Be a Better Guesser With Fermi Estimation

like they just chewed it all the time. Like every weekend it was what what Bond movie will be sort of watching this weekend? And you would you would hope where I would often those days, I would hope it would be the Sean Connery. Nowadays, I think if I were to do what, I would say, Roger Moore please. Yeah, the more ones are the cheesier ones, they're better for

Thanksgiving Day. Yeah, I think so, like the Sean Connery ones might be better movies, but they kind of just they have this tinge of alcoholism and misogyny that well, no, I guess the Roger Moore wins due to they do. It's kind of just part of the character I think you find that in every variation. Yeah. Anyway, So James Bond, what does he do when he walks up to a

gambling table? What happens every time he walks up, lights a cigarette, makes some dirty word play with a female gambler or something like that, and then he gets a black check hand. What happens, Well, he tends to win. He wins every time. He always wins. When James Bond never loses, unless it's like a specific scene where gambling is crucial to the plot and he must lose, like in Casino Royality. Yeah, like, I can't even I think I can't remember if he won or lost in gold Finger.

But there's a scene in gold Finger where, uh, gold Finger himself, you know, the villain of the piece, like cheats at cards. I think by by having somebody in in one of the high rises. Oh yeah, here's thinking James Bond isn't playing he gold Fingers cheating somebody else? Okay, but does he then play Goldfinger and win? It sounds like the kind of thing Bond would do. I don't think he ever played. He plays him, he plays him

in golf and then and then they both cheat. Anyway, getting past this, okay, Yeah, but so he always wins. He all, he goes up, he hits twenty one right on the first throw every time first throwers what you call it the first hand. Um, And so my question is do you believe that there are people like that? Obviously there is luck in the sense that there are differential outcomes. You can have a lucky thing happen to you, you can have an unlucky thing happened to you. But

do you believe there are people who are consistently lucky? Well, I'm sure plenty of our listeners have played the various role playing games, you know, video games as well as pin and paper games, and if you have, you've probably encountered characters or character management systems where there's an actual numerical luck rating for the character. Right, so you can like eight yourself higher on luck. Yeah, so you know, well,

this character and then their strengthened in that grave. Their dexterity is a little lacking, but their luck skill is amazing. That's not a skill well I know, or an attributed ll but but yeah, if you play enough role playing games, that makes you think, yeah, I wonder what my my my luck rating is? Am I on a nine or a ten. Um. So is it like that in real life? Well, I think obviously the answer is no. Um. Though actually I want to go back on what I said a

second ago, because I said, that's not a skill. It may be true in the sense that some things that look like luck are in fact skills, But personally I don't don't believe in this karmic version of luck. I would assume Robert, you probably don't either, I know, not not per se not not scientifically speaking, not in terms of like you having some kind of store of spiritual

capital holding sway over future outcomes, right. I mean, if I was to adjust my the lenses through which view reality and uh and choose to load up more mystical religious views of the world, I might engage in this into a certain amount of magical thinking. Some folks are are lucky that some folks are, I don't know, guiding themselves to the multiverse of possibilities along like the most

victorious line possible. But from a strictly like real world scientific pragmatic point of view, no, absolutely not, however, though I mean, I think we can both agree that even in the sense of a real world scientific pragmatic point of view, there are some people who do seem to be more consistently lucky than others, And I think this is because random events are it's or it's not because of random events being brought to heal by luck magic.

It's because people are able to influence events in ways that are not in fact random, just look random from the outside. So, for example, a person who's really confident and positive might not actually have more good outcomes on average than somebody else. But when you think of that person, when you think of your friend who's really confident and positive, you're more likely to count the hits and discard the misses. You know, this selection bias thing. Good outcomes seem in

character for that person. They sort of get added to the character sheet. You're like, yeah, that's that's them. Well, you know, bad outcomes you just ignore. That's like that's noise. Yeah, I mean James Bond is a classic example. We think about James Bond to you know, of course, the fictional character spread out across various movies and books, and we think, oh, he wins all the time, he always gets the girl. But there's a scene in What's the George lasonby movie

um on Our Majesty's Secret Service. Yea, his wife is murdered by by Telexavalis's Blowfield's Man. You know, just spoilers well killed and spoiler for you know, arguably one of the lesser James Bond films. Oh no, it's some people's favorite. Uh. I enjoyed it. But but yeah, like there's a super traumatic moment like who would want? I wouldn't want? I would I would not want all of the you know, alleged benefits of Bond's life if I also meant I

had to experience like that kind of a low. So even with James Bond, we're forgetting all the torture scenes and the injuries and the dead wife, and we're focusing on the stuff that we are in via stuff. Sure, okay, so that's just like influencing people's perceptions of you. But what what if you are actually you actually have more good outcomes than average. I think in in cases like this, there are a lot of things that we think of as luck that are in fact skill. One example would

be some forms of gambling. Now it's true that there's no skill involved in getting lucky cards at blackjack, but there could be skill involved in other aspects of gambling, like in poker, knowing how and when to bet so as to manipulate your opponents. Uh, you can turn even

a bad hand into a winning hand in poker. In black jack, you you know you can't control what cards you get, but if you can count cards, if you know the odds on any given play, if you know you know, okay, here are the cards I have, and here's what the dealer is showing. I know the odds of what I should bet. You can sort of start to leverage an advantage. In black check. I think you still probably can't get better than but but there is some skill involved there. And don't count out just flat

out cheating. Oh of course, I mean the most important skill in peopling. It's the skill that the house has leveraged against you. With your consent, you agree to a game that they openly acknowledge they have rigged. This is true and nice call back to our slot Machines episode that we recently republished. Right. Uh. And another way to think about this, Uh, this concept of skill versus luck

is in the realm of guessing. I think guessing is a really interesting phenomenon for human beings because we use this word a lot of different ways. Some times we use it to mean, uh, you know, just going with a gut feeling when you have no information. Sometimes we use it to mean coming up with an answer on very limited or little information. But but generally it means like trying to produce a piece of information without a

strong determinative process to get you there. Well, I think in a lot of cases it's it's the kind of it's kind of artificial scenario that would not exist out of the human realm, such as I think one of the classic examples would be a multiple choice test. Then maybe you didn't study for all that well, right, and so you have suddenly are forced to answer a question that you just have no idea about. Maybe you can

eliminate one possible answer. If you're still left with three likely answers, and you just have to go with your guy, you just gotta guess. You gotta get a wild shot in the dark. Yeah. And and from this concept we we have this concept of the lucky guess. Of course, people who are lucky guessers who seem to have a much better than average hit ratio at tossing out a correct or nearly correct answer to a question even when you've got essentially no knowledge or very little information to

work with. And that's what I want to talk about today, about this, this process of guessing, and about how in many cases things which appear to be random lucky guesses are not in fact random. There's a skill, you know, there's a skill and art and a science to many different kinds of guessing and smart guessing. Uh. And there are even a few techniques that you can harness for yourself to get a little bit better at guessing than you might be if you're just always going with your gut.

So one thing I wanted to do. I don't know how many good answers we can really come up with here, but I was wondered, like, who are some people who are some famous, really good guessers. I've got one answer, but other than that, I don't know. You know people like this personally, right, You've got friends who you know are better guessers than others. But in terms of finding like historic moments and saying like legends of guessing. I did some poking around, and there aren't a lot of

great options, like you know, military history, etcetera. There aren't situations where someone just takes a wild guess and it pays off and it becomes the stuff of just absolute legends. Yeah, one of the few examples I could come across. And again, this is not a high stake situation. I mean, it kind of is for one specific person, but it's not a warfare scenario, and it's taking place within a very artificial human environment, not the multiple choice quiz but the

game show. All right, So Wheel of Fortune, Wheel of Fortune, this was This occurred on a two thousand fourteen episode. So you had this contestant by the name of Emil de Leon and he had If you're familiar with Wheel of Fortune, it's where you have you know, those blank uh blank places where the letters go on the It's like a combination of Roulette and scrabble. Yeah, so it's

it's it's a very specific game. It's you know, if you're like me, you at least grew up watching your grandparents watch it, and a lot of people watch it regularly. It's a it has a certain system in play, and it's kind of neat to to sit there and play along at home, you know what. It's actually more like, I don't know why we're explaining this. Everybody's seeing wheels watch but no, I mean if you actually haven't. It's like the game Hangman, where you guess letters. You have

a set number of spaces. Uh you know they're like eight maybe you know there are eight letters in this word and you're trying to guess letters and if you get one right, it gets filled in there you go, Yeah, it's it's Hangman, with with with with with monetary rewards and Pat say Jack, okay, okay, So uh, the leon is playing all right, and there's like a there's a three word problem up on the board and the only letter up there is in, so that the it's in

blank blank space blank blank blank blank space blank blank blank blank blank. Right, that's what it is. That's it. That's always got to go on. What would you guess? I don't know, see unlikely leon. I haven't put a lot. I haven't put a lot of thought into the system of it. Like here's a guy who watched it pretty religiously and then he was gonna, you know, he got to go on the show. So I think he was he was very much in the mind to try and game the system. I look, if I were to look

at those blank spaces. I don't know what I guess, uh new rats lover. That doesn't work now, I give up. Well, but you got the new, all right, so you figured that part out. And indeed he also guessed the new, but he also went all the way and guessed new baby Buggy and one sixty three thousand. Yeah, cheating must

have been cheating. Well, some people leveled that charge and he uh, he ended up explaining himself because this was apparently a big deal, like even Pat say Jack said this was the craziest guests ever in his history of hosting the show and when they When Leon Julianne was interviewed, he said that, well, first of all, he'd been watching the show for some time. He knew the game inside out, and he knew that knew had to be the first word like that was even we got that. You know

that if it's in blank blank? How are many? How? What what are some more common words that come to mind? Not many? Maybe not not not now, but he he, I guess watched it enough to know that a lot that's probably gonna be new. And then he said that since he was studying for nursing exams, he had babies on the brain, so he just kind of it just happened to be that that, like baby is the perfect

four letter word. I don't is new baby buggy like a like a common phrase I don't not in in my experience, So that's like an expression that I'm not familiar with. I mean, I guess it's like a new baby. Is it like a some sort of a rhyming nursery rhyme kind of a thing or tongue twister? I guess is a tongue twister. Maybe that's the origin there, but uh yeah, it just seems kind of crazy that that he just instantly produces the answer to this seemingly out

of nowhere. Uh As it turns out it's not quite out of nowhere. He at least had a very educated guests on that first word, and then his prior experience just happened to ease him into those last two words. Okay, Well that that might you might actually just call that luck in some ways, like it might know the game

well enough to see new there. But I mean, those other words could have been anything, right, but his experience prepared him to be lucky in a way that other people would not have been lucky, like if they had not a watch the show a bunch of times, which I don't know if anybody ever just shows up on Will of Fortune, they've basically never seen the show. They do this new baby buggy puzzle every other week. Yeah, so you know, I I think you can you can

make the argument either way. But yeah, I would say that his his experiences put him in just the right position to to to be a little quote unquote luckier than other people. Okay, well, I mean, so whatever is happening in that scenario, we do know that, at least in much the same way, somebody who appears to be a consistently lucky gambler might just be a skilled gambler

counting cards, calculating odds, manipulating opponents. Um. When it comes to numerical values, uh, somebody who appears to be a lucky guess or with numbers is more likely to be a skillful guesser figuring out how to leverage existing knowledge that you wouldn't even thought of to take into account into a kind of ballpark accurate guess. And one person who's famous for this is the Italian physicist Enrico Fermi So Fermi lived from nineteen o one to nineteen fifty four. UM.

He grew up in Italy. After the passage of anti Semitic restrictions and fascist Italy in ninety eight, for Me and his family fled to the United States, where he ended up working on the Manhattan Project and in his role for Me, was present for the first test of the atomic bomb on July sixteenth, ninety the Trinity Test. You've heard about this, and at the time, this was new territory. Nobody had ever tested a nuclear weapon before, you know, a fission weapon with this big yield. They

didn't know exactly what was going to happen. You know, the physicists had their calculations. Uh, they were fairly confident that the device would explode. It was this plutonium implosion bomb that they called the Gadget, and they thought it would generate a large explosion, but the outcome was all theoretical at that point. They weren't sure what the level

of energy output would be. Yeah, I remember reading that like on the extreme ends of the spectrum, that where there was the possibility that it could be a dud or it could catch the air on fire. About that that sort of thing. Yeah, and so they didn't know. So Enrico Fermi that this great physicist who's famous at good guesses he's there to watch the test. So picture him there. Uh, he's there with his colleagues, and he's at a camp about ten miles away from ground zero,

ten miles from where the bomb goes off. Jay Robert Oppenheimer's there like scribbling notes into a Hindu epic. I'm sure, I'm sure. Yes. So they're behind some shielding for good reasons. Uh. And Fermi watches the blast through a board that's got a viewing window made of welding glass. And there's a two thousand five issue of the Nuclear Weapons Journal that includes an article with some great quotes from Fermi and others who were eyewitnesses to this to the event, and

Fermi wrote, So he's there, he's looking through the welding glass. Um, and uh that he very first saw quote a very intense flash of light that was brighter than full daylight, and then a conglomeration of flame that rose into the sky, and a huge pillar of smoke with an expanded head, like a gigantic mushroom. Here's where we get our mushroom

cloud um and that rose rapidly into the clouds. Now, when there's an explosion and you're pretty far away, there's a time gap between when you see the flash and when you feel the blast. Right could because why light travels faster than sound. It's the same thing that happens between lightning and thunder. You see the light and then you hear the sound of the thunder. Uh So it was about forty seconds after the visible explosion that the air blast actually hit the observation camp. And when the

air blast arrived, Fermy did something really weird. He held up a handful of scraps of paper about six ft off the ground, and he dropped them and he let them flutter away in the force of the air blast, and then after seeing where they fell, he released some more,

just in regular air, no blast. And then after he looked at how far they went, I think it was like two point five meters or something, he quickly guessed that the detonation had been about ten kilo tons worth of explosion, meaning it released the same energy as ten thousand tons of t n T. Now, when the actual readings came in, it was about twenty kill a tons, about twice Fermi's estimate. So he wasn't exactly right, but this is still a remarkably good guess for having no

direct readings to work with. I mean, after all, you think about it, can you look at an explosion ten miles away and say how many tons of T n T you think it's equivalent to know? I wouldn't even know how to. I wouldn't know what order of magnitude no tons to kill a tons to mega tons um. So with just some scraps of paper watching how far they blew in the wind, FIRMI was able to do some quick calculations in his head and correctly guess within

the true order of magnitude. So how did he do it? Well, we'll come back to that in a bit when we get into the Fermi estimation method. Now, before we move on, and I think this is also of interest that the U. S Army as well as other U S Armed forces, have used the acronym SWAG before, which stands for a scientific wild ass. Guests, now, you're not you're not swearing

on the podcast? Now? No, no, no, not necessarily. I guess it depends on your your viewpoint here, But uh, this was a now Robert, Uh, you know what we're talking about here. Of course, as a guestimate, a guest made by an expert or institution with a certain amount of expertise in a given topic. Um, you know, it's still a guests but but hopefully you're leveraging your best

information and making that guess. It's I think it's generally considered a guest that comes from somebody who should know what they're talking about, even if they don't have direct information to work with. So you know, you might be in a situation where, uh uh, somebody has some weird array of symptoms and they don't really correspond to any known medical condition, and maybe you don't have any instruments. You can't take their temperature, you can't do any lab

work or whatever. But you could still have a doctor look at them and guess what's wrong with them, or just have a I don't know, a football player look at them and guess what's wrong with them. Even though the doctor doesn't have a lot of his or her tools at their disposal. Um, they still might just have some intuitions based on their experience. Right right now, now, you have to say it might be a football related injury.

In which case the football player might have insight that someone else might not have, so in the in their case it might be a swag if you will. Now, I do want to point out that the wild ass part of this is technically not um me being obscene, because as William Saffire points out has pointed out before, I believe in the New York Times, uh he said that the wild ass is not a mirror of vulgarism, as it can be found five times in the King James Bible, most notably job behold as wild asses in

the desert go, they fourth to do their work. So there you go. Well, of course, yeah, I knew that's what you meant. Yeah. So, now that we've biblically grounded the episode, I think maybe we should take a quick break and when we come back we will jump into mathematical estimation. So we're talking about guessing as a skill rather than as pure blind luck. In one way you can maybe get better than chance at certain kinds of guessing is to leverage the power of simple observations and

rough math. There are a lot of situations in your life where you might be asked to guess something and it's at first not apparent that you can do any better than just got feeling just come up with a you know, this number sounds right. Uh. You know, somebody asks how many buildings are in Atlanta and you'd be like, uh, I don't know. You might come up with a number and be like a hundred thousand, you know that feels about right, but you have nothing to work with there.

In many situations like this, you can do better, and you can do better without going to the you know, encyclopedia or the you know, city statistics to look up the information you need, because you can just leverage simple observations with math. One great example of this, I think would be the gumball jar contest. Oh yeah, you see variations in this everywhere you go, Like it might be gumballs,

that might be jelly beans, but it's Yeah. This is a wonderful example because one of the problems with be how many buildings in Atlantic question is that just off the top of my head, I mean, I know Atlanta, I know how to get where I need to go, but I don't have like the firmest vision in my head of its limits and its size and it's true shape and and scope and Unlikewise, I don't have a great idea of like just off the top of my head, like how many buildings tend to occupy, say a given

square of you know, of of urban real estate. Now, I think you could still do better than chance guessing at this, even not knowing those things, if we just uh leverage the power of making wild donkey guesses, uh, and then and then bring it together with some math in in terms of the thing we're going to talk about in the mid in a bit, which is firm me estimation. But back the gumball, the gumball jars, that's doable. You might look at a gumball jar and what you

probably do is try to gut feel it. Right, Yeah, because with the gumball um the container, I can see how big the overall container is. I can make a rough visual guess about how many gumballs occupy a given area and then just sort of roughly multiply that area in my mind until it fills up the space of container. Yeah. Yeah, So yeah, you're you're trying to eyeball it. Uh, but I contend you can do better. So Okay, So you might Robert picture yourself at the County Fair is that

usually where the gumballs would be. Oh, I tend to encounter them in like school fair scenarios. Okay, school fair, you know, that's exactly I was talking to Rachel about. She used to when she was a kid. She always wanted to be able to guess the number of gumballs that were at their school spring fling, I think, and she never got it right. They had to do them at you know, bars and restaurants. More like a container of pickled eggs. That's perfect. You know how many pickled eggs.

Guess the number of pickled eggs. Get a free pickled egg. Okay, so, but you're at a school fair then, Robert and uh, it's guess how many gumballs are in the jar. The closest guests gets a prize. What's the prize? It is a deep fried, unopened can of corned beef. Hash uh laughing at my own jokes. That's bad. Uh. So now this game is easy to play, right because you can

eyeball it. You look at the jar somewhere deep behind the curtain in your brain, a damon rises out of the darkness and just plants this random, wild ass number in your mind. It's like two hundred and thirty, and you look at the jar again and you think that sounds about right, you write it down. You hope you win, but you don't win because who won. The person who

won was somebody who did some rough math. Because if you stop to think about it, you do have some ways of knowing about how many gumballs are in the jar. If you've got some basic like high school geometry and a pair of eyes, you can start getting a solid rough estimate to work with. So, Robert, I put a picture of some gumballs in our notes here, and I already did some calculations on this. But um, so this is a jar of gumballs, right? You attest that it?

Truly it does look like a jar of gunballs. No, this is a two dimensional image. I have no idea how how long this could be. This could be I'd assume that it shaped like a are, but it could be shaped like something else. Yeah, well we'll just assume it's basically circular. So for simplicity's sake. One thing that's a really good method when trying to come up with these rough math guesses is skip standard units of measure.

Don't measure things in terms of inches, centimeters, pounds, whatever, measure in terms of something that you're directly looking at. So instead of measuring the size of the jar in inches or centimeters, we're gonna calculate it in units of gumballs. Okay, like, don't try and measure in calories. Continue. So, look, you look at a jar and you think how many gumballs are wide? Does it look like this jar is in diameter ten? Maybe? I guess nine if you want to

go with nine, nine sounds good, okay. And then how many gumballs high? Do you think that the jar looks? Oh, I'd say more than that, like twelve or thirteen. I guess ten. Okay, we'll go with ten. Okay, let's go with him. Yeah, okay, Now now I feel like I've stomped all over your guests. No, no, no, no, I think it's I think that's good because if I sort of turn it sideways, it's it's still it's a very square looking jar, all right. So it's about nine in diameter,

about ten tall. Now, a jar is roughly a cylinder, right, You remember from geometry, what's the formula for the volume of a cylinder. It's not that complicated volume of a cylinder is the area of the circle times the height. The area of the circle is pie times the radius squared. So you start with the base of the jar the circle pie, which is three point fourteen times are. The diameter was nine, right, if it's nine across are, the radius is four point five because it's half of that.

The first you square the radius four point five squares is a little over twenty. We just go with twenty, and then you multiply that times three point fourteen, which is sixty two point eight. I'm glad we could agree on the the fat the figures here, because otherwise we would have had to recalculated everything in our notes. You have you have seen through my insistence whatever. Okay, so you got sixty two point eight times the height of how many gumballs high? Ten? Ten? Alright, So that says

they're about six hundred and twenty eight gumballs in the jar. Now, that's probably not going to be right on the money, but I'd say it's also probably going to be a lot closer than the real number to the real number than if you just eyeballed it. Right, if I had eyeballed the jar, I might have said, I don't know three hundred and fifty, But now looking back at it, I'm like, oh, you know that probably is more than

three hundred and fifty. Yeah. Yeah. I feel like when I was first looking at it, I would have probably gone on ten by ten hundred and then try to like I think, like, all right, maybe three or four deep and I would have gone three hundred four hundred. Yeah, but but I think our estimate now is actually probably better. Uh. And that's one of the last things you should do whenever you do this kind of mathematical calculation is you'll get the jar again and you think, is my estimate

within the realm of possibility? Is it stupid? If I came up with thirteen point eight billion gumballs in the jar? This is an indication that the math or the counting went wrong somewhere along the line. You should back up and try again, or the jar is is seriously spooky and you try not have anything to do with it. Yeah. Another way of checking against reality is to test the method in the real world. So would such a method

actually win you a gumball jar guessing contest? Well, I thought I'd do some googling, and I did, and sure, enough. I found a blog post about a guy who won a gumball jar guessing contest. Somebody asked him what method he used, and he said he calculated the volume of the cylinder in the jar, and then he randomly added twenty five to that number. So it's sort of like being the the the the the area of error in

his calculations. Huh, yeah, I guess it could be. So he came up with like seventeen uh, one thousand seven five gunballs, and actually it was one thousand, seven hundred and fifty. So yeah, so so, so you've got these principles, right you. You don't have to just surrender to your gut instinct when it's time to guess something. You can

couple very simple rough math. You know, this is not complex calculus or anything like that, with observations that you can just get by looking at what's in front of you or by drawing on really basic knowledge or even just guesses. All you need to do is think about the logical relationships between numbers and know how to look for those relevant pieces information that might be in your

memory or might be right in front of your eyes. Now, I think it's time to get back to Enrico Fermi, so, as we mentioned earlier, for me, was apparently known for being a really good guesser when it came to numbers. And there is a classic example that's often used as an example of how his method of estimation works. Um, it would be how many piano tuners are there in the city of Chicago. Now, I have found lots of different versions of this all over the internet, you know,

people working it out in different ways. But the goal of Fermi estimation is not to hit the number exactly, but it is to get into the right ballpark, get in striking distance of it, if you will. Yeah. And so one version of how many piano tuners are in Chicago appears on NASA's Glenn Research Center page. And and this is their version. Uh. So they start with how would you even begin to calculate that? Well, one number you can work with is the population of Chicago. Yeah, okay,

so that will give you something to start with. So they go to the almanac. They say, at this time, the Chicago as a population of about three million people. Now assume that the average family has four members, so like four members per household, So the number of households in Chicago is going to be three million divided by four, so that's about seven fifty thousand seven households. How many

households own a piano? They guess one in five. I think that's probably kind of high, but I don't know, Yeah, I have, I just have no way of of Well. One thing you can do in these scenarios that that I'll get to in a little more depth than just a minute is if you don't know how to guess something like what percent of families have a piano in

their household, you come up with boundaries. So you say, Okay, what's the lowest number that would make any sense, what's the highest number that would make any sense, and then you take what's known as a geometric mean between them, which means you multiply them together, and then you take the square root of that number. Okay, so the process here could be one in ten people have a piano. That sounds like that would make pianos a bit too rare. One in three. I don't know if they're that common.

Let's split the difference more or less and go with one in five. Yeah, that that's actually really close. So if you if you multiply together, um, one in three, which would be about point three. Uh, and then one in ten, which would be point one. And then you take that number and get the square root of it. Your answer is like point seventeen, which is close to point two, which is one in five. So there we go.

We're on track. So if one in five families has a piano and there are seven hundred and fifty thousand families in Chicago, that means there's gonna be one hundred and fifty thousand pianos in Chicago. There's a number to work with. All right, you got a hundred fifty Now that is a number of pianos that are available to be tuned. So this can give us a foothold to

try to figure out how many tuners there are. If you've got an average piano tuner, I mean, how many pianos do you think they could tune in a day in a work day? Okay, this is going with the assumption that like they're design like the piano tuner makes this his or her um life. Like, they're not just doing a little piano tuning on the side, right, this is their full time job. Oh I don't know. Um lets you have to travel there, you have it I mean comfortably, what maybe three or four a day? Well,

in this estimation they come up with four. I think four is a reasonable guests. Yeah, Like I think of other jobs, like you know, forst is, my wife's a photographer. She's not tuning pianos, but she has to travel somewhere, do a session and then come back. And I think, like, if she was just just crazy busy, how many should could you fit in a day? You know? Like that

seems about right. Yeah. Another option, if we didn't believe that four days, we could do the geometric mean again, we could say, well, it's got to be more than one, and it can't be more than what like six, I mean that that'd just be care you can't be certainly

can't be more than eight. Um. So then you'd get a GMO tricked me and that that probably put it a little bit lower than four, but you'd still have some number in that, you know, three something like that, Okay, And then of course you assume they don't work on the weekends and they've got a two week vacation during the summer. So that's fifty weeks in a year of tuning four pianos a day, five days a week. So that means in one year, the average worker, the average

piano tuner, would service one thousand pianos. Now, if we said that there are a hundred and fifty thousand pianos in the city of Chicago, that means there should be about a hundred and fifty piano tuners in the city. I don't know, does that number sound reasonable. It's at least got you in the ballpark. I guess it sounds reasonable. I it's I mean, I guess this is a difficult thing to check because is there like a Piano Tuners Association of America that you can check with on this

sort of thing. Well, I've seen other estimates that work out the number differently, so they they you know, they might say, well, I think that your estimate on step four here is not smart. I would change it to this, and that actually gives me, uh, you know, something more like forty piano tuners in the city of Chicago. And one thing you can check is you can look at

see how many are in the phone book. Then again, I mean, in this day and age, there's probably a lot of things that aren't in the phone book, right, Yeah, you kind of end up like the the the yelp versus phone book uh tug awar, depending on where you're going, is it a yelptown or are they still yellow pages down? And and then you're you're you know, you're you're also forgetting about all the black market piano tuners out there.

Uh yeah, but those black market piano tuners get less piano tuning done because they're also moonlighting as uh piano wire assassins. That's that's true. Now, when you're estimating big numbers based on little data, one of the things that's really helpful, this helpful concept is the idea of orders of magnitude. We've talked about this a little so far,

but just to be clear about what this is. Um when you read about really big a very little numbers in science, you'll often see those numbers expressed not in full notation, written out. But you've seen this before where it is scientific notation. It's a like four point eight times tend to the nineteen or something like that. That

would be a really big number. And so U instead of writing a thousand, you write like ten to the three, or instead of writing point zero zero one, it's ten to the negative three, and you get more precise instead of two thousand, five hundred, you write two point five times ten to the three or instead of point zero zero zero zero eight seven, it's eight point seven times tend to the negative five. Right, So you've you've got orders of magnitude, and they are the exponent in that

type of notation. Every time the exponent goes up or down a number, that's an order of magnitude. Another simpler way of thinking about this is that the order of magnitude is just the number of digits in a number. Get single digit number, double digit, triple digit, quadruple digit, um. When somebody is talking about the number of figures in a salary, they're concerned about orders of magnitude. You know.

One thing this reminds me of is, of course, the the classic educational film created by the Aims uh the Powers of Tin which granted that so there's a visual, very strong visual element to that as well, but it basically seeks out to explain and make digestible the scale of the universe. This is that classic zooming in and out. That thing is great, it is, it's still it's wonderful, still holds up really well today and uh and it's

just you know, phenomenal to watch. But yeah, by considering the order of magnitude, like, it's able to make some of these that the scale is able to make the scale of the universe more digestible. Yeah. Now, if you haven't seen that, go out and google it right now. You can put us on pause. It's it's worth that you should really watch. I think it's on YouTube, isn't it. Yes, I believe that there's an official YouTube version of it. It's just it's fantastic. Um. But yeah, So back to

why why to orders of magnitude matter? Well, for me, estimation that this uh process that was really made immortal by Enrico Fermi, is a way of easily guessing numbers by rounding up or down by orders of magnitude and then calculating based on these easy to work with round numbers. So we started doing that in our last example right

when we were taking geometrical means. Um. But the basic way that a Fermi estimation problem works is you start by figuring out what are the key assumptions, what are the factors you would need to know in order in order to calculate your answer. So in the piano tune or example, you'd be like, well, Okay, if we know the city of Chicago has a certain population, and we know that piano tuners can tune a certain amount of pianos each week, we can derive from those numbers what

we need to calculate our answer. So the next step would be like thinking about what order of magnitude your your key pieces of information are on. So like when you're making a guess, this is where the boundaries come in. If you have no idea for a number, if somebody asks you, um, how many lucky charms marshmallows have ever been manufactured on planet Earth? You have no idea, right, I mean I wouldn't even know where to start, absolutely no idea. But actually you you do know where to

start because you can play with boundaries again. Okay, so what's a low number that you you know it's got to be more than ten thousand? I mean that's ridiculous, more than ten for sure. Yeah, but you keep keep bringing your lower bound up so you know it's more than a hundred thousand, right you know? Well yeah, because you know, in fact, you probably know it's more than a million, because what do you think at least a million people of eating a bowl of lucky Charms at

some point in history. Yeah, it's been around for at least decades. Yeah, and so if at least a million people of eating a bowl of lucky Charms and each bowl had more than one marshmallow in it, you know there's at least more than a million. Um. I that we could even go safely to ten million, but I don't know. I'll stick to a million. That's our lower bound. And then, uh, you know what's the upper bound? I mean, you know there cannot have been ten trillion of these marshmallows, right,

there's just too many. Way Yeah, Okay, so now you've actually got boundaries, so you know there's less than ten trillion, and a geometric mean between one million and ten trillion is ten billion? Is that anywhere close to the right answer? Well maybe not, But now you've got something to work with that's better than you started with, which was just I have no idea. Well, this is quite a useful tool.

We've been we've been talking about those far because I can already see the ways that this can be easily applied to say the person's work week. You know, how much how much of um, you know, my given work can I fit in could I, you know, could could I write this many articles? Could I write this many? What's the what's the most extravagant and the smallest number?

And then ending that middle ground. Right, So yeah, but remember it's not just the simple mean, because what what you're really looking for is the geometric mean, which again is instead of so the simple mean simple average is you add them together and divide by two. The geometric mean is multiply them together and then take the square root. So if you say, how many articles do you think you could write in a week, Robert, what's the what's

the highest possible number? That's kind of crazy, the highest possible number. We'll just without boring anybody about details and get into a big conversation about which form of article, etcetera. Let's just go ahead and say, um, twenty articles twenty Okay, Now, what's a really low ball number, lazy as heck, Let's say four or five. Let's say five just to keep it cleaner, maybe, or four, whichever one is easier to compute. Okay, so four times twenty. Then take the square root of

that number. It's about eight point nine or nine. So that's a number, all right, That that's better than not having anything to work with. One of the key things about this type of estimation is that it's useful, but it's only useful if you treat it critically. I mean, obviously you can't just generate numbers using this method and then go with them. But it does give you a

place to a foothold, essentially for thinking about numbers. Whereas you started with paralysis, you're starting staring into a void of all possible numbers and you have no idea where to start FIRMI estimation helps give you a place to start with and say is that reasonable? And you can work up and down from there. Um. But okay, so so you've got that. When when you want to get a factor and you have no idea what it is,

put some boundaries in place and then take a geometric mean. Um. Now, once you use these assumptions, you make a rough calculation like they did with the piano tuners example, and then you look at your answer and you do a reality check. You say, is this reasonable? Is this number within the realm of possibility? And do I need to go back and adjust anything I did before. Now this might be a terrible example, but I kind of wanted to just have us try one on the fly. Okay, let's do it. Okay,

so you want to guess a totally unknown number. And here's my question. How many pounds of hair do Americans get cut off their heads in total each year? Not individual Americans, all of America? How many pounds of hair are cut? All? Right? Well, the obvious starting point there would be how many Americans are we dealing with? Right? Okay, so there you go. So how many Americans there? I

think there are what like three? Do you want to go with the three hundred and there are more than three hundred million, but we could round down to make it simple. Three hundred millions sounds good. Okay, so we've got three hundred million Americans? Uh, in a very rough estimate. Now, how many pounds of hair on average does American have? This is going to vary widely. Some people have dreadlocks

to their knees, some people are totally bald. But what's a good average that would put us right in the middle, like the pounds and like how much hair they haven't cut off or just how much hair they have have? Al Right? Well, alright, well, I think what do I know the weight of the human brain is about three pounds. I feel like hair weighs less than a brain in general, so I would say a pound of hair. It still

kind of feels big. Yeah, I would tend to think that people on average have less than a pound of hair. I mean, somebody who has really long hair maybe might have a pound of hair. I don't know. Maybe this is the beauty of it. Just rough gas, Okay, like a quarter of a pound. Okay, let's start with five pounds of hair per person. Okay, Well, I did just do the calculation of how many pounds of hair there are in America, but we might not actually need that figure.

So three million people times a quarter pound of hair per person is seventy five million pounds of hair. But like I said, we might not need it. In fact, let's just stick with the quarter pounds of hair per person. What percentage of your hair does the average person get cut off in a haircut? Again, this is going to vary wildly. Some people get there, you know, long hair shaved completely off. Some people get a tiny little trim. But on average, what what is the mass of your

hair that is removed in a haircut? Um off? Off hand? I'm thinking, Okay, I would guess kind of higher. I was thinking I probably wait too long to get a haircut, So with me, I think it's like fifty percent um. But maybe we can get get in between them. I don't know if everybody other people wait as long as I do and look as scruffy as I do by the time I go in, or or just get people get you know, really well groomed all the time. Let's say, uh, ok or you can go with high thirty if you want.

I feel like like thirties, not too high. Okay. It feels like enough to where you would say, hey, you got a haircut, didn't you, Whereas if you go too low, you more attempted to say, hey, your hair is a little wetter than normal or something, you know. I mean, thet seems like it would be like a comfortable level of notice, but not a woe did you join a

cult level of haircut? Okay, Well, that gives us a number. Actually, So if we say that the average person has a quarter pound of hair, and that thirty percent of their hair is removed in the average haircut, that means that the average haircut in America removes point zero seven five pounds of hair Okay, Now that's going to vary widely up and down again, but we're just trying to get

an average. Now, if we say that the average haircut removes x amount of hair, all we need to know now are how many haircuts there are in America every year, So we already know how many people there are. How often would you say that the average person gets a haircut? Oh, this is this is a tough one, right, but I'm guessing once every two months. Okay, so six times a year. Yeah, that feels maybe a little. That's a little higher than what I actually tend to do, like I might do

it four times a year. Now that they think about it, well, let's take the average and go five times. I feel like I'm not being very consistent with my mathematic people are trying to figure out how fast my hair grows based on my strange figures. Here, I guess, but you

know that sounds good. Okay, So in this case, uh, if you get point zero seven five pounds of hair removed every time you get a haircut, and you get a haircut five times a year, every year, you get point three seven five pounds of hair removed from your head point three seven five pounds removed every haircut or every year. Every year, it's point zero seven five removed per haircut, five times a year. That's point three seven five pounds. All right, Well that number is that feels

right to me? Okay, Well, now all we need to do is multiply by our three d million people each each one of them gets an average of point three seven five pounds of hair removed free year, and there are three million people, so that gives us a total mass of hair removed from human heads in the United States every year of about a hundred and twelve million pounds hundred and twelve million, five hundred thousand pounds. Does

that sound right? Mhmm, Well, we feel it feels more right having done the leg work, you know what I'm saying, Like, we're able to break it down. If you just come up with that number just on the fly, I might have really kind of um, you know, set there and crunched it for a while thing, And I don't know if that feels right. But since we did the legwork and we dealt with with with quantities that were more relatable in order to get there, I'm certainly more inclined

to trust it now. One of the beautiful things about this type of estimation is that errors tend to balance each other out. So one of the things we were saying as we're going through is we're using very rough figures. Obviously, the population in the United States is more than three million. We just rounded down to make it easy. Um, the amount of hair on each person's head, we don't really know. It's a quarter of a pound. That was just a guess. That might be too much, that might be too little.

But as you keep going through the experiment, at each stage, you are making a guess, and that guess if unless you're consistently biasing in one direction or another, always overestimating or always underestimating, your errors will start to balance each other out. And this kind of helps keep your answer within the bounds of possibility. Even if you're wrong on one thing, you might be wrong in the opposite direction

on another guess. It's kind of like life, and exactly it's a lot like the game of life, or you mean the life of life. Just just uh, a life in general, not Life magazine, but you know that's part of life. Oh, I should smack myself for that joke. I'm sorry, But anyway, whether or not our answer is correct. It maybe totally off the mark, but we've started to

give ourselves something to work with. And if we really cared about this, like if it mattered how much hair is removed from Americans heads every year, this would give us a good starting place to start working with. One of the next steps I think would be would be to go back and look at our individual factors that we put in throughout that that calculation process and try

to hone them and say, really, what's reasonable. You know, we could start looking at our own heads, the heads of people around us in the offenses and saying, it's a quarter pound of hair real that sounds kind of high. I don't know, but but you you can start refining it once you've got something to work with. And that's

one of the big values of firmi estimation um. Even though the method isn't likely to give you a precisely correct answer every time, scientists and engineers find this type of guessing extremely useful because it gets you into a sort of order of magnitude ballpark where you can start to check your gas against other modes of estimation or against experiments and discoverable facts, and it also helps you get your mind around what assumptions are necessary in order

to compute your final precise number. Does that make sense? Like you start to realize what the uh? You take things that were unknown unknowns turned into known unknowns. Now you at least know what the variables are, even if you don't know exactly what the numbers should be. And turning an unknown unknown into a known unknown is halfway along the process to turning it into a known known or even a gnome. Well, let's hope it didn't go

that far. All right, We're gonna take a quick break, and when we come back we will jump back into this question of of estimating, gus estimating and UH and so forth. Okay, we're back. Now let's look at one of the most famous examples of a Fermi estimation type problem him in history, and this would be the Drake equation and the Fermi paradox. That is an interpretation on it. Yes, all right, So in order to get this down, we

have to go back to nineteen fifty. Now, if you remembering from earlier, that's what three years before Fermi's death. So go back to nineteen fifty. Firmis having lunch with his fellow egg heads at the Lost albumost Jet Propulsion Lab Cafeteria. Alright, he's flipping through a copy of The

New Yorker when he happens upon a particular cartoon. Now, I have a picture of the cartoon for really, it's the original, the original, Yeah, this is the one, and I'll try to include a link to this on the landing page for this episode of Stuff to Blow your Mind dot com. So what's going on. There's a flying saucer and some space people are carrying baskets to and from it. Yeah, they're they're collecting garbage apparently, uh furiously enough, I don't have the caption here, or I don't know

they were doing the caption contest back then. But if if the caption contest from The New Yorker makes its way across your social media feeds, you know exactly what sort of cartoon we're talking here. So it's not quite far side. It's not a laugh out loud funny, but you look at it and your your your wheels began to turn a little bit. And that's what happened with Firmy. He looks at this, and if he were to enter the New York the New Yorker caption contest. His caption

would have been where is everybody? Because that is, according to this story, the question he asked, and he was referring to the aliens, to life beyond this insignificant rock of ours. He wondered, uh, more specifically, you know, not only like where are where these aliens at, but he wondered whether interstellar travel was even possible. And indeed, as

far as we know it has not occurred. You know, I mean this when we get we kind of broke it down some of this in our the episode the Christian and I did on the expanse and the idea of just like the vast distances in our universe, like even the instances between our planets in our Solar system are pretty colossal, and when you start extrapolating that beyond our system, uh, it just gets increasingly just incredibly distant. There is so much space in space. And so he

was saying, well, you know, where are they? Is it even possible for for life forms to travel between stars? Why aren't we seeing them? Why aren't we hearing from them? Exactly so FIRMI died, you know, foot four years later, at the age of fifty four, but the question that he asked lived on, and the problem filtered through the firm, these coworkers, his contemporaries, and it became something of a legend.

And in nive, the astronomer Michael Hart declared that the reason we don't see any aliens is because they do not exist, which you know, that's that's one possible answer. It certainly is. And then in nineteen seventy seven and astrophysicists by the name of David G. Stevenson said that heart statement could answer firm's question, which he officially dubbed Firm's paradox. So to be clear, Fermi himself did not

pose the question. The paradox is merely named for him in honor of him and in accordance with this sort of folkloric idea. Right, But the sort of general mode of guessing or gues estimating that's now known as Fermi estimation or a Fermi type problem is related to this because there is what's known as the Drake equation, and the Drake equation is kind of like playing the how many piano tuners game or in Chicago game with the

Milky Way galaxy. It is a Fermi guess formulation designed to estimate the number of piano tuners in the Milky Way, or wait a minute, no, the number of technological civilization in the Milky Way galaxy, meaning the number of civilizations whose electromagnetic emissions like radio waves, we should be able to detect today. And so it takes to form. There's actually an equation, says okay, in that's the answer, and that's the number of civilizations in the Milky Way galaxy

whose electromagnetic emissions are detectable. And the version of this I'm using is the one that st has on their website. And to calculate in you multiply are which is the rate of formation of stars suitable for the development of intelligent life, by f P, meaning the fraction of those stars with planetary systems. Not all stars are going to have planets, and then you multiply that by in e the number of planets per solar system with an environment

suitable for life. So every solar system uh might might have planets, but wouldn't necessarily have planets within the habitable zone. It might be all too hot or too cold. And then you've got f L the fraction of suitable planets on which life actually appears. Might be a lot of nice planets out there, but they're just dead. Uh. And then f I the fraction of life bearing planets on which intelligent life emerges. Maybe a lot of planets out

there just to have bacteria on them. And then f C the fraction of civilizations that develop a technology that releases detectable signs of their existence into space, So there might be intelligent life out there, but they're not making radio waves. And then finally, multiplied by L the length of time such civilizations released detectable signals into space. So many of the variables in this in this calculation are pure unknowns. Answers are all over the place for this reason.

But a lot of things in here are not as unknown as they once were. For example, we're starting to get a very good sense of the fraction of stars with planetary systems and the average number of planets suitable for life in the Milky Way galaxy. We're starting to say, okay, this is about how many planets are out there. Here's the proportion of them that are, you know, not too hot or too cold to sustain life. Those are coming to within reckoning distance. Other variables about like the prevalence

of emergence of life and intelligence. Those are still just big question marks, but you can still play the same game with them. You could try to set up boundary conditions, Right, what's the lowest boundary. While the lowest boundary would be I don't know, some fraction of one. I mean, obviously wouldn't be zero because we're here, so we know that

it's a non zero chance that these things happen. What's the highest possible thing, Well, obviously we're not seeing these uh, these planets with life on them in our solar system other than other than Earth. Well, actually we don't even know that for sure yet. But anyway, there are a lot of ways you can try to put numbers in

where these variables exist. And so I've seen estimates using the Drake equation turn up answers less than one, meaning we're almost definitely alone in the galaxy, and even our existence is a real stroke of luck. Uh. And then I've seen ones that are in the hundreds of millions. But in that case, what's the deal. Why aren't we detecting anything? Are we in some kind of protected zoo where we're you know, the aliens hiding from us? The

nature reserve theory. Right. Yeah, But one interesting thing is what we mentioned earlier. Whenever you're doing these types of of estimations, uh, it's good to check them against reality. So you might think of our actual radio astronomy as a reality check on the numbers generated or the gu

estimates of the Drake equation. So this is this is fascinating again because you've taken something that is like a giant gaping mystery and unknown and you boil it down into a series of essentially smaller unknowns uh nowns and and guessable factors. Yeah, exactly, You're you're making the problem workable and and so this is a way in which fermi estimation has multiple uses. I guess one of them

is practical. It's just practical, and you know, when you don't know any of the actors, you can use it to come up with a reasonable guests for an answer. But the other thing is what we've been talking about. It's making a problem more understandable, even if you don't actually come up with a reasonable answer. It starts to help you get your mind around what you would need to know in order to solve it. All Right, we're

gonna take a quick breaking. We come back, we're gonna discuss some of the softer social science of guessing and try to conduct an experiment of our own. Alright, So we've discussed how guesswork is art as well as science, and indeed there's certainly a social art to it in some cases, so the art of overestimation or underestimation in social situations. I think we've all encountered situations in which

guessing isn't merely about making a correct guess. It's also about making a guess that lands with an appropriate level of social grace. It's like guess what my s A T score was? Yeah, like a weird questions like that like another A notable example would be guess how old I am, which is generally a question you only ask a child or you ask if you are a child. Um, because it's floated right, and I've en to your point. You also see guess how how much I make as

being another question that is sometimes asked. Uh. The need for for such a guest might not come up directly, but of course we can all imagine situations where it ends up. When they end up coming up, you know, like you're trying to figure out if a friend of yours is into the same movie that you are, and you're like, oh, well, how old are you? You're such and such. You know, so you might indirectly, indirectly find yourself having to make such a guess. So this is

a very conundrum. Is actually explored in the Art and Science of Guessing by Shin, c. Zong and Duh And this is published in the journal Emotion in twenty eleven. So they ask, you know, are we are we gonna be happier with over guessing or happier with under guessing just in general, like people guessing too high or guessing too low? Yeah, how does that make you feel when someone get over or under estimate something about you? Now?

Is this limited to certain types of factors? Are they trying to get a general effect for any sorts of numbers? Um general? But like they're they're focusing around very specific questions as as we'll discuss. So they predicted that over

guessing would reign supreme. Uh, though obviously not with guessing another person's age, because that one kind of stands out generally you want people to get through you're younger than you are, Okay, So naturally the research has conducted a few tests to try this out, and it's important to

note culturally, as we'll get into that. Some experiments were conducted into China and others in the US, and that's especially important with experiment one, which concerns asking friends how much money they make, which I don't know about about you, but generally that that's not something that is done at dinner parties. Did I go to where people say, hey, how much money do you make in a year? Not my friends. I asked my enemies how much? Yeah, you know,

I guess with family members, maybe it's more practical. Originally, friends and contemporaries are not asking that question. It's kind of taboo, but according to the research in China, it is was more common. So they used forty employees from multiple companies in a large city in China, and I'll spare you the monetary details of the study, but the finding was quote contrary to what common wisdom and existing literature would suggest. The study revealed a happier with under

guessing effect. So someone thinks, oh, well, you just you probably make thirty thousand a year, but you actually make thirty five, but you feel happy, So I guess it's like like, oh, you get to prove them wrong. You get to prove them wrong. Yeah, you're like, oh, you think I'm only worth that much, but I'm actually worth this much. I'm fantastic. That's kind of the response. No,

that makes sense to me. So. Experiment to tackled academic performance with American test subjects a hundred and seven business students guessing each other's GMAT scores as a graduate Management admissions test. The results the under guest was most pleasing, the over guests was least pleasing, and the accurate guest was in between. I think it's interesting here that the accurate guess is somewhere in between, Like, nobody really wants

to be pinned down completely. No, it doesn't feel good, yeah, even, but it also feels bad to be overestimated, Like it's the the inner Like if you're underestimated, you you get that that feeling of oh, I'm actually I'm actually better than you think I am. But if they if you're overestimated, there might be like this superficial feeling of oh they think I'm they think I'm better than I am, but

but I'm actually not. It might be nice to have people guess, like what your favorite movies are or something. But it does not seem like it's nice to have people correctly guess what numbers are true about you. Yeah, it's it's a quantitative aspect that makes accuracy unpleasant. It's like being pinned down to a chart. So then came Experiment three two thousand and nine. Business students from a large university in the United States engaged in imagined scenario. Okay,

you work at a large company. Your annual bonus will be between three thousand and thirty thousand dollars. Exact amount will be confidential. So participants were then told, in this imaginary experience experiment here uh scenario that they'd receive fifteen thousand dollars, and they were asked to imagine that they

heard a colleague guessing about their bonus. The guests was thirty thousand in the over guest condition and three thousand in the under guest condition, And then they were asked to indicate whether they felt better or worse about hearing the guests The results. Again, the overguess resulted in the most happiness, But the researchers drive home that a lot of that results boils down to what's more important. To

the individual individual truth or impression. So really, really, what ends up mattering more to a specific individual the actual amount of money they take home or the amount of money that people think they take home. And this is interesting, right, because so much in life is this mixture of substance and perception. Do you want to be rich or do you want to appear rich? Do you want to be smart or appear smart? And and and there's kind of this this up is this push and pull of both factors.

We're back to the charm effect, the James Bond effect, And we were talking about at the beginning some people might actually not be uh better, more lucky than others, but they can sure appear that way just by sort of projecting a successful latitude. Yeah. Yeah, So the soft science of guessing becomes even softer some more you you you tease at it. Okay, one last thing, I want

to look at a totally different kind of guessing. We've talked about tools to make you better at guessing, but I want to think about what goes on in the human mind when we guess. When we've got absolutely nothing to work with, no info, no probabilities, no plausible boundaries, just the opaque magic of pure randomness, because this is this is sort of the core of guessing. When we say guessing, you know, a lot of what guessing conjures

in the mind is scenarios of total uncertainty randomness. Okay, so I want to do an experiment with you, Robert. I've got a deck of cards fanned out here. Here's the experiment. I'm holding up a card to Robert. Okay, what is the suit of this card? Now you are not looking at the face of the card. Robert is looking at the back of Well, this is awesome because I I have a one in four chance, right right, I'm gonna say clubs, Nope, jack of spades. Now let

me try it again. Now, think really hard, this time the exact card. No, you are guessing the suit. Okay, I'm gonna say clubs, nope, hearts. But here's the question. Where did your answers come from? Your accuracy was actually not important to me. There, I'm thinking about the subjective experience. Try it one more time, Nope, spades. Why though, why did you say clubs when you have no reason to prefer clubs over any other I don't know, it just

came to my mind. For I was for it's it's almost like not that I was at a loss for the words, but like that was the one that came up first. Yeah, I mean, it's it's a weird thing. It's like, next time you make a guess without a conscious methodology, you out there listening, look inside yourself and ask this question, where did that guests come from? Why did I say clubs and not something else when I had no logical reason to prefer clubs over anything else.

I will say I stuck to clubs because I thought clubs has got to come up, like I might as well, even though I guess it's it's yeah, yeah, it seemed like the thing to do, like I just should should just stick to clubs and clubs will do me ride eventually. Well, that actually would be a smart strategy. If I was like removing cards from the deck and you were yeah, okay, okay, Well, then I guess the question would be, what what did

you guess the first time? Or what would you have guessed if I was not removing cards from the deck, Because that yeah, there there's no there's just nothing you can do, and yet our brains still are able to come up with an answer. And I think this is one of those everyday moments that sort of passes by us without much fanfare. Just it's very humdrum, But if you force yourself to stop and examine it, it becomes so deeply weird and mysterious. We've we've got these voids

inside our minds that produce information on no input. It's kind of like you you go somewhere in the back of your mind and there's one of those drive through bank teller boxes, you know, where it slides out and you open the shutter, and what you put in is just a request for a random response, and you push it in, and a split second later, the box slams back out, pops open with an answer for you. What happened inside? Where did that random answer come from? Uh?

That might not even occur to you as something to think about being odd, But I don't know. It strikes me as very odd. Why do our brains come up with random answers on command, with no logical reasoning behind them. One example that I do encounter with this sometimes is in yoga class will be and we'll be doing a plank, and in order to pass the time, we'll go through the alphabet and like name trees that begin with each letter, and it's curious to self reflect and be like why

did that tree come up? Why did that animal come up? Yeah, and sometimes it feels like the brain just spits it out randomly, like a like a hand with a deck of cards just shooting one to the surface. Yeah, so what's causing one card to come up instead of another? Um? So, in terms of coming up with true randomness, I've actually read a little bit about research into people studying humans ability to generate random numbers on command, Like this is

actually a field of study. It's like, can you please list a series of random one digit numbers? One problem is that people are actually very cruddy random number generators, Like they they either have too much symmetry in their answers or too little symmetry. Um Like that they get caught up in trying to make it random, and thus they make it non random. But yeah, I just think it's interesting, Like what's what's the biological purpose of that? Like,

why is that something brains can do? It's something you specifically have to have to command computers to figure out how to do. Computers by nature don't generate random numbers. You need to come up with a way of them to you know, draw on some kind of vada variable or data to generate random numbers. UM, So like why do brains do that? And where do the numbers come from? Uh?

There there was one study that I looked at that I thought was kind of interesting, and it's a study by Elliott Rees and Dolan in the journal Neuropsychologia and uh. And what they did is they used f m R I to see if there were any differences in activation patterns in the brain between reporting on knowledge and random guessing. So in one group, researchers would show subjects a playing card on the face side. Here you go, Robert, what card is this? That would be a five clubs? Right.

Because I'm showing you the card, you're just reporting. This is working memory in the brain. You're taking in information, you're spitting it back out. Not all that weird. It's a very different thing to hold up the back of a card and say what's the card here? You have no information at all, So you randomly guess six of diamonds, four of diamonds. Kind of close, kind of close. That's like a ballpark. Uh, you're within an order of magnitude. But I think I randomly said six only because I

had just said five. Right. But when you're when you're guessing the front of a card, just looking at the back, there's no gunball logic, there's no firmi estimation to help you. It's just random. And yet the authors found that something's going on in the brain when we're generating random guesses.

There is activity. Uh, they write, if their analysis is correct, they write, quote, these data suggests that while simple two choice guessing depends on an extensive neural system, including regions of the right lateral prefrontal cortex, activation of orbit of frontal cortex increases as the probabilistic contingencies become more complex, as it becomes harder to understand, you know, what's going on,

so they say quote. Guessing thus involves not only systems implicated in working memory processes, but also depends upon orbitofrontal cortex. This region is not typically activated in working memory tasks, and its activation may reflect additional requirements of dealing with uncertainty. Their specific patterns going on in the brain when you're trying to generate random answers, and I just think, like, what's the biological function of that. Where does that come from? Why? Why?

Why do animals have this ability with the brain to generate randomness? I don't know that's that. It's a wonderful question. Though. We've been talking a lot about cognitive tools rules of thumb, But there is another way of thinking about people who are good at guessing. As we said, you know, obviously some people are better at guessing and guestimating than others, but obviously not all of them are using these tools.

Right when you think about people you know who are very good guessers, they're not necessarily doing firm me calculations, coming up with numbers in their head, uh, exploring boundaries, taking geometric means, and multiplying things together. A lot of

times it seems to be just intuitive. So I wonder if there's another way to think about differential skill levels and guessing, and if it's more like finesse at certain sports and athletic activities, meaning that when you think about somebody who's good at hitting shots in basketball, what is that skill? It's obviously not an issue of raw strength. It's not speed, it's not endurance. If somebody can't hit three pointers, it's usually not because they're not strong enough

to get the ball to the hoop. When you shoot in basketball, at some level, what you're doing is math. Obviously you're not consciously making calculations, but you're you're trying to calculate and execute a precise arc trajectory, factoring the distance and the distance to the hoop, presence the backboard, the bounciness of the ball. It's kind of like you're playing you do you ever play that old game the gorilla throwing the banana at each other? No, but it's

it sounds fun. Yeah, but yes, well it's an old game, like an old basic game. You'd have two guerillas standing on rooftops and you'd enter the angle and the velocity of this bomb banana throw. Yeah. I like though that this is like it's like you're just throw bananas at each other in Virginia Guerrillas. But well, that would involve calculating precise arc trajectories too, I mean, trying to hit something by throwing it. In a sense, you are doing math,

even if you're not consciously doing math. Um. So perhaps in some ways I wonder if certain kinds of skill in sports should be thought of as having less to do with the power of the body and being more like an unconscious version of the mind of a highly skilled guesser, like an intuitive for me. And in the same way, I wonder if there's something unconscious in your nervous system that's able to make good guesses about precise

angles and velocity to sink a three pointer. Uh, there might be other ways in which we have un conscious intuitions that are nevertheless doing some kind of math. Math is is being calculated in the brain, even if we're not aware of it, in some cases, giving some people better intuitions about guessing than others, even without doing all this math. I don't know, just something to think about. All right. Well, on that note, we're gonna go ahead close out here. Hey, as always, check out stuff to

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