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ELI5 and Hate Computer Science: P = NP

lethargilistic profile image Mike Overby ・3 min read

Can a human run a mile in less than four seconds? "No," you say? "That's ridiculous," you yell. They used to say the same things about the four-minute mile. It was impossible to run around the standard quarter-mile track four times so quickly. The absence of evidence was evidence of absence.

In 1954, Roger Bannister ran it in 3:59.4.

One month later, John Landy had it in 3:58.0. Around the same time, Diane Leather broke the five-minute mile for women, crushing her own records three times in a row over two years. In 1999, Hicham El Guerrouj ran one mile in 3:43.13.

The "four minutes" of four-minute mile fame was an arbitrary barrier, and once someone shattered that assumption, the way we thought about running changed forever. So, why don't we cut the quitter talk and get to work on defeating this equally arbitrary four-second barrier?

One of the things in the way the four-second mile is, to quote Wittgenstein, "the limits of my language means the limits of my world." We are held back by the bleeding edge researchers have yet to cross. Their work is insufficient to describe what we want to do, let alone how to get there, but it is the only means we have to progress through rigorous analysis. To advance our work, we must take a leap of faith from our current understanding, but we must be brave enough to do so in pursuit of the unknown.

That current understanding comes down to steps: the number of them it takes to go from one point to another. The fewer steps you need to move yourself from here to there, the faster you will accomplish it. There does not seem to be an easily-accessible record of the numbers of steps athletes have taken to break the four-minute mile, but we do have an approximate average for an eight minute mile: 1,400 steps at 7.5 miles-per-hour. We can extrapolate to 700 steps at 15 miles-per-hour to break four minutes. And, obviously, we've done better than that. To crack the four-second mile, the math comes out to about 46.6 steps in four seconds. This is the target.

Our projection may seem intuitively damning to those unfamiliar with the problem, but it is merely confirmation that it is infeasible with known methods. There is no proof that it cannot be done. Can we optimize—reduce our required steps to cross the same distance—to conform within our time constraint? Today, God only knows. Tomorrow, we will join Him.

To do this, we require radically altered training regimens and, certainly, running technique would have to change. Perhaps we would have to resort to drastic measures like replacing limbs with more advanced prosthesis. There's been debate on the subject of whether or not amputee runners' blades give them unfair advantages today, so why not take that even further? Is a man with a rocket strapped to his back any less human than Jesse Owens or Genzeb Shumi? If we cannot win the game, then we must change the game. Getting there may be difficult. It may push our bodies beyond every limit we can set up for ourselves, but checking the number and seeing that "3" at the end will be just as easy as it was before we leapt through this "impossible."

Sure, there are naysayers aligned against us, leaning on their intuition from studying the problem alongside us with no solid proofs to their names. They have merely bedtime stories of unprepared bodies coming apart at their seams from the strain required by 11.7 steps-per-second. Their goal is to prove their negative by showing a lower bound of steps that's physically insurmountable in our pursuit of the four-second mile.

Personally, I say there's more productivity in positivity, and my life is dedicated to shattering their illusions. They'll watch me earning my IAAF Award, then I'll see them all in Hell.

Discussion (1)

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itr13 profile image
Mikael Klages

Though having a rocket strapped to your back wouldn't make you any less human, it would most certainly make it harder to define the action performed as "running".

Not to mention possibly killing you.

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