Bread on the water 3

The vorpal (redux)

If the universe is the skin of a vorpal, how thick is it?

The first answer is: Extremely thin! The fourth dimension has a magnitude too small to be registered by our finest instruments so far.

A clue may be available in the in the so-called tunnelling phenomenon. Subatomic particles in radioactive substances are able to escape impenetrable energy barriers .

The largest such particle is the alpha particle. If, instead of drilling through the barrier, the particles “jump the fence”, their size might be an indication of the skin thickness.

The vorpal is timeless. It has no questions, no answers, about beginning and end. Individual stars mau be born and stay until they are weary and sick of shining but the vorpal itself, like Ol' Man River, just keeps rolling along.

Science is about the here and now, the past and the future but not about the origin, not about the end. Those are questions for mythology and religion. Science deals with  things we can know, faith is a firm conviction about things we cannot know.

Zero, by definition, does not exist, and Infinity has no boundary, yet both concepts are necessary adjuncts to the vocabulary of science. They are the meat and  the bread of religion.

The search for faith, the quest for knowledge, are both in our genes. When the twain meet, trouble starts.
 
There is a sweet irony in the vorpal model, if true. What we consider a straight line is in the model a segment of a vorpal's great circle.  Then the old sages have the last laugh; natural motion is a circle.

Pedestrian Physics 11

Vorpals


I can not visualize four-dimensional objects but I also cannot deny their existence. Our three-dimensional constraints are empirical, not logical.

Among such objects, one is of special interest. It shares with the circle and the sphere the property that all points on its surface are equidistant from a center in its interior.

I know of no name for this object; until I know better I shall refer to it as a “vorpal”.

The space capacity of a vorpal is

8π²(R⁴)/17

where “R” is the radius vector, The volume of its shell is

32π²(R³)/17

Any two points in the surface may be connected by a segment of a great circle. This is the shortest trace within the surface. There is a shorter route across the interior of the vorpal: the chord connecting the points. The distinction is important, but for points in close proximity the difference may be insignificant.