Impossibility: The Limits of Science and the Science of Limits

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Brains must be able to perform these abbreviations. This also requires an environment that is simple enough and displays enough order, to make this encapsulation possible over some dimensions of time and space.

Impossibility: The Limits of Science

Our minds do not merely gather information; they edit it and seek particular types of correlation. They have become efficient at extracting patterns in collections of information. When a pattern is recognized it enables the whole picture to be replaced by a briefer summary form which can be retrieved when required.

These inclinations are helpful to us and expand our mental powers.

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We can retrieve the partial picture at other times and in different circumstances, imagine variations to it, extrapolate it, or just forget it. Often, great scientific achievements will be examples of one extraordinary individual's ability to reduce a complex mass of information to a single pattern. Nor does this inclination to abbreviate stop at the door of the laboratory. Beyond the scientific realm we might understand our penchant for religious and mystical explanations of experience as another application of this faculty for editing reality down to a few simple principles which make it seem under our control.

All this gives rise to dichotomies. Our greatest scientific achievements spring from the most insightful and elegant reductions of the superficial complexities of Nature to reveal their underlying simplicities, while our greatest blunders often arise from the oversimplification of aspects of reality that subsequently prove to be far more complex than we realized.

Our penchant for completeness is closely associated with our liking for symmetry. We have a natural sensitivity for pattern and an appreciation of symmetry that quickly picks up subtle deviations from perfect symmetry.

Extreme Physics

Our desire for a full and perfect description of the world owes much to this curious sensitivity. Where does it originate? A powerful means of understanding why we possess many odd abilities is to recognize that our mental faculties evolved several million years ago in environments that were very different from those in which we now live. In that primitive environment certain sensitivities would tend to enhance the survival prospects of those that possessed them with respect to those who did not.

Those attributes which made survival more probable would be the expression of some complex genetic cocktail with no predetermined purpose. Although one feature of an attribute might aid survival, there might be by-products of this attribute which showed up subsequently in all sorts of unexpected ways.

Many of our aesthetic sensitivities have arisen in this indirect manner. Accordingly, we can identify good evolutionary reasons why we might be expected to have developed an acute appreciation for symmetry. If we look at the natural environment we see that lateral left-right symmetry is a very effective discriminator between living and non-living things in a crowded scene.

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You can tell when a living creature is looking at you. This sensitivity has a clear survival value. It enables you to recognize potential predators, mates, and meals. This biological source of our appreciation of symmetry is supported by the fact that our most acute sensitivity for symmetry is manifested in our appreciation of the human form, especially the face Fig.

Symmetry of bodily form--especially that of the face--is our most common initial indicator of human beauty, and we go to enormous lengths to enhance it and protect it. In lower animals it is an important indicator of mates. In humans it has had all manner of by-products which influence our aesthetic appreciation and underlie our acute sensitivity to patterns, symmetry, and form. Remarkably, no computer has yet managed to reproduce our many levels of visual sensitivity to patterns. This sensitivity means that deviations from symmetry are quickly identified and have a sophisticated interpretation all their own.

Because they capture our attention so dramatically they are much used in English humour. Simple games, like noughts and crosses, are entirely predictable. With a little thought you can devise a strategy that prevents you from ever losing, no matter who goes first and what moves your opponent makes. Draughts and chess or Chinese chess are games that are more satisfying because they lack this completely predictable completeness.

Each player has an L-shaped token which can be placed anywhere on the small board. After placing the L-piece, either one, two, or neither of the black spots may be placed on the empty squares. The aim of the game is to prevent your opponent from moving his L-shape on the next move.

The starting positions and a typical winning configuration are shown in Fig. Some games with deceptively simple rules, like John Horton Conway's Game of Life, possess so many developments of great complexity that it is impossible to determine all the possible configurations that could arise. In fact, this game has been shown to share the same level of complexity as the whole of arithmetic. We might wonder whether our investigations of the natural world will eventually be completed in any sense.

Perhaps all the laws of Nature might be found, even if all their outworkings might not be listable? Like the perennial noughts-and-crosses addict, would we then cease to be surprised by anything we found in the natural world? In later chapters we shall return many times to look at this question from a variety of different angles. Those for whom all things are possible With men this is impossible; but with God all things are possible.

Most human cultures have displayed a desire to worship or acknowledge beings or spirits greater than themselves. Their powers may be exaggerated human ones, or powers that humans do not possess in any measure at all. In the most extreme case the gods may possess limitless powers which enable them to do anything at all and to know everything. This deceptively simple idea is not without its problems. We can see that it is attractive for the adherents of a particular deity to believe in their god's limitless powers, if only to avoid subservience to the god next door.

But looking a little deeper, we see that if their god's actions were limited in some way, then whatever, or whoever, was doing the limiting would have a greater claim to be in control of events than the god.

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If your god has no jurisdiction over the wind, then the wind has a justifiable claim to be a superior deity. Eventually, someone will appeal to the superior power of the wind. Although a deity of limited powers has a credibility problem, one of limitless power seems to have far deeper problems of principle.

How can there exist a Being for whom nothing is impossible? Surely some things must be impossible or chaos and contradiction beckons?


If a deity has defining characteristics then there must exist opposites of those attributes which define impossible actions for him or her. Few traditional religions now grapple with these hard questions, yet they are questions that clearly trouble many scientists. The late Heinz Pagels tells how this question was decisive in destroying his early belief in God: When I was in high school I remember reflecting on what kind of being God could possibly be--I was curious I also remember asking that if God was all-powerful, could he do things like change the laws of logic?

If he could change the laws of logic, then he was a kind of lawless Being incomprehensible to the human mind. On the other hand if he couldn't change the laws of logic, he wasn't all-powerful. These alternatives left me dissatisfied Ancient authorities tried to distinguish more finely between actions which were in character and those which were out of character, regarding the latter as logically impossible for a being with the attributes of deity.

But these distinctions seem rather slippery to modern ears. Some apologists for the miraculous stress the incompleteness of our knowledge of what is possible in the Universe, and have sought to accommodate God's action in exceptions to the laws of Nature, while others have tried to explain it by our inability to determine the future course of chaotically sensitive situations. This feature also serves to establish one of the defining differences between God and mankind: human limits are what fix the great gulf between God and humanity.

Thus, when magicians and shamans arise they seek confirmation of their status by demonstrating apparently miraculous powers and by their ability to perform acts which are impossible for the rest of us. They endorse a view of the Universe in which there is a hierarchy of beings whose status rises as the limitations on their actions grow fewer and weaker. Our religious traditions reveal that restrictions on human thoughts and actions are often imposed by the gods. These are not limits which our mortal nature prevents us surpassing: they are like the motorway speed limit rather than the law of gravity.

They are presented as taboos that we ignore at our peril. A huge range of human cultures have taboos, whether it be on naming gods, visiting certain places, or counting their populations. Just as earthly rulers distinguish themselves from their subjects by the imposition of constraints upon their behaviour which are not of any obvious benefit to the rulers, except to impress their subjects, so it is imagined that the deity must follow similar practices.

The habit of obedience is thought to be a valuable lesson for everyone to learn--a notion that any army sergeant-major will heartily endorse. Thus we see that the notion of impossibility has lodged itself effortlessly at the heart of our religious thinking in many different ways. Eating from the Tree of Knowledge was forbidden in order to prevent awareness of some new form of knowledge.

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