are related to Old Jolyon, the figure Galsworthy quite arbitrarily chose as the family’s founder […] Galsworthy’s neat [family tree] makes it easy to forget [certain branches in the family tree that are of] no importance to [his] narrative.
None of this implies in any way that Galsworthy was “wrong” to omit this information: he could not have included all of it even if for some strange reason he had wanted to do so. In fact it is impossible to say exactly what “all” the information would be in this [context].
[…] the specific path traced through what are actually indefinitely complex family interconnections is essentially conditioned by background interests and values […] Particular families are generated out of this network by means of operations that are essentially conditioned by specific interests and values.
But “in the actual world, in which everything is bound to and conditioned by everything else,” families are nothing like what these neat representations suggest. It is not just difficult but actually impossible to determine the family to which an individual belongs without assumptions dictated by our conventions, purposes, and values […]
Our concept of the family is tied to the idea of shared behavioural, morphological, or genetic features. But this is only because we are usually concerned with what is really the very short run, with the few generations within which such similarities may be important and obvious.
[Alexander Nehamas]
Nietzsche: Life as Literature, p. 100-2
There has been both over-reaction and under-reaction. Power grabs and abdications of responsibility to use power properly in crisis alike.
As a reaction, no one is thinking in superpositions. They are breaking off whatever pisses them off and reacting to that fragment.
Elon is breaking off the over reactions, power grabs and alarmist messaging creating panic. Those are real. But there are also under reactions and failures to act which he is ignoring. It’s multi-variate.
So expect everyone to rebel against the bungling with a simplified take.
[Eric Weinstein]
We cannot simply go from saying “things are ordered” to saying “things are un-ordered” and leave it at that; things are both ordered and un-ordered at once, because in reality order and un-order intertwine and interact.
Kostof puts it well in his description of cities: “. . . the two primary versions of urban arrangement, the planned and the ‘organic,’ often exist side by side. . . . Most historic towns, and virtually all those of metropolitan size, are puzzles of premeditated and spontaneous segments, variously interlocked or juxtaposed. . . .”
In other words, it is useful to artificially separate order and un-order so that we can understand the different dynamics involved, but we should not expect to find one without the other in real life.
[Cynthia Kurtz & Dave Snowden]
'The new dynamics of strategy: Sense-making in a complex and complicated world'
We like stories, we like to summarise, and we like to simplify, i.e., to reduce the dimension of matters. The [narrative] fallacy is associated with our vulnerability to over interpretation and our predilection for compact stories over raw truths.
Think of the world around you, laden with trillions of details. Try to describe it and you will find yourself tempted to weave a thread into what you are saying. A novel, a story, a myth, or a tale, all have the same function: they spare us from the complexity of the world and shield us from its randomness.
The narrative fallacy addresses our limited ability to look at sequences of facts without weaving an explanation into them, or, equivalently, forcing a logical link, an arrow of relationship, upon them. Explanations bind facts together. They make them all the more easily remembered; they help them make more sense [...] Myths impart order to the disorder of human perception and the perceived “chaos of human experience.” Where this propensity can go wrong is when it increases our impression of understanding.
[...] narrativity comes from an ingrained biological need to reduce dimensionality [...] Information wants to be reduced […] it is impossible for our brain to see anything in raw form without some interpretation [...] Compression is vital to the performance of conscious work […] By finding the pattern, the logic of the series, you no longer need to memorise it all. You just store the pattern.
Our propensity to impose meaning and concepts blocks our awareness of the details making up the concept. However, if you zap people’s left hemispheres, they become more realistic - they can draw better and with more verisimilitude. Their minds become better at seeing the objects themselves, cleared of theories, narratives, and prejudice.
Why is it hard to avoid interpretation? It is key that […] brain functions often operate outside our awareness. You interpret pretty much as you perform other activities deemed automatic and outside your control, like breathing.
[Nassim Nicholas Taleb]
The Black Swan, p. 64-9
When thinking of a category we normally visualise the clear cases, not the vague ones. Chair evokes a dining room chair, not a beanbag chair.
Why do we focus on prototypes? In 1978, looking back on her work Rosch suggested that the purpose of classes was “to provide maximum information with the least cognitive effort.” There is a trade-off: information versus labour. And prototypes ease the burden. For instance, the eye can discriminate 7.5 million colours. If definitions were sharp, if blue ended at a single hue, people would need a pointless acuity of perception.
Cognitive economy also likely increases the speed of the brain, enabling it to work with essences rather than time-consuming fringe items […] words summarise, and prototypes summarise further. They catch the gist of the fuzzy set.
[Daniel McNeill & Paul Freiberger]
Fuzzy Logic, p.88
We evolved to make decisions very quickly based on a partial data scan, privileging our most recent experiences.
In modern cognitive science we don’t call these biases, we call them heuristics. Evolution doesn’t produce things that have no utility. So-called biases are actually heuristics that allow us to make decisions faster.
If you look at all of the so-called ‘cognitive biases’ they’re all about reducing the energy cost of making decisions. On average they pan-out better. Reduction in energy cost is critical in evolution, and particularly for humans because our brain takes up so much energy, disproportionate in many ways to its utility.
[Dave Snowden]
'Dealing with unanticipated needs – Dave Snowden' and 'Naturalising Sense-making w/ Dave Snowden. September 3rd, 2020'
Heuristics are simplified rules of thumb that make things simple and easy to implement.
But their main advantage is that the user knows that they are not perfect, just expedient, and is therefore less fooled by their powers. They become dangerous when we forget that.
[Nassim Nicholas Taleb]
Antifragile, p. 11
“Anger” is a cultural concept that we apply to hugely divergent patterns of change in the body, and there’s no single facial expression reliably associated with it, even in the same person. (Some cultures don’t have a concept that corresponds to “anger”, such as the Utku Inuit of Canada’s Northwest Territories.)
The same is true, astonishingly, of “happiness”, “excitement”, “disappointment”, you name it. No emotion is tied to a single, objective state in the body. Rather, emotions are cultural artefacts.
Don’t babies and toddlers fuss and bawl at some obstacle long before they have a word to describe the feeling? And don’t the Utku also experience their blood pumping faster and their muscles tensing up when confronted with a difficult problem? The answer is that of course they do, but that “anger” is merely one interpretation of these events, a culturally specific attempt to give them meaning.
[Lisa Feldman-Barrett] argues that the universal components of human experience are not emotions, but changes on a continuum of arousal on the one hand, and pleasantness and unpleasantness on the other. The term for this is “affect”. It is a basic feature of consciousness, and people in different cultures learn to mould this raw material into emotional experiences in different ways.
[David Shariatmadari]
Complex dynamical theory [...] teaches that if you look only at the outside, as behaviourism did, differences both in the way information is generated and in the constrained pathways along which it flows will be overlooked.
Focusing on the differences in […] starting points and the way these differences interact with the environment, on the other hand, can reveal a dynamical process. Even when the behavioral output (the trajectory's sink) is the same, the pathways taken to get there may be very different.
As a consequence of the modern paradigm, there was no way of explaining how some behaviors can be voluntary and intentional because they flow from an agent's meaning-bearing states, whereas other, empirically indistinguishable behaviors are not. Modern philosophy and science, as we have seen, were unable to account for, say, the difference between an involuntary smile and one commanded, which is now known to be a difference in trajectory […]
And yet how successful the old modern worldview was! Pretending that everything is a closed, linear system gives the illusion that one can, without penalty, abstract from time and context, starting with the interference of friction. And doing so did indeed make many difficult problems tractable and yielded spectacular results. Who in the fifteenth century would have thought that planetary orbits could be so accurately predicted?
But this tidy picture was doomed from the start, because the scientific and philosophical problems posed by the nature and behavior of open systems cannot be ignored. Very few people anticipated the mischief - and benefits - that the nonlinearity of positive feedback unleashes on the modern paradigm.
I propose that from now on the covering-law model of explanation (including its probabilistic incarnation) should be considered the limit of explanation, adequate for those phenomena that can be idealized as atemporal and acontextual.
For isolated, linear systems, the covering-law model often works fine. For those phenomena, the tighter the inference, the better the explanation and the more accurate the prediction. For open, complex dynamical phenomena in which context-dependent constraints (both bottom-up and top-down) create interlevel interactions—that is, for phenomena which that "strange form of causality" progressively individuates and marks as essentially historical and contextual - the deductive model simply won’t do.
[Alicia Juarrero]
Dynamics in Action, p. 221
Such logic exists within a world of thought that operates using a structure of categories, something our own language does very well. This logic and language tells us that an object cannot simultaneously be a member of two mutually exclusive categories: An action cannot be both bad and good, something cannot be both subjective and objective, an electron cannot be both a wave and a particle.
Today we know that indeed an electron is both a wave and a particle. Niels Bohr suggested that within the quantum world science had to adopt what he called complementary descriptions - rather than having a single description that exhausts the phenomenon in question, science has to employ complementary, mutually contradictory, accounts.
The world, at the subatomic level, does not accord with the traditional way our English-Latin-Greek language structures reality.
As soon as we begin to drop our obsession with categories and boundaries in thought many of these problems and paradoxes fall away. Quantum theory constantly emphasizes that the context in which events occur is of key importance. Set up an experiment in one way and the result is particles. Do it another way and it must be interpreted in terms of waves. It is impossible to separate a phenomenon from the context in which it is observed. Categories no longer exist in the absence of contexts.
Within Indigenous science, context is always important. Nothing is abstract since all things happen within a landscape and by virtue of a web of interrelationships. The tendency to collect things into categories does not exist within the thought and language of, for example, Algonquin speakers.
This leads to a profoundly different way of approaching and thinking about the world. For, in the absence of categories, each thing is mentally experienced on its own merits, and for what it actually is. Rather than indulging in comparison or judgment, Indigenous speakers attempt to enter into relationship with them.
In English we have the general category of "fish," which is the result of classifying, in terms of differences and similarities, the various creatures that live in the water. It therefore becomes convenient within our minds to gather together objects of different shapes, sizes and colors and treat them all as members of the one category "fish."
The Algonquin family of languages, for example, does not make use of such categories or boundaries in thought. Rather, it is concerned with processes that are happening in the water and with the peoples' relationships to such processes. Iroquois languages for their part would tend to picture the world in terms of a complex web of relationships. Instead of using logic to reach a single truth, an Indigenous scientist is more concerned with achieving balance and harmony.
Within Indigenous science, language is irreducibly tied to landscape, culture, and thought. A non-Native linguist, Benjamin Lee Whorf, came to similar conclusions. As a result of his study of the language of the Hopi people, he found that their language reflects the non-Newtonian universe in which they live.
[F. David Peat]
Blackfoot Physics, p.233-4
These things are difficult, I admit; their formulation can be disconcerting. But would there be so many problems and misunderstandings without this complexity and without these paradoxes?
One shouldn’t complicate things for the pleasure of complicating, but one should also never simplify or pretend to be sure of such simplicity where there is none. If things were simple, word would have gotten round, as you say in English.
There you have one of my mottos, one quite appropriate for what I take to be spirit of the type of ‘enlightenment’ granted our time. Those who wish to simplify at all costs and who raise a hue and cry about obscurity because they do not recognize the unclarirty of their good old Aufklärung are in my eyes dangerous dogmatists and tedious obscurantists. No less dangerous (for instance, in politics) are those who wish to purify at all costs.
[Jacques Derrida]
Limited Inc.
Some interesting new perspectives are supplied by the work of Gregory Chaitin (1975, 1987). In his reinterpretation of information theory, in what he has termed 'algorithmic information theory', randomness is defined not in terms of unpredictability, but in terms of 'incompressibility'.
[…] randomness becomes a measure for the amount of information in a sequence, but, and this is vital, randomness understood no longer in terms of unpredictability, but in terms of the denseness with which the information is packed. It also provides us with an interesting definition of complexity: the complexity of a series is equal to the size of the minimal program necessary to produce that series (Chaitin 1975: 49).
In a certain sense we have taken a long route to arrive at a truism: complexity is complex. A complex system cannot be reduced to a simple one if it wasn't simple (or perhaps merely complicated) to start off with.
A complex system cannot be reduced to a collection of its basic constituents, not because the system is not constituted by them, but because too much of the relational information gets lost in the process.
On an intuitive level […] the notion of 'incompressibility' remains very fruitful. It reminds us that when dealing with complexity, there are no short-cuts without peril.
The notion should nevertheless not be used absolutely. The complex systems we are interested in are never completely ‘minimal'; they contain a lot of spare capacity or redundancy. This is necessary for more than one reason: it provides robustness, space for development and the means for plasticity.
A clearer picture of why some 'free space' is necessary will emerge in the next section when we examine two important aspects of complex systems which our models have to capture. For now we can conclude that a strict measure for complexity does not seem feasible. To describe a complex system you have, in a certain sense, to repeat the system.
[Paul Cilliers]
Complexity and Postmodernism, p.9-10
This leads us to an extremely important point: the network used as model for a complex system will have to have the same level of complexity as the system itself.
It will therefore be just as difficult to construct a theory of what the network is doing as it would be to construct a theory of what the system is doing. If certain general principles exist that can assist in describing the behaviour of the system, they could possibly be found by analysing the behaviour of the network. However, if the system is truly complex, a network of equal complexity may be the simplest adequate model of such a system, which means that it would be just as difficult to analyse as the system itself. This has serious methodological implications for scientists working with complex systems.
A model which reduces the complexity may be easier to implement, and may even provide a number of economical descriptions of the system, but the price paid for this should be considered carefully.
[Paul Cilliers]
Complexity and Postmodernism, p.70
Despite the fact that we cannot represent the essence of a complex system in determinate terms, we cannot resist, or perhaps even avoid, the construction of some kind of interpretation of the nature of the system at a given moment.
These interpretations, however, are in principle limited. We are always constrained to taking snapshots of the system. These shots are always taken from a certain angle and reveal some aspect of the system at some moment. Nothing prevents us from attempting explanations of the system - we can take as many pictures as we want - as long as we realise the limitations of each particular one.
Since a complex system is constantly changing, i.e. not in equilibrium, it is also not possible to link a series of pictures together like pieces in a puzzle that fit exactly into their true positions. We can juxtapose, compare, make collages, combine them in sequences that develop a narrative, and thereby, in perhaps a more creative way, develop our understanding of the system. The danger lies in falling under the spell of a specific picture and claiming a privileged position for it.
Since it would not only deny the limitations of the specific angle, but also prevent further explorations, this spell must be broken by relentlessly showing the contradictions that result from fixing the boundaries from one perspective. Pointing out the contradictions that follow from such a closure is an activity that Derrida calls ‘deconstruction.’
[Paul Cilliers]
Complexity and Postmodernism, p.80-1
Such logic exists within a world of thought that operates using a structure of categories, something our own language does very well. This logic and language tells us that an object cannot simultaneously be a member of two mutually exclusive categories: An action cannot be both bad and good, something cannot be both subjective and objective, an electron cannot be both a wave and a particle.
Today we know that indeed an electron is both a wave and a particle. Niels Bohr suggested that within the quantum world science had to adopt what he called complementary descriptions - rather than having a single description that exhausts the phenomenon in question, science has to employ complementary, mutually contradictory, accounts.
The world, at the subatomic level, does not accord with the traditional way our English-Latin-Greek language structures reality.
As soon as we begin to drop our obsession with categories and boundaries in thought many of these problems and paradoxes fall away. Quantum theory constantly emphasizes that the context in which events occur is of key importance. Set up an experiment in one way and the result is particles. Do it another way and it must be interpreted in terms of waves. It is impossible to separate a phenomenon from the context in which it is observed. Categories no longer exist in the absence of contexts.
Within Indigenous science, context is always important. Nothing is abstract since all things happen within a landscape and by virtue of a web of interrelationships. The tendency to collect things into categories does not exist within the thought and language of, for example, Algonquin speakers.
This leads to a profoundly different way of approaching and thinking about the world. For, in the absence of categories, each thing is mentally experienced on its own merits, and for what it actually is. Rather than indulging in comparison or judgment, Indigenous speakers attempt to enter into relationship with them.
In English we have the general category of "fish," which is the result of classifying, in terms of differences and similarities, the various creatures that live in the water. It therefore becomes convenient within our minds to gather together objects of different shapes, sizes and colors and treat them all as members of the one category "fish."
The Algonquin family of languages, for example, does not make use of such categories or boundaries in thought. Rather, it is concerned with processes that are happening in the water and with the peoples' relationships to such processes. Iroquois languages for their part would tend to picture the world in terms of a complex web of relationships. Instead of using logic to reach a single truth, an Indigenous scientist is more concerned with achieving balance and harmony.
Within Indigenous science, language is irreducibly tied to landscape, culture, and thought. A non-Native linguist, Benjamin Lee Whorf, came to similar conclusions. As a result of his study of the language of the Hopi people, he found that their language reflects the non-Newtonian universe in which they live.
[F. David Peat]
Blackfoot Physics, p.233-4
These things are difficult, I admit; their formulation can be disconcerting. But would there be so many problems and misunderstandings without this complexity and without these paradoxes?
One shouldn’t complicate things for the pleasure of complicating, but one should also never simplify or pretend to be sure of such simplicity where there is none. If things were simple, word would have gotten round, as you say in English.
There you have one of my mottos, one quite appropriate for what I take to be spirit of the type of ‘enlightenment’ granted our time. Those who wish to simplify at all costs and who raise a hue and cry about obscurity because they do not recognize the unclarirty of their good old Aufklärung are in my eyes dangerous dogmatists and tedious obscurantists. No less dangerous (for instance, in politics) are those who wish to purify at all costs.
[Jacques Derrida]
Limited Inc.
Some interesting new perspectives are supplied by the work of Gregory Chaitin (1975, 1987). In his reinterpretation of information theory, in what he has termed 'algorithmic information theory', randomness is defined not in terms of unpredictability, but in terms of 'incompressibility'.
[…] randomness becomes a measure for the amount of information in a sequence, but, and this is vital, randomness understood no longer in terms of unpredictability, but in terms of the denseness with which the information is packed. It also provides us with an interesting definition of complexity: the complexity of a series is equal to the size of the minimal program necessary to produce that series (Chaitin 1975: 49).
In a certain sense we have taken a long route to arrive at a truism: complexity is complex. A complex system cannot be reduced to a simple one if it wasn't simple (or perhaps merely complicated) to start off with.
A complex system cannot be reduced to a collection of its basic constituents, not because the system is not constituted by them, but because too much of the relational information gets lost in the process.
On an intuitive level […] the notion of 'incompressibility' remains very fruitful. It reminds us that when dealing with complexity, there are no short-cuts without peril.
The notion should nevertheless not be used absolutely. The complex systems we are interested in are never completely ‘minimal'; they contain a lot of spare capacity or redundancy. This is necessary for more than one reason: it provides robustness, space for development and the means for plasticity.
A clearer picture of why some 'free space' is necessary will emerge in the next section when we examine two important aspects of complex systems which our models have to capture. For now we can conclude that a strict measure for complexity does not seem feasible. To describe a complex system you have, in a certain sense, to repeat the system.
[Paul Cilliers]
Complexity and Postmodernism, p.9-10
This leads us to an extremely important point: the network used as model for a complex system will have to have the same level of complexity as the system itself.
It will therefore be just as difficult to construct a theory of what the network is doing as it would be to construct a theory of what the system is doing. If certain general principles exist that can assist in describing the behaviour of the system, they could possibly be found by analysing the behaviour of the network. However, if the system is truly complex, a network of equal complexity may be the simplest adequate model of such a system, which means that it would be just as difficult to analyse as the system itself. This has serious methodological implications for scientists working with complex systems.
A model which reduces the complexity may be easier to implement, and may even provide a number of economical descriptions of the system, but the price paid for this should be considered carefully.
[Paul Cilliers]
Complexity and Postmodernism, p.70
Despite the fact that we cannot represent the essence of a complex system in determinate terms, we cannot resist, or perhaps even avoid, the construction of some kind of interpretation of the nature of the system at a given moment.
These interpretations, however, are in principle limited. We are always constrained to taking snapshots of the system. These shots are always taken from a certain angle and reveal some aspect of the system at some moment. Nothing prevents us from attempting explanations of the system - we can take as many pictures as we want - as long as we realise the limitations of each particular one.
Since a complex system is constantly changing, i.e. not in equilibrium, it is also not possible to link a series of pictures together like pieces in a puzzle that fit exactly into their true positions. We can juxtapose, compare, make collages, combine them in sequences that develop a narrative, and thereby, in perhaps a more creative way, develop our understanding of the system. The danger lies in falling under the spell of a specific picture and claiming a privileged position for it.
Since it would not only deny the limitations of the specific angle, but also prevent further explorations, this spell must be broken by relentlessly showing the contradictions that result from fixing the boundaries from one perspective. Pointing out the contradictions that follow from such a closure is an activity that Derrida calls ‘deconstruction.’
[Paul Cilliers]
Complexity and Postmodernism, p.80-1
Taking the Rough with the Smooth
Standing the Strain
Digging Deeper
A Difference that makes a Difference
Which difference makes a difference?
How Simple is Too Simple?
Discrimination
Conscious / Unconscious
Escaping Uncertainty
Simply Put
Scale
Complexity
