Zeno's Paradox

 This is the first if the typed rough drafts, I must get it down in some form to refine it and welcome any part of the discussion.


"His essential question was how can you do an infinite amount of tasks in a finite amount of time?"
How does this idea of addition/subtraction  solve this statement.
I often introduce Zeno's paradox in my math classes as a way to discuss asymptotic behavior and limits.  I am not the only one to do this for many teachers find it a nice way to consider these things.  The general arguments against Zeno involve limits but I was wondering if there was another way around it for even philosophers don't feel that such  mathematical disprove ends the philosophic argument.  In my musings and considerations, I stumbled upon both a simpler mathematical approach and perhaps a different way to answer it in terms of metaphysics.  At the center of Zeno's argument is that you can not divide something and have nothing. This is true. Even if the limit definition says the same the thing for the limit is not about the point of dividing by infinity but what that point would look like if we could do so.  Calculus added an extra definition for continuity at that point in case we care about its existence.  If one wants to argue against the paradox using the mathematics of limits one must also include that the lim f(x)= f(a) and that f(a) exists.
Zeno, like all good Greek thinkers, loved proportions.  He argued that the arrow would never make its target because it would always be 1/2 the distance closer. This simple statement is where he skipped a stepped of mathematics, logic, and philosophy.  A proportion is a form of division.  Division is the inverse of multiplication and multiplication is repeated addition.  We do perceive, measure, and understand the passage of the arrow or Achilles by addition.  (Recall that subtraction is just a different form of addition.)  While we can never divide something to be nothing or multiply nothing to be something, we can easily add something to nothing or take away to be nothing.  This element is true in the scenario but it was not expressed in the paradox.  In all logical or mathematical arguments, we need to express these things in the beginning for the argument may lose sight of simple definitions.  We turn the passage into a problem of division, which does not allow for the zero space but our original conditions do so.
The illusion of motion is turning the addition of intervals into a zero sized one.  It is viewing flight as photograph and stating that because it does not travel in zero time so it never travels.  Consider this photograph if we were in it, for that is how Zeno presented it.  If time is frozen, we will not perceive any motion or much of anything for we will always be puppets of the infinitesimal.  This moment is one of those semi-pointless exercises in philosophy for we know the arrow to travel and we know time to pass.  Theoretical physics can change the speed of time, and even pause it for light, but not for us. 
As for that original question, of which, I need to refind the source. Consider the whole path the arrow travels as one.  It goes 1/2 the distance in 1/2 the time, and therefore makes 2 intervals.  We can keep dividing the distance and increase the number of intervals.  It will go 100 intervals of 1/100th the time.  In this manner, we can find an infinite amount of tasks in a finite amount of time.  The challenge really highlights our analytic need to make things discrete and countable and the simple continuity of a line. 

Escaping in the moment.

A few phone pictures from late.  Not sure who made the snowman but it was outside of CK's after our one snow of the year.  He was about a foot tall with a leaf hat and pine needle arms.

It's another rough of a story. Some day, I will get them more better but I need to at least get them this far for me to feel like I have done anything.

    Three people stood in line behind her at the corner store.  They were all agitated at everyone taking so long since their lives were so important.  Either that or if they may get fired if they were late to work.  Regardless, their jobs were the most important ones in the world.  They had places to be and just couldn't wait on her getting something she obviously did not need at 8 A.M.
    Malinda Simpson was long past the point of caring, or at least not acting on it.  She knew they were looking at her and squinting their noses at her dingy coat overflowing with receipts.
    "Two 4'2, three 5's, and a 9."
    The clerk pulled the commercial rainbow of tickets off the stack of rolls.  She passed no judgement.  Her time selling people their daily needs taught her that all are hooked on something.  What they bought said nothing about them.  How they conversed through their bodies said much more.  She could see the condescending eyerolls of racist pigs and caught the sideways glances of the beasts needing to dominate.  There were the kind strangers helping someone buy food and even those who bought beer for the wino.
    "Everyone is a little bit of everyone and no one is like anyone," she told the young man who stopped by every morning to get coffee, cigarettes, and two honey buns.  Those words led him finish his EMT classes so he could help people, no matter who they were.
     Malinda left the store and sat in her car parked directly in front of the door.  She needed to keep it running since it might not start again.  People in the store could see it was full of clothes, food wrappers, cleaning supplies, and scratch off tickets.  Her car was her home, if home is where one sleeps.  It could just be how she got around and where she kept her few things. Malinda stayed in the parking lot of Gene's Quik Fuel.  They let her use the showers and it was generally a safe place to be.  There was a Clean Coin Mat next door.  The parking lot was were she landed after the turbulence of her actions and reactions to being ignored by her parents and then preyed upon by series of beastly men and women pushed, pulled, and spun her around in tales of our need to carry on despite the misery existence.  After one more trip to the free clinic, the nurse told her to go to Annie's Shelter for Women.  It was clean and warm and they didn't use her.  After some time, they gave her some odd jobs and she carved out a way for herself.  Few people cared but she knew that the women coming through the door felt better in a clean place.
     Malinda pulled out one of the tickets. It was red and green, Santa's Suprise, a jackpot was all but guaranteed.  She was nervous and excited.  A big smile at the dream of winning.  She started scratching of the metal powder, the action was freedom.  One of the all important agitated men behind her came out of the store and could see her eyes light hope and a real hope while she searched for winning numbers.  He wasn't sure if he felt joy or pity but he knew that his wait wasn't worthless for her. 

Time stops in the dark.

Some bad pictures of some work..

I am seeing if I can figure out how to write again. Not sure why, got a lot going on but sometimes the more you do, the more you can.  I'll probably burn out an go insane at some point but let's see if I can find some balance before then. This is first draftish...

At some point, they found themselves doing donuts in the park they grew up in.  It was not the best of ideas, but it seemed like a good one at the time.  No pain, no misery, no sorrow, just a distant sense of the need to be in the moment as the motor roared an rear tires skated across wet grass.  The tracks would disappear by spring, the headache would be gone sometime in a day or so.  A bottle of Colt 45 made them teenagers once again and it was not such a bad thing.
      Murray Strand buried his father a few weeks before and  Josh Breese poorly carried the weight of disappointment.
     The two grew up blocks apart, made fun of the same teachers, ran away to each others' houses, got drunk for the first time, loved the same women, got tattoos together, and all things boys share as they grow into life-stained men.  At times they fought, one or the other would dissappear to a new side of the country, only to be sucked back into the languid embrace of home.
     "Come by." Murray said in the message.
    "Why not," Josh figured.  It's late and everyone's in bed.  He was leaving work, a second shift at Steel America.  The man had been calling non-stop. He couldn't figure out how to be a good father, much less a decent husband.  About all he was good at was drinking and working.  Of course, the two things didn't like each other but they supported each other, a couple of codependents in a constant fight.  He figured he would just turn into an old drunk or a dead young one at some point.  He still had his pride and the silly belief he could  be a force of change but he generally killed his dreams after leaving the bar.
      "What up man?
     "Shit, same old."
     Murray and Josh embraced though it had only been a few days since they had seen each other.
     The stood on Murray's porch, watching a light rain drift down, falling like snow in the street lights.
    "Work's been kicking my ass."
    "I hear you, operator."
    Soon, they were to sharing a pack of cigarettes and reaching for the last beer.
    "Damn, I'm hungry."
    "I got an idea."
    They walked into ** Diner. It was late enough to be quiet before drunk punks stumbled in. Murray gave the man at the end of the counter $5 to play music.
    "That's how you do it there."
    It as another song about love. A man pining for his woman.  It may have been about lust but who can tell the difference.
    "Eggs are better with bacon."
    "What's Matts up to?"
    "Let's check."
    They drove over to Matts' house.  He was almost asleep but led them on a game of fifty states,
    "I bet you can't write down all 50 states."
    Josh did.  Iowa was the last one, it seemed hard to remember being wrapped up in all those other states he had driven across. He had to bum a menthol from Matts, maybe it was his girlfriend.  It went well with cheap beer.
    "Man, you should go to bed. We'll check you later."
    "Cool, bro. Good seeing y'all."
    They left and found a corner store.  Time did not exist for it had turned to the present.  They talk about relativity in physics, time and space are axises on some strange graph.  The whole problem is time is a creation of the self-aware.  Place is a fact of perceived existence.
    "That was my house."
    "Yes it was."
    They were in the playground in the park. The same place they once played baseball in.  Back before they found out about drinking and stupidity.
    "Malt liquor ain't as bad as I remember."
    "It probably is."
    Murray commented as he walked across the top of the tyke's swingset.  He always had good balance.
    "Feels good to be here."
    "That it does."
    Back in the truck, Josh decided to drive across the park.  He pressed the gas and watched the needle spike; the ass end of the truck went hither and tither until it broke free into a real donut.
   Murray held onto the handle and yelled at something.
   The moment was real and would soon be gone. Not the right thing but something needed to be done.