Infinitum minus Atomos

When you draw an asymptotic curve in a coordinate system, it gradually approaches the zero line, which is generally drawn horizontally, without ever reaching it.

The gap between the asymptote and the zero line (horizontal) becomes smaller and smaller but never disappears.  The curve never reaches the zero line.  This is the definition of an asymptote.  It must be a significant curve to mathematicians because they gave it a name.  (At the end of this essay I have provided a drawing depicting my thoughts.)

A coordinate system has also a vertical axis, generally referred to as y-axis.  For the practical reasons, because paper pages offer only limited space, we choose a scale for these axes, to suit the purpose of what we intend to display.

However, to indicate and remind the viewer of the fact that these axes actually extend further beyond the edge of the paper,  this continuation is annotated with a little arrow point at the of those axes.  Mathematically, practically or not, they span into infinity.

Let’s return to our asymptote closing up onto the horizontal zero line.  Somewhere in this infinite distance, our curve will have very closely approached the zero line, and the distance between them becomes undividable, in a physical sense (not mathematically), to a point of matter, where matter cannot be divided anymore.

About three thousand years ago, Greek philosophers called this undividable piece of matter atomos; this was a philosophical expression they derived at, assuming, following logic, everything physical, after an infinite number of divisions, must end up turning undividable.

Unfortunately, scientists of our modern age, pursuing the science of matter, have misused the term Atom.  They used this word to name constellations, made up of protons, electrons and neutrons, which determined the constellation’s qualities.

Since the Greeks have already done all the thinking, I would like to borrow the word atomos and use it for this really undividable gap at the end of an asymptote.  Are you with me?  Then we have a common vocabulary, and I can take you to the next step.

Allow me to state it clearly:  The undividable distance between two points I suggest calling:


Where does the vertical axis go?  Into the infinite, of course.  Yes?  Now, following the vertical axis, out there, in the infinite yonder, we find an imaginary line marking infinity, which we could call the infinitum line, which is parallel to and as long as the horizontal zero line.

Ok?  Imagine an asymptote (2), snuggling up to this line.  Again, as above, we have this upper asymptote approaching the infinitum line and, eventually, we end up again with an undividable gap, a distance we called atomos.

Now, reversely, the distance of the upper asymptote (2) approaching the infinitum line has an ever-increasing distance from the zero line and at the end of the zero line, where the lower asymptote has an atomos distance to the zero line the distance of the upper asymptote to the zero line is:

infinitum minus atomos

I guess if sneaking up to zero and never quite getting is this important, then trying to grow into infinity cannot be a bagatelle.  Approaching zero receives more mentioning because zero is much easier to imagine than infinity.

This reasoning should not prevent us from acknowledging the importance of something growing to almost infinity and therefore it would be more than appropriate to bestow this situation with a name, too.

The infinite space, with no borders, has already been given the name Kenon [1], by Democritus, two and a half thousand years ago.

Realising that the infinite space under the upper asymptote is actually bordered, I would suggest another word from ancient Greek, namely Choros, a masculine noun, which means ‘space’ in the sense of a limited area with borders.

Therefore I proclaim per definitio:

infinitum minus atomos equals  CHOROS

As it has been proven in history over and over again, once something has been given a name the world will find a use for it.  Therefore, I leave it up to the reader to determine when and where to apply this word and the small insight my essay may have provided, humbly.



[1] See my paper on Empty Space = Kenonics





Wolfgang Köhler
30 November 2009

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