Indicator and Beyond

May 9, 2018

How many possible shows could the Indicator do? How many indicators will there be? How many almost-indicators will never see the light of day? The answer to all of these questions is: infinity

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STACEY VANEK SMITH, HOST:

So, Cardiff, it is our hundredth show.

CARDIFF GARCIA, HOST:

Yes, it is. Happy anniversary.

VANEK SMITH: So are - thank you. Thank you. I mean, it's funny because our show isn't actually that old. We launched on December 4, I think. But here we are - hundredth show.

GARCIA: Yeah. We're not going to do this every hundred shows, are we?

VANEK SMITH: We're absolutely doing this every hundred shows. So I was trying to think of what the perfect Indicator would be, and a hundred seemed way too obvious.

GARCIA: Yes.

VANEK SMITH: And, you know, so I started looking around, and I came up with some kind of fun numbers. For instance, we have said the word, economy, 281 times. Also, we've said the word, money, 260 times.

GARCIA: Money 260 times. OK.

VANEK SMITH: We've said the word, data, 106 times. And in one story, actually, we said, data, 16 times.

GARCIA: (Laughter) Data.

VANEK SMITH: Data.

GARCIA: Data.

VANEK SMITH: Data?

GARCIA: Data.

VANEK SMITH: Data. Data.

GARCIA: Data. Data.

VANEK SMITH: Data. Data.

GARCIA: Wait, how did you say it?

VANEK SMITH: Data.

GARCIA: Not data?

VANEK SMITH: It's data.

GARCIA: OK.

VANEK SMITH: I think we may - maybe we should flip for that at the end of the show and just have a standardized pronunciation.

GARCIA: OK.

VANEK SMITH: Anyway, but - so I had all these numbers. And I was looking around, but none of them seemed quite grand enough for this august occasion.

And then I had this moment where I looked at the logo for our show, and it was just right there. And I realized that I had the perfect Indicator for our hundredth show. But first, Cardiff. I'm going to let you do the honors for the cool 100.

GARCIA: OK.

VANEK SMITH: This is THE INDICATOR.

GARCIA: This is THE INDICATOR, where every day, we tell you a story about the economy - a short story about the economy.

VANEK SMITH: You have to say your name.

GARCIA: Oh, right. I'm Cardiff Garcia.

VANEK SMITH: We're going to nail this on the 101st show.

(LAUGHTER)

GARCIA: OK, fine.

VANEK SMITH: I'm Stacey Vanek Smith. Stay on the show. It's our 100th episode, and things are about to get a little weird.

EUGENIA CHENG: It's not a whole number, and it's not a fraction, and it's not an irrational number, and it can't be any of the numbers that sit on the normal number line. So it's a different type of number.

GARCIA: Oh, my God.

VANEK SMITH: (Laughter).

GARCIA: My mind has been blown.

VANEK SMITH: Right?

GARCIA: What is going on?

(SOUNDBITE OF DROP ELECTRIC SONG, "WAKING UP TO THE FIRE")

VANEK SMITH: One of the great parts about a daily show that we talk about a lot, Cardiff, is that we can really cover anything on any given day, and the possibilities are just endless, right?

GARCIA: Yeah.

VANEK SMITH: But also sometimes, and we talk about this, too, it can feel a little daunting because you just have endless shows stretching out into the future.

GARCIA: We work so hard. We agonize over a show. It goes out. We're incredibly proud of it. And then the next day, there's a whole other show to make. Yes.

VANEK SMITH: The next day, exactly. So it occurred to me that both the good and the bad parts of a daily show have something in common, something which is also weirdly part of the logo of our show - the loopy rollercoaster.

GARCIA: Yeah.

VANEK SMITH: And it is infinity.

GARCIA: Infinity.

VANEK SMITH: Infinity.

GARCIA: Yes. OK.

VANEK SMITH: We have infinity shows stretching out in front of us, and infinity possible shows we could do on any given day, and that's just a lot of infinity that we're dealing with all the time.

GARCIA: Yes.

VANEK SMITH: So today's Indicator was going to be infinity, but it is not because that's not really accurate. Because we've done a hundred shows, we cannot redo those exact shows. So then I thought maybe, like, infinity minus a hundred would be our Indicator. Right? So then, though, I wondered if you could even do that - if you could even have infinity minus a hundred because infinity's sort of a strange concept number.

So I decided I was out of my depth, so I called up Eugenia Cheng. She is a mathematician and Scientist in Residence at the Art Institute of Chicago. She is also author of the book "Beyond Infinity." And Eugenia says you can't just do anything with infinity because it is a number, as she said, but it is also not a number. And so if we want to involve infinity in our Indicator today, we have to be careful.

CHENG: It took mathematicians thousands of years to pin down what infinity might be in a rigorous way that actually withstands logic because if you just follow your gut instinct, you go, whoa, infinity's the biggest possible number or something. And if you add one, it's still infinity.

But then you can get weird results. Like, you can discover that then zero will equal one, and it will equal two, and everything will equal zero and strange things like that. And so you have to be more careful than that.

VANEK SMITH: So if we do, like, infinity minus a hundred, is that possible? Can we do that math?

CHENG: No.

GARCIA: (Laughter)

VANEK SMITH: No.

GARCIA: No, we can't.

VANEK SMITH: No.

GARCIA: I love this. This sort of reminds me of, like, when you're a kid, and you're like, we're going to do a million bajillion shows.

VANEK SMITH: (Laughter).

GARCIA: You know what I mean?

VANEK SMITH: There are days it feels that way, right? Anyway, so infinity minus a hundred was out. That cannot be our Indicator. But that can't not be our Indicator because that is what has happened. We have infinity possibilities minus a hundred, so we pressed on.

CHENG: Well, it depends whether - where you take the hundred away from. In normal numbers, it doesn't matter. We know that one plus two is the same as two plus one.

VANEK SMITH: Yeah.

CHENG: So if you have some people in a queue, you can remove people from anywhere you want. You can remove them from the front of the queue, or you can remove them from the end of the queue, and you know there'll still be the same number of people left. But if you have an infinite line, you can't remove people from the back 'cause you don't know where the back is.

VANEK SMITH: OK.

GARCIA: (Laughter).

VANEK SMITH: So she had to explain this to me several times. So to be able to subtract a number from another number, the first number has to end - right? - like 10 minus two is eight. But if the 10 never ends, you can't subtract the two. So the infinity never ends, you never get to the point where you can be, like, stop, I'm subtracting a hundred. So that's the problem.

But what you can do is take the number away upfront because infinity, in this case, has a beginning. Our show started on December 4. So you can't have infinity minus a hundred.

CHENG: No. You can only have minus a hundred plus infinity.

VANEK SMITH: So minus a hundred plus infinity - that is the number of Indicators that we have ahead of us. And, Cardiff, this was going to be our Indicator - minus a hundred plus infinity - but then I started thinking that a lot of what we do in a day isn't just making the show that airs that day. We also have a lot of, like, half-baked ideas...

GARCIA: Yeah.

VANEK SMITH: ...And shows that we start and that we don't finish - little scraps of things that we work on that never quite see the light of day, and...

GARCIA: And it's a good thing, by the way, that a lot of those don't see the light of day.

VANEK SMITH: That they don't see the light of day. So not only do we have an infinite number of shows that are going to air every day, every single day, there are also an infinite number of, like, botched shows and half-shows and weird ideas that do not make the air.

GARCIA: Yeah. Like, we start working on the idea, and that idea's no good. And then there's ideas that we do like, and we start reporting them. We've got to throw those away.

VANEK SMITH: Yes.

GARCIA: There's definitely way more of those than there are shows that actually go to air. I agree.

VANEK SMITH: So we have infinity shows ahead of us. And we also have infinity semi-half-baked shows...

GARCIA: Yeah.

VANEK SMITH: ...That...

GARCIA: Garbage shows.

VANEK SMITH: Garbage shows that do not air, and there are more. So both of those are infinities, but the infinity of failed shows is bigger than the infinity of shows that are going to go to air - right? - because we can only have one show go to air a day, but there are infinity failed shows.

GARCIA: Yeah. There's, like, 10 ideas for every idea we actually use.

VANEK SMITH: So one of the infinities is bigger than the other infinity.

GARCIA: Which is crazy.

VANEK SMITH: Which sounds crazy, but, in fact, this relates to a theory from a man named Georg Cantor, who was born in 1840. And he postulated that, in fact, there are different kinds of infinities.

CHENG: And that's really mind-blowing, I think, because we think of infinity as being the biggest thing.

VANEK SMITH: Yeah.

CHENG: And yet, whatever you decide it is, there's a bigger one. And then there's a bigger one than that, and a bigger one than that. So not only is there a bigger infinity, there's actually an infinite hierarchy of bigger infinities.

VANEK SMITH: So, Cardiff, that is our Indicator - infinite infinities.

GARCIA: I like an infinite hierarchy of infinities. Yeah, that's a great Indicator.

VANEK SMITH: It is all the shows we will do and will not do, stretching ahead of us forever. And, I figured, if that Indicator is not big enough for our hundredth show, I don't know what - I mean, I don't actually think it's possible to get bigger than infinity infinities.

GARCIA: Ladies and gentlemen, Stacey Vanek Smith.

VANEK SMITH: (Laughter).

GARCIA: This is why she is so great.

VANEK SMITH: Right (laughter)?

GARCIA: What a lovely and poetic meditation on the nature of infinity for our hundredth episode. It's been so great...

VANEK SMITH: It has been great.

GARCIA: ...To go through this, like, creative process, with all the frustrations and pleasures that it involves, with you and with Darius, with our two editors Jacob and Paddy.

VANEK SMITH: Yes.

GARCIA: It's been a blast. But most of all, I guess, we need to thank the listeners.

VANEK SMITH: Yes, we do.

GARCIA: We had no idea when we started this that listeners would show up, and they have. And they give us feedback. And they're pretty awesome.

VANEK SMITH: And pictures of graphing calculators and answers to who won debates and pretty much the best.

GARCIA: Yeah. They're great.

VANEK SMITH: Yes.

GARCIA: So thank you.

(SOUNDBITE OF DROP ELECTRIC SONG, "WAKING UP TO THE FIRE") Transcript provided by NPR, Copyright NPR.