Software Engineering discussion
Gödel, Escher, Bach
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Two-Part Invention
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After more thought, I think the "reference the future" lines are more in regards to the "self reference" themes in this book rather than a "Prime Mover" idea.
Consonant with an earlier comment, I see the Dialogs as examples of the concepts played out on stage for us to view. The Two-Part Invention is another example of the Zeno half-way puzzle acted out in the first Dialog, Three Part Invention. Only this time Achilles and Tortoise are trying to cover the distance of a proof of geometric congruency. Unfortunately, T. keeps inserting a new proposition prior to the conclusion and so makes A. stop “half-way”. Thus he never gets to the conclusion of the proof. Is this the second version in an endlessly rising canon?
I thought about how I could experience the original Zeno puzzle. As it is presented I see there is one factor unspoken: to actually prove Zeno’s point, the walker must shrink in size as he approaches the finish line. Otherwise, just be shear size the walker will cross the finish line because he can’t ‘walk’ one-half of say a millimeter or nanometer.
The way I thought of this puzzle is to start 12 feet from the wall. Assume you are exactly 6 feet tall. You move one-half way to the wall stopping at 6 feet distance from the wall. Your size will now shrink to one-half of your original height. You are now 3 feet tall. The ratio of your height to the distance to the wall is reestablished. If your height is always maintained at one-half of the distance between you and the wall, then I think you will never reach the wall. You will always be twice your height distance from the wall and so never reach the goal.
While I am patting myself on the back for this observation, no doubt someone will point out that was already discussed by Zeno. You see, I never read the original puzzle. I just have GEB as my reference.
Good thought. BTW... none of Zeno's original writings survive.
I'm not sure why they reference the future often. (Example: "Shorthand isn't invented yet") These lines add humor, but I'm guessing they have additional purpose. I would guess they are some "Prime Mover" or "Chicken & Egg" concept.
I see some parallel ideas between Zeno's paradox and the attempt to take steps in doing the A, B, Z proof. The steps to get to Z keep getting smaller, which is similar to the "Motion in Imposible" paradox.