Sophism #6: The Dichotomy Paradox

One sunny Monday morning Homer decided to go to his favourite bar to get a can of beer. Right before leaving the house, he paused to think for a moment:

"The bar is located 1km away. If I start walking now, I will first have to spend some time and effort in order to walk half of the whole distance to the bar (i.e. 500m). Continuing from there, I will have to spend yet more effort to walk half of the remaining distance (250m). Covering half of whatever remains requires time and effort again, and so on forever! No matter how close I am to the bar, I always have to spend yet more time walking half of the remaining distance first. It seems I will never reach that bar today. I better stay on the couch where it's safe!"

If you watched the video referenced in the previous sophism you should already know that this is another one of the famous Zeno paradoxes. It is closely related in essence to the story of the Achilles and the Tortoise: in both cases the confusion arises because we represent a finite process as an infinite sum.

For other sophisms check out this list.