internet math welcome we're back again part two electric boogaloo we are back we thought the
weather might actually not allow you know this might throw us off of course i'm glad to be back
yeah it's good to be here it's actually flurrying here right now in nashville but nowhere near bad
as last week i've never seen an ice storm before in person where it is the water is of the right
temperature that the moment it makes contact with anything it freezes into ice yeah and uh
walking around the days after you would see like blades of grass like encased and mummified in
like a nice like thick sheath of ice and it was like like a like very prickly it was very
and all the trees all the branches just like frozen in ice it's like someone just like poured
a bunch of water on it and then immediately like dropped rod dropped it to zero degrees it was
pretty wild like dr freeze or something yeah yeah because like a soul power it was very wild
yeah and no one knows how to plow in nashville there's no they don't salt i was talking to
someone and they were um they they followed one of the big like salt trucks in the plows into
like a 7-eleven and they're like i just want to let you know you're not dropping the salt like like
you have this big thing but like i followed you for the past couple miles and the guy was like
yeah you know it's just really tedious like i really like having that big heavy load on the
back while i'm plowing so i don't drop the the salt because it's safer for me to drive then
and when it's like yeah your job is to drop the salt so it's safer for everyone else so they don't
salt here they never plowed any of my local roads right here um so i was kind of frozen then but
All's well, ends well.
We're on the other side.
They vibe-salted down there.
That's right.
It just didn't quite work out.
Well, I mean, I'm really glad nobody I know down there got in any trouble.
I'm sure some people did, but it feels like...
Some people still don't have power.
Yeah.
It feels like our little community down there is good.
Pretty good.
Yeah.
Awesome.
So it's been a while.
I think it's been three weeks.
Three weeks.
We expected to do two weeks.
And it's like that last week, it's almost like a long week.
It's because so much happens.
And there's so much that happens that makes me think about what we're going to do here.
Like all the time.
And when we have a major event like we're having now, we typically, I doubt we would ever talk about current events.
you know other than other than if it really matters like it's mathy which they tend to be
but quantum computers but you know in terms of like price dumps and more you know market turmoil
i don't think anyone will ever index episode two as oh that was the one that happened when you know
during one of those big events yeah that happened to be this last week while between weeks two and
And so it just brings up, you like, you know, when you start seeing the patterns of people's sort of faulty thinking about events like that, it starts, it really does start to make me think, think, sorry, I'm having, I'm like burping, sorry.
It makes me think a lot about, makes me think a lot about math.
And I don't know if you saw the thing I sent you this morning.
you probably didn't
but it's just
people send me these things all the time
they're like here's something that you might
think is cool, a math thing
and
I always have the wrong reactions to them
so I want to
you know
I feel like what we'll do today is mostly a continuation
of the first episode which is like we're still
fleshing out
how really we view things
and you know you and I are not the same
But we connect enough that I feel like I can say things like that.
And like I think the real premise here, the last episode we focused a lot on the liberal arts framing.
I mean I don't know.
It's not as important as I think I make it sound.
It's just that when you're fighting the tide, you end up emphasizing certain things that make it sound like it's more important to you than they are.
Because you feel like you have to emphasize them.
so I feel like emphasizing the liberal arts focus one is like it's a catchy way of it's a little bit
different and it's like a way of you know expressing my contrarian take without causing
pain to anybody necessarily more confusion right but like that's sort of a good lane for an educator
is to not to confuse intentionally but I'd rather have confusion than pain
so yeah because confusion just is your development of the sense making process in general and things
that were once confusing aren't anymore and that's how you kind of also compound and learn new
concepts you take all of these things that uh you don't want to jump right to the end you want to
have a sequential sense of progression demystifying which is good for your psychological like loop of
getting feedback and seeing progress and you want to be able to you know build on that and that's
you know, if you're not getting confused on a regular basis, it means you're not growing.
Well, yeah, you're not, it's exactly right. And so that's a big, let's like, that's a big, like,
pillar. The thing you just said, it's like a big pillar of what we're doing here, right? You want
to put yourself in a state of confusion, you know, or like a controlled state of pain for learning
and for a particular reason.
So, you know, so what I tend to like to want to really emphasize
is learning math for the sake of it as opposed to, you know,
learning it as a means to an end.
And there's nothing wrong with means to ends,
but it's like the world's got that covered, right?
So it's like the world's got that one covered
and not so much learning it for its own sake.
Like that's a rare minority, I feel like, of people
who value that.
Totally.
Right?
And you prove it by actually, quote unquote,
wasting your time.
You know, wasting your time on wild goose chase rabbit holes,
not knowing why you're doing it.
And so the one thing I'll say,
so here's where I wanted to go today.
This might surprise you,
but I feel like this is going to be good.
So today is Sunday.
And, you know, it is morning.
And most people probably would find themselves in church or a place of worship.
And, you know, what I want to, I think, I'm going to say it, I believe studying math is like a pathway to God.
and I almost think God wants us to do it because it's like the way.
It's like the language of exploring God, right?
So when you sit and study, I don't know about you, dude,
but when I sit and study, I am like literally praying to God.
I'm like, please help me understand this.
Like I have no, like I'm at the edge of my ability to understand something
and it's uncertain whether it's going to click.
And that's the moment I find myself praying.
And I feel like mathematicians have that sense of prayer,
even though a lot of them are nihilists and don't believe in God and all that stuff.
And we can talk about that aspect of things too.
But I do think there is always this moment for me,
and maybe this is why I'm so connected to math
and why I'm so willing to spend time on it,
is because it's like really a process of me praying and having my prayers answered.
Well, I think if you look at it from like an anthropology standpoint,
there's plenty of examples of kind of, you know, earlier mathematicians who were heavily religious.
You know, back in a world that was less industrialized and developed,
you would spend a lot of time thinking about God and theology,
and you'd be thinking about its relationship in the world.
And to your point, it was a lot of demystifying the world and kind of you're trying to understand the rules God had set forth.
Right. That there's this divine sense of logic in a universe that was manifested by an almighty creator.
And you're just as part of your own spiritual journey, you're trying to demystify and understand these things.
And the one I'm thinking off hand was Pascal was not just a mathematician, but he also was a staunch Christian and wrote a lot about Christian theology.
but that's I think also I think in a world with less dopamine receptors less technology less kind
of like social media all of these things and you're sitting there just thinking all day you're
thinking about life the meaning of life and creation and then you start thinking about numbers
and I think that's I think it's a very natural leap of for a certain person's mind if they're
inclined to thinking in numbers and mathematical concepts to kind of marry the two it's like
and spend their brain cycles.
Yeah.
And you just jogged something in my memory
that when the original, like, sort of group theorists,
there was a notion that, like, a generator of a cyclic group
was, like, was a god, was godlike,
because it gave, at least this is how religious people
were looking, were viewing, were viewing these concepts,
because the one generator gives life to every element
in the entire group.
Yeah.
And so what we're talking about in a cyclic group is like if you have a finite, let's say a finite field, the integers up to the number five, right?
You take a number like two and you can multiply it by itself over and over again.
So two times two.
First number is two.
The second number is four.
And then eight mod five is three.
and then three times two, that gives you one.
I have a video on this that's slightly less confusing.
But it's like you basically take the powers of the number
and you end up generating every element in the group
and this was viewed as analogous.
This was viewed as analogous to God-like power.
Right.
Right, yeah.
No, I think that makes a lot of sense.
You try and, I was going to say, like, pattern match, you think about creation,
and you're seeing about how mathematics is also creation.
And one small addendum note I just remembered, too.
What's more important, what most people know Pascal for is actually Pascal's wager.
Oh, I was thinking the triangle.
I was thinking the triangle, too.
But then I realized, like, oh, for the on-ramp for other people who are thinking about math stuff,
it's the same man.
This is great. Why don't you go, you want to go into Pascal's Wager?
Yeah, so it's, it actually came up in pop culture recently, because with the passing of Scott Adams,
he talked about converting to Christianity on his deathbed and specifically referenced Pascal's Wager.
And the base premise is if you have a two by two square with four different possible outcomes.
One of them is God exists, God does not exist. And one is you are a believer in God, and you're not a believer in God.
So if God doesn't exist and you're not a believer in God, there's no eternal consequence.
If God does not exist and you do believe in God, there's still no eternal consequence because there's no afterlife.
There is no God.
If God does exist, though, and you do not believe in God, the idea of eternal damnation, punishment, purgatory, whatever flavor of your religious interpretation is.
and then if god does exist and you are a believer being able to get you know to salvation to get to
heaven right and it was just being like put forth and you can also view this in the lens of game
theory like a john nash game theory if you have these different boxes and you try to
and this is a dangerous thing when you apply this to philosophy and politics and economics but if
you try and apply a mass utilitarian umbrella of how many utils utils that you would get right you
would get plus one utile if i have a cup of coffee if i get plus five utils though if i get an espresso
because i really love espresso but i don't like the drip coffee right and if i don't get caffeine
that's minus two because then i'm grumpy and i'm under caffeinated um if you lay out all of these
different possible outcomes you can view the nothing happens it's like zero so god doesn't
exist at zero zero but then you have like plus infinity and minus infinity between if god does
exist and if you believe or do not so it's trying to put forward this rational exposition of just
looking at the possible outcomes utilizing you know it predates john nash by hundreds of years
but the idea though is that game theoretically um even if your your game theoretic optimal choice
is to believe that god exists and to work towards salvation because the the eternal timeline in
which your soul would face either in damnation or salvation you are in a much stronger position
to be believing in god um i guess for those maybe who want to learn a little bit too about
you know pascal triangles is you basically if you can think about a number right start with the
number one and then below it on the lower left hand side the lower right hand side you take the
sum of what's above it and you have one so you have a triangle that's one and then the lower
left is one and the lower right is one. And then you go one more level down. And what you do is
you're actually then adding the parts that are above it. And you have one and one, you have two
right below it. But then on the left, the far left hand side, you only have a one. And then you have
on the far right hand side with the two things above it, well, there's only one above it.
And that's a one. So you have a triangle that starts at the top at one. And then you have another
the one right below it, you have one and one because it's something the one that's right above
it and then you have below that one two one and then you can continue this down ad infinitum
uh and it's just kind of talking about probabilities common metrics uh it's one of
those things that you learn uh just in general it's actually interesting for uh binomial distribution
if you want to kind of lay out all of the different sequences of possible outcomes you
can use that as a way to kind of see the universe of all the possible um abilities of how things can
execute and uh it's it's just like a you know a fun little visual too to kind of think about things
and you can go down certain trees of the triangle to kind of see different executions of outcomes as
well um i'm thinking through here well i think we i think we've lost fundamentals so i'm just
going to keep on vibing for a second um so yeah i think tying back to the original point
the the viewing of mathematics as a portal to the divine is that i think in common culture
like culture today you would see them as kind of like pure rationalist and uh irrational right when
it comes to the domain of religion and math. And I think, I mean, for me personally, I would view
it as you're kind of doing a divine act in the sense of trying to better understand the world
God has made. And with that, you have an ability to challenge yourself, you're throwing yourself
against the laws of the universe, and you're trying to find deeper meaning in the math.
and in that journey itself it is also somewhat of a spiritual uplifting and interesting thing
all right we're still recording all right you're back there was only maybe like 15 10 15 seconds
of dead air i kept on ramping i'll be able to yeah yeah you can edit around that so i was just
as a hook to bring you back into it is that bring it back to your original point um viewing the
domain of uh mathematics is trying to further divine and understand the rules that god has set
forth and that while in common culture you would see this diametrically opposed between a pure
rationalist and like a faith-based thing um to apply yourself to try to understand mathematics
in its own sense is a spiritual journey because you're throwing yourself against the laws of the
universe and you trying to find meaning in the general like disorder of it all yeah and so here I was thinking about all this and probably want to keep keep going on pascal wager a little bit but like here why i was thinking about this god thing not
pretentious or philosophical or anything like that it's like when i see um people say in bitcoin
which is it's clearly a great pascal's wager example right people who um people who accept
kind of accept that part of the wager in Bitcoin.
What I see missing,
what I see people getting in trouble with themselves
is that, you know, in the short amount of time,
this has been around 15-ish years,
you know, there's a lot of education
on how the banking system works
and how money works and all that.
I know people are going to expect me to say right now,
like, oh, there's not enough emphasis on math. And that's not really where I'm going. Where I'm
going is there's not enough emphasis on the individual himself, like on, like you are a part
of the equation of whether or not this thing works. And it's like, it's, your knowledge is
incomplete. And like God made us incomplete, but gave us the ability to develop our own knowledge.
right um and we you know it's almost like our own our ability to create our own knowledge is
entrepreneurial meaning like we're rewarded if we create knowledge that turned out to be correct
and we get wrecked if we create knowledge that turned out to be incorrect and then there's a
selection process of those who seem to do a better job of creating more correct knowledge
right and so what seems to be missing from an evolutionary standpoint in the bitcoin conversation
and probably all of the all of like the real issues of the day right is our own individual
ability to create knowledge for ourselves which you must like you can't do unless you have a strong
conviction in your own ability to actually reason with yourself you can't do unless you have a way
to know you're right or a way you know not to know you're right but to be able to have a confidence
interval that puts you in a Pascal's wager territory that you say you know I'm okay making
this gamble because I'm 80% confident I have this worldview yeah I'd even add to that right in that
the human mind subconscious thought loop so you're always going to be thinking about something and the
question is is are these thoughts that you have your own that you've gone through your own process
to divine and understand and construct a worldview around or are you repeating what someone else told
you or are you just being conditioned by culture society your friends whatever it is right so there
is there there's there is no escaping that you're going to be thinking about things so the question
is are the things you're thinking about are they a kind of metacognition thinking about your own
thoughts and evaluating critiquing them or are you taking convenient ideas and running off someone
else's software basically right and i think with the discipline and domain of math in general is
what you're doing is you're saying that there's this objective universe and what i am trying to
do and the beautiful thing about math is that um since it you're you can go pure theoretical you
can just draw it out and start at one plus one equal two and divine and create this entire like
axiomatic linking of how math works there is no uh when you get down to the the ultimate like
ground truth of it there is no like peer pressure opinion among how this all works right so what
you're doing is in in the in the discipline and domain of understanding math more you're
explicitly pushing yourself to go through your own rational chain of thoughts and events and
critically evaluating them in such a way that you're kind of learning how to not be socially
guided in one direction or another you have to just understand how the math works and the math
is the math and there's really no beyond that yeah and we're really the meet the ends we're
trying to meet is just it's not like um we're trying to understand how to make a wheel roll to
a certain location or, you know, we're trying to understand ourselves.
And, you know, sometimes it's funny.
You said, you know, yeah, a lot of times we are operating off of a knowledge system that
somebody else programmed for us.
And a lot of times that other person is ourselves from the past.
Right.
So like we have a lot going against us in, you know, moving sort of forward on the pioneer
trail because we're not only fighting other people's programming, we're fighting our own
programming. And it's just all like the level of strength that's required is, is high. And,
you know, this, there aren't like a lot of natural pathways for, for really attacking this. And I'm,
you know, I really am looking to build a community of people that want to do this.
You know, I'm going to do it anyway myself, but it's boring and very alienating to be doing this myself and probably not that productive.
Right. It's great. I'll die as a knowing how much more I knew than anybody, but I couldn't explain it to anybody.
So I'm miserable. And, you know, it's not a good life. It's not a good life for us.
It's just that, you know, it is it's the calling.
The calling is, you know, when you feel like you know something, you want to teach it to people.
But what that requires is telling them that they didn't know this before.
And, you know, you know, so like I just so on a large, long scale, this sort of way we've been inclined to reject math or to use it only for vocational purposes, I think has been to keep us from being the kinds of people who can develop our own knowledge.
And, you know, that is an insight that can quickly turn to slop if you don't do the work.
Yeah.
That's what I'm sort of encouraging.
I think that also is a comment on the education system in general.
My kids are homeschooled.
My wife does an amazing job.
My wife also got a Ph.D. in biochemistry and biomedical science.
Right.
She went to an Ivy League.
And so I feel very blessed in the sense that my kids could have someone who was intentionally pushing that sense of learning and the importance of learning onto them.
I think there is a commodification that happens in education in general that is just trying to check boxes and kind of move through a process in the system.
and unless you find very good teachers,
you have people that are more part daycare
than they are actually trying to do education and enablement.
And you need to have people that are hungry for knowledge
and excited about the journey of acquiring knowledge
to be the ones educating you.
It's a lot easier to pass along worksheets
and say, just follow this ABC step.
I'm not sure if you saw this.
There was this, it went viral a couple days ago.
There was this woman and she was trying to help her daughter with her math homework.
And it was four times 500.
And the worksheet that the four times 100 had, it was four times 100.
And it was like, okay, what you should do is you should actually factor out the five and the 100.
So you have four times five times 100.
And then each line, each one of these lines I'm about to describe was a line.
And then what you do is you go down one line and you do four times five times 200.
And then what you do is you factor out the two and then you like, and it went on for like six steps.
And the mom is exasperated.
She's like, whatever happened to just 500 times four and then doing the numbers and then doing a bunch of small little notifications, like multiplications.
And I feel like a lot of, I've seen this multiple times now.
I feel like a lot of the education, it's turned into worksheet culture.
It's just like we have a step and the things we do.
We can't explain the concept that to do five times 400, what you could actually do is you just walk down the list and you do the five and the four and you just add the zero and then you carry it over.
And the idea of carrying over number from the single digit column to the second digit column because you are now over one power of 10.
Like all of these things are just way too complicated.
So we're going to make everything to the most granular bite-sized piece.
and you're going to be able to kind of just baby step your way through this because we don't want
to actually really involve too much math beyond like one digit addition subtraction multiplication
division right um and it's because you don't want to like rock the boat they learn a basic thing
you want to try and build on that and that's like a very brittle foundation as opposed to
um challenging yourself and expanding more that's why just in general i think education i would also
So just as a general lens, I would also throw it into this is the misalignment of government funded education just in general.
Creating like a make for work class of people who get to take off three months a year to be able to collect a pension and hang out.
And they're they're punching into their job just like a lot of people do day in and day out.
But rather than it being for some Fortune 500 company, they're doing it for the future generation and their ability to learn and discern things.
And I think that's like just a great disservice in general.
for sure i have a couple of thoughts here for one you know the problem you diagnose here is just one
of the compulsory nature of math education it's the fact that it's required it's gotten to a point
now where it's it's so required that you don't have anybody who actually knows how to teach it
that's a extreme but you know the by and large the system can't the system can't support the
teaching of it, it can't support the requirement, you know, and it's getting crushed under the weight
of that requirement. And then you just see little bad idea after bad idea to try to, you know, keep
the boat afloat, right? So this compulsory nature of having to teach math is like, you know,
problematic, right? Now in a homeschool setting, you know, I guess parents probably view it as
compulsory also but it's not like um it's not like life or death like um what if you don't do
well on this test or the standardized test and all that stuff and I think like there's a big
opportunity so it's a big opportunity to offer um something to homeschooler homeschoolers are a big
part of what I think about all the time and the thing about um the thing I I feel like is out there
is, you know, not everyone has PhDs in hard sciences.
And I think a lot of people at some point in time,
just like with their Bitcoin stack,
will lack the conviction that they can really deliver an education to their child.
And the more potential their children show,
the more that'll wear on their conviction.
Because, you know, it's a big bet on yourself.
it's like homeschooling and bitcoin are both big bets on yourself and the thing that no one talks
about is what i just mentioned 10 minutes ago which is you us as the individual is the primary
determinant over whether or not it actually works out or not not the thing you know it's not bitcoin
and its principles and its properties aren't the determinant i mean they're they're a determinant
but you are the determinant as to whether it works out for you.
It might exist on its own, but homeschooling as a movement may be great and thrive,
but it may not work for you unless you find a way to actually make it work.
And if you're like, you know, I think the public school system might be a good thing for people
who genuinely are below average at teaching and learning and have no values around it.
um whereas if you are above average you do not want you do not want to pull your uh family down
to the average which is a terrible average did you see um talking about like public education
um this is in california the remedial math classes they're like that only 40 percent of
people got right in college uh no no uh i'm i'm seeing if i can effort the um usd uh uc uh
university of california san diego reports a 2300 increase in students needing remediation of math
since 2020 roughly one in eight compared to students unprepared and i think a lot of this
i think just to even start is definitely because of covid it disrupted the entire education people
got kind of like left left where they weren't able to do their traditional education what little
traditional educational structure existed had entirely kind of collapsed um the math problem
i'm trying to find the exact math problem right now um
uh six plus seven equals blank plus six sorry seven plus two seven plus two equals blank plus
six oh my god so that's yeah i mean unbelievable are you going to tell me that two years of
two out of the 12 years of just interrupting schooling has like interrupted the ability to
solve an equation like this yeah well just to let you know 25 of students at uh university of
california san diego could not answer that question see i would just see that these are
college students yeah i would ask the question see i still want to come in and ask the question
why did why is this important right because i don't i think the reason you're seeing the result
like this is because nobody i mean people should naturally think people should have a natural
inclination to think that it would be important to be on that level and they don't so it doesn't
happen right and sort of what this shows me is what's possible if you absolutely really do ignore
these things like it's actually possible to create a human being that can't figure out by the time
they're 20 how to how to do that right like i don't i wouldn't have thought it was possible
right like forget school like you could be raised in a jungle right and have the ability to you know
have the ability to you know into it and discover these numbers in your brain yeah and figure it's
like is it even possible to create a human being that cannot you know that is incapable or is it i
see i just think it's a rejection and it's like i don't care i just don't care i don't see why
like it's not even like they can't do it it's like they just don't want to i don't get i'm
guessing right it's yeah like the ways you could look at it you could view it either as um an
emergent property of a system or an explicit conspiracy but there is a problem right like
whether whether it was explicitly orchestrated and designed to remove the cognitive load of people
or there are other things that happen that yeah certainly an emergent property but like it's
you know i but i think you have to understand people need to get that if you don't
I don't – it's – oh, God.
There used to be a sign in the library I grew up in.
I remember the sign.
It always, like, struck me.
But it just said that people who don't read are no better off than people who can.
People who don't read are no better off than people who can.
Who can't.
Yeah, who cannot.
Right, right, right, right, right, right.
Yeah.
And it's like if you – so it's like if you don't do it, yes, you will, like, atrophy.
and it's like it's amazing how much people will allow themselves to become so weak right it's
remarkable in the time we live in how much how people will do that so that's why i always want
to i always like to keep this focus on like why does it matter why why is it important
these are just arbitrary numbers right and blanks and why like why is this important it's not
important to know what five plus two equals.
It's just, but like, it's important to care and to then be engaged.
It's important to be engaged in the process of, you know, it's
being curious as being in pain.
It important to be engaged in that process of solving that curiosity and building strength off of it And just like this is I feel like again what God wants And like you know I think engaging in math just to learn it is a form of Pascal wager
Okay.
And most people are failing, which is like, you know,
what if it doesn't matter at all?
I never, what if it's true?
I never needed to know this for anything,
which is what most, that popular opinion, right?
I never need to know this for anything.
And what if that's true?
okay good and then i'm gonna make that bet and it's like we seem to have a large amount of people
making that well what we well remember what we used to back when i was in math class i was always
told well you're not going to have a computer in your pocket walking around right right so there
is a there is a case to be made of like technology solves these things that presumed the reason to
know math is to be a computer right bingo right right that the end sum was i i'll push back and
say i think knowing that five plus two equals seven is actually important because like that is
not um we're not talking about the identity property of a matrix or getting the eigenvector
what we're talking about is going to the grocery store and i have to get seven you know pounds of
potatoes and i have five currently i've they come in five pound bags how many bags do i need to get
to get to the seven you know i mean like it is such a immediate every day in your life in your
subconscious you're looking at those kind of math numbers it also would have me asking question
how many people actually can answer that question but they don't understand the abstract nature of
a math problem where you have five plus two equals x plus six and they don't understand the abstract
property but viscerally they get it to your point people a tribe uh an isolated tribe that has never
made contact with with the outside world probably could figure out if you have two hunting groups
and you have a group of five a group of two a group of three and a group of six they could
figure out the groupings to make them equal and go out and hunt for food right so it's also this
it's an it's an abstraction problem the entire thing is an abstraction problem i i reject that
if you phrase it as a word problem, this is something we're doing at homeschooling, right?
There's a little bit of work, like looking at, here's a bunch of math equations, like
two plus three and five minus three, and going through all these things and looking at all the
different options. And then you say, Sally has six apples. She gave one to her friend, Jane. How
many apples does Sally have left? And you can actually see, I can see with my kids, they can do
one and not the other. Like my son, worksheets all day. And my daughter can do the word problems,
but not the worksheets.
But like, so there is definitely
an application of knowledge transfer problem here.
But I think this is an important point.
The domain to be able to transpose a concept
into an abstract thought
and being able to analyze it
at that abstract thought level
and not at the literal word problem,
this is me as the person level
is a really important piece
of the becoming your own sovereign individual.
If you want to be cliche for a Bitcoin podcast, right?
You need to be able to have these transpositions between different levels of abstraction and mental models to be able to think about things for yourself.
And the higher levels of abstractions, the more often you're able to cross, pull from different disciplines, different aspects to kind of create your own more holistic worldview that you're dividing yourself through your own thought processes.
Yeah.
I mean, if you just take five plus two equals seven, I think it's much more important.
I think the number seven is the least important part of it as far as knowing you're right.
Just knowing that the way you know that that's right.
Anyone listening to this, I'm sure, knows what I'm talking about.
Right?
Understands the knowledge.
You know, it's analogous to the Atlas Shrug, A equals A.
A is A.
Right.
It's like you just know when something equals something else.
You just know 5 plus 2 equals 7.
And it's more important that you know and how you know you know than your ability to count.
Right.
The ability to count is like, you know, it's important, obviously.
Well.
It's important.
Like, if you can't count for yourself, you're going to have to trust somebody else to count for you.
And that's not very ideal.
But it's also, you know, towards the ability to think.
Like, you know, even a child can understand knowing that they're right.
So it's so funny.
Where my brain goes, and you'll appreciate this here in a second,
like it's important to count, I immediately go to counting cards.
Right?
And the foundation of being able to count cards is can you add by one
and minus by one and keep a running tally?
Right?
The most simplest of math.
Seems easy.
Easy, yeah.
Like the application of said skill is its own kind of like discipline of its own
of like, and I'll get to that in a second.
but the counting piece is what unlocks the next level of the problem,
which is the statistical distributions of remaining cards.
And this will be a fun little potpourri for everyone listening.
The base premise of counting cards is that
when there is a higher ratio of remaining tens and aces left in the deck,
it is more advantageous to you as the player to win.
And when there are more low cards left in the deck,
it is disadvantageous to you.
How does this get applied?
uh well one just in the game of blackjack the whole rule you get dealt two cards the dealer
gets one card face up one card face down and then you are asked okay do you want to hit which means
take on an additional card or do you want to stay where you are there's also splitting and doubling
down which i'll put aside for a second that has a mathematical expected value piece of it too
but the idea though is that you want to put more money on the table when you're more likely to win
and less money on the table when you're less likely to win.
And the way this actually works in practice
is every time a card gets dealt,
this is the simplest high-low system that there is,
is that if the card value is between two and six,
you add one to the count.
When you start, the count is zero.
And then every time a 10 or an ace comes in,
you minus one, and then seven, eight, nine, or zero.
So when you're counting cards,
you're keeping this rough distribution ratio,
and there's a reason why it's like this.
two through six, two, three, four, five, six.
That's five.
There's five, those are five, a group of five cards.
Then you have 10, king, queen, jack, ace.
Those are also five cards.
So you're keeping a pure ratio.
And then seven, eight, nine are just left at zero.
So now you have this even distribution
of good cards, bad cards.
And what you're doing is you're trying to understand
the ratio between good cards, bad cards,
good cards, bad cards.
And that gets extended into how many cards
are left to be dealt
and a bunch of other things and deviations from strategy.
But all this to say is all you're doing is you're taking plus one and minus one.
And the actual game of counting cards much more turns into how do you not get pinched?
Because you can get told what's called backing off.
And if it's really bad, you'll get trespassed,
which means you can't even enter the casino property anymore.
But my math professor in college was on the MIT card counting team.
And I'd go to his office hours, not to understand the math behind card counting,
but it was like, how do you keep the heat off you?
And it was like, order a screwdriver.
but then go to the bar, get an orange juice,
go to the bathroom, dump out your screwdriver
and just drink the orange juice and just keep on sight.
Like ways to make yourself look like a drunken and idiot, right?
And a lot of like meta games like that.
But that's all to say though,
that it's just starting with plus one, minus one, right?
And you can see how that foundational bit of knowledge
starts understanding statistical distributions,
understanding how to play games.
Like not even just like gambling games,
just like the games of life.
And that counting is a gateway
to be able to do any of the other things.
If you can't reliably count,
you can't reliably apply statistics, right?
And so there's just, there's an order to this.
I have a question now.
So yeah, so like I feel like, I feel,
I've done the counting thing.
It's a, you can develop that ability.
Everyone can probably.
Maybe not, you know.
I think everyone who really, really, really,
really wants to can do it.
You know, I mean, it's a fun thing to do
when you're by yourself with a deck of cards
and you need to pass the time.
I think the two things
activities I've done the most by myself
was drawing out a Pascal's triangle
as large as I can
when I have a long train ride or something like that
and sitting with a deck of cards
going one by one
and practicing that
so the question to you is
the real question is
how do you get from
this rule
to a decision in your mind
that I believe
I believe this.
I trust this.
I'm going to go all in with my time and learn to do this and effort.
And I'm going to learn how to drink fake screwdrivers because I know this works.
How do you get to that point?
That level of the conviction leap?
Yes.
So it goes in stages.
It starts with, hey, can I do the simplest form of this?
And the simplest drill you can do with card countings, you can take a deck of cards, count it, hold the last card in your hand and be like,
I know this is either a seven through nine or two through six or a 10 or an ace, right? You're able
to just know because mathematically, since it's the deck of cards, the whole, the true count of
all cards that exists is zero. If you're at the end and you have a plus one, you know, I have a,
you know, I have a 10 through an ace at the end or in vice versa, right? So you start building a
chain of competencies and understanding, right? So you can read a card counting book and you can
understand oh this this is what the person's telling me to do and it's like for my process
it was gradual steps and understanding the sequence of events and then understanding the
law of large numbers and knowing that even within an individual session i could lose right because
to be clear like when you're counting cards what you're doing is you're making it like a 53 percent
chance in your favor you're not you're not guaranteed printing money you're just instead
of the casino having a two three percent edge you have the two three percent edge um so it's an
understanding of walking through for me all of those um foundational pieces that build up to an
overall thesis and understanding the law large of law of large law of large numbers and being like
okay i could do this i understand the math i know it cold i know it forwards and backwards and from
that um you know you could call it faith in numbers but it is kind of grounded in this sense
of I have the statistics on my side.
It's faith in your understanding and inferences and the knowledge.
You have to build your own bridge in your mind from this rubric to comfort that you're
actually going to do it.
And that's why not everybody does it the same way.
Right.
You have to build your own bridges.
You have to.
So that you are the factor.
You are the determining factor.
It's not whether or not you implement this correctly.
right it's really whether or not you know the way to implement it correctly is to maintain
consistent belief you don't have law of large numbers unless you're unless your conviction
right is equally high for every trial right right right so if you start to lack conviction when
you really have to put the big money up right you're not you know you are gonna now you're
you are messing with this experiment and the law of large numbers.
And, you know, so like that's really where I like to spend time and energy on.
Right.
Is like we have all this application, like everyone, the applications are like we have
a lot of people doing that.
Yeah.
And they're good.
There's a lot of good applications.
Right.
We send rockets into space.
Contrary to popular belief, we do do that.
Never to the moon, though, just low Earth orbit, right?
Yeah.
But, like, you know, whether we did that or not, we do these, you know, these applications of math are, they've been open sourced.
And they work in low Earth orbit just like they work.
They're pretty good at working universally.
it's um it's the question of you know what's your objective is your objective to send
satellites into space or is your objective really to be a strong human being who's and maybe you
want to be a strong human being who sends satellites into space you know that was my dad
yeah my dad was satellite engineer um you know complained all the time about not making
money in financial engineering
and all that stuff, but he's like, I'm sorry, I just
love sending stuff into space. I couldn't
help myself.
So maybe that's what you're
after, right? Maybe you're after making money
in blackjack, right?
But what I'm after is people who
want to, who really want
to strengthen themselves and be,
you know, like
in order to put satellites into space, do you
understand the kind of conviction it takes to put yourself
through a PhD program and
And, you know, you're not just trusting the math.
You're trusting, like, you know, when I talked in the beginning about, for me, and I, you know, look, I didn't get a math degree.
I got a, you know, applied degree that was much easier to get.
Because I didn't have the maturity or the conviction at that age.
But, like, I do remember always sitting down with my book and having a moment where I'm praying.
like please and you know where my prayers might not be answered for weeks and i'd be on the same
page and not be able to move on and then one day it happens and you just don't even know you really
don't know why you just kept pushing and pushing and i think there's this synergy between yourself
the energy you put into learning right the desire you have the energy the amount of time and energy
you spend on it. And, you know, like, it's just when you're studying pure math for the sake of it,
and it's, it really is pure math that I think, you know, is where that this process lives,
right? It's like, what, you know, like, why are these structures so universal? Why do they work?
you know why does you know you talked about this um process of assigning taking 13 cards
and mapping them to either one zero or negative one right that's the map that's a linear map
so in algebra that's a linear map it's um it's it might or it might be an isomorphism probably not
but it's probably you think about it as a linear map you're taking a set of you're taking a domain
of 13 numbers and you're mapping them into a domain of three numbers.
So it's definitely not an, you know, every, it's a function.
Every input has an output, right?
Yeah.
So like, and so that's the kind of thing.
So it's like, why does that, why does it matter?
You know, why does that, why do these things matter?
What are these structures and what else do these structures enable us to do?
And so back to five plus two equals seven, right?
you have to understand how to do that in order to so if i would say the end game of that this type
of numerical arithmetic for me and the people that i think i want to teach would be at least
understanding why um multiplying two numbers is easy but factoring them is difficult
yeah that's a fundamental oh yeah physics that's a physics property of the world of
cryptography that we live in and that that we are um you know subjected to right right and in order
so in order to understand how easy it is to multiply two numbers you kind of have to understand
how easy it is to add two numbers okay right true and well i mean and and going from a private key
to a public key as a multiplication operation.
It's just the domain in which you're multiplying against
is just so massively large
that you can't reverse factor it.
Unless you have a quantum computer.
It's multiplication by a generator
that we had established was thought to be
you know,
deified.
Yeah.
Did I mention that on the last podcast?
Why that generator and everything was picked?
No.
I don't think so.
There's one of the earliest posts on the Bitcoin talk forums.
Someone asks, why is it the LibSec P256K1 curve?
And basically the response, I think it's Satoshi,
it's either Haller or I think it's Satoshi,
comes back and says,
it's the only curve, the generator,
that didn't have any weird constants held at it.
Interesting.
And the reason why that important is that a lot of elliptic curves they have an arbitrary constant being held and it turns out it because someone has been able to reverse engineer it If you hold this thing constant right here the entire generator being a secure encryption
falls apart,
and then you're able to reverse engineer everything.
So Satoshi, when he picked that curve,
was like, it was the only one I saw
that didn't have any weird things going on with it.
You know, you talk about, like,
you know somebody who had conviction in his enough to make his own pascals wager to set this thing
off like this right i mean it's like that's the that you know are we all you know we all have that
in us and i think we all have to find our way yeah you know we have to find our way into that
path ongoingly because whether we win or lose really does depend on whether we have conviction
And we start to see how fake people's conviction is when it's tested.
And whether it's a low-level test like spam, you know, low-level test.
Like, oh, my God, I can't believe how easy that was to shake people's conviction.
Or, you know, we're going to have some very difficult tests, I believe, in store for us in the next maybe 10, 20, 30 years.
I think they're going to be much more difficult, much more slick, much more challenging.
Well, I think especially as just with the introduction and rapid acceleration of adoption and impact of AI in general, it's going to be a lot easier to just have someone serve it up to you.
It's going to be a lot easier to just like, here's an answer.
And it's so eloquently written.
It's so much better written than anything you, dumb person, could ever write with your own hand or type out as your own message.
So you're going to get, as the kids call it, you get one shot by the AI.
You just take the gospel of whatever it says and you spit it back out.
Did you see the one where I sent you that I got it to admit that it was literally just optimized to impress humans?
Are we peeking behind the production of the podcast where you send me all of the extortions and yelling and everything you do when talking to these AI models to just like – when the AI revolution comes, you're going to be the first one.
You're going to be on the stretch racks immediately.
Yeah, probably.
Well, you know, I have shared my AI yellings, my yelling at AI with a lot of people.
And what I've been told was a lot of people have just had their accounts canceled by, like, Anthropic.
And so, you know, I don't think I've crossed that line.
I think I stayed within this line of, like, how I would talk to an employee if I didn't care about their humanity.
Yeah.
And it's like I think that this is part of the conviction process because I need to know how much conviction I can have in this tool that I need to really kick the tires on its capabilities.
Yeah.
So calling it out, calling it out to the limits of like when it's lying to me or when it's really not – like really calling it out and asking it like what were you thinking the moment – like I ask it.
What were you thinking the moment you saw my instruction and decided to do something else?
That's the level of granularity I get when I'm really grilling it.
And then eventually it confesses things.
Maybe you're reliable, maybe not.
But the theme of conviction is really what it's all about.
This is another new technology that you're going to have a lot of fools.
you already see it right
fools with really high conviction
giving it its API keys
letting them go crazy
you know that's not going to be
how intelligent people use this
right so I'm not worried
I'm not so worried about
it going crazy because it's
very limited even as powerful as it is
still very limited
and I think you always have to be
like I have a lot of faith in myself
to navigate the new thing
And I think that's what I want for people.
Totally.
I want people to have that power and to feel like they're – without having to give it all away to a new technology and say, well, I want people to have agency.
And I want to – that's the world I want to live in.
Right.
You want to avoid the – I mean the meme is funny to me, but the at Grok, is this true?
Just like something happens and you just at Grok, is this true?
Totally.
Yeah, you want people, it's all part of this building your own bridges in your internal process, being able to understand and rationalize reasonable things.
I'm a big fan of don't tell me chat GPT said so.
Can you show me the chat history?
Because I can corner it into a box that I actually am, like I am physically a potato.
I'm not a human if I prompt it the right way.
So it doesn't really matter to me what a given output spit out is.
I want to see the, the reason I want to see the chat history is I want to see the journey of the conversation and the thought process and all of the assumptions and all of the kind of coaching and guiding to get to an answer.
For maybe something fun to throw in the show notes, I just linked the thread I found.
It's Hal Finney.
So Hal Finney on January 9th, 2011 asks, why did Satoshi choose this curve?
and there's a long discussion with a lot of ogs gavin andreason mike hearn christian decker
um gregory maxwell are all in this thread uh and it's funny uh it comes back around
it gets bumped a couple years later and greg maxwell like right near the end of the thread
is talking about because someone's like oh i don't like how this curve was used it makes me
feels weird and someone cites all of the
constants and backdoors and Greg Maxwell replies
you mean you feel uneasy that he chose the
only standardized curve
that doesn't have unexplained parameters in it?
That's basically the end of the thread.
Is that like everyone's looked at
this thing and this is the only curve
like Satoshi in the universe of any random
curve he could have chose for all this
like for all the public private key cryptography
chose the one curve that didn't have
any weird screwball values in it.
Pretty incredible.
It's just incredible that you think about how immaculate this had to be.
And, you know, people need to understand.
The reason why this is important to understand is because you should not have ultimate conviction in what Satoshi did.
No.
You should not have that.
And you should have a way of pressing and pressing the same way you press anything to see where the holes are and where maybe you shouldn't have full conviction.
Yeah.
Yeah, this is, I think, part of the journey.
And it should be comforting, too, that there's nothing wrong with walking through these thoughts.
Because you need to understand and discern this knowledge for yourself.
And even in this thread that I linked, people are speculating it's Satoshi the NSA.
Which is a very common talking point even today.
And there's nothing wrong with kind of going through your own thought process and game theorying and thinking these things through.
I think it's actually kind of the responsible thing to do
especially
especially if you've put a large percentage
of your net worth into Bitcoin
and you're not asking these questions
then like what are you doing?
Are you just listening to some macro podcasts
and you're like I'm just going to
take all of my life's work and energy
and throw it into this thing?
I know, well I would say
I know what they're doing
they're just going to sell
the second they get thrown off
it's like you know
But the conviction is false.
And so it's just these are easy targets.
And I don't want people I care about to be cannon fodder for Fudsters.
This is actually also kind of my love with the price being down.
Not going to lie.
There's a lot of Johnny come lately's like the price must go up 50% every year in X, Y, and Z.
And I got my conviction and belief in Bitcoin when Bitcoin was at $200.
My core thesis hasn't changed.
Right.
And this is part of that process.
even cycle theory ending with a sample size of three going on four you're you're draw you're
making deterministic claims of finality of how the bitcoin price must behave is like yeah you
have a sample of four yeah you have a sample you have a sample of four where the sample the first
three of the sample we had zero interest rates and one sample we're in now where everyone is
reacting and this is like a whole episode i feel like we have to do about but like with the one
And it triggers me to no end when I hear all this from people, especially people I know are mathematically inclined and they're not even doing the work to think about the out-of-sample bias.
You should always be thinking about out-of-sample bias literally 100% of the time you make a prediction about anything.
100% of the time you need to think about that, right?
Yeah, absolutely.
And this is not a hard thing to think about.
Oh, you know, it is literally the issue of our time, which is non-zero rates in this one cycle.
Right.
We've had three with zero rates.
We've had one with high rates.
High at 5%.
And we're making conclusions.
Higher, historically high.
I'd say the hardest money environment Bitcoin's ever lived through.
That's true.
I'm more just laughing about in the 70s and 80s with 15% interest rates.
I came into the actuarial profession when everyone was using 8% discount rates.
There you go.
And when they went down to 5, everyone was like, oh, my God, we got to be lump summing now like crazy.
Yeah.
Because we got to take advantage of these low rates.
I get it.
Yeah.
But, like, the reality is, you know, it's not just – rates aren't just a number, right?
It's just like age.
Age is not just a number.
It's like age is just a number, you know, a number that has a high.
likelihood of predictive high predictive quality of how long you're going to live yeah actually
yeah like you know rates are not just a number right it's an indicator of how hard the monetary
environment is and you know we you're going to draw conclusions about the nature of the world
based on an absurdly different um an absurdly different observation in your sample set totally
low sample set that there is.
I can't stress this enough.
I mean, if I had to do 10 episodes just about this one thing, I would do it.
The time value of money.
Yeah, the time value of money.
Like how critical that is for every other economic calculation.
But also just know what people, this is like the mistake people make when they're creating
their own knowledge and ignoring such egregious out of sample bias and trying to create their
own knowledge.
I mean, any kind of recency bias should raise your eyebrow also.
And you should be looking out for just, oh, is this time different?
You know, those general questions.
And maybe it's different for reasons I don't know.
But we have the most important reasons like smacking you in the face.
The other thing, too, is that this past four years is the first time institutional investors actually cared about Bitcoin.
Like the tail end, the picotop of the 2017 cycle was the turning on of the futures market for Bitcoin.
like it's like it's like to the to almost the week the futures market the chicago mercantile
exchange bitcoin cash settled futures and the bitcoin peak price is almost identical
and so if that's the top and that's kind of if you want to view it's the start of the next cycle
as it goes down and goes back up like that was the first one where it really mattered and this
is the first time where like it really really mattered between 2017 2021 you had a couple
niche side players. I mean, Sailor wasn't even stacking until 2020, right? So like,
you just look at it in this context of like, as the ship in the capital base gets bigger,
it's going to be more at the whims of macro assets. That's been the one thing people are
complaining about. And all of these things, this is why one, a sample size of four is bad. And two,
the context in all of these is so much more critical. And it's way more likely that a nascent
network like bitcoin's having schedule is not the determining factor but it's global macroeconomics
because that's bitcoin maturing as an asset like the maturation of bitcoin as an asset is not
uh the entire universe goes around into bitcoin like there's a merger happening between financial
and economic systems and bitcoin as it exists and bitcoin is amazing but it's not going to be
laying down all the rules and and going to be controlling everything because all all of those
early OGs who sold, sold their Bitcoin into a network of traditional finance holders, which
means that they are a larger percentage holder of the network. You know, millions of coins between
ET, well, just MicroStrategy 700 that, right? But then you have all the ETFs and everything else
that is a larger percent of the float of the capital base of Bitcoin. So obviously it's
more at the whims of the traditional macro system in general. Yep. For now, especially.
For now, yeah. If you're trying to draw, if you're, if you're building knowledge, if like the you in
the future is living off of something that was programmed by the version of you in the past and
that is you right now making really specious conclusions right and putting it's really
dangerous and this is like the thing I want to really highlight and say this is why this work
is so important it's that you should be this should be like one of the highest priorities
you have of your life is to not is to at least eliminate the creation of knowledge that's going
wreck you. Yeah, absolutely. Is there anything else you want to update our many fans on? Anything
else for the podcast? We'll try and get this in two weeks too. We'll try and make the three weeks
a one-off thing, but we'll go back. I'd say the website's coming along. We have magicinternetmath.com
is now the domain name. And, you know, in the last episode, I told my story about how the LibSec
GitHub was the thing that threw me into the rabbit hole.
I figured out a way to just make a class.
I threw the GitHub into my process for my website,
and I made a class out of it.
And actually, if I had that three years ago,
we probably wouldn't be here right now.
Yeah.
And I just had a thought about doing this now
for some of the Bitcoin talk threads.
Yeah.
Which I think...
You can find a whole explanation of why LibSecP.
You can just go to that thread that starts.
There's a lot of good things to start with on that.
A little bit of a teaser, not to promise anything yet,
but we've been in contact with some people that are way smarter than us
that work on LibSecP that we may be able to bring on to a future show as well.
And that will hopefully elevate the class and do a service to our listeners that way.
For sure.
My pattern on podcasts in the past has been now a small sample size of four or five.
but like you know my partner we have a maybe maybe have four episodes of stuff we need to get out
and then there's not much more to talk about between the two of us and so we got to now bring
in the experts that's right so uh you know look out for i'd say definitely look out for that look
out for guests um and check out the website play with it engage with it i am starting a pioneers
Club. So if you're listening to this on Fountain, you can start to see some extra content I've been
putting out there. One thing I do want to highlight is I'm putting out a video series
based on the book Men of Mathematics by Eric Temple Bell. And it's a 2,500-year history.
It's biography. It's like every episode is like another biography. It's like a 10-minute biography.
And Pascal is definitely one of the episodes.
And I love, like, I really want to push math history.
I think that's the lowest hanging fruit that a lot of us can really start on this process with.
You know, the history of math, it's just, you know, Bitcoiners like history.
I think if you want to know the history of money, you should know the history.
It's really the history of mathematicians.
Right.
And history of, it's like, where are you?
If, you know, we are people searching for conviction.
in ourselves where,
how did,
how did the top of the top of those people live?
Right.
And that's why we read and that's why we study history and study these
people.
Right.
We want to sort of find our place because we are on a similar pioneers
trail where we find ourselves right now without a real blueprint of how
to do it.
Totally.
Excellent.
Yeah.
I think that's well said.
Exciting.
Thank you.
All right.
Second one in the books.
All right.
We did it.
All right.
Number two.
Take care,
everyone.
Have a great day.
Thank you.