Be a Better Guesser With Fermi Estimation

Episode Transcript
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Speaker 1 (00:03):
Welcome to Stuff to Blow Your Mind from how Stuff
Works dot com. Hey, welcome to Stuff to Blow your Mind.
My name is Robert Lamb and I'm Joe McCormick and Robert.
I want you to think about something I know you've
seen many times before. Okay, you've watched James Bond movies, right,

(00:23):
of course. I grew up watching James Bond movies mostly
on I think TBS on Thanksgiving Day and that one
they show it. I think they would, but it seems
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

(00:45):
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.

(01:06):
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

(01:26):
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

(01:49):
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,

(02:13):
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

(02:34):
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

(02:56):
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

(03:18):
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

(03:38):
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

(04:00):
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

(04:22):
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

(04:44):
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,

(05:06):
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,

(05:27):
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

(05:50):
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

(06:13):
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,

(06:34):
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

(06:56):
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

(07:16):
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

(07:38):
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

(08:00):
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

(08:22):
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,

(08:45):
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

(09:07):
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

(09:29):
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

(09:52):
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

(10:13):
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

(10:34):
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

(10:57):
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

(11:19):
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

(11:40):
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.

(12:01):
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,

(12:21):
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

(12:43):
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,

(13:05):
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

(13:27):
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

(13:48):
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

(14:09):
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

(14:29):
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

(14:51):
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

(15:12):
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

(15:35):
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.

(15:57):
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.

(16:20):
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

(16:43):
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.

(17:03):
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,

(17:25):
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

(17:46):
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

(18:07):
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

(18:29):
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

(18:50):
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

(19:11):
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

(19:31):
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

(19:53):
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,

(20:13):
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

(20:35):
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

(20:57):
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

(21:18):
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

(21:40):
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

(22:01):
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

(22:22):
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

(22:44):
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

(23:05):
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,

(23:26):
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

(23:46):
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,

(24:09):
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

(24:31):
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

(24:55):
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,

(25:17):
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,

(25:37):
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

(25:59):
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

(26:20):
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

(26:43):
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

(27:03):
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

(27:26):
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,

(27:50):
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,

(28:13):
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

(28:34):
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

(28:58):
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,

(29:20):
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

(29:42):
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

(30:03):
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

(30:25):
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

(30:47):
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,

(31:11):
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

(31:33):
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

(31:56):
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,

(32:20):
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

(32:41):
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,

(33:03):
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

(33:23):
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,

(33:46):
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,

(34:09):
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

(34:30):
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

(34:52):
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

(35:13):
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

(35:36):
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

(35:59):
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

(36:22):
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

(36:44):
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

(37:05):
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,

(37:25):
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

(37:47):
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

(38:11):
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

(38:31):
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

(38:52):
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

(39:14):
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

(39:35):
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

(39:57):
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

(40:19):
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

(40:43):
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

(41:04):
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,

(41:27):
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

(41:48):
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,

(42:09):
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?

(42:31):
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

(42:53):
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

(43:16):
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.

(43:37):
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

(43:59):
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

(44:19):
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

(44:39):
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.

(45:01):
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

(45:23):
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

(45:44):
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

(46:07):
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

(46:29):
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

(46:50):
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

(47:13):
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,

(47:34):
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,

(47:55):
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

(48:17):
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

(48:40):
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,

(49:02):
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

(49:23):
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

(49:46):
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

(50:09):
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,

(50:32):
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

(50:52):
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.

(51:13):
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

(51:33):
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

(51:56):
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

(52:16):
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

(52:39):
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

(53:02):
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

(53:24):
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

(53:47):
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,

(54:07):
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

(54:28):
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

(54:49):
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

(55:12):
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

(55:34):
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

(55:56):
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

(56:17):
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.

(56:39):
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

(57:01):
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

(57:21):
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

(57:42):
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

(58:04):
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

(58:27):
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

(58:49):
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

(59:13):
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

(59:34):
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

(59:55):
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

(01:00:18):
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

(01:00:38):
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.

(01:00:59):
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.

(01:01:22):
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

(01:01:43):
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.

(01:02:04):
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

(01:02:24):
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

(01:02:45):
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,

(01:03:09):
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

(01:03:30):
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

(01:03:50):
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?

(01:04:11):
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

(01:04:33):
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

(01:04:53):
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

(01:05:16):
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

(01:05:38):
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,

(01:05:58):
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

(01:06:20):
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,

(01:06:44):
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

(01:07:06):
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

(01:07:28):
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

(01:07:49):
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,

(01:08:12):
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

(01:08:34):
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,

(01:08:59):
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,

(01:09:20):
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

(01:09:42):
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

(01:10:03):
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.

(01:10:26):
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,

(01:10:47):
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

(01:11:09):
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

(01:11:31):
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

(01:11:51):
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,

(01:12:12):
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

(01:12:33):
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

(01:12:53):
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

(01:13:15):
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.

(01:13:35):
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

(01:13:57):
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.

(01:14:17):
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,

(01:14:39):
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,

(01:14:59):
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

(01:15:21):
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

(01:15:42):
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

(01:16:05):
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.

(01:16:27):
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

(01:16:49):
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

(01:17:10):
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

(01:17:31):
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

(01:17:54):
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

(01:18:14):
this math. I don't know, just something to think about.
All right. Well, on that note, we're gonna go ahead
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