Monday, May 26, 2008

The Chicken and the Egg - An Inductive Analysis

In a slight departure from my usual computer science focused musings, I'm going to analyze another logical conundrum that has raged for centuries. Which came first, the chicken or the egg?

One of my many online debates clued me into the fact that there is a widespread belief that the egg came first. I even found a "paper" providing an in-depth analysis concluding the same. Unfortunately, the analysis appears flawed. An e-mail to the author bounced, so I figured I might as well post my brief analysis here.

A simple inductive analysis suffices to conclusively determine the causal chain.

Base case: single celled organism, asexual reproduction via mitosis (given our current knowledge)
n implies n+1: species n produces, by its own reproduction mechanism Rn, an offspring n+1 with a slightly different reproduction mechanism, Rn+1.
Conclusion: the "chicken" came first.

In this case, our "chickens" were not hatched from "chicken eggs", but were instead hatched from the "chicken's" progenitor's egg type. The authors of the paper attempted to disregard this semantic interpretation under "Chicken Precision", but as this is a metaphor, a "chicken" is merely a stand-in for a particular species to be substituted at will.

Thus, the only universally quantifiable proposition is that the "chicken" came first, since the first egg-bearing species, Sn+1 and Rn+1, was produced from some non-egg-based reproduction mechanism, Rn. The contrary proposition that the egg came first contradicts the base case of the above inductive argument where we know reproduction was based on asexual mitosis.

Unless our understanding of early biology changes radically, metaphorically and literally speaking, "chickens" came first.

[Edit: I posted an update to elaborate on why I believe my interpretation is more faithful to the original intent of the question, as first formulated in ancient Greece.]

4 comments:

stonemetal said...

I guess it depends on your definition of chicken egg then. Reading your analysis I still get the chicken egg coming first. If you define a chicken egg as an egg containing a chicken then chicken -1 lays an egg containing the first chicken therefore chicken egg comes before chicken. If you define a chicken egg as an egg laid by a chicken then the chicken comes first.

Sandro Magi said...

Defining a "chicken egg" as an egg containing a chicken is invalid.

Here's another way to think about it. We have two universally quantified propositions:

1. The egg came before the "chicken"
2. The "chicken" came before the egg

They are mutually exclusive, such that 2 = not 1. I disproved proposition #1, thus, proposition #2 must be true.

The proof is by counter-example. I argued that the first egg-bearing species was not produced from an egg given our knowledge of biology, but was produced from the reproductive system of its progenitor, be it mitosis, birthing, etc. This is a *direct* counter-example to proposition #1, thus proposition #1 is false. Thus, proposition #2 is true and the chicken came first.

You can think of it another way if it helps: and egg from each species has a certain chemical composition. The chemical composition of the egg is determined by the parent species, as the parent produces the egg, not the embryo. Thus, a chicken would have been hatched from an egg produced by the chicken's progenitor with a checmical composition different from an egg produced by a chicken. Thus, it is not a chicken egg, and the chicken came first.

Nate said...

"I argued that the first egg-bearing species was not produced from an egg given our knowledge of biology, but was produced from the reproductive system of its progenitor, be it mitosis, birthing, etc."

This doesn't seem to be really explicit, but you seem to be assuming that the first egg-bearing species was a chicken. Why would you make that assumption? Wouldn't you think there would be millions of years of proto-birds laying eggs before something that could be defined as a chicken?

Sandro Magi said...

This doesn't seem to be really explicit, but you seem to be assuming that the first egg-bearing species was a chicken.

I'm not making that assumption. Not sure where you got that actually. The first egg-bearing species was probably some microscopic multicellular organism in fact, so definitely not a chicken.