The CS Primer Show

- 3D printing dinosaur skulls, where do we begin?
- It's really interesting that there seems to be
a large market for relatively cheap 3D printed
fossil skulls, like a Sabertooth tiger skull right here,
but none of them, at least virtually none of the ones
that I've been able to find are actually to scale.
Sabertooth tigers did not evolve
to fit inside of the requirements
of contemporary three-dimensional printers.
And I spent actually a long time kicking it around online
with people who were making things that looked like
maybe they would be like this before I had to just go
with the oldie but the goodie.
There's a company called Skullduggery, skullduggery.com.
I recommend it to everybody, fell in love with this.
But ours, just like looking over, this sounds embarrassing.
Like before I went to bed at night,
this adolescent boy just like looking over
the Skullduggery catalog, just going like,
oh, it'd be so cool.
Oh, this would be so cool to have,
felt like a velociraptor club.
I was like, now that like I'm an adult
and therefore rich beyond my wildest dreams,
like compared to my nine-year-old self's ideas,
I can afford to invest in something like this.
- I love that it's an investment as well.
This is all just like, it's an asset in your business
and something, and definitely you're gonna get more customers
because you've got a Sabertooth tiger
just like propped on your shoulder.
- Always a question of like, what could I have in the back
that would actually turn people off?
Because one of the things that we try to do,
- Well.
- Is to cultivate like a, it's sciency, right?
Like we're like very sciency, we're very deep sciency,
but we're not just for kids who understand themselves
to be into science.
Like we're into kids who are into almost any kind of thing
because we use the rest of the world
to make science interesting, not the other way around.
- Well, I'm imagining you should put it on a little motor
and have it like slowly turn or do something
and like not even bring it up,
just let it do something in the background.
And then like you could lean into it eventually
and discover it.
And then you're talking like "Pee Wee's Playhouse"
"Zombie" the thing.
You could have a whole interactive series
of dinosaurs back there.
You know what you could do?
You could like put a little actuator on the jaw
and just have the jaw open and close.
And this will be fun if you did it programmatically
based on like a word or something,
a thing that happens in the class.
And when the students figure out what it is,
they'll start triggering it for you.
- You've said the magic word.
Oh man.
- Yes.
- I spent a long time as a kid, like drawing.
I remember how in "Pee Wee's Playhouse"
they had like the little dinosaurs,
the claymation dinosaurs that lived in the wall.
I thought that like I could dig in my bedroom wall
and like make a little dinosaur cave there.
And then maybe dinosaurs would come and live in it.
I don't understand how this knowledge fit with my knowledge
that dinosaurs were extinct.
I avoided science classes as a kid, right?
Like this is like science did not used to be my metier.
So yeah, entirely irrational beliefs about this.
- Well, I was playhouse.
Nobody does that anymore.
- I love "Pee Wee's Playhouse" and "Pee Wee's Big Adventure".
Like every morning I'm like,
why do I not have a Rube Goldberg machine preparing pancakes
of which I will, I don't think he even eats it.
He just looks at it, plays with the face and moves on.
I was like, that's how I want to start a day.
- Watching Paul Reubens eat is nobody's idea of a good time.
- Yeah.
I was gonna say too on the like childhood,
like things with dinosaur bones, I found a, I was convinced,
I found a velociraptor bone in our backyard,
which very clearly, like I brought it back, showed it to my mom
and she was so good to sort of allow me to think
that it wasn't just a raccoon that had removed it
from our trash and put it somewhere in the back.
And I was like building up a diorama
and basically digging up our whole backyard,
looking for the rest of this velociraptor bone.
And I think eventually my parents were good enough
to throw it away, but they allowed me to believe
that I could be my own archeologist back there.
- Was it like a chicken bone?
- Oh yeah, it was like chicken bone from like Thanksgiving.
Two weeks, like two weeks ago, but I was convinced.
- Well, I'm gonna tell you the truth.
Birds are a type of dinosaur.
- Okay, I'm following.
- And there is still some debate as to modern day birds
where they branched off of the dinosaur family tree.
It is not, I believe it is not impossible
that all birds alive today, including ducks
and stupid things like that, are literal raptors.
And frankly, if they're not, like the kinds of theropods
that they descend from would be in most people's eyes
indistinguishable from like, oh, it's a raptor type dinosaur.
It stands on two legs, sharp teeth.
Maybe it does have a big claw on its foot.
Maybe it doesn't and they're smaller, but whatever, right?
So like, yeah, like you, that was a theropod bone.
- I found it, you're right, I found a dinosaur.
That actually completely changes that memory for me.
- You're welcome, yeah. - Thank you.
- Also, at Thanksgiving, we eat dinosaurs.
Sorry.
- Brandon, that reminds me a little bit about your planet,
your blog post about how many planets we have,
which, you know, I don't want to spoil anything about that.
So go read it, go in there maybe, dear listener,
with a preconception about how many planets there are.
And I emphasize the word are there and read the article.
You'll enjoy that.
But what I wanted to ask you, Brandon, in the vein
of how many planets are there,
would you say that birds are a reptile?
Or are reptiles and birds two things?
Like if you open up a science book for kids,
there's a chapter on birds and there's a chapter on reptiles.
Are birds reptiles?
Are birds and reptiles different?
- Yeah, okay, so this gets to the heart
of a lot of what I try to do.
There's a, for your dear listeners, I'm sorry.
Is that like your general term that we-
- No, no, good Lord, no.
We don't even have, we don't have many listeners.
So we refer to them by their first names, usually.
- Hi, Ivan.
- Yeah, exactly.
- How do I say this concisely?
There's a really good, I don't know how to,
so I'll just refer to a really good Slate Star Codex post.
That was my first hit into Slate Star Codex, the old blog.
Now it's Astral Codex 10, famous in Silicon Valley,
by the wonderful Scott Alexander,
called "Categories Were Made for Man,
Not Man for the Categories,"
which points out that, look,
we can define words however we want.
And we need to understand that if we're getting
to a fight about like, well,
the definition of this word is whatever,
like that's a stupid argument
'cause we could have defined it a different way.
And we should define words in the ways that are useful
for what we want to do.
With dinosaurs and birds and reptiles, right?
So we'd say that a bird is a type of dinosaur,
a dinosaur is a type of reptile.
But if you want to play that one out,
you can then say a reptile is a type of amphibian.
And that's actually maybe the most tendentious
of all of these things, but like something like an amphibian.
And whatever that thing is, if we call it an amphibian,
is a type of fish.
That the thing that, we call vertebrates.
We call vertebrates a type of fish, right?
- Right. - Right.
Like I remember in school, I was taught this idea like,
well, like the vertebrates are defined by,
they have a vertebra and they have a something,
something, something, something, something.
Yeah, take all of that and just say like, screw it.
What all of these things are types of fish.
You are a type of fish, I'm a type of fish.
And once you understand that,
you understand how all vertebrate life works
in this beautifully harmonious way
that is absolutely not what you can get to
as long as you are trying to hold this careful definition
in your head of what a vertebrate is.
We understand that like, okay, like all fish,
and this is true of all fish.
- Including us.
- Yeah, yeah, including us, including, yeah, yeah.
Everything on earth, everything on the land
that's not a bug, you know, the slimy bug,
like a snail or something like that.
Or, you know, the opposite of slimy, the segmented bugs,
like a bug, like an insect or a centipede or a spider.
We're all types of fish and we all have these things that we
take for granted.
Like the fact that we have two eyes,
the two eyes are on our heads, right?
This is not true of all animals.
This is not true of most animals.
We have a head, we have a neck, we have a body.
This is true of all of the fishes that exist.
We have, you know, four legs and this part gets weirder,
right, because you can evolve them away,
like whales or whatever.
But you know, every once in a while you'll find a whale
that still has like some little dangly sort of appendages
coming off of where their hips are,
'cause they have those hip bones.
They sometimes have the leg bones just covered in muscle
and fat, and you see out the nose in the middle,
the, oh, the jaw that opens like this, like insects, right?
Like they go, they're like fish, like they go like this.
We're this wonderful big family tree.
And we are stuck, we are stuck with these older definitions
for what a bird is, for what a reptile is,
for whatever, that comes back from when we had no idea
what anything in the world actually was, right?
Like we get this from Carolus Linnaeus, who in the 1500s,
like, oh, I'm gonna go around and use some kind of
common sense.
He was like married to systematic reasoning
to like think through like what all these types of animals are.
And he was the person who gave us
a lot of our modern categories of these things.
I think he was the person who invented mammals,
if I'm correct about that.
But now that we know these,
now that we know the rest of the story,
we understand how everything fits together.
Like it's okay for us to go back
and start understanding that we are a type of fish,
that a bird is a type of fish,
that a bird is a type of reptile,
that we are a type of reptile.
And once you can kind of like rejigger those categories,
that is a cheap, amazing way
into understanding all sorts of nonsense
that otherwise is technical and it's hard to understand.
I'm in a fight with a friend of mine right now,
who, Emanuel, I hope that you watch this.
This is a promo for our next fight.
We are in a fight about whether I should have told kids
that they are lava monsters,
that they are literal lava monsters.
Because if you understand that ice is a type of mineral
and a mineral is a type of rock,
then that means that ice is a type of rock, right?
And you see the glaciers or whatever,
like these layers of the earth.
And then, okay, what do you call a melted rock?
You call it lava.
Well, what do you call melted ice?
You call it water.
Water is one type of lava.
You're 60% water.
You yourself,
you are a lava monster.
To which he responds, I'm talking too much.
He didn't say that, I'm saying that.
Sorry, I'm going meta for a second.
- No, you gotta at least finish the story.
- I suppose that was a terrible place to stop.
- You gotta present the other side of the fight
and then we'll move on to the next, the next fight.
- I think he's going to say something like,
"Yeah, but defining the word lava to include
like the thing that I am drinking right now to make my,
my tea is stupid because if somebody, you know,
says I'd like a cup of lava,
and you give them a cup of actual lava,
their head will burst into flames.
It will be very, things will go badly.
And it's useful to define it in a way
that is not as expansive as possible,
that is not as awesome as possible,
but that it is as lethal-less as possible.
And I feel like that would be a really good argument for-
- Yeah, that's just take off. - Yeah.
- That's taking the safe way out.
I love this idea though, of reach, like telling kids,
it's okay to make your own categories for things.
So I have a two and a half year old.
She loves naming things.
So she wants to know the name of everything.
And now she's trying to get into like,
okay, what is the name of, what does this thing eat?
So that's the next thing she's getting into.
But it also jives with what I remember
where all I wanted was to discover something.
I just wanted to be like, you know,
discover a new bug, discover a new bird.
And I think that's connected to this naming and category.
I think that's connected to this categorization.
And it feels like you're giving me an unlock for,
maybe I should work with my kid
and have them just create their own categorization,
just like you're sort of doing.
You're like, yes, it's probably valuable
that you know the difference between a fish
and mammals and things like that,
but let's make our own thing.
Let's make our own category.
And we're like, you're allowed to do that.
That's sort of like, sometimes I forgot going through school
that like, hey, I'm allowed to do exactly
what these people did in 1500.
I mean, it might not be as-
- Well, you guys will know the Steve Jobs quote
that he gave at the Stanford graduation,
the truth is that everything around you
is made by people who are no smarter than you.
I forget how he ends it.
And you could do that, right?
Like Carolus Linnaeus was a brilliant person.
I rather, I'm a fan of his,
but just because he had his way of breaking things up
does not mean it's the best way.
Although then like, once you understand
these categories, these definitions,
these terms are things that you yourself,
that anybody can do, you can say,
okay, why did Linnaeus do it his way?
Like what is the actual genius that his way reflects this?
'Cause it is, right?
Like mammal is actually a ridiculously important class.
We have conquered the world, right?
We've flipping reconquered the skies with bats.
We are weirdly good at everything as mammals.
Like what is the mammal secret sauce for this?
Not just about, I would say like,
we can like do whatever we want.
That's not what you said, like we can do it too,
but it's this way of saying we can do it too.
The things that we are learned about are not like objective,
are not always objective.
Obviously sometimes they are objective,
but like the terms that we use for them,
the way that we conceive of them
are things that have human fingerprints all over them.
They affect the way that we think about them.
And we can go back in time in our imaginations
and say, what the heck was going on here?
What do we think about this?
It's this wonderful, Egan takes history,
seriously in a whole bunch of ways that nobody else does.
And it gives us this totally different view on the world.
And then his way of teaching
is just to kind of get into that.
- So we'll segue into Egan.
I'm very excited to talk to you about Egan.
And maybe part of that can just be a question
on this topic.
When you were teaching kids,
do you feel like you are, there you go, hello.
- Osh, where's yours?
Come on.
We're back on it this morning, actually.
It's been off for the last few months.
I'm really happy that I chose today to do that.
Sorry, wait, I'm teaching kids.
- Are you actively taking that approach of saying,
I am going to pick a framing for this topic
that is not true, quote unquote, in some ways
that would not be appropriate right now.
Like you are three and don't care about phylogenetics.
And so we don't need,
to know that like reptiles are not monophyletic or whatever.
We're gonna talk about birds and reptiles
as two separate things.
And that's good for now
because that simplifies the storytelling aspect
of what we're doing here.
The like simple contrast and so on.
And the subtlety will come later.
Do you like move, to me it feels like there's a kind of,
not necessarily a ladder of abstraction,
but like a zone of understanding
that's, are you actively moving through that?
Or maybe, should we give more background on Egan's work?
- I think we should, yeah.
- Or do you wanna just answer that question?
- I would also love a background.
You know, I'm new to this, you know,
leading into this convo, I have attempted to read this.
I'm like, I don't know, 25% of the way in.
And in the first chapter, my mind was like,
oh, socialization might not be the best.
I know, it just, I wanna talk about that,
but I'm someone who-
- Brandon's got a blog post, the gist of it being,
that this is not the best place
to start understanding Egan.
But maybe I should just leave that to you, Brandon,
since you're right here.
- If you, I guess I have most of his books
behind me right now.
If you guys have specific, like,
I recommend different of his books
based on different needs of people.
If one is a teacher, there's a particular book
that I recommend.
If one is interested in the history of educational ideas,
there's another particular book that I recommend.
Actually, this one is, I would say, the best opening
one for almost no one.
I did my review of it for the Astro Codex book review contest
because it's like his big giant theoretical one.
So I thought if I do any of them, I should do this one.
I'm happy that I did that, but like,
there are better places to start in Egan for that.
Here, I'll just, if one is teacher,
this is definitely the best of his,
an imaginative approach to teaching.
It's written just better.
I mean, he's not writing for theorists right now.
He's not writing for polymaths.
He's writing for in-service teachers.
And my personal favorite of his is
Getting it Wrong from the Beginning,
Our Progressivist Inheritance.
This is not the political progressivism.
From Herbert Spencer, John Dewey, and Jean Piaget,
where he, I feel like because he's not trying to express
the so hard to express understanding that he has
what education actually is, that he's actually doing,
this much smaller thing.
So he can like unpack it in a very sensible way.
He's not trying to cram too much in,
and it's beautiful and it's compelling.
And I thought I'd give it a read at some point.
With the book, we have a book club that we do
with my sub staff, we're about to start it next week.
We should do this one at some point in the future with them.
That wasn't a thing.
Yeah, yeah.
- No, I like the plugs.
I'm looking forward to the book club.
But I was going to say,
my kind of goal with having you on other than my own selfish
interest in talking to you about Egan,
was to see what our audience,
who are mostly self-taught in some way,
self-educating in some way,
usually continuously so through their careers,
what they could take from Egan's ideas.
So they are teachers in a way,
primarily of themselves and some of their peers,
but not classroom style teachers.
They're not in the system.
They can pick and choose their own way
of approaching a learning goal.
And their learning goals are,
I mean, for some of them,
it's just the edification of understanding things better.
And for some, it's, you know,
understanding their specific fields better,
software engineering or adjacent fields.
And in all of those,
we're constantly looking for better approaches.
And I feel like,
as software engineers,
we sometimes get stuck on the very specific tactical
approaches like this space repetition system or whatever.
And there's generally a lack of a more theoretical
or strategic way of thinking about one's own education,
where it's like, well,
over this extended period of time,
how should I approach increasing my understanding?
What kind of understanding do I even want?
I feel like Egan may have some,
some role to play there
in providing a kind of theoretical framework.
Does that overall,
we should probably should have,
we probably should have raised this with you
before we started recording,
but is that objective of this podcast?
- No, no.
In the initial email that you sent out,
you had said,
you had said this,
which was why I've been so excited,
which is why I said yes,
even though, right?
Like, oh, it's time.
I have no time to do anything.
I'm taking on all these projects
because I had never thought about how does Egan's,
his philosophy approach,
metaphery apply to autodidacts?
Those of us who just teach ourselves everything.
I don't think he ever wrote about,
he was an autodidact.
I don't think he ever wrote about this.
His system is really geared,
explicitly geared toward people who are teachers
and have a bunch of time to like get really,
to really understand something
and then express it to people who are not that interested
in it and make them like bring them emotionally into it.
So I wanna try to explore this with the both of you.
Right now.
And I feel like the incentives for the both of you
ordinarily would be to,
whatever we come up with to say,
oh, this is very good.
Nice job, Brandon.
Like, that's a very good thing.
But I'm more interested in being crucified on the,
my failure, my probable failure
to be able to get a compelling answer to this.
Once we come up with some specifics of what is,
what do we imagine somebody wanting to teach themselves?
'Cause I have some ideas,
but I,
I don't think they're going to be very good,
but in part that's because I,
I think I've been stuck in my head into imagining
how does one teach oneself coding with this?
And coding is one of those things that's like,
I've just never been able to learn.
All my attempts to learn it have sputtered and died.
So my,
I recommend that we come up with a,
a knowledge based thing,
a topic that somebody wants to teach themselves
so they can understand it.
And then a skill based thing,
that some person might want to teach themselves
so they can master it.
- Okay.
Do you,
do you want to give a kind of overview of the Egan
worldview?
Or,
or should we just dive in?
What do you think would be useful for someone
who's approaching this for the first time?
- Let me do a really brief,
ridiculously high level overview.
And then I think the interesting things
will come out in the specifics
of how we explore this.
My realization recently is that Egan
is the only educational theorist I know of
who takes seriously what humans are.
So, right, like,
most educational theorists just sort of say,
okay, like we are these brains
and we have these certain cognitive abilities
and we should be able to figure things out
in a certain kind of way.
That's,
that's too simple,
but it's closer to being true than it ought to be.
And Egan says, okay, like,
we evolved into being humans
through this 3 billion-ish year process,
which gave us these emotional reactions,
that we engage with things emotionally
on a deeper level than we do cognitively.
And we've never jettisoned our emotions.
All of our cognition is shot through with emotion.
So whatever we do when we teach something or we learn,
we probably don't want to just make it a head thing.
We want it to be an entire sort of head things,
obviously long it is all in the head,
but cognition thing, logical thing, knowledge,
dry knowledge thing, it should matter to us.
It should have meaning.
And that comes from emotions.
From our human past,
we in the last 200,000-ish, 500,000-ish years,
depending who you follow,
we have also evolved these specific set
of language-based tools to make sense of the world
in ways that no other animal seems to be able to, right?
Like we spin stories.
We can use metaphors.
We use, I don't know, like rhyme and rhythm
and things like that.
And we can, because of this,
we can paint this understanding of the world
that goes far beyond what we ourselves have imagined.
And humans are better
at telling stories.
We care more about stories,
even when they're garbage stories,
than we do often about like actual correct knowledge
when that knowledge is done really dryly.
So like any kind of education should have lots of emotions
and it should be, you know,
at least use the elements of really good storytelling,
the same sorts of elements that a documentary filmmaker
will use, right, when he or she makes a documentary.
And then, and only then did we evolve these ways
of thinking about the world that we could call abstract,
that we call scientific, that we call philosophic,
that we could call modern, rationalist.
And these things, they're based in emotion.
They're based even in some of the aspects of storytelling.
And so like, that's like the tip of the iceberg.
When we teach, we should do all of these things
because of our specific weirdo evolutionary path
through history to get to the present moment.
Schools assume they're like, oh, everybody, kids are smart.
They can definitely do this sort of modern math,
modern science, modern whatever.
But maybe the fact that everybody sucks at those
so profoundly, not everybody, but really almost everybody,
including people who have like fancy science degrees,
oftentimes do not understand,
they show that they're not able to think scientifically.
Maybe it's because this one weird way of thinking
is a absolutely weird way of thinking, of feeling,
of encountering the world.
And that the way to get to that
is by kind of thinking about the things that we passed by,
the things that we built that understanding on
in the first place.
That's Egan in a nutshell, standing on one foot.
I think I actually have one foot tucked
underneath me right now.
And the other one is lightly touching the floor.
So it literally was, I think, Egan on one foot.
Still too long and whatever, but okay.
- No, no, so that makes me think,
I'm thinking through something specific.
And one thing that we can maybe, maybe Oz, you have
a different idea, but as a working software engineer,
you often sort of enter as a typically like front-end
engineer or full stack.
So you're like making websites and things like that.
And that's how you can kind of break
into the field typically.
And then you do that for a little while and you,
and what typically happens is there has to be
something more to this.
The work starts to get a little bit repetitive typically.
And then you try to find some subdomain or some area
where you can go deep beyond the frontier of knowledge.
Maybe that's in databases, maybe that's in networking, maybe that's
in AI.
And if we wanted to get specific, a lot of people are thinking
like, oh, could I write my own neural network?
Could I work for an AI company?
And in many ways, they've abstracted it away that any,
anyone can sort of easily use these simple libraries and use
a neural network, but to actually write one,
then I have to know linear algebra and math.
And when I've encountered it, I've sort of looked at that.
I didn't learn linear algebra in school.
So then I'm like, oh, it's based on I better go further back
and go all the way to algebra and go all the way to basic
arithmetic.
And then that's my mental map.
It's like I have to keep going all the way back to like scratching
things on a chalkboard.
And then only then will I be comfortable to go to that level.
So that's one maybe specific context.
And the other thing, your overview, your one-legged overview made me
think, which I think you touch on in your blog post, is that what
you're describing, the sort of story-based, emotional, that's like
the complete opposite of a linear algebra textbook.
And e-commerce, they figured that out.
They're using lust, envy, greed.
They're using stories for movies.
Like e-com's got to figure it out.
Instagram feels fairly egonized to me.
But when I open that linear algebra textbook, unless it's written by
someone with a sense of humor, there's no stories.
There's like maybe reading comprehension puzzles, which are just like
masking the equations I'm meant to practice.
But I look at that and that doesn't touch on anything that you're
describing for Egan.
And that's probably why I never made it through the textbook.
At least now that maybe this is giving me an excuse.
For never having made it through that textbook.
Yeah, textbooks suck.
Textbooks ignore all the tools that people have figured out over the
eons to make things meaningful, content-rich, interesting.
And they just ignore all of those and say, let's give you the facts.
What's ironic is they try to simplify in order to make it easier.
But oftentimes what they then cut away are the things that make it easier.
It's weirdly easier.
To learn an example of this is the names of the planets.
It's easier.
You know, the names of the planets thing, because I think I mentioned it
in that blog post, maybe it was in a footnote or something like that.
But do you guys know the whole like the rationale behind the names of the
planets in order?
There was like a mental game, my mother something.
So there's sort of like there's like a PEMDAS thing.
Yeah, yeah, yeah.
I can't remember.
it but i i've memorized that one before yeah um someone pointed out to me a few years ago that
mars his father is jupiter mars is aries right just the latin version of the roman version of
the god of war which is why it's red it's supposed to be covered in blood i thought it was covered
in blood um and then who's the father of aries the father of aries is zeus zeus is jupiter right the
roman version again because we named the planets of the roman versions zeus pater father zeus zeus
pater is just about that jupiter jupiter jupiter right jupiter for you who was jupiter's father
who's zeus's father it was uh bronis chronos that god yeah yeah exactly right so there there was no
roman chronos so they had a borrowed obscure deity um saturn they had a scythe kind of like it or
something like that got a minor harvest god from turkey if i'm remembering correctly um uh so but
anyway like jupiter's father supposed to be chronos who is chronos's father gaia mother
mother who did gaia mate who'd guy who'd guy have sex with to uh to make it's in i have that
delayers book of greek myths and i i there's a big beautiful picture but i can't remember
guy's face is uh all um all done by oh no guys the earth and then the father's face uh uranus is a
greek uranus uh yeah uranus whatever you want to say right i remember his face then his stars in
that book i like that book yeah um uh but uh so it's it's uranus okay so uranus is after
saturn and then the next planet when they found it william herschel found it in 1805 or something
like that what did he name it because uranus didn't have a father uranus is one of the original
two gods him and guy again um so he named it george named it george after the king of england
at the time because he wanted the king to give him money so the final planet was supposed to be called
george yes but my understanding is that was the french were like nope
nope nope no not gonna work nope um sorry that was all a stupid illustration attempt to illustrate
the idea that it is weirdly easier to learn both the names of the planets in order yeah and this
story of uh of greek creation epics than it is to learn either of them by themselves like it's just
like story forms and like with this like this ridiculousness of the planet george and then he
went with zeus's brother neptune right like um uh the ridiculousness of that story actually makes it
easier it makes it more memorable even though it's more information we we we we try to boil
things down and we make it harder because of this yeah mathematics seems like the the absolute
the end stage of that phenomenon where you pick up
a book and it's like here are the axioms and here you know here is the minimal proof
from the axioms to get to here and like there's nothing extraneous there's definitely no
storytelling uh but even just like verbal filler of like why do we have these axioms how do we get
you know let's have let's have a conversation about the different ways that you might have
trust in this this this conclusion other than the formal proof or whatever uh it seems like it just
makes it incredibly hard unless you have taught yourself or been trained to pick up a book like
that and approach it in a particular way it's useless to you because it's so it's so far against
and it feels like undergraduate mathematical education is primarily about uh bringing people
into the fold of like what you know they call rigor or something but it's really about like
communicating in a format um that is devoid of other ways of human understanding
it's like our form of understanding is very specific here we don't do the other kinds of
understanding it's i'm like one of my current obsessions is um the history of where greek
mathematics where our modern mathematics comes from fantastic um in the in the answer is turkey
uh the island i think it's an island of ionia off the coast of turkey part of the greek one of the
greek cities sorry i only has the name for that whole area um malik malik is malik malik malik
melita uh yeah thank you um uh that uh and you can like look to see historically like what the
heck is going on when this very small group of people had this phase change and i i really
thought that this was blown out of proportion until i started learning the details like this
had this phase change of how to understand the world um and uh and so i've been interested in
like where where
they're this way of doing math how that comes into it because they also reinventing science
and they were also inventing historiography and all this sort of fun stuff political theory
philosophy in general um and the place that it looks like they got their math from was from
astrologers who had been in babylon but have been kicked out of babylon because cyrus the great
who's a zoroastrian
and had no time for this astrology nonsense um he fired them and so they have no other
way of making a living they're wandering around the area they are you know trying to apply their
trade to um they invent personal horoscopes um uh because now they don't need to predict the affairs
of state they can just predict the affairs of an individual so they've got horoscopes to do this um
but they've been trained in all of this careful mathematics in order to keep track of where the
stars are in the sky and where when certain astronomical phenomena are going to recur
because then they can predict the future because everybody knows whether
comet coming to the heavens or something like that portends great doom or great fortune or
whatever um and and so the greeks the greeks come into contact with this as these men on the road
telling math riddles and then challenging one another with these riddles
and you can figure out like almost any of these riddles but this is like sort of like
lower maybe a fourth grade sort of geometry sort of stuff this is like not hard stuff by our by our ways
but what they put a value on is how ingenious i mean can you figure out the answer but also like
how do you get to the answer how clever is your answer and you could you know any kind of math
problem you can brute force bruce root i can't say those are brute force it's you can like have an
insight where you go oh my gosh i can't yes this other thing you can take something you learn from
another field of math you can apply it in this really weird way to this um you can just like step
back and like come up with a new definition that allows you to crack the entire thing open but like
it was from this riddling these games that our way of doing modern math which is like really abstract
and which is really simple it prizes simplicity above all else um uh where it comes from
but we we miss the fact we forget the fact that it comes from this context of like what are clever
ways to solve this simple riddle and we just say okay here's a way do the stupid way memorize the
stupid way do it this way we've taken the art out of it because we've taken it out of its context
and just taken the i mean i don't want to say that everything that we do in math education is bad it's
not but um but yeah yeah oh this is like a this is a reframing of typical coding interviews so
maybe you've seen it or maybe heard about like when you're trying to be an engineer at facebook
or something like this you're given a like a basically a puzzle and they're like do this on
the board code on the board and more often than not like the brute force isn't going to get you
through that interview but you have to get there so you sort of first do the brute force force
iterative thing you go through you're trying to you know check if a
particular string is a palindrome or something and you might kind of go through it iteratively
maybe twice or something uh and then you're like great but i'm looking for something that can do
this uh you know in one pass or something like that and then you're like crap so as an engineer
you're super stressed out about finding this but if it was more like bar room having fun
like riddles with travelers maybe that's my sort of reframe uh motif to go into the next round of
interviews and just pretend i'm coming from uh ancient babylon and uh i'm trying to do a
impress some greeks this is one of the things that i mean i don't know if this is useful advice
um for coders but maybe for coders who have kids and want to raise their kids in a riddling sort
of context they're good books that are just collections of clever riddles that you can work
out and some of them are math some of the books from the collections are mathematical and some
of them are not um there's a man named robert smoylan smoylan um who wrote a number of different
collections of riddles my favorite is uh the riddles of shahrazad i think is the title of it
something like that um and when i my wife and i used to run an elementary school classroom we
would every week just like take a really nasty one from that and we'd put it up on the wall and
just be there that's it right anybody could like try to futz with it or not and it's just like a
trying to create a culture of people who valued who enjoyed who enjoyed solving pointless
pointless problems that valued cleverness that that was not the most helpful thing
that we ever did the kids frankly there was not with the kids that we had like a
particularly great connection there um if i had continued to teach there i think i would have
modified that you had you had the janitor every day was solving it like matt damon and you're like
dude we get it okay how do you like them apples yeah we call that nerd sniping in the software
engineering by the way when you get a problem that's like really just just a a thing on the
wall that you can't avoid anyway i tried to get my work done but there was a problem on the wall
yeah so i think the the the way that i want to try and connect this back to
autodidacts is in a context where a lot of really useful stuff is uh in a form that that does not
recognize this diversity of approaches to understanding where we do have very good textbooks
when good is measured by how far it's gone down this path of say distillation into a simple form
one way to approach that maybe and maybe linear algebra is a reasonable intersection between our
like areas of familiarity for us to talk about that would that be reasonable brandon as a as a
kind of example not at all no no no okay i i think linear algebra sort of sits in my head is like the
scary thing that i'll never oh okay well let's let's get away from it i got an 800 on the gre
so i can like deal with middle school math and anything below it really well but nothing above
that nothing above high school math at all okay well i'll find those smart things i'll find i'll
find that yeah well maybe we can talk about it generally so like so let's say this is a topic
that you're trying to understand or some like equivalent topic a technical topic uh you know
we could also talk about operating systems or something but maybe linear algebra is at least
a bit more approachable as a concept than that but you we've got textbook in this area we've got 100
of them uh whether it's operating systems or linear algebra or or whatever the mammalian
physiology went on uh you we could look at this and say hey i understand based on my appreciation
of egan's framing that i would like to approach this topic in a way where uh i'm i'm compelled
to continue with the process i would like to retain information from it i would like to
enhance my excitement around this and adjacent topics but the textbooks available do not do that
for me they have a piece of this does that mean that i should look at this spectrum of textbooks
and say well i want to take this one rather than that one like in linear algebra specifically
you could take gilbert strang the mit professor who's got a fantastic textbook but it's
dry it's like very distilled but you need to be in the mode of taking on something distilled
or you can take something like coding the matrix
which is also a linear algebra textbook also used in universities but its orientation is
that you are writing programs which code the matrix which do like interesting things with
graphics and you know instead of like gilbert strang presenting with you with a um like a proof
about a transformation of a matrix sorry we are getting into specifics here aren't we but hopefully
the following one instead of strang which gives you the proof of this coding the matrix says i
challenge you challenge you challenge you challenge you challenge you challenge you
to write a program that would rotate this image uh and by doing that you so you know you got a
kind of spectrum of textbooks you could choose from or would you like take strang and say i'm
using strang for this type of understanding of the material and then i need to supplement that
myself as an autodidact with the storytelling with the hey maybe there's a somatic understanding
of linear algebra as well uh you know maybe maybe that you're going to bring your own ironic
understanding of linear algebra and you need to like a la carte piece together the modes of
understanding of this and just see the textbook as never being able to be the full way of
understanding the material but like fitting in a piece does my my overall like my challenge
to you brandon is like as someone who is in a world where there is good pieces do you like
do you build up a um a skill of identifying the things that cover more of the surface area
of what's going to be good for you as a learner or do you build up a skill of like just doing your
best with what's available and like filling in the gaps yourself or do we need do we need to reinvent
everything and encourage people to write textbooks that tell stories something i mean i think that
that there's a lot of money to be made in that at least potentially so i think that we should
encourage me i one of the things that would make me very happy is if i was able to ever work with
somebody who's trying to come up with a new type of textbook uh and attempts have been made at this
before uh some more successfully than others uh daniel williams book on cognitive textbook on
cognitive psychology um is a really is a really good one for that and he does just some very basic
things but they're very good um like for example he frames everything just in terms of simple
questions and answers so every chapter you know there's a theme or whatever some piece of uh
cognitive science um research but then um every subsection heading or whatever is a
simple question and then you read to find out the answer which is just amazing i would say that
there actually though is a potential way of bringing those things together that did not in a
very organized way that did not exist um i guess maybe it's about a year old now of course i'm
talking about llms um where i know that now you know when i'm like walking my daughter
on a like a little mile hike or whatever just so she falls asleep and i get some exercise
um one of the things i used to just listen to podcasts and i still listen to podcasts but one
of the things i also do is try to just talk to chat gpt um which because i can just ask anything
right with my earbuds or whatever in and i can talk and it can give me this nice little answer
there and i can go deeper and whatever in it i've heard of people tyler cowan mentioned somebody who
he's reading i don't know likeness or something somebody really heidegger or somebody really hard
um and he would just have chat gpt on so he could ask an in real time question about what is heidegger
what might heidegger mean when he says this and it'll give him immediate feedback so what i'm
wondering is can one take and get one get the best of both worlds if you take the hard text by the mit
so i'm going to go ahead and read the first question and then i'm going to go ahead and
read the second question and then i'm going to read the third question and then i'm going to
read the third question and then i'm going to read the fourth question and then i'm going to
read the last question and then i'm going to read the last question and then i'm going to read the
last question and then i'm going to read the last question and then i'm going to read the last question
and then i'm going to read the last question and then i'm going to read the last question and then
i'm going to read the last question and then i'm going to read the last question and then i'm going
to read the last question and then i'm going to read the last question and then i'm going to read the
last question and then i'm going to read the last question and then i'm going to read the last question
and then i'm going to read the last question and then i'm going to read the last question and then
but in my ability it from its ability to put things in a way that my brain can understand
because of course the way that chat gpt's natural language is
horribly boring hr speak um monstrous it is an impediment sometimes to understanding
it's terminologically high but you know like my base model for chat gpt now is issue
complex vocabulary speak as if i were an eighth grader make your sentences short and punchy i
don't know if you've seen this round there's a new thing going around twitter where if you tell it um
that you don't have hands or something you know it will actually when you ask it for coding it'll
give you like here's one example and then it comments out the rest if you literally say i
can't type it says oh i'm so sorry for you and it gives you the full answer so people are like gaming
it in super weird ways um yeah so look into that one so what i have been finding is that when i
have something really hard and i want i wanted to explain it to me in a way that will intuitively
make sense to me i'll say give this to me as a limerick or i'll say which is just it's weird
right like it's goofy and it's oftentimes the limericks don't quite rhyme the way that a limerick
you want it in your guts to rhyme um but it gives
it to you in a punchy way that is short and then i can go huh and because it was a poem you know
other there are other obviously poetic forms rather than um than limericks um but uh but
because it's in a poem now it's sticking in my head while i'm you know walking around the block
and i'm kind of puzzling over what do i feel like how do i think about that what do i still
not understand about that um another way that i can
uh that i've done it is give this to me in a simple story but maybe the most helpful thing
for for linear algebra actually i like this because i don't really know what it is
um is to say okay like i'm learning about this thing here's this one
you know algorithm give me act as a excellent storyteller who uses emotional binaries and vivid
mental images and uh delightful metaphors uh in your storytelling um tell me the story like where
did this algorithm come from and then why like what was this person trying to do with this
algorithm like what is what is the actual historical function of this thing which again
seems on the surface like it should just be extra information that is just going to be
harder to remember except with with my experience of all the science stuff that i
that i prob it for and sometimes math stuff too um it's not more information it's the information
that makes the thing that i'm learning suddenly like even oftentimes conceptually click
why did she use this phrase why did he use this term to denote this sort of thing
what might you even guess oh dear chat gpt that she was trying to do when she said that and you
know for our sake it doesn't even so much matter if these things are historically correct
or not um it matters that they are emotionally viable right and you know 90 of the time it will
be correct um and you'll you'll end up learning oh it can i say brandon sorry to interrupt but it
won't and nor will the stories that the teachers tell and i've got a fantastic book for you on on
that uh in a minute if you'd like but let me say like this historical narrative thing i think when
we think about what's going on in the world today we think about what's going on in the world today
we think about what's going on in the world today if we think about what's going on in the world today
we think about what's going on in the world today we think about what's going on in the world today
we think about what's going on in the world today we think about what's going on in the world today
we think about what's going on in the world today we think about what's going on in the world today
we think about what's going on in the world today we think about what's going on in the world today
we think about what's going on in the world today we think about what's going on in the world today
we think about what's going on in the world today we think about what's going on in the world today
we think about what's going on in the world today we think about what's going on in the world today
we think about what's going on in the world today we think about what's going on in the world today
we think about what's going on in the world today we think about what's going on in the world today
um can i push my uh just can i push for that because i remember in math it's like uh integrals
or something it's like measuring that we needed to do this to measure the area of a curve or what's
under the curve and they probably gave me some that i'm like great that'll be useful next time i have
something area under a curve which is never in my young oh yeah yeah i mean with i i feel like
i can do that with adult students who come here voluntarily because they already have motivating
problems yes in the in the in the general area and all i need to do is connect that like bridge
that to this specific technical knowledge it's like you had a bug you're trying to fix it you
couldn't do that now you need to know more about operating systems including this virtual memory
system but you know so follow me even on this journey for this one class that you're motivated
to take because of your like professional interests um i still need that that hook for that
one yeah yeah it's like oh this is another example brandon it's like uh some data some api call on
your website is looking really slow and it turns out like looking into the database and
understanding you need to add an index which is a more efficient way of looking things up
and then like that solves the problem and then if you present
that to oz if he's like has anyone had like a slow query every person raises their hand
and then oz can go in and explain how an index works and like why that matters and
you're right the hook's already there because i felt the pain which i was also thinking
you know with volume of water and stuff if i was in that situation in die hard two or three where
the bomb's gonna blow if i don't put the water in the different jugs and everything maybe i'd care
about how to calculate volume and so i don't are you familiar with that scene is that a class that
we've been talking about for a long time yeah yeah yeah i think it's a dynamic you can solve
it with dynamic programming but that die hard problem sorry sorry sorry for the tangent yeah
i just nerd sniped a few listeners as well do not go and watch the die hard scene where he's pouring
jugs of water and then try and find a dynamic programming solution to that don't do that keep
listening please all right so i think that's it for today thank you so much for joining us
all right sorry what i was gonna what i was gonna say i was actually going to watch die
hard 2 with my kids last week and uh we something came up and we ended up watching something else
but now i am going to watch die hard 2. no no no stay don't hang up don't hang up we're gonna i've
got more questions uh yeah so this okay one thing that i was going to say about that i developed
that habit for myself only after i started using it for teaching only recently like in the last
no no no the the finding the historical context of every problem uh like i got to the age of 30
or something um before i recognized that for myself i need to know why something is the way
that it is in order to internalize it including very technical things including things that are
otherwise motivated like i'll be fired if i don't know this i still need to be like all right so
i'm gonna go ahead and i'm gonna go back and i'm gonna go back and i'm gonna go back and i'm gonna
go back and i'm gonna go back and i'm gonna go back and i'm gonna go back and i'm gonna go back
and i'm gonna go back and i'm gonna go back and i'm gonna go back and i'm gonna go back and i'm
gonna go back and i'm gonna go back and i'm gonna go back and i'm gonna go back and i'm gonna go back
and some people voted this way and some people vote that way and then we ended up here and
that's why this language this programming language has this feature or whatever okay now
i am allowed to have that in my brain um firstly how can we maybe maybe firstly firstly
how specific is that to the individual like do i have is it you know just everyone has these
five modes of understanding and we all have them in relatively uh in in in generally equal amounts
and like we can understand brains generally this way uh or is it very specific to the individual
i don't i'm not talking about learning styles the you know tm discredited thing i'm i'm talking about
like uh can we generalize from one one person's effective learning to other people's
and secondly either way can we expedite that process so that
we can expedite that process so that i learn that i learned that about myself
i learn that i learned that i learned that about myself
i learn that i learned that i learned that about myself not at the age of 30 but at the age of 12 or
not at the age of 30 but at the age of 12 or
not at the age of 30 but at the age of 12 or something
something
something and my whether i'm using an llm or i'm
and my whether i'm using an llm or i'm
and my whether i'm using an llm or i'm using my own neural net to like
using my own neural net to like
using my own neural net to like decide my own learning resources or
decide my own learning resources or
decide my own learning resources or whatever
whatever
whatever um
um
um how how i can get that for my whole
how how i can get that for my whole
how how i can get that for my whole learning experience in school teaching
learning experience in school teaching
learning experience in school teaching myself whatever as a teenager as an
myself whatever as a teenager as an
myself whatever as a teenager as an adult
adult
adult i feel like you put your finger on the
i feel like you put your finger on the
i feel like you put your finger on the most important thing which is to
most important thing which is to
most important thing which is to understand why is this important
understand why is this important
understand why is this important um i mentioned
um i mentioned
um i mentioned before the three billion year
before the three billion year
before the three billion year evolutionary history of our species
evolutionary history of our species
evolutionary history of our species and
and
and what do bacteria
what do bacteria
what do bacteria what can we even say about bacteria
what can we even say about bacteria
what can we even say about bacteria cognition
cognition
cognition it's that whatever information processing
it's that whatever information processing
it's that whatever information processing evolved before there were brains before
evolved before there were brains before
evolved before there were brains before there were neurons before their uh
there were neurons before their uh
there were neurons before their uh before there were specialized cells
before there were specialized cells
before there were specialized cells was that
was that
was that those general cells these bacteria archaea
those general cells these bacteria archaea
those general cells these bacteria archaea sort of uh thingamajiggers um they
sort of uh thingamajiggers um they
sort of uh thingamajiggers um they lived in a world full of death
lived in a world full of death
lived in a world full of death and they needed to they were you know
and they needed to they were you know
and they needed to they were you know they replicated quickly and they were
they replicated quickly and they were
they replicated quickly and they were almost destined to die without
almost destined to die without
almost destined to die without replicating again
replicating again
replicating again um and uh and they needed in order to
um and uh and they needed in order to
um and uh and they needed in order to survive they needed to be able to
survive they needed to be able to
survive they needed to be able to process information
process information
process information at the beginning of the history of
at the beginning of the history of
at the beginning of the history of thinking is
thinking is
thinking is danger
danger
danger is this adventure where you need yeah
is this adventure where you need yeah
is this adventure where you need yeah yeah you need to understand what's going
yeah you need to understand what's going
yeah you need to understand what's going on um
on um
on um what am i trying hold on i i feel like
what am i trying hold on i i feel like
what am i trying hold on i i feel like in my head this was actually naturally
in my head this was actually naturally
in my head this was actually naturally connected to the idea of why that you've
connected to the idea of why that you've
connected to the idea of why that you've been talking about needing to understand
been talking about needing to understand
been talking about needing to understand why i guess i guess because it's it's
why i guess i guess because it's it's
why i guess i guess because it's it's why not just like why am i doing this
why not just like why am i doing this
why not just like why am i doing this right now but like why
right now but like why
right now but like why well i guess
well i guess you'd understand like okay the answer
you'd understand like okay the answer
you'd understand like okay the answer to why i am doing something right now is
to why i am doing something right now is
to why i am doing something right now is always because if i don't disaster will
always because if i don't disaster will
always because if i don't disaster will befall me you know
befall me you know
befall me you know in some way or another why was this
in some way or another why was this
in some way or another why was this invented in the first place well because
invented in the first place well because
invented in the first place well because someone was facing something like
someone was facing something like
someone was facing something like potential disaster and they wanted to
potential disaster and they wanted to
potential disaster and they wanted to create something in coding or in
create something in coding or in
create something in coding or in algebra
algebra
algebra that would help make everything easier
that would help make everything easier
that would help make everything easier help
help
help allow them to flourish um asking why
allow them to flourish um asking why
allow them to flourish um asking why is identifying what problem
is identifying what problem
is identifying what problem a thing was trying to solve what danger
a thing was trying to solve what danger
a thing was trying to solve what danger what threat there was that this thing
what threat there was that this thing
what threat there was that this thing was the solution a potential solution to
was the solution a potential solution to
was the solution a potential solution to seems like the least
seems like the least
seems like the least individualized
individualized
individualized aspect of minds
aspect of minds
aspect of minds possible
possible
possible it seems like it's the thing that we
it seems like it's the thing that we
it seems like it's the thing that we share with manta rays and fungus and
share with manta rays and fungus and
share with manta rays and fungus and bacteriums
bacteriums
bacteriums um
um
um to ground it in in the sense of
to ground it in in the sense of
to ground it in in the sense of threats and salvation
threats and salvation
threats and salvation um
um
um so i'd say that no i'd say probably
so i'd say that no i'd say probably
so i'd say that no i'd say probably everybody should do that
everybody should do that
everybody should do that okay done
okay done
okay done uh
uh
uh can i just like close the circle on the
um the thing that I was going to say about all this being wrong chat GPT is allowed to be wrong
because so so yeah I wanted to yeah there's a book I just read called the cult of Pythagoras I don't
know if that's a tempting name for a or if you've encountered it before maybe if you're going into
the history mostly not on the cult of Pythagoras no no it's not it's not yeah yeah yeah yeah yeah
it's um uh I picked it up because I was like oh I want to learn more about cults and and mythology
in in mathematics and um there's like there's very little on cults there's almost nothing on
Pythagoras and um there is a little bit on on on myth uh but what's interesting I mean what the
book is good at in particular is looking at the historical record in relation to stories that are
commonly told in mathematics in the history of mathematics which are also incidentally very
commonly used by people who are trying to motivate mathematics they'll be like here we're going to
talk about
irrational numbers now there was this guy who was part of the cult of Pythagoras who was drowned
whatever and it's all wrong uh it's all wrong but it's been perpetuated for this this time and the
book is good it has actually has a table of all of the you know the the meaningful accounts of
this and how they've evolved over time it's like remember that table yeah yeah uh and um and so
it's um it's it's good it's it's kind of a buzzkill for all of the fun stories that we like
to tell
um as math teachers I guess uh to motivate this stuff and um you know that's his objective and
he also is the point it doesn't matter if it's true us bad I mean I think to him it does matter
to the author uh it's like the historical record doesn't justify what we say about this
um and I was hoping that he would explore more this idea that maybe it doesn't matter because I
mean that's what I've been thinking about recently in the context of Egan like the storytelling is
important and truth is also important like the finding of truth is also important but maybe it's
important at other times for other people or in different ways and uh as educators including self
educators maybe we should be better at like enjoying the story knowing it's a story uh like
seeing how this fits into the historical motivation for other people even if the story was
wrong should be interested in this as well or even just
um saying if it's totally made up who cares if whether there was a person or not at this time at
this period of time like let's just imagine that you're part of a cult and you really believe that
all numbers were rational and someone showed up with this like how would that make you feel maybe
that's that's a valuable thing as like you're saying Brandon an emotion and an emotionally
evolved being to actually have that be part of the experience of learning something where we
do progress out of that and um want to be able to
to get into a mode of thinking where we don't have the emotion maybe that that might cloud us
but that the but that the wrong story is actually valuable along the way
I mean I think you're doing a great job of laying out the pluses and minuses uh to um the false
stories that are very memorable and help us get interested and actually understand some of these
things better I think that I I think a lot about this uh just from the perspective of teaching
history which is the thing that
I've actually I'm actually professionally trained to do um of there's so much great history that's
probably of dubious historical value and what do you do with that like do you tell it so then
you can untell it later and it's interesting to untell it and um I I think the sort of easiest
um uh compromise position on this would be to say that one story about George Washington one story
goes as such and then we can say ah like you know maybe maybe not probably not with this one maybe
with this one uh you know I don't know you can look this up if you want most kids most people
won't look it up they don't get it they they they they want to they want to keep Santa you
know they they want to they want to keep their stories and that's fine um I will say that um two
things and one of them is specifically on the idea of cults because I think I have a good idea about
um uh it's cult related um for auto didacticism but I wanted to recommend this book um it's it's
well I knew you were gonna do that when you started talking about the history of mathematics
in that in that way but sorry not to interrupt your recommendation I had this in the bathroom
earlier so actually it's um it's a universe it's a Princeton University Press and uh it
goes through like here's how they derive these things um but it vacillates between that and
really great stories
um of some of these things um and uh he points out that sorry can I first just uh some a lot of people
are listening to this and not watching so I will say it's a new history of Greek mathematics reveal
nets would that would that be the pronunciation of the author's name yeah um he this is this is this
is the book that Tyler Cowen last year is after reading a few pages or something now I'm making
up stories after reading his he
was like I'm one chapter in and it's clearly the best book of the year sorry he actually included
it as his uh in in his like official best books of the year list oh I may I may have missed that
in the best books of the year yeah as he was reading it he was like yeah I'm just a few I'd
be like five words in and it's definitely the best book I've ever read it was like sixty dollars or
something like upon like because I was interested in the topic and like upon his recommendation of
that like bye bye yeah um one of the things that this points out is that there's that story about
Pythagoras when he discovered the um the Pythagorean theorem uh that he was so happy that
he sacrificed 50 Bulls to the gods and how that that was definitely meant as a joke story like it
was never supposed to be true because the one thing that everybody knew about Pythagoras is
that his cult was a bunch of vegetarians so the idea that he'd be so happy and sacrifice 50 Bulls
to the gods right I remember telling having told story students that story before and then like but
then I would like
also like remember every once in a while wait a second I said he also a vegetarian this is this
is really weird um I would say but having to do with cults okay so one way of understanding
what Egan is talking about um when it comes to really academic heavy analytical disciplines
is that these things usually arose as specific movements that were
uh this next part is my innovation that we're trying to mend the world I'm thinking specifically
of economics like economics there's a really good book in economics that I can never remember the
name of um that talks about the early history of economics there's a bunch of people saying like
wait a second supply is is it supply or is it demand that runs the world if we could figure
this out maybe we could fix all of society and banish poverty forever and um and it was from that
that you get all these really technical wonky
um sort of uh um economic understandings and and what am I saying and that
that's happening right now with uh large language models or with AI more broadly just by the way
there are cults forming around very technical topics and like it's like so thank you because
these things start as cults and they start like with cults that are trying to change the world
um and they have like their own values they have their own in speak they have their own all of
these things
um Egan's one way of putting Egan's major insight is that like human minds are not atoms that we we
go really wrong when we look at individual Minds ability to understand the world you guys uh probably
know the researcher um Joseph Henrik in his book The Secret of our Success and the weirdest people
in the world and his big insight from there is that why is it that people from some cultures have
disproportionately invented like all of mathematics or all of philosophy or all of the certain kinds of
Sciences or whatever
and this whole thing is like it's not that the people that the individuals are so smart is that
there's something going on socio socio-culturally where these minds are finding ways of connecting
together and it's not like you have whole countries connecting together or anything like that it's that
you have relatively small networks of people forming really tight and I'm not gonna say
tight communities tight cultures it's just like the seniors I think is the term it's like genius
in a scene I feel like that's oh that's a great word I didn't I didn't make up I didn't make it
up I think it's uh it's cropping up in the Twitter sphere seniors yeah okay so you want to make it you
want to you want to find your scene you want to find um a group of weird individuals who are
trying to achieve something and you want to be part of that group and not just like
use their insights but like be part of that group because that is the thing that will motivate you
and you will just casually pick up on a lot of like the nascent ideas and the thick under and the um the
hard understandings um that are going on there the terminology becomes second nature to you which is
you know a a neat way of saying that is you want to join a cult then you probably want to get out
of the cult well this is what companies want this companies want to be a cult they all wear the same
logo t-shirt you hope that you know people are idly having to shatter and some in some cases it
does we love Oz and I always talk about Bell Labs Hamming's article um you and your research doing
great work and he's like
like look keeping the door open that yielded some pretty good results um yeah so I just I just want
to maybe we can start a cult now um uh but it is tough over like online to sort of figure out the
cults um to figure that out remotely yeah kind of related to that actually and this is just maybe
another general piece of advice for for we autodidacts um to pick fights or maybe to find
fights like when you join
a community that is really interested in a certain thing ask for what are the fights that are
animating the internal fights that are animating this community not like our fights with the rest
of the world that show that we're smart and the rest of people are just drooling cretins but like
what are the things that people are like vociferously divided about that no one outside of
this group would understand in any way um uh because in that in those fights right you will
get so much motivation
um just
naturally um and uh you'll be able to get smart fast about something now that's probably hard when
we're talking about something like linear algebra probably well trodden no more vicious fights going
on there um but for something like llms uh probably more 3D printing I don't know there's that xkcd
right all communities are riven with stupid factions um uh and this this nested fractally uh
uh it goes on it goes down forever so find all of the fights that you can find and that will gin up
the motivation to get good in that field but I mean is the idea that you find the fight that you
care about and ignore the others no no you just like you just engage in all the fights you don't
know what you'll care about at first right you have to pick your fights uh obviously um but like
I'm trying to think
like
like in what's the field that I know something about I don't know in paleontology right like
it's my bona fides I realize right now that I'm oh yeah I was supposed to wear this the gym today
oh sorry uh for people who are listening to this I happen to be wearing a Jurassic Park shirt I'm
gonna leave my my official teaching sweater um but you know like for a while it was like our
dinosaurs warm-blooded or cold-blooded um what killed the dinosaurs which is actually kind of
a live debate now still I'm friends with mostly some people in the asteroid camp but I'm weirdly
tempted toward the volcano camp um because if it's insofar as it's true that we learn in communities
of people that we learn at least with other people even when those people aren't there with us when
we're imagining the fights right when we're like thinking like oh this person on the internet is
wrong that still motivates us to do some of our best thinking yeah um so to find the fights that
are inside of dinosaurs right now um
uh would be a great way of connecting your mind to a live wire of motivation that will then also
power you through all of the other stuff that you need to learn if you know one is a budding young
paleontologist as we all had aspired to be at some point in our lives Oz you didn't actually say
anything with dinosaurs earlier no yeah not as many as you might imagine at least there's just
the fossil record is not very good because of geology
uh old rocks yeah geology uh we got a handful and we really cling on to them there's there's one uh
sorry this is a tangent I've got young kids and I want them to see dinosaur bones they want to
see dinosaur bones they're not happy with the chicken bones uh uh and there's one that's really
a driving distance of us so uh we don't have many dinosaurs we cherish them yeah we need an app
dinosaurs near me um what was I gonna say look I I it's
I feel like um some some people may just need to hear that they have permission to learn things in
different ways and I think sadly the like the debunked learning style framing of you'd learn
things in different ways may have thrown people off of that like just the visual learner versus
whatever those were um may have been just like an unfortunate quirk of like pedagogical research
um so to hear this and say well look just think of yourself as this evolved being that may respond
to a fight that may respond to a story or something and say this is okay this is it's
fine like it is true that we like to do mathematics in a certain way for these reasons but you are
allowed to embrace the part of yourself that gets excited about a false story or that gets excited
about fighting someone who's wrong on the internet um
um and that this may drive the kind of thing that created the the proof in the first place
um that other people had this drive as well even if you know we have our reasons for focusing on
what's like definitely true or whatever um we we have other aspects of our being that enables us to
to learn this stuff I think that's a useful thing and I'm realizing now that there's been a through
line and I've been giving all of the least helpful answers
I knew it no I'm just kidding yeah I knew it we had stopped recording like 40 minutes ago don't
worry this is this is never gonna see the light of day don't worry Brandon this is what YouTube
clips are for so yeah go ahead um okay are you ready this is going to be a clip now Charlie take
a note of the timestamp yeah Brandon no pressure this is going to be a YouTube clip you have been
you have been asking a bunch of questions
that touch upon the idea of individualization and I hadn't realized that you put a really high
value on that which good yes absolutely that makes sense and I think every time I have been focusing
on my answers on the opposite of of of that which I I'm okay with the things that I've said
um except for that one moment that we cut out because of all of the screaming and cursing
yeah yeah but other than that under that moment I'm happy with all of it um
the thing in Egan that I feel like really does connect with individualized learning
is to say that the core thing for learning is that it has to matter to you
and we are each of us individually I'm going to say the ridiculous way of saying this we are our
own unique snowflakes we are all very different from each other and
even oftentimes the small differences will make a huge have a huge effect on what it is that we find
meaningful um and so when one has the pleasure of teaching oneself one should always start with the
why might this matter to me and maybe then the best thing the best way that we can bring in llms
to this is to say something like is to ask it something like
like okay like here's the thing I'm trying to learn I'm confused about this little thing
here's like my situation in life right now here are my interests and maybe like one wants to make
like a separate you know window for a chat GPT or whatever just you never close or put this in
its um its long-term instructions or whatever um and say like give guess why this thing might matter
to me given my background given my
psychology that's cool my set of interests the fact that we're Jurassic Park shirt given my
career aspirations like the aspirations that I have of potential using this Sunday in the future
like tell me a story where I am um I am what was what was the character's name John from a from a
die hard oh um where I am Bruce Willis's character and die hard and I have to try
to save the high that dismantle the bomb create a situation where
this could actually matter um and uh and then it could do that uh and and that would actually
reflect uh that would respect um the individuality of every person starting at the mattering and
using an llm to come up with ways that maybe it could matter to us maybe that's the secret sauce
now now I'm going to push back on that Brandon and and say yeah while you are right about all
that yes and uh the thing that that I find so interesting about Egan is that it's an earnest
attempt to find what is Universal uh and and and and and serious insofar as as he points out the
other schools of of of Pedagogy have not been honest about the richness or complexity of our
ways of of growing and learning where you know the progressivist got some things right but they
were wrong from the beginning uh and uh you know the the platonic Academy
teaching is also wrong in in these ways Egan is making an earnest attempt to reconcile some things
and find what to him is Universal and so this idea of having and I don't think we we spelled
this out for people listening but his his five uh forms of understanding are things like somatic the
way that we just are born and understand through our bodies and as you're saying Brandon in the
context of of literacy having it well I skipped one tonight uh that you know there's a mythic understanding and look
Brandon's written a summary of this so that you can look up we'll link to but long story short he
comes up with five modes of understanding which he makes a a reasonable argument are generally
Universal and we have them in different degrees and we never move beyond one we keep we we keep
even our somatic and mythic understanding as we progress through romantic and philosophy through
ironic and maybe some of us don't even get to the final the final ironic to to kneel in an extent as
it is but I I like that you can pick up Egan and say hey maybe I could understand linear algebra
through dance like maybe that's a reasonable thing to even consider and maybe that may be
more me than other people um and uh like but it's not outlandish there's not just the one true way
to do this and probably most people could have some connection to linear algebra through story
uh you know maybe maybe dance is too far too far out for that particular topic but um but you know
maybe Pythagoras to come back to Pythagoras uh you know maybe you can when I was trying to give
my kid an intuition for how to build a straight wall obviously I'm not going to pull out the
Pythagorean theorem but there is a somatic understanding of straightness and right-angledness
that you can get like literally through standing up and feeling gravity and and you can you can you can think
universally as humans we might have a somatic a mythic a romantic understanding of these topics
and at least I could consider those okay I'm going to bring this back to the llm idea um I like I like
your idea I don't think lms currently or maybe even ever based on how lms work would be able to
reflect back to you and say Brandon based on your context that you've given me I think here is a good
way of uh of approaching
this but we could do something pretty uh similar I think in effectiveness right now which is for
you Brandon I know you've got a lot of projects on your plate but here's here's one more could
you come up with 100 prompts for chat GPT 100 system prompts that presents information in a
different way right so one of one of them is tell me a story with a character whatever one of them
is tell me a limerick one of them is
uh ask me a question of this style come up with 100 of these so not the five cured modes of
understanding but maybe there's like 30 mythic understanding ones and 40 romantic understanding
ones or something they're all different system prompts for chat GPT and then I can if I'm learning
a topic pick a handful of those maybe one doesn't really do it for me it's not a good limerick but
I can move on to the next one uh and like just just kind of dabble a little bit and get them back if
I've got some ideas for how I might approach something where I'm getting stuck and I'm not
just given like the axiomatic proof or whatever and I'm like I'm not fit out I'm not fit for
learning linear algebra because this was not a good way of understanding at least I know that
there are lots of different ways of approaching I'm going to stop but do you know what I'm saying
like I don't I think like maybe picking off a menu of ways of understanding a problem where
we have a sense that across all of humanity these hundred prompts are could be useful or
understanding any topic and I can just I can just try a few and see what I like I so here's what I'll
point you to I um this right here is my website science is weird although people should also know
about um I teach I teach I run a blog Substack I write a blog a Substack lost tools at substar.substack.com
the lost tools of learning um but if you go down to workshops it'll be right there I did one and it's
actually free on the website unlocking chat GPT and I talk about actually some things uh like this
and I think when you get it I think um look at the recording blah blah blah blah blah incorporates
homeschooling fun I think that I have on I think you also automatically get um a sheet
that I have some prompts for but you know I was doing those in the context of like here is
how to use it not just specifically egonized ones uh for people who had no idea how to do anything
and I I would like I would be interested in coming up with a list of uh uh I don't know 100 but uh 10
or 20 um specific things that I many of them I use myself all the time so yeah that's I can do that
probably I sort of feel like the place for me the power would run out I I think it's like
if I encountered one of these things the first time like oh this limerick really taught me this
concept
that's great but then if I try the limerick thing again I'm sort of imagining that it's going to
lose its power uh which is why 100 might be useful because I could sort of cycle through it but to me
like the it's like I like accidentally learning and it's like wow I read this story and it taught
me this thing isn't that great but if I go in knowing that there's going to be this unique
approach then now it starts to feel like teaching and oh man that's annoying to me so I'm just so
Charlie here's here's the part of the project that I'm gonna nerd snipe you on okay you could build a
website and it's funny that you say accidental because I was actually going to suggest a roulette
wheel like graphic visualization with an animation and stuff where you just like are randomly
presented with a way of understanding it about that yeah I know maybe that maybe that is less
less stressful than this is the one true way to learn at least for Charlie or at least some degree
of like accidental discovery of different ways of approaching a topic um it may may
make it fun and then you don't have to at least not having to like copy paste the prompt
of just like saying oh have you this just happens to be a way that like the state of the art LLM
presents information if asked to do that as a joke or something or with with an accent I don't know
can I ask a question can I ask a question that's been on my mind for a while in this convo uh
Brandon then I need to go to dinner oh yeah yeah Calvin and Hobbes in philosophy class at an hour
okay yeah yeah um I don't know if this is the best one to answer but Brandon you you had said I don't
know linear algebra I'm I don't know linear algebra I don't know linear algebra I'm
wondering uh with Egan in mind are you of the mindset that if you had the time Egan provides
you the tools to sort of learn anything I always think like oh man if I had six months and I was
had Liam Neeson training me on a mountaintop I could become Batman do you believe with the
tools of Egan you could learn anything if you had the time to do it I'm just trying
to think of the experiences that I had in my life where I really like failed terribly
failed at languages terribly numerous times and so that's part of what my mind goes to I mean I I
suppose like I could also j but you know like Liam Neeson on a mountaintop and also he only speaks
Dutch well okay probably I'll learn Dutch or like beat me up every morning yeah yeah except to learn
Dutch better um you know like I can come up with some sort of context yeah example of like could I
learn you know some kind of math that is so complicated that it won't be invented by AIs
for another thousand years okay probably not that probably can't fit inside of my head yeah
but like is there anything that I I I uh I some of the really higher level math things
you know like I don't it it's not clear to me that do you guys know John Mighton the the man
he's actually he's actually in the he plays a minor character in um the movie um Good
Will Hunting actually he's the the inspirational teacher in Good Will Hunting but also like when
he's not in Matt Damon movies he is a mathematician who runs a non-profit out of Toronto called jump
math what they have done is they've reinvented the a the K through kindergarten through eighth grade
math curriculum to say okay all the things that we teach like can we just break each of these concepts
into like a bunch of very small
small escalating problems that start with something that is easier than you know and ends up like it's
something that is like way harder than you than you even need to learn um I referred to this he
doesn't have a name for his method that I know of I refer to it as the micro scaffolding method where
instead of like being a ladder that one needs like try really hard to climb up the steps like it's
just like broken down into individual tiny little pieces which is something that Bertrand Russell and
I worked with in their 2014 whatever Principia Mathematica um uh this idea that you could
decompose any really complicated thing down to like an arbitrary number of analytical steps
um and um and dang it it works it works really well so I don't know like even maybe some like
the really high level you know Andrew while solving for Ma's last theorem sort of things
right like maybe if it was just broken down with all those steps and I had Liam Neeson to
pick me up when I didn't work I feel like mine would just end in an Escher staircase and I'd just
be circling somewhere do you think that there's anything in your like at some level you can just
take neurons and you can connect them together right every neuron like short of having an
interest this is my model of how mine how brain works I don't really understand how a brain works
um but like short of having really interesting um trauma in your cortices like you can connect any
other neuron anything that when you imagine something Oz that is like linear algebra like
really high level like there are certain there are certain pattern of neurons that are firing
there right like we could describe it using shapes we could describe it using you know
some sort of picture if I can get that same series of neurons to fire in my brain then I
think I should be able to understand that too by definition it would be weird if I couldn't but then
you know I don't really understand how brains work so I don't know I'd assume that yeah I honestly the
Egan stuff when when it's just a question of can I understand X I feel like the Egan stuff is not
even as as useful for thinking about that question just like real cognitive psychology neurology sort
of stuff is is the most is the most uh powerful for cracking that mask yeah well Brandon
for me yeah yeah go ahead I was just gonna say for me the the lesson of it is not that you you
cannot get to 100 like you you're you're at 20. there's not that oh you can definitely do this
thing and achieve the outcome maybe you can get to 21 or 22 in ways that you didn't imagine
um because you you're just fixed in your your expectation of how you should learn this thing
because every textbook is presented in this way your assumption is that it can only be learned in
this way and uh
uh so when you when that doesn't work for you you give up or just go to a different staircase I I feel
like I'm trying to learn this I get to 21 and then I see there's another staircase over here and that
looks kind of cool too and why not do that that feels like that comes out the other thing I wanted
to say before you go which I just loved in your website with Egan too um the world is fascinating
and I love learning and if nothing else I took that away who cares what staircase I'm walking
on I could be walking in circles as long as I'm having a good time
that's how I feel yeah yeah it's been a real pleasure Brandon I want to talk to you as well
about weirdness and I love the fact that your your school is science is weird I wanted to talk to you
about eclecticism in education but maybe that's a topic for another another conversation if you'd
like to have me back on in some time I would be delighted to to do it if we ever do did that I'd
be interested in send send me a like I would be interested in taking on it's like an hour-long
thinking enterprise exercise a person is struggling to learn X where X is some sort of coding sort of
thing like how could Egan and I don't know other cognitive psychology stuff like how could that be
useful I would love to spend an hour thinking about that specifically so if you even like want
to like float out to your um your people with who have discrete first names uh listeners uh Adam uh
like does he want to like volunteer for this sort of thing I could spend an hour kind of
brainstorming with a bespoke Eganized self-study way of uh of of exploring or mastering this skill
or understanding this topic that sounds awesome yeah thank you so much uh looking forward to seeing
the saber-tooth Tigers chomping in your next video so hopefully you can figure that out it's plaster
it's very very delicate very delicate not with that attitude all right thank you have a good dinner