The Beginning of Infinity: Explanations That Transform the World (6 page)

Suppose for the sake of argument that you thought of the axis-tilt theory yourself. It is your conjecture, your own original creation. Yet because it is a good explanation – hard to vary – it is not yours to modify. It has an autonomous meaning and an autonomous domain of applicability. You cannot confine its predictions to a region of your choosing. Whether you like it or not, it makes predictions about places both known to you and unknown to you, predictions that you have thought of and ones that you have not thought of. Tilted planets in similar orbits in other solar systems must have seasonal heating and cooling – planets in the most distant galaxies, and planets that we shall never see because they were destroyed aeons ago, and also planets that have yet to form. The theory reaches out, as it were, from its finite origins inside one brain that has been affected only by scraps of patchy evidence from a small part of one hemisphere of one planet – to infinity. This
reach
of explanations is another meaning of ‘the beginning of infinity’. It is the ability of some of them to solve problems beyond those that they were created to solve.

The axis-tilt theory is an example: it was originally proposed to explain the changes in the sun’s angle of elevation during each year. Combined with a little knowledge of heat and spinning bodies, it then explained seasons. And, without any further modification, it also explained why seasons are out of phase in the two hemispheres, and why tropical regions do not have them, and why the summer sun shines at midnight in polar regions – three phenomena of which its creators may well have been unaware.

The reach of an explanation is not a ‘principle of induction’; it is not something that the creator of the explanation can use to obtain or justify it. It is not part of the creative process at all. We find out about it only after we have the explanation – sometimes long after. So it has nothing to do with ‘extrapolation’, or ‘induction’, or with ‘deriving’ a theory in any other alleged way. It is exactly the other way round: the reason that the explanation of seasons reaches far outside the experience of its
creators is precisely that it
does not
have to be extrapolated. By its nature as an explanation, when its creators first thought of it, it already applied in our planet’s other hemisphere, and throughout the solar system, and in other solar systems, and at other times.

Thus the reach of an explanation is neither an additional assumption nor a detachable one. It is determined by the content of the explanation itself. The better an explanation is, the more rigidly its reach is determined – because the harder it is to vary an explanation, the harder it is in particular to construct a variant with a different reach, whether larger or smaller, that is still an explanation. We expect the law of gravity to be the same on Mars as on Earth because only one viable explanation of gravity is known – Einstein’s general theory of relativity – and that is a universal theory; but we do not expect the
map
of Mars to resemble the map of Earth, because our theories about how Earth looks, despite being excellent explanations, have no reach to the appearance of any other astronomical object. Always, it is explanatory theories that tell us which (usually few) aspects of one situation can be ‘extrapolated’ to others.

It also makes sense to speak of the reach of non-explanatory forms of knowledge – rules of thumb, and also knowledge that is implicit in the genes for biological adaptations. So, as I said, my rule of thumb about cups-and-balls tricks has reach to a certain class of tricks; but I could not know what that class is without the explanation for why the rule works.

Old ways of thought, which did not seek good explanations, permitted no process such as science for correcting errors and misconceptions. Improvements happened so rarely that most people never experienced one. Ideas were static for long periods. Being bad explanations, even the best of them typically had little reach and were therefore brittle and unreliable beyond, and often within, their traditional applications. When ideas did change, it was seldom for the better, and when it did happen to be for the better, that seldom increased their reach. The emergence of science, and more broadly what I am calling the Enlightenment, was the beginning of the end of such static, parochial systems of ideas. It initiated the present era in human history, unique for its sustained, rapid creation of knowledge with ever-increasing reach. Many have wondered how long this can continue. Is it inherently bounded? Or is this the
beginning of infinity – that is to say, do these methods have unlimited potential to create further knowledge? It may seem paradoxical to claim anything so grand (even if only potentially) on behalf of a project that has swept away all the ancient myths that used to assign human beings a special significance in the scheme of things. For if the power of the human faculties of reason and creativity, which have driven the Enlightenment, were indeed unlimited, would humans not have just such a significance?

And yet, as I mentioned at the beginning of this chapter, gold can be created only by stars and by intelligent beings. If you find a nugget of gold anywhere in the universe, you can be sure that in its history there was either a supernova or an intelligent being with an explanation. And if you find an explanation anywhere in the universe, you know that there must have been an intelligent being. A supernova alone would not suffice.

But – so what? Gold is important
to us
, but in the cosmic scheme of things it has little significance. Explanations are important to us: we need them to survive. But is there anything significant, in the cosmic scheme of things, about explanation, that apparently puny physical process that happens inside brains? I shall address that question in
Chapter 3
, after some reflections about appearance and reality.

Explanation
   Statement about what is there, what it does, and how and why.

Reach
   The ability of some explanations to solve problems beyond those that they were created to solve.

Creativity
   The capacity to create new explanations.

Empiricism
   The misconception that we ‘derive’ all our knowledge from sensory experience.

Theory-laden
   There is no such thing as ‘raw’ experience. All our experience of the world comes through layers of conscious and unconscious interpretation.

Inductivism
   The misconception that scientific theories are obtained by generalizing or extrapolating repeated experiences, and that the
more often a theory is confirmed by observation the more likely it becomes.

Induction
   The non-existent process of ‘obtaining’ referred to above.

Principle of induction
   The idea that ‘the future will resemble the past’, combined with the misconception that this asserts anything about the future.

Realism
   The idea that the physical world exists in reality, and that knowledge of it can exist too.

Relativism
   The misconception that statements cannot be objectively true or false, but can be judged only relative to some cultural or other arbitrary standard.

Instrumentalism
   The misconception that science cannot describe reality, only predict outcomes of observations.

Justificationism
   The misconception that knowledge can be genuine or reliable only if it is justified by some source or criterion.

Fallibilism
   The recognition that there are no authoritative sources of knowledge, nor any reliable means of justifying knowledge as true or probable.

Background knowledge
   Familiar and currently uncontroversial knowledge.

Rule of thumb
   ‘Purely predictive theory’ (theory whose explanatory content is all background knowledge).

Problem
   A problem exists when a conflict between ideas is experienced.

Good/bad explanation
   An explanation that is hard/easy to vary while still accounting for what it purports to account for.

The Enlightenment
   (The beginning of) a way of pursuing knowledge with a tradition of criticism and seeking good explanations instead of reliance on authority.

Mini-enlightenment
   A short-lived tradition of criticism.

Rational
   Attempting to solve problems by seeking good explanations; actively pursuing error-correction by creating criticisms of both existing ideas and new proposals.

The West
   The political, moral, economic and intellectual culture that has been growing around the Enlightenment values of science, reason and freedom.

– The fact that some explanations have reach.

– The universal reach of some explanations.

– The Enlightenment.

– A tradition of criticism.

– Conjecture: the origin of all knowledge.

– The discovery of how to make progress: science, the scientific revolution, seeking good explanations, and the political principles of the West.

– Fallibilism.

Appearances are deceptive. Yet we have a great deal of knowledge about the vast and unfamiliar reality that causes them, and of the elegant, universal laws that govern that reality. This knowledge consists of explanations: assertions about what is out there beyond the appearances, and how it behaves. For most of the history of our species, we had almost no success in creating such knowledge. Where does it come from? Empiricism said that we derive it from sensory experience. This is false. The real source of our theories is conjecture, and the real source of our knowledge is conjecture alternating with criticism. We create theories by rearranging, combining, altering and adding to existing ideas with the intention of improving upon them. The role of experiment and observation is to choose between existing theories, not to be the source of new ones. We interpret experiences through explanatory theories, but true explanations are not obvious. Fallibilism entails not looking to authorities but instead acknowledging that we may always be mistaken, and trying to correct errors. We do so by seeking good explanations – explanations that are hard to vary in the sense that changing the details would ruin the explanation. This, not experimental testing, was the decisive factor in the scientific revolution, and also in the unique, rapid, sustained progress in other fields that have participated in the Enlightenment. That was a rebellion against authority which, unlike most such rebellions, tried not to seek authoritative
justifications for theories, but instead set up a tradition of criticism. Some of the resulting ideas have enormous reach: they explain more than what they were originally designed to. The reach of an explanation is an intrinsic attribute of it, not an assumption that we make about it as empiricism and inductivism claim.

Now I’ll say some more about appearance and reality, explanation and infinity.

A galaxy is a mind-bogglingly huge thing. For that matter, a star is a mind-bogglingly huge thing. Our own planet is. A human brain is – in terms of both its internal complexity and the reach of human ideas. And there can be thousands of galaxies in a cluster, which can be millions of light years across. The phrase ‘thousands of galaxies’ trips lightly off the tongue, but it takes a while to make room in one’s mind for the reality of it.

I was first stunned by the concept when I was a graduate student. Some fellow students were showing me what they were working on: observing clusters of galaxies – through
microscopes
. That is how astronomers used to use the Palomar Sky Survey, a collection of 1,874 photographic negatives of the sky, on glass plates, which showed the stars and galaxies as dark shapes on a white background.

They mounted one of the plates for me to look at. I focused the eyepiece of the microscope and saw something like this:

The Coma cluster of galaxies

Those fuzzy things are galaxies, and the sharply defined dots are stars in our own galaxy, thousands of times closer. The students’ job was to catalogue the positions of the galaxies by lining them up in cross-hairs and pressing a button. I tried my hand at it – just for fun, since of course I was not qualified to make serious measurements. I soon found that it was not as easy as it had seemed. One reason is that it is not always obvious which are the galaxies and which are merely stars or other foreground objects. Some galaxies are easy to recognize: for instance, stars are never spiral, or noticeably elliptical. But some shapes are so faint that it is hard to tell whether they are sharp. Some galaxies appear small, faint and circular, and some are partly obscured by other objects. Nowadays such measurements are made by computers using sophisticated pattern-matching algorithms. But in those days one just had to examine each object carefully and use clues such as how fuzzy the edges looked – though there are also fuzzy objects, such as supernova remnants, in our galaxy. One used rules of thumb.