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Robin Hood Math
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In this episode of Breaking Math, Dr. Noah Giansiracusa discusses his book 'Robin Hood Math', emphasizing the importance of mathematical literacy in navigating an algorithm-driven world. He explores how math can empower everyday people, the writing process behind his book, and practical applications of math in daily life, including social media algorithms and financial decisions. The conversation highlights the simplicity of the math that truly matters and encourages listeners to reclaim agency through understanding mathematics.
Takeaways
- Math is a powerful tool that can empower individuals.
- The concept of Robin Hood Math aims to redistribute mathematical knowledge.
- Mathematical literacy is becoming as essential as reading.
- Algorithms are deeply embedded in our daily lives, influencing decisions.
- Understanding expected value can improve decision-making.
- Averaging guesses can lead to better predictions.
- Social media algorithms prioritize engagement, affecting content visibility.
- Credit scores are calculated using weighted sums of various factors.
- Many important mathematical concepts are simpler than they appear.
- Mathematical literacy can help close equity gaps in society.
Chapters
- 00:00 Monetizing Social Media for Educators
- 02:25 The Birth of Robin Hood Math
- 05:18 Empowering the Everyday Person with Math
- 08:01 The Writing Process and Surprising Discoveries
- 10:37 Practical Math Lessons for Everyday Life
- 13:22 Understanding Algorithms in Social Media
- 21:56 Understanding Engagement Algorithms
- 24:28 The Impact of Mathematics on Financial Decisions
- 29:54 Empowering Through Mathematical Literacy
- 32:23 Exploring Key Themes in Mathematics
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Transcript
Introduction to Dr. Noah Gianciracusa
00:00:00
Speaker
Welcome to another episode of Breaking Math. I'm your host, Autumn Finaf. And today we're joined by Dr. Noah Gianciracusa, an associate professor at Bentley University and visiting scholar at Harvard University.
00:00:13
Speaker
He spent most of his career studying algorithms and society. Now, he often discusses AI-generated misinformation and the importance of mathematical literacy.
Focus on 'Robin Hood Math'
00:00:24
Speaker
Today, we're here to talk about his newest book, Robin Hood Math. Noah, thank you for coming on the show, and welcome to Breaking Math.
00:00:36
Speaker
Can you tell us a little bit about why you wrote Robin Hood Math? Yeah, i started out my career as a regular mathematician, meaning, you know, typical kind of pure math, theorem proof, dissertation, writing papers, academic journals, that whole thing.
00:00:52
Speaker
um academic, the ah pandemic rolls around and I just couldn't get myself psychologically up to writing more papers. We had a little kid at home that, you know, during pandemic, we ended up homeschooling and it's just, life seemed really different.
00:01:05
Speaker
And I was just in the mood to try something different. And for whatever reason, what came to mind was try writing a book. And I don't know why that seemed like the right time to do it. Life, I would say was harder than it had been, but I also had a lot of time at home.
00:01:16
Speaker
So thought, let me try writing a book. And i i wrote one that was more or less self-published and, you know, sold maybe. 10 copies total. But I loved every minute of the whole experience. I loved writing. I loved producing a book. I loved putting it to the world.
00:01:30
Speaker
And kind of that was the moment where thought, I got to do more of this.
How Algorithms Shape Our Lives
00:01:33
Speaker
So Robin Hood Math was me doing more of this. like I got an agent and she and I ah She's been wonderful. She and I brainstormed ideas and really tried to think of things that might resonate with people.
00:01:43
Speaker
And the but thing that struck us and that the book ended being about is so much of our life, what we go through, is just filtered through these the lens of algorithms. I wake up and I open my phone. I'm on social media and an algorithm shapes what I see.
00:01:57
Speaker
i get up and I drive to the bank. Maybe I'm interested in taking out a loan for something. An algorithm is involved in my FICO score. Algorithm involved in whether I get the loan approved or not. I look up college rankings. There's algorithms. I apply to college. There's algorithms.
00:02:11
Speaker
I'm teaching my students and they're using chatbots which involve algorithms. I'm using chatbots which just Everywhere is algorithms. I search for information, that's algorithms. And so he just felt algorithms are everywhere.
00:02:22
Speaker
And there's been a lot of writing about the harms of this, how there's bias, how there's inequity. There's a lot of addiction. There's a lot of downsides. And I just noticed whenever I read about these issues, it's very, for me, compelling, like,
00:02:36
Speaker
I always think like, oh, shit, things are really bad. It's really scary. These tech companies have a lot of power. We don't know what's happening to society. We don't know, especially, again, as a parent, like what's happening to the next generation, but even our own generation.
00:02:48
Speaker
And I just felt like, where's the positive note? Where's the, let's do something to make it better. At best, I would see, you know, Congress is discussing some new law, some regulation, and it never gets approved.
00:03:00
Speaker
There seems like there's zero hope that, you know, that's going to come from the federal government, at least. And so I thought, look, I'm a mathematician. I know algorithms run on math. Isn't there some way that we can understand these algorithms? And maybe with that understanding, kind of, I don't know, turn the tables on them. so We're manipulating them a little bit more than just them manipulating us. And that's kind of the idea behind the title Robin Hood Math is, can we take math from the elites, like the tech companies and the bankers and all that, and give that math, that mathematical power to ordinary everyday people so that they can better navigate this world we live in? Wonderful.
00:03:33
Speaker
Now, the book is titled Robin Hood Math. Can you explain that significance for me as well? Yeah. So let me go in deeper. idea is that math is a powerful tool, and I hope your audience will have no trouble accepting this.
00:03:47
Speaker
Math is a very powerful tool, right? That's probably why we're all in it or interested in or studying it, wherever we are in that journey. Absolutely. Right. We're talking to you and your audience. We love math. There is power. But what happens to a lot of people who study math and graduate? Some of them go on and become math professors. That's fine.
00:04:03
Speaker
Some of them become economists. That's fine. Some of them become work on Wall Street, do hedge funds. That's fine. Some of them work for National Security Agency doing code breaking. There's a lot of really nice job outcomes there.
00:04:15
Speaker
A lot of them nowadays, like when I was, I've been teaching more grad courses lately, but when I was teaching undergrad, a lot of them were double majoring in computer science. And they'd go off and get jobs at like Facebook and and these tech companies and Google, which is fine.
00:04:28
Speaker
But if you think about it, there's a lot of power. There's a lot of mathematical power that's flowing into the top echelons so of the economy. Tech is just dominating the the economy right now.
00:04:38
Speaker
If you think of the richest people in the world, most names you come up with, other than Warren Buffett, the names you come up with, they're all Zuckerberg and Bill Gates and Elon Musk. They're all tech people. So the idea with the title is math is power.
00:04:51
Speaker
And this power has kind of pushed a lot of very quantitatively literate, techie, mathy people to the top in society. And a lot of people have been left behind. Those are us ordinary people. And the idea with the Robinhood math is, can we somehow take that math from the rich and give that math to i don't want to say the poor, but to the rest of us, the everyday people.
00:05:10
Speaker
Can we somehow close that gap that's grown between the Elon Musks of the world and the factory workers, the Jeff Bezos's and the people who work, um the software engineers at at Amazon make plenty of money, let's say.
00:05:22
Speaker
But the factory workers don't. So why is there this huge gap? I think part of it is mathematical literacy.
The Future of Mathematical Literacy
00:05:28
Speaker
The book is, you know, it's not going to fix these problems, but it's aimed at reducing that gap and and saying, can we make math more accessible to a wider public by really focusing on practical things that help people in the world we live in today?
00:05:41
Speaker
And that world today is, well, as we all know, it's a very algorithmic world. I think I stated the other day in another episode is that mathematical literacy is just going to be um the same as being able to read in the future, especially since everything is now being driven by ai and other technology. Things do change with AI, because sometimes I feel math is like one of the few things left that's giving us humanity, that's helping us think clearly, that's kind of rising above the the sea of AI.
00:06:14
Speaker
And sometimes I do succumb to a more pessimistic view and feel like, I don't know, AI is going to do the math anyway, so why do we even need that math education? You know, whatever whatever I want to compute or calculate or think about, like if I'm trying to figure out, is it safer to fly or take a train, instead of doing some cool little estimates and calculations, just ask ChatCPT and it does it for me. right But that's not the same. I mean, I'm trying to let myself not buy into that argument that, oh, we can just give up.
00:06:42
Speaker
I really do think math is the enduring principles that help us rise above automation and everything else. These are ideas that have been around for literally hundreds, if not in some cases, thousands of years. I think it would be a shame to just because a few apps came out in the last couple of years to say, oh, guess what? We don't need math or math literacy anymore. i feel like I'm going to trust the historical trend. you think we just, we need it more at this point.
00:07:06
Speaker
Now, I think that's true. And I hope that's true he a math educator. That's my job as That's our job in one way, shape, or form. That's all right. Now, I'm curious, you use a lot of real-world examples throughout the book, ah whether it's been some sort of scandal with the U.S. news and college rankings or Sam Bankman Freed's Rise and Fall.
00:07:29
Speaker
So did you find anything shocking in your research when going through this book, whether it was in the book or not? Well, let me... I love this question. So let me zoom out and add a little pre-context, which is I'm not a writer, at least I wasn't. I haven't been trained as a writer. I'm a mathematician.
00:07:45
Speaker
So when I started writing this book, you know, i knew I wanted a chapter on, let's say, Bayes' formula. So I write a bunch of math around Bayes' formula. I try to make it, I'm a math teacher, so I try to make it really accessible and understandable.
00:07:56
Speaker
And then I hand it off to my editor and she wisely says, you need a ah frame, an opening frame for this. And I write back, I respond back. What does that mean? I don't even know. Like, I don't even know the lingo, right? I'm really not a writer.
00:08:09
Speaker
So I learned a lot through this process. But what she really meant is, especially in popular nonfiction, you know, it's different if you're writing a novel or if you're writing a memoir, but in popular nonfiction, it really helps to have a real gripping anecdote or opening experience for every chapter, not just the book, but every chapter that kind of sucks the reader in and gets some thinking, wow, that happened. I wonder why. I wonder what's going on. I wonder what the you know what's what's behind that anecdote so something tantalizing it's almost like ah an amuse-bouche or an appetizer and a meal something that sucks you in where then you have the reader and you can expound on that and you can kind of zoom back and explain the math and then show how it works and then tie in and say now that you know this math you know now you can understand that anecdote so for um sam i'll give you explain this in one example and then i'll finally answer your question
00:08:56
Speaker
So for Sam Bankman-Fried, what happened was I wanted one chapter basically on the expected value formula, which many of your listeners probably know or have heard of, but this basic formula and probability theory. And I wanted to just kind of teach it to readers and explain why it's important or relevant.
00:09:10
Speaker
So then I think, okay, I need some story, some anecdote, something in the news that involves expected value. And I'm just browsing, reading this article. about Sam Bankman-Fried. I was and working on the book a couple years ago when he was more in the news.
00:09:22
Speaker
And it mentioned that the article I reading said, every decision he makes is based on the expected value formula. And I thought, well, holy crap, this guy's in the news every day. Everyone wants to know about Sam Bankman-Fried, his rise, his fall, everything.
00:09:36
Speaker
And apparently he's using the the expected value formula just obsessively. So that became an easy hook, right? Start the chapter by talking about what he did and then slowly explain the formula and the relevance.
00:09:47
Speaker
So that's that's just to give your listeners kind of a sense of the writing process of, I didn't, you know, when when you hear, you mentioned research, as a math professor, mathematician, when I think of research, I think of like trying to prove a new theorem. I'm going to go read some journals and see what arguments are. out there It's very different book kind of research.
00:10:04
Speaker
So for book research, I knew the math I wanted to convey. I'm not researching the expected value formula, but research meant finding these real world relatable stories that gave it relevance in life and something that people connect to.
00:10:17
Speaker
And now I'll finally go answer your actual question. During all this research, was anything surprising?
Real-World Math in Society
00:10:22
Speaker
Yes, the thing that surprised me the most was I expected, I kind of outlined what each chapter would be as far as math.
00:10:29
Speaker
You know, one chapter is going to be about predictions. One chapter is about expected value. One's on Bayes formula. One's on, I can't remember all the chapters now, but and each one has a math topic and I round it out with a story and application, et cetera.
00:10:41
Speaker
What I found strange when it all came together was the math involved in all these in almost every single chapter was basically the same. It was this thing called weighted sum.
00:10:52
Speaker
And a weighted sum, as you probably know, is just you have a bunch of numbers that you add up. That's the sum part. But you weight them by multiplying each of these numbers by some constant ahead of time. So you can apply different weights.
00:11:03
Speaker
And it turned out, so I had one chapter on college. ah You said college news, you U.S. News college rankings. yeah They use weighted sums to produce these rankings. Then I mentioned expected value.
00:11:13
Speaker
Well, you can think of expected value as weighted sum. You can think of it as the sum of the probabilities weighted by the value of the outcomes, or you can think of it as the sum of the values weighted by the probabilities.
00:11:25
Speaker
There's a chapter on social media algorithms, and it turns out expected weighted sums show up. So that was the biggest surprise to me is the simplest math thing, right? Like just adding and multiplying numbers, like literally just arithmetic, well sh shy of calculus or anything like that, was everywhere, was all over the world and all over the book, every chapter. And I i didn't anticipate that, but it was kind of cool to see that happen.
00:11:47
Speaker
What I found really interesting was that you teach readers math that they can use to navigate their challenges and decisions that they face in life. Now, do you have a favorite math lesson from the book?
00:12:00
Speaker
Good question. Or maybe even favorite topic from the book? I would say it's probably predictions. And because it's so simple, I do have one about managing risk that I enjoyed, but I have to admit, like, you have to read it a couple times, and even I have to kind of reload it mentally each time But with predictions, it's so, so simple.
00:12:19
Speaker
And it comes up in a lot of very current things like machine learning and even AI. So the idea is, what do we mean by a prediction? Let's suppose you're trying to guess or estimate some quantity.
00:12:30
Speaker
This could be like, I'm looking at a jar full of marbles. don't want to guess how many are in there. So I make a guess and we open up the jar and recount them. It could also be predictions. So maybe I'm trying to predict what the weather will be tomorrow.
00:12:42
Speaker
Let's make it specific. Let's say the temperature the high temperature or the low temperature or the total amount of precipitation. So numbers in the world that we're trying to estimate or predict. Okay, so there isn't much science to it. You just guess, you pull a number out of your ass.
00:12:56
Speaker
Sorry to say, you come up with a number. And maybe you have a lot of expertise. so you can do this in a more refined way. Maybe you don't. Maybe you' a lot of experience guessing. But what's interesting is if you just take two guessers and you average their guesses together. So maybe, Autumn, maybe you guess and I guess, and then we add our guesses and we divide by two. So we average them.
00:13:16
Speaker
That tends to do better than either of us individually. And it improves as we add more guessers. And even as a mathematician, I admit, when I first heard this, I thought, come on. I mean, like, really?
00:13:27
Speaker
Wouldn't a single really good guesser be better than a whole bunch of people who are just mediocre guessers? Like, why why would that work? But if you actually go through the formula, there's some formula with expected value invariance.
00:13:38
Speaker
It just turns out that the variance of the errors decreases as you add in more people, which just means you're your guess tends to like hone in on the true value. It becomes more accurate. Unless there's some systemic bias that's pushing it away.
00:13:52
Speaker
And that does tend to happen. So, for instance, you know think in politics, like with the 2016 presidential election, I think most of society or much of society underestimated Donald Trump's chance in that election.
00:14:10
Speaker
So we all thought like, oh, you know, he's this kind of eccentric character. He's running. He's getting a lot of attention. But like, he's not really going to win. Hillary Clinton, if you remember, was the the candidate running against him. and And she ended up losing.
00:14:21
Speaker
And a lot of us were shocked that she lost. And I think part of that was there was this systemic bias that a lot of us were guessing he was going to lose. Yeah. And we were skewing, like averaging, polls are basically a way of averaging, and averaging a bunch of guesses that are all skewed in the same direction doesn't deal with that skew.
00:14:39
Speaker
That's very different than if you have a whole bunch of people guess what the stock market's going to be or what the inflation rate will be or things that you kind of don't have as much skin in the game, then it turns out that averaging really does tend to benefit.
00:14:50
Speaker
But thats that's what I'd say the lesson is, is you just tend to make better guesses or estimates if you combine a bunch and average them.
Social Media and Financial Algorithms
00:14:56
Speaker
Or in some cases, and this harkens back to our previous question, you can put weights on some of the guesses to give them more weight in your average and do a weighted sum of a weighted average of guesses.
00:15:07
Speaker
Turns out that tends to work really well. For instance, a lot of us in our you know nerdy numbers type of people have heard of Nate Silver. He did a lot of political predictions and things. His system was pretty complicated. You know, he was a poker player. He had a lot of complicated understanding of risk and betting and stuff.
00:15:22
Speaker
But The main ingredient under the hood of his system was weighted average, where he took a bunch of polls, he averaged them, and then he weighted them by how well they succeeded in the previous elections.
00:15:33
Speaker
So if one had a really good track record, he didn't just jump in and say, let's use that one, because what if it suddenly falters and ends up not doing well? It's better to include a whole bunch of them, but give ones with better track records more weight and include others that haven't been as reliable with lower weight because maybe now's their time to shine. Maybe they're going to do better on this particular election than the others did.
00:15:52
Speaker
Sometimes you never know. That's right. And it comes down to the last minute. now Now, what are some of the practical formulas and hacks that readers can use that they can incorporate into their everyday lives?
00:16:06
Speaker
Yeah. So there are some kind of general mathy things that I want to help show people is relevant, like using the expected value formula. I think it's relevant in your day-to-day life. But let me zoom in on the one that I think is going to be most relevant and interesting to a lot of our viewers, which is social media. Who amongst us hasn't spent far too many hours on it?
00:16:26
Speaker
um So we all know the basic experience. You go online, whatever your app is, the platform, and you see a lot of content, right? You might be swiping or scrolling, whatever it is, or on YouTube, things are being recommended.
00:16:38
Speaker
There's just a lot of stuff and it keeps going and it's all automatic. And you have very little agency, right? It's just it knows you. The algorithm knows you better than you know yourself. So it's not like in the old days. I'm dating myself here. But the old days when you to go to Blockbuster Video and, you know decide what I want to watch and pick up the video.
00:16:54
Speaker
It's more like the only people that I think that listen to us. We only have a couple viewers that I am aware of. that are in India that are not at least of our generation.
00:17:07
Speaker
Okay, so there we go. So you're not dating yourself that much. I'm not dating myself. I'm dating your entire podcast. ah we are Yes, pretty much. I can live with that. Yep.
00:17:18
Speaker
But you have to admit there is a big difference between... Yeah. the user the viewer to make their choices which is how society used to be in so many ways not just videos to suddenly switch into entrusting an algorithm which really means entrusting a tech company but the tech company is hands off right it's not like brita is sitting there like i bet autumn will like this photo on instagram No, they just create an algorithm which creates the feed. So we're very hands-off, right? Everything, our entertainment, I mean, we talk about AI coming in and automating and changing things, but a lot of our entertainment hasn't been produced in a content production way by ai but the distribution very much is AI. Some algorithm is deciding who watches what when. So you wanted something practical. So let's let's zoom in on this. So when I go on a platform, there's a whole bunch of things I could see. Let's just do TikTok because I know that's a very popular one. So TikTok is a big platform. You go in there and you see a video and you can swipe past it and you get another video and you keep kind of scrolling or swiping through and you see a whole ah sequence of videos. And somehow you're swiping patterns. It learns a lot about you and it hones in on what you're interested in without you even knowing what you're interested in
00:18:27
Speaker
How is that happening? Well, in... 2021, a journalist for the New York Times, Ben Smith, got a hold of a document that was meant to be used internally at TikTok to train.
00:18:40
Speaker
Basically, it was like written by the engineering team at TikTok to help give a sense to all the employees outside of the engineering team, how the algorithm works and what it does. So kind of it was an explainer, not overly technical explainer of the algorithm, but it was meant for TikTok guys only. That was the intention.
00:18:57
Speaker
Of course, it leaked. Ben Smith looked at it. He published it. um I had a look at his article. There was this formula. I don't recommend reading his original article. He doesn't know LaTeX. That formula was not typeset in any legible way.
00:19:09
Speaker
We're not going to talk about It was not. Anyway, I will help translate it for you. So he gives this formula and it's a mathematician can recognize and I can help you go through the weeds here. It's an expected value formula.
00:19:21
Speaker
The formula is basically there's some weight on likes times the probability of a like plus a weight on comments times the probability of a comment plus a weight on watch time times the expected watch time.
00:19:35
Speaker
So what the heck does that mean? What's going on? Every user that logs in, that goes online, that that's on the app, they could see one of a billion videos or probably more. And the app has to somehow score these from highest to lowest of what one is thinks you're most interested in in watching.
00:19:51
Speaker
So how does it do that? It uses this expected value formula. Basically, it wants to know what video is this user most likely to engage with? But engage could mean liking. It could mean commenting. It could mean watching.
00:20:04
Speaker
Could be watching twice. Could be watching five times. So there's lots of different forms of engagement you can do on TikTok. And what they do is a weighted sum. So there we go. The same concept we talked about before.
00:20:16
Speaker
weighted sum that combines all the different forms of engagement. Now, we don't know who's going to like and comment and watch a video before they've shown you. So all we have are probabilities. This is where the AI comes in.
00:20:26
Speaker
The algorithm is guessing the probability that you will like it or comment or how much you'd watch it. So the algorithm takes all those estimated probabilities of different forms of engagement, weights them and adds them up.
00:20:37
Speaker
And that gives you the sort of total estimated engagement, total predicted engagement, which is an expected value if you think in probabilistic terms. The algorithm then sorts your videos from highest to lowest according to this this score.
00:20:50
Speaker
So if it thinks this one video will get more weighted engagement from me than this other video, then it plays that first video first. So the punchline is TikTok never told us the weights here. So it's frustrating. I don't know how much like is worth relative comment versus watch time.
00:21:05
Speaker
But just knowing this formula, I think already is helpful. Because I always heard that, oh, you know, social media is driven by engagement. It's all about engagement. But I think this gives kind of a clearer sense. Like one of these factors is watch time. So let's unpack what that means.
00:21:19
Speaker
Because the number of seconds I watch a video is in this formula with some weight. Let's say the weight is just one. So a second of watch time is one point, whatever that means. If I watch a video, a 10 second video one time, that's 10 points.
00:21:31
Speaker
If I watch it three times, that's 30 points. The funny thing is, as I was writing this chapter, sometimes I noticed I was on, I didn't really use TikTok, but was on like Facebook Reels or something. And I'd be watching something and it would say like, you won't believe what happens at the end or watch what this one guy does at the end.
00:21:48
Speaker
Or it's a comedian telling some joke or something. And I watched the whole thing and I missed it or I didn't get it. So I watch it again. And still, like, nothing's happening. I watch it a third time. don't have something intentionally. There's nothing there. Right. And then I scroll by. Well, now I know exactly why and all of us know.
00:22:03
Speaker
And maybe it's not so surprising in hindsight, but I think the math helps elucidate this, which is, yeah, if you can trick, if you're a content creator, if you can trick someone into watching your video three times instead of one, you get three times as many points in this silly formula that that shapes everything.
00:22:21
Speaker
um Same with comments, right? if i If I post something that elicits lots of comments, and this has been an issue on Facebook, some conspiracy theory thing shows up. My temptation is to write, this is you know bogus, don't fall for this, it's not true.
00:22:35
Speaker
Facebook just sees, that's a comment, that's engagement. It makes that post more popular, and it makes me see more other posts like that because it's just boosted my probability of commenting on conspiratorial posts.
00:22:47
Speaker
So just being aware of this formula helps It helps us know the rules of this game that we're all playing, which is we got to start choosing our engagement a little more carefully.
00:22:58
Speaker
So yeah, just use social media, have fun. But just remember, every time you like, that's not just telling the person created the video, this is good. That's telling the algorithm, I want more of this content.
00:23:08
Speaker
every time you comment, you're rewarding that content and you're encouraging the algorithm to give you more of that content. If there's something like, let's say, a TikTok video that's really bad, you watch it once. Don't watch it again out of hate. Like, oh, that was horrible.
00:23:21
Speaker
Just move on. You know, the minimal amount of time, the minimal engagement, just get out of there. That or automatically dislike it. Yeah, except who knows? You know, they might use dislikes as engagement signals. And, ah you know, that's where we don't know the details. So it's frustrating.
00:23:36
Speaker
Yep, it might not be in your algorithm, but it might be in someone else's. I'm worried that one day, instead of having to, one day not too far in the future, instead of having to trust our likes and our comments and our ah thumbs up and our happy faces and our ha-has and all that stuff,
00:23:51
Speaker
They'll just have our webcams on and they'll use AI to do facial recognition. That way, as I'm scrolling, they can really see when I'm angry, when I'm happy, when I'm looking away. i mean, there's so much data, to be valuable data that they could use if they did that.
00:24:05
Speaker
That is horrible and creepy as it is. And for me, like this is full dystopian. I don't see why. like ah can't see them resisting that in the long run. It just seems too tempting. Because it's the data the algorithm really needs.
00:24:16
Speaker
It's not me saying ha ha. It's not me saying angry face or sad face. It's them actually knowing what my actual physical reactions are. Good point there. That's not here yet. So let's not worry about that yet. But be careful.
00:24:28
Speaker
Now, to switch topics a little bit here. um Now, understanding mathematics helps people make a lot better decisions about their finances, such as improving credit scores or making investments. Can you share some light on this? It's not financial advice, but it is in the book.
00:24:48
Speaker
Yeah, for sure. So start with the easy one, which is when I first was seeing that this weighted sum formula was all over the place, more than I expected, I was just like Googling, curious where else it shows up.
00:24:59
Speaker
And it was really interesting to see, this is less kind of in the advice setting, but I'll try to circle back to that, but just mathematical curiosity. So credit scores, the the most famous one in the US, but it turns out they're all very, very similar internationally. But in the US, it's interesting. I didn't even realize this until I was writing the book.
00:25:16
Speaker
There's one basically one centralized credit scoring agency. So banks don't really assess your credit individually. This one company that provides these things called FICO scores does that for everyone.
00:25:29
Speaker
And then all the banks will basically just tap into FICO services. The UK, there's a couple, like it's a little bit more distributed, but in a lot of countries, it's it's completely decentralized.
00:25:40
Speaker
So if I go for a ah loan at Swiss Bank, Swiss Bank, well, they don't use a FICO score. They'll just assess my credit the way FICO does, but they just do it in-house. Anyway, the punchline is as far as, so FICO, I know this is true, but as far as I can tell, all the others around the world do very similar.
00:25:54
Speaker
They use a weighted sum. which means they have a bunch of factors that they've deemed important for your credit. So for FICO, you can look up, I have in the book, and I forget them off at the top of my head, but they they have on a webpage what their different primary fact considerations are. One is something like paying back your your loan payments on time.
00:26:13
Speaker
So if you miss loan payments, that dings your credit. Another is requesting credit. If you request too many new credit cards and bank accounts and lines of credit, if you do that too often, that that lowers your credit. So there's a few other, and don't know, bank bankruptcies or something like that.
00:26:27
Speaker
There's a few criteria that end up being relevant for them. But how do they combine these different criteria into a single overarching one? They use the weighted sum. So they assign each one weight and they even tell us what, i again, I forget the top my head, but they tell us what these weights are, the numbers that combine these different factors.
00:26:44
Speaker
So I think it's really helpful instead of like when I see my FICO score, it'll suddenly be lower. It is what it is. And I just feel like what happened? Like what's going on? But just knowing that basically there's six main ingredients and each ingredient has a certain weight that And, you know, this one might be 30 percent. This one might be 20 percent.
00:27:01
Speaker
Just seeing that gives me a lot. It kind of takes for me some of the anxiety away of where these numbers are coming from. And it helps you focus on the most important ones. Look at the ones with the highest weight. um I think the highest weight one was paying back your your loan payments on time, which not surprising, but good to know.
00:27:17
Speaker
So just recognizing that, I think, can help guide your actions. I think it's illustrative of a broader phenomenon. So I can't you know and remember everything and educate everyone on everything.
00:27:28
Speaker
But it's just to say so much of our society is based on fairly opaque systems and decisions that often when you probe into them a little bit, you'll find that they just use pretty simple formulas.
00:27:39
Speaker
And I just kind of want to recommend to our our listeners that it's often worth the time to just, you know, scratch that top layer and see how is that decision made? What is a FACO score? What are the ingredients? How are they weighted? And it doesn't mean you can suddenly game the system completely, but it often gives you more...
00:27:54
Speaker
agency and strategy for kind of playing these numbers games. So that's FICO score. Another one that I thought was kind of cool is ah stock indices. So the NASDAQ, S&P 500, a whole bunch of international ones.
00:28:07
Speaker
They're all basically weighted sums. which is more or less what these indices do is they look at the number of stocks that are traded on the market for each company, and they weight those numbers by the value of the stock, and they add that up, and they divide by some number that kind of normalizes things to some extent.
00:28:26
Speaker
But basically, it's it's a weighted sum that's what's called the market capitalization, you know those terms. But I'm a mathematician, not a finance person. I thought, hey, that's kind of cool that that S&P 500 is more or less weighted sum. um That one, I don't think knowing that affects your life in a day to day, but I thought you for a mathematical audience, that's pretty cool.
00:28:45
Speaker
It's always wonderful knowing some of the other mathematics that's involved in your everyday life. Yeah, exactly. We overlook that so much and we just go through things and sometimes it's just, wait, I forgot about that.
00:29:00
Speaker
Yeah, it's just kind of satisfying. I mean, as someone interested in math, it's cool to see like, hey, this math is useful. It's in the world. And even if you're not, you know, in math, it's kind of, well, goes back to what you were saying, Autumn, about mathematical literacy is yes the world is using formulas in a lot of places and just being aware these formulas and being mindful of what they're conveying instead of just closing your eyes and saying like, you know, FICO score, I don't know. i have no idea what S&P 500 is. I have no idea what NASDAQ is.
00:29:27
Speaker
is to realize like they use math, but it's not as hard of math as I would have expected. You know, I'm not, again, not a finance person. So when I was writing about this, I had to read about it and I just found it really satisfying to think, cool, that's math, but it's honestly like pretty easy math. And I'm not saying that in like a cocky way. Like that's really simple math.
00:29:45
Speaker
It's really nice to know that that the world's using that and makes me feel like, you know, next time I'm teaching fractions, why not teach 500? It's fraction. Yeah. a fraction Now, out of curiosity, I know that you're doing some book signings. We have a big following in the Boston area. When are they? I know some people, especially our math following at Harvard or other places.
00:30:08
Speaker
Yeah, so... might want to come and say hi. That would be fantastic. I would be thrilled to, even if just one of them come, that would be so cool to meet a person like that. So I don't know how best to convey, like to write or email, but basically August 5th, so this Tuesday at 7 p.m., we're having, that's the official book publishing publication date.
00:30:29
Speaker
And at 7 p.m. at the Harvard Bookstore is a free and open to the public event. You don't have to get tickets or RSVP or anything. You just show up. um So that'll be our first event. And then a little bit later on, I think it's a Saturday, August 16th at 3 p.m.
00:30:44
Speaker
at the Silver Unicorn bookstore in Acton, Massachusetts, which is where I happen to live. We're gonna have another event. Wonderful. Now, is there any sort of larger math lesson that you want folks to be of knowledge for throughout the book or, you just about life. I usually ask people about that. Is there any advice that you want to share with people or takeaways?
00:31:08
Speaker
For sure. i i I would say the big message that I tried to convey in the writing, but honestly, it was just as much that I learned in the process of writing, is that We live in a very, very algorithmic world, as we discussed at the beginning.
00:31:22
Speaker
And algorithms run on math. That is just indisputably how they work, what they are. So you could then therefore say we live in a very, very mathematically driven world.
00:31:34
Speaker
And what I want to say is I think the key to reclaiming some agency and empowering people and closing some of these equity gaps and just making the world more fair and better and pleasant and fun and empowered for individuals, it has to boil down to mathematical literacy and mathematical ability because that is our tool for climbing up in this mathy world.
00:31:55
Speaker
And I just want to say like the the biggest takeaway for me and the biggest message is it's so much easier than you think. It's easier than I thought. That math is everywhere, but most of the math that matters is very, very simple.
00:32:06
Speaker
Yeah, there's some firm on Wall Street that's using some crazy complicated stuff to solve the stock market or whatever. Who knows? Don't worry about that. The math that matters to you and me as individuals in our day to day, it's very simple. It's addition and multiplication, some simple formulas, but that little bit can go a long way.
00:32:23
Speaker
Once again, Noah, thank you so much for coming on the show.
Conclusion: Stay Curious and Informed
00:32:27
Speaker
And as always, stay curious and stay informed about the world around you. Until next time on Breaking Math.