Translator: Ile Mon Reviewer: Dawn Theresa Suffling
Surfing the internet, I once stumbled upon a program
whose name I would translate
as a search engine for numbers that Fermat missed,
but that he nearly got.
Close, but no cigar.
It's a very simple program that tries different number combinations,
attempting to construct equations like the one we have before us,
X to the n, plus Y to the n, equals Z to the n.
For example:
3 squared is 9, 4 squared is 16,
5 squared is 25 and 9 plus 16 is also 25.
This program that I'm talking about
seeks to build more equations in this way but with an additional restriction:
the n exponent must be greater than 2.
I mean, instead of working with squared numbers,
it seeks to work with cubed numbers
to the power of four, to the power of five,
to any power greater than 2.
And we know that under those conditions,
it is impossible to build equations with that format.
We know this because it's called Fermat's Last Theorem.
A theorem that is pretty famous,
because it was proposed in 1670, and only proved in 1995.
It took over 300 years for mathematicians
to succeed in demonstrating something that this guy Fermat
had said back in the seventeenth century.
Now, I said that the program seeks to build equations
under specific conditions,
and then I added: it's impossible to build equations with these characteristics.
So, what is happening here?
The program seeks to build equations in this format and the restrictions,
but it also allows errors, as small as possible.
This is one of the equations generated by this program.
It has the desired format.
In this case, it works with the power of 12.
It satisfies the condition of being greater than 2,
but it's incorrect; that equality isn't really achieved.
You can see here the 2 terms created on the left.
The value of the sum
and the true value of the term on the right.
There's an error from approximately the tenth significant number.
That's so small, so tiny,
that if I verified that formula using a common calculator,
it would accept it as correct,
because the error is too small for a calculator to detect.
And I would find an equation that the theorem says shouldn't exist.
To the creator of this program, that honestly is of no interest;
it's a joke that makes us believe it found something that mathematics prohibits.
The program was created by David Cohen.
He is a graduate in physics from Harvard University.
He also has a PhD in Computer Science from Berkeley.
But the most interesting thing about this guy
is that he is one of the creators of Futurama,
along with Matt Groening,
and penned the scripts for many episodes of The Simpsons.
So, that formula that you saw a while ago
should not be so unfamiliar to you,
as it appears in a Simpsons' episode,
The Treehouse of Horror VI, 1995, when Homer goes into the third dimension.
We see it there over Homer's head.
The is fact that Fermat’s theorem has held out for more than 300 years.
The efforts to prove it made it reach the newspapers
when it was finally proved,
which doesn't happen often,
something about mathematics being published in the mainstream media.
And when this Simpsons' episode aired,
even more so when it was being written,
in the world of mathematics and not only among mathematicians,
people were talking about this,
about whether Fermat's theorem was finally proven,
after more than 300 years,
or if it was a false alarm, like the times it was claimed in the past.
And this joke that The Simpsons made
by inserting this apparently harmless equation into an episode,
was the way in which they made a reference
to the most famous mathematics news story of the twentieth century.
The Simpsons came back to the same subject a few years later,
by showing another equation from the same family,
and generated by the same program.
Homer wrote it on a blackboard
in the episode where he finds out who Edison was and tries to emulate him,
and invents things like an electrical hammer,
a shotgun that applies makeup
or an alarm that goes off when there is no problem:
the "everything's all right" alarm.
(Laughter)
You may think that only someone like David Cohen,
a man that doesn't have one, but two university degrees in sciences,
only someone like him could come up
with a joke about a theorem and a mathematical formula.
But he's not a special case.
Take a look at all of these others here:
a degree in mathematics,
a PhD in inorganic chemistry,
a degree in physics and history of science,
a PhD in computer science,
a university professor,
a PhD in applied mathematics,
an electrical engineer,
a mathematics graduate,
a neuroscience graduate.
These are are some of the screenwriters for The Simpsons
or people involved in making the show.
And that's why there are all these mathematical and scientific jokes.
The Simpsons is full of them, episode after episode.
Let's look at some examples.
Good news, Simpsons!
We found your daughter's belongings.
Where did you find these?
Giant tongue.
Oh, I knew it!
We also discovered something very unusual at that museum.
Oh my God! What?
Well, if you drop a feather and a bowling ball in a vacuum,
they'll fall at the same rate.
You think you've seen it all in this job,
and then something like that comes along.
(Applause)
The fact that a feather and a bowling ball,
a rock or any other heavy object,
fall at the same rate is not obvious.
If I did the test here,
you'd see the feather would fall much more slowly.
Galileo was the first to accurately explain
that the feather falls more slowly because the air slows it down,
and that if the same experiment were done in a vacuum,
they'd fall at the same speed.
Galileo reached that conclusion purely through reasoning,
not by actually doing the test to see what would happen.
He couldn't do the test in his era,
because there was no way to make a vacuum in a room or container
in order to perform the experiment.
The vacuum pump
was only invented a few years after Galileo's death.
Today, the test is done routinely at science museums,
or it can also be done without making a vacuum,
by going to a place where there's a natural vacuum.
(David Scott, video) In my left hand, I have a feather.
In my right hand, a hammer.
(C. Sanchez) This was filmed on the Moon in 1971, during the Apollo 15 mission.
The astronaut has a feather in his left hand,
a hammer in his right hand,
and he says he's going to test Galileo Galilei's claim
that things should fall at the same speed in a vacuum,
and what better place for that than the Moon.
(Video) We thought we'd try it here for you.
The feather is, appropriately, a falcon feather for our Falcon.
(C. Sanchez) He has the feather,
he raises both, he's going to release them.
(Video) Hopefully, they'll hit the ground at the same time.
(C. Sanchez) Look closely.
(Video) How about that!
This proves Mr. Galileo was correct in his findings.
(C. Sanchez) "Mr. Galileo was correct."
If you search for "Galileo was correct" on YouTube,
you will find the original video.
That is from the episode
when the bus that takes the kids to school falls into water
and the boys end up on a desert island and they fight over food,
they're chased by a wild boar and they put war paint on their faces.
And the whole story is inspired
by the novel The Lord of the Flies, by Nobel Prize winner William Golding
that also talks about some kids
whose plane falls into the sea and they end up on a desert island.
And they fight for food, there's a wild boar that scares them,
they put on war paint.
And the novel has a very interesting detail,
where the author made a mistake.
I am talking about the novel, not the episode inspired by it.
In the novel, the boys have to build a fire at a certain point,
to cook their food
and to use as a signal fire for a ship to come and rescue them.
They don't have matches, they don't have a lighter.
They try rubbing twigs together, without success.
Then one of the boys takes another boy's glasses
and lights a fire by focusing the sun's rays with the lenses.
The problem is that the main character,
the owner of the glasses, is short-sighted,
and short-sighted glasses aren't suitable for making a fire.
We can do it with a magnifying glass,
because it can focus the rays, the sun's energy, in one point.
That's why magnifying glasses are called converging lenses.
Shortsighted people's glasses, like mine,
have diverging lenses.
They spread the sun's rays.
It's absolutely useless trying to make a fire
with glasses like these.
If the novel's author knew this,
he would have made the character longsighted
instead of shortsighted, which is the opposite.
Longsighted glasses do work as magnifying glasses,
and they could be used to start a fire.
The fire incident with the glasses is recreated in this episode,
but it's resolved in a much more ingenious way
and without so many optical complications.
They simply hit the glasses against a rock to make fire with the sparks,
because this episode's writers
did know that longsighted glasses are not useful for making fires.
We could go on, there are dozens of these examples,
literally, dozens of jokes like these in episodes of The Simpsons.
And you could ask, then,
do you have to be an engineer
or a physics graduate to watch The Simpsons?
No, of course not.
But now that we know this, we can re-watch all the episodes,
paying attention to those jokes hidden in the background,
to discover and understand them.
Making an effort to understand those jokes
is an excellent and stimulating intellectual exercise.
In fact, there are many things that I now know
because they sparked my interest when I saw them in a Simpsons' episode.
I hope that from this moment on
you can also enjoy this intellectual stimulus.
Thank you.
(Applause)