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Exploring The Impossible

Chris Lucas

Alice laughed. "There's no use trying," she said:
"one CAN'T believe impossible things."
"I daresay you haven't had much practice" said the Queen.

Lewis Carroll, Through the Looking Glass, 1872, Chapter 5

"We shall not cease from exploration
And the end of all our exploring
Will be to arrive where we started
And know the place for the first time."

T.S. Eliot, Four Quartets, Little Gidding, 1942, V

Introduction

Here we will look into the possibilities for human evolution, the growth in the power of our minds and our connectivity to a wider universe. We shall look at the vastness of state space and the new methods that we can employ to explore this universe, the world of the impossible.

What is possible and not possible depends upon how we approach it, yesterday's impossible becomes tomorrow's possible with the advances of today. Each new step widens the options available to us in life, it drives us into new active areas of state space, reducing our entropy as we accumulate new information, and seemingly going against the inevitable decay that awaits a closed passive universe.

The Brain

What proportion of our brain do we use ? Often it is claimed that we only use 10%, with the implication that the rest is idle or empty. But another view of this remains possible, in which all parts of our brain have a function, yet most remain unused. In this view the brain is like a toolbox, of which we only ever use the hammer. We usually have in mind conscious thought here, but the vast majority of our brain functions occur sub-consciously, we comprise many hundreds of modules each specialised in a particular task, and arranged in interconnected layers.

The interconnection of these building blocks, like a Lego kit, allows an infinite variety of structures to be assembled. Their interconnections are made by our neural wiring and this reflects the associations and analogies that we make within our world of experience. We can also revise these modules, improving them and constructing new ones, building upon the genetic foundations of our inheritance and erecting as a result skyscrapers of towering achievement in science, art, technology and spirit. Brain evolution is very open ended.

The Body

Our senses provide all our information about the outside world, yet here again we can ask what proportion of this information do we use ? The eye, the ear, the nose, the skin all have vast numbers of receptor cells, hundreds of millions in total, each providing at least one bit of information. Most of us ignore this information, we respond only to change, our minds are so arranged so that the normal is suppressed (presumably to prevent information overload), we habituate to the known and therefore detect only the unknown, the contrast between current and past sensations.

But this mapping between the senses and the brain depends to a large extent on exercise, if we do not stimulate or use a sense it atrophies, just as muscles do. The area of brain concerned will gradually lose efficiency and can even change its function in order to respond to a quite different sense or modality. We need to consider our senses as complex apparatus and train them to respond to subtle clues and delicate stimuli, much as we would tune up a car or a musical instrument.

The Environment

By viewing ourselves as a selective lens that extracts limited data from our environment, we can regard the total environment as a vast repository of additional information, the current state of which comprises what we call the present. We see to a large extent what we wish to see. For example, in the countryside a botanist may see flowers, a zoologist wildlife, a city dweller perhaps only the absence of shops and a property developer just the opportunity for profit !

Yet the depth of detail in any environment is astonishing. Some disciplines, meditation for example, try to teach us to really see what is there, both inside our minds and outside in the world. The possibility for action in either realm depends upon being aware of the valid options, and this in turn requires that we can distinguish them, that we can discriminate amongst the richness already available in our world.

History

The present is the end point of a trajectory through history, and our records of this provide further information which can influence our choices. This includes our memories, written records, archeology and surviving artworks, along with the inheritances of our sciences and literature. All human knowledge is information, data about the structure of our world, the shape of its fitness landscape. We can use it both to recognise the possibilities that have already been tried (actualised) and to imagine those that are still untested, opportunities that have not yet been evaluated for fitness.

By learning from the past we can avoid earlier errors and dead ends, we can preserve the valuable discoveries and artistic beauties of our heritage. We are also better able to position ourselves in our own society and more effectively compare the alternative cultures around the globe. Diversity is a major enabler for change, the more variety there is (i.e. the more options we have to choose from) then the greater is the maximum fitness that we can reach. Preserving the past actually enhances our future.

Society

We are never alone. Even those of us without friends, without money, without hope are part of a larger society. People are all around, we interact with others all the time. Every interaction is a learning situation, whether positive in nature (loving) or negative (hating). If we make mistakes then we try to avoid the same ones in the future. If a transaction proves beneficial then we try to repeat it. Trial and error is part of life, we cannot live and not get some things wrong, we cannot avoid taking chances.

Each error shows us an trajectory taking us downhill, towards a lower fitness state, each success a path upwards to a better fitness. We navigate around our own fitness landscape looking for peaks, looking for opportunities to improve our lives. Yet this is often done in a short sighted, selfish way. If we instead take account of the needs of others then we can usually piggy back on their success. Mutual help allows us to explore far more options than does selfish thinking. A co-operating group can achieve many things that an individual cannot. It pays us to help each other in exploring the vast information bank that is life.

Isomorphisms and Homomorphisms

This world we have outlined is bursting with detail, so much so that we cannot possibly handle it all. Information relates to structure and we are lucky that structures can take many forms that are identical in effect, i.e. all will behave the same. This aspect of systems thinking is called isomorphism - the equivalence of different system representations. We see it in computer modelling, where the model echoes the real world, in mathematics where the equations do so, and in topology where different shapes all have the same properties. In this way we can compress many options into a shorthand form.

But another aspect is yet more important to us, and that is homomorphism. This is the idea that we always simplify our world, we do not try to model all the variables at once but only a few. We reduce a high-dimensional stream of data to a manageable low-dimensional one by ignoring irrelevant detail and thus can create a model that is isomorphic to just a simplified subset of the whole system. For any full system, there are very many ways of doing this, in fact a continuum exists between including every detail (all dimensions/parameters, atoms upwards) and just one (a single system value). Neither extreme is very useful, the first is impossible to calculate, the second contains zero bits of information. We must choose a level of detail that is possible, useful and (most importantly) sufficient for the conclusions we wish to draw, leaving out only what is genuinely irrelevant to the property we are studying.

Subtle Options

This difficulty in choosing a representation for a complex system shows us that any goal has multiple solutions, there are many paths to the same end, just as there are many routes between two countries. We choose routes according to our knowledge and constraints, a pilot may fly, a seaman may sail, a passenger can do either. Which route is easiest or fittest (valid for our purposes) is a contextual decision, not one based upon cultural values or truths. Truth only relates to single dimensions, but in a multidimensional mind we need to relate many conflicting and interacting parameters, we need to compromise between accuracy and difficulty.

Nonlinear decision making of this type needs subtlety, a fine balance between possibility and probability. We need to take account of the likelihood of the world changing, between the time we try to execute the plan and the time we expect to finish. The longer this time may be the more uncertain becomes the end result, the more minor inaccuracies grow. Additionally, the more strongly our actions affect the world the more likely it is to change and make us miss our target. This consideration suggests that we need to choose a stable path through what is always an unstable world, and that we can best achieve our goal by making a incremental progression towards it, rather than by planning ahead. This requires that we frequently re-evaluate the direction in which our shifting goal lies and then re-choose from those options that still remain useful or from the new ones that may become available after each step. Navigation is achieved, in fact, by cunning and knowledge and not by brute force...

Escaping the Possible

So far we have looked at using the information that exists to drive ourselves into new combinations of options, new states. There are many such states possible, yet all form part of what is already available, our current world possibilities. Going beyond this needs something else, a way to add an ingredient that takes us beyond the possible into the impossible. This is a jump to a newly created area of state space, a quantum leap into the unknown, into options that didn't previously form any part of reality.

Such possibilities require randomness, a move away from deterministic methods of analysis and control into a new world of chance and hope. Here we enter the stochastic world of probabilities, a world where what happens isn't based on the past at all but can come into existence spontaneously. This sort of thing is familiar from quantum theory, where particle pairs can materialise from the quantum vacuum and dematerialise again, but this is is usually considered irrelevant to our macroscopic world. Yet in the new thinking, based upon chaotic systems, even such quantum effects can create massive outcomes, the tiny perturbation is amplified exponentially until it shifts the macro system to a completely novel state, a bifurcation in properties - state space expands into a new modality, its maximum entropy grows but local order increases also.

The Future

The future is always indeterminate, sufficient chaos resides in life's processes such that all plans are merely possibilities, assumptions from limited knowledge. Certainty is not part of life. Given this, our future state cannot be predicted from our present one, we could not predict the personal computer from the steam engine, or the plastic mackintosh from the bearskin. Which direction we choose to pursue is entirely our choice, all options are open to us unless we deliberately close them off, unless we deliberately restrict our own choices out of fear or prior knowledge.

All human cultures have constraints, some are sensible (e.g. do not kill), some trivial (e.g. fashions), some may have had historical significance but are now mere tradition (e.g. do not eat pork). Our choices are environmentally affected, what was silly in past cultures (jumping off cliffs) may be all the rage today (if you have an hang glider!). Past rules are replaceable, past constraints transcendable. The impossible just hides behind the wall of ignorance and prejudice. Tomorrow we can let it out...

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