### Nephew Chris' rebuttal to Zeno's Paradox Sept. 2005

Sept. 2005

To Art of the Day Club:

I am now offering purchase incentives (not really) for anyone who purchases one my pieces.

Offer #1 - I'll cook you pancakes every Saturday for 3 months. I'll bring maple syrup but you provide the pancake batter. Bacon or sausage are optional.

Offer #2 - Free gardening service for next spring and summer, includes tilling, pruning, watering, and weeding. I get to take a few flowers home with me.

Offer #3 - I'll mow Susan's yard for a year.

Offer #4 - I'll walk your dog twice a week for a month. I will not, however, pick up your dog's doodoo. Except I won't walk my friends Jerry and Cassia's dogs; they nearly broke all his ribs and he couldn't golf for a month. He can walk his own dogs. Sorry, Jerry. You'll have to pick something else.

Offer #5 - Free listening for five months or 10 phone calls whichever comes first. I'll say stuff like "uh uh," "wow," "really?," "no kidding," " I can understand that," "gosh," and "you are really something for putting up with stuff like that."

Offer #6 - I am willing to negotiate.

Offer #7 - Under no circumstance will I wear one of my friend Matt's hats. I will wear his neck ties, however.You know the old saying about the glass being half full or half empty - it's all in how you look at things.

Well, right now the glass is either totally arid, bone-dry, empty, barren, dried up, and desiccated, OR there is still a tiny bit of residual water vapor clinging to a dust mote on the bottom inside of the glass. I'm trying to be positive and look at things as the latter instead of the former.In addition, remember the old saw about the frog who each time jumps half again as far from the bottom of the well and the question is how many jumps to get out? and the answer is the frog never gets out because he only jumps half of the remaining distance each time never reaching the top. Zeno’s paradox.

Well, I am interpreting this in reverse with a car driving over a cliff analogy. This ride has been exhilarating and creative and fun and exciting and if I subdivide the remaining distance to the bottom of the craggy rock strewn cliff bottom in half and continue to subdivide the distance to infinity, the car and I never crash on the bottom. I just experience time in ever increasingly small bits. So my ride in my Corvette artist convertible with the top down over the cliff of art with the wind streaming through my hair and my eyes watering and the car ever arcing downward in a graceful parabolic downward curve nearing the vertical but never becoming exactly vertical and never crashing..........into those rocks of nonart. This will be my glass is half full mixed metaphor.Just be aware that I was not in my right mind when I wrote this. And I will deny having any part in its creation or dissemination.

Thank you.

Bud

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Dear Uncle Bud

I don’t mean to burst your bubble, but your logic is flawed.First of all, while the frog in a hole analogy is theoretically sound, in reality the distance to the top of the whole would become so infinitesimally small that, taken in relation to the size of the frog, he would not even need to jump and could simply step out of the hole, or wait for a strong breeze to come along and blow him out.

Second, this frog analogy cannot be applied to a falling object, because, pertinent to the laws of physics, any falling object accelerates at a rate of 32 feet per second per second. This means that for every second you fall, you will be approaching the ground 32 feet per second faster than you the last second until you reach terminal velocity at which point the friction of air will make it impossible to accelerate; so you will simply continue at that rate until your convertible encounters something that will provide a greater resistance to acceleration (i.e. an outcropping of jagged rock).

Third, once again, while theoretically sound, your parabolic descent hypothesis does not factor in variables such as wind resistance or initial velocity. A fifteen mile an hour head wind factored in with a tall cliff and a slow initial velocity could result in not only becoming vertical, but actually rotating BEYOND the vertical. Another problem with the parabolic decent hypothesis is that any quadratic equation with a negative lead coefficient (which it would have to be in this case) will cross the x axis on the Cartesian coordinate plain (which represents the bottom of the cliff) and continue on infinitely below unless it's vertex starts below the x axis, which would inherently make it inapplicable in this scenario. The point where the parabola crosses the x axis is referred to as the solution, but even those parabolas which do not cross the x axis have solutions: they are simply imaginary solutions.

So even if you were to incorrectly apply a parabola that didn’t cross the x axis to this situation, you would eventually smash to pieces in some parallel universe.Finally, even though time is relative and you may experience time in ever decreasing increments independent of the rest of the universe, you would have to remain alive infinitely for you get infinitely closer to the ground without actually striking it. Obviously you cannot remain alive infinitely, even if you find your perception of time different from that of the rest of the universe.With that I wish you the best of luck in the days to come.Remember, should you need it, you can always count on me for moral support.

Sincerely,

Your Newphew,

Chris

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