Zeno's Paradox Explained

Here is just a random link i found in case you are not familuar with the thoughts.
www.franzkiekeben.com...

Simple answer here that i would like anyone to steer me in the right direction if i am mistaken. The whole series of paradox's arise out of equations givin to us under the guise of having the proper information for us to solve them but no agreement can be found because of a flaw in the origional thoughts. The measurement of distance has never been correct to properly measure any element or vastness inbetween.

If i say half of the distance you say ok but you do not know or have properly measured the whole so therefore you have never identified the true half. Taking it a step further it seems that atoms may be the measurment that should be used because of the actions thet follow when it is cut in half. What say you?

a reply to: deadeyedick

Do you see a relation between this paradox and the one about "can God create a rock so heavy, that even He cannot lift it?"

Also, the "possible binary nature of the universe" thread I read recently reminds me of paradoxes: www.abovetopsecret.com...

I am big into philosophy but perhaps my inferior understanding forces my train of thought to stop short. When there is a paradox, it is difficult to come to an ultimate conclusion/solution and I have a hard time letting things go. I think paradoxes are causing me to lose sleep at night

Another sleepless night for me, it will be. Sadly I also have an accounting exam tomorrow If I fail, I succeeded in my attempt at least. But either way, it is still a failure AND a success (another 1 for ya)

Here is the best explaination i found a bit ago while walking.
Let's say there is a candy jar full of gum drops.
One person measures it and says it is 8in in dia.
Another person measures it and says it is 16 gumballs wide.
Now if you cut the measurements in half and half and so on then the one in inches fails but the one measured in something real does not. These paradox's were put in place to confuse us. We could even now say that the jar before the gumballs was void and without form.

a reply to: deadeyedick

I like that paradox a lot. I never thought it makes for a big problem, but some argue it does. Regardless, the universe obviously does not care, things don't take forever to get to their destinations. We know why: If the thing travelling the distance is reduced down to a simple tiny particle travelling at a constant known velocity, then it doesn't actually have a distinct location at a any time. Its a a probability blur as to where it might be. At some point, the probability of it being around its destination approaches 1, and we observe it there with high probability. However, as we keep cutting the space in half between in and its destination into smaller and smaller slices, the probability of us observing it in that slice of space approaches 0 as the slices get smaller. So when can never observe Zeno's paradox taking place... and guess what? We in the physical universe we never do.

a reply to: tridentblue

I see your point however it is not correct. The particle is a portion of the whole distance traveled so then we know that the distance can never be less than the size of the particle. Paradox ends there. Breaking the whole down into measurments of the particle will give us every point and speed can then be determined at any point within.

a reply to: deadeyedick

I don't understand you, so maybe you're correct or maybe not.

To me though it never took fancy things to solve it. There is this thing called velocity. If the ball is a meter from the target, and travelling a meter a second, then it will get there in a second. It will cross the last half in 1/2 a second, the last 1/16th in 1/16th of a second, the last 1/2^10000000000000000th in 1/2^10000000000000000th a second, and so on. As the divisions get smaller the time is takes to cross them become less, and that was always enough to satisfy me.

a reply to: tridentblue

If the ball represents a meter then what is a second? You are totally correct with the numbers but in order to find the truth every measurment has to represent something real. Numbers are not real. The divisions arise because of the false value of the numbers. You could say that seeconds are eaqual to the ticking of the clock then the last tick will be the stopping point.

Say that what you are calling a meter is a stick and the ball is eaqual to the length of the stick and is one stick length from the target. The smallest point in that scenerio will be one atom of the stick past that point it does not exist because of the decay that will happen if you cut the atom in half. The numbers will go on forever but the actual space that is made up of atoms does not and they are numbered. Leet's just say for kicks the stick has one million atoms then you cut that in half and so on until you get to 1. Paradox ends.

If it were truely a paradox then the ball would never hit the target. All things made manifest are comprised of parts that can be measured but to get to the truth you have to start with the sum of the smallest part. Coult be called a unit but there really is not a single standard unit because all things are somewhat different.

The question is erroneous. The question is trying to force you to use time as a qualia (which are timed actions) while simultaneously using time as a qualia independant of the prescribed actions -- in doing so, it invalidates the question.

In the question, time should only be measured by the timing of the actions (timed actions):

e.g.
You can make:
action one = 30 seconds
action two = 15 seconds
etc

until your actions equal "1 minute" (infinity), but you cannot both ask for time independance for a singular action and then in the same breath ask that the time be dependant upon "universal time" (a "real" minute/a clock's minute/relative time).

It must be either relative to the clock, or timed actions, but it cannot be both.

These are not exactly paradoxes. They are just trick word problems which play on mathematical concepts, and only appear as paradoxes.

For example... The Racetrack Paradox is just a play on division and infinitesimals. He asks you to divide the race track in half, and run to that point. Then divide the remaining half in half, and run to that point. Then divide the remaining quarter in half, and run to that point, etc. He is just asking you to divide the remainder in half, over and over again.

Each time you divide the remainder in half, you end up with a smaller remainder. Sooner or later the remainder becomes so infinitesimally small that you don't even appear to be moving, but you are technically still moving closer to the finish line. But, you will never reach the finish line while doing this because of one simple fact...

Mathematically (on paper) you can divide something infinite times. So you will always have an remainder, even if its infinitesimally small. In terms of the racetrack, you will always stop short of the finish line, infinitely. But that is only on paper (and in the mind) as a concept. In reality, when the remainder of the racetrack left to the finish line is 0.999999999999999999... you would just round up, and consider the race complete because its such an infinitesimally small value that you can't tell the difference.

This concept of the racetrack is often used to "prove" 0.999... repeating is equal to 1. Which I don't agree with, because it is not, because you always have an infinitely small remainder left. But math nuts will talk about "limits" and other concepts which are just wrong. Our decimal system lacks the ability to represent 0.999... and most people lack the ability to understand infinite.

You can read more about it here:
en.wikipedia.org...

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When you step back and take a good look at the racetrack "paradox", you see why it's not a paradox. You are just being asked to do a repetitive task (infinitely divide remainder), and are being told this repetitive task is equal to running a lap around a racetrack (which is not true), and it forms the illusion of a paradox.

The problem with it is, you can't equate running a lap around a racetrack with running and stopping an infinite amount of times.

a reply to: WeAre0ne

Yes and my point is that you can never find the halfway point to begin the exercise unless you start at the finish and get a true representation of what one eaquals. The one at the smallest level can not be cut in half and still exist in a measurable manner because of decay. We could say the track is a thousand air molocules long and then find the halfway point. But if we just say it is 1000meters long we do not know what units or material things are comprising the whole. That would get you close but not exact.

All in all it shows how numbers can fail us and many minds have been brought into the mindset of the paradox.

Before you can travel an inch, you must travel a half of an inch...before that a quarter of an inch...you can make an infinite amount of these sub-divisions...therefore, even to travel an inch, an infinite number of motions must occur...infinity being unreachable, distance and space must be an illusion...

Before a second can come to pass, a half a second must pass...before that a quarter of a second...there are an infinite number of sub-divisions, therefore an infinite number of moments must come to pass before a second can come to pass...infinity being unreachable, time must be an illusion...

a reply to: TheJourney

An inch of what? Unless you determine what the parts are that comprise an inch the math will be wrong. In the case of the ruler an inch is a certain number of wood fibers comprised together to form the whole inch. In order to get to the answer you need to set the number of fibers and then cut that in half and so on until you get to one. To cut the last fiber in half you need to know how many molucules or whatever makes up that fiber. You will continue until you get to a single smallest unit or molocule and then the paradox ends because the smallest unit can not be destroyed and still exist to be counted in any manner because time and decay will then become factors. Everytime we use measurments we just ballpark the answer enough to get the job done but to get a true reading all parts of the whole need to be counted in order to begin to apply math in a manner that is not just an average or just a guess.

To me, Zeno's paradoxes have never made much sense. I mean, sure, you can divide a set distance up into a series of fractions, 1/2, 1/4 and so on, but you are still going a set distance. For instance, the racetrack. Let' assume he is going at a rate of a foot per second, and the racetrack is 60 feet long. As long as he keeps going at that rate, it doesn't matter how far down you want to break up that distance, our runner will still reach the finish line at the end of the minute. I don't know whether it was on purpose or accidental, but Zeno's paradoxes always forget velocity, and its relationship with time(the faster you are moving, the more you are travelling through space, and less through time.)

An infinite process that completes.

Here is a video from Numberphile discussing it.

Time is just another false measurement that we get by with because we get it close enough to satisfy our needs. To properly measure time one needs to account for all actions from point a to point b. In our case the measurments that get us close enough are just actions of a clock hand moving. Move to the digital age and we have more precise ways to measure actions even down to the milli second but what we are really measuring is basicaly processor speeds and such actions within a set amount of actions.