These days see a tremendous number of significant scientific news, and it is hard to say which one has the highest significance. Climate models indicate that we are past crucial tipping points and are irrevocably headed for a new, difficult age for our civilization. Mark Van Raamsdonk expands on the work of Brian Swingle and Juan Maldacena, and demonstrates how we can abolish the idea of spacetime in favor of a discrete tensor network, thus opening the way for a unified theory of physics. Bruce Conklin, George Church and others have given us CRISPR, a technology that holds the promise for simple and ubiquitous gene editing. Deep Learning starts to tell us how hierarchies of interconnected feature detectors can autonomously form a model of the world, learn to solve problems, and recognize speech, images and video.
It is perhaps equally important to notice where we lack progress: sociology fails to teach us how societies work, philosophy seems to have become barren and infertile, the economical sciences seem to be ill-equipped to inform our economic and fiscal policies, psychology does not comprehend the logic of our psyche, and neuroscience tells us where things happen in the brain, but largely not what they are.
In my view, the 20th century’s most important addition to understanding the world is not positivist science, computer technology, spaceflight, or the foundational theories of physics. It is the notion of computation. Computation, at its core, and as informally described as possible, is very simple: every observation yields a set of discernible differences.
These, we call information. If the observation corresponds to a system that can change its state, we can describe these state changes. If we identify regularity in these state changes, we are looking at a computational system. If the regularity is completely described, we call this system an algorithm. Once a system can perform conditional state transitions and revisit earlier states, it becomes almost impossible to stop it from performing arbitrary computation. In the infinite case, that is, if we allow it to make an unbounded number of state transitions and use unbounded storage for the states, it becomes a Turing Machine, or a Lambda Calculus, or a Post machine, or one of the many other, mutually equivalent formalisms that capture universal computation.
Computational terms rephrase the idea of "causality," something that philosophers have struggled with for centuries. Causality is the transition from one state in a computational system into the next. They also replace the concept of "mechanism" in mechanistic, or naturalistic philosophy. Computationalism is the new mechanism, and unlike its predecessor, it is not fraught with misleading intuitions of moving parts.
Computation is different from mathematics. Mathematics turns out to be the domain of formal languages, and is mostly undecidable, which is just another word for saying uncomputable (since decision making and proving are alternative words for computation, too). All our explorations into mathematics are computational ones, though. To compute means to actually do all the work, to move from one state to the next.
Computation changes our idea of knowledge: instead of treating it as justified true belief, knowledge describes a local minimum in capturing regularities between observables. Knowledge is almost never static, but progressing on a gradient through a state space of possible world views. We will no longer aspire to teach our children the truth, because like us, they will never stop changing their minds. We will teach them how to productively change their minds, how to explore the never ending land of insight.
A growing number of physicists understand that the universe is not mathematical, but computational, and physics is in the business of finding an algorithm that can reproduce our observations. The switch from uncomputable, mathematical notions (such as continuous space) makes progress possible. Climate science, molecular genetics, and AI are computational sciences. Sociology, psychology, and neuroscience are not: they still seem to be confused by the apparent dichotomy between mechanism (rigid, moving parts) and the objects of their study. They are looking for social, behavioral, chemical, neural regularities, where they should be looking for computational ones.
Everything is computation.