- If you look at the distance between yourself and the doorway and realize that you would have to get half way to the door before you could get to 3/4 distance before you got to 5/8th before you got to 11/16th before ... ..., you could never get to the doorway.

I recently did a web search for solutions to this paradox and found something that bothers me still. All of the proposed solutions are only "pseudo-solutions" it seems. Maybe there is one out there that reveals the simple truth of it, but I can only find the solutions from Bertrand Russel and other famous and professional people who more often than not are simply dismissing the paradox, not resolving it. Some come up with "solutions" that aren't really applicable, but they don't seem to realize it. And I am again temped to proclaim, "What ... is ... wrong ... with you people??", not that I don't already know, I just have a hard time fully accepting it.

So okay, maybe if I think that I know the solution and so very many others don't seem to know it, maybe "my solution" has something wrong with it (many would love to think so). So gauge for yourself and argue as you will;

The JSS solution to Zeno Paradoxes

It is true that if one takes half of the distance between where ever one is and where ever he is going, there will be an infinite number of such steps. And if each step took the same amount of time, he could never get anywhere at all. Fortunately, each step doesn't take the same amount of time.

For each division of distance traveled, there is an equal division of time it takes to traverse that distance. If we say that half way to the door is 1 meter (thus the door is 2 meters away) and this takes 1 second, then the next step, only half of that half, is 1/2 meter and only requiring 1/2 second, and so on. So the problem concerning the time it takes to get to the door is a simple infinite series;

- 1 + .5 + .25 + .125 + ....

Or

1 + Σ (1/2)^n for n = 1 to infinity

And the solution to that series is simply 2.

And what is 2 times half of the distance to the door? The whole distance to the door.

And that is how people get to where they are going as well as how Achilles overtakes the tortoise.

Now what am I missing such that famous philosophers and mathematicians throughout history haven't been able to just say that instead of the complex, excuse making explanations they gave?

And then another more philosophically clever solution is simply that all things are actually always in motion, thus "the doorway" wasn't the real destination, but rather past the doorway. And one can get to part way to one's destination without Zeno's infinite number of steps concern.