So my room is 10 feet across, and I need to walk from one side to the other. Yet in order to go 10ft across my room I must first go half and another half. So 5 ft and then another 5 feet. But in order to go 5 ft I need to do half of that, and then another half. But every number in math can be broken down by halfs. So in order to walk across my room I must walk an infinite number of halfs! How can anyone walk infinity and how can one walk such a long distance in such a short distance of 10ft? Not my idea and not original, just thought i'd bring it up.
The reason it would take infinitely long if you measured it out is because there would be a pause between measurements. If you just walk it out there would be no pause, therefore you can make it to the other side.
because the halves are immeasurably small, you would travel an infinite number of them with each step
Yea, I never understood how something that isn't infinite in extension can be divided infinitely; the idea that a finite space can be divided infinitely never made sense to me. Because it simply begs the question: how far is the space between each infinite division? RIP Zeno
I'm pretty sure you would measure into nanograms and then reach singularity, so it would just take a lot of steps. But i could be talking out of my ass...
Nothing is definite. It is only how you see it is. The present will become the past, as well as the future. And everything in between is an expansion of the same longevity.
The space between two points is not infinite, it is defined as the space between 10 feet in this equation. The space in the middle is confined by the two end points, meaning that as division occurs, the space between two points does not change, only the label placed on the points does. While it would be endlessly cluttered with points, the end points would confine it as a defined point, cannot be infinite. And you most certainly can divide any number in half until matter inverts, as splitting an atom has unexpected consequences, as im sure that those who studied einstein and world history know. But a better question is what if we could split an atom and then split half of half of that atom by freezing the process in real time? Truth is, human minds do not have the ability to understand what occurs in terms of "infinite and finite" as we have been taught to categorize as a way to simplify a mathematical process that we are incapable of grasping in terms of intelligence, so we build super computers to divide for us, and a good example would be protein folding. And to the op, the fact that your foot is measurable and larger than a torrent of the points means youd have to use a better and much smaller nano measurement to define a "step"
The space between two points is not infinite, it is defined as the space between 10 feet in this equation. I never said that the space between the two points is infinite. My post was directed to those who assert that infinite divisions can be divided within a finite space; I mean, that's exactly what the paradox is alluding to. The space in the middle is confined by the two end points, meaning that as division occurs, the space between two points does not change, only the label placed on the points does. While it would be endlessly cluttered with points, the end points would confine it as a defined point, cannot be infinite. That's exactly my point... how can a space that's restricted be filled endlessly? That's a contradiction in terms.
Oh forgive me i wasnt calling out your post, more using it as a foundation to base my opinion on. I actualy agreed with your post lol Edit And by the way, endlessly is a human term for "unable to grasp the full scale of labels" Mentally speaking of course. Its why words like plethora and torrent were invented in my honest opinion.
Here's an interesting read I found. http://www.slate.com/articles/health_and_science/science/2014/03/zeno_s_paradox_how_to_explain_the_solution_to_achilles_and_the_tortoise.html
The smallest length we know of is planck length which is 1.616<span style="margin-left:.25em;">199(97)x10<sup>−35</sup> meters</span>
thats just the smallest measurable distance, i can imagine half a planck distance, half of that and so on \n\n this was a pretty interesting thread i thought , did you read it ?