ST. PETERSBURG, Fla. – Nine equals eight. It's true.
Mathematics professors at Michigan State University say so. They can prove it.
So can the Tampa Bay Rays. All season they've worn T-shirts with what seemed a mathematically impossible message: 9 = 8. About as impossible as the Rays preparing to host the Boston Red Sox in Game 1 of the American League Championship Series at Tropicana Field on Friday at 8:37 p.m., right?
Manager Joe Maddon came up with the formula when riding his bicycle. Maddon takes long spins to clear his mind and, apparently, dream of equations that those in the math world refer to as "ill-formed problems." In this case, it was a catchier way of conveying to the previously moribund Rays what Maddon really meant: nine players going hard for nine innings equals one of eight playoff spots. So it's really more like 9*9 = 1/8.
Hmmm. That doesn't really add up.
This proof, provided by Michigan State assistant math professor Ignacio Uriarte-Tuero, would seem to prove that, in fact, nine does equal eight, as Tampa Bay Rays manager Joe Maddon has asserted all year.
It doesn't, of course, as nine can't equal eight. Though the error is difficult to spot. Can you find it?
Step 1: Let x = y. Multiply by y to get
xy = y2
Step 2: Subtract x2 to get
xy − x2 = y2− x2
Step 3: Factoring, we get
x(y − x) = (y − x)(y + x)
Step 4: which simplifies to
x = y + x
Step 5: and now using that x = y we get
x = 2x
Step 6: Simplifying again, we get
1 = 2
Step 7: so that when we add 7 to both sides we get
8 = 9
Step 8: or put in other words,
9 = 8
But 9 = 8? Absolutely.
The "proof" (see graphic right), sent along by assistant professor Ignacio Uriarte-Tuero, shows that by making x = y and adding in some fancy addition, subtraction, multiplication and division, nine can equal eight.
Before you think the whole world is imploding – hey, 14,000 = 9,000 in just a couple of months' time – fear not. Despite Uriarte-Tuero's best effort to prove otherwise, nine does not equal eight. He is using a proof espoused by sneaky mathematicians everywhere, in which Step 4, calling for the simplification of the proof by removing (y-x) from both sides of the equation, is fallacious. It would require dividing by zero (because x equals y), which is impossible.
"This is a game mathematicians will play," said Patti Lamm, the ill-formed problem expert at Michigan State who emailed her colleagues for help in answering the question of how 9 = 8. "It's preying on people's gullibility to go along with math."
The game Tampa Bay plays, on the other hand, preys simply on its opponents' weaknesses by flexing its strengths.
One of which is decidedly not math.
"I stopped doing math when they started putting letters in there," outfielder Jonny Gomes said.
"I was able to test out," said outfielder Fernando Perez, a Columbia graduate. "I didn't have to do any math or science after high school."
"I'm not very good at math," Maddon said, though he took a stab at the proof.
"OK, because xy - x² … OK, I see," Maddon said.
He was making progress.
"OK. Yeah. Yeah."
He was almost at the bottom.
"No. I still don't know what any of this means."
Such was the reaction on the first day of spring training when Maddon told his players that the slogan for the season would be 9 = 8. The room, full of furrowed brows, figured this just another oddity from Maddon, a fine-wine-drinking, good-book-reading Renaissance man in a baseball uniform.
"I like to be esoteric," he said.
Whatever the case, 9 = 8 resonated.
For some players, it represented hope. Prior to this season, the Rays had finished in last place nine of their 10 years in existence, and their previous high in victories was 70.
"It gave us a phrase to attach our winning to when no one else could figure out what was going on and people were doubting it was real," reliever Trever Miller said. "It gave us a podium to stand on: 9 = 8. That's why we're doing this.
"Once you start winning, the 9 = 8 thing that was kind of corny at the beginning takes on its own identity."
By the middle of the season, Maddon had revealed the second part of his equation. (Oh, yes, it got even more complicated than 9 = 8.)
He wanted the team to play 27 games better than last season, a 96-win pace that would've registered as ludicrous had the Rays not kept winning and winning. Maddon divvied up those 27 victories: nine from its bullpen, one of baseball's best after finishing among the worst of all time in 2007; nine from its fielders, whose improvement was nearly as staggering; and nine from its lineup, fortified by rookie Evan Longoria and others.
"I didn't look at 27 as much as I did nine," reliever J.P. Howell said. "Little bits. Little increments. It helped me. Instead of making everything complicated, we made it a little simpler."
Maddon really is a genius. Getting his players to think that 9 = 8 simplifies things.
However little sense it made, the mantra kept growing. In Detroit, where the Rays clinched the AL East title, first baseman Carlos Pena used a marker and a white board to try to explain to his teammates how 9 = 8.
"I'm putting up algebra equations, functions," said Pena, an engineering major at Northeastern, "and at the end of it all, I write: 'If you want proof, look at the standings.' "
One peek shows the improbable: 97 wins. And an easy dispatching of Chicago in the AL Division Series. All spawned from a Maddon bike ride that birthed a motto that doesn't make much sense at all.
Oh, sure, there are places where 9 = 8. Golfers habitually shave a stroke off a bad hole. Jack Calcut, another professor at Michigan State, used a branch of math called topology to posit that 9 = 8 when "=" means "isomorphic" and the two numbers meet "at infinity of k copies of Euclidean n-space."
The best example, though, came from another Michigan State professor, Keith Promislow, who didn't need to tap into his vast reservoir of math skills to show that Maddon was right, that his motivational tactic was rooted in truth, that nine does, in fact, equal eight.
"I think anyone from Florida in 2000," Promislow said, "should understand how 9 = 8 is a distinct possibility."
- Joe Maddon
- Michigan State University