|
Author
|
Topic: What is Complexity?
|
Elend
Member
Member # 326
|
posted 17. July 2002 01:55
After reading several papers and message boards here at ISCID and at other web-sites, and also at the advice of a Moderator I decided this may be a productive board. The results of this discussion may end up in a FAQ about ISCID terms.
It still seems to be little agreement over what complexity is. In short, there are positions which simply say complexity is given by the improbability of a system. Others go a little further and claim that the length of the procedure to arrive at a certain state means complexity (sort of like Kolmogorov complexity). Even others bring in order and organization to describe complexity. All seem to have advantages and drawbacks.
Post your understanding or formal definition of complexity and let us analyse it. The goal of this discussion is in principle to come up with a standard definition of complexity (and other terms such as order and organization) but I would be happy even if we just end up with a survey on definitions for complexity.
IP: Logged
|
|
Micah Sparacio
Member
Member # 6
|
posted 17. July 2002 08:12
Complexity:
1) ...the (minimal) length of a description of the system.
2) ...the (minimal) amount of time it takes to create the system.
The length of a description is measured in units of information. The former definition is closely related to Shannon information theory and algorithmic complexity, and the latter is related to computational complexity.
IP: Logged
|
|
James A. Barham
Member
Member # 50
|
posted 17. July 2002 08:17
In my view, any general understanding of "complexity" is going to have to make some allowance for the distinction between inorganic and organic systems.
There is certainly a sense in which the standard information-theoretic measures (Kolmogorov's, Chaitin's, Bennett's, Lloyd & Pagels') can also be applied to living things. But I do not believe that this approach captures what we intuitively feel is important about biological "complexity".
In my paper "On the Objectivity of the Scala Naturae" (Evolution and Cognition, 1999, 5: 2--1), I propose that an appropriate metric for biological complexity that will capture something like our intuitive sense of the "scala naturae" must take cognitive capability explicitly into account. I then propose a metric I call "epistemic depth" based on my dynamical model of the "epistemic interaction" that I see as fundamental to all biological functions. Roughly, the epistemic depth of an organism is the number of different ways in which in can interact with the world. This allows us to explain why we want to attach such importance to brains---not because we are "brain chauvinists," but because brains increase the number of different possible epistemic interactions exponentially. There is a real difference in cognitive capabilities between a flatworm, say, and an octopus. The scala naturae is not just an anthropomorphic illusion of perspective.
But regardless of the details of my model, I think it is important to realize that we cannot possibly capture our intuitive notion of biological complexity with pure information-theoretic means. We are going to have to somehow take cognitive capacity explicitly into account, if we are going to avoid paradox.
[ 17 July 2002, 08:20: Message edited by: James A. Barham ]
IP: Logged
|
|
Micah Sparacio
Member
Member # 6
|
posted 17. July 2002 11:50
Richard Johns' paper on ISCID, Dynamical Complexity and Regularity provides an interesting angle on biological complexity. All text from this point on is from that paper.
Dynamical Complexity
A dynamically-complex object is, roughly speaking, one that the dynamical laws have little or no tendency to produce from a random initial state.
It is generally recognised that living organisms are highly complex. Since the work of von Neumann (1966) on self-reproducing automata, some attempts have been made to understand what biological complexity is, and how (or if) it can be produced naturally.
The main difficulty with this project, at present, is that we do not have a general definition of complexity that can be applied to biological systems. While there are a number of such definitions, they are all rather arbitrary. Any definition of complexity requires some sort of “reference frame”, relative to which complexities are evaluated – complexity cannot be defined in a vacuum, so to speak. The choice of reference frame seems arbitrary, so that no complexity measure is uniquely correct.
The two main kinds of reference frame are (i) a language, and (ii) a universal Turing machine. Once a language L has been chosen, for example, then the (linguistic) complexity of an object s relative to L can be defined as the length of the shortest complete description of s in L. Or, if a universal Turing machine M has been chosen, then the (algorithmic) complexity of s is the length of the shortest program that, given to M, produces the output s.
The rough idea of these definitions is that the complexity of an object is the amount of information needed to specify it. This is the right idea, I believe, but the question is: Which language, or Turing machine, do we choose? Each language, or Turing machine, gives rise to a different complexity measure. The answer seems to be that there is no single complexity measure that is useful in every context; rather, one chooses the reference frame according to the problem at hand.
In evolutionary theory, the problem is how the world managed to produce complex living organisms. Thus, for this context, the best “reference frame” is surely the dynamical laws of the real world. The real world is not a Turing machine, so that any choice of Turing machine will be arbitrary in this context. Also, the physical world does not provide us with any language. The idea, then, is to use the dynamical laws of physics in something like the same way that Solomonov, Kolmogorov and Chaitin (SKC) used a universal Turing machine.
This notion of complexity I shall call dynamical complexity. It should depend only on the object, and the dynamical laws of the system. The rough idea, as always, is that the complexity of an object is the amount of information needed to specify the object, within the reference frame. As with the SKC definition, the object’s being “specified” has something to do with its being produced by the system. Dynamically complex objects are, roughly speaking, ones that have little or no tendency to be produced by the system.
1.2. Complexity and Irregularity
There is an intuitive notion of complexity that is not exactly captured by formal definitions.1 We think of a complex object as heterogeneous, aperiodic, elaborate, or patternless. Complexity is opposed to simplicity. A simple object is something like a crystal, which has a small number of basic parts, arranged in a way that is easily specified. The more symmetry, self-similarity, or repetition an object contains, the simpler it is. A complex object, on the other hand, has little or no pattern to it. Let us call this intuitive kind of complexity irregularity. Note that an irregular object must be composed of many parts; no object with few parts is elaborate, no matter how the parts are arranged. Also, an irregular object need not do anything useful or interesting—its parts may even be arranged randomly.
There is a link between irregularity and the formal definitions of complexity, but they are not exactly equivalent. Consider linguistic complexity, for example. The sequence <0,0,0,0,…,0> (all zeros) strikes us as simple, as it is highly regular. It is invariant under many different transformations, including all translations. It is also easily specified in English, e.g. “All zeros”. So linguistic complexity matches irregularity in this case. On the other hand, consider a sequence that strikes us as complex, such as the binary form of War and Peace. It may seem that this is linguistically complex, as it is a very long string of English words, but what if the language includes a name for the string, such as “War and Peace”? In that case, the object is specified with only 13 letters, and so is linguistically simple. Thus, for linguistic complexity to coincide with irregularity, it seems that we require a “simple” language, containing no short names for irregular objects.
The same situation exists with algorithmic complexity. A long, irregular string may be built into a Turing machine, so that it is produced by a very short program, one that effectively says “print out the stored string”. In that case, the irregular string has low algorithmic complexity for that machine. Again, we seem to require the Turing machine to be “simple”, in order for algorithmic complexity to approximate irregularity.
In a similar way, the dynamical complexity of an object will depend upon the set of dynamical laws in question, so that no rigid link exists between dynamical complexity in general and irregularity. Fortunately, however, we need only look at the actual laws of physics, so that there is no need to consider all possible sets of laws. The question then arises: “What is the relation between dynamical complexity, for the actual dynamical laws, and irregularity?”
This question is more easily answered than one might think, since the actual laws of physics have certain general properties, which are (I think) sufficient to show that complexity and irregularity are linked in the following way:
Regularity Principle
Dynamical complexity ≥ Irregularity
Thus any object that is irregular is also dynamically complex, but the converse does not hold. A dynamically-complex object may actually be quite regular, if the regularity is of the “wrong kind”, i.e. the pattern is one that is not easily produced by the laws. For example, a cubic crystal of carbon atoms is a very regular object, but the laws of physics do not allow its formation, so that it is dynamically complex. The only real carbon crystals, i.e. graphite and diamond, have quite different structures.
What are the general properties of the laws of physics that lead to the regularity principle? They are (i) causal locality, and (ii) symmetries (of various kinds). Causal locality means that causal processes form a continuous world line of time-like separated points. Roughly speaking, every event is directly caused only by neighbouring events, in its immediate past, so that there is no “action at a distance”. The symmetries include invariance under spacetime translation and spatial rotation, among others.
These properties of locality and symmetry effectively mean that the laws cannot directly control the global structure of the state of the system. They can directly control only the local structure, which is not always sufficient to determine the global structure. An irregular object has a global structure that is largely independent of its local structure, so that a law with these properties cannot (reliably) produce any particular irregular object.
The concept of irregularity is relevant to biology, since living organisms are generally held to be highly irregular. From the regularity principle, it would then follow that they are dynamically complex.
IP: Logged
|
|
Elend
Member
Member # 326
|
posted 18. July 2002 03:19
I found Richard Johns' paper interesting, but I have some doubts on the validity of his initial assumptions:
1.) Johns claims the world is not a Turing machine (no reference or at least intuitive proof) yet he goes on and uses a Turing machine like model do describe it. I'm not sure what makes his model (based on the laws of physics) more than a Turing machine. Is it nondeterminism?
2.) Causal locality seems to be one basic assumption for proving that irregularity implies complexity. Yet, we know that the locality breaks down at quantum level. (entangled particles)
3.) For the GIGO theorem, as I understand it, Johns assumes there is one (unique) possible "program" described by the laws of physics that can operate on the initial randomly chosen state.
4.) In the Archive message board discussing the paper, Johns claims that a random arrangement of particles has a high dynamic complexity since it exibits very low regularity. Yet this seems to kill the whole model since the dynamic complexity is computed starting from an initial random state. An empty program would produce... a highly complex state.
I have to say I didn't read the whole paper yet... soon.
A general comment on complexity:
Random noise in an object has to be filtered out whenever describing the object. It does not matter much if a horse is white or brown - it is still a horse. One instance may indeed look very complex, yet the exponent of a class of objects may actually exhibit lower complexity.
[ 18 July 2002, 05:29: Message edited by: Elend ]
IP: Logged
|
|
Cre8ionist
Member
Member # 140
|
posted 18. July 2002 08:53
Without expecting to give the definitive response to Elend's post, I'd at least like to become part of the survey by offering the following (largely from Thaxton/Bradley):
According to them there are two kinds of complexity, ordered (low information), e.g., the snowflake, and specified (high information) e.g., DNA, random complexity being non-complexity (also low information), in their view.
This view corresponds to Micah's first definition, in fact, in their article Information & the Origin of Life they cite Orgel:
quote:
"Roughly speaking," says Leslie Orgel, "the information content of a structure is the minimum number of instructions needed to specify the structure." The more complex a structure is, the more instructions are needed to specify it and the more information it contains.
pg 206
I don't know of another type of complexity which wouldn't fit into their definition. Although, I'd like to hear what others think. Anyway, I'm enjoying reading the posts here.
[ 18 July 2002, 08:58: Message edited by: Cre8ionist ]
IP: Logged
|
|
Evan
Member
Member # 164
|
posted 18. July 2002 09:42
Just for the record, Dembski's definition is that complexity is purely a measure of improbability - the more improbable it is that natural causes could have produced something, the more complex it is.
Problems with this definition were discussed here at ISCID some months ago. But it's important to understand, I think, that it is this defintion that underlies Dembski's use of the word and the arguments in No Free Lunch - and thus his arguments that design can be, at least in theory, inferred if the probability of something having occurred can be established.
IP: Logged
|
|
Moderator
Administrator
Member # 1
|
posted 18. July 2002 10:12
Hi Brainstormers.
I am requesting that this topic not turn into a discussion about Richard Johns' paper. I will shortly be starting a separate thread to discuss the paper in detail. In this thread, please just take note of Johns' use of complexity.
IP: Logged
|
|
Cre8ionist
Member
Member # 140
|
posted 19. July 2002 08:24
The way I see it, Dembski's statistical description of complexity (i.e., his complexity = improbability) is a way of quantifying complexity, not of qualifying it. The same way Shannon's theory of information describes information from a statistical viewpoint only. This type of quantification, while extremely useful, does not entirely describe the contents of its subject.
This is why there is some confusion. Dembski must always check for specification prior to making a design inference, complexity (based on his definition) alone will not trigger an inference to design, only specified complexity (and I realize that this term is out of vogue), can be a reliable indicator of ID.
IP: Logged
|
|
Elend
Member
Member # 326
|
posted 20. July 2002 01:51
First, I think most people would agree that complexity is a relative measure, not an intrinsic property of an object (local state in a system).
Also, for some reason I consider the process of arriving at a complex state rather important. A state that can be obtained after a single event seems less complex than a state that needs a chain of causal events, even if their (im)probability is rather equal.
Dembski's definition (complexity = improbability) seems to handle poorly some situations. Uniform probability distributions with very many outcomes (very low probability for a state, yet equal for all - say p) seem to yield many "complex" states. Yet, for another probability distribution a state with probability p may be complex (p smaller than that of many other states) or on the contrary, simple (p larger than many other states). Also this definition doesn't care of the actual process (the length of the causal events) that lead to the certain probability value. In this sense I like Johns' definition better.
IP: Logged
|
|
Leonid Andreev
Member
Member # 282
|
posted 23. July 2002 00:00
The key issue of the complexity problem is: Is there any objectivity at all in the nature of complexity and how can one define it? The subjectivity of perception of complexity is self-evident and is based on numerous constituents, such as semantic, gnostic, intelligence, sensory, psychological, and other factors. The premise of an object’s complexity being the amount of information needed to specify a given object only emphasizes the subjectivism of such an approach. Indeed, a phenomenon of alternating strata at a sheer cliff will present different degrees of complexity to a layman, a geology student, and a petrography professor familiar with geological structure of a given location. Each of them will employ a different amount of information in order to specify the observed object.
Mathematics – an ultimately abstract science – cannot be of much help in the quest for the abstractive subjective meaning of complexity. In the absence of a universal but accurate definition of complexity, any theorem may be deemed proven – until a certain theretofore unaccounted factor may surface that will make a given theorem totally senseless.
R. Johns’ “GIGO” theorem connects an object’s complexity in bits with the time needed “to produce the object for a given set of laws from random initial state”. The syntagmata of “a given set of laws” and “random initial state” make the whole theorem-proving meaningless. In the emergence and evolution of the living matter there is no any “given set of laws” and “random initial state” whatsoever. R. Johns writes, “If the dynamical complexity of an animal in one million bits, or greater, and the time available is only a few billion years, then its production from a random initial state is effectively impossible. The time required is greater than this by many thousands of orders of magnitude”. To make his statement fully correct, R. Johns should have added: “for we have no clue as to what kind of emergence and evolution vectors could have allowed the living matter to defy the GIGO theorem”.
IP: Logged
|
|
Stephen Wright
Member
Member # 195
|
posted 23. July 2002 15:39
Complexity can be considered as the realization of potential levels of interconnectedness. This implies that the proximate situation between one object or event can have a relationship to another on three commonly acknowledged levels. Interaction within a location and through intersecting vectors brings connection in terms of physical, informational and intentional exchange.
Matter/energy units have the potential to be related through each of the four forces when these units exist together within the sphere of influence appropriate to each force. The more fields exerting influence and the more significant their strength, the higher the degree of potential complexity. Complexity is realized from this potential state in accordance with the laws of physics and chemistry.
Information and/or negative entropy associated with an object or an event is likewise in a gradient of potential states. Information is contextual within its environment. Locally, a greater density of units with interconnecting potential for receptivity and transference leads to a greater chance for complexity to be concentrated in an ordered system. Realization of information transfer is conservative and understood to obey mathematically predictable principles.
Intentional activity is characterized by contact and recognition between organisms. Potential for interaction and an increase in complexity is apparent in an increased number of contacts and more importantly in the commonality of goal fulfillment between them.
Complexity is holistic in the respect that there exists mutuality between the levels. A married person may come in close proximity to an attractive member of the opposite sex. A physical reaction can occur in terms of hormone releases creating a changed state of energy. Informational potential can be realized in terms of connecting with an unconscious drive and bringing it into personal observation. It is my understanding that at the intentional level this situation is the exact definition of a “complication”. ![[Wink]](wink.gif)
[ 23 July 2002, 16:02: Message edited by: newchurchguy ]
IP: Logged
|
|
|
Printer-friendly view of this topic