The Secret to Learning & Problem-Solving in Life with Ben Orlin

Episode Transcript
Available transcripts are automatically generated. Complete accuracy is not guaranteed.
Speaker 1 (00:00):
There's this infinite series of actions you have to complete
just to high five somebody. And this is true of
all motion. It feels like all change, anything that you
want to happen, you can decompose it into an infinite
series of steps, which, certainly from a perspective making change
in your life is very daunting thought that somehow any
change is infinite in scope.

Speaker 2 (00:25):
Welcome to the one you feed throughout time. Great thinkers
have recognized the importance of the thoughts we have. Quotes
like garbage in, garbage out, or you are what you think,
ring true. And yet for many of us, our thoughts
don't strengthen or empower us. We tend toward negativity, self pity, jealousy,

(00:45):
or fear. We see what we don't have instead of
what we do. We think things that hold us back
and dampen our spirit. But it's not just about thinking.
Our actions matter. It takes conscious, consistent and creative effort
to make a life worth life. It This podcast is
about how other people keep themselves moving in the right direction,

(01:05):
how they feed their good wolf.

Speaker 3 (01:10):
Math has always been a challenge for me, so naturally,
I figured why not have a math expert on the podcast?
Really as a way to explore how we handle challenges
in general. Today, I'm talking with Ben Orlan, who's a
math teacher and author who makes problem solving feel surprisingly human.
We'll explore why struggling is actually a good sign, how

(01:30):
humor helps us push through tough moments, and even what
a dog retrieving a ball can teach us about calculus.
I've spent most of my life intimidated by complex math,
but as I talked with Ben, I realize that how
we approach math mirrors how we approach any challenge, whether
it's breaking a habit, learning something new, or facing uncertainty.

(01:52):
By the end of this episode, you might not just
rethink math, you might rethink how you take on hard things.
I'm Yeric's and this is the one you feed. Hi Ben,
Welcome to the show.

Speaker 4 (02:04):
Yeah, hi Erk, thanks so much for having me.

Speaker 3 (02:06):
I'm excited to have you on. You are a little
bit of an odd guest for us. I don't mean
that you're odd as a person, although perhaps you are.
I think that's a good thing.

Speaker 1 (02:14):
But yeah, I get that at dinner parties want to
show up. You're odd guest for us.

Speaker 3 (02:18):
Yeah, you're writing books about mathematics, which is a topic
we have literally never covered except me trotting out some
sort of cliched like happiness equations or something. But I
was really taken by first the title of your book,
and then as I look deeper into your work, some
of the other titles and some of the ideas that
you're playing with. And your new book is called Math

(02:38):
for English Majors, a human take on the universal language.
So I think there's a lot that we can cover that. Listeners,
I think you're going to be surprised at how interesting
this is, particularly if you don't like math or you're
afraid of math. This is a great conversation. So we're
going to start, however, like we always do with the parable.
And in the Parable, there's a grandparent who's talking with

(03:00):
their grandchild and they say, in life, there are two
wolves inside of us that are always at battle. One
is a good wolf, which represents things like kindness and
bravery and love, and the other's a bad wolf, which
represents things like greed and hatred and fear. And the
grandchild stops and they think about it for a second.
They look up at their grandparent and they say, well,
which one wins? And the grandparents says the one you feed.

(03:24):
So I'd like to start off by asking you what
that parable means to you in your life and in
the work that you do.

Speaker 1 (03:30):
Yeah, I think of the feeding as the what you
do every day. I think sometimes I give into the
temptation to want to imagine I have this self which
is somehow separate from the way I spend my time.
There's this me and I have this high opinion of myself. Maybe,
but if you look at what I'm doing day by
day and week by week, it's like, well, am I
doing those things that I claim to value?

Speaker 4 (03:48):
And so as a teacher, I think about this.

Speaker 1 (03:50):
As a teacher, you're sort of always on the clock
in some sense, you know, when the students are in
the classroom with you. Yeah, they're taking the lesson from
whatever it is you're doing that day. They're not taking
some lesson you've imagined in your head. And so to me,
that's what the feeding is, as how are you spending
every minute, every hour.

Speaker 3 (04:03):
I love that idea. There's a concept out there that
I know has a name, but I don't know what
the name is. It's a concept in the mental health
world a little bit and it basically says that if
you want to know what somebody values, look at what
they do actually do, not what they say. I think
that's a little reductive. I get it because I do
think it's true that that does show at least what

(04:26):
our operating values are at the time. But I also
think that there are ways in which we can get
better at bridging the gap between that idealized self that
you talked about in your head and the actual self
that shows up day to day. Because there's a lot
of time in my life if you took who I
was only measured by what I did, you'd be like,

(04:48):
that guy is a piece of shit, right, Like that
guy is a real asshole, because I mean I was
a heroin addict. I mean I was not behaving well,
and I like to think that wasn't all that was
true in those moments.

Speaker 4 (04:58):
No, I think that's fair.

Speaker 1 (04:59):
Maybe that's why I think having the multiple wolves and
the stories is an apt metaphor, because we're not these unified,
coherent people. Yeah, you can't look at someone and say, ah, yes,
this is the explanation for their behavior and who they
are and what they do. It's like, we're not that tidy.
We're not characters in a fable. We're something much more
complex than that.

Speaker 3 (05:16):
So let's take that idea there that we're something much
more complex than that, because we really are. And if
there's one thing that I sort of push against in
the space that I'm in is the idea of easy answers,
the idea that like there's this one size fits all formula,
or there's these five easy tricks or all of that.
And I heard you say on a different show. I'm

(05:38):
not going to get this exact, but you basically said
that one of the things to be a good problem
solver is, instead of trying to immediately solve the problem,
is to relax a little bit into what the problem
is and explore it a little bit more before you
move on to solutions. Say a little bit more about that.

Speaker 1 (05:57):
Yeah, Yeah, I've talked about this with students and in
my writing a little bit. I think if there's certainly
these four stages of solving a problem, and mathematics is
a really good place actually for learning these stages, because
mathematics is a series of challenges of problems that you
run into, and some of them are routine, you know,
sort of exercises. It's like doing your weightlifting for the day,
and you don't get stuck on those. You can just
kind of move through them. But sometimes you run into

(06:18):
a problem and you don't know what to do. The
first thing you try it doesn't work, and then there's
a temptation to just bounce off that problem and go
do something else with your day. Especially in math, there's
a lot of ways to spend a day other than
doing mathematics. So I know this with my students, like
there's other ways to spend their time. So when a
student runs into a problem that they're stuck with, my
first piece of advice is to stop trying to guess
the answer or stop trying to solve it right away.

(06:40):
I remember one time, this is a class of seventh
grader as I was teaching, and it gave them a
problem that I thought was going to take the whole
lesson to solve, but they weren't accustomed to problems like that,
so some of them just started shouting out guesses, right,
is it twelve?

Speaker 4 (06:52):
Is it fourteen?

Speaker 1 (06:52):
And it was like, you're probably not going to guess
the answer in the first thirty seconds. So my advice
in those situations and beyond math too. Is two explore
the problem, to make the goal for that next ten minutes,
for that next half hour, not to solve the problem,
but to figure out what would a solution look like.
What are the obstacles here, what's the tension in this problem?
Why isn't there an easy answer? What other things that

(07:15):
people have tried maybe for this problem? You know, to
view it as you're researching and playing with the problem
rather than trying to solve it. This is something that
research mathematicians, the people who are trying to solve new
math problems, tend to be very very good at because
those problems can take years to solve. I mean some
of them can take centuries. They're sort of passed on
generation to generation, and so you have to be patient.

(07:35):
And sometimes progress on a problem doesn't look like a solution.
It looks like an idea of what the solution would
have to look like, or ruling out possible solutions.

Speaker 3 (07:44):
I love that, and I do think that that really
does apply to challenges in our life. Changes we want
to make or problems that we're having. Is that if
we can spend time really looking at the problem or
the change that we want to make without immediately jumping
to a conclusion of what we should do. It really helps.
And you mentioned like there's contradictions and there's opposing tensions,

(08:07):
and it's like, you know, let's say I suddenly am like, well,
I want to begin reading for thirty minutes a day.
I'm just making something out. If you don't spend some
time to acknowledge like what's been blocking me from doing that,
you know what other tensions are pulling on me in
those moments like that sort of exploration can be really
really valuable. We tend to jump right to action, and

(08:29):
it's interesting I think a lot about like one of
the most accepted models for behavior changes called the trans
theoretical model of behavior change, most commonly known as the
stages of change model, and there are three stages before
you even ever get to action, and if you don't
do some of the work in those stages, very often
your action just isn't going to go anywhere. It's going

(08:50):
to just peter out really quickly. And sounds a lot
like what you're saying, which is like I'm just going
to start shouting out answers hoping that this problem is
solved in three minutes and I'm onto the next thing.

Speaker 4 (08:59):
Yeah.

Speaker 1 (09:00):
I like the preparation before the solution seems important. And
I think another thing that I learned from mathematics is
the hardest problems don't always look hard, and the easy
problems don't always look easy. There's a very famous one.
This is a problem that was first just kind of
jotted down in the margins of a book four hundred
years ago, and it was someone who was reading an
old geometry book Skypierre, and he jotted it down and

(09:21):
he's like, oh, I've got an idea for another equation here,
but there's a certain kind of equation that I think
doesn't have a solution, and he jotted it down in
the margint He says, oh, and I can actually I
know the solution to this. I could prove this to you,
but I don't have quite enough space in this margin
of the book. And then it just sort of sat
there in the margin of his book for a few years.
His son discovered it a few decades later and published
it with his writings, and people started looking, what was
this proof that he had come up with that he

(09:42):
didn't quite have space for. And it took three to
fifty years. He probably had it wrong, right, His proof
was probably false. But the thing he was trying to
prove that this kind of equation didn't have a solution.
It's a very simple equation. I've showed it to eighth
graders and it's true what he said. But it was
one of the hardest problems anyone had ever uttered in
mathematics up to that moment. You know, it wasn't solvable
with the mathematics at the time. You needed three hundred

(10:04):
and fifty more years of mathematical developments for that to
be solvable. So it looks really simple, and you know
sometimes in LEO, I want to read for thirty minutes
a day. It sounds so simple. It's like I got
books on the shelf, I've got thirty minutes in the calendar.

Speaker 4 (10:15):
This seems very.

Speaker 1 (10:16):
Easy, right, right, But maybe that's tapping into issues of
attention and patience and anxious worries that keep you from focusing,
like it can happen into so many.

Speaker 4 (10:24):
Difficult issues exactly. And so yeah, I.

Speaker 1 (10:26):
Find mathematics is a very crisp model of those things.
Often because in math it seems like, of all places
it should be easy to tell what's an easy problem.
What's a hard problem? But things can be simple and
very hard or complex and actually not so hard. You
know a lot of surface complication, but if you just
understand what the terms are, it's actually a straightforward problem.

Speaker 3 (10:45):
This is a question about problems like that, like how
does someone know that they're proposing a mathematical problem or
proof or quandary versus just writing down a bunch of nons?
Like are there points where people are like, we're trying
to prove something that should not be proved because it's
not true or real, or like, I know this isn't

(11:08):
a question that probably is like three podcast interviews, but
I'm just curious because I often think about that.

Speaker 1 (11:14):
Yeah, that's a nothing more. I think it's interesting to
hear what mathematicians say about this. I'm a math teacher, right,
I don't do my own mathematical research, but knowing lots
of people who do, often they'll run into a question
where you're trying to decide, Okay, it's this statement true
or false, And actually if you sit there wondering whether
it's true or false, you never get anywhere. What they
have to do is they have to commit to the thought. Okay, today,
I'm going to try to prove it's true. I think
it's true.

Speaker 4 (11:35):
I'm going to try to.

Speaker 1 (11:36):
Prove it, and they'll work to prove it, and maybe
in the process of trying to prove it, they'll find
out that it's false, or maybe they just don't get anywhere,
and the next day they go, Okay, given I couldn't
find a proof yesterday, I think this is false, I'm
going to look for an example that shows this is false,
something that breaks the purported rule, and then they'll do that.
But what I've heard from a lot of Matheaticians is
you can't occupy both states at once. You have to

(11:57):
at least temporarily commit yourself to one side of the ledger.
You know, I'm going to push in this direction today,
And even if you don't know which direction to go,
you learn a lot by picking a direction and trying that.

Speaker 3 (12:08):
I find that ability to sit with a problem like
that for years astounding. I recently, very recently figured out
that I can solve crossword puzzles. Now, as a fifty
year old man of fifty plus years who loves words,
I should have known that sooner, but I didn't because
I would get stumped early on and be like, Eh,

(12:30):
I can't do this. Now I realize like, oh, I
can do this. I love doing this. This is fun,
this is enjoyable. There is some switch in me, And
I don't know if that switch was that I suddenly
started to believe that I could do it, and then
that enabled me to stick with it. But I think
that we could extrapolate this idea a little bit to

(12:51):
how do we stick with things that we feel like
we can't do. Now. You must face this all the
time as a math teacher, right because one of the
most common things you'll hear people say is I'm not
good at math. You know, if you ask people what
they're good at or it comes up, you're gonna hear
I'm not good at math a lot. So I think
there's a similarity here to me and my crossword puzzles.

(13:14):
So let's talk a little bit about that process, maybe
in how you teach it for math, and then maybe
we can broaden it out to how we apply it
to other areas of our lives that may be more
impactful than a crossword puzzle.

Speaker 4 (13:27):
Yeah, yea, Although I love crossword puzzle, that's pretty high impact.

Speaker 1 (13:29):
You know, you can spend a fifteen minutes a day
sort of enjoying the New York Times puzzle.

Speaker 4 (13:33):
That's a nice way to spend the time.

Speaker 3 (13:34):
It is. It is.

Speaker 1 (13:35):
Yeah, it's definitely true what you say about people identifying
as not a math person. It's sort of funny because
everyone when they present it, they present it as sort
of this idiosyncratic fact about them personally. It's like, oh,
you know, it's just me. I'm just this funny person
who's like, ah, I didn't really math didn't really click
with me. It's like, yeah, there's hundreds of millions of people.

Speaker 4 (13:52):
Like that in the United States.

Speaker 1 (13:53):
Like this is a solid majority of the country. I
would say, so it's obviously not and maybe that's I
think the first step for people. And it's not some
personal failing of yours. And I try not to blame you.

Speaker 4 (14:02):
I'm a teacher. I love lots of other teachers.

Speaker 1 (14:04):
I try not to blame. It's not the teachers have failed.
It's a weird thing we're trying to accomplish in math education.
We're taking these five year olds and setting them down
on this ten year journey where they're supposed to come
out the other side having learned sort of like centuries
worth of mathematical ideas, becoming expert in stuff that really
only a very small elite would have ever had to
learn in a lot of past generations. You know, these

(14:26):
very abstract ideas that come with their own language that's
presented in a pithy, very sometimes too short to brief
the glimpse you get of these ideas. To me, there's
no shock when someone struggles with mathematics or with mathematics education.
That's sort of the default state. And I think for
me that's a first step when there's something that I'm
struggling with mathematical or something else, or when I see

(14:48):
a student struggling, is to depersonalize it a little bit.
It's not some shortcoming, some gap within you. You know,
there's some missing jigsaw piece in your brain that you're
never going to be able to get this. It's like
not things are hard to learn. It takes time, it
takes effort to take the teacher to walk you through it.
So that's the first step for me. The second step
is often motivational, why would I want to learn it?

(15:08):
For a lot of students, the benefit to learning math
is you can pass math classes and then stop taking
them like that that's really it's a thing you want
to learn so you can cease ever having to think
about it. And so this varies a lot from person
to person, but I try to find something that that
feels meaningful to them, that will open something up for
them in their life. Just a student the other day
actually is their first day coming to my class. They

(15:30):
enrolled late and missed the first week. And we were
doing a little bit of work in spreadsheet programs, just
in Microsoft Excel, and the student was saying it was
just sort of like mouth open. They're like, my mom's
been running a small business for years and doing the
accounting with literal spreadsheets, like sheets of paper spread out
and a hand calculator and adding up the numbers, you know,
hours every month to get that to work. And I

(15:52):
was like, oh, yeah, no, take this home. By the
end of the semester, you'll be able to do that
hours of work in five to ten minutes of updating
the spreadsheet of people. I think it's's personal finance. You
can give you a grasp on money and where you're
putting it and how it's flowing and where it goes.
You know, when the money's gone from the bank account.

Speaker 4 (16:10):
Where did it go?

Speaker 1 (16:11):
Just a little bit of extra grasp on mathematics and
mathematical tools can really help with personal finance. So, especially
for a lot of the adults I teach at community college,
that's a very relevant one. And then especially for younger students,
but for some adults too, mathematics is just this kind
of beautiful set of ideas. It's connected to everything a
little bit. It's kind of like this underground water source

(16:32):
or something underground river that sort of connects all these
different parts of the landscape that you wouldn't have thought
were connected. And so, you know, one of the things
I love to do is kind of collect great thinkers
who are fascinated by mathematics. And you know, Abraham Lincoln
loved mathematics, right, He read a lot of Euclid the geometry.
He in fact memorized the whole geometry book. While he
was in law school he was sort of working on

(16:53):
his legal studies. He goes, oh, I'm never going to
be a good lawyer unless I really understand argument, logic
and proof. So okay, so I guess I've got to
go read ancient geometry texts and learn it that way.

Speaker 3 (17:04):
And memorize them.

Speaker 4 (17:05):
Is there, Oh yeah, he memorized the arguments.

Speaker 3 (17:07):
Yeah, I guess you can just get a lot done
if you don't have TVs or cell phones or you know.

Speaker 4 (17:13):
Right right, all you had to do back then was
chop chop.

Speaker 3 (17:16):
Electric lights.

Speaker 1 (17:17):
I mean, that's what I've been saying for you is
electric lights are a huge distraction for us. It's really
you know, it's shortening our attention span. It's we really
got to got to go back to candles. Is rambling
here in this answer, but yeah, I think the reason
I ramble a little bit is because every person needs
to find their own connection here. You know, for it
was logic, it was mathematics as a model of logic,
and for people who love Sudoku puzzles, that's a little

(17:39):
bit the same thing. That's that's all, you know, air
tight logical reasoning. And for some people it's you know,
mathematics being connected to the arts and sort of the
ways geometry plays into different artistic traditions. Cosmology is a
topic that I'm always fascinated by, like what is this universe?
And how does it work? And what on Earth is
going on here? How did we get here, and mathematics

(18:00):
really central to answering some of those questions. So for
some people they sort of you get excited about science
and maybe learning a little bit of mathematics will help
open doors there.

Speaker 3 (18:07):
That is a quandary I run into often, which is
the last time I took math would have been a
long time ago. My main attempt in most of high
school was simply how do I not go to school?
How can I get out of going? So if I
could have used mathematics to help with that, I probably
would have. But I love popular science, but a lot

(18:29):
of it. I'm reading the introduction and I'm like, okay,
I'm cruising along here, and then start the equations, and
all of a sudden, I'm like, you know what, to
understand this, I'm going to have to go back a
little ways. And I just never quite take the time
then to go back and go you know what, some
basic algebra W has served me really well in getting

(18:50):
into all of these ideas.

Speaker 1 (18:52):
Yeah, yeah, I think of algebra especially it opens a
lot of doors.

Speaker 4 (18:55):
It's a key.

Speaker 1 (18:56):
It's a key that's very hard to acquire, right. It
takes a few years of education, and you know, in
the USB teach course called algebra to you know, usually
fourteen year olds or so. And I've taught that course
and students don't really internalize it, don't really learn it
until usually three four years later at the earliest, when
they're when they're taking calculus or something like that. It's
having to use those algebra skills later on that really

(19:17):
forces you to absorb them. So it's not easy to
learn algebra, but it just opens up so many doors
down the road that you wouldn't have guessed. Yeah, especially
in the sciences, but well, I don't know. Sciences touch everything,
So you know, if you want to learn about economics
or finance, or astronomy or or population biology or epidemiology
and think about predicting the next pandemic, any of that, Yeah,
just having the language of algebra really pays off.

Speaker 3 (19:40):
I'm trying to balance the desire to keep this conversation
somewhat about what the one you feed talks about versus
chasing it down mathematical rabbit holes. So I'm going to
pull back up here for a second and say, like,
let's keep going with this question of Okay, there's something
in life that I can't seem to do or I'm
intimidating by how do I work through it? And we've

(20:02):
talked about how recognizing you're not alone in doing it
is really important, right, recognizing that there is a problem
lots of people share, humanizing it. We've moved on to
trying to connect it to why it matters, and I
think that's really important too. Same thing with like reading
a book for thirty minutes, Like, Okay, why why does
that actually matter to you? If we're unable to articulate that, well,

(20:25):
we're not going to have sufficient motivation to stick with it,
which I think is what you're saying about math. You've
got to get the student interested somehow. So okay, now
you've got the student recognizing I'm not alone and not
liking math. Okay, I can see why this might be
valid to me. You know, I have always wanted to
read Brief History of Time by Stephen Hawking and I can't.
And so, okay, algebra, where do we go next?

Speaker 4 (20:48):
Yeah?

Speaker 1 (20:49):
Yeah, for solving any particular problem. What I like to say,
sort of the next step, once we've kind of walked
around the outside of the problem and we're motivated to
solve it, is getting a wrong answer down on the
page deliberately wrong, right, Like you're not trying to answer
it correctly, yet you're trying to get sort of maybe
an obvious wrong answer, and then that gives you something
to work on that sort of solves that blank page problem.

Speaker 2 (21:09):
Right.

Speaker 1 (21:09):
Anyone who's written knows that it really helps to have
a draft in front of you, right. Getting that first
draft down is pulling teeth. That's that's the hard part
when solving a problem, just getting an answer down. In math,
one of the questions I like to test students is,
you know, what's an answer you know is much too big?
And what's an answer you know is much too small?
If we're trying to solve for some number, and that
can start to build some intuition. It sort of says, okay,

(21:29):
this is the sort of thing we're looking for. Or
you know, if you're looking for some problem solving method,
you say, okay, well, why wouldn't this work. It's another
way of teaching yourself about the problem, introducing something that
you know isn't quite the right solution. Yeah, it gives
you a first draft to build on.

Speaker 4 (21:45):
Excellent.

Speaker 3 (21:46):
I want to jump back to a loop I didn't
close earlier, which is you talked about, like, I think
you talked about four steps of solving a problem, or
four stages, and I think we got through about half
of them. So maybe we can pause right now and
close that because I think it's relevant to where we
are in the conversation.

Speaker 1 (22:03):
Yeah, yeah, this doubles I think making mistakes sort of
like getting a wrong answer down. I would call that, yeah,
sort of my second step there. Once you've explored the problem,
once you've explored it further and you've worked for a while,
one very important step I think is to step away
from it, to not have a false sense of urgency
that you have to solve it in the next ten minutes,
and just give it some time, especially once it's kind
of circulating.

Speaker 4 (22:22):
Around your mind.

Speaker 1 (22:23):
The back of your brain can do incredible things given
a little space to breathe. So for me, it's you know,
putting on headphones and going for a walk or going
for a run, although I have to be careful when
I'm on a run off and I'll have ideas that
I think are brilliant at the time, and then I
get home and look at like the little note I
took on my phone. It's like waking up after a
dream like, oh that that wasn't wasn't the idea I
thought it was.

Speaker 3 (22:41):
Yeah. What's interesting about that is I do think it
mirrors an experience I used to have when I was
a heavy substance users. I would write some part of
a song or something and be like this is incredible
and wake up in the morning and be like not
so much. And for some reason, walk seem to do
a little of the same thing. Some of the ideas
are great, but I'm a little bit of stick by
how some of them. I'm like, there must be something

(23:02):
about the state of flow or it is what you
want to have happen when you're initially brainstorming, which is
the critic takes a vacation for a little bit like
go away, critic, and walking seems to do that for me.

Speaker 1 (23:14):
Yeah, yeah, I think it puts me a little more
at ease. And it's a good reminder to someone who
very much lives in my head, you know. I think
math induces this, and people who sort of like you
spend a lot of time with your thoughts and looking
at screens, looking at paper. But it's good to remember
I'm a body, you know, That's what I am. That's
what I have, and then it moves around the world.
I'm not just a computer where you can predictably feed
me inputs and get the right outputs. You know, I

(23:35):
need I need a little bit of serendipity. I need
some surprises and things in front of my eyes that
I didn't expect to see. I think stepping away and
going for a walk, or cooking a meal or whatever
it is that gives you something to keep your hands
or your feet busy, and then your brain can keep
working in the background. And then the final step is
sort of the counterpoint to that, which is then you've
got to go back to work. Yeah, you can hope

(23:56):
that some inspiration will come, But this is true even
of artists, right. A lot of the artists I admire,
they have a very strict writing regimen, right. I mean
Paul Simon when he was writing albums, he would just
be writing a certain number of hours every day and
that's how he generated it. Stephen King wrote, you know,
three thousand words a day or some completely superhuman number
of words.

Speaker 4 (24:14):
And I think, you know, most working artists, I should say,
they do.

Speaker 1 (24:18):
They have to write, otherwise you don't create what you
need to create, Otherwise you don't solve the problems you're
trying to solve within each work. Even if you feel uninspired,
you've got to go back to it.

Speaker 3 (24:46):
Let's shift direction just a little bit here. We're still
talking about sort of overcoming fear or overcoming being stuck.
I want to talk a little bit about the role
of play in that, the role of humor, because you know,
your first book was I think called Math with Bad Drawings.

Speaker 1 (25:06):
Yeah, that's right, Yeah, yeah, you it's its fund seeing
how translators handle that. There's one one where it just
translates Math with the Worst Drawings.

Speaker 4 (25:13):
Got I've got demoted here.

Speaker 3 (25:15):
So yeah, you draw humorous little drawings that are intended
to illustrate the concept, but also oftentimes just have fun. Right.
There are times I see they help me figure out
the concept, and there are other times I think they
just sort of make light of the whole thing a
little bit, which I think causes a reduction in the
strain around trying to figure it out. So talk to

(25:36):
me about play and humor and why that is the
direction you've chosen to go.

Speaker 4 (25:41):
Yeah.

Speaker 1 (25:41):
Yeah, for me, the bad drawings, there's a few things
that led me to them, and one is my inability
to draw or I just can't do it. And math
is very visual, so you need you need pictures to
explain things, and you need pictures to kind of punctuate,
you know, the end of a thought. So I needed
to draw, and I've never doodled as a kid. I
really I should have practiced more. Yeah, But anyway, so
I arrived in a and wanted to write these books
about math and wasn't able to draw.

Speaker 4 (26:02):
So okay, we're going to do stick figures.

Speaker 3 (26:04):
We're going to do you embraced your limitation.

Speaker 4 (26:07):
Yeah, exactly.

Speaker 1 (26:08):
Yeah, And I think it wasn't a calculation on my part.
It was sort of a shrugger of the shoulders and like, Okay,
I guess that's the best I can do. But I
think it creates a different tone or a different kind
of space for people coming to mathematics, maybe not super
enamored with the subject, because you come thinking, oh, I'm
not really a math person. And it sort of activates
people's defenses around being good at things being bad at things.

(26:28):
And so to have the person you're learning this stuff
from be very self evidently leading with something they're bad at,
right kind of putting their worst foot forward. Yeah, yeah,
I think it kind of demystifies a little bit. Or
we're coming here as fellow human beings, with our strengths
and our weaknesses and our gaps and our knowledge sets.
We're here to share things. I'm not here to stand
on a mountaintop and pronounce the truths of mathematics.

Speaker 3 (26:48):
One of your earlier books is called Change is the
Only Constant. It's about calculus. I may not have that
title exactly right, but as a person who studied a
lot of Buddhist and Eastern thought, this idea of impermanency
is central to the whole game. Talk to me about
the role that change plays in mathematics. Yeah, and maybe

(27:11):
how math brings that concept alive. And I'll say one
last thing and then I'm to turn it over to you.
There's a phrase from the Japanese poet bas Show, who says,
I'm not going to get it exactly right. You learn
more about impermanence from a falling leaf than like a
thousand words about it. So, but math probably shines a
different light on that same idea. Right, there's another way

(27:31):
of learning more about impermanence. Talk to me about it mathematically.

Speaker 1 (27:35):
Yeah, change was something that mathematics always struggled with. I
think it's one way to put it. That's somehow. A
lot of mathematics that was developed by brilliant mathematicians dealt
with static situations, and it was actually change in motion
that presented some of the most vexing mysteries, and of
course one of the most ancient ones. And this comes
up in the Western tradition, comes up in the Chinese

(27:58):
school of Nams was a philosophical school, is what we
call Zeno's paradox. So the idea that you know, if
you and I are going to high five each other,
you know, would phrase it a little differently. But if
we're going to do a high five, like to complete
that high five, we need to get halfway there, right,
Like our hands start three feet apart, we got to
get to a foot and a half apart, and then okay,
that takes some amount of time. But then to complete

(28:18):
the high five, now we need to go halfway again
and get to you know, three quarters of befoot apart
or nine inches apart now, but we're still not there yet.
There's another step. We got to go halfway again, and
now our hands are really close, but there's still another step.
You got to go halfway again and halfway again, and
so there's this infinite series of actions you have to
complete just to high five somebody.

Speaker 4 (28:36):
And this is sort of true of all motion. It
feels like all.

Speaker 1 (28:38):
Change, anything that you want to happen, you can decompose
it into an infinite series of steps, which, certainly from
a perspective making change in your life is very daunting
thought that somehow any change is infinite in scope.

Speaker 3 (28:49):
It often is. I think there is change that is
goal oriented, as in I'm going to run a five k,
But if your bigger goal, the reason you want to
run a five k, is that you value your physical health,
then change is infinite because there's never a day that
your physical health is like, Okay, I have established it.

(29:11):
Now it is set. I will go about all my
other business and it will remain in place. It's the
same thing with like we can't just eat once.

Speaker 1 (29:20):
I've locked in healthy eating. I had a salad for
lunch yesterday. It was delicious, that was it, and now
I'm done. Now I can have cinnamon buns.

Speaker 3 (29:26):
Every day and yeah, yeah, exactly.

Speaker 1 (29:28):
Yeah, So maybe that's right, though, Yeah, Zeno was onto something.
I think, as you know, was certainly onto something. Obviously,
as Zino understood, you can complete an action, right, we
see people walk across a room and they get all
the way to the end. So clearly there's something a
little tricky about his logic. But Bertrand Russell, the twentieth
century philosopher, said that sort of every generation since Zeno
has had to reckon with that paradox. Right, on the

(29:50):
one hand, we do complete actions. On the other hand,
there's this sort of compelling argument that it's impossible, that
it's infinite, that we'll never get there, and so every
generation has sort of had a different answer to that question.

Speaker 3 (30:00):
What does your generation? I think we're probably sort of
a generation apart, not quite so, what would Russell say,
your generations wrangling with Zeno's paradoxes?

Speaker 1 (30:12):
Oh, that's interesting, right, I guess I'm sort of a
squarely in the millennial generation.

Speaker 4 (30:16):
Yeah, yeah, I don't know.

Speaker 1 (30:17):
I think the millennials that looking at us from the outside,
I think we have a reputation for being a little square,
a little earnest, you know, compared to Gen X, which
was always steeped in irony and gen Z, which sort
of finds millennials hopelessly straightforward in earnest. I think there's
something about millennials maybe that just want to be like, no, no,
I'm gonna I'm gonna get there, I'm gonna I'm gonna
go halfway and halfway again. I'm going to complete that

(30:38):
sequence of actions.

Speaker 3 (30:40):
Yeah.

Speaker 1 (30:40):
So maybe, yeah, maybe the lesson for millennials would be
to embrace a little more, a little more mystery in that,
a little more accepting it as a paradox.

Speaker 3 (30:49):
So listener, consider this. You're halfway through the episode. Integration reminder.
Remember knowledge is power, but only if combined with action
and integration. It can be transformative to take in it,
to synthesize information rather than just ingesting it in a
detached way. So let's collectively take a moment to pause
and reflect. What's your one big insight so far and

(31:10):
how can you put it into practice in your life? Seriously,
just take a second, pause the audio and reflect. It
can be so powerful to have these reminders to stop
and be present. Cant it if you want to keep
this momentum going that you built with this little exercise,
I'd encourage you to get on our Good Wolf Reminders
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(31:31):
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(31:54):
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are good Wolves together. So there's a recent post on
your blog about the poet Adrian Rich and really about
this idea of change. Can you share a little bit
more of what you wrote there?

Speaker 1 (32:14):
Yeah, yeah, I came case you're in Rich very sideways.
It was just through I came across a quotation of hers,
totally out of context, that the moment of change is
the only poem, and I thought that was lovely. Didn't
know anything about Adrian Rich because I'm not particularly noulptible
about poetry. And so this is actually while I was
working on that Calculus book, I went and read, you know,
a few of her collections and essays she'd written, and
found her a fascinating figure and really someone who embodied

(32:38):
change in her life because she had, say she was
living in doing her best work in the sixties, seventies, eighties,
and so as of the late fifties into the early sixties,
she was living a very sort of conventional looking life.
You know, she was, I think mostly a homemaker, housewife.
She had a few kids, her husband was a professor
at Harvard, and she wrote very careful and sort of

(33:00):
immaculate but fairly traditional poetry. And anyone who knows Adrian
Rich knows her as a radical feminist, lesbian, you know,
who had female lovers and wrote about sort of breaking
loose from societal constraints and completely reimagining out of the
world around us. And so how did she get from

(33:20):
the one spot to the other? And it was sort
of this gradual process. One of the things she started
doing was putting the date the year in parentheses at
the end of each of her poems. You know, I'm
sure it was just a sort of artistic intuition, but
later when she reflected on it, she said they were
starting to feel more like snapshots, less like completed works,

(33:41):
and more like, yeah, moments.

Speaker 3 (33:43):
Of an ongoing dialogue.

Speaker 1 (33:45):
Exactly, Yeah, yeah, something ongoing and evolving. And that poem
that has the line the moment of change is the
only poem. It's dedicated to the French film director Godard,
and so yeah, it begins the opening line is driving
to the limit of the city of Words, which I
love as a line. The word the limit happens to
be a very important word in mathematics and calculus. She's

(34:05):
coming out the kind of the same idea from a
different direction. She's saying, what are you trying to do
in film or in poetry? You're trying to go right
to the edge of what words can tell us and
let those words gesture at something beyond themselves. And then
towards the end of the poem she kind of circles
around this thought or uses this thought to propel herself forward.
She says, the notes for the poem are the only poem,

(34:29):
which I sort of like that.

Speaker 4 (34:31):
You know.

Speaker 1 (34:31):
The idea is that the poem itself is too polish,
too final, and like, really, the magic the poetry is
in those notes, is in that first impression. And then
a few lines later she comes back, she just know
the mind of the poet is the only poem. Now,
even the notes there's something, there's something recorded and documentary
about that, and really it's just what's happening in the airspace.

(34:53):
And then the very final line of the poem is
the moment of change is the only poem. It's like, no, no,
it's not even really the mind. It's something I don't know, like,
can't I can't explain in words because she's gesturing beyond words.
I wrote a whole chapter that I wound up cutting
from the Calculus book because it was more about poetry
than it was about calculus. But it really shaped my
thinking about when I was writing that book about calculus.
I suspect I'm the first author of a calculus book

(35:14):
to really have my thoughts on the subject shaped by
Adrian Rich and her radical poetry. But it really it
felt very true to the insights of the math to
me that there's something about trying to reach towards something
infinite that you can't ever quite attain, but there's a
lot of meaning and purpose in that reaching.

Speaker 3 (35:32):
Yeah, that whole thing is such a Zen idea. I mean,
Zen is a form of Buddhism that really talks a
lot about how, yeah, words, you need them because they're
the main thing we have. And yet they're only pointing
at something, you know, they're only trying to get you
to look in a certain direction, in a certain way.

(35:52):
And then that same idea of we tend to think
that the end output is the thing, and Zen would
say no, no, no, it's much more the doing, the
being one with the doing. And then ultimately it would
go on to say, sort of that last level is
that even the mind itself is in change. You can't

(36:14):
pin it down to anything. You know. What you think
is your mind is this constellation of conditions that have
come together extraordinarily temporarily right, and that you're freezing. And
so change is the only poem resonated so much with me.
I thought the way you wrote that up and her
lines are really beautiful.

Speaker 1 (36:34):
Yeah, and I think you no, I really do. I
love that poem. It's a fun wonder revisit.

Speaker 3 (36:37):
On the subject of your calculus book, I read your
latest book, which is the Math for English majors a
human take on the universal language, and really enjoyed it.
But I sometimes dig a little bit deeper with guests,
and so I opened up your Calculus book about change
and the chapter titles. If I wasn't like an hour
and a half from an interview with you, I would

(36:59):
have bought that book, and like, I've got to read this,
and I may go back because the chapter titles are
so good. But I thought maybe we could talk about
a couple of them. And the first is when the
Mississippi ran a million miles long, how Calculus plays a prank.

Speaker 1 (37:16):
Yeah, So there's this fun passage in Mark Twain. One
of his nonfiction books is The History of the Mississippi,
and he talks about this funny fact about rivers, which
is that they create these meanders right over time. They
sort of have these curves and so you get these wide,
you know, almost circles, and every so often the river
will actually complete the circle. So just time going on

(37:37):
and the water changing course, it'll sort of jump the gap,
especially during a flood. And so this has happened periodically
on the Misissippi. We have we have decent records of this,
and so in the century or two. You know, sort
of before when Twain was writing this, you could sort
of chart the decrease in the length of the Mississippi
as it sort of jumped those gaps, and so a
long kind of circular meander became straight jump. He's just

(38:01):
sort of applying arithmeticul learned in school. He said, well,
here's what you can do. You can say, Okay, if
the Mississippi River has I'm gonna get the number is wrong,
but the missip River has gotten one hundred miles shorter
in the last one hundred years. Well, that means Mississippi
is shrinking by about a mile a year. So a
million years ago, the Mississippi River would have been a
million miles long, right, it would have stretched out four

(38:22):
times past the moon. It would have been this, you know,
visible from deep in the solar system, just this extraordinary
astronomical river or maybe wrapping many times around the Earth.
Who knows how you want to do it. And then
his line, which I love. Twenty is such a brilliant stylist.
He says, that's the marvelous thing about science or mathematics, say,
is nowhere else can you get such a wholesale return
of conjecture from such a trifling investment of fact, which

(38:46):
is very astute I think as to what science and
mathematics can often do. Say that again, a wholesale return
of conjecture from a trifling investment of fact.

Speaker 3 (38:57):
I would say that might be shaping a lot of
our online political discourse at this point.

Speaker 4 (39:02):
Also, No, I think it very limited investment effects.

Speaker 3 (39:06):
We've got a whole lot of conjecture, not very fun conjecture,
to be honest, for a trifling amount of fact.

Speaker 4 (39:12):
No, I think we'd be better off.

Speaker 1 (39:13):
I mean, I spend more time reading social media than
I do Twain, but I should probably defert that into
into reading more Twain. The lesson I take away from
that Twain knows that that's not what happens, right like obvious,
Thessissippi River did not wrap many times around the earth.
But it's actually it's quite an important lesson in mathematics
and I think in life, which is that there's growth
patterns that mathematicians talk about, and in particular linear growth,

(39:36):
which is what Twain was talking about, where sort of
every time period the same thing happens. You know, each
year it gets one mile shorter, and then there's other
growth patterns. So we saw this very vividly at COVID,
for example, where from day to day you would get
big increases. Right, I'm thinking like March twenty twenty when
the caseloads were starting to explode. You know, day to
day wasn't the same change. You know, March second, you

(39:58):
get one hundred new cases. Mark third, you get three
hundred new cases. March fourth, it's five hundred new cases.
So it's the change is not linear, it's accelerating. But
the funny thing about changes like that is that if
you zoom in enough, they always look linear. Yes, So
it's only at a big scale that you see the
actual pattern of the change, yes, which is almost never

(40:20):
linear forever. It's sort of analogous to how the Earth
looks quite flat. You know, every experience I've ever had
of the Earth, it looks very flat. But I know
it's a sphere. It's just that I'm very small. The
Earth is very big, and so if I got up
in a spaceship, I could see the whole thing and
see the curvature. But from the zoomed in perspective, it
just looks linear. Everything looks flat, And so the same
thing is happening there with Twain. Obviously, over time, the

(40:42):
Mississippi River has grown and shrunk and changed length in
a very nonlinear way. It's probably over thousands of years,
it's gone up and down, you know, extends a little
bit through those lakes, and it gets cut off and
you know, some of your tributary joins it. So at
the big scale, it's very nonlinear. But over a few
hundred years, that's actually a pretty small scale for a
geological feature like a river. Yeah, So that's the takeaway

(41:03):
lesson on that chapter is that if you zoom in
really close on something, you're going to think it's some
more predictable kind of change, but over large scales you
get surprises.

Speaker 3 (41:36):
I love that idea. It really echoes a couple of
things that I talk about and teach, and one of
them is that idea of you little by little, little
becomes a lot right that day to day doing a
little thing and a little thing and a little thing,
you don't really see much, but you zoom out far
enough and you're like, oh, that actually really did add
up to something substantial. And then the second is that

(41:59):
idea of zooming out in general as a way of
having a different perspective, right. I mean, there's that phrase
that people use, like making a mountain out of a
mole hill. The way you make a mountain out of
a molehill is you get really close to a little
bump on the ground and you stare at it, right,
it looks really big. Then you stand up and you're like, oh,
it's just a little bump on the ground. And so
that same idea of if we can zoom out, if

(42:22):
we can change our perspective, would be the core thing.
But zooming out is just a really easy way to
do it.

Speaker 1 (42:28):
Yeah, yeah, yeah, I think that's right. Not always easy
to do. It's actually easier on a graphic calculator. And
then it is like graphic get the minus buttoning of
mines Zu amount.

Speaker 3 (42:36):
One hundred percent. Okay, what about There's so many great
titles in here. I'm just going to read a couple.
We're not even going to talk about them. But that's
Professor Dog to You, in which Calculus vaults a dog
to start them. That's a pretty good one. What the
wind leaves behind when Calculus poses a riddle another great one.
But the one we're going to talk about is if

(42:57):
pains must come in which calculus takes the measure of
your soul.

Speaker 1 (43:01):
Yeah, right, which I don't know. It makes my soul
shutter a little bit. I'm not sure I want calculus
taking that.

Speaker 3 (43:06):
Measure precisely, it would come up with an equation I'm
certain that I wouldn't be able to solve, and I
would be no further along in understanding soul than I
am today. But yeah, you might be able to understand.

Speaker 1 (43:16):
It, right, I mean, I think one of the things
I take from math, and actually there's very much theme
of this chapter is that math, although it feels complex
when you're learning it, math is designed to offer us
simplified answers. And because they're simplified, they're almost never quite right, right.
They're always capturing some feature of the world but leaving
something else out. But they can still be useful because
they're these simple schematics. They're sort of these stick figure

(43:37):
drawings of reality. So the one there, I think it
opens with a quote from the economist Jeevans, a nineteenth
century economist, and he was writing at a time when
there was sort of a lot of excitement about math
is doing so much for us, right, Like, look at
what math did for physics. You know, we went from
a world where it was kind of hard to explain

(43:58):
how things move and the basic mechanics of stuff in
the world too. We've got great equations for this, we
can predict it with exquisite accuracy, and economists in his
day we're hoping like, maybe we can do the same
thing for a lot of human behavior, you know, not
just for markets, but for for individuals, for sort of
you know, your your moral sentiments or even your sort

(44:20):
of sense of happiness in life. What he does, what
Juveans does, He sort of imagines a graph of your happiness,
your state of mind, and he says, well, you know,
imagine overtime sort of we got this line going up
and down, and if you feel bad, it goes down,
if you feel good, it goes up. Maybe that's it.
Maybe maybe that's the model of what happiness is. You
can sort of picture this line going up and down,
and you get to the end of the day, and

(44:41):
what you actually want is you want to maximize the
area under the curve, because if it's very high all
day long, there'd be a lot of area under there.
And if it's very low all day long, right, it'd
sort of be very close to the bottom of the graph,
and there'd be a very little area under the curve,
and you can sort of make up for things, right
if it's kind of low most of the day, but

(45:02):
then it has a really high spike, then you'll get
a lot of happiness total. But it's sort of about
adding up the area under the curve, which is what
the calpulist teacher would call an integral and what Jeeven's
calls an.

Speaker 3 (45:14):
Help me understand the curve. I'm not visualized in this.

Speaker 4 (45:16):
Oh sure, sure, I try a picture. Imagine.

Speaker 1 (45:18):
Let's say you've got a big piece of paper on
your wall and you mark it along the bottom, you know, midnight,
one am, two am, you know, all the way to
the next midnight, and every hour or even every minute,
you go and you sort of extend a line starting
from the left, and if you're feeling really unhappy, the
line goes down towards the bottom of the page yep.

(45:41):
And if you're feeling great, you're feeling really happy, the
line goes soaring up towards the top yep. And what
you'd be able to do at the end of the
day is look at this picture and it would be
kind of this abstract picture of your experience of that day.
And you know, maybe you know, if you had a
great breakfast, it sort of starts out low, but then
it spikes really high, delicious eggs, and then it maybe

(46:02):
goes back towards the middle. Is you know, you go
to work and it's kind of it's hovering around the middle.
You have a boring meeting, it dips towards the bottom,
you have a nice afternoon, it kind of rises up.
You get home and you're for me getting home and
having my little ones run up to me is like
that's my happing a spiking way up high. Right, you
two year old jumps into my arms. I gotta, I
gotta extend the paper at the top and then she

(46:22):
throws a tantrum.

Speaker 3 (46:24):
Later you're exhibit yeah, that's right.

Speaker 1 (46:26):
And that network back towards the bottom, and then you know,
you get this this kind of abstract picture of your day,
this mountain range. And what Jeevens is suggesting he wasn't
the first to suggest it. He just he put it
very nicely. Is why I quote him, is that maybe
this mountain range, maybe that's your day. Maybe that's it,
Like that's you know, it's the highs the lows, and
what you want in a day is you want kind

(46:47):
of a big mountain range. And there's a few ways
to have it. It could be a very flat mountain
range and not a lot of up and down, but
it's just at a pretty high level. Or maybe it
has some real lows but also some incredible highs, and
that would be another way to get a big mountain range.
Robert Frost has a poem that's titled Happiness makes up
in height what it lacks in length.

Speaker 4 (47:08):
Wow.

Speaker 1 (47:09):
Yeah, maybe getting the phrasing slightly wrong there, but anyway,
but the same idea, right, Happiness can be kind of
an intense, exultant happiness can make up for its brevity.

Speaker 3 (47:17):
Say that again, happiness.

Speaker 1 (47:20):
Yeah, happiness makes up in height what it lacks in length.

Speaker 4 (47:23):
I think that's it. I see something along those lines.

Speaker 3 (47:26):
Love that. So that makes me think about these sort
of half baked equations I occasionally hear for happiness or
for well being. There's two that I really like. There's
one that I love, and it's suffering equals pain times resistance,
And I like the mathematical precision of this one. Actually,
if you assume suffering is to the total amount of

(47:48):
overall suffering that you have in relation to something. You
can break that down and say, well, some of that
is pain. So let's just take like, my back hurts.
There's a physical sensation of pain, and then there is
all the things I'm thinking about that pain. Oh God,
it shouldn't be happening. Oh if I feel like this

(48:09):
at fifty, what am I going to feel like at eighty?
My mom has all that And so a lot of
that is we could call sort of resistance to the pain.
And so if you were to make this mathematical, and
let's say you might say that your pain is a
five and your resistance is a five, you've got twenty
five total units of suffering. What I love about this

(48:31):
is oftentimes I can't change the pain, right, a lot
of situations in life, you can't change the thing that's wrong.
So I'm going to have five units of pain no
matter what I do. But if I can lessen that
resistance from a five to a three, well now I
have fifteen total units of suffering, which is way better
without changing the underlying problem. And I'm not a believer

(48:55):
that resistance ever goes to zero. Maybe that's what enlightenment
is when resistance go to zero. But for most of us,
we're not going to get there. But if we can
turn down the what would be the way to say it,
turn the dial, all of a sudden, you have less
units of suffering. So that's one that I've always really loved,
and I've understood the math of oh.

Speaker 4 (49:14):
Yeah, to jump in.

Speaker 3 (49:15):
No.

Speaker 1 (49:15):
I like your thought on zero, the unattainability of zero there,
because that was my first thought. When you when you
multiply two things, if one of them is zero, then
it's gone, you know. So if you can get the
resistance down to nothing, then somehow you could have pain
without suffering. Yeah, and maybe that maybe when I think
about I'm a very amateur student of Buddhism, but when
I think about the Buddha like that sort of seems
to be the image that that's conjured for me, that somehow,

(49:36):
I for the resistance vanishes entirely, then there can be pain.
But maybe it's not pain that really matters. Maybe it
is suffering.

Speaker 3 (49:42):
Yeah, yeah, I mean that is a core Buddhist idea
and core Buddhist message. I've had big enlightenment like experiences.
You know that were like everything you read about in
the book, and I would say, yeah, resistance was near zero,
but boy, it just doesn't want to stay there, because
it does seem to me that if you look at

(50:03):
things from an organism perspective, we move away from what
causes pain and we move towards what is nourishing or
causes pleasure. You can see this in an amoeba, right,
put something that's toxic to it on one side and
put something that's nutritive to it on the other side.
You know which side is going to go to, and
so if you try and push it towards the toxic side,
it's probably going to be like, no, thank you. And

(50:25):
so it almost feels like some degree of resistance to
me seems built into being an organism. Yeah, you know,
it's so deep that hoping to make it go away
on any kind of permanent basis is to hope to
be something that as a living creature. I don't know
that will ever be, but I do think you can
turn that resistance down in a truly meaningful way.

Speaker 4 (50:48):
Yeah.

Speaker 1 (50:49):
Yeah, I think about athletes too. When I see athletes,
there can be a time when it's quite painful to
be doing what you're doing, you know, Michael Jordan during
the flu game or whatever. Yeah, but the resistance is
in their case maybe negative. They're not resisting the pain.
They're they're embracing it. You can't do that all day,
as you say, or even for an hour, but yeah,
people can find moments.

Speaker 3 (51:07):
Yeah, that's another great example of being able to look
at that from a slightly different perspective. The last one
that I want to talk about, and this is one
where I haven't quite figured out why the equation is
written as it is, which is that happiness equals reality
divided by expectations. So the core idea makes sense. Our
happiness tends to be higher when reality meets or exceeds

(51:30):
our expectations, right, and when it disappoints us, we feel
less happy. I don't quite know why it's a division, though,
I'm asking the mathematician I happen to have on this
call here to say why any ideas?

Speaker 4 (51:42):
Yeah, yeah, I think division seems right to me there.

Speaker 1 (51:45):
Okay, because what division does is it if you have
a vast number right, say the it was reality over expectations. Yeah,
m so take someone whose reality looks tremendous to any
outsider right, Like we would call that a million, you know,
somebody a celebrity who's got sort of every material comfort
and adulation and followers and all the social media platforms,

(52:05):
you know, whatever you'd be hoping for. And what we
tend to think is we sort of bring our very
mortal expectations. I'm expecting one hundred out of life. So
if I had a million and I was only expecting
one hundred, my happiness would be huge, right, A million
divided by one hundred is an enormous number.

Speaker 4 (52:19):
It's ten thousand.

Speaker 1 (52:21):
But if you're in that situation as a celebrity, probably
your expectations are very similar to that yeah million they're having.
In fact, maybe you look over there and you know
the two other people in your field, yes, who have
a bigger audience, who have better reviews. You know, like
your comparison set becomes very restricted to the absolute top performers.
And so now you have a million, but you're expecting

(52:42):
two million, and so that's only half of what you're expecting.
That's you know, your happiness is at one half rather
than even being at a comfortable you know, one where
reality meets expectations. So there's something that the ratio has
the nice property that if you double the reality, but
you also double the expectations in terms of happiness, nothing
has changed.

Speaker 3 (53:02):
Yep, yep. Would subtraction not do essentially the same thing.

Speaker 1 (53:06):
It would do very similar, but it wouldn't quite have
that exact doubling property. So for example, let's say that
you're expecting it to make up numbers. You're expecting five
and you have a ten. Yep, if you double both
of those, now you're expecting a ten, but you have
a twenty. So you've a sort of gotten the happier
have you in a ratio?

Speaker 3 (53:24):
No?

Speaker 1 (53:25):
Because twenty divided? So yeah, if you well, we're getting
into the into the weeds. I need to whiteboard to.

Speaker 3 (53:31):
Draw this, okay, and I'm not going to understand.

Speaker 1 (53:34):
It was subjection, so right, I think subtraction would capture
a similar a similar thing. Given that these aren't precise numbers, anyway,
you could probably write the same thought with subtraction.

Speaker 3 (53:42):
Division works. Yeah, As it was preparing for this interview
and thinking about these two equations that I've used, and
here I decided to say what other equations are out
there for happiness? And there was some crazy out of it.
Some Chinese research lab equation that like, I think would
take me literally the rest of my life to try

(54:02):
improve or disprove because it was so convoluted. But their point,
which they then summarize this crazy long who knows what
went into this equation, I just think this is interesting
And they said, well, essentially it comes down to, you know,
reality divided by expectations, except if you take your expectations
too low. That doesn't work either. To suddenly expect that

(54:25):
everything is always going to be terrible is not a
recipe for happiness either, because then I guess you don't
try to do anything and pessimism invades every aspect of
your life. But I just thought it was interesting that
they then had some fancy equation to sort of then say,
but you can't have zero expectation or that's going to
be problematic.

Speaker 1 (54:44):
Yeah, yeah, yeah, I think that's right. And to me
that suggests not so much a shortcoming of the equation itself,
like it's a nice equation. Then yeah, the reality about
of expectations, but actually just a shortcoming of equations writ large,
like equations are not as complicated as reality. Reality is
very complex, and equations have a couple of terms. They're
meant to show us a little a little schematic picture

(55:04):
which yeah, to close the loop actually on Jeevans and
the graph of your happiness that mountain range where I
land on it in the book is that like just
doesn't work.

Speaker 4 (55:12):
It's not right. I like social psychology research.

Speaker 1 (55:15):
So there's a nice set of studies where one of
the things they did is they made people stick their
hand in ice for a minute.

Speaker 4 (55:22):
You know, you're right familiar with this study.

Speaker 1 (55:24):
So you know, you spend a minute with your hand
in ice water, really cold, and then half of the
people that's it. You take your hand out. You've spent
sixty seconds in ice water. You're done, and half the
people you stick your hand in ice water, and then
you get another thirty seconds in slightly warmer ice water.
You know, the original bucket was maybe thirty five degrees.
The next bucket is forty degrees, so it's still still
uncomfortably cold, but not as cold. And then when they

(55:47):
looked back on their experience, the second group liked it better.
They rated that as less unpleasant. They rated that as
like a happier time than the first group did. The
first group thought it was more unpleasant. The conmoments diversity.
The researchers talk about peak end theory that when you
look back on a memory, you're not actually looking at
the whole mountain range. That's not how we remember. We
look at the peak, what was the most extreme experience,

(56:08):
you know, the greatest bliss or the greatest pain, and
we look at how it ended, like what happened at
the end of the day. Yeah, and that actually matters
much more than the specifics of the mountain range, because
the mountain range theory would tell you another thirty seconds
of pain, even if it's less pain, it's still more pain,
more total pain. That should that should be worse. Yeah,
So that's the limitation of you know, again, a little
graph of a mountain range of your happiness. That's not

(56:31):
actually your mood. That's a little picture. One of the
reasons I like trying to spread a little more awareness
of math is that it makes people were able to
call bs you know, like mathematics is often it's simplified.
It's useful, but simplified. And if you viewed as magic,
you can't call BS on it. You can't be like, no,
that there's something missing from that picture.

Speaker 4 (56:46):
And here's what it is.

Speaker 3 (56:48):
I had not heard that version of the study. There
seemed to be a whole bunch where they plunge people's
hands into ice water. I love reading psychology studies. They've
gotten more ethical as time has gone on. You can't
get away with quite what you used to be able to,
but there's still a lot of really funny things. The
version i'd heard of that was people getting to dental
procedure and for the last couple minutes, the dentist just

(57:10):
hangs out in their mouth, don't do anything really particular right.
But you would think that then you would rate the
whole thing as worse because you had a dentist in
your mouth for longer, which is inherently uncomfortable. But the
people whoe are it ended relatively low pain compared to
maybe what it was before. Like you said, they rated
it as a better overall experience. I think this is

(57:33):
also really fascinating because the other thing that I think
factored into this this Chinese paper, in its equation, is
another idea that I'm often fascinated by and that psychologists discuss,
and what they're discussing is two broad ways of measuring happiness.
One way would be to simply like ping you randomly

(57:54):
throughout the day and say how do you feel? Right,
plot your mood on a chart, you know, four seven, one, whatever,
and you just add all that up and basically that's
kind of how happy you are. There's another way of
doing it, which is you actually ask people, broadly speaking,
how happy are you? How satisfied you are with your life?

(58:15):
And those can produce different results, and I find that
sort of fascinating. This equation apparently also tried to take
some measure of that into effect, or maybe it was
a different paper, but it was this idea of they
were calling it you demonic versus hedonic happiness, right, hedonic
meaning moments of pleasure, you demonic meaning overall broad satisfaction.

(58:40):
And I just always think about how you measure those
two things, and there's a lot of debate about which
is the right method.

Speaker 4 (58:47):
Yeah, yeah, that's nice though. That's interesting.

Speaker 1 (58:49):
The right the trying to decompose happiness. So it's such
a vast word with so many meanings that it makes
that that's a good start I think on decomposing it.
You say, okay, right, moment to moment pleasure and then
of life satisfaction and you're kind of the narrative you're
telling about your life, but I'm sure you could decompose
it into many more elements than that exactly.

Speaker 3 (59:08):
I mean, like, no equation solves us as a human right,
It's just it's not possible. You mentioned children earlier, and
that's another one of these weird findings is that they
find that if you measure moment to moment happiness, most
parents will end up with a net negative when they
have children. But if you're measuring meaning and purpose and
overall fulfillment and satisfaction, people will say they will rate

(59:30):
children much higher than that. And so it's sort of
this like what we think we're experiencing versus what we're
telling ourselves we're experiencing, or the story that we're putting
on it, which are not separate from each other.

Speaker 4 (59:42):
Right, They're intertwined and complicated ways.

Speaker 1 (59:44):
Yeah, yeah, may be misremembering this, but I think another
another study along similar lines was that if you ask
parents if young children, how are you doing? How satisfied
are you? You get one answer, but if you want
a higher answer, you just first asked them how are
your kids doing? Okay, they talk about their kids for
a minute, and then and they say, Okay, now, how
are you're doing interesting and just activating that different side
of what they're thinking about. This hard to say because

(01:00:05):
I've read about this for a lot of psychology studies
in the last twenty years to trouble replicating and this
defects generalize, but they still give I think, an illustrations
of intuitive effects sometimes. That's one I can vouch for
that as a parent of young kids. If you if
you ask me, you know, sort of how's my mood
compared to before I had kids, Like you know, day
to day, probably a little rock here, But if you
start get me talk about my kids and then ask me,

(01:00:26):
it's like, oh, I'm going to be glowing exactly right.

Speaker 3 (01:00:28):
It's a priming effect to some degree, right, It's what
it's bringing to your mind. My version of this that
I would play, And this is a story I tell
often that I kind of go back to just because
it was so illustrative, right, was you know, me complaining
that when the boys were like middle school age about
every single day driving them to some sporting event one
or the other of them and finding myself saying like

(01:00:50):
I have to do that, I have to do that
and then finally ultimately realizing I didn't have to do it,
I was choosing to do it. But I think a
version of the study would have been would be to
ask me like, what's your son get out of soccer?

Speaker 2 (01:01:01):
You know?

Speaker 3 (01:01:01):
Or how much does your son like soccer? And I
would have answered that question. Then you would have said like, well,
how do you feel about driving him to soccer? And
I'd been like, I feel great about it, right, Like
it just would have reset my mind in a direction
of something that matters, which is honestly a lot of
what the mental psychological game is is how do you
sort of move your mind from here to over to here? Yeah?

Speaker 4 (01:01:23):
No, that makes sense. Yeah, yeah.

Speaker 1 (01:01:24):
I think something I find from writing about math and
then putting it in contrast with lots of more human
social topics or the social sciences and philosophy, is that
math always gives us this vision of simplicity and you know,
singularity and very straightforward things you can define, and those
are useful, but you need multiple lenses like that. You've
got to move between different models because we are so

(01:01:46):
much weirder and more complex than that, you know, with
each got a city inside our minds of these different selves,
and so how do you coordinate.

Speaker 4 (01:01:53):
Them and lead them?

Speaker 1 (01:01:53):
You know, how to get them to agree on goals
like it helps to adopt a simplified lens for a
little bit, but precisely because it's yes only for a
little bit.

Speaker 3 (01:02:01):
So listener in thinking about all that and the other
great wisdom from today's episode. If you were going to
isolate just one top insight that you're taking away, what
would it be? Not your top ten, not the top five?

Speaker 2 (01:02:13):
Just one? What is it?

Speaker 3 (01:02:14):
Think about it? Got it? Now? I ask you, what's
one tiny, tiny, tiny, tiny little thing you can do
today to put it in practice? Or maybe just take
a baby step towards it. Remember, little by little, a
little becomes a lot. Profound change happens as a result
of aggregated tiny actions, not massive heroic effort. If you're
not already on our Good Wolf Reminder SMS list, I'd

(01:02:37):
highly recommend it as a tool you can leverage to
remind you to take those vital baby steps forward. You
can get on there at oneufeed dot net slash SMS.
It's totally free, and once you're on there, I'll send
you a couple text messages a week with little reminders
and nudges. Here's what I recently shared to give you
an idea of the type of stuff I send. Keep practicing,

(01:02:58):
even if it seems hope. Don't strive for perfection, aim
for consistency, and no matter what, keep showing up for yourself.
That was a great gem from recent guests Light Watkins.
And if you're on the fence about joining, remember it's
totally free and easy to unsubscribe. If you want to
get in, I'd love to have you there. Just go
to one ufeed dot net, slash SMS all right back

(01:03:21):
to it. Knowing when a broad principle of well being
or happiness or whatever will serve you, even of parenting
anything will serve you, like Okay, that's useful, and then
also recognizing when it's like okay, that sort of applies.
But I have to trust myself that that's not useful
here anymore. Yeah, ultimately trusting ourselves. You and I are

(01:03:44):
going to continue for a few minutes in the post
show conversation because I have realized I cannot get away
without knowing about Professor Dogg. That's Professor Dogg to you,
in which calculus vaults a dog to start them, so
you and I are going to cover that in the
post show conversation. We may also talk about how mathematics
makes us want to quantify everything, which we've been doing

(01:04:06):
for the last fifteen minutes, trying to quantify happiness or
expectations or put a number on everything, and you know
what are some of the costs of that. So, listeners,
if you would like access to the post show conversation
we're about to have if you like ad free episodes
as well as a special episode I do each week
where I share a song I love, I teach you
something useful based on the show. Then you can go

(01:04:28):
to one feed dot net slash join and become part
of our community. Ben, thank you so much. This was
really fun. I've enjoyed being in the math world a
little bit for the last week and diving into your
world a little bit. It's always hard when we have mathematicians,
which we've never done before, but I have had visual
artists on before whose drawings are a big part of
what they do, and obviously we couldn't do that here.

(01:04:51):
So I will make a call out for listeners, which
is his books are much better with the drawings than
they may have sounded in you know in our discussion.
So his latest book is Math for English Majors, a
human take on the universal language.

Speaker 4 (01:05:05):
Thank you, Ben, Yeah, thanks so much, Eric, I appreciate
the conversation.

Speaker 2 (01:05:24):
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Speaker 3 (01:05:40):
Now.

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Host

Eric Zimmer

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