Beyond Entailing Law?

This is the fourth in a series of posts whose central scientific point is stated as a conclusion, not a question like the title above. We seem, in the biosphere, to be beyond Newton, beyond Laplace, beyond Einstein, beyond Schrodinger, beyond Reductionism, and beyond Entailing Law.

If so, we must rethink our view of the world and our place in it.

The previous three blog posts were: i. Law, Useless Entailment, No Law. ii. The Re-Enchantment of Humanity. iii. From Physics to Biology And Society: Are Finance and Scientific Images Of The World Related, by senior mathematician Giuseppe Longo of the Ecole Normal Superieur, Paris.

The central scientific issue of my and Longo's posts is this: In the evolution of the biosphere, and human life, we cannot pre-state the ever-changing state space of the ever-changing and evolving biosphere.

It follows that we can have no entailing law for we do not know and cannot know the boundary conditions which Newton taught us are necessary for entailment. We truly are beyond entailing law.

I begin with Longo. In his post of June 13, he pointed out from his 2006 book that the fundamental laws of physics rest in symmetries, as spelled out by Noether's theorems (and Weyl's work). These symmetries arise arise in a fixed and pre-stated space or set of possibilities. And these spaces of possibilities may be mathematically pre-given, because they are themselves given in terms of the symmetries.

But for the evolution of life and human life, says Longo, the state space is ever changing and cannot be pre-stated, so too for human life. This means we cannot do what Newton taught us to do.

Consider a billiard table with balls rolling on it. Newton tells us to: i. measure the positions and momenta (and diameters of the balls), ie the initial conditions; ii. state the boundary conditions comprised by the edges of the table; iii. use his three laws of motion in differential-equation form; iv. integrate those equations, subject to the initial and boundary conditions, to obtain the future and past (often deterministically chaotic) trajectories of all the balls. This is the paradigm of entailing law, even when deterministic chaos renders prediction weak or absent since we cannot measure initial conditions to arbitrary accuracy.

But Newton's move requires that we be able to state the boundary conditions. Suppose, instead, that we had no idea of the shape of the table and, even worse, it was changing all the time in ways we did not know. Then we could not integrate his equations to yield the entailed trajectories of the billiard balls. There would be no entailing law.

Similarly, if we do not know the ever-changing state space of the evolution of the biopshere, or economy, we cannot state the boundary conditions, since they are co-constituted along and by the very dynamics of evolution (or history), so can have no entailing law.

Then there really is no entailing law for the detailed evolution of the biosphere, where we do not have to think of human, responsible free will, or the economy either. We are, if this is correct, as it surely seems to be, beyond Newton, Laplace, Einstein, Schrodinger, Reductionism and Entailing Law.

Joseph Traub, professor of computer science at Columbia University, added in conversation that we have no mathematical model, nor can we simulate a system without knowing its boundary conditions.

I have made the same point in my books Investigations, 2000, Reinventing the Sacred, 2008, and in many past posts, including two of the past three.

I build my case on the now familiar Darwinian pre-adaptations. Recall that such a pre-adaptation is a causal feature of an organism of no selective value in the current environment that might become of selective value in a different environment. Typically, a new biological function arises.

My standard example is the swim bladder, a sac in some fish partly filled with air and water, whose ratio adjusts neutral buoyancy in the water column. Paleontologists believe the swim bladder arose from the lungs of lung fish. Water got into some lung(s) and these were poised to evolve into swim bladders. I'll skip most of my familiar issues to get to the central one: Do you think you could finitely pre-state all possible Darwinian pre-adaptations in the next million years just for humans?

We all say "no." Why? Well, how would we specify all possible selective conditions? Know we had listed them all? How would we pre-state all the features of one or many organisms that might become preadaptations? There seems to be no way to do so.

But this means that we do not know what I call the adjacent Possible (state space) of the evolution of the biosphere by Darwinian pre-adaptations. Like Longo, I claim we do not know the ever changing configuration space of possibilities for evolution of the biosphere, econosphere and upward.

Now a given adjacent possible empty niche corresponds to the boundary conditions that confine and mold natural selection in the evolution of the biosphere. But we do not know ahead of time those boundary conditions.

Then, once again, we cannot follow Newton's prescription: specify the initial conditions; specify the boundary conditions; specify the laws of motion and integrate to derive the entailed future trajectory of the system. We cannot do this because we do not know ahead of time the boundary conditions. This suffices to show that there is no entailing law for the evolution of the biosphere, econosphere or history.

I see as yet nothing wrong with the implications of Longo's and my arguments. They require careful scrutiny for, if correct, we must modify our age-old dream of a final theory that entails the entire becoming of the universe, as S. Weinberg argued in Dreams of a Final Theory.

If the above is correct, we truly are beyond Newton, beyond Laplace, beyond Einstein, beyond Schrodinger, beyond reductionism and beyond entailing law.

But we are not bereft of the possibilities of a positive science beyond reductionism and entailing law. I will begin to discuss this in my next series of posts, starting with collectively autocatalytic sets, and cells and the biosphere and its evolution, all fulfilling Immanuel Kant's dictum that, roughly, in an organized being, the parts exist for and by means of the whole and the whole exists (in the real universe) by means of the parts.

Here the explanatory arrows not only point upward, as Weinberg would have it in reductionism, from the parts to the whole, but downwards from the whole to the parts whose behaviors it organizes. Following Kant and Kepa Ruiz Mirazo of the University of the Basque Country, call such systems "autonomous." They mutually can make co-evolving worlds together, such as the biosphere, beyond entailing law.

I thank Giuseppe Longo for his useful comments on this post.