Winston Churchill was a Carrot: a mathematical proof

[Hidden]

The following is taken from Charles Seife's book, "Zero: The Biography of a Dangerous Idea." It is a tremendous book, and I recommend it to anyone interested in the history or philosophy of mathematics.


Let a and b each be equal to 1. Since a and b are equal,

(eq. 1) b² = ab

Since a equals itself, it is obvious that

(eq. 2) a² = a²

Subtract equation 1 from equation 2. This yields

(eq. 3) a² - b² = a² - ab

We can factor both sides of the equation; a² - ab equals a(a - b). Likewise, a² - b² equals (a + b)(a - b). (Nothing fishy is going on here. This statement is perfectly true. Plug in the numbers and see for yourself!) Substituting into equation 3, we get

(eq. 4) (a + b)(a - b) = a(a - b)

So far, so good. Now divide both sides of the equation by (a - b) and we get

(eq. 5) a + b = a

Subtract a from both sides and we get

(eq. 6) b = 0

But we set b to 1 at the very beginning of this proof, so this means that

(eq. 7) 1 = 0

This is an important result. Going further, we know that Winston Churchill has one head. But one equals zero by equation 7, so that means that Winston has no head. Likewise, Churchill has zero leafy tops, therefore he has one leafy top. Multiplying both sides of equation 7 by 2, we see that

(eq. 8) 2 = 0

Churchill has two legs, therefore he has no legs. Churchill has two arms, therefore he has no arms. Now multiply equation 7 by Winston Churchill's waist size in inches. This means that

(eq. 9) (Winston's waist size) = 0

This means that Winston Churchill tapers to a point. Now, what color is Winston Churchill? Take any beam of light that comes from him and select a photon. Multiply equation 7 by the wavelength, and we see that

(eq. 10) (Winston's photon's wavelength) = 0

But multiplying equation 7 by 640 nanometers, we see that

(eq. 11) 640 = 0

Combining equations 10 and 11, we see that

(eq. 12) (Winston's photon's wavelength) = 640 nanometers

This means that this photon--or any other photon that comes from Mr. Churchill--is orange. Therefore Winston Churchill is a bright shade of orange.

To sum up, we have proved, mathematically, that Winston Churchill has no arms and no legs; instead of a head, he has a leafy top; he tapers to a point; and he is bright orange. Clearly, Winston Churchill is a carrot. (There is a simpler way to prove this. Adding 1 to both sides of equation 7 gives the equation

2 = 1

Winston Churchill and a carrot are two different things, therefore they are one thing. But that's not nearly as satisfying.)

What is wrong with this proof?


I'll leave you with that cliffhanger. Charles Seife does in fact answer his own riddle, but I want to see the enterprising minds of KHI work on it first. Have fun!

 

[Solo]

Must... resist... replying...

But I can't. Oh gosh, I feel like a nerd.

So a = b, which means a - b = 0. The problem lies in moving from eq 4 to eq 5. When you divide both sides by (a - b), you're dividing by 0. One does not simply divide by zero, because a black hole will form, grow, and eradicate humanity.

... jokes aside, I rest my case.

 

[Solar]

carrots are red, winston liked fascism

 

[Hidden]

Must... resist... replying...

But I can't. Oh gosh, I feel like a nerd.

So a = b, which means a - b = 0. The problem lies in moving from eq 4 to eq 5. When you divide both sides by (a - b), you're dividing by 0. One does not simply divide by zero, because a black hole will form, grow, and eradicate humanity.

... jokes aside, I rest my case.

THANK YOU! You're 100% correct, and Charles Seife even echoes your dire warnings against dividing by zero. "From there we can prove any statement in the universe, whether it is true or false. The whole framework of mathematics has exploded in our faces. Used unwisely, zero has the power to destroy logic."

carrots are red, winston liked fascism

Aha, but carrots are what famously allowed Churchill and the RAF to beat back the Germans in the Battle of Britain, and were one of the few foodstuffs not rationed in England at the time. As the old saying goes, you are what you eat.

 

[Nostalgia]

If a & b = 1, then you can't divide by (a - b) because that's dividing by zero, which breaks the math behind the derivation. The mystery is solved.

 

[Rydgea]

I feel the need to reply, because I love riddles and need to perpetuate their existence on this forum. I also completely missed the step 4 conundrum at first.