DRAFT 6/4/2007
Emergence Explained: Entities are nature’s memes
Russ Abbott
Department of Computer Science, California State University, Los Angeles
and
The Aerospace Corporation
The Aerospace Corporation
El Segundo, California
Abstract. We apply the notions developed in the preceding paper ([1]) to discuss such issues the nature of entities, the fundamental importance of interactions between entities and their environment (functionality vs. mechanism), the central and often ignored role (especially in computer science) of energy, entities as nature’s way of remembering, the aggregation of complexity, the reductionist blind spot, the similarities between biology and economics.
Emergence Explained 2/30
DRAFT 6/4/2007
1 Introduction
In [1] we characterized emergent phenomena as phenomena that may be described independently of their implementations. We credited [Anderson] with being one of the first prominent physicists to argue that new laws of nature—laws not derivable from physics—exist at various levels of complexity. While re-reading [Schrodinger] we found a significantly earlier statement of that position.
[L]iving matter, while not eluding the 'laws of physics' … is likely to involve 'other laws of physics,' hitherto unknown, which … will form just as integral a part of [the] science [of living matter] as the former.
As we pointed out in the earlier paper, there are indeed new laws, which, while consistent with the laws of physics are not reducible to them.
2 The problem
In a review of Holland’s book, Shalizi [Review] wrote the following.
Someplace … where quantum field theory meets general relativity and atoms and void merge into one another, we may take “the rules of the game” to be given. But the rest of the observable, exploitable order in the universe—benzene molecules, PV=nRT, snowflakes, cyclonic storms, kittens, cats, young love, middle-aged remorse, financial euphoria accompanied with acute gullibility, prevaricating candidates for public office, tapeworms, jet-lag, and unfolding cherry blossoms—where do all these regularities come from? Call this emergence if you like. It’s a fine-sounding word, and brings to mind southwestern creation myths in an oddly apt way.
In [Still Autonomous] Fodor wrote the following reaffirmation.
The very existence of the special sciences testifies to the reliable macrolevel regularities that are realized by mechanisms whose physical substance is quite typically heterogeneous. Does anybody really doubt that mountains are made of all sorts of stuff? Does anybody really think that, since they are, generalization about mountains-as-such won’t continue to serve geology in good stead? Damn near everything we know about the world suggests that unimaginably complicated to-ings and fro-ings of bits and pieces at the extreme microlevel manage somehow to converge on stable macrolevel properties.
Although Fodor does not use the term, the phenomena studied by the special sciences are the same sort of phenomena that we now call multiscale, i.e., emergent. Why is there emergence? Fodor continues as follows.
[T]he ‘somehow’ [of the preceding extract] really is entirely mysterious … . Why is there anything except physics? … Well, I admit that I don’t know why. I don’t even know how to think about why. I expect to figure out why there is anything except physics the day before I figure out why there is anything at all … .
2.1 Review of emergence
A key insight of the earlier paper is that new laws may arise when levels of abstraction are implemented. In software a level of abstraction is defined as a collection of object types (i.e., categories) along with operations that can be performed on objects of those types. A simple example is the collection of patterns (e.g., like gliders) in the Game of Life. Even though gliders are epiphenomenal (the only thing that really happens in the Game of Life is that cells go on and off), one can speak of gliders and glider laws, such as the velocity of a glider across the board and what happens when a glider interacts with some other pattern. One can also use gliders and other patterns to implement yet higher levels of abstractions such as a Turing Machine — and then use such a Turing Machine to do real computations.
Levels of abstraction allow one to define the notion of downward entailment, a philosophically acceptable form of what might otherwise look like downward causation. For example, glider laws allow one to speak as if a glider (which is really only an epiphenomena) is “going to a cell and turning it on.” Similarly, computability theory allows one to conclude that the halting problem for the Game of Life is not decidable.
2.2 The reductionist blind spot
In the earlier paper we argued that emergence produces objectively real phenomena (because they are distinguishable by their entropy and mass characteristics) but that interaction among emergent phenomena is epiphenomenal and can always be reduced to the fundamental forces of physics.
But the impulse to reduce away epiphenomenal interactions should be resisted. Doing so typically results in a reductionist blind spot. Clearly one can reduce a Game of Life Turing Machine to the primitive Game of Life rules. But in doing so, one loses sight of the Turing Machine’s functionality. And there is no way to get it back; one can’t write a closed form equation that takes Game of Life rules and maps them onto the computation carried out by a Turing Machine. The only way to map Game of Life rules onto a Turing Machine’s computation is by building that computation as a Game of Life epiphenomenon.
3 (Material) Entities
Our focus in the earlier paper was on the phenomenon of emergence itself. In this paper we explore the (material) entities that arise as a consequence of emergence.
As human beings we seem naturally to think in terms of entities—things or objects. Yet the question of how one might characterize what should and should not be considered an entity remains philosophically unresolved. (See, for example, [Boyd], [Laylock], [Miller], [Rosen], [Varzi Fall ‘04].) We propose to understand a material entity as any material instance of emergence that produces a physically bounded result.
In the earlier paper we distinguished between static emergence (emergence that is implemented by energy wells) and dynamic emergence (emergence that is implemented by energy flows).[1] Just as there are two categories of emergence, there are two categories of material entities: static and dynamic.
Some material entities (such as an atom, a molecule, a pencil, a table, a solar system, a galaxy) are instances of static emergence. These entities persist because they exist in energy wells. In particular, they are at an energy equilibrium.
Biological entities (such as you and I), social entities (such as a social club, a corporation, or a country), events (such as a baseball game, the meeting of an organization, a ceremony, and most other socially regimented interactions among entities) are instances of dynamic emergence. These entities dissipate energy. For such entities to persist beyond the period during which some initial energy capital is dissipated (biological entities are good examples), these entities must acquire energy from their environment. Material entities that both acquire and dissipate energy are commonly referred to as being far from equilibrium.
We do not include in our category of material entities what might be considered conceptual or Platonic entities—such as numbers, mathematical sets (and other mathematical constructs), properties, relations, propositions, categories such as those named by common nouns (such as the category of cats, but not individual cats), and ideas in general.
Nor are intellectual products such as poems and novels, scientific papers, or computer programs (when considered as texts) entities. Time instances (e.g., midnight December 31, 1999), durations (e.g., a minute), and segments (e.g., the 20th century) are also not material entities. Neither are the comparable constructs with respect to space and distance.
Since (according to our definition) every material entity is an instance of emergence and since (again according to our formulation) emergence is fundamentally a physical phenomenon (that is, it reflects either an energy well or a far-from-equilibrium system), all material entities consist of matter and energy arranged to implement some (independently describable) abstraction. Hence the referent of an idea can’t simply ipso facto be an entity. One of the prerequisites for the referent of an idea to be a material entity is that it exist in the material world. Clearly not all conceptual entities (e.g., the number 2) involve matter or energy.
Our explanation for why we tend to think of idea referents as entities is that we (i.e., human beings) evolved to understand the world in terms of material entities. We evolved to have ideas about the physical world and to attach ideas to physical entities. As a result we have implicitly and without thinking about it attached the notion of an entity to the referent of any idea. There is really no justification for doing that. Put another way, we have nothing to say in this paper about non-material entities. From here on we use the term entity to refer to material entities.
3.1 Static emergent entities
Statically emergent entities (static entities for short) are created when the fundamental forces of nature bind matter together. The nucleus of any atom (other than simple Hydrogen, whose nucleus consist of a single proton) is a static entity. It results from the application of the strong nuclear force, which binds the nucleons together in the nucleus. Similarly any atom (the nucleus along with the atom’s electrons) is also a static entity. An atom is a consequence of the electromagnetic force, which binds the atom’s electrons to its nucleus. Molecules are also bound together by the electromagnetic force. Macro-sized objects like automobiles and tableware are also static entities. They are bound together primarily by electrostatic forces. On a much larger scale, astronomical bodies, e.g., the earth, are bound together by gravity, as are solar systems and galaxies.
Static entities, like all instances of emergence, have properties which may be described independently of how they are constructed. As Weinberg [W] points out, “a diamond [may be described in terms of its hardness even though] it doesn't make sense to talk about the hardness … of individual ‘elementary’ particles.” The hardness of a diamond may be characterized and measured independently of how diamonds achieve that property—which, as Weinberg also points out, is a consequence of how diamonds are implemented: their “carbon atoms … fit together neatly.”
A distinguishing feature of static entities (as with static emergence in general) is that the mass of any static entity is strictly smaller than the sum of the masses of its components. This may be seen most clearly in nuclear fission and fusion, in which one starts and ends with the same number of atomic components—electrons, protons, and neutrons—but which nevertheless converts mass into energy. This raises the obvious question: which mass was converted to energy? The answer has to do with the strong nuclear force, which implements what is called the “binding energy” of nucleons within a nucleus. For example, a helium nucleus (also known as an alpha particle, two protons and two neutrons bound together), which is one of the products of hydrogen fusion, has less mass than the sum of the masses of the protons and neutrons that make it up when considered separately.[2] The missing mass is released as energy.
The same entity-mass relationship holds for all static entities. An atom or molecule has less mass (by a negligible but real amount) than the sum of the masses of its components taken separately. The solar system has less mass (by a negligible but real amount) than the mass of the sun and the planets taken separately. Thus the entropy of these entities is lower than the entropy of the components as an unorganized collection. In other words, a static entity is distinguishable by the fact that it has lower mass and lower entropy than its components taken separately. Every static entity exists in what is often called an energy well; it requires energy to pull the static entity’s components apart. Static entities are also at an energy equilibrium.
Manufactured or constructed artifacts also exhibit static emergence. The binding force that holds manufactured static entities together is typically the electromagnetic force, which we exploit when we use nails, glue, screws, etc. to bind static entities together into new static entities. As a diamond implements the property of being hard, a house implements the property of having a certain number of bedrooms.
A static entity consists of a fixed collection of components over which it supervenes. By specifying the states and conditions of its components, one fixes the properties of the entity. But static entities such as houses that undergo repair and maintenance no longer consist of a fixed collection of component elements thereby raising the question of whether such entities really do supervene over their components. We resolve this issue when we discuss Theseus’ ship.
3.2 Dynamic entities
Dynamic entities are instances of dynamic emergence. As in the case with all emergence, dynamic emergence results in the organization of matter in a way that differs from how it would be organized without the energy flowing through it. That is, dynamic entities have properties as entities that may be described independently of how those properties are implemented. Dynamic entities include biological and social entities—and, as we discuss below, hurricanes.