The world’s most mind-boggling paradoxes


Productivity hacks

When it comes to leaving you scratching your head in disbelief, nothing beats a good paradox. A paradox is a statement that contradicts itself and is generally used as a thought experiment to help your critical thinking. They come in various forms, from the mathematical to the logical and philosophical. Almost all of them leave you shaking your head and struggling to find an answer.

Here are some of the best paradoxes for promoting critical thinking and forcing you to ask the larger questions in life.

Braess’ paradox – Improving traffic infrastructure makes it worse

We’re going to start with a paradox that talks about something we can all relate to: traffic!

In 1990, officials closed New York’s 42nd Street. In 1999, one of the three main traffic tunnels in South Korea was closed. Despite both of these being main roads for drivers, the expected traffic chaos never came. In fact, traffic flows improved.

Braess’ paradox refers to traffic that gets worse the more routes are added. This can happen because despite faster routes being available, more drivers will take the ‘fast’ route, causing it to become congested. Oasys has a full explanation.

Schrödinger’s cat – Alive or dead?

This is a thought experiment that has a basis in science and is often referred to as a paradox. It uses the theory of quantum mechanics to ask whether a cat in a box is alive or dead – or whether it is both at the same time.

Imagine a cat in a steel box. The box has a Geiger counter, bottle of poison and a radioactive sample. If the counter detects the radioactive material has decayed, it will smash the bottle of poison and kill the cat.

Because you cannot know whether or not the material has decayed and because the material has a 50/50 chance of decaying, you cannot know if the cat is dead or alive. Unless you look in the box, the Copenhagen interpretation says that the cat is both alive AND dead at the same time.

The Ship of Theseus – Is an exact replica the same object?

This philosophical question is becoming more poignant as topics like digital immortality rise. The Ship of Theseus comes from Plutarch, who asked whether a ship that had been restored by replacing every single wooden part was still the same ship.

Is an object that is taken apart and put back together with the same material the same object? Taking the example further, what would happen if you took apart the ship, rebuilt it with new materials and then used the original material to build the same ship? Which would be the original then?

In science fiction, this paradox is often posed to readers who see a character having parts of their body replaced by exact mechanical replicas. Eventually, the person is an android – but are they still the same?

Omnipotence paradox – Can a god create a more powerful god?

If an omnipotent force is all-powerful, can it build a rock so heavy that it cannot lift it? This is an example of the omnipotence paradox – can a being that can do ANYTHING create a task that it cannot perform?

This is mainly a semantic paradox around the word ‘omnipotent’. If you are all-powerful, could you technically create something even more powerful? Can anything ever be truly omnipotent?

Liar Paradox – What is true cannot be false?

The statement on this line is true.

The statement above is false.

Which of these sentences is true? For either of them to be truthful, the other is wrong. This paradox means that putting a truth value to a statement produces a contradiction.

Bootstrap paradox – Creating infinite loops in time

This is a favourite of time travel enthusiasts. If you were to travel back in time to visit Shakespeare and find that he hadn’t written anything yet, you may panic. In your panic, you head back to our time and pick up the complete works of Shakespeare. You take them back in time to Shakespeare, who copies them.

When you head back to our time, who created the works of Shakespeare? You’ve created an infinite loop where information is never actually created.

The ‘Kill Hitler’ Paradox – If you kill Hitler in the past, why kill him at all?

Another paradox related to time travel, the ‘Kill Hitler’ paradox is a version of the grandfather paradox — if you travel back in time and kill your own grandfather, do you cease to exist? Will time prevent it?

If you travel back in time to kill one of the world’s most notorious criminals, Adolf Hitler, and you are successful, then Hitler is dead. This means you’d have no reason to go back and kill him in the first place. If you killed Hitler on a trip back in time, none of his actions would occur and therefore you’d have no knowledge of them to make you go back and kill him.

Arrow Paradox – Every instant is frozen

In a single instant, zero seconds pass. The arrow paradox is created when someone shoots an arrow into the air. If you could analyse a single instant at any point, the arrow is not moving backwards nor forwards and occupies its own space in that instant. This repeats each instant, with the arrow never actually moving despite the fact that it is. Therefore, motion itself does not happen. It takes a special understanding of relativity to explain this one.

Two Envelopes Problem – How can you ever know which value is higher?

The ‘Exchange’ paradox is a brain teaser. Someone gives you two indistinguishable envelopes, both of which have money in but one has twice as much as the other. You have to pick one envelope, but once you’ve picked you get a chance to take the other envelope.

Technically, both envelopes have as much chance as the other to have more money in them. How do you know which is the best decision to make? There is no logical way to make the choice.

The Catch 22 paradox – can you escape an impossible situation?

Joseph Heller wrote a satirical novel called Catch 22 which describes a paradox wherein pilots try to get out of combat duty by proving they are psychologically unfit, but by trying to get out of combat duty they prove they are sane.

The term describes any situation where you cannot escape because of contradictory rules. A common example is when you apply for a job but need years of experience, but you need the job to get that experience.