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Definitions of Evolution

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on July 3, 2006 at 3:23:53 pm
 

Definitions of Evolution Termology

 

I find that there are a variety of words and terms used in the discussion of evolution that can be confusing and easily misunderstood. Consider these three terms: evolution, theory of evolution and evolutionism. None are the same and they should not be used interchangeably. Another stickler is the science definitions of 'theory' and 'law'.

 

Here are meanings and/or context for terms used in discussing evolution issues that the average reader may be unsure of. The entries are selected from fairly extensive web searches to obtain the best explanation.

 

For each term in this glossary, I will provide the web page title, author, web location and anything near to a publication date if they are available.

  • Actual copied text is in black
  • My comments are in blue

 


Big Bang

Here is a great one! Who has not heard of the Big Bang? But what is it? Lets take a look.

 

Title: The Big Bang Theory: Representation of the universe according to inflationary cosmology.

Web Location: http://liftoff.msfc.nasa.gov/academy/universe/b_bang.html

Date: Updated December 2, 1997

The Big Bang Theory is the dominant scientific theory about the origin of the universe. According to the big bang, the universe was created sometime between 10 billion and 20 billion years ago from a cosmic explosion that hurled matter and in all directions.

In 1927, the Belgian priest Georges Lemaître was the first to propose that the universe began with the explosion of a primeval atom. His proposal came after observing the red shift in distant nebulas by astronomers to a model of the universe based on relativity. Years later, Edwin Hubble found experimental evidence to help justify Lemaître's theory. He found that distant galaxies in every direction are going away from us with speeds proportional to their distance.

The big bang was initially suggested because it explains why distant galaxies are traveling away from us at great speeds. The theory also predicts the existence of cosmic background radiation (the glow left over from the explosion itself). The Big Bang Theory received its strongest confirmation when this radiation was discovered in 1964 by Arno Penzias and Robert Wilson, who later won the Nobel Prize for this discovery.

Although the Big Bang Theory is widely accepted, it probably will never be proved; consequentially, leaving a number of tough, unanswered questions.

Genesis 1:1 (RSV): "In the beginning God created the heavens and the earth..." Above: "explosion of a primeval atom". Now, what is that? It gets sticker and sticker. John 1:1: "In the beginning was the Word, and the Word was with God...” Now which is more real, the primeval atom or the Word? We can't measure either!

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Biological Evolution

  • Title: What is Evolution?
  • Written by Laurence Moran, Last Updated January 22, 1993
  • Web Location: [http://www.talkorigins.org/faqs/evolution-definition.html]

Most non-scientists seem to be quite confused about precise definitions of biological evolution. Such confusion is due in large part to the inability of scientists to communicate effectively to the general public and also to confusion among scientists themselves about how to define such an important term. When discussing evolution it is important to distinguish between the existence of evolution and various theories about the mechanism of evolution. And when referring to the existence of evolution it is important to have a clear definition in mind. What exactly do biologists mean when they say that they have observed evolution or that humans and chimps have evolved from a common ancestor?

 

One of the most respected evolutionary biologists has defined biological evolution as follows:

"In the broadest sense, evolution is merely change, and so is all-pervasive; galaxies, languages, and political systems all evolve. Biological evolution ... is change in the properties of populations of organisms that transcend the lifetime of a single individual. The ontogeny of an individual is not considered evolution; individual organisms do not evolve. The changes in populations that are considered evolutionary are those that are inheritable via the genetic material from one generation to the next. Biological evolution may be slight or substantial; it embraces everything from slight changes in the proportion of different alleles within a population (such as those determining blood types) to the successive alterations that led from the earliest protoorganism to snails, bees, giraffes, and dandelions." - Douglas J. Futuyma in Evolutionary Biology, Sinauer Associates 1986

It is important to note that biological evolution refers to populations and not to individuals and that the changes must be passed on to the next generation. In practice this means that:

Evolution is a process that results in heritable changes in a population spread over many generations.

 

This is a good working scientific definition of evolution; one that can be used to distinguish between evolution and similar changes that are not evolution. Another common short definition of evolution can be found in many textbooks:

"In fact, evolution can be precisely defined as any change in the frequency of alleles within a gene pool from one generation to the next." - Helena Curtis and N. Sue Barnes, Biology, 5th ed. 1989 Worth Publishers, p.974

 

One can quibble about the accuracy of such a definition (and we have often quibbled on these newsgroups) but it also conveys the essence of what evolution really is. When biologists say that they have observed evolution, they mean that they have detected a change in the frequency of genes in a population. (Often the genetic change is inferred from phenotypic changes that are heritable.) When biologists say that humans and chimps have evolved from a common ancestor they mean that there have been successive heritable changes in the two separated populations since they became isolated.

   Unfortunately the common definitions of evolution outside of the scientific community are different. For example, in the Oxford Concise Science Dictionary we find the following definition:

"evolution: The gradual process by which the present diversity of plant and animal life arose from the earliest and most primitive organisms, which is believed to have been continuing for the past 3000 million years."

 

This is inexcusable for a dictionary of science. Not only does this definition exclude prokaryotes, protozoa, and fungi, but it specifically includes a term "gradual process" which should not be part of the definition. More importantly the definition seems to refer more to the history of evolution than to evolution itself. Using this definition it is possible to debate whether evolution is still occurring, but the definition provides no easy way of distinguishing evolution from other processes. For example, is the increase in height among Caucasians over the past several hundred years an example of evolution? Are the color changes in the peppered moth population examples of evolution? This is not a scientific definition.

Standard dictionaries are even worse.

"evolution: ...the doctrine according to which higher forms of life have gradually arisen out of lower.." - Chambers

"evolution: ...the development of a species, organism, or organ from its original or primitive state to its present or specialized state; phylogeny or ontogeny" - Webster's

 

These definitions are simply wrong. Unfortunately it is common for non-scientists to enter into a discussion about evolution with such a definition in mind. This often leads to fruitless debate since the experts are thinking about evolution from a different perspective. When someone claims that they don't believe in evolution they cannot be referring to an acceptable scientific definition of evolution because that would be denying something which is easy to demonstrate. It would be like saying that they don't believe in gravity!

   Recently I read a statement from a creationist who claimed that scientists are being dishonest when they talk about evolution. This person believed that evolution was being misrepresented to the public. The real problem is that the public, and creationists, do not understand what evolution is all about. This person's definition of evolution was very different from the common scientific definition and as a consequence he was unable to understand what evolutionary biology really meant. This is the same person who claimed that one could not "believe" in evolution and still be religious! But once we realize that evolution is simply "a process that results in heritable changes in a population spread over many generations" it seems a little silly to pretend that this excludes religion!

   Scientists such as myself must share the blame for the lack of public understanding of science. We need to work harder to convey the correct information. Sometimes we don't succeed very well but that does not mean that we are dishonest. On the other hand, the general public, and creationists in particular, need to also work a little harder in order to understand science. Reading a textbook would help.

Note that our author uses two terms,"biological evolution" and "evolutionary biology". Are these the same?

I find the definitions Mr. Moran likes are innocuous while those he dislikes are of the type that are at issue today. Perhaps it would be better to find definitions for "Theory of Evolution".

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Biological Evolution (2)

 

Biography: “Austin Reed Cline is actively involved in educating people about atheism and secular humanism on the Internet. This site exists to provide people with information on atheism, agnosticism, skepticism, philosophy and religion. “

 

“Evolution can be a confusing term because it is used in more than one way. Many people in the general population have developed an incorrect understanding of evolution for a number of reasons. One is the misinformation spread by creationists — by misrepresenting evolution, they may hope that it will be easier to get people to disregard it. Another is simple ignorance of the topic itself and the specific ways in which science uses certain terminology.

Because evolution is so complex, however, it is important to get a handle on the different ways in which the term can be used. There are, of course, broader uses — we can talk about the evolution of the universe or the evolution of the planet Earth. In such cases, evolution simply refers to change over time, but that isn’t what concerns us here.

 

Biology, in contrast, uses the term evolution a bit more specifically. At its most basic, evolution in biology can be used to refer either to the change in the gene pool of a population over time or to the concept of descent with modification. Here are some examples from basic biology texts:

“In fact, evolution can be precisely defined as any change in the frequency of alleles within a gene pool from one generation to the next.” Helena Curtis and N. Sue Barnes, Biology, 5th ed. 1989.

“Biological evolution ...is change in the properties of populations of organisms that transcend the lifetime of a single individual.” Douglas J. Futuyma in Evolutionary Biology, 1986.

 

The two definitions look a bit different, but they are expressing similar things — the first is to a large extent more technical. An allele is a particular form of a gene and if a single gene is responsible for eye color, then one allele is for brown eyes, another allele is for blue eyes, and so on.

   So, if the frequency of the allele for blue eyes changes in a population over time, that means that evolution has taken place. This may not seem like a very significant step in evolution, but the fact of the matter is most evolutionary steps are quite small — large changes are the result of many, many smaller steps.

   The second common use of the term evolution within biology is

for the concept of common descent, the idea that all living beings are descended from a common ancestor.

This typically occurs in the context of allele frequencies changing in populations over time, but there are also other factors as well. Thus, “change in allele frequency over time” is a narrow and technical definition of evolution while “descent with modification” is a broader understanding. “

Mr. Cline steps on the toes of Mr. Moran with his second definition. So who is correct and what is the real definition of "biological evolution"?

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Evolution (Biology)

  • Randon House Dictionary of the English Language, Unabridged
  • Hardback, 1983
  • ISBN 0-394-50050-4

Biology Change in a gene pool in a population from generation to generation by such processes as mutation, natural selection and genetic drift.

Note the new terms! Are you familiar with 'genetic drift'?

 

Geologic Time Scale

This term came from state and/or district science standards. After about 20 attempts, I found the interesting text below, bringing up concerns about the entire concept:

"Well, the earth's crust consists of many layers of sedimentary rock (called "strata"). Geologists assume that each layer represents a long period of time, typically millions of years. This is actually a secondary assumption based upon the primary assumption of Uniformitarianism. These layers of sedimentary rock contain billions of fossil remains and some of these fossils are unique to certain layers. The layers are catalogued and arbitrarily arranged into a specific order (not necessarily the order in which they are found). This order reflects the assumption of macro-evolution (the widely held notion that all life is related and has descended from a common ancestor). The creatures thought to have evolved first are considered to be the oldest and are thus placed at the bottom of the column of layers. The creatures thought to have evolved later are higher up and so on. This has led many competent, accredited scientists to object, as this poses a circular argument: how can evolution be the basis for geologic conclusions while geology is taught as the basic evidence for evolution? "Are the authorities maintaining on the one hand, that evolution is documented by geology and, on the other hand, that geology is documented by evolution? Isn't this a circular argument?" (Larry Azar, "Biologists, Help!" Bioscience, vol. 28, November 1978, p. 714).

A variety of fossils from each layer of strata have been chosen to be what are called "index fossils". Index fossils are how we date the sedimentary rock layers. Paleontologists assume the age of an index fossil by the stage of evolutionary history the fossil is assumed to be in. They guess how long it would take for one kind of life to evolve into another kind of life and then date the fossils and rocks accordingly. Once again, this is a circular argument. "And this poses something of a problem: If we date the rocks by the fossils, how can we then turn around and talk about the patterns of evolutionary change through time in the fossil record?" (Niles Eldridge, Time Frames, 1985, p. 52)"

I have found other references to micro/macro- evolution. The second is to describe the slow changing, entirely through nature, of new species from old, all species from an original life form. It is with macro-evolution that we have the main problem. Very much theory and riding on the back of micro-evolution for authority.

 

The 'circular argument' point is seriously true. The age of the earth is speculative so the time spans in the geologic time scale are not empirically verified. Thus the current tables of this scale could be passing out some very erroneous information.

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Fossile Record

Ever since recorded history began, and probably before, people have found pieces of rock and other hard material with indentations from the remains of dead organisms. These are called fossils, and the totality of these objects and their placement in rock formations is referred to as the fossil record.

 

The fossil record is one of the primary sources of data relevant to the study of evolution. Scientists examine fossils in order to understand the process of evolution and the way particular species have evolved. (See timeline of evolution).

 

William Smith (1769-1839), an English canal engineer, observed that rocks of different ages (based on the law of superposition) preserved different assemblages of fossils, and that these assemblages succeeded one another in a regular and determinable order. He observed that rocks from distant locations could be correlated based on the fossils they contained. He termed this the principle of faunal succession.

 

Smith, who preceded Charles Darwin, was unaware of biological evolution and did not know why faunal succession occurred. Biological evolution explains why faunal succession exists: as different organisms evolve, change and go extinct, they leave behind fossils. Faunal succession was one of the chief pieces of evidence cited by Darwin that biological evolution had occurred.

 

The fossil record and faunal succession form the basis of the science of biostratigraphy or determining the age of rocks based on the fossils they contain. For the first 150 years of geology, biostratigraphy and superposition were the only means for determining the relative age of rocks.

 

Some observers are perplexed by the rarity of transitional species. The conventional explanation for this rarity was given by Darwin, who stated that "the extreme imperfection of the geological record," combined with the short duration and narrow geographical range of transitional species, made it unlikely that many such fossils would be found. Simply put, the conditions under which fossilization takes place are quite rare; and it is highly unlikely that any given organism will leave behind a fossil. Stephen J. Gould developed his theory of punctuated equilibrium in part to explain the pattern of stasis and sudden appearance in the fossil record.

 

Since the latter half of the twentieth century, absolute dating methods, such as radiometric dating (including potassium/argon, argon/argon, uranium series, and carbon-14 dating which works only for the very recent past, the last 50,000 years before the present), show that the earliest known fossils are over 3.5 billion years old. Various dating methods have been used and are used today depending on local geology and context, and while there is some variance in the results from these dating methods, nearly all of them provide evidence for a very old Earth, approximately 4.6 billion years. (See geologic time scale).

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History of Descent

Seems to be a code word for the evolutionary origin of man. There is also a 'Theory of Descent' and 'Descent with modification' see the second reference.

 

If we, as scientists and students of science, are capable of understanding the world around us and the ways of science, then organisms have changed over time and have descended from a common ancestor. Therefore, Organic Evolution is a Fact.

 

Evolution means descent with modification. In order to understand the history of life, we have to understand the patterns of evolution. We use phylogeny (Greek: phylum = tribe, genos = birth or origin) to show relationships of ancestors to descendants, therefore, phylogeny explains the history of descent of organisms.

Note the outrageous first statements. He is saying that since he is capable of understanding, organic evolution is a fact! Is this scientific investigation?

 

Evolution lies exposed in the imperfections that record a history of descent...

It will be useful to formalize Gould's argument. I have drawn the following premises from the cited passages.

 

(1) If p is an instance of organic design, then p was produced either by a wise creator, or by descent with modification (evolution).

 

(2) If p (an instance of organic design) was produced by a wise creator, then p should be perfect (or should exhibit no imperfections).

 

(3) Organic design p is not perfect (or exhibits imperfections).

 

From these premises, the conclusion follows that:

 

Organic design p was not produced by a wise creator, but by descent with modification. Some organic designs are evidence of evolution.

 

Note that premises 1 and 2 are theological; they refer directly to a creator, and the actions expected of him. Stephen Jay Gould's terms for the creator include "a perfect engineer," "a sensible God," "a rational agent," and "a wise creator." Note further that premises 2 and 3 refer to "perfection," and we may reasonably infer from the cited passages that Gould holds that humans can readily discern the presence or absence of perfection when they examine organic designs.

The conclusion requires of course both that perfection and imperfection be patent qualities of organic design, and that a wise creator would only create perfect organic designs. If these premises are granted, it will follow that any imperfect organic design is not the product of a wise creator. Rather it has come to be via the historically contingent processes of descent with modification.

And, according to Gould, examples of imperfect organic design abound. He writes of "vestigial organs," "odd biogeographic distributions made sensible only as products of history," and "adaptations as contrivances jury-rigged from parts available" 14 -- all of which, on the imperfection argument, provide evidence for descent.

The above is taken from an essay by Professor Nelson. The essay's purpose is to note that evolutionists commonly use theological terms in their initial assumptions underlying the theory of evolution. This article is well worth the read.

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Phylogenies

Defining and identifying species is one major area of research into the evolutionary process. Equally important is the study of how different species are related to each other. Because species originate by the branching process of speciation, each species living today has a history of descent that passes through many species that no longer exist. Every species that has ever existed shares a relationship with every other species through a common ancestor species that lived at some time in the past. For some pairs of animal species, like chimpanzees and humans, the ancestor is very recent, within the past few million years. For other pairs of species, such as humans and turkeys, the most recent common ancestor lived hundreds of millions of years ago. The account of all such ancestral relationships within a group of animals is called a phylogeny.

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  • Title: Kansas Science Education Standards
  • Author: Kansas State Board Of Education, Science Standards
  • Date: Approved in late 2005

Patterns of Cumulative Change

The current forms and functions of objects, organisms, and natural systems are the result of the accumulated changes over time. These changes may be gradual while other changes are sporadic. In general, it is thought that current forms and functions have arisen from previous forms or materials. An example of cumulative change is the formation of galaxies, explained by cosmological theories involving (among other theories) gravitation and the behavior of gasses, and the present diversity of living organisms, which the biological theory of evolution, or descent with modification of organisms from common ancestors, seeks to explain. The present position of the continents is explained by the theories of continental drift, which involves plate tectonic theory, fossilization, uplift and erosion. Patterns of cumulative change also help to describe the current structure of the universe. Although science proposes theories to explain changes, the actual causes of many changes are currently unknown (e.g. the origin of the universe, the origin of fundamental laws, the origin of life and the genetic code, and the origin of major body plans during the Cambrian explosion).

Are you getting this. The state science standards use the term "descent with modification" and USD446 has "history of descent". Both terms point to the study of Phylogenies which is how we all derived from a single life form.

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Primeval

Existing in or persisting from the beginning (as of a Solar System or Universe).

 

Primeval Atom

"That was done by a Belgian, Georges Lemaître. Early in the 1930's Lemaître went backwards in time, to the period when the whole universe was a "primeval atom." In this first and single atom, everything was squashed into a sphere only a few times as big as the Sun, with no space between atoms, or even between nuclei. As Lemaître saw it, this unit must then have exploded, fragmenting into the atoms and stars and galaxies and everything else in the universe that we know today. He might justifiably have called it the Big Bang, but he didn't. That name was coined by Fred Hoyle (the same man who did the fundamental work on nucleosynthesis) in 1950."

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Redshift

A shift toward longer wavelengths of the radiation caused by the emitting object moving away from the observer. When this occurs we see the light from the object become more red. See also Doppler effect.

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Theory (Dictionary)

  • Randon House Dictionary of the English Language, Unabridged
  • Hardback, 1983
  • ISBN 0-394-50050-4

(1) a coherent group of general propositions used as principles of explanation for a class of phenomena: Einstein’s theory of relativity.

(2) a proposed explanation whose status is still conjectural, in contrast to well-established propositions that are regarded as reporting matters of actual fact.

 

Theory by Michael Loop Ph.D.

Before looking for "theories" that were "proven wrong", make sure you understand what a (scientific) theory is, because a scientific theory is more specific than the colloquial use of the word theory as "a guess".

 

A scientific theory is:

"A well-substantiated explanation of some aspect of the natural world; an organized system of accepted knowledge that applies in a variety of circumstances to explain a specific set of phenomena."

So for an explanation to pass the test of being a "scientific theory" it must meet a higher standard of rigor and generality than "my guess". First: Scientific theories are seldom, if ever, "right" or "wrong" in an absolute sense. Second: One has to be careful about tossing the term "proven" around loosely. What does "proven" mean? By its definition:

a scientific theory is "organized", "generally accepted", and "widely applicable". However, a "scientific theory" explains or applies to a "specific set of phenomena".

Examples: Newton's theory of mechanics and Maxwell's theory of electromagnetism are well established theories within the context of their applicability, but they are not "universal", in the sense that one can find some set of conditions where they do not apply. Neither theory applies to atoms and molecules. A new theory, quantum mechanics, was developed to "explain" the behavior of atoms and molecules -- but even quantum mechanics has its boundaries of applicabilty. Neither Newton's, Maxwell's, nor "quantum" theory applies to conditions where the speed of particles approaches the speed of light. Here Einstein developed the theory of special relativity. And even special relativity does not apply in circumstances where gravity is a significant factor. In such cases the "general theory of relativity" must be used to correctly describe, explain, and predict

experimental observations.

 

Remember -- the "gold standard" is: "Does the theory correctly predict some phenomena that can be measured experimentally."

 

To this day there is no satisfactory theory that correctly predicts conditions where both "gravity" and "quantum mechanics" play a significant role. That does not make either one "disproved". It only identifies their boundaries of applicability.

 

A "hot debate" these days is the "theory of evolution". Proponents of "creationism" and "intelligent design" proclaim the "theory of evolution" is ONLY a theory, but they are using THEORY to mean "a guess". This is a misuse of the term as scientists use the term THEORY. However, "creationists" and "intelligent designers" have no experimental data to "put on the table" to be examined, verified, or refuted. Instead, they proclaim that "evolution" is not universal, that it does not explain every aspect of biological development. Nobody who understands "evolution" claims that it does. All "theories" are the product of human intelligence, and there is no theory of "everything".

   Advances in chemistry are unraveling the chemical structure of DNA and other complex biological molecules. In the not too distant future the connection between various species (and even individuals) will be a "simple" matter of chemical analysis of the molecules that define "species" and "individuals" within species. Then the protagonists of "creationism" and "intelligent design" are going to have to refute "chemistry" as a science. They will have to claim that the chemical analysis of the building blocks of species and individuals are "theory", "just a guess". Interesting.

Dr. Loop provides good direction in understanding what a theory. I particularly like his examples. If he had shown in such concise manner the constraints on the theory of evolution we would have a measuring stick to compare with what is taught in Kansas schools. Unfortunately he does not go the distance. I have found experimental data for Intelligent Design (e.g. blood clotting - see link to Intelligent Design. The proponents of ID I have run across have argument when the Theory of Evolution is used to explain the origin of man and/or the universe. At this point, to use Dr. Loop's words, the theory is outside "their boundaries of applicability"

 

I find Dr. Loop's last paragraph an excellent basis for a science fiction book. Has anyone found these "molecules that define species"?

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Theory by Vince Calder

Every scientific theory is wrong in some respect. There is no scientific theory of "everything". The point is this.

A theory is "a well-substantiated explanation of some aspect of the natural world; an organized system of accepted knowledge that applies in a variety of circumstances to explain a specific set of phenomena." [definition from "WordWeb Pro"]

Physical theories are not "proven" or "disproved". They apply, or do not apply, to some set of observations. In mathematics "proved" means the theorem (statement about the elements of the axioms) are logically consistent with the axioms. That does not mean it is "true", that is, "right" versus "wrong". So for example, the theory of real numbers is totally encompassed by the theory of complex numbers, but that does not make the theory of real numbers "wrong". It only specifies its limits and consistency within the axioms of the mathematical theory.

 

Physical theories, for example, Newtonian mechanics, applies to a

certain range of measurement. It applies to most of the world as we observe it with our senses. However, at the atomic level, it does not make the correct prediction of what is OBSERVED. At conditions where the speeds approach the speed of light it does not make the correct prediction of what is OBSERVED. In these two examples, quantum mechanics and relativistic mechanics respectively, do predict what is OBSERVED. This doesn't make Newtonian mechanics "right" versus "wrong".

 

There is a current, actually recurrent, debate on whether "the theory of evolution" is "right" or "wrong". The debate misses the point. It is neither "right" nor is it "wrong". The measure is: Does "evolution" explain many of the OBSERVATIONS of the genetic relation between species. Most scientists believe it does, and have experimental DATA to support their OBSERVATIONS and the limits of their observations . Advocates of "creationism" and/or "intelligent design", on the other hand, invoke absolute "right" or "wrong" based upon articles of Christian faith. Other faith traditions, even Christian traditions, do not accept that position. So physical theories do not address absolute "truth" versus absolute "false".

 

It is interesting and ironic that a Catholic monk, Mendel, first "explained" genetic relationships and Georges Lemaître, a Jesuit priest, first proposed what is now called the "Big Bang". Neither felt their "faith" was compromised.

Here again we find that theory is constrained by certain assumptions. In context of public education the debate centers on if these constraints are acknowledged and identified in the classroom or if the theory is presented as fact. In addition, it is known that there have been several hoaxes presented to validate the theory, sometimes still being published in school textbooks. In one reading about Georges Lemaître it is stated he estimated that the cosmological redshift caused the plasma to cool until it became favorable for electrons to combine with protons and form hydrogen atoms. This happened at around 3,000 K or when the universe was approximately 380,000 years old. Compare this with statements that our planet is millions of years old. It does get confusing, doesn't it? And what does the Big Bang have to do with the origin of man, generally thrown in with the theory of evolution.

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Law

  • Randon House Dictionary of the English Language, Unabridged
  • Hardback, 1983
  • ISBN 0-394-50050-4

Philosophy, Science, etc. (a)a statement of a relation or sequence of phenomena invariable under the same conditions. (b)a mathematical rule.

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