# How Jack and Rose could have both fit on the door: Mathematicians debunk famous film and TV scenes

For most of us, when hooked on a gripping action sequence or in stitches at a comedy, the last thing we are thinking about is maths.

But some just cannot enjoy a movie or TV show if they know that Keanu Reeves would not have dodged that bullet, or Kate Winslet could moved over to let Leonardo DiCaprio fit on the door.

In fact, they go away and do the equations to show how Ross Geller could have got the sofa upstairs, or Jack Traven’s bus could not have jumped the gap in the freeway.

Well, it turns out that Homer Simpson is not as dim-witted as he lets on, because he discovered the mass of the Higgs Boson in an episode of ‘The Simpsons’.

MailOnline reveals seven times mathematicians have debunked iconic moments in cinema and TV history.

A group of schoolgirls from Adelaide, Australia claim they proved how Jack and Rose could have both survived the sinking Titanic

A mathematician found that Ross Geller would have been able to get his sofa up the stairs without cutting it in half, if he had only taken measurements

## Jack and Rose could have fit on the door in Titanic

It’s the question that’s dogged movie fans for 20 years – could Rose have saved Jack during the 1997 blockbuster Titanic?

After the ship goes down, the couple attempt to clamber onto a piece of debris in the freezing cold North Atlantic Sea.

It seems there is only room for one on the door, so Jack sacrifices his spot for Rose.

But a group of schoolgirls from Adelaide, Australia claim they have proved how they both could have both survived the sinking ship.

They say they could have both stayed on the door if they had put their life jackets underneath it to float to safety.

‘We looked at how buoyant the door would have been, and how that would have changed if there were people on top of that,’ Abigail, 15, told The Daily Telegraph.

‘There was a lot of exploring and testing, and we had to fiddle with different buoyancies and look at what materials were realistic for that time.’

To celebrate the film’s 25th anniversary in February, director James Cameron also performed experiments to end any speculation on the fate of Jack and Rose.

Using two stunt people – dressed in the clothing worn by Kate Winslet and Leonardo DiCaprio in the film and submerged in a swimming pool – scientists went through different scenarios to see if they could both survive.

They found that they would have both died if both of them had tried to get on the door, because significant parts of their bodies would have remained in the hypothermic water.

If the two had also hoisted their upper bodies out the water with their arms they would have both survived for a few more hours.

After the Titanic goes down, Jack and Rose attempt to clamber onto a piece of debris in the freezing cold North Atlantic Sea. It seems there is only room for one on the door

The mathematicians say that both Jack and Rose could have stayed on the door if they had put their life jackets underneath it to float to safety

But their best option would have been for Rose to hand Jack her life jacket, as Cameron admits this may have stabilised him to the point he might have survived until a lifeboat came.

The director admitted: ‘Jack might have lived. But there’s a lot of variables.

‘I think his thought process was, “I’m not going to do one thing that jeopardises her.”

‘And that’s 100 percent in character.’

## Ross Geller could have pivoted the sofa in Friends

Friends episode ‘The One with the Cop’ includes a scene with Ross frantically shouting, ‘Pivot!’ as he, Rachel and Chandler attempt to move a sofa up flights of stairs in a New York apartment.

The trio were unable to manoeuvre the couch around the stairwell, which forced them to cut it into pieces.

However, a mathematician found the endeavour would have been successful if they had only taken measurements.

Data Science Consultant Caroline Zunckel ran 10,000 simulations based on different measurements of the stairwell and couch, and found the sofa only needed to be tilted upwards to move around the corner.

Data Science Consultant Caroline Zunckel ran 10,000 simulations based on different measurements of the stairwell and couch, and found the sofa only needed to be tilted upwards to move around the corner

‘By applying Pythagoras’ theorem to the estimated measurements of Ross’s sofa in a vertical position, and dimensions of the stairs, I was able to establish that it would have been possible to get the item upstairs. It’s quite simple really,’ Zunckel said in a blog post from apartment finder SpareRoom.

The final equations is: Angle of vertical tilt (T) =44.15064 -11.94274xWS (Width of the Stairwell) + 8.69119xWC (Width of the Couch) + 3.65961xLC (Length of the Couch).

Although the mathematical equation looks complicated, it can be broken down into steps with the first suggesting Ross should have measured the width of the stairs and width and length of the couch.

By lifting the front of the couch toward the ceiling, Ross, Rachel and Chandler would have been able to clear then column and move it into the apartment.

The trio were unable to manoeuvre the couch around the stairwell, forcing them to cut it apart

## Cady Heron’s maths question was wrong in Mean Girls

In the 2003 comedy Mean Girls, Lindsay Lohan’s character Cady competes at the Mathletes Championship finals.

She is tasked with answering the last question, which would determine whether her team, from North Shore High, or the opponents takes the crown.

The quiz master asks her and Caroline Krafft, from the other school, to find the limit of an equation he shows on screen.

Caroline answers -1 but is told she is incorrect, and then Cady thinks about her answer.

She mumbles ‘if the limit never approaches anything, the limit does not exist’ under her breath, before exclaiming ‘the limit does not exist!’.

In the 2003 comedy Mean Girls , Lindsay Lohan’s character Cady competes at the Mathletes Championship finals. She is tasked with answering the last question, which would determine whether her team, from North Shore High, or the opponents’ takes the crown

The quiz master asks her and Caroline Krafft , from the other school, to find the limit of an equation he shows on screen.

But Ray Douse, director at Maths-Whizz, a virtual maths tutoring service, says that this is not actually correct, because neither was the question.

He told The Mirror: ‘The film was technically wrong to ask what was the limit of the equation because it wasn’t an equation on the screen, it was an expression.

‘Cady’s answer was correct, however, because whether x approaches 0 from a positive or a negative number, the expression resolves into either positive or negative infinity, and infinity has no limits.’

## Will Hunting did not finish the second problem in Good Will Hunting

One of the most famous maths-related movies is Good Will Hunting, which starred Matt Damon, Ben Affleck and Robin Williams.

Damon plays Will Hunting, a janitor at the Massachusetts Institute of Technology (MIT) who correctly answered a difficult maths problem a professor left on a blackboard.

The next day, after none of his students took credit for the solution, the professor left another problem on the blackboard.

He then caught Will chalking out another answer, but mathematicians say he didn’t actually fully complete the solution.

One of the most famous maths-related movies is Good Will Hunting , which starred Matt Damon, Ben Affleck and Robin Williams. Damon plays Will Hunting, a janitor at the Massachusetts Institute of Technology who correctly answered a difficult maths problem a professor left on a blackboard

The first question asks for the proof that for every positive integer ‘n’, the number of possible ‘trees’ with n labelled points is nⁿ⁻². In this case, trees are dots of different colours joined together by lines, and there are only a defined number of variations depending on the number of coloured dots

The first part of the question asks for the proof that for every positive whole number ‘n’, the number of possible ‘trees’ with n labelled points is nⁿ⁻².

In this case, trees are dots of different colours joined together by lines, and there are only a defined number of variations depending on the number of coloured dots.

The equation is known as Cayley’s formula, and has a number of known proofs, according to mathematician Jørgen Veisdal, and Will was able to provide one.

The second part of the question asks to draw all of the ‘homomorphically irreducible’ trees where n = 10.

Homomorphically irreducible means that no single point in the tree has only two lines coming from it – ie, they cannot be of degree two.

Mr Veisdal told Cantor’s Paradise that each tree must have ten dots and nine lines, and the number of points with different degrees can be worked out mentally.

With that knowledge, the trees can be drawn out, and Will manages to write down eight trees, but in reality there are ten.

However, his track record of MIT-level mathematics means this was probably just because he was interrupted mid-solution, or ran out of space.

The second part of the question asks to draw all of the ‘homomorphically irreducible’ trees where n = 10 (pictured). Will Hunting manages to write down eight trees before he gets interrupted, when in reality there are ten

## Homer Simpson was capable of professor-level physics in The Simpsons

He is best known as the hapless, doughnut-obsessed safety officer at Springfield nuclear power plant, but Homer Simpson may have beaten some of the brightest minds on the planet.

A physicist has discovered that Homer may have predicted the mass of the Higgs boson 14 years before physicists discovered the particle at the Large Hadron Collider in Cern.

Dr Simon Singh found the solution written on a blackboard in front of Homer during a 1998 episode of the long running cartoon – showing Homer isn’t as dumb as he seems.

In ‘The Wizard of Evergreen Terrace’, Homer becomes an inventor in an attempt to follow in the footsteps of Thomas Edison.

He is best known as the hapless, doughnut-obsessed safety officer at Springfield nuclear power plant, but Homer Simpson may have beaten some of the brightest minds on the planet. The formula written on Homer’s blackboard above is said to correctly predict the mass of the Higgs boson

Speaking to the Independent, Dr Singh said: ‘That equation predicts the mass of the Higgs boson.

‘If you work it out you get the mass of a Higgs boson that’s only a bit larger than the nano-mass of a Higgs boson actually is.

‘It’s kind of amazing as Homer makes this prediction 14 years before it was discovered.’

The existence of the Higgs boson – sometimes nicknamed the God Particle – was first predicted by Professor Peter Higgs, a theoretical physicist at the University of Edinburgh, and five other physicists in 1964.

The elementary particle is required to explain why other fundamental particles in the universe have mass.

The theory said that all subatomic particles interact within an energy field known as the Higgs field, giving them mass.

Like electromagnetic radiation, which can exist as both an energetic wave and a particle simultaneously, the Higg’s field also has a corresponding particle – the Higgs boson.

Proof that the particle existed, however, did not appear until March 2013 when scientists working on the Large Hadron Collider – the worlds biggest atom smasher – announced they had discovered a particle that matched predictions of the Higgs boson would be like.

In an experiment costing £8.6 billion ($13.25 billion), they were able to prove the existence of a new particle with a mass of 125Gev/c2.

Dr Singh claims the formula written by Homer while he is attempting to come up with a series of madcap inventions, including an electric hammer and make-up gun, gives close to the same answer.

He said: ‘The equation is a playful combination of various fundamental parameters, namely the Planck constant, the gravitational constant, and the speed of light.

‘If you look up these numbers and plug them into the equation, it predicts a mass of 775 giga-electron-volts (GeV), which is not unreasonably higher than the 125 GeV estimate that emerged when the Higgs boson was discovered in 2012.

‘Indeed, 775 GeV was not a bad guess bearing in mind that Homer is an amateur inventor and he performed this calculation fourteen years before the physicists at CERN, the European Organization for Nuclear Research, tracked down the elusive particle.’

## Jack would not have survived the bus jump in Speed

The thriller Speed came out in 1994 and brimming with high-octane action sequences involving a bus rigged with a bomb.

In one memorable scene, Keanu Reeves’ character officer Jack Traven must keep this bus driving over 50mph (80 kph) along a freeway or it will detonate.

When the vehicle meets an incomplete section of the road, he knows the only hope for him and the rest of the passengers is to accelerate over the gap.

In one memorable scene, Keanu Reeves’ character officer Jack Traven must keep this bus driving over 50mph (80 kph) along a freeway or it will detonate

When the vehicle meets an incomplete section of the road, he knows the only hope for him and the rest of the passengers is to accelerate over the gap

Fortunately, with a bit of movie magic, they make the jump and manage to offload everyone off the bus before it detonates.

But not everyone can just sit back and quietly watch the laws of physics get defied.

This includes those at ZME Science, who calculated if Jack really could have made that jump.

By studying the scene, it was estimated that the gap they had to jump was 50 feet in length (15 m), while the speedometer showed they were travelling at about 67 mph (108 kph).

An object’s time falling is independent of its horizontal velocity, so in order to jump any distance the bus is assumed to have launched at a slight incline.

As the bus was mid-air for just 50 seconds, the mathematicians calculated that it would have descended by about 4.3 feet (1.3 m).

This meant it would have likely fallen through the gap before it reached the other side, and exploded when it made contact with the ground below. Shame.

By studying the scene, it was estimated that the gap they had to jump was 50 feet in length (15 m), while the speedometer showed they were travelling at about 67 mph (108 kph)

Fortunately, with a bit of movie magic, they make the jump and manage to offload everyone off the bus before it detonates

But as the bus was mid-air for just 50 seconds, the mathematicians calculated that it would have descended by about 4.3 feet (1.3 m) in reality. This meant it would have likely fallen through the gap before it reached the other side

## Neo could not have dodged the bullet in The Matrix

The boundaries of physics are tested many times throughout The Matrix, but one of the most iconic ways it does so involves quick reactions, and some very bendy knees.

During their mission to save Lawrence Fishbourne’s character Morpheus from Hugo Weaving’s Agent Smith, Keanu Reeves’ Neo battles some agents on a rooftop.

One of the agents turns into Smith and shoots at Neo, but he dodges the bullet by by bending completely backwards.

The boundaries of physics are tested many times throughout The Matrix , but one of the most iconic ways it does so involves quick reactions, and some very bendy knees

During their mission to save Lawrence Fishbourne’s character Morpheus from Hugo Weaving’s Agent Smith, Keanu Reeves’ Neo battles some agents on a rooftop

In this scene, time slows down to emphasise Neo’s lightning reactions, but some analytical brains have worked out if this would be possible in reality.

Mathematician Kerry Cue estimated that Neo and the agent are 39 feet (12 m) apart, and that the weapon used was equivalent to a Smith & Wesson .40 M&P.

The muzzle speed of this firearm is 1,000 feet per second (305 m/s) , so it would take 0.04 seconds to travel to the protagonist.

As the average human reaction time is 0.25 seconds, there is no way that Neo would have been able to duck the bullet – at least outside of the Matrix.

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