Theos-Talk Archives (June 2002 Message tt00109)

Eldon: "There are a number of trick questions, which
mislead us into some form of circular thinking and a
false paradox. The question, "which came first, the
chicken or the egg," is one.

Since the egg is a single cell of life and the chicken
the result of the single cell dividing some finite
number of times, it is reasonable to assume that a
single cell must have come first. The paradox comes
from the erroneous assumption that the original
unicell organism must have somehow bene produced by a
female chicken (the Great Chicken in the Sky?) which
is not necessarily so. Ultimately all multicell
organisms must have originated with a single cell a
billion years ago.

Eldon: "Two other trick questions : (1) Zeno's
paradox, where you get 1/2 of the way to the wall,
then you're 1/2 of the remaining distance, then 1/2 of
the rest of the way, but never reach it.

It is not true that you never reach it, because this
is an infinite series with diminishing members. Such
a series is said to converge. Only if the series
fails to converge do you never get there. Consider
this:

We start out with 1/2
We then add 1/4 and so on. We have:

.5 + .25 + .125 + .0625 + .03125 + .015625 + .00078125
...

Adding up just those members of the series we get:

.9921875

I would have to write a program to compute the series
into the thousands of members, but I suspect this
series converges to 1. If we calculated an infinite
number of members of the series and added them
altogether, in other words, we would probably get 1. 
That is only harder to see if you do not use decimal
fractions.

Infinite series is a topic covered in the third
semester of calculus, or was when I was going to
school. They are used to calculate interesting and
useful numbers such as pi and e, among other things. 
For more information, refer to a text on advanced
calculus and look in the table of contents or index
for McClaurin, Taylor, and Fourier series. Piece of
cake. Nothing to it.

I knew all that education nonsense would have some
value if I just lived long enough.

Eldon: "(2) What happens when an irresistible force
meets an
immovable object?"

Elementary, my dear Eldon. Newton's second law of
motion is f=ma, where f is force, m is mass, and a is
acceleration. If we rearrange that simple equation,
we get a=f/m, where we are calculating acceleration,
given the force applied to an object and its mass.

An irresistible force is an infinite force and an
immovable object is an infinite mass. Infinity
divided by infinity is said in mathematics to be
"indeterminate" since any value of acceleration will
satisfy the equation. This can be seen from the
original form of the equation f=ma, where any value of
acceleration (including zero) multiplied by an
infinite value for mass yields an infinite value for
force. Thus the answer is that anything can happen. 
The mass may move, or it may not, and the rate of
acceleration may be any positive value. As one
physicist put it, when an irresistible force meets an
immovable object, there is an inconceivable collision.

Now one last. This is another one they answered when
I was in university, or answered indirectly anyway,
since they gave us all the bits and pieces of the
puzzle. Why are planets round instead of square,
hexagonal, or whatever?

Does anyone know?

The answer requires a fairly high level knowledge of
physics and advanced mathematics, so don't feel too
bad if you have a hard time guessing it.


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