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?
