Is Consciousness Simple or Complex?

I agree with this analysis.

The brain takes no part in decisions on:
how to grow bones so that they'll support the structure
how to align muscles right
regulate and respond locally to environmental signals

Let's get it clear. Are you claiming that legs and brains are of equal complexity?

If so, how are you defining complexity?

And then what sources are there that show by your chosen measure that the complexity is in fact equivalent.

Neither does the foot. The foot as an "organ" (er...body part) performs little to no information processing outside vanilla homeostatic and hox-gene mediated structural differentiation performed by almost every other body part.

I can build you a artificial foot that behaves, functionally, almost exactly like a real foot, but we lack anything approaching the computational power to simulate the information processing that goes into making a functional brain.

I wouldn't go that far. Every part of the body is incredibly complex with multiple interacting tissue types.

No, I'm not claiming this.

Well I'm not but my definition here of complexity would be the number of components and interactions between said components. I assume that you are using a different definition?

If you want a source start with something like Grays and look at the diversity of organs and tissue types in a limb verses the brain.

One of the problems with studying the mechanisms and history of complex systems is the lack of a working definition of complexity. We have intuitive notions that often lead to contradictions. There have been numerous attempts to define the complexity of a given system or phenomenon, usually by means of a complexity measure -- a numerical scale to compare the complexity of different problems, but all of them fall short of expectations.

The notion of Algorithmic Information Content (AIC) is a keystone in the problem. The AIC or Kolmogorov complexity of a binary string is defined as the length of the shortest program for a Universal Turing Machine (UTM) whose output is the given string [127,79,19].

Intuitively, the simplest strings can be generated with a few instructions, e.g. ``a string of 100 zeros''; whereas the highly complex ones require a program slightly longer than the string itself, e.g. ``the string 0010111100101110000010100001000111100110''. However, the minimal program depends on the encoding or ``programming language'' chosen; the difference between two different encodings being bound by a constant. Moreover, AIC is uncomputable. Shannon's entropy [121] is a closely related measure (it is an upper bound to AIC [80,136]).

Further research on the matter of complexity measures stems from the notion that the most difficult, the most interesting systems are not necessarily those most complex according to algorithmic complexity and related measures. Just as there is no organization in a universe with infinite entropy, there is little to be understood, or compressed, on maximally complex strings in the Kolmogorov sense. The quest for mathematical definitions of complexity whose maximums lie somewhere between zero and maximal AIC [10,82,58,53] has yet to produce satisfactory results. Bruce Edmonds' recent PhD thesis on the measurement of complexity [33] concludes that none of the measures that have been proposed so far manages to capture the problem, but points out several important elements:

1.
Complexity depends on the observer.
The complexity of natural phenomena per se can not be defined in a useful manner, because natural phenomena have infinite detail. Thus one cannot define the absolute or inherent complexity of ``earth'' for example. Only when observations are made, as produced by an acquisition model, is when the question of complexity becomes relevant: after the observer's model is incorporated.

2.
``Emergent'' levels of complexity
Often the interactions at a lower level of organization (e.g. subatomic particles) result in higher levels with aggregate rules of their own (e.g. formation of molecules). A defining characteristic of complexity is a hierarchy of description levels, where the characteristics of a superior level emerge from those below it. The condition of emergence is relative to the observer; emergent properties are those that come from unexpected, aggregate interactions between components of the system.

A mathematical system is a good example. The set of axioms determines the whole system, but demonstrable statements receive different names like ``lemma'', ``property'', ``corollary'' or ``theorem'' depending on their relative role within the corpus. ``Theorem'' is reserved for those that are difficult to proof and constitute foundations for new branches of the theory -- they are ``emergent'' properties.

A theorem simplifies a group of phenomena and creates a higher lever language. This type of re-definition of languages is typical of the way we do science. As Toulmin puts it, ``The heart of all major discoveries in the physical sciences is the discovery of novel methods of representation, and so of fresh techniques by which inferences can be drawn'' [135, p. 34].

3.
Modularization with Interdependencies
Complex systems are partially decomposable, their modules dependent on each other. In this sense, Edmonds concludes that among the most satisfactory measures of complexity is the cyclomatic number [33, p. 107][129], which is the number of independent closed loops on a minimal graph.
The cyclomatic number measures the complexity of an expression, represented as a tree. Expressions with either all identical nodes or with all different nodes are the extremes in an ``entropy'' scale, for they are either trivial or impossible to compress. The more complex ones in the cyclomatic sense are those whose branches are different, yet some subtrees are reused across branches. Such a graph can be reduced (fig. 1.1) so that reused subexpressions appear only once. Doing so reveals a network of entangled cross-references. The count of loops in the reduced graph is the cyclomatic number of the expression.

Perhaps this whole complexity discussion deserves it's own thread. Anyway, this thesis introduction by a graduate student at Brandeis outlines the main issues with defining complexity:

I still think a limb has all the complexity you could ask for, as defined quantitatively by Kolmogorov analysis.

The quest for mathematical definitions of complexity whose maximums lie somewhere between zero and maximal AIC [10,82,58,53] has yet to produce satisfactory results.

But as the grad student says, high algorithmic complexity in fact implies randomness, not order.



So if say limbs scored higher on AIC than brains, what would you conclude?

That doesn't seem to me to be a defensible position. Almost any cellular or genetic process that occurs in the foot occurs in the head, so the differences we're looking for are large scale, emergent properties of tissues and cellular networks. Most of these (e.g. blood flow) occur in both the brain and the foot, so we're left with the fact that the brain performs large scale parallel, distributed information processing, whereas the foot does...what? Incredibly fine and detailed muscle contractions, yes, that are programmed by the brain. The statistical procedures performed the brain alone would fill many a textbook, each with fairly sophisticated mathematical prerequisites. Did you know that an ensemble of neurons, each experiencing Hebbian synaptic changes, can perform principal component analysis? Your brain is literally deriving optimal basis vectors to best express the information fed to it by the outside world.

Perhaps this whole complexity discussion deserves it's own thread. Anyway, this thesis introduction by a graduate student at Brandeis outlines the main issues with defining complexity:

I still think a limb has all the complexity you could ask for, as defined quantitatively by Kolmogorov analysis.

http://pages.cs.brandeis.edu/~pablo/...tml/node9.html

Often the interactions at a lower level of organization (e.g. subatomic particles) result in higher levels with aggregate rules of their own (e.g. formation of molecules). A defining characteristic of complexity is a hierarchy of description levels, where the characteristics of a superior level emerge from those below it. The condition of emergence is relative to the observer; emergent properties are those that come from unexpected, aggregate interactions between components of the system.

The important part i see in the paper is that complexity or emergence is observer dependent. That means consciousness cannot be the result of it.

That's a bit of a misinterpretation. It's not that emergence and complexity doesn't exist without humans, it's that humans draw their boundaries between classifications in an arbitrary manner. The decoder and the code together can be objectified, but the code cannot. We often have the problem of being "trapped" in our decoder scheme. That's not to say that the things we're encoding aren't real, just that our codes/symbols/definitions fail to completely describe them.

Consciousness is still a big mystery, and I've always wondered what causes it.

Let's focus my quote-post a little more:

... A defining characteristic of complexity is a hierarchy of description levels, where the characteristics of a superior level emerge from those below it. The condition of emergence is relative to the observer; emergent properties are those that come from unexpected, aggregate interactions between components of the system.

I think a discussion of complexity needs to focus on the difference – which occurs at every level – between the things involved and the relationships that can happen between those things. For example, between atoms and the relationships atoms have with each other, which are the basis for forming molecules.

That is, instead of thinking in terms of simpler things (systems) “aggregating” to form larger things, we could imagine the hierarchy in terms of things having relationships, which allow for the formation of more complex kinds of things, that can have more complex relationships, etc.

“Thing” in this context means a structure that lasts over time and continues to be what it is, though it may also change, over time. Things typically have both constant and variable properties.

A “relationship” is something that happens between things, made of specific interactions taking place at a certain times. A relationship between two things can last over time, but only to the extent there is a repetitive pattern in their interactions. The characteristics of relationships are not properties they possess in themselves, but have to do with the effect these patterned interactions have on the things involved.

When it comes to consciousness, for example – if we look at the brain as a thing, an organ consisting of an aggregate of cells, its complexity is perhaps comparable to other organs. What makes the brain different is the kind of relationships that happen through synaptic connections between neurons. These relationships support a kind of real-time information processing that’s specific to the neural system, which operates at a much higher level of complexity than anything else in the body, or anything else that we know of.

The new kind of “things” that these neural relationships make possible are animals. Whether or not we think of animals as “conscious” is purely a matter of how we like to use that word. But we are not yet at the level of human consciousness.

The kind of simple unity that we indicate with the words “I” and “You” – that we experience and think about as “subjective awareness” – doesn’t emerge out of any characteristic of the neural system, per se, though our brains have obviously evolved to support it. But it can develop only in a certain kind of relationship that can happen between two animals.

So far as we know, this kind of relationship is highly evolved only between humans, though many other animals have relationships with some of the same characteristics. But to the extent we humans learn to talk to each other and think about each other, we also learn to talk to ourselves and think about ourselves. This kind of "internal self-awareness" is not comparable with whatever internal processing may happen in other animals. We can call both "consciousness" if we want to, but we're talking about two different things.

And of course, it's out of this kind of communicative I-You relationship that there arises a whole new hierarchy of “things” like words and ideas and corporations.

I guess my point is that a word like “complexity” doesn’t capture very well the profound differences that can emerge in the hierarchy of systems. At each level, the types of complexity that pertain to things is quite different from the kinds of complexity that can happen in their relationships.