Math class is hard (E)

0:00Talking Barbie was a great gimmick. a little computer chip made the classic doll able to talk. And so they had her talk about her friends, maybe even about school. But then the folks at Mattel made a big mistake. They created a talking Barbie that perpetuated a stereotype, one that ran deep with a lot of people.

0:31Hey, it's Kevin Beach, and this is a special archived episode of Akemba.

0:41Math class might be hard, but math? Math isn't what we think it is. One reason that math class feels hard is because math isn't what they teach in math class. It may be that you think you are no good at math, but you are probably mistaken. You might mean that you are no good at arithmetic because arithmetic is boring and you know how to do arithmetic with a computer. It might be that you're not good at memorizing formulas that make no sense to you, and that's probably a good idea because of all the things to be good at, memorizing formulas that make no sense to you is not one of them. School was built to create people who could do well on tests, and so, quote, math, unquote, educators, also in quotes, decided that the easiest way to have people do well on the tests was to teach them arithmetic and have them memorize equations that they didn't understand.

1:48But this is not a podcast about math class. It's a podcast about math, because you're good at math. All of us are good at math. We do math every day. If you are the NBA champion for the season, you are doing extraordinarily complex math without even realizing it. Because, of course, the force of gravity is exerted against the ball. And you have to toss the ball at the right velocity, in the right direction, so that gravity counteracts the energy and force you put into the ball, so that the ball goes in an arc and lands in exactly the right place, and goes to the basket. That is math. As Plato understood, math is the real thing.

2:36We can be fooled by our eyes or our ears, that our senses never tell us exactly how the world is, but math, math is pure and math is real and we are good at it. And so when Leo, who is two and a half years old, holds a bunch of grapes in his hand, he knows he has five grapes, not three grapes or eight grapes, five. He knows that not because someone taught him the formula for counting, but he knows that because math is true. So we make these decisions, these trade-offs, these choices, and we spend a lot of time with probability. Oh, I'm so excited. I don't know what to say to you, Evelyn Arnold, except that, did you like that deal that I just made for myself?

3:25Well, I'm going to let you have the same, same deal for the clutch purse and whatever you got inside there. That, of course, was Monty Hall. And if you're over 30, you know that Monty Hall was the greatest game show host of his generation. Let's Make a Deal was built on a simple but endlessly complicated conceit, which is that people in crazy costumes who are jumping up and down would be given something and the chance to trade it for something else. Or you could have that curtain that pretty Carol Merrill is pointing to right now, way over And those trades, those endless series of trades involved math, straight up math.

4:06The probability of figuring out if what you had was worth more or less than what you wanted to trade it for. Which brings us to our point, the famous and not very well understood Monty Hall problem. I'm going to take a couple minutes to describe it to you because even people who think they understand the Monty Hall problem might be glossing over just how disturbing it is and how important it is to each of us as we make decisions in a complicated world to understand how we can be led astray. So the way Let's Make a Deal works is simple. Monty gives you a choice and often it involves three curtains.

4:53Curtain number one, curtain number two, and curtain number three. Behind one curtain is a really juicy prize. And behind the other two curtains might be what was called a zonk, which could be an actual literal goat. And if you read the fine print of the rules, you didn't even get to keep the goat. They just got to humiliate you with the goat. And so, here we go. Behind one of the three curtains is$3 million. Behind one of the curtains is a goat. and behind the other curtain is a goat. So there you go. What are the odds? Well, most of us, without even taking a probability class, understand that the odds are one in three, that the expected value of this game, if you play it enough times, is a million bucks, one in three.

5:43That if Monty says to you, here's$1 ,000. Do you want to trade in the$1 ,000 for a chance to pick one of the three curtains, you should probably take that bet because the bet's worth a million dollars, a one in three chance to win$3 million. Okay, so you take the money and you pick curtain number two. And now, Monty shows you that behind one of the other two curtains, there is a goat. So there we go. Now there's only two curtains left. The curtain you picked, which in this case is curtain two, and the curtain Monty did not show you behind, which, let's say, is curtain number three. Here's the question he asks you.

6:32Do you want to switch? Do you want to switch from curtain two, which is the one that you picked in the first place, to curtain three? Now a lot of people will say the odds are the same. It doesn't matter whether you switch or not. And some people say, no, it's a little bit better to switch. Well, the fact is this. It's twice as good to switch. Your odds aren't 50 % if you switch. Your odds are 66 % if you switch. Stick, you got a one in three chance still of winning. Switch, you have a two thirds chance. In fact, you should be willing to pay up to a million dollars for the chance to switch to curtain number three.

7:25How can this be? How can it be that the odds for the new curtain are so much better? How can it be that if you stick, your odds are still one in three? Now, if you've been brainwashed by Barbie, brainwashed by the thing called math class, you are now in a fog. You're in a fog because you say to yourself, I am not good at math. Or you say to yourself, what's the formula? Because we have been pushed to memorize the formula. And the problem with memorizing the formula is that life rarely looks like a textbook. So how to think about what's going on here? Well, first, let me give you a minimalist explanation and then an extreme edge case that I think will help you see what's going on here.

8:13Here you go. What information did you get from Monty Hall when he told you there was a goat behind curtain number one? Because the fact is, you knew, even if you got the right answer, or even if you got the wrong answer, that one of the other curtains had a goat behind it. It had to, because there are two goats. So Monty hasn't told you, the person who picked curtain number two, anything you didn't already know. That if you are sticking with curtain number two, it doesn't matter if he showed you a goat behind one or three, you knew there was a goat behind one or three. It doesn't change the odds based on your decision.

9:02Because Monty was showing you based on what he knew. He didn't say, I don't know what's behind the curtains. Let's open curtain one and see. That's different. He was forced into showing you a curtain that had a goat behind it. So maybe curtain number three has$3 million. Maybe it has a goat. We don't know anything new about it. If a friend of yours walks in without knowing what Monty just did, and there are only two curtains left, then for him, based on the information available, which is there are two curtains, one has a goat, it is in fact a 50-50 chance. But for the person who switches, for the person who switches, Monty has demonstrated a huge amount of information because he didn't show us curtain number three when he could have.

10:02So what that means to us is that the odds of it being behind curtain number three are much improved. So here's the edge case and the way to intuitively understand math. What if instead of three curtains, there were a hundred curtains? If there were a hundred curtains, and you had picked curtain number two, and then Monty showed you a goat behind one and five and nine and 26 and 34, and on and on and on and on and on and on and on, 98 times, and all that were left were two curtains, and the only thing we know is he wasn't allowed to show you what was behind the curtain you had picked, it's pretty clear that that other curtain is a really good bet, because a lot of information has gone in to that curtain being a good one.

11:07The probability cloud of there being a goat has moved further and further away from that one. In that situation, I hope that most of us would understand intuitively that switching is a no-brainer. But sticking, the odds are still one in a hundred because the probability cloud hasn't changed because he hasn't given you any information about your curtain. He's just given us information about which of the other curtains have goats, and all of the added value went to the curtain you didn't choose. Alert listeners have probably noticed that the odds of switching or not switching keep adding up to one.

11:55That there was a one-third chance when there are three curtains, but if you switch, a two-thirds chance of winning. That if there are 100 curtains, you begin with a 1 % chance of winning. But if you switch, there's a 99 % chance of winning. The insightful Nicholas Krzyzewski comes through with the best explanation of all. Here we go. The only way to lose if you switch is if you had gotten it right in your initial guess. So when there are three curtains and you picked curtain number two, you had a one-third chance of being right, which means that there's a two-third chance you were wrong. But if you switch to the only remaining curtain, all of that wrongness turns into your right answer.

12:50and it becomes crystal clear when there are 100 curtains. Because when you picked curtain number two the first time, you had a one in 100 chance of getting it right. But as Monty took away curtain after curtain after curtain and there's only one to switch to, you're switching from your one in 100 shot must create the scenario where you have a 99 in 100 chance of being right. because the only way you could be wrong in switching is if you were right in the first place. Thank you, Nicholas. So I know this doesn't sit well still with a lot of people who are good at throwing basketball free throws because we don't experience this kind of probability choice in real life, or at least we don't realize we do.

13:43But the fact is it's there. We just don't build a game around it. We don't train kids when they're five or seven or nine to play these sorts of games, to understand in our bones how probability works, what infinity is, where we stand when the amount of information and data in front of us shifts. This is one reason why it's so difficult to ignore sunk costs, because we're really bad at getting past the emotions and seeing the actual costs and the actual probability. probability. So my suggestion here is not that you go learn the formulas of Bayesian probabilities, but that instead we spend a little bit of time going back and forth with each other, trying to navigate the odds of a royal flush, trying to figure out what it means when we see some cards get played and we don't know which other cards are left in the deck.

14:46Thanks for listening. Odds are, we'll see you next time.

15:16We love getting your questions. We got a few good ones this week. You can visit akimbo.link, that's A-K-I-M-B-O dot L-I-N-K, and ask your question about this episode or anything in the past. We're going to get to two good ones this week, but first, a recap from 50 episodes ago. The thing that comes up over and over when I talk to people, which is the difference between a freelancer and an entrepreneur. This week, Akimbo is launching two workshops, a brand new one for freelancers and a repeat of a classic, a proven one for bootstrappers. You can find out about both of them at akimbo.com, A-K-I-M-B-O dot C-O-M.

16:07So what's the difference? Why launch two workshops on the same day? Because I want you to choose. Freelancers get paid when they work. Using our own fingers, our own skills, we do the work. So when I am making a podcast, it's me. When I am writing, it's me. When I am giving a speech, it's me. We get paid when we work, and that's the only time we get paid. Entrepreneurs, on the other hand, build something bigger than themselves. They build assets. If you are an entrepreneur and you are busy hiring, the most easily available, best qualified, and cheapest person to do every job means you're hiring yourself.

16:51And if you're hiring yourself to do all the jobs, there's one job you're not doing, And that's the job of the CEO, of the person who figures out how to build something bigger than yourself. So the hard work of being an entrepreneur is hiring someone to do every single job that can be done by someone who's not you. It's a totally different way to be in the world. So if you're interested in this dichotomy, I hope you'll check out the little video we posted at akimbo.com. And now, on to your questions.

17:54Hi, Seth. but very welcoming and people like it. So the heart of my question, online meeting technology like Skype, FaceTime, etc. Those types of technologies. Although this replicates a face-to-face meeting and certainly works when my meeting mate is in Pakistan, what about a client that is 30 minutes away? What about three hours? A six-hour round trip for a 30-minute meeting seems very inefficient, but I find it more effective in building relationships with my clients that I can't effectively foster with online meetings. Do you have any thoughts about replacing interpersonal face-to-face interaction with a quasi-face-to-face technology like Skype?

18:37And if so, when would you implement something like this instead of face-to-face? Thanks, Seth. Thank you, Tony. You're touching on a great point here, and it's simply this. lots of people are born or given different privileges. Some people are taller or given more talents. Some people are born to wealth or end up with better resources than others. But one thing is true. Everyone, every day gets 24 hours. That's all. And so when we spend, interesting word, when we spend time on other people doing things that apparently are inefficient, we are doing something really important that is actually efficient.

19:30We are spending time, something that is precious that we can't get more of, to demonstrate to the other person that we see them and that we value them. So that driving three hours, or in the case of my friend Scott, flying to India twice a year, which takes, I don't know, a week of his life, back and forth, time zones and everything else, is a statement. It is a statement that has nothing to do with the information in the meeting. It is information about your care and your presence. The shift to video conferencing is really important. It will save many millions of barrels of oil. It will save countless hours of time.

20:20But we need new conventions. Because a meeting of any kind isn't as efficient as sending an email. We have a meeting for a reason. And the reason is because we are trying to say something beyond the words. So what's missing from most online video conferencing is convention. Have I taken the time to get the lighting right? Have I taken the time to use a USB microphone instead of just shouting into the machine? When we do group chats on Zoom, I'm amazed at the posture of some of the people who are slouching, sitting there in a darkened den, pretending that they don't care. We wouldn't do that in real life, and yet we treat it as if there's something between us and the other person.

21:12Of course, there is. There's thousands of miles of Ethernet cable, but we don't have to act that way. So I guess my point is this. We can invest the time to go to that meeting the first time, to show up and show that we're willing to burn six hours as an homage to the person that we are meeting with. But going forward, we can earn enrollment and we can say this project we are working on together, it's important enough that we can skip the six hours of backing and forthing and instead devote our energy to being fully present with each other right here, right now, across the distance using this software.

21:55But these conventions are going to take a while to establish, and it's up to us to lead that by acting as if, by acting in a way that lets other people see that we're putting extra energy into the system to make up for the fact that we didn't put in six hours on the road. Hey, Seth. This is Zach from Nashville. I run a business in the commercial animation industry. Net 30, 60, and even net 90 payment terms are industry standard. And as you say, we end up effectively giving loans to large companies like Amazon or Google, while we of course have fixed expenses every month like employee salaries and benefits, which we can't delay.

22:37Sometimes we're able to negotiate 50 % deposits, but often it feels like we have very little power to negotiate when going against large businesses and agencies that have entire finance divisions with fixed policies on these things. We could certainly make a fuss, but then we risk damaging our relationship with the client. I'd love to hear if you have any ideas on how we might change this culture of payment terms, especially for creative service-based industries. Thanks, Seth. Thanks, Zach. You're exactly right. Cash flow lies just beneath the surface. It may look like your product or service is at parity with your competitors, but if your competitors can afford an extra sales rep and 60-day terms, they're going to get the business.

23:28That's just the truth of what it is to deal with a large corporation. Because there are people at large corporations whose only job is to pay you later. That's how they earn their salary. And if you were in their shoes, you would probably do the same thing. And so the challenge, the challenge is to accept the fact that cash flow is one of the key factors of competitive advantage. And that if you don't have that competitive advantage, you have to come up with a different way to be able to be the one and only. And that way involves having no substitutes. That if there are no substitutes, someone above the person who's stretching you out will say to that person, nope, this one, we pay on time.

24:22Because if we don't pay them on time, we can't get them. The other variation of this, if you are working with a system that's too hard to break, is to do what big companies do when they sell each other stuff. They raise their price. That, sure, you want to pay me 60 days? It costs extra. That when you build that into your pricing, when your standard pricing acknowledges the overhead that big companies bring to the table, you might not get quite as many gigs. but the gigs you get will pay for themselves. And what's happened as we've industrialized and corporatized is we have confused low price with high value.

25:07You can't survive as the low price provider. And if you keep trying to be the low price provider, you will disappear. So no value will be created. The alternative is to dig in deep and figure out what they actually value at this company that you are selling to. Maybe it's the extra service, the person who answers on one ring. Maybe it's the fact that you make something no one else can make. There are lots of factors that go into you being chosen to work with a big company. You get to pick which factor you're going to play by. But one thing is certain, you cannot beat a generic big competitor when you make what they make and their pockets are deeper than yours.

25:55Thanks for listening. We'll see you next time.