What good were five weeks reading the cult classic by David Deutsch, The Beginning of Infinity (Allen Lane, 2011)? Other than being seen reading it on the Tube, here are a few ideas.
Knowing
Mr Deutsch takes issue with the idea that testability is the only requirement of a good theory.
Some background. The scientific method is understood to mean that a theory must be both "falsifiable" and "testable". Falsifiability means its predictions ought to be such that certain outcomes can be imagined which could in principle prove the theory wrong. Testability means that those outcomes can be sought in practice. Religious doctrines are unfalsifiable because they do not, even in principle, admit outcomes which could prove them wrong: they predict the world being exactly the way it is, so that any observation cannot but confirm them. By contrast, String Theory is said to be falsifiable but untestable, because its predictions can only be evaluated in scenarios where both quantum and gravitational effects are simultaneously observable - meaning inside either a black hole or a big bang or a large hadron collider the size of a galaxy. By these definitions, testability subsumes falsifiability.
Mr Deutsch's argument is that making predictions (even accurate ones) does not amount to having a theory. In a conjuring trick, predicting that the person sawn in half would later appear on stage unharmed may prove accurate. And one could even acquire a bundle of such predictions and call them "A Theory for the Outcomes of Conjuring Tricks". However, while being testable, such a theory would not address, let alone solve, the question of how conjuring tricks actually work. What is missing is "an explanation: a statement of the reality that accounts for the appearance". In other words, we need a story. Not everyone agrees: instrumentalists prefer to "shut up and calculate", rather than aspire to make any grand claims about the nature of reality. They, says Mr Deutsch, are wrong.
However, not any story will do. Plenty of theories, while both testable and explanatory, are nevertheless wrong. Ancient Greeks, for instance, ascribed the bleakness of winter to Demeter's sorrow, each time her daughter Persephone had to go on an annual trip to Hades (god of the underworld), which was stipulated in their marriage contract and enforced by a magic seed. Such a theory is testable (seasons can be observed) and provides an explanation. However, the explanation is bad. It is bad because "nothing in the problem of why winter happens is addressed by postulating specifically a marriage contract or a magic seed". The details are completely arbitrary and "whenever it is easy to vary an explanation without changing its predictions, one could just as easily vary it to make different predictions if they were needed". So if the Greeks had travelled to the southern hemisphere and had encountered Summer in winter time, instead of abandoning their myth, they could have simply altered it to match this new observation: Demeter only "banishes warmth from her vicinity", say. Think - Problem of Evil and how flexibly religions bend their explanations to take it into account, without however changing their conclusion (that God is omniscient, omnipotent and benevolent). By contrast, consider the good explanation for why seasons happen: Earth's rotational axis is tilted relative to the plane of its orbit and this varies the angle at which sun rays encounter Earth's surface; this changes - throughout the year - the amount of energy bestowed on any given area of land. This explanation cannot have any of its details changed arbitrarily and still make sense. In other words, along with being testable and explanatory, it is also precise. There is no superfluity. Moreover, it obeys the laws of logic and finally, it fits in neatly with all other good explanations: those concerning gravity, geometry, thermodynamics and so on.
Finally, good explanations have reach. The axis-tilt explanation was proposed to explain variations in the sun's angle of elevation throughout the year, but combined with some knowledge about heat and spinning bodies it also explains seasons and, without further modifications, the differences in seasons between hemispheres, the lack of seasons in tropical regions and the months-long days around the poles. Good explanations have reach because they elucidate underlying laws of reality, which themselves have reach. This is a consequence from the nature of reality: "the reach of explanations cannot be limited by fiat". It is good fortune that we live in a "computation-friendly, prediction-friendly and explanation friendly" universe (the fine-tuning problem is discussed at length).
Knowledge is the accumulation of "good explanations": stories that are testable, explanatory, hard to vary while still fulfilling their function, consistent with logic and consistent with each other. Good explanations have reach.
***
How do these good explanations come about? Not through observation, argues Mr Deutsch, against the grain of empiricism. "[No] amount of observing will correct [a] misconception until after one has thought of a better idea". Instead, the seeds of progress are creative conjectures, that is - imaginative educated guesses. These are candidates which, to become good explanations, must survive the arena of critical thinking, where their explanatory prowess, consistency with logic and consistency with existing good explanations are challenged and settled. Testability, then, is just one of the many tools employed by the tradition of criticism in its pursuit to turn the best candidates into new good explanations. "We do not test every testable theory", remarks Mr Deutsch, only the plausible ones.
Moreover, testability actually relies on existing good explanations: all observation is laden with theory. The book recounts the anecdote of Karl Popper starting his lectures with the single instruction "Observe!", followed by a long silence; eventually, someone would ask "What?", proving his point that knowledge is required in advance of any observation. To observe a distant galaxy, astrophysicists interpose a lot more technology between it and their eyes than those ancient astronomers staring at the night sky: a telescope, a camera, software for aiming and tuning its lenses, software for sifting through the large piles of raw data, another camera, a photographic lab and a microscope. Yet, they "see" the galaxy much clearer, for all that.
In other words, "theories aren't testable in isolation". Since observation is laden with theory, any experiment ends up testing a whole bundle of hypotheses, not just the one under investigation. Consequently, a negative result can be ambiguous: maybe your hypothesis was false, but maybe the machine was miscalibrated or the protocol forgone, or indeed perhaps an altogether unknown phenomenon interfered.
Finally, theory cannot be derived from observation because: there is no shortage of data points. We are drowning in evidence of real phenomena. However, as any company now sitting atop a mountain of raw information can attest, such evidence is useless unless someone knows what to do with it. Creative conjectures must come first. I was once told that programming is the future of journalism, but I reckon programming merely helps with testing a conjecture, that is - once and only once one has been creatively imagined. If programming was the only skill required of a data scientist, I would be typing this from Mars.
Good explanations are formed through the alternating process of creatively generating new conjectures and pitting them against one another in the arena of rational criticism (where testability is but one of the tools).
***
From this epistemic outlook, it follows that there is such a thing as objective reality. That is, Mr Deutsch opposes postmodernism with its claim that "because all ideas, including scientific theories, are conjectural and impossible to justify, they are essentially arbitrary". Nonsense, he replies: conjectures can be evaluated in the arena of critical thinking. And rejecting all criticism as mere "narrative", as postmodernism would have it, is deadly - for it removes the means of identifying and correcting errors.
In other words, while on a timescale long enough all explanations are wrong, right now some are objectively less wrong than others.
The aim of knowledge creation is not certainty, however pleasant an emotion that might be. The aim of knowledge creation is progress - from being wrong, to being less wrong and from these problems to other, ever better problems. (He reckons science would be better served if its theories were known as 'misconceptions': thus, "Einstein's Misconception of Gravity was an improvement on Newton's Misconception, which was an improvement on Kepler's".) Such thinking might prevent people from needing to be reminded "that science claims neither infallibility nor finality". Or, as Karl Popper put it: "It might be well for all of us to remember that, while differing in the various little bits we know, in our infinite ignorance we are all equal".
Hence his rejection of instrumentalism, with its coyness in making statements about reality. He notes the split within the scientific community. The Copenhagen interpretation of quantum mechanics prefers to "shut up and calculate", while paleontology speaks of dinosaurs' existence as an "explanation of fossils" (rather than "an interpretation of our best theory of fossils").
Objective knowledge therefore is attainable because competition in the arena of critical thinking is a real possiblity. There are real criteria by which competing conjectures may be assessed: reasonableness, testability, usefulness, consistency with logic, consistency with our current best explanations and so on. In the end, all good explanations are pieces of the same puzzle: the puzzle of reality.
In conclusion, people who converge on truth, converge with each other. And progress is the best defense against irrationality, postmodernism, pessimism and relativism.
Footnote. Elsewhere in the book: "And then we hone our guesses, and then fashion the best ones into a sort of waking dream of reality.. A waking dream that corresponds to reality. But there is more. It is a dream of which you then gain control".
This got me thinking: his epistemology works even if you accept the postmodernist view that all theories are mere "narratives". After all, existence is just energy and mass, a spasmodic stream of sensations, chaos. It lends itself to various interpretations. It doesn't really matter if the explanations represent "what is really there": they just have to be precise, compelling, consistent with observation (meaning physics), with logic and with each other. Who cares if they are not what the universe intended? More power to us. The universe has no intentions.
However, "reality" exists in the sense that it is the name by which we call the external, shareable story we are all weaving together. It is made "real" and "objective" through our communal participation. No single human can alter it substantially, but as a species there is nothing really preventing us from changing the story any way we want (subject to physics, logic etc). Individually, we are restricted. Together, we are free. (I feel compelled to appreciate the irony.)
The reality of abstractions
Next, Mr Deutsch attempts to show that, in addition to accepting good explanations as being statements about reality, it is important also to accept that the higher-level abstractions which these explanations often reference are realities too. This is his anti-reductionist stance.
To this end, he uses a thought experiment created by Douglas Hofstadter in I am a Strange Loop (2007). Imagine a computer built out of dominoes. The pieces are spring-loaded (they both fall and rise), there are loops. bifurcations, junctions and logical gates. A stretch of fallen dominoes represents 1; left standing - 0. One domino represents the 'on' switch. The input is a number (say 641). The output is binary: a particular domino left standing if the number is prime and knocked over otherwise. Now the calculation begins. There is a flurry of motion, dominoes falls and rise in waves and loops and complicated patterns. It all goes on for some time (a computer made out of dominoes is not very efficient). Now imagine that an external observer notices the particular domino which, despite the general commotion, remains standing. Why, she asks, is that domino never knocked over? To this sort of question, there are two types of answer.
The first type of answer, the reductionist answer, will try to give an account in terms of basic principles, meaning dominoes: the domino in question never falls because none of its neighbours ever fall, which is to say none of the patterns of motion initiated by knocking over the 'on'- switch domino ever included it. This is correct. But we knew that already. The reductionist answer feels unsatisfying because it attempts an explanation at the wrong level of emergence.
The second type of answer will simply say: because 641 is prime. This answer certainly seems to make a lot more sense. However, it makes no reference to the dominoes at all. Instead, it explains why the domino is left standing by referencing a pure abstraction: primality. And that is the point: Hofstadter's argument is that primality must be part of any explanation attempting to elucidate why the domino did not fall. In fact, the notion of causation itself is emergent and abstract. We cannot perceive causation, remarked David Hume, only a succession of events.
As another example, take trying to explain why "one particular copper atom at the top of the nose of the statue of Sir Winston Churchill stands in Parliament Square in London". An explanation in terms of atoms alone may well exist, perhaps a law that describes the trajectory of that atom from the mine via the smelter to the sculpting studio, given a known earlier state of the universe. But a more satisfying and potentially more useful explanation, would be one which referenced war and politics and the culture of celebrating influential people by moulding their shapes in copper and mounting them onto the pedestals of public squares.
"There is no inconsistency in having multiple explanations of the same phenomenon, at different levels of emergence".
Consequently, he rejects the notion, supported by Dan Dennett and eventually even Hofstadter, that consciousness, or indeed Artificial Intelligence, is just a bag of tricks. He would like an explanation at a higher level of emergence.
And in Ethics, he rejects the claim that, just because "you can't derive an ought from an is", there can be no morality justified by reason. "Certainly you can't derive an ought from an is, but you can't derive a factual theory from an is either. That is not what science does". Reductionism in philosophy, he continues, therefore fails in just the same way. Rather than deriving an ought from an is, better to attempt an explanation at a higher-level of emergence (using concepts such as tolerance or virtue). And in any case, what is (pleasure, pain, preference) may very well be shaped by the high-level abstraction of what constitutes a good life.
Read on: David Deutsch on optimism, societies and Ethics
