Math is a spiritual practice & here's the proof w/ Edward Doolittle

Episode Transcript
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Edward Doolittle (00:03):
I want myself and all students in mathematics
to approach mathematics as wholepeople, the mental but also the
physical, the emotional, and thespiritual.
We often have this deficitthinking around indigenous
culture.
How do we help those indigenouspeople get better at math or do
better at standardized tests.
But we ought to look at alsowhat indigenous people can offer

(00:26):
the world.
And we have a different point ofview that can actually help the
whole world and help us alllearn mathematics better.

Vanessa Vakharia (00:35):
Hello.
Hi, it's me, Vanessa, andwelcome to your weekly hit of
Math Therapy.
Okay.
To kick things off today, I havea fun little multiple choice
question for you.
What is my favorite topic torant about here on Math Therapy?
Is it A cults, B astrology, Cspirituality in math, or D, all
of the above.
If you answer D, then you aregoing to love this episode

(00:57):
because it truly was aconversation written in the
stars.
So last month I was keynoting aconference in Saskatoon, and so
was today's guest, Dr.
Edward Doolittle, who I happento have wanted to interview
forever.
During his keynote, he casuallydrops this absolute bomb that
Pythagoras, like the Pythagoras,may never have even existed by
that in entire cult ofPythagoreans did.

(01:20):
So I literally went back to myhotel room and emailed him and
was like, can I please interviewyou tomorrow, I need to talk
about this immediately, andthank God he said yes, because
it was one of the most fun andheartfelt convos I've had this
year.
Also, because this was a totallyimpulsive decision, I didn't
have a mic with me, so Irecorded the entire thing with
my phone.
Why am I telling you this?
Because David forced me to tellyou this because he was like,

(01:41):
the audio quality is not exactlya hundred percent up to snuff.
Please let them know.
Okay.
Anyways, Edward Doolittle is aMohawk mathematician and
scholar, and he shared aperspective that genuinely
stopped me in my tracks, whichis this: math is not something
we discover or create.
It's something we come to know.
Seriously, wait till you hear'emexplain, it's gonna blow your

(02:02):
mind.
We talk about indigenousmathematical thinking, how math
shows up in ceremony and gamesin the body, in the breath, and
what it might look like toactually bring our whole selves
for real into learning math.
We also talk about historicalfigures like Kepler, who was
both an astrologer and amathematician, and suddenly,
aren't you like wait, when didmath get separated from all of

(02:24):
that?
So if you've ever felt like mathwas cold or rigid or just not
for you, this episode mightactually change your mind.
And before we get into it, Iwant you to think of that one
person who would never expectmath to be talked about this
way, or even better, that oneperson who's always hated math
because it's so like, meh.
I want you to send them thisepisode.

(02:44):
And don't forget to text thepodcast using the link in your
app and tell me what you think,because I just know you're gonna
have big feelings about thisone.
All right, let's get into it.
Edward, welcome to the podcast.

Alright.
Thank you.
Glad to be here.

I don't even know how to start really.
We met, less than 24 hours ago.
I saw you do a riveting talk atthis conference, and I'm gonna
be honest, I have a bunch ofquestions for you, but the first
one I do want to just come inwith is one that I've been
thinking about ever since I sawyou speak, because in your talk
you told us that Pythagoras doesnot exist.

Well, it's unknown whether he exists or
not.
I, I, this is certainly amythology constructed around
Pythagoras and I tend to believethat constructed mythology is
generally maybe rooted in truth,but not true.
And so, the Pythagorean cultcertainly existed, whether
Pythagoras was their master ornot, oh, whether there's a

(03:42):
person named Pythagoras, I thinkno one is really sure.

Okay.
But let's back up'cause you justso casually said, Pythagorean
cult.

Yeah.

Can you

Well, they,

I mean,

they were,

just so you know, you don't know this about
me, but I'm obsessed with cults.

Okay.
Well then you're talk, you'retalking about the right thing
here.
This was a cult.
That worshiped number, andworship is not really the right
word, but they, uh, a group ofpeople who believed that, the
universe was constructed out ofnumber.
And so everything was built fromnumber and that you could
influence the properties ofsomething by making say a house

(04:16):
out of, uh, 284 bricks wouldhave have certain properties, My
car has a license plate that hasnumber 496 on it, and so that's
a perfect number.
The Pythagoreans would'verecognized that as a perfect
number,

But hold on a second.
Hold on a second.
You're saying it's a group ofpeople who believe the world
revolved around numbers?
Yeah.
Isn't that just a mathematicianor someone who believes that
math is real?

So I think, I think what we understand the
difference between mathematicsand a mathematical cult is that
the cults can't, can't provewhat they, they, they don't
prove to be true what theybelieve.
And so a lot of it waspronouncements of their
leadership would say, this isthe way we are going to be.

(05:02):
So they had a number ofobsessions.
One was number, another wascleanliness, and their motto was
Hygieia, clean.

I'm sorry, what?
Okay.
So a cult that is obsessed withnumbers and cleanliness.

Yes.

This honestly doesn't sound like a bad idea.

Yeah.
No, I, I might have joined if Iwere back in the day.

Would you have?

I might have I, we'll see what the membership
fees are and so on,

Because cults, I mean, they start off as a
well-meaning thing, but theyusually go awry.

Yeah.
And, and in this case, uh, theymade a number of, of very
interesting discoveries.
And so our musical system, wewere just talking about music.
Our musical system is based ontheir discoveries.

Like what?

Uh, so they apparently, the, the myth is
that one of their members waswalking past a blacksmith who
was hammering, and the hammeringwas making harmonious musical
sounds.
And so he investigated.
Why, why?
What are you doing?
Well, here's, here's what I'mhammering is what blacksmith
said.
And the pythagoria noted that,well, these are two rods that

(06:03):
are of, uh, rational ratio thatthey, that they have two to
three or or four to five orsome, you know ratio like that.
And so they, they come, came tounderstand that, these ratios,
certain ratios, certain rationalnumbers as we say now are
associated with harmony andmusic and it's true.

(06:24):
And so we built the entiremusical system, 12 foot scale
out of that.

I am sorry.
This cult sounds like it'sactually been very productive
and helpful.

They were, yeah..
And so, um, they discovered,well, they didn't discover, but
they may have proved, it's notreally clear.
Uh, the Pythagorean Theorem.
Pythagorean Theorem was knownfor millennia, probably before
that.
Right.
But, uh, they certainly gave aproof of it.
Probably their bestmathematician was a person named
Hippasus, and Hippasus probablyproved the Pythagorean theorem.

(06:56):
A myth is that they sacrificed160 oxen.
When they discovered thePythagorean theorem,

Why?
Just to celebrate?

Uh, yeah.

What about like a confetti cannon?
Why did they do that?

Well, what would please the gods?
It's not a question of whatwould please you.
You, confetti cannon.
160 oxen, gods.

Got it.

Okay.
So, uh, yeah.
And, and, but, but on the otherhand, they're also known to have
been vegetarians and so itdoesn't make sense that they
would sacrifice animals.
To please the gods.

That's actually, sorry, this has
nothing to do with math now, butnow I'm actually wondering if
the two are similar.
Like I guess if you're avegetarian, maybe you care
somewhat about animals.
You're not gonna just sacrificethem.

Yeah, I guess, I mean, it kind of makes sense
so it raises questions anyway.

It raises a lot of questions.

The mythology is not, you know,
self-consistent for one thing.
they're also known, uh, to havehated beans, so they, they
wouldn't eat beans.

How can a vegetarian subsist without
beans, what's their proteinsource,

I don't know.
So, again, doesn't make sense.
so they had the thing againstbeans.
Um, they,

okay.
This sounds like a really weird,kind of like picky, a bit of a
diva of a cult.
So here's the thing though,right?
Is like you telling us this, Idon't know if you noticed this,
but when you started talkingabout this yesterday, people's
eyes lit up, right?
Everyone was like, what?
Tell me more.
And I've actually alwaysthought, you know, we talk so
much about like making mathengaging and relevant, and we're

(08:26):
trying to compare it to thingsin kids' lives.
But this stuff, it'sfascinating.
Like if we, if we told more of.
The history and the lore of themathematicians that created the
math we use, like, don't youthink people would be like more
into it?

Yeah.
I think it's, I think it'sreally interesting and it's part
of what interested me inmathematics as a young person.
Uh, I think we ought tointegrate this into, into our
education system.
I don't know why it's not donethat.

Well this kind of leads to what you're all
about, right?
I mean, I actually heard most,the thing I heard most about you
and saw that really intrigued mewas that you tied, um, for lack
of a better term, just usingkind of the title of your talk
yesterday, you tie spiritualityand math together in a way,
right?
Like you're, talk you in a, in asense, appreciate the spiritual

(09:12):
nature of mathematics, would yousay?

I, uh, I'm, I guess I do, I'm very interested
in it.
Yeah.
I mean, that's the idea of, ofbasic research, just curious
about it and trying to learnabout it.
I believe it plays a prominentrole, but, I don't think we
understand that.
We tend to shy away from that asa culture.
I believe.
You know, kind of western or,you know, non-indigenous culture

(09:37):
shies away from spirituality.
I believe that's probably due toa history of, of, uh, religious
fanaticism and warfare inEuropean history.

Wait, tell me more about that.
So you're, you, tell me moreabout how you feel that has
caused us to sort of, shy awayfrom anything mystical or
spiritual when it comes to math.

Uh, let me give you an example.
I told you yesterday, one of my,my mathematical ancestors is
Johannes Kepler.
So he supervised someone whosupervised someone and so on and
so on.
Who supervised my supervisor,who supervised me.
So,

so guys, this is like Six Degrees of
Separation with Kevin Bacon, butfor math, right?
Right.

Yeah, right.

Okay.

and people even more famous than Kevin
Bacon.
So, uh, Johannes Kepler,

come on.

But, Kepler, um, so he made his living doing
astrology.

I'm sorry, what?

Yes.
Yeah, Kepler was.
Oh, kind of.

I'm freaking out

as foundation an astrologer.

Okay.

And so that's why he became interested in
astronomy is to draw moreaccurate astrological charts.

Okay.
When, when was this?
Like, what year are we talking?

Uh, 1530, I think.
Okay.

Can I just say why this is.
So crazy.
Okay.
Because I'm not into Duns andDragons.
Yeah.
But I'm so into astrology.

Right.

Okay.
Like I'm obsessed.
I still dunno your sign, I willguess by the end of the
interview.
Okay.
But what's so crazy is I alwaystalk about how Astra like,'cause
people are always like, peoplewill say to me, how can you be
into astrology and all thiswoowoo stuff and also be into
math.
Yeah.
And I'm always like, you know,back in the day, astrologers
were mathematicians.
You actually needed to be amathematician to cast a birth

(11:20):
chart.
Right.
And as a result, by the way, allof the astrologers were men.
Right, because women were toofragile or whatever to do math
and they weren't allowed to.
So we took astrology veryseriously, right.
Now, things have shifted.
There's an app you can use.
You don't need to like, actuallydo any math to cast the birth
chart.
So it's not taken seriously.
It's been divided, but, butastrology was considered one of
the math.

(11:40):
So I, and I didn't even knowabout Kepler, so this is
actually very cool that you'rebringing this up.

yeah.

Okay.
Go ahead.

Well, Kepler is, is kind of one of my heroes
too.
I'm, I'm, I was very, uh,gratified to, to learn that
Kepler was one of my ancestors,just because he kind of crosses
two worlds.
That mystical world on the oneside and, and the very rational.
Uh, mathematical world that,that, and he, you know, found,
he was at one of the giants,Isaac Newton said, I, you know,
I've seen this further thanothers because I was stood on

(12:07):
the shoulders of giants, hemeant Kepler.

What did he do that was like, so cool
mathematically?

Well, he, he took all these astronomical
observations and thensynthesized them into Kepler's
laws that these are the laws ofthe motion in the solar system.
and, uh, he actually made fourKepler's laws, I think.
but we only, we only have threebecause his fourth law was not
correct.
So he was wrong.
But that, that's part of being ascientist or being a

(12:33):
mathematician.
You're wrong a lot of the timetoo.
And eventually you have to beable to double check everything
that you say.
And so that's an important partof mathematics and science.
Kepler's a very interestingperson.
Kepler wrote, science fiction.
He's credited with writing thefirst science fiction novel.
Yeah.

What this guy is really on it.

Yeah.
Yeah.
Okay.
Insomnia it was called.
In Insomnia, uh, a demoncommunicates with the
protagonist's mother and givesinformation.

Okay.

And so, uh, church, uh, Lutheran church
found this and, actually seizedKepler's mother and threatened
her, threatened to torture her.
Oh, yeah.
And so they didn't actuallytorture

Well, because they thought that he was writing
it about his own mother

Yes.

And that she was like demonized.

Yeah.
Yeah.
Oh, wow.
That he, that he and his motherhad had, communicated with
demons.
And so they brought her inbecause they really wanted
Kepler, but he was traveling.
He was away.
So they, they, uh, brought inhis mother and then laid out the
instruments of torture to showher these are the instruments of
torture.
This is what is going to happenunless your son comes back.

(13:43):
So Kepler immediately returnedto, uh, his hometown and, and,
um.
Face charges for, for, you know,this.

For what?

For, uh, for writing about demons.
And, you know, I mean, he hadto, he had to show that he
wasn't under actual demonicinfluence, I suppose.
I don't know.
I don't know the details

of you weren't like alive at the time.

Uh, well,

it feels like there was a time when
mathematics and spiritualitywere not divorced from one
another.
when you read about like theseancient mathematicians and their
discoveries and their lives andlike all the stuff you're
talking about, all the Lord, itfeels like there was a point
where mathematics was moremystical.

Yeah.

Am I right?

Well, I, I, I believe so.
And, and one way I think aboutthis is to run it backwards in
time.
Mathematics was essentiallyastronomy if you go back years.
Yeah.
So they weren't calledmathematicians.
we were called astronomers.
Yeah.
And so

this is blowing my mind.

So, yeah.
And so as time has passed.
These disciplines have kind of,become their own thing.
They're separated.
So mathematics is separate fromastronomy now, and separate from
physics is separate fromchemistry and so on.
But you start to run itbackwards in time and these
things become integrated.
And so, you know, it kind ofmakes sense and, and the

(15:02):
philosophers and historians of,science and so on would known
better than me.
But my belief is that knowledgewas much more integrated in the
past.
and possibly there are a timeand time in the past where you
just didn't have someone who wasa mathematician, a medical
doctor, whatever.
You just had a sage.
Knowledgeable person.
And so, uh, I believe thatindigenous cultures are still in

(15:26):
that state.
Where we don't have thatdivision of knowledge.

I would love to even just pick up on what you
just said.
That is such a beautiful thoughtthat there's this idea of a wise
one.

Mm-hmm.

Right.
And mathematical knowledge isjust integrated as part of their
knowing.

Yeah.

Can you tell me a bit more about how it works
and how indigenous mathematicsis different in that way?

Yeah, so I think, I think we need possibly
to think about mathematicalthinking as opposed to
mathematics.

Love

it.
We talk about mathematics.
We we're creating that, thatcrystallizing that as a subject
in itself.
But when we talk aboutmathematical thinking, we can
think, think about it inrelation to all kinds of other
thinking and, and it's reallysomething all people can do.
It's something that'suniversally open to us as human
beings, mathematical thinking.
It's just like, if I do this,what's the consequence?

(16:15):
Or if I want this to be theconsequence, I'll run that
backwards.
What I have to do,

I need to stop actually hitting the table.
Take the microphone.
David will actually kill me.
It was not me for once in mylife.
Oh my God.
The bracelets.
Oh, he's gonna kill me.
Oh no, they're probablyjingling.
Oh my God.
Fuck.
Okay.
Don't worry.
It's all good.

Okay.

Okay, keep going.

We're gonna need AI to process this thing.
It's like, please take out thebracelet jingling.

Okay, there we go.

Anyway, uh, yeah, so,

so mathematical thinking versus
mathematics.

Yeah.
Mathematical thinking.
And so I, I, you know, it's opento all people and we see it in
children, we see it.
It's part of being human, isbeing, is having mathematical
thinking.
and so, uh, we, I am interestedin searching for mathematical
thinking in my culture and othercultures, indigenous cultures.
I'm currently working on a paperon this with my, uh, grad

(17:11):
student, and he's done a lot ofthe work, we just have to kind
of form it into a paper andsubmit it now.
So the idea is that there's aceremony we have and it's a
game.
So our mid-winter ceremony, myculture is, uh, Rotinonhsyonni,
or, uh, Mohawk culture.
Iroquois cultures, how it'soften said in English.

(17:33):
Uh, Rotinonhsyonni, we have madethe longhouse.
We have midwinter ceremony.
It's our, probably our oldestceremony.
And so I participated inmidwinter ceremony.
And at the end of midwinterceremony there's a game, Peach
Stone Bowl game.
And we, um, usually we put upstakes and it's, uh, usually
something handmade, somethingvery valuable in the sense that

(17:54):
it's taken somebody a long timeto make.
A, a year of, of, you know,sometimes beautiful jackets that
are beading on, put up onstakes.
And, at the end of the game,there's a winner and, and the
winning side will take all thestakes and the losing side gets
nothing.
The real interesting question,uh, which is raised to me by
people playing the game, is howlong is it gonna take to finish

(18:16):
the game.
Because it's part of ceremony,once you start, you have to keep
playing it.
And you know, you, you may haveother things to do, a job to
attend or whatever, but

how long does this go?
Like

It could take about a week.

Well, I Under a week.

Yeah.
So it kind of goes back andforth.
You, you know, you, you get awinning outcome.
You get some beans from theother side counters.

Oh my god and Pythagoreans would have hated
those beans.
Am I right?

That's right.
yeah.
and then so we use thesecounters and the game can go
back and forth.
Okay.
And it can go on for days.
And, and so the real interestingquestion is how long it does it
go on for?
It was designed to go on acertain amount of time, I
believe.
Consciously designed.
It's not just random, but it'sdesigned to take between three

(19:04):
to six days or so.

Okay.

How do people arrive at that?

At that, yeah.

And

you'd have to, like,

we used markup theory and we used computer
simulation.
Those were not accessible to myancestors.

Hmm.

How did they answer the question?

Hmm.

It was trial and error.
I'm sure.
I mean, I, I, I'm, I'm notabsolutely sure, but it seems to
be the, the, the obvious answer.
That trial and error, was usedto develop how many, how many
counters to, to use to, to makethe game last a certain amount
of time.
But there has to be some kind ofmathematical thinking there.

Okay.
I am totally with you here.
This idea of mathematicalthinking.
Let me, tell me, I'm gonnareflect back and tell me if I've
like understood this.
Yeah.
First of all, I love the ideathat mathematics as a field is
different than mathematicalthinking.
And tell me if you agree.
I feel like mathematics as afield is very constrained.

(20:02):
Like we're kind of like, it'sthis, that, the other thing,
it's these things.
Whereas mathematical thinkingfeels so much more open.
Yeah.
And broad and infinite.
Right.
There are so many ways to thinkmathematically about everything.
You don't need to be thinkingabout something in the category
of mathematical field.

Well, yeah.
I, I think that that is exactlyone reason why we use
mathematical thinking is tobroaden our, our area

and to show that it can be applied to
anything, like, which is thenext piece where you're like,
mathematical thinking inIndigenous math is integrated
into everything, including thisgame.

Right.
and so then the questionbecomes, what do we really mean
by mathematics?
I think mathematical thinking isalso a little more well defined
perhaps than mathematics.
Some people say, well,mathematics is proof.
and that's, it is kind of ago-to many my colleagues
mathematicians will say thatmathematics is, all about proof.
And if you're not provingsomething, it's not mathematics.

But if you're adding two plus two.

uh, you can prove that two plus two is equal
to four.
But, uh, but, but

go on.
We have to think about this.

There are, there no, there are lots of
problems with that there,there's a conjecture as part of
mathematics.
Well, there's no proof there.
It's just like a kind of an, uh,

a hypothesis.

A, you know, it could be intuition, it could
be experiment that gives youinspiration.
It could be just a lucky guessor whatever.
These are, these are whereconjectures come from.
So these are not proof.
So there's a whole bunch ofstuff.
But I think one of the bestarguments is that we go back to
a time, the first mathematicianin the sense of proving things

(21:34):
was Thales of Miletus, greek.
And, uh, what about before him?
Was there any mathematics beforehim?
Well, yes there was.
Of course, of course there was.
There was.
There's a whole, whatever humanrace, uh, we've had mathematics,
we've had counting, we've had,um, you know, ideas of, of
consequence.
Uh, this happens then thathappens in order.
Uh, so ideas of ordering.

(21:55):
All these things go back wellbefore the existence of proof.
So proof is not the fundamentalpart of mathematics.
It becomes then more difficultto define what mathematics is.
That's really the problem.
And I ask people, and I getdifferent definitions from
everyone I talk to.

What's your definition?

My mine is going to be very strange.
My definition

Shocking.

My definition is that mathematics is a
spiritual being is like a being.
Yeah.

Say more.

Yeah.
Well, one thing we want to knowis, is where did mathematics
originate?
And as I mentioned, itoriginated at the time of
creation.
The world was created, theuniverse was created.

does it mean something to you that I have
Euler's Theorem tattooed to myfinger.

Uh,

in terms of what you're saying,

I strongly approve.
Uh,

but don't you think it proves what you're
saying?

That, I dunno,

because the reason I have it

Okay, yes.

Is because Euler's theorem, part of the
idea of this proof is that it isso perfect and it's complexity
that there's no way that humanscould have created it.
It must have been something thatwas more akin to what you're
saying.
It's something we discoveredwhen we came here because it
already existed.

Right.
So, so part part of my point ofview on this is that we don't
discover and we don't, we don'tcreate.

Okay.

Okay.
So you're a human being.
You're a being.

Yeah.

I didn't discover you today.
I mean, that's just whollyinappropriate to say, oh yes, I
discovered you.

Right,

right.
maybe your producer discoveredyou, but I didn't discover

No, but that's like an ego-based way of
thinking,

Right, it's ego-based.

Yeah.
I see what that

Exactly, it centers us.
As human beings.
The same with creation.
It's centers us as human beings.
But that's not, you know,mathematics exists independently
of us and is something muchlarger than us.
And so we come to know, wedon't,

we come to know,

yes, we come to know mathematics.
We don't discover it.
We don't create it.
So the debate in mathematics is,is discovery versus creation.
And that's all ego driven.
And we take the ego out of it.
We humble ourselves, which isthe indigenous way, and we now
come to know mathematics as abeing.
And some of us come to know thisbeing better than others.

(24:14):
We, we, you know, I, I, I feelI'm on a first name basis with
mathematics, but many people arenot.

I am getting emotional over this.
That was really, reallybeautiful.
And I think I, that I feel likethat I just checked myself there
to be like, oh wow.
Like we are so egocentric in theway that we talk about math.
I also think it's so beautiful,this idea of some come to know
mathematics more than others.
And I think this is beautifulbecause, you know, at its core

(24:44):
my work is about math, trauma,and, and our relationship with
math.
And we come to know mathematics,at different levels, at
different stages of our lives.
And just because we, some of usare not on a first name with
math, you know, a first namebasis with mathematics now
doesn't mean that we can't be.
And I really wonder if, like, ifwe looked at math as more inter

(25:06):
integrated in this way, youknow, the way that we're like,
you know, there are, we knowthings, we are engaged in
mathematical thinking in allthat we do.
If that would change the way somany of our students feel about
math.
'cause right now it feels likewe are looking at math in the
in, in isolation.
Like it's this like bucket, likethis, this what you were talking
about.
Like, oh, math is proof, or mathis this thing.

(25:26):
And if you're not in thatbucket, then you are not engaged
in mathematical thinking and youcan't access it.
But the way you're talking aboutit as, hey, math is here.
We come to know it at differentstages in our lives, in
different ways.
It is, it is there, you know,ready to greet us when we're
willing and able, if that wouldchange the icky, horrible way

(25:47):
that most people feel aboutmath.

Yeah.
I, I, I agree.
I think, uh, this is an exampleof how indigenous culture can
teach the whole world something.
So we often have this deficitthinking around indigenous
culture.
How do we help those indigenouspeople get better at math or do
better at standardized tests?

(26:09):
But we ought to look at alsowhat indigenous people can offer
the world.
And we have a different point ofview.
We have a point of view that canactually help the whole world
and, and help us all learnmathematics better.

How can we, if someone's listening to this
right now, which I know they arebeing like, I love that.
I love this.
I teach math.
How do I, what's something I cando right now in my classroom to
bring this way of knowing intomy room?
What can they do?

Yeah.
that's a, that's a harderquestion.
My, my area, of research is, isI guess you might call'em basic
research.
I'm interested in ideas and, I'mnot good at the implementation.
I don't have a degree ineducation, for example.
So I, I try to partner withother people to bring this into

(26:56):
the classroom, and it's a slowprocess because there's so many
factors.
You know, I think there's this,also this religious.
we were, we were talking aboutKepler and, and the point of
Kepler is that there are a lotof religiou violence, socio
religious fanaticism in Europeanhistory.
The Lutherans versus theCatholics and on and on and on

(27:17):
and wars fought and so on.
And so I think that's why peopleshy away from that.
And, they mistake spiritualityfor religion.
And that's something our elderstell us is very different that
we can, we can introducespirituality into the classroom
without interfering withpeople's religious beliefs.
I believe that's true, but ittakes agreement and it takes,

(27:40):
you know, understanding.
So it's gonna take time to buildthat.
But I, I aim for that tointegrate, I want myself and all
students in mathematics toapproach mathematics as whole
people, which is the mental,,but also the physical, the
emotional, and the spiritual.
So we as if we, in thatintegrated way, address

(28:03):
everything that we learn,including mathematics, I think
it leads to much healthieroutcomes.

Can I ask to you what the difference is
between spirituality andreligion?

Yeah, it's one of those things that, uh, I, I
know it when I see it.

Same like, like, so I'm only asked because
I am the exacts.
Like, we're so similar in thisone.
We're so dissimilar in manyways, but we,

I don't know,

but we are so similar in this, and I've always
felt the exact same way.
You know, to me, math has alwayshad a spiritual, uh, role it's
played in my life.
Like the meditative nature ofworking through a, a beautiful
problem.
And, what that does for yourmind, the curiosity and wonder
and those aha moments, thequestions, the curiosity, the,

(28:49):
the intuition you get when youfeel like you're on the right
track with something, when youdon't even know what a formula
is that you might need.
Right.
Yeah.
There's a lot in there.
But you're right.
As soon as you start talkingabout spirituality, a lot of
people get their backs up, and Ithink you're totally right.
It's because from spirituality,we get to religion.
From religion, we get todivisiveness because that's how
it's been used so often andthere's kind of this shutdown.

(29:10):
But if I never say the word.
Right.
And you probably, maybe, maybeexperience this sometimes if I
never use the words likespirituality or, you know, magic
or whatever.
And I, I, um, engage someone inan experience where they
themselves feel it.
There's something that happens,right there is this spark, there

(29:30):
is something that happens there.
So I wonder how like we aseducators can create those
moments for our students,without wading into the hot
button of having to label themoment as spiritual.

Yeah, I think possibly, yes.
one of my models for this is notjust indigenous culture, which
is my main interest in being anindigenous person, but

do people associate, when, when you're
talking about indigenousculture, do you think people
automatically start thinkingreligion?

when we talk about things like creation story

Yeah, I got

people, people talking.
You know, there's a famousexample in, uh, the writing of
Vine Deloria Jr.
God is Red.
Excellent book, I highlyrecommend.
but he writes a story about, a,Christian religious figure, I
believe a Catholic priest, I'mnot sure though, in
conversations with someindigenous people.
And, and, they tell him theircreation story and then he's

(30:31):
listens patiently and then hereplies with his creation story.
And he said, they asked him, doyou believe it?
And they say Yes.
Do you believe ours?
And he says, well, no, we can'tbelieve the two things.
And he said, no.
We said, we believed your story.
Why won't you say you believeours?

(30:52):
That was kind of unresolved.
So we have a history in NorthAmerica, at least as indigenous
people, of religious toleranceor spiritual tolerance that goes
back to time immemorial that we,uh, respect the spirituality of
religion of other people.

(31:13):
And that was one of the mostkind of confusing and
astonishing things about thesettlers is their lack of
tolerance.
So I don't think we've everreally come to, come to grips
with that.
But, we,

so I guess we're like, we have to, in a way
to make math like palatable toeveryone, you have to take any
sort of spirituality, like I'musing air quotes out of it.

Well, it's, I don't know.
I mean, not not just math, butall of education.

Sure.

Right.
And people recognize thatteachers are in a powerful
position and can manipulateyoung minds.
And so they want to be carefulthat the teachers don't
contradict their religiousbeliefs and you know, I, I guess
it's a, it's a complicatedthing.
So, yes, I think it's possibleto maybe stealth introduce

(32:00):
spirituality, but that againruns counter to some basic
principles of informed consent.
You want people to, give consentand give informed consent when
we engage in any kind ofrelationship.
And so education is exactly oneof those things.
And I think that's a problemwith our education system, it
doesn't have conform consent.
It's a government saying, thisis the curriculum, this is what

(32:21):
happens in the classroom.
It's not a matter ofnegotiation, which is really
what it should.
And so I think, I think that,that there's probably a better
way to build a classroom, uh,experience is to gather everyone
involved, uh, together and justsay, here's what we hope to do,
or here's what we hope toaccomplish, let's all agree on
some basic principles.
Let's agree on the curriculum,let's agree on so on.

(32:43):
And I think it's possible.
Uh, I think this happens all thetime.
Uh, and for example, diplomaticprotocol.
You bring people from differentcountries together and, uh, they
have to come to an agreementabout how they're going to
behave.
You know, how hierarchicalrelationships are represented.
Who goes first?
Who goes second?
Are you gonna shake hands?
Are you going to bow?
Are you going, whatever.
So these things are, it'sunderstood.

(33:05):
Human cultures are different,but when we come together, we
have to come to an agreementabout how we're gonna proceed.
And this is not done ineducation now, and I think it
needs to be done.
So I think that we need to, nottry to sneak this in, is we have
to be very clear and open aboutit and everyone should agree on
it.
But on the other hand, I thinkwe can introduce spiritual

(33:26):
experiences that are maybeuniversal.
One of them is giving thanks.
We all give thanks, all culturesgive thanks and, you know, we do
it maybe in different ways, butwe can find a way to give thanks
together.

Tell us how to give thanks in the math
classroom.

Uh,

you've got this.

Yeah.
I don't know.
I'm sorry.
I don't got this.
Uh, I,

no, let's, let's talk it through though,
because, because let me tell,tell me if I think I'm on the
right track.
Something that actually a lot ofresearch is now showing can be
really useful is a gratitudepractice.
Yeah.
And I actually think this is,well that's similar, right?
Exactly.
Yeah.
And so a lot of our tutorsbefore a student's math session
will say, before we start oursession, let's give gratitude to
three things.
Okay.
Like, just three things you'refeeling really thankful about.

(34:11):
Doesn't actually even have to beabout math.
Anything.
I'm thankful that I woke up thismorning and it was sunny.
I'm thankful for the, you know,my, the amazing breakfast my
parents made me.
I'm thankful that I, I walkedhere'cause I live so close.
It actually puts your body,mind, soul in a, just a better
mind frame with which to tacklethe challenge that lies ahead,
which might be mathematics.
So what about that?

Yeah.
Yeah.

There we go.
We just did it together.

We did it.
Alright.

We did it.
Yeah.

High

five.
High five.
Okay.
But that's, I think that is, andI think, you know what, I do
wanna pause and be like, look,we're using the word
spirituality, we're talkingabout religion.
It can seem like we're goingreally deep, but at when we
strip it away to its coreprinciples, I really like what
you said.
You are calling it a spiritualexperience that is almost
cross-cultural that, you know,giving thanks.
A lot of people would be like,what the fuck are you talking

(34:57):
about?
That's not a spiritualexperience.
And that's why it's like, forgetthe word.
It's like I say, we don't needto use the word math trauma,
okay.
We're just talking about did youhave an icky root experience
with math?
Don't bring up a heavily loadedword if you think it's gonna
throw people off.
But, when we're talking aboutuniversal experiences, I think
you and I would probably belike, a lot of those are

(35:17):
spiritual experiences.
Giving gratitude to me is aspiritual experience.
But if that word is throwing youoff, you don't have to use it.
But I think those littlemoments, and I'm saying they're
not little, but I'm sayingsomething that takes five
minutes, can actually putsomebody into the mind frame of
getting to know mathematics,right?

Yeah.
And so another example inindigenous culture that we use
very often is kind of acleansing ritual.
Say for a pipe ceremony, we'llgather together, but we begin
with smudging.
So we'll smudge and it, it issymbolic cleansing.
It's like washing, you know,I'm, I'm cleansing.
Uh, and, and now I know to beclean.
I, I'm going to treat otherswith respect in this space and

(35:57):
so on.
So that's another thing that canbe done.

I love this.
Sorry,

we're going back to the Pythagoreans.

I was just about to say the obsession with
cleanliness.
Yeah.
Um, but the idea of cleansing isto, tell me the purpose of it,
because I, I also like cleansemy space.
I do it.
I did it before my talkyesterday.
Like, I always like to, I kindof feel like I'm resetting
myself and the energy.

Uh, I am no expert.
I'm no ceremonialist and so on.
I participate in ceremony and Ithink that's an important part
of, of becoming a complete humanbeing.
So, I long ago left a ChristianChurch.
But I

You were in the Christian Church,

uh, was raised as a Christian.

Interesting.
Okay.

Yeah, till 14, I, and it's kind of a long
story, but I disavowed that.

Got it.

At that point.
But I still feel the need forspirituality in my life.
And so, uh, I have found anindigenous spirituality that,
fulfilled that need.
But, I've had to learn all ofthat because I wasn't raised
that way.
And so I, I attended manysessions all over the place.
But when I was a student at theUniversity of Toronto, they

(37:01):
brought in ceremonials andspirituals and so on.
Joe Couture was the name of oneman, and he I think had a degree
in spirituality and religion.
So he talked about it in arational way as well as just
doing it or experiencing it.
He said, this is kind of areset.
I, I'm not sure what the exactwords he used.
It's like a reset or a centeringthing that you do is this

(37:23):
cleansing ritual.
So it prepares us for, to openourselves up to the next
experience that comes.

Well, and I would say to that there is so
much work around, um, thenervous system and polyvagal
theory.
So like, let's put spiritualityaside for a second and talk
about like cold hard science theidea of, we are evolved to
co-regulate, right?
So we walk into a room andeveryone's energy around us, we
absorb that energy.
We want to kind of matchpeople's energy.

(37:50):
So the idea of a reset is veryin, and the idea of grounding
and centering, how much workhave we done lately on the idea
of putting our feet on thefloor, you know, all of the
breathing exercises, taking awalk around the room, use of
fidget tools for kids who justneed to center.
So I would say that those twoare basically the same thing.
Again, we're using lang,different language.
We're using the term cleansingand reset, or we're using the

(38:11):
term centering, grounding,regulating, right?
So I would say these thingshappen in math classrooms and
can happen on a greater level.
And I love the idea of reallymaking it a part of, and again,
I'm gonna use the word ritual,which you might be like, oh my
God.
But it's like, what is ritual?
It's the same thing as aroutine.
That's all it is.
Right?
A routine that gets kids comingin.

(38:33):
A nice cleansing might besomething like, let's all take
three cleansing breathstogether, center ourselves,
those breaths.
Yes, they emotionally regulateus, but they actually put us
into parasympathetic.
They actually regulate ournervous systems.
So we're now relaxed and readyto absorb the material.
So I think in these ways, likethese things you're talking
about can really be brought intoeducation.

(38:55):
And you're kind of saying likeyou've seen through your
research that indigenousmathematics creates this more
whole picture of a person who'sable to bring their whole self
to mathematics becausemathematical thinking is not
separate from who they are as aperson.

Mm.
That's the one of the majormessages of indigenous education
in general.
So we we have to address thewhole person.
The whole person includes thesespiritual things.
And, and it's not like they'rejust made up.
They're actually connected withthe human, the human nature that
these, I prefer the termceremony to ritual.
I don't know why.
Okay.
But that's been my education inthis, is that we, we tend not to

(39:34):
talk about rituals and why in,uh, in, I don't know, uh, in, in
indigenous culture, we justdon't use the word ritual.

Interesting.
And some people may hate both ofthese words.

Well, too bad for them.
I'm gonna say ceremony.

Yeah.
It's your interview.
Say whatever you want.

Okay.
So, yeah, so, so.
We, uh, we talk about ceremonyall the time, and, and it's, I
mean, there, it's so complicatedand it's something that people
study, you know, spend theirlifetime studying.
So I can't, I can't contributevery much to that.
It's not my field.
I can just say, people havethought hard about it that, that

(40:12):
there's part of a universalhuman experience and that we
all, you know, we have needsthat need to be addressed, and
ceremony helps with that.
and, and, you know, anyone Ithink can benefit from engaging
in ceremony.

Ugh.

And they find the ceremony that suits them.
Yeah.
It's, you know, I,

I feel like going to the gym is ceremony for
some people, like going to aspin class.

Sure.
I, I would not say no.
I mean, people will find thatthey will find their own level,
they will find their own way.
But

Did I misuse that term?
I'm sorry.
I don't wanna like

No, no, no, no.
It's not, uh, it's not a misuse,but it's just, what's may be
lacking and, you know, may ormay not be lacking in that
context is guidance.
And I think that's one thingthat we need is guidance from,
uh, more knowledgeable, moresage, more, uh, wise people in
spirituality.

Yeah.
What an amazing talk.
We have to wrap up.

Okay.

I mean, I can't believe it.

Yeah.

It's been so fun.
Did you have a good time?

I did.
I did.
I,

I feel

like I'm just getting started here.

I know, right?
We could talk forever.
Yeah.
This has been so amazing.
There's, I mean, you're such awealth of knowledge.
We are just getting started.
There's so much more I wanna askand I just, I think it's really
cool because I think sometimeswe neglect like, like you in a
way, like are, you have all ofthis wisdom, you don't have an
ED degree, so it's not in theclassroom, but it is wisdom that

(41:32):
would be so useful in theclassroom.
So I really hope this bridged abit of the gap and I'm really
excited for teachers to hearthis.
If you're listening to thisright now, I'm sure you have a
million questions.
Not only about like thePythagorean cult, but about a
lot of what, Edward has saidhere about how we can create a
more holistic picture ofmathematics.
So text the podcast.
You can hit the link in yourshow notes and text us.

(41:53):
And I have to ask you the twoquestions I always ask everyone.
Okay.
Okay.
You have 30 seconds to answereach one.
Okay.
Ready?
The first one is, what is onething, if you could pick one
thing to change about the waymath is taught in schools, what
would it be?

I think we should use manipulatives at all
levels.

Oh, whoa.
Throwing in manipulatives out ofnowhere.

Well, it's, it's part of the whole person.
Mental, physical, social,spiritual, or, sorry, emotional
and then spiritual, uh,manipulatives are like the
easiest way for people to getstarted in that journey around
that circle.
We're all mental now, and weneed to break that and introduce
more of the physical.
So,

oh my God.
We could do a whole interviewjust on that.
Okay.
And now imagine someone'slistening to this and they're
like, oh, I love what you saidabout getting to know math and
you know, all of this, buthonestly Edward, I'm just, it's
never gonna happen for me'causeI'm not a math person.
What would you say?

Well, it's, it's part of the universe around
us as part of ourselves.
We're all math people.
I'm sorry to say.

Okay.
And finally.
I need to guess your sign, andI'm honestly, this is a tough
one for me.

Really.

It, I,

I think it's obvious, but

do you I do.
Okay.
That

I, I, on the other hand, I don't know as much
about astrology as I should.
I do draw charts for friends andfamily.

You do,

I Do

You draw birth charts?

Uh, yeah.
I can draw various charts.
just using, existing softwareand so on.

Oh my God.

Okay, so give me your date of birth.
Your time of birth, and yourlocation.

You sound like me.
This is what, this is now whatI'm supposed to say now.
Okay, so let me just do amental, I'm trying to see if I'm
getting an intuition.
For some reason, I'm getting anintuition that I really don't
think there's something about itthat is not tracking for me, but
I'm going to put that in thepocket of one thing and then I'm
gonna go with my rational mindand think.
I just, it, it's, honestly, thisis a really tough one for me.

(43:42):
Really?

Okay.

Are you an earth sign?
Okay, so my first guess isactually gonna be Aries.

No.

Okay.
And I didn't think that wasright.
Okay, so fine.
My next guess is going to be,

there's only 12 guesses.

I know there's only 12 guesses.
I know there's only 12 guesses.
I get that

Right.

Like are you,

Which, which again is.
Uh, in my culture there's 13.
What?
There's 13.
We divide the year into 13phases now.
12.
So, so, uh, you know, this is,uh

oh.
Okay.
Wow.
This just rocked my world,

right?

Are you a Taurus?

No, my sister is.

Are you a cancer?

No.

Oh my God, guys, I just, I can't after
three.

I'll give, I'll give after three.
That's it.

It's over.
Fuck.

Isn't it obvious?

I was, I'll tell you what honestly happened.
Okay.
I was between Taurus and Virgo.
Okay.
I was like, okay, it's gonna beone of the earth signs.
But you don't actually seemparticular enough to be a Virgo.

Oh, you don't know me either.

It's true and I don't.
Right.
That's the thing.
That's his.

I'm so particular

You are.
You seem so chill.

I try very hard to be chill.
Oh, internally.
It stresses me all the time, andI'm not particular.

Okay.
And so, so

I'm very, very, I'm, you know, it's, it's
something I'm trying toovercome.

You're working on it.
Do you know what your risingsign is?

no.

Do you know when, oh, you do know when is
your birthday?

My birthday?

Yeah.

Uh, September 6th.

Keanu Reeves is September 2nd.

Really?

Yeah.

Okay.

I know, right.
And he seems really chill.
Maybe he's really particular.

Okay.

Thank you so much.

I think that's how we can meet Keanu Reeves is
to say, I know someone who has,um, born just a few days apart
from you.

I really appreciate you trying to help me
out here.
Okay.
We're ending this, the end.
Oh, I have to say bye.
But it's weird to see by yournext.
Okay.
Bye.
Okay, well that was easy.

(47:15):
Tell us what a dodecahedron is.
Is that 10?

It's 12.
Dodeca is 12 in Greek.
Yeah.

So 12 sides.
12 angles.

12.
12 sides you've probably neverplayed Dungeons and Dragons, but
if you do, how

do you know that?
Why did you make thatassumption?

I just, I don't know.

I have not.

Okay.

I mean, I am interested in Dungeons and
Dragons, like I would like toplay a game, actually, to be
honest.
I don't understand how it works,but yes, you're right.
The so back,

it's still great fun.
Yeah.
I'll hook you up with a dungeonmaster.
You can, anyway.

Told you this is gonna be salacious interview.

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