Projections, Analogies and the weight of grain
A number (greater than zero) of years ago, (comma) I had a discussion with a friend of mine.
It was about religion. WAIT! Don't go away yet.
It was about the futility of attempting to map (ie. project) an n-dimensional (where n>2, possibly >>2) object on to a lower dimension.
For example, how do you accurately quantify, describe, identify, etc. a moving object (3-D + time, hence, in 4-space) provided only its shadow is visible?
Over the years, (comma) I've kicked that idea around, never really pushing it forward, growing it, <enter clever metaphor here>, until recently, when discussing real-world geometry with a friend. The problem was how to measure the area of a surface that wasn't flat.
This led to the concept of projections.
I'm not sure, but I would imagine that my aforementioned friend would be of the opinion that everything is relative, and that particular vantage point comfortably encapsulates the whole projections thing.
I'm of a different mindset. Having been steeped in a mathematical mentality, in my world, there are rules. Things are as they are. Analogies are fundamentally flawed. They break down. As such, projecting from one sub-space to another, or one concept to another would be only partially describing it and, therefore, yield an incorrect outcome.
Essentially, to define an object based on its relationship to, or similarity of attributes of, another object cannot be effectively done.
Consider, if you will, the anecdote of me at the grocery store, circa 1985 (I picked that year arbitrarily so as to put myself in an era where there may actually have been grocers in existence.):
[Me] How much does this bag of apples weigh?
[Grocer] Five pounds.
[Me] And this bag of wheat?
[Grocer] Five pounds.
[Me] So, they're the same?
[Grocer] Ummm, no.
[Me] Ok, so, how much does a pound weigh?
[Grocer] *Pause* Have a nice day.
According to the measurement Powers-That-Be:
There are big guys in uniform situated somewhere in Europe.
They have guns.
They guard a rock.
In that rock, there is a cave.
In that cave, there is a vault.
In that vault, there is a nondescript piece of metal.
That piece of metal is the standard of measure representing one pound.
There are no analogies to break down. It is what it is: one pound.
Just ask the big guys with guns.
Don't ask the big guys with guns. I was just kidding.
It was about religion. WAIT! Don't go away yet.
It was about the futility of attempting to map (ie. project) an n-dimensional (where n>2, possibly >>2) object on to a lower dimension.
For example, how do you accurately quantify, describe, identify, etc. a moving object (3-D + time, hence, in 4-space) provided only its shadow is visible?
Over the years, (comma) I've kicked that idea around, never really pushing it forward, growing it, <enter clever metaphor here>, until recently, when discussing real-world geometry with a friend. The problem was how to measure the area of a surface that wasn't flat.
This led to the concept of projections.
I'm not sure, but I would imagine that my aforementioned friend would be of the opinion that everything is relative, and that particular vantage point comfortably encapsulates the whole projections thing.
I'm of a different mindset. Having been steeped in a mathematical mentality, in my world, there are rules. Things are as they are. Analogies are fundamentally flawed. They break down. As such, projecting from one sub-space to another, or one concept to another would be only partially describing it and, therefore, yield an incorrect outcome.
Essentially, to define an object based on its relationship to, or similarity of attributes of, another object cannot be effectively done.
Consider, if you will, the anecdote of me at the grocery store, circa 1985 (I picked that year arbitrarily so as to put myself in an era where there may actually have been grocers in existence.):
[Me] How much does this bag of apples weigh?
[Grocer] Five pounds.
[Me] And this bag of wheat?
[Grocer] Five pounds.
[Me] So, they're the same?
[Grocer] Ummm, no.
[Me] Ok, so, how much does a pound weigh?
[Grocer] *Pause* Have a nice day.
According to the measurement Powers-That-Be:
There are big guys in uniform situated somewhere in Europe.
They have guns.
They guard a rock.
In that rock, there is a cave.
In that cave, there is a vault.
In that vault, there is a nondescript piece of metal.
That piece of metal is the standard of measure representing one pound.
There are no analogies to break down. It is what it is: one pound.
Just ask the big guys with guns.
Don't ask the big guys with guns. I was just kidding.
posted by Mr. Metallic Vinca at 11:23 PM
0 Comments:
Post a Comment
<< Home