The 'laws' of physics discovered at low levels of complexity would then simply be 'downward-emergent' approximations to the character of a more subtle and supple causal story in which the whole truly did influence the behaviour of the parts. ... Making us of science's account of future behaviour in this open metaphysical way by no means demands us to abandon the principle of sufficient reason, requiring a full explanation of the origin of what actually occurs. It is simply to conceive that the portfolio of causes that bring about the future is not limited solely to the description offered by a methodologically reductionist physics and framed only in terms of the exchange of energy between constituents. Instead, the concept of causal influence can be broadened at least to include holistic effects of an informational, pattern-forming kind. One might called this top-down form of causality 'active information.'In my opinion, Polkinghorne gets overly technical in a book apparently designed as an apologetic work for the public. In any case, here's what he's basically saying: reductionist scientists have a solely "bottom-up" approach, whereas Polkinghorne believes that a lot of our discoveries demand a more "top-down" explanation.
Let's think about this dichotomy for a bit. First, I want to stress that it is a metaphor. That is, we are not talking about a literal "top" and "bottom" to the universe. Many times metaphor is simply the only way to talk about abstract concepts like the nature of causality, but nevertheless it is often important to acknowledge the limits of our metaphors, and to be aware of the influence they have on our thinking. In this, I'm not sure the influence of the metaphor on our thinking is entirely good.
To illustrate the influence of the top down/bottom up metaphor on our thinking, consider the realm of economics (we'll talk about metaphysics a bit later). A "bottom up" approach focuses on how the microeconomic principles governing individual actors in the economy work together to form a complex order without the control of political authority. A "top down" approach focuses on the need for authority to correct and guide the behavior of the economy as a whole. Thus the "top" here refers to political authority, whereas "bottom" refers to individuals independent of political authority. The metaphor works because traditionally height has been associated with power. The king rules over his people, and his orders go down the chain of command.
The empirical question in economics is whether a complex order that allows large-scale human cooperation is possible without the guidance of political authority. In metaphorical terms, as the Keynes vs. Hayek video puts so well, should we have more bottom up or more top down?
Before turning to the metaphysical realm, we have to recognize a couple of things about the economics debate. Most free market advocates do not advocate anarchy (anarcho-capitalists excepted). In the classical theory arising from Adam Smith, laws enforced by the political authorities help shape the economic order. The difference between a command economy and a free market economy is not a matter of the government doing something versus the government doing nothing. The difference is between the government directing the whole system toward a particular goal, on the one hand, and the government treating all individuals equally without respect to particular goals, on the other hand.
Now let's turn to the realm of metaphysics, and in particular let's talk about the nature of causality. We seem to have a debate framed in terms analogous to the Keynes and Hayek debate don't we? One picture of the universe is one in which all events are reducible down to the interaction between matter and energy, the fundamental units of the physical world. The other is one in which "information" or "mind" can be taken to be another fundamental piece of the universe, guiding the physical world according to some transcendent order. It's bottom up versus top down.
The distinction is tailor-made to fit into the age-old controversy over the existence of God. Just as in economics the top down/bottom up metaphor refers to the controversy over the role of government, so in metaphysical discussion the metaphor almost has to refer to the role of God, who, it must be admitted, has often been described in terms of political authority (King, Sovereign, etc.). If we can demonstrate that order emerges in the universe, not through any conscious direction, but through the application of universal laws to material substances, doesn't this damage the case for the existence of God who intervenes in the universe? And if, on the other hand, we can demonstrate the poverty of the reductionist approach, doesn't this suggest a case for the existence of God?
Our views on this matter seen to be shaped to a certain degree by moral intuition, and, conversely, the way we think things are often influences the way we think things should be. For instance, the empirical claim that government intervention is not required to create economic order often allies itself with the moral claim that government intervention is generally wrong. Likewise, the metaphysical claim that the universe may be reduced to physical causes often allies itself with the (implicit or explicit) moral claim that God should not interfere with human freedom.
This means that often the same observations can lead to curiously different conclusions. For instance, when Polkinghorne says that he sees room for a "top down" form of causation in the universe, to me he seems to be saying no more than that the universe is not in a state of anarchy. It hardly seems like a case for the existence of God. It might be a case for a form of Deism, the belief that God has merely constructed the laws governing the universe, and everything simply goes on according to those laws. The idea that "information" can be a source of "pattern-forming" causality is really nothing more than the idea that mathematical laws applied to a large number of particles can result in order, which is the logical result of those mathematical laws. (This, by the way, is the whole point of my own mathematical research on dynamical systems.) I would think an atheist could write very nearly the same thing as Polkinghorne, and make the exact opposite theological conclusion: clearly God is not in charge of the universe, since it gets on just fine by blindly following certain laws, without conscious direction.
I can't help but think the top down/bottom up metaphor is basically misleading. To think in this way inevitably leads to a tug of war between two opposites, and I'm not sure if this is really all that enlightening. (I say this equally for both economics and metaphysics!) As Christians, we acknowledge that rather than play tug of war, Christ "emptied himself," exchanging his authority for humility. What might we say about the metaphysical nature of causation based on this upside-down image of God's authority? Unless we look for ways to upset our normal categories, I think the debate will be somewhat fruitless.