Update: I win! At least according to the BBC.

Foreword

This is a silly little thing that came out of my high school years. But I think it's fun to read, so I might as well give everyone else a chance to have a taste of my teenage naïvete. Actually, I think that parts of this proof are still true, so I must have been somewhat logical back then.

I have made no changes to this document except for minor formatting adjustments. The text is exactly as I distributed it four years ago, with the exception of this foreword, which has been added in retrospect on December 24, 2003 at 5:37 PM (see, my style hasn't changed so much ;-). The introduction was in the original.

Introduction

On March 20th, 1999, at 10:17 PM, I, Charles Duan, distributed by e-mail a general proof solving the well-known dilemma, "which came first, the chicken or the egg?" Within two days, two responses were made to that proof as well as another by the author of the original document. Presented here is the full transcript of the proof and all follow-up responses to it, excluding any irrelevant comments attached. Combined they form a complex but cohesive demonstration of the solution to this problem.

The following documents are presented in the chronological order of their writing.

Question: Which came first, the chicken or the egg?

Proof by Charles Duan

The standard logic in approaching this problem is to consider that the first chicken must have come from an egg, but the first egg must have been laid by a chicken, leading to an impossible circular reference. In disproving this it becomes inherent that either the first or second clause is untrue, and by disproving one of those two clauses the primary originating source of the chicken/egg family may be determined.

What is the definition of a chicken? With numerous differing breeds of animals all of which are chickens, and with numerous similar birds none of which are chickens, a precise definition of the chicken is hard to come by. Let us take the definition from the Random House Dictionary of the English Language, First Edition: "A gallinaceous bird descended from the jungle fowl, Gallus gallus." Given that "gallinaceous bird" refers in general to domestic fowls (chickens, pheasants, turkeys, etc.), we may assume that all chickens are descendants from some archaic--and thus extinct--bird Gallus gallus.

What is the definition of the egg? We know that the unfertilized female gamete may be defined as an egg; for our purposes, this should suffice. Note that such a definition, however, does not encompass all eggs.

Gallus gallus was a jungle fowl. Thus the said bird was not domestic, and did not fall under the category of "gallinaceous." Therefore, Gallus gallus was not a chicken.

Without loss of generality, let us take some chicken C, which descended through the maternal line from some bird of species Gallus gallus which I will call G. Through the maternal lineage between G and C there must have existed a bird P which was not defined to be a chicken, who had a daughter bird Q who was defined to be a chicken. Define the egg from which Q was born to be E(Q).

Let us assume that E(Q) was not a chicken egg. A species may be defined by certain aspects of its genetic sequence. The mutation in the genetic sequence that would change the non-chicken species into a chicken could only occur, as all mutations occur, during cell division (unless the egg was zapped by radiation into the proper genetic sequence, but in that case it would be a chicken egg). That would mean that after the first division, one cell would be a chicken cell and the other a non-chicken cell, after the 2nd division 2 chicken and 2 non-chicken cells, and after the nth division 2^n-1 chicken and 2^n-1 non-chicken cells. Thus the final bird would not be a whole chicken, meaning that Q is not a chicken. But since Q was defined as a chicken, this must be a contradiction, meaning that the assumed statement was false. Thus E(Q) must have been a chicken egg, and since chronologically E(Q) must have preceded Q, the egg must have come before the chicken.

Thus concludes the proof.

Reply by Jonathan Lerner

This proof does not work. Mutations generally occur in the haploid gametes of the parents, before they unify in fertilization. The resulting animal has identical genetic material in each cell (barring certain rare exceptions such as in cancer cells and cells which do not undergo normal differentiation in the embryo stages). Therefore, there are not x number of "chicken" cells and x number of non-chicken cells; all cells are the same, genetically speaking. If the mutation were to occur during the cell division that immediately follows conception, only those cells that were daughter cells (and descendants of these daughter cells) of this originally mutated cell would be genetically different from the normal cells of the species.

Mutations only affect offspring if they occur in reproductive cells of the parent (or cells which will differentiate into reproductive cells). Therefore, if the mutation occurred in somatic tissue, this would have no affect [sic] on offspring. However, a mutation in reproductive cells would have an affect on offspring, while the parent would still be a member of the previous species.

Evolution does not work in the way you have defined it to. Mutations constantly occur (mostly benign though). Once so many generations have passed that an animal can no longer mate with a member of the species from which it has descended, the animal now constitutes a new species. However, each parent along the genetic tree from a member of the previous species to a member of the "new" species is neither strictly a member of one species, nor of the other. For this very reason scientists constantly debate definitions of different species, where one parent species ceased to exist and another offspring species arose. A human ancestor, Homo erectus, evolved around 400 years; this is a time period, not a specific date where one can pinpoint an ancestor mother, and her Homo erectus child.

But, for the sake of argument I have come up with a more logical proof to the classic chicken-vs.-egg question which conforms to your definitions. Without loss of generality, assume Gf and Gm are a female and a male, respectively, of the species Gallus gallus and their union resulted in a chicken, C. A mutation occurred in some of either Gf's or Gm's reproductive cells that left those cells with definite chicken genes; however the parent is still definitely a member of Gallus gallus (an animal's specious remains the same throughout life). Let one mutated gamete and one normal gamete united to form a fertilized chicken embryo. This embryo is enclosed by a hard shell, and together they make up an egg. A chicken hatches from this egg which contained the chicken in its early stages. Therefore, the egg was a chicken egg because the chicken simply hatched from it without a change in genetic information (a mutation in the egg stage would not change the species for reasons set forth above), and the egg came before the chicken.

The underlying concept that has caused the chicken-vs.-egg debate is that people do not realize that a chicken hatches from it's own "chicken" egg, identical genetically, just in the incipient stages of being a chicken. However, a member of Gallus gallus could lay an egg whose contents constituted a chicken: the egg is a completely separate being. Strictly in terms of a certain animal species, the egg came first.

The fact is, though, that this entire debate is asinine. If the question were generalized to the entire evolutionary tree, and we forget "definitions" of species and concentrate on what came first, the egg or the offspring/parent we run into a world of weak definitions, exceptions, and circular reasoning. Let's say we have an organism X that reproduces without sperm and egg (a very primitive organism) that produces offspring Y. If offspring Y does reproduce with sperm and egg, resulting in offspring Z, which of X, Y, and Z constitutes the organism that answers our generalized chicken-vs.-egg question? Depending on one's definition and syntax of argument any of X, Y, and Z could be the answer.

Summary and Analysis by Michael Maas

Please allow me to make an attempt to translate the previous two proofs which have come very close to short-circuiting many of our brains: (translations appear in light blue [light blue changed to italics. --ed.] ). It must be noted that I have attempted to divide each agruement into seperate paragraphs. However mistakes may have occured because the transmissions which I received did not denote clearly the paragraph divisions. I have attempted to divide them myself, sometimes using what appeared to be spacing left to indicate a new paragraph and other times dividing when a new idea was presented. It should also be noted that in no way am I attempting to provide an alternate proof, nor am I attempting to discredit either one of the authors. As a final note I must iterate [sic] that I this is not an attempt at humor, it is obvious that the two authors have spent time and thought on these proofs. I am merely trying to clarify their words for the reader.

[Editor's note: The original text of this analysis included the full text of the original documents as well as comments; since the original texts are presented above, they have been reduced in the presentation below.]

Analysis of Duan's Proof

The standard logic...family may be determined. The author establishes the dilemma and points out the conflicting logics in solving the "problem".

What is the definition of a chicken...is hard to come by. Note the "What...chicken" rhetoric and the following sentence which implies that the author will soon present his defintion for which his proof will be built upon. Let us take the definition...archaic--and thus extinct--bird Gallus gallus. A definition from a reliable source (in this case a dictionary) is given along with the author's clarification of his the use of 'gallinaceous.'

What is the definition of the egg? We know that the unfertilized female gamete may be defined as an egg; for our purposes, this should suffice. Note that such a definition, however, does not encompass all eggs. The author defines what his use of 'egg' will encompass and emphasizes that this is not true in all cases.

Gallus gallus was a jungle fowl....Thus E(Q) must have been a chicken egg, and since chronologically E(Q) must have preceded Q, the egg must have come before the chicken. For those of you who have not been in an advanced science course, do not be intimidated by the language and seemingly very technical jargon used in the previous paragraphs. Simply read it slowly (reread it if you must), and one can see the point being made by Mr. Duan including his appeal to logic at the end.

Thus concludes the proof. Closure. The reader is left with no doubt as to when the proof ended (although since this is the end of the author's email transmission, one must naturally assume that the proof is concluded).

Analysis of Lerner's Reply

This proof does not work....the parent would still be a member of the previous species. This paragraph opens with the simple "This proof does not work." Mr. Lerner here has made it quite obvious that his problem is with the proof; this is not an ad homineum. In no way does the author of this document attempt to discredit Mr. Duan (please note that Mr. Duan's proof shall no be known as 'the proof,' while Mr. Lerner's rebuttal shall now be known as and referred to as 'the rebuttal'). The author of the rebuttal is merely stating his opinion and is showing that he has the foundation to back up his arguement.

Evolution does not work...an ancestor mother, and her Homo erectus child. At the onset of this paragraph, the reader may notice a change in Mr. Lerner's rhetoric. He appears to be addressing Mr. Duan and his proof. Again an explanation is offered to Mr. Duan stating Mr. Lerner's 'problems' with the proof.

But, for the sake of argument...and the egg came before the chicken. Now in the rebuttal, Mr. Lerner offers the reader a more logical proof. If to present his own proof, was the purpose of the rebuttal, perhaps it would have been to Mr. Lerner's advantage to have seperated his rebuttal and his proof (now known and referred to as 'proof 2'). An appeal to logic is employed by Mr. Lerner here, much like Mr. Duan's appeal to logic in his proof.

The underlying concept...in terms of a certain animal species, the egg came first. The reader now sees that Mr. Lerner was not trying to state a contradicting opinion, but rather he felt that Mr. Duan may have overcomplicated the matter. Mr. Lerner arrives at the same conclusion as Mr. Duan, but in a more logical manner.

The fact is, though, ...any of X, Y, and Z could be the answer. Mr. Lerner here has stated his own feelings towards this 'debate.' Is it really needed? He shows and leaves open another theory to this 'debate'.

Reply by Charles Duan

Ironically, a careful reading of the rebuttal would lead one to realize that it simply supports the true statement and does not disprove the fact that the false clause (that the chicken came before the egg) leads to a contradiction, as by the rules of logical proof such a disproof would require that a non-contradictory case be brought forward; that is, if a proof of a condradiction against a statement is to be shown to be erroneous, it is necessary to demonstrate that there is at least one case in which the statement is true.

But to finalize the argument, there is a much simpler method of proof. The definition of a chicken involves the fact that it must be a domesticated animal. In order for the chicken to be domesticated it must not only be owned by humans, it must have been brought up and raised by humans (essentially, if one were to catch a stray wild animal and take it in, the animal will never be considered domestic). Again by indirect proof, assume that the chicken came before the egg. That would mean that upon birth the chicken was in the possession of a human, but immediately prior to the chicken's hatching it (in the egg) was wild. Assume that the chicken hatched at time t. Now define the time at which the human came into possession of the chicken to be T. Since the continuum of time may be put at a 1:1 correspondence with the real numbers, it is arguable that the probability that t = T is zero (basically the same proof that if I picked any random real number, there is a zero probability that I would pick 15.967238 exactly). Thus another contradiction is found, and it becomes obvious that the human must have owned the egg prior to owning the chicken (note that there is no such thing as a "domesticated" egg) and thus the egg must have preceded the chicken.