10 Completely Mind-Bending Paradoxes
10.
Hilbert’s Paradox of
the Grand Hotel
Imagine if you will, there is a hotel with an infinite number of rooms and each room
is booked with an infinite number of guests.
If that were the case, then every single room would be booked, right?
Because an infinite amount of guests would fill an infinite amount of rooms.
But the hotel has a weird paradox where there are always vacancies and they are always booked.
This can be seen when a new guest shows up.
To find him a room, David Hilbert, who thought of the paradox, suggested that everyone move
to the next room.
For example, one moves into two, two moves into three and so on.
But what happens if more than one person shows up, say another infinite amount of people?
Hilbert says that the people in the rooms could just go to the room number that is double
their current number and then there will be room for everyone.
This paradox speaks to the nature of infinity and has fascinated mathematicians for decades.
It also probably has given more than a few hotel employees terrible nightmares.
9.
The Raven’s Paradox
Logician Carl Gustav Hempel first proposed his “raven paradox” in the 1940s and it
questions our belief in confirmation.
We make confirmations in both science and everyday life based on observations.
For example, let’s say a detective was trying to solve a crime.
He would find evidence and the evidence would back up his theory, disprove his theory, or
the evidence could be neutral.
The evidence could also be strong or weak.
What Hempel asks is what does it take for a piece of evidence to confirm the hypothesis,
rather than disprove it or be neutral about it?
To demonstrate the paradox, Hempel talked about ravens.
He said that after observing a few ravens and noticing they were all black, someone
may infer that all ravens everywhere are black.
But that is impossible to check, because there have been so many ravens throughout history
and there will be more in the future and just one non-black raven would disprove the theory
that all ravens are black.
Also, there is the contrapositive, which is another theory that is the opposite of the
hypothesis but it is still true.
For example, the contrapositive for “all ravens are black” is that “all non-black
things are non-ravens.”
That means that every single thing that is non-black and non-raven, like a blue shirt
or a yellow tennis ball, proves that ravens are black.
Of course, there are way too many non-black non-raven things in the universe and so that
type of information really does not contribute to the hypothesis that all ravens are black.
The raven paradox is meant to be a warning against generalization and that there needs
to be a limited scope if a scientist wants to prove something beyond a doubt.
8.
The Friendship Paradox
An interesting paradox involving social circles is that you most likely have a friend who
has more friends than you do.
This seems like a pretty broad statement considering we don’t know you personally, but we’re
sure we’re right.
The reason we can assuredly say you have a friend who is more popular than you is because
nearly everyone has a friend who is more popular than them.
But, why is that?
Well, first and foremost, people with a lot of friends are more likely to be your friends
anyways.
But why everyone probably has a friend more popular than themselves is because popular
people are part of more social networks so they are misrepresented in averages because
they appear more times.
This makes it look like there are more popular people, but popular people actually just spread
themselves out more and this effects probability.
Of course, the paradox is much more complicated than we’ve explained, but if you like to
learn more, visit this great New York Times article about it.
So if it seems like other people are more popular than you, they probably are, but that
is due to the laws of probability.
7.
The Barber Paradox
The Barber Paradox from British Philosopher Bertrand Russell takes place in a small town
with some strict personal hygiene laws.
In the town, by law, all men must be clean shaven and they have a choice as to how they
shave.
They can either be shaved by the one male barber in town, or they can shave themselves.
The paradox that arises is: who shaves the barber?
When he shaves, he is shaving himself and he is being shaved by the barber.
We highly recommend not asking your hairdresser about this paradox next time you get your
haircut; they may lose their concentration while thinking about it!
6.
Buridan’s Bridge
Written by the Ancient Greeks and first described by philosopher Jean Buridan in the late middle
century is the paradox of Buridan’s Bridge.
In the paradox, Socrates is travelling and wants to cross a bridge that is being guarded
by Plato.
Plato tells Socrates he can only pass if he tells him the truth.
But if Socrates were to lie, Plato would throw him over the bridge to drown him.
Socrates responds by saying, “you will throw me in the water.”
So what will Plato do?
Throw Socrates in the water?
That would mean, Socrates was telling the truth and should have been allowed to pass.
But if Plato allows him to pass, then Socrates wasn’t telling the truth.
5.
The Liar’s Paradox
The liar’s paradox can be summed up in one sentence: “Everything I say is a lie.”
But it is impossible for that sentence to be true because if everything I do say is
a lie, then that sentence would be true, meaning that not everything I say is a lie.
To illustrate the point, let’s look at two variations of the paradox.
For the card paradox, pretend you had a card or a piece of paper, and on one side of the
card it says, “the statement on the other side of this card is true.”
While on the other side, it says “The statement on the other side of this card is false.”
Both sentences can’t co-exist with each other on the card because they cancel each
other out.
Another variation of the liar’s paradox is the Pinocchio paradox.
In the paradox, Pinocchio lies and says, “My nose grows now.”
Since he’s lying, his nose should grow, but if his nose grew, then he wouldn’t be
lying.
Hopefully Pinocchio doesn’t test that paradox in the upcoming movie about him; his little
wooden head might explode.
4.
The Sorites Paradox and The Ship of Theseus
These two paradoxes are similar because they are paradoxes about vagueness, so we’re
going to make them one entry.
First is the Sorites paradox, otherwise known as the heap paradox.
For the paradox, there are two presumptions:
A million grains of sand is a heap.
A heap minus one grain of sand is still a heap.
That means if you removed one grain of sand, 999,999,999 grains of sand would be left and
that is still a heap according to the second presumption.
But what if you kept removing grains of sand one at a time, when would the heap stop being
a heap?
If the second presumption is true, then even one grain of sand or a negative amount of
sand would be considered a heap.
If that wasn’t thought provoking enough, then hopefully The Ship Of Theseus will get
you thinking a bit more.
Imagine there was a boat and piece by piece, the entire ship is replaced.
Is that still the same ship?
Another example is Washington’s ax.
Is it still his ax when the handle has been replaced three times and the blade twice?
Both speak to the nature of identity and asks the question, when does an object stop being
that object?
Interestingly enough, debates about these paradoxes are starting to emerge with the
possibility of human and computer augmentation.
If a person gets computer or machine upgrades on their mind and body, at what point do they
stop being a human and become a machine?
3.
The Birthday Paradox
If you had a group of 23 people, what are the odds that two of those people shared the
same birthday (month and day, not year)?
Logically, it seems like a pretty small number.
After all, there are 365 days in a year and only 23 possible birthdays.
Yet, there is a 50 percent chance that two people will share the same birthday.
If there is a group of 30 people, then there is a 70 percent chance and if there is a group
of 70 people, then there is a 99.9 percent chance that two of them will share the same
birthday.
But why is that?
Well, it’s a rather complicated process involving the laws of probability.
To make this easier, we’ll look at the probability for each person.
When the first person walks into the room, there is zero chance anyone has the same birthday
as him or her because no one else is in the room, making the probability 365/365.
Then the second person walks into the room and the chances of them having a unique birthday
are 364/365.
Then for the third person, it is a 363/365 chance that they will have a unique birthday.
This continues on until the 23rd person, who has a 343/365 chance of having a unique birthday.
Then you multiply the 23 probabilities together and it equals 0.491 and then you subtract
that from 1, which leaves you with 50.9.
Which means that the odds that two people out of 23 will share the same birthday is
50.9 percent.
To test the theory for yourself, try random combinations of 23 people on your social media
accounts.
About half the time, you should find two people with matching birthdays.
2.
The Bootstrap Paradox
Paradoxes are a fundamental part of time travel and one of the more interesting ones is “the
bootstrap paradox”, also known as causal loops.
The paradox gets its name from the short story “By His Bootstraps” by famed sci-fi author,
Robert Heinlein.
The paradox works like this: let’s say you bought a copy of Romeo and Juliet and travelled
back in time to the English Renaissance.
Once there, you find a young William Shakespeare and you give him the copy of Romeo and Juliet.
He copies the play word-for-word and then he simply presents the play instead of writing
it.
As the centuries go on, it’s finally the present day and you find the same copy of
Romeo and Juliet that you gave to Shakespeare.
Now, if you gave Shakespeare the story, then who wrote Romeo and Juliet?
1.
Specious Present
This paradox purposes the question, is anyone or anything ever really present?
To consider the paradox, it is important to ask what exactly is “the present.”
A second?
A nanosecond?
Well, those units of time can be broken down into three parts; the beginning, the present
and the end.
But then each time it gets dissected, the new present could be divided again into the
beginning, middle and end.
And theoretically, this can just keep going on indefinitely and the present can always
be divided into three smaller parts.
So if time can always be divided, does the present ever exist?
Because if the present can always be broken down, that would mean there is no duration
known as the present and there is no gap between the past and the future.
A further extension on the paradox is that in order for something to exist in our universe,
it has to have a duration.
For example, something can’t exist for no amount of time.
So if the present has no duration, does that mean the present doesn’t exist?
And if there is no such thing as the present, what does it say about the existence
of the universe?