tops and bottoms

 

What follows is probably pretty subjective, mostly in  

the same way that the notion of a top and a bottom is pretty arbitrary.

From the perspective of what we know about the history of mathematics,

and how I interpret it, it seems like there was a terrific focus on flat

surfaces, that lasted almost until the 10 th century a.d., when people

began to feel or sense that they did have a pretty good idea of what

flat was.  This evolved a while until sometime in the 17th or 18th century

when mathematicians became a little more focused on spherical things.

This may have had a lot to do with navigation and drawing maps

during that period and how important map making became.

It's hard to say, but  two prominent mathematicians 

Sophus Lie 1842 - 1899 and Bernhard Reimann 1826 - 1866

certainly began focusing a lot of energy on thinking about

spherical objects and surfaces. Of course, many of these

concepts and ideas have become thoroughly entrenched

it what we think of as " modern " science.

wiki pages:

https://en.wikipedia.org/wiki/Sophus_Lie

https://en.wikipedia.org/wiki/Bernhard_Riemann

Of course, if somebody hands you a ball, determining

what may be the top of the ball or the bottom, can

be very difficult.  In reality it is mostly impossible because

a sphere has no particular way of being positioned that

way.  It is only by a kind of arbitrary decision that we

can assign the top or the bottom to these objects.

However, when it comes to social matters, the general

way of thinking is to assign these issues to a top and

a bottom.  For example, we might say someone has

" reached the top ", or " he's on his way down ",

in a social or maybe employment situation.  And so

in thinking about social things we do tend to have

a kind of top or bottom sense to how social situations

work.  

Of  course looking at history we do tend to see a more

or less hierarchal structure imposed or accepted in

societies.  So we have, throughout history had kings

or queens, and then other important people under 

their authority.  A lot of this, I think, has to do with

how necessary information can be collected and communicated.

Just a guess.

In the current environment or time we live in, this notion of 

top and bottom has become somewhat more arbitrary, because

of how information is collected and distributed today, almost

like how a sphere really doesn't have a top or bottom.  This

kind of makes some sense.  Actually, I could spend a lot

of time going on about why this does in fact make sense,

but I am not sure how useful that might be.

Nevertheless, it has become extremely comfortable

for us to think in this way of top and bottom

associated with how society works, and  my

general feeling about this idea is; it is becoming less

meaningful all the time.

Now, there has to be a point to this, but the only

point I can find is an arbitrary point on the surface of

a sphere. It's just mostly about how we think about

things and how comfortable we are with those

ideas.

One final note: How comfortable an idea is, does not

necessarily make it more correct. Sometimes, we

need to work through uncomfortable ideas, in order

to reach more effective modes of action or understanding.

Okay, one last thing. When you throw imaginary

numbers at this, things get really wacky fast.

(rabbits)