Question on The Dichotomy Paradox

[LGram16]

Okay, I didn't really know where to post this, but whenever I hear about this paradox it is in a conversation relating to physics. Anyway, for those that don't know the paradox, it states that to get to point 'B', one must get halfway there before they can be all the way there. And to get halfway there, they must get halfway to halfway there (1/4) and so on. In saying this, it is rendered impossible to get to your destination. I am asking why. The distance you are at acts much like an asymptote, getting closer and closer to 0, while never reaching it. If it never reaches 0, then shouldn't there always be a distance to travel, no matter how far you break down 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, 1/128 and so on? If there is always a distance to move, than it is possible to begin moving, correct? The paradox assumes that movement is impossible because the pattern continues infinitely, meaning there is no beginning distance for the smallest halfway point to begin, which is true, but the smallest is not needed because an object can simply begin moving, speedily making it's way to 1/4 the distance, and then to 1/2, and finally to point B from point A. Just a thought I had, and wanted to share it with others to see if I was right or wrong.

 

[Gordianus]

The paradox you're referring to is a very old one and is called Zeno's paradox. It's over two thousand years old.
Check the following link:

http://en.wikipedia.org/wiki/Zeno's_paradoxes

 

[LGram16]

The paradox you're referring to is a very old one and is called Zeno's paradox. It's over two thousand years old.
Check the following link:

http://en.wikipedia.org/wiki/Zeno's_paradoxes

I know. I meant how is it true?

 

[russ_watters]

It isn't true. (assuming you mean how is it a real paradox) It's basically just a product of an underdeveloped understanding of math (at best!).

 

[pmacias]

I can provide some insight into the Dichotomy Paradox. This paradox is based on the concept of infinite divisibility, where a distance can always be divided into smaller and smaller distances. This means that, theoretically, there is always a distance to travel no matter how small you break it down.

However, in reality, we know that there is a limit to how small a distance can be divided. At the smallest level, distance becomes quantized and cannot be divided any further. This concept is known as the Planck length, which is the smallest unit of length that has any physical meaning.

So, while the paradox may seem to suggest that movement is impossible because there is always a distance to travel, in reality, there is a smallest distance that can be traveled. This means that movement is possible, as an object can simply start moving and reach its destination without being hindered by infinite divisibility.

Additionally, this paradox also assumes that time and space are continuous, when in fact, they may be discrete at the smallest level. This further supports the idea that movement is possible, as there may be a smallest unit of time that an object can travel in.

In conclusion, while the Dichotomy Paradox may seem counterintuitive, it is based on theoretical concepts that do not necessarily reflect the reality of our physical world. As scientists, we must consider all possibilities and theories, but ultimately, we must rely on empirical evidence to determine what is possible and what is not.