How Can Math Help You Imagine The Impossible?

Transcript

GUY RAZ, HOST:

Earlier in the show, we met Randall Munroe. He has a physics background, but he now mainly writes and illustrates a really popular web comic. It's called "What If?" And the way it works is every week people write in questions for Randall to answer in the form of a comic. So for example, what if you were playing baseball - right? - and you were the batter? What would happen if the pitcher threw the baseball impossibly fast, like 90 percent the speed of light?

(SOUNDBITE OF CHARGE ANTHEM)

RAZ: Here's Randall's answer...

(SOUNDBITE OF TED TALK)

RANDALL MUNROE: So I did some calculations.

RAZ: ...From the TED stage.

(SOUNDBITE OF TED TALK)

MUNROE: Now, normally when an object flies through the air, the air will flow around the object. But in this case, the ball would be going so fast that the air molecules wouldn't have time to move out of the way. The ball would smash right into and through them. And the collisions with these air molecules would knock away the nitrogen, carbon and hydrogen from the ball, fragmenting it off into tiny particles, triggering waves of thermonuclear fusion in the air around it. This would result in a flood of x-rays that would spread out in a bubble along with exotic particles centered on the pitcher's mound. Now at this point, about 30 nanoseconds in, the home plate is far enough away that light hasn't had time to reach it, which means the batter still sees the pitcher about to throw and has no idea that anything is wrong.

(LAUGHTER)

MUNROE: Now after 70 nanoseconds, the ball will reach home plate, or at least the cloud of expanding plasma that used to be the ball. And it will engulf the bat and the batter and the plate and the catcher and the umpire and start disintegrating them all...

(LAUGHTER)

MUNROE: ...Followed by a blast wave spreading out, shredding trees and houses as it moves away from the stadium and then eventually a mushroom cloud rising up over the ruined city.

(LAUGHTER)

MUNROE: So the Major League Baseball rules are little bit hazy, but...

(LAUGHTER)

MUNROE: ...Under rules 6.02 and 5.09, I think that in this situation, the batter would be considered hit by pitch and would be eligible to take first base if it still existed.

RAZ: This is the kind of question Randall answers every week in his web comic "What If?" Questions like, how fast could you visit all 50 states, or how long would a staircase to space take to climb, or what would happen if all the rain in a thunderstorm dropped at once in the form of a single raindrop? Short answer there - nothing good.

MUNROE: In the case of the raindrop that's this big and falling this fast, when the bottom hits, there's so much more water coming and it's coming so quickly that there isn't enough time for the first part of the splash to get out of the way before the next part of the raindrop is already there. And this causes a thin jet to shoot outward along the ground, away from the point of contact. And - in sort of all directions you'll get these jets of water moving at, you know, much higher than the speed of sound. Yeah, you would want to watch this from a safe distance away. Yeah...

RAZ: Like from a mountaintop.

MUNROE: Yeah, make sure to have a mountaintop. And even if you've got a mountain between you and the raindrop, you'd want to make sure you are not downstream of that raindrop.

RAZ: How do you think - how do you think you approach something unknown differently than other people do?

MUNROE: Well, I have always had a little bit of trouble managing my time and just clicking random Wikipedia links or reading random papers. And then before I know it, I've spent like three hours trying to solve a question that I'm not even going to write an article about. And I once drew a comic about how you could sort of use this maliciously, this tendency science people have where - I had a comic about someone who sat outside an engineering building by the side of the road. And when the physics professor was halfway across the road, they would hold up a sign with an interesting problem on it. And the physics professor would stop immediately to like - and start thinking about OK, how do I solve this? Take the square root of - and then wham, they get hit by a car. And so I invented this sport that I called nerd sniping. But part of what I did with my idea with "What If?" is that I'm nerd sniping myself. I'm getting all of these questions sent to me that then I will have no choice but to try to answer.

RAZ: Like a couple of years ago, when he got the following question - say all of the world's known data were stored on punch cards - you know, those paper cards with holes that used to be fed into giant computers?

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UNIDENTIFIED MAN: A card punch translates words and numbers into the same information in the form of holes in cards. A typist with very little extra training can operate the card punch.

RAZ: Anyway, the question was if we still stored data that way, how much physical space would Google need to store all the data that Google has? Google, of course, wasn't going to tell Randall how much data they do have, so Randall came up with an answer he thought was plausible.

(SOUNDBITE OF TED TALK)

MUNROE: I came up with my estimate, which I felt pretty good about, that was about - about 10 exabytes of data across of all Google's operations. And then another maybe five exabytes or so of offline storage in, like, tape drives, which it turns out Google is about the world's largest consumer of. So I came up with this estimate, and this is a staggering amount of data. It's quite a bit more than any other organization in the world has as far as we know. There's a couple of other contenders, especially - everyone always thinks of the NSA. Adding all of this up, I came up with the other thing that we can answer, which is how many punch cards would this take? And so a punch card can hold about 80 characters and you can fit about, you know, 2,000 or so cards into a box. And you put them in, say, my home region of New England, it would cover the entire region up to a depth of a little less than five kilometers, which is about three times deeper than the glaciers during the last ice age about 20,000 years ago. So this is impractical, but I didn't expect to get an answer from Google because of course they've been so secretive. They didn't answer any of my questions. And so I just put it up and said, well, I guess we'll never know. But then a little while later, I got a message a couple of weeks later from Google saying, hey, someone here has an envelope for you. So I go and get it, open it up, and it's punch cards...

(LAUGHTER)

MUNROE: ...Google-branded punch cards. And on these punch cards, there are a bunch of holes, you know? And I said thank you, thank you. And I was - OK, so what's on here? So I get some software and start reading it and scan them. And it turns out it's a puzzle. There's a bunch of code. And I get some friends to help and we cracked the code. And then inside that is another code. And there are some equations. And then we solve those equations and then finally - and out pops a message from Google, which is their official answer to my article. And it said no comment.

(LAUGHTER, APPLAUSE)

MUNROE: So - and I love calculating these kind of things. I just - and it's not that I love doing the math. I do a lot of math, but I don't really like math for its own sake. What I love is that it lets you take some things that you know and just by doing these, you know, moving symbols around on a piece of paper, find out something that you didn't know that's very surprising. You know, and I have a lot of stupid questions and I love that math gives the power to answer them sometimes - and sometimes not. This is a question I got from a reader - an anonymous reader - and the subject line just said urgent. And this was the entire email. If people had wheels and could fly, how would we differentiate them from airplanes? Urgent.

(LAUGHTER)

MUNROE: And I think there are some questions that math just cannot answer. Thank you.

(APPLAUSE)

RAZ: Randall Munroe. His talk is a ted.com and his web comic is at xkcd.com. On the show today we're solving for X, how numbers shape the world. Next up, how one equation might help you find true love.

HANNAH FRY: WT+1 = w+RWWT+IHM(HD). But this only maximizes your chances of finding the perfect person for you. It doesn't guarantee it.

RAZ: I'm Guy Raz, and this is the TED Radio Hour from NPR. Transcript provided by NPR, Copyright NPR.