- Prepare to have your head spin, again!
(eerie music)
The Coastline Paradox argues that any single coastline
can have different lengths
and reaching a definitive length is basically impossible.
In a satellite image of a country,
the clear outline of a country against the ocean,
is defined by its coastline.
But the closer you zoom in,
the more ambiguous it becomes.
That's because coastlines have fractal properties
like fjords and bays.
A straight line is defined by the shortest distance
between two points, so length will all depend
on the units of measurement.
Using centimeters to measure the length of a curve
will get a bigger number than using meters or miles,
which would miss out on all the small details.
As an example, Australia is said to have a coastline
of 12,500 kilometers,
but the CIA's World Fact Book, has it listed
as 25,760 kilometers.
That's an over 13,000 kilometer difference
for the same landmass.
Look up the measurement problem, it's a mind twister.
The Paradox of the Court
dates all the way back to ancient Greece.
The story goes that the philosopher Protagoras
agreed to teach Euathlus law,
with an agreement that Euathlus would pay for the lessons
after he won his first case.
But after finishing his training,
Euathlus decided he didn't want to be a lawyer
and wouldn't pay.
So Protagoras sued him and argued to the court
that if he wins, Euathlus would have to pay him
by court order.
But if he loses, Euathlus would still have to pay
because he'll have won his first case.
But Euathlus counter-argues that if he wins,
he wouldn't have to pay because of the court ruling
and if he loses, he won't have to pay
because he will have lost his fist case.
The paradox arises with the use of counter-dilemma
in response to the initial dilemma.
Did you catch all that?
Rewind it, play it back if you need it, but it's a good one.
The Unstoppable Force Paradox
dates back to the Chinese philosopher Han Feizi
in the third century B.C., who wrote,
what happens when an unstoppable force
meets an immovable object?
He presented the conundrum of a man selling
an indestructible shield and a spear
that could pierce any object.
When asked what would happen if the spear hit the shield,
the seller had no answer.
This paradox assumes unstoppable forces
with infinite torque and immovable objects
with infinite mass are separate entities.
But these are self-contradictory since each
should cancel each other out.
If you have an unstoppable force,
an indestructible object cannot exist.
But if you have an indestructible object,
an unstoppable force cannot exist.
And basically the only reasonable answer is see
is that both forces would just explode,
kind of like my brain just did.
The physicist Erwin Schrodinger
devised this thought experiment
to dispute the Copenhagen interpretation
of quantum mechanics and quantum superposition,
which states that any physical object can exist
in all possible states at the same time.
The experiment consists of a cat in a steel box,
with a Geiger detector,
a small amount of radioactive material,
a vial of poison, and a hammer.
But don't go trying this at home,
it's just a thought experiment.
Once the Geiger detects the radioactive substance,
the hammer will break the vial of poison, killing the cat.
But because radioactive decay is random,
there's no way to predict when the cat will actually die.
So as long as the box is sealed, the paradox has it,
that the cat is both equally alive and dead.
Schrodinger disagreed with the premise in large objects
and believed that it would only work in tiny things,
like electrons.
Galileo's Paradox is about the possible infinite series
of square numbers.
In mathematics, if a set is finite,
it contains a finite number of elements.
However, if a set is infinite, like natural numbers are,
it can go on forever.
There are more natural numbers than square numbers,
but the paradox has it that there has to be
the same number of both.
Galileo used an infinite series of positive integers
and a subset of square numbers.
Some numbers are squares, but not all of them,
so the total of the numbers must be more
than the amount of squares.
But every square has a positive number
that is the square's root,
and every number has one square.
So you can't have more of one than the other
and the subset can also be infinite.
Basically the paradox uses the one-to-one correspondence
and Galileo concluded that less, greater, and equal to
can only be applied to finite sets and not infinite sets.
Okay, that one hurt my brain.
Hopefully you followed it, if you didn't Google it,
it's really interesting.
In artificial intelligence, there's been an assumption
that creating simulated reasoning will be difficult,
but low level skills will be easy to design.
Moravec's Paradox was first proposed in the 1980s
by a group of engineers, including Hans Moravec,
who were researching AI.
They argued that very little work is actually needed
to develop reasoning in robots
and get them to do tasks that we consider
to require high intellect, like playing chess
and doing well on IQ tests.
It turns out, actually trying to get robots
to perform the simple sensory tasks
that we do subconsciously are the biggest challenges
and also require the biggest computing requirements.
This is because they're the hardest
to successfully reverse engineer.
Essentially, it's the opposite of our logic.
Exhibiting adult-level performance
on intelligence tests is easy,
and giving them the skills of a child
for perception and mobility is actually hard.
The Problem of Evil is believed to have been originated
by the Greek philosopher Epicurus
and is based on traditional theology that has been debated
by theologians and philosophers for centuries.
It's a trilemma based in logic that argues firstly,
God exists and is all knowing, all powerful, and all loving,
also known as omniscient, omnipotent, and omnibenevolent.
Second, there's evil in the world.
And third, that if the second is true,
then such a God does not and cannot exist.
The paradox arises when you consider that this God
cannot coexist with evil.
The argument goes that if there's evil in the world,
then God is not all-encompassing and all-loving
and by extension, doesn't exist.
But if there is a god, who is both these things,
then evil cannot exist.
For both God and evil to exist
would be a logical contradiction.
The Potato Paradox is a veridical paradox,
which means that the result seems ridiculous and impossible
but math is sneaky and can logically be
demonstrated to be true.
To understand this paradox,
imagine you have a pile of 100 pounds of potatoes.
So basically you're in heaven
and for the sake of this example,
those potatoes are made up of 99 percent water
and one percent pure potato.
Overnight some of the water evaporates,
so that the next day, they're only 98 percent water.
So how much do they weigh now?
Well, get ready to have your brain mashed
because the answer is 50 pounds.
The reason for this is kind of simple.
If pure potato weight is one pound,
which is one percent of 100 potatoes,
then two percent must be 50,
because for the percentage to be doubled,
the total weight has to be half as much.
Oh man, I think I'll stick to french fries.
Gabriel's horn is named after the archangel Gabriel,
whose horn was associated with the divine
and by extension, all that is infinite and finite
in the world.
Follow me on this.
It all starts when 1/X, is plotted with X equaling 1,
to X equaling infinity, all while rotating
around the X axis, which forms a geometric figure
in the shape of a horn.
Now the horn has infinite surface area
because from the large opening,
the horn gets continually smaller and smaller
going on forever without ever closing.
But despite this, mathematically it also has finite volume.
This becomes known as the Painter's Paradox
when you consider painting the horn.
The paradox has it that because the volume
of the horn is finite, you could fill the horn
with a finite amount of paint.
But in contradiction to this, a finite amount of paint
would not be enough to paint the entire
interior surface area because it's infinite.
(screams) Oh we're still recording,
sorry I think my brain broke.
The Penrose Triangle or Penrose Tribar
is a paradox illusion, or an impossible image.
It was first designed in 1934
by the Swedish artist Oscar Reutersvard
and made popular in the 1950s
by the mathematician, Roger Penrose
and were common in the work of the artist M.C. Escher.
The image of the triangle is essentially an optical illusion
that is impossible to reason.
At first glance, it appears to be a two-dimensional triangle
drawn as a three-dimensional object,
but despite what Labyrinth would have you believe,
no 3D object could fit the dimensions it's been given.
That's because the perspective of the image
is shifted to a contradicting position
within the same image.
Both perspectives are equally represented
and you can view it both ways,
but you can't make sense of both perspectives
at the same time, and so it becomes ambiguous.
Okay, headache achieved, let's wrap it up.
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