Internal Recursive Exhaustion Example

This image shows not only the Brooklyn bridge but it’s history.

Here is a fictional account of recursive exhaustion over the time domain, from an unfinished novel.  In it a brilliant young woman mathematician explains internal recursive exhaustion.  In it, the idea is not to to extend the number of data fields, but to capture changes over time in a single set of fields.  A builder could put up multiple signs to show stages in the construction process.  But they would obscure the onlookers view of the site site itself.  Instead a single sign can be used.

“Let’s start with an analogy. Suppose that a company is putting up a new building. To inspire the workers and keep the public informed of their progress the owner requests that a large sign showing the building at the previous state of development be posted in front of the site.

“The first sign shows a messy building lot, with a lot of junk and garbage on it. Behind, it an actual viewer on the ground would see a nicely cleared lot, already for work to begin.

“Can you visualize that, the cleared lot with a sign in front showing the old uncleared one?”

The others nodded and looked intensely at her. Such an intelligent young women, all four men thought, not quite able to ignore her other appealing attributes.

“Alright then. Suppose that this viewer is actually the official company photographer. The picture he now takes shows that empty lot, with the existing sign in the lower right hand corner. To again show their progress, the company takes down the old sign and puts a copy of this picture up as the new one.

“As soon as the foundations are dug, with forms and rebar in place, the photographer comes and takes a new picture. It shows that amount of progress, plus the last sign, which is in the lower right corner. A copy of this photograph is put up as the new sign.

“Someone taking a close look at that lower right hand corner would see that it has the image of a sign in its lower right hand corner. And that sign has the image of a smaller one in its corner.

“Months later a person could see the entire history of the building, though she might have to use a magnifying glass to see the original uncleared lot.”

The image above is a badly flawed example.  See why in a post about the details of compressing image and numerical data.

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