Stephen Jay Gould regards the evolution of complex creatures as almost an inconsequential departure from life’s bacterial mode. In his book; Life’s Grandeur humans are described variously as a “dribble at one end” a “little blip” the “right tail” a “tiny twig” and a “motley series of disparate forms”. He writes:

If we could replay the game of life again and again, always starting at the left wall and expanding thereafter in diversity, we would get a right tail almost every time, but the inhabitants of this region of greatest complexity would be wildly and unpredictably different in each rendition - and the vast majority of replays would never produce (on the finite scale of a planet's lifetime) a creature with self-consciousness. Humans are here by the luck of the draw, not the inevitability of life's direction or evolution's mechanism.

Without a direction or purpose for the more intricate designs of living systems and our human consciousness, it is necessary for Gould to explain complexity. He rather seems to suggest that it is difficult to know what is really meant by the term. This is surprising because ‘complexity’ is a commonly used word and an accomplished writer such as Gould should know what it means. Yet if he were in doubt, he could look it up in a dictionary. The New Oxford Dictionary of English provides the following:

Consisting of many interconnected parts, intricate – Involving many different and confusing aspects.

Or he might prefer Webster’s New World Dictionary:

Complex refers to that which is made up of many elaborately interrelated or interconnected parts, so that much study or knowledge is needed to understand or operate it [a complex mechanism]; complicated is applied to that which is highly complex and hence very difficult to analyze, solve, or understand …

Key words here would be ‘interconnected parts’, ‘intricate’, 'confusing’, ‘much knowledge is needed to understand’ and ‘very difficult to analyze’ yet it seems Gould prefers a definition provided by Dan McShea of the University of Michigan that relates complexity to the:

… number of different parts it has, and of the irregularity of their arrangement. Thus, heterogenous, messy, or irregularly configured systems are complex, such as organisms, automobiles, compost heaps, and junk yards.

He notes that junkyards and compost heaps may be functionally simple. However they; “... might be quite complex to other users in this case, to the seagull who must distinguish all the little bits while searching for morsels of food.” Gould is probably correct when he says a seagull would find a compost heap complex. It may also be true that they cannot distinguish between the irregular arrangements of a junkyard and the functional design of an automobile or human eye. We should not, however, conclude that birds have the last word on this matter. Most would agree there is a difference between the design of a human eye and a junkyard, even if seagulls have not noticed this.
After lumping the intricate design of body parts and human consciousness into the same category as a compost heap and a junkyard, Gould presents results of a number of studies. His purpose is to discover if there has been a general shift towards improved design in living organisms. Given the premise on which he is evaluating his data, it is not surprising to learn that he finds there has been no overall trend to greater complexity.
It is impossible to know what can be achieved by an analysis of data presented this way. The primary purpose in studying evolutionary theory is to understand the origin of life and how complex living systems came into existence. To relate the complexity found in a human eye to compost heaps and junkyards, is an absurdity. An eye might be a heterogenous and irregular configuration - yet was designed for a purpose. There is little purpose to design in a junkyard. By putting such different types of complexity in the same category makes it impossible for a meaningful statistical analysis to be made. It does not place a value on the abundance of design present everywhere in nature that cannot be explained by the random process of natural selection.

Above is an excerpt from my book; God Gametes and the Planet of the Butterfly Queen - page 274