# THE DICHOTOMY PARADOX

Imagine that you’re about to set off walking down a street. To reach the other end, you’d first have to walk half way there. And to walk half way there, you’d first have to walk a quarter of the way there. And to walk a quarter of the way there, you’d first have to walk an eighth of the way there. And before that a sixteenth of the way there, and then a thirty-second of the way there, a sixty-fourth of the way there, and so on.

Ultimately, in order to perform even the simplest of tasks like walking down a street, you’d have to perform an infinite number of smaller tasks—something that, by definition, is utterly impossible. Not only that, but no matter how small the first part of the journey is said to be, it can always be halved to create another task; the only way in which it *cannot* be halved would be to consider the first part of the journey to be of absolutely no distance whatsoever, and in order to complete the task of moving no distance whatsoever, you can’t even start your journey in the first place.

This is one of the 2400-year-old formulations of Zeno’s paradox, for which there have been a number of explanations over the centuries.

From a mathematical perspective, the paradox is resolved using a convergent infinite series. This is a series (such as 1/2 + 1/4 + 1/8 + …) which has an infinite number of terms, the sum of which converges on a finite value (1 in this case). When you consider that the time it takes to cover each segment converges towards zero along with the distance, you can illustrate that a finite time is required to cover the finite distance, regardless of how finely the distance and time are divided.

Zeno’s paradox has some interesting consequences when viewed in the context of quantum mechanics. The entire notion that reality is quantized into discrete increments means that time and distance cannot be infinitely divided into ever smaller chunks. There is a limit, a smallest distance (Planck length = 1.617 x 10^-35 meters) and a smallest unit of time (Planck time = 5.391 x 10^-44 seconds). These two units are related: a Planck time is how long it takes a photon moving at the speed of light to travel 1 Planck length. If time is quantized, then there is no point in time that exists between T and T + 1 Planck time. Likewise, the photon does not exist at any intermediate position along its path of travel between D and D + 1 Planck length. At time T it is at point D and at time T + 1 Planck time it is at point D + 1 Planck length.

In the context of quantum mechanics, Zeno’s paradox is resolved. The photon does not “move” from D to D + 1 Planck length. At time T it exists at D and at T + 1 Planck time it exists at D + 1 Planck length. A distance of 100 m can be repeatedly divided in half about 122 times before it reaches the Planck length and can be divided no more. The journey starts with a movement of a Planck length rather than the postulated “no distance whatsoever”.

### Your Answer

## More puzzles to try-

### Defective stack of coins puzzle

There are 10 stacks of 10 coins each. Each coin weights 10 gms. However, one stack of coins is defective ...Read More »### Farmer with bundles of hay tricky puzzle

A farmer has three fields. One of them has 3 bundles of hay, another has 4, and the last has ...Read More »### Always Changing

It is passed from person to person but no hands are needed. It often change in this exchange. Always changing ...Read More »### THE RAVEN PARADOX

Also known as Hempel’s Paradox, for the German logician who proposed it in the mid-1940s, the Raven Paradox begins with ...Read More »### Truck under overpass

John was driving his truck under an overpass when suddenly he came to a screeching halt. John wasn’t paying enough ...Read More »### How will you write 6 times?

Assume 9 is twice 5; how will you write 6 times 5 in the same system of notation?Read More »### Keep in suspense

How do you keep someone in suspense?Read More »### Help Arun to come out of maze puzzle

Arun got stuck in a maze with a many-headed Minotaur ready to kill him any instant. He has only one ...Read More »### Best Man Always wear me

A finger goes in me. You fiddle with me when you’re bored. The best man always has me first. What ...Read More »### Optical Illusion Puzzle – Can you identify what the picture is?

What is shown in the picture? don’t be distracted?Read More »### Wife murder investigation puzzle

A man murders his wife with a knife in their car. Nobody is around to see this. He throws her ...Read More »### Brother age easy puzzle

A boy is 2 years old, his brother is half as old as him. When the first boy is 100, ...Read More »### What is the color of that Bear?

A Bear has fallen from a height of 10m from ground and reached the ground in sqrt(2) seconds. Luckily it ...Read More »### Three house puzzle

There are 3 houses black, red and white . The black one is in the north ,the red one is ...Read More »### Weightless Elephant

What is bigger than an elephant yet weighs nothing. What is it?Read More »### How old did he live to be?

A man was born on January 1st, 23 B.C. and died January 2nd, 23 A.D. How old did he live ...Read More »### Find the odd Car

Optical Illusion: People with hawk eyes can spot a different car in 5 seconds. Can you? Test your vision now!Read More »### Fount in Caves

It is first found in caves, now prolific online; It is a depiction, a drawing, a symbol, or sign. It ...Read More »### Balance Checking

Today, my friend told me to help him check his balance. I did this without going to the bank. How?Read More »### Murder Mystery Riddle

One evening there was a murder in the home of a married couple, their son and daughter. One of these ...Read More »