I am trying to write a post a day throughout August. I wanted to have a graphic for today's post, but I realized that I wouldn't get the picture done before the deadline.
Even worse, I am not sure if a static image could convey the message of the post.
Instead of drawing a picture, I simply ask that you close your eyes and read the post.
No, that won't work.
You need your eyes to read. Okay, how about this. Keep your eyes open and imagine the picture that I will describe later in this post.
So, in yesterday's post I mentioned that Pythagoras was driven to distraction because the hypotenuse of the unit square could not be expressed as a ratio of two whole numbers.
In other words: the square root of two is an irrational number.
This is not an isolated problem. This simple proof discovered in antiquity shows that any framework that we create for our ideas will be incomplete.
The problem of the hypotenuse is not isolated to one square in the grid. Imagine two pieces of grid paper laying on top of each other.
Twist the top grid paper and you will see that the vertices and lines no longer match up.
This leads to real world problems.
Close your eyes and imagine a surveyor who painstakingly draws out a grid and measures all of the features of an island on a map.
Are your eyes still closed?
Now imagine that a second surveyor comes and measures the island with a grid that is slightly askew to the first surveyor.
Because the maps are askew, all of the measurements of the first surveyor will appear irrational to the second surveyor.
A person with a mathematical inclination would realize that the maps have different frames of reference and would set into reconciling the two surveys with conversion tables and formulas.
The political mind tends to approach the twisty grid by siding with one of the surveyors and vilifying advocates the other surveyor.
I guess in the left right split, the conservative would side with the first survey and call the second surveyor satanic for re-examining the layout of the island. The progressives would side with the second survey and seek the destruction of all those who built on the first survey.
I call this problem the "twisty grid." By twisting the grid, the vertices and lines no longer line up.
The problem is not unique to graph paper. It applies to all of our thoughts.
When people have different frames of references, the ideas expressed by others will appear irrational.
This happens because we all see the world from different points of view.
Not only does each person have a different point of view. Points of view change radically as people move from place to place.
The generation after Pythagoras was clearly struggling with problem of perspective.
Heraclitus of Ephesus (circa 535) was an Ionian philosopher who noted that "no man ever steps in the same river twice."
If everything is in constant flux, how can we do or say anything?
Anyway, it is past 2:00 AM, as expected, I didn't finish the graphic.
Anyway, this is the inglorious end of this post.
You can open your eyes now.