Stephen Jay Gould in the context of "Robert Bakker"

A scientific theory is an explanation of an aspect of the natural world that can be or that has been repeatedly tested and has corroborating evidence in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation of results. Where possible, theories are tested under controlled conditions in an experiment. In circumstances not amenable to experimental testing, theories are evaluated through principles of abductive reasoning. Established scientific theories have withstood rigorous scrutiny and embody scientific knowledge.

A scientific theory differs from a scientific fact: a fact is an observation, while a theory connects and explains multiple observations. Furthermore, a theory is expected to make predictions which could be confirmed or refuted with additional observations. Stephen Jay Gould wrote that "...facts and theories are different things, not rungs in a hierarchy of increasing certainty. Facts are the world's data. Theories are structures of ideas that explain and interpret facts."A theory differs from a scientific law in that a law is an empirical description of a relationship between facts and/or other laws. For example, Newton's Law of Gravity is a mathematical equation that can be used to predict the attraction between bodies, but it is not a theory to explain how gravity works.

The Cambrian chordates are an extinct group of animals belonging to the phylum Chordata that lived during the Cambrian, between 538 and 485 million years ago. The first Cambrian chordate discovered is Pikaia gracilens, a lancelet-like animal from the Burgess Shale in British Columbia, Canada. The discoverer, Charles Doolittle Walcott, described it as a kind of worm (annelid) in 1911, but it was later identified as a chordate. Subsequent discoveries of other Cambrian fossils from the Burgess Shale in 1991, and from the Chengjiang biota of China in 1991, which were later found to be of chordates, several Cambrian chordates are known, with some fossils considered as putative chordates.

The Cambrian chordates are characterised by the presence of segmented muscle blocks called myomeres and notochord, the two defining features of chordates. Before the full understanding of Cambrian fossils, chordates as members the most advanced phylum were believed to appear on Earth much later than the Cambrian. However, the better picture of Cambrian explosion in the light of Cambrian chordates, according to Stephen Jay Gould, prompted "revised views of evolution, ecology and development," and remarked: "So much for chordate uniqueness marked by slightly later evolution."

The history of life on Earth seems to show a clear trend; for example, it seems intuitive that there is a trend towards increasing complexity in living organisms. More recently evolved organisms, such as mammals, appear to be much more complex than organisms, such as bacteria, which have existed for a much longer period of time. However, there are theoretical and empirical problems with this claim. From a theoretical perspective, it appears that there is no reason to expect evolution to result in any largest-scale trends, although small-scale trends, limited in time and space, are expected (Gould, 1997). From an empirical perspective, it is difficult to measure complexity and, when it has been measured, the evidence does not support a largest-scale trend (McShea, 1996).

Simon Conway Morris FRS (born 1951) is an English palaeontologist, evolutionary biologist, and astrobiologist known for his study of the fossils of the Burgess Shale and the Cambrian explosion. The results of these discoveries were celebrated in Stephen Jay Gould's 1989 book Wonderful Life. Conway Morris's own book on the subject, The Crucible of Creation (1998), however, is critical of Gould's presentation and interpretation.

Conway Morris, a Christian, holds to theistic views of biological evolution. He has held the Chair of Evolutionary Palaeobiology in the Department of Earth Sciences, University of Cambridge since 1995.

Niles Eldredge (/ˈɛldrɪdʒ/ ELD-rij; born August 25, 1943) is an American biologist and paleontologist, who, along with Stephen Jay Gould, proposed the theory of punctuated equilibrium in 1972.

In evolutionary biology, a spandrel is a phenotypic trait that is a byproduct of the evolution of some other characteristic, rather than a direct product of adaptive selection. Stephen Jay Gould and Richard Lewontin brought the term into biology in their 1979 paper "The Spandrels of San Marco and the Panglossian Paradigm: A Critique of the Adaptationist Programme". Adaptationism is a point of view that sees most organismal traits as adaptive products of natural selection. Gould and Lewontin sought to temper what they saw as adaptationist bias by promoting a more structuralist view of evolution.

The term "spandrel" originates from architecture, where it refers to the roughly triangular spaces between the top of an arch and the ceiling.

The fossils of the Burgess Shale, like the Burgess Shale itself, are fossils that formed around 505 million years ago in the mid-Cambrian period. They were discovered in Canada in 1886, and Charles Doolittle Walcott collected over 65,000 specimens in a series of field trips up to the alpine site from 1909 to 1924. After a period of neglect from the 1930s to the early 1960s, new excavations and re-examinations of Walcott's collection continue to reveal new species, and statistical analysis suggests that additional discoveries will continue for the foreseeable future. Stephen Jay Gould's 1989 book Wonderful Life describes the history of discovery up to the early 1980s, although his analysis of the implications for evolution has been contested.

The fossil beds are in a series of shale layers, averaging 30 millimetres (1.2 in) and totalling about 160 metres (520 ft) in thickness. These layers were deposited against the face of a high undersea limestone cliff. All these features were later raised up 2,500 metres (8,000 ft) above current sea level during the creation of the Rocky Mountains.

Wonderful Life: The Burgess Shale and the Nature of History is a 1989 book on the evolution of Cambrian fauna by Harvard paleontologist Stephen Jay Gould. The volume made The New York Times Best Seller list, was the 1991 winner of the Royal Society's Rhone-Poulenc Prize and the American Historical Association's Forkosch Award, and was a 1991 finalist for the Pulitzer Prize. Pulitzer juror Joyce Carol Oates later revealed the non-fiction jury had unanimously recommended the book for the prize, but the selection was rejected by the Pulitzer board. Gould described his later book Full House (1996) as a companion volume to Wonderful Life.