The Myth of Infinity

Gerald M. Melino

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I don't understand the concept of infinity.

Imagine you have an infinite number of items and you cut each on in two, you now have
twice as many items. Therefore your second infinite number is twice as large as your
first. It simply makes no sense to me.

Take a look at Zeno's paradox for example. Zeno demonstrates that you can never really
get anywhere because to get there you have to travel half way there first. But once you
are half way there, you still have to travel half the remaining distance to your destination.
You can do this an infinite number of times and still never reach your destination. The
reason for this weird behavior is the supposition that there is such a thing as an infinitely
small distance that can be further divided into yet smaller distances.

I don't think so. In my universe I postulate that there is no such thing as an infinitely small
distance. In fact, I will make this my first law; "There is a specific amount of space that
can not be subdivided into smaller units." I will call a unit of such space in one dimension
a basic spatial unit.

Zeno's paradox no longer holds any water since you can no longer divide a finite line
into an infinite number of points. Fractions are eliminated (much to the delight of sixth
graders everywhere). Sooner or later, you will cross that last unit and reach your
destination.

The problem of the infinitely large still remains however. While I admit that this is
conceptually easier to swallow than the infinitely small (i.e. "there is infinite time
remaining in the life of the universe"), I am uneasy with this concept when it comes to
distances. I therefore propose Axiom Two, "All distances are composed of finite number
of basic spatial units." You just can't go traveling through my universe in a straight line
forever. Sooner or later you will either arrive at a point where further travel is impossible
or, more likely, loop back to your starting position.

In summary, with the following axioms the conceptual problems and paradoxes
associated with infinity are eliminated :

(1) There is a specific amount of space that can not be subdivided into smaller units

(2) All distances are composed of finite number of basic spatial units.

Gerald M. Melino works in Information Technology and  lives in Tuscan, Arizona.