May 17, 2011 • 37 mins
In this episode, Robert and Julie take a sweeping look at math, addressing several important questions. For example: What is math? Where does math come from? What mathematical skills are we born with and how much can we understand?
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Episode Transcript
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Speaker 1 (00:03):
Welcome to Stuff to Blow your mind from how Stuff
Works dot Com. Robert Lamb and I'm Julie Douglas, and listeners,
do not run away. We are we are talking about
math in this episode, but we're not going to talk about, um,
you know, a whole bunch of rat We're not gonna
rattle off a bunch of equations and talk about, um,
(00:25):
you know, the the inner workings of Alderbar geometry or calculus,
because if you're like me, you probably never really got
into mathematics in school and you're not particularly good at it.
And uh, anytime a math question comes up, you try
and force it on other people. And you absolutely cannot
go to a bowling alley that does not have automated
score keeper right right, Or you always say something like
(00:47):
I'm an English major yeah to the response of what's
seven times three or something ridiculous like that, But I
will say yes, stick around absolutely, because nobody has more
anxiety about math and I do, and nobody's less of
a mathlete than I am. And yet I find this
question that we're going to pose to you into ourselves
absolutely fascinating. Yeah, we're getting into the philosophical area of
(01:10):
mathematics to a certain degree and just talking about what
it is and uh and indeed the question is mathematics
a human creation, a human invention, or is it a
human discovery? So think think about that. Mathematics this thing
that powers everything pretty much everything that we do, uh
that from the device that you're listening to this podcast
(01:32):
on right now to the the science that has enabled
civilization to reach the point that it has reached. But
what is math? Right? Yeah, what is math? We should
back up. We're gonna back up. We're gonna we're gonna start.
You know, we're not gonna really go back into the
history books and talk about like who invented this in
that because a lot of mathematics is pretty ancient to
(01:53):
the point where we can't really place uh, you know,
attributed to one particular individual or another. But we can
back up to birth to you, when you were a
baby and you were just you know, spit out on
the world, uh gleaming with with goog um. Even then,
(02:13):
your brain had some mathematics and you didn't even know it. Yeah,
a minor mathlete at least. Yeah, because you were you
were born with something that we call number since all right, Um,
and a number. Just to to break it down, a
number is a word and a symbol representing a count. Okay, uh,
(02:34):
Like that's the basic though you may call it too,
you may attribute it with the numeral two, or you
may have some other system of referring to it um.
For instance, in China they have they have small they
have shorter words for their numbers, which is one of
the reasons they're supposedly better at at mathematics because there's
s less just you know, it's kind of like cutting
(02:54):
a penny off of every transaction. It adds up and
that allows everything to to move. You don't have to
have a new word for two hundred um. You just
well anyway, we won't get into that math system. But
it's pretty cool. But but this is necessary because it's
imagine yourself in the wild and you encounter a dog,
like a wild dog that's barking at you. And then
(03:15):
and then you were to encounter two wild dogs barking
at you. Being able to differentiate between the two is essential.
It's it's all about navigating a world full of multiple
objects and moving objects. You know, there are a lot
of like if you're just walking around the forest, there
are a lot of trees, there are um wild dogs
moving around, There may be other humans. I mean, just
(03:35):
think all the things in your life that are in flux,
and you have to be able to navigate that world.
And that is what mathematics helps us do well. And
this is your brain in action, right, I mean, when
you enter a room, of what you are seeing is
not coming in through your eyes, it's actually what your
brain is inferring. And so we're pointing to here is
(03:57):
our brain structures and this idea that we might be
hardwired to to spatially differentiate as much as possible. That's
what you're talking about. Right, When you come into a room,
you're looking at the height whether or not you know
you're looking at the height of the walls. You're you're
sort of creating this pattern in your brain of pattern recognition, right,
And other animals do this too. But but those other animals,
(04:20):
like the gooey infant that you once were, uh, they
have wiped that off actually after a while. Yea, all
the infants on encounter gooey, some of the adults are
gooi um. But such a child will have no grasp
of the human number system. They are not going to
know what two is, or what three is, or what
three times eight is. Those are things are going to
(04:41):
come with in time via education, but they still have
that number. Since then they can identify changes in quantity
and this basically equates to something called logarithmic counting. And
neuroimaging research is actually studied the brains of infants and uh,
I mean scientists have studied the brains of infants through
(05:02):
near imaging research and they've they've registered these, uh the
mental activity going on as they identify integral increases in
physical quantity. So like a baby, for instance, wouldn't be
able to tell that much difference between five and six
heady bears, but five and ten they'll definitely see because
there there's a definite um logarithmic increase in quantity. Yeah,
(05:27):
and I thought this is really fascinating. Um uh To
that point, there's an article from futurity dot org and
it's called babies can compt before they can communicate, And
what they say is our findings indicate that humans use
information about quantity to organize their experience of the world
from the first few months of life. Quantity appears to
be a powerful tool for making predictions about how objects
(05:50):
should behave And what I think is really important about
that is predictions because that is what math is about
at the end of the day. Right If I'm sitting
there adding one in one, then then I'm trying to
predict what the following number is going to be. And
that's at the most basic level. I mean, we know
this is applied throughout physics, throughout every single field that
you can think of, in order for us to try
(06:10):
to make sense and categorize our lives and predict future outcomes.
Even chaos theory is an attempt to predict the unpredictable.
Now here's the thing, though, and this is where math begins,
because we're not even really dealing with math yet. We're
dealing with numbers. We're dealing with with numbers. Since but
as we're navigating this environment around us, um, the the
(06:34):
higher the higher the math gets, the more the larger
the numbers become, the harder it is for us to
to to to process it like even um like humans
are systematically slower to compute four plus five than they
are to compute two plus three. Like when I was
going over that in my notes, I could actually notice
(06:55):
it since I'm not good at math. I mean I
could actually feel the difference in in computing four place,
you could feel the brain power. Yeah. But but this actually,
this is something that everyone experiences, everybody because we are
not evolved to do arithmetic, higher arithmetics, certainly not geometry
or anything. But I do think this is actually started
looking through some information about autism UM, in particular savants
(07:18):
UM and ten percent of autistic population is savant, by
the way, and estimated one percent of non autistic population
is a savant. But when you think about that, and
the reason I bring it up is because it's clear
in those instances that the brain is working at a
much higher cognitive function level than than what we would
(07:40):
normally be used to, right. So that's why you've got
someone like Daniel Talmot. He's an autistic savant UM And
from the Guardian article Genius explains Talmont, they say that
Talmot broke the European record for recalling pie the mathematical
constant to the furthest decimal point to twenty two thousand,
five hundred and fourteen decimal places. He yes, I mean,
(08:02):
you know what I'm saying, and we most of us
can just say three point one, four and then yea
two decimal points right right. Um, So he says that
he found it easy because he didn't even have to think.
To him, pie is an abstract set of digits. It's
a visual story. Um. It's almost like a film projected
in front of his eyes. So in that case, we
know that he has a brain that is hardwired for
(08:25):
this kind of thinking. Um, and this really complex level. Right.
But even he, even someone is is gifted uh for numbers,
UM has has to turn to an outside system. They
have to augment their their number since even if it's
particularly phenomenal one And that's where mathematics begins to play. Well, actually,
(08:46):
even before mathematics really becomes into play, we have we
was we've discussed in our five Fingered Evolutionary podcast. We
start using our fingers. That's why we are so much
of our our number system is based on us on
units of five, tune or twenty, because that's what the
tools that we had. It's like, you know, you can
easily imagine this ancient and you know, prehistoric individual doing
(09:08):
mathemis like, well goodness, I'm having a hard time processing
numbers beyond like three or four in my head, What
can I turn to to help me? Oh, look at
these things? And uh, and you know, starts using his fingers,
starts using his toes. From there starts using other things rocks, twigs.
Uh and before long you have a an emerging mathematical system.
(09:29):
And yeah, and that's why we have these like ten
based twenty based mathematics decimal system or the other twenty
is of vegesimal system twenty base right. Yeah, even our
even our numerals um, like the the Phoenician symbols that
are number numbers are are based on those were in
their original archaic forms, which are our current system is
(09:50):
derived from. If you look back at the the the
ancient versions of it, the number um, you could tell
what the number was by the number of angles in
the symbol. I remember this from your article how math works. Yeah,
And a lot of it doesn't stack up because like
our nine is a lot different from the the ancient
Phoenician nine. Take the number zero. Zero zero has no
(10:11):
angles in it because it is nothing. The numeral one
has one angle in it, right because it is one.
Two has two angles in it in the arcade version,
et cetera. So that that's that's fascinating. But that's another
example of of you know, the human brain can only
do so much and you have to build outward. It's
like that the trailer that one is building onto and
(10:31):
creating all these additional rooms. Um, we're the trailer and
we've begin building the system and out from ourselves to
help us to better compute the world around us. Well.
And again it's this idea of symbols and abstraction, which
is pretty fascinating, right because math becomes something that's much
more than just you know, trigonometry or even one plus one.
It is a system of symbols that we use to
(10:55):
you know, extrapolate our existence in a sense. But I
did I didn't want to talk a little bit about
pattern recognition. I know we've already brought it up, but
I wanted to say a little bit more about the
brain and the fact that we're pretty much pattern recognition machines. Um.
So you know, you all have all these causal connections
between A and B. And this is from a Scientific
(11:16):
American article called Turn Me On, dead Man. We can
talk about that TI if you want to. Um, But
they say that as when our ancestors. Uh so, the
causal connection between A and B are like when our
ancestors associated the seasons with the migration of game animals.
We are skilled enough at it to have survived and
passed on the genes for the capacity of association learning.
(11:39):
So again, what we're doing is attributing some sort of
symbol to these associations, these patterns that we see to
document our world and try to navigate it in a
better way. Yeah, And I mean that's why pattern recognition
is one of the pillars of artificial communication. Yeah, I mean,
(11:59):
and that's why I um, that's and that's why pattern
recognition is one of the pillars of artificial intelligence, like
being able to instill that in a machine, which incidentally
is essentially made out of math. Yeah, right, And because
it's a it's a type of communicating right um. And
and AI we know was sort of based on the
way that we think, right um. And even I was
(12:20):
thinking even like morse code, something like the sort binary code.
These are again attempts to communicate ideas, um. And there's
this idea that that math is fundamentally universal. Right, So
what you end up with is basically a tower of mathematics,
which we're going to discuss, right after this quick break.
(12:45):
This presentation is brought to you by Intel Sponsors of Tomorrow,
and we're back a tower of mathematics. Now, hang with
me on this particular analogy, um, which I came up
with for the out Stuff Works article how Math Works,
which is a broad, um, you know, a broad look
(13:07):
at what math is for generally, you know, for people
who are not super into math. It's you know, more
about the philosophy of and what it is and the
kind of stuff we're discussing here. Um. I was really
proud of this analogy until I realized that other people
had also developed it years before. Your intuition, your pattern recognition, right, yeah, exactly, So, yeah,
you can think of math is this tower that we've built.
(13:29):
Imagine a human standing on a plane, all right, a
big grassy plane. He can only see so far he
or she he, I don't know, she whatever, whatever the gender,
This human can only see so far. Given there there
their natural born height and the site. Now, if they're
going to see better, they're gonna want to climb on
(13:49):
top of something, right, climb a tree or something. There
no trees around, so they need to build something, and
they build a tower, all right. So and in this analogy,
the natural born height equates to one's natural born limited
mathematical abilities. And then the tower that we build is
the system of mathematics. Each level of the mathematical tower
(14:11):
enables humans to see farther and achieve more UM. And
this this tower like just as a structured you know,
physical tower is built of materials and systems. You know,
you would you would, you know, have the guys bring out,
you know, some stone for it, some woold et cetera.
And then you have you know, you probably need plumbers,
(14:32):
electricians and other various uh specialists. I'll come out to
build the systems that make up the tower. Well, our
tower of mathematics would be made of of integers, would
be made of rational numbers, irrational numbers, complex numbers, um,
real numbers, and these are explained in that article that
I reference to how math works. You would also have
(14:53):
such systems as arithmetic, algebra, geometry, trigonometry, calculus. Uh. In
each of these you can think of as a different
level of complexity. Yeah, building block building on the last.
And the higher the tower gets, the more humans are
able to achieve to they you know, they reached the
point where they're able to use mathematics to better navigate
(15:13):
the physical world. They're able to use it to better
navigate and understand the world beyond our planet, to build
artificial machines and artificial intelligences, and create the computer world
that we have today. All of these things become possible
by building building this tower, working on the backs of
(15:35):
other geniuses, as we can sending on the shoulders of giants, right.
And I think that's really interesting, even like you're talking
about using this system to to get outside of ourselves, right,
to get outside of our our particular planet, our universe. Um.
And we can see that proven out through math managed
throughout history, right. And I was thinking at the very
(15:57):
basic level, and we began to understand, uh, you know,
pattern recognition in nature. You know, something like the Fibonacci sequence,
which you have an excellent article on as well. Um.
And if for those who are not familiar with it,
Fibonacci sequences essentially like a number wherein each number is
that some of the previous two? Yeah, and they in
(16:19):
this number sequence is not It's not like the secret
code of everything, like it doesn't it doesn't correspond with everything,
but it corresponds with the alarming number of things from
like propagation numbers in various uh uh species. You know,
the number of rabbits for instance of the classic example,
like if you can predict how many rabbits will be born, right,
and how the population will grow based on that growth
(16:40):
points and trees, pedal counts, sunflower seed arrangements. Uh. They're
just expressed in multiple ways in nature. And this is
called the golden ratio to write this number. Um. And
what I thought is when, of course, when us vain humans,
when we apply to ourselves, we can see it, right, Um.
We can see this um in the number of body
(17:00):
parts that we have, the way that our body parts
are arranged in spaced they all follow this golden ratio.
So there's there's that aspect of math. You know that
it it helps us understand the world. It helps us,
um predict things in nature that we haven't actually observed
yet or proven. Um. You know, certainly when it comes
(17:21):
to things like dark matter. Well in dark matter is
this problematic thing, right, um? And what I think is
interesting about math it's contribution to physics is that we
again we arrive at this understanding because we have this
universal language and many different uh, epochs of time, people,
cultures have all contributed to this. So we have this understanding.
(17:44):
But then you get to something like dark matter, and
it is purely a result of math. And if I'm
understanding it correctly, our computational models of the universe weren't
really washing and it was cosmologists who finally figured, you know,
via math, that in order are for the mathematical models
to make sense, there had to be some sort of
matter not seen, known or measured really to us that
(18:09):
was occupying the space of the universe. And this is
dark matter. It's like an accountant looking at the books
for a business and saying, hey, we've got some money
missing here. Somebody's embezzling, you know, But in this case
the embezzler it's the universe itself, which apparently has the
right to embezzle. And then it's just figuring out, well,
what does that what where does this money go? What
is it paying for? Well? And I love this idea
(18:31):
of dark matter um as an example of what what
are the limits of our knowledge? You know? What's noble
because it's still very much a mystery, but now it's
a known mystery, right, It's a known quantity of mystery
and um. It furthers us to the edge of understanding,
just as the theory of relativity did and every other
mental constract that helped us to define something like say,
(18:54):
quantum mechanics that now we are beginning to use in
a very concrete way, right Like you've got the Hadron
large clider, and we're hoping to answer some really fundamental
questions about physics through that. Here's the other thing about math.
Look back through the history books and show me one
war that was waged over disagreements about mathematics. You know.
(19:16):
It's it's like, mathematics is the is like the one
thing that we have where everybody's like like, yeah, yeah,
we can agree. I mean, you can get into disagreements
about certain things with with mathematical theory or mathematical philosophy,
and you know, you'll have scholarly debates and I'm sure
in some cases some bitter rivalries among math mathematicians. But
(19:37):
for the most part, this is the thing that we
we all understand and we can agree on. And while
we may use it to uh, you know, to to
prove or or or dictate science, which can at times,
as we we know, can can become a little problematic
and uh, and there'll be disagreements about things that are scientific,
but the mathematics you cannot. You can all you can
(19:58):
argue with mathematics, but the reason behind it, the mathematics
itself is pure. It's an elegant system, right, and it's
not saddled with and I don't know, as far as
I can tell, it is not saddled with um a
lot of the problems that we have culturally, right and
in communicating, because it is universal. So in every single culture,
(20:19):
this number system is going to represent the same thing
um and maybe just a little bit differently, but you know,
certainly and where we are in history right now, it's
widely used. And so to your point, you know, it's
how can you sit there and argue about the following
equation when it is bearing out at least in theory.
(20:42):
So we come to the inevitable, inevitable question about mathematics.
We've talked about this, this thing that composes the tower
by which we achieved everything we've achieved. You know, our
our culture, also our science, everything rests on it. Our
ability to command as much of the physical world as
we seem to be able to command. It comes down
to mathematics. So is this something that we created. Did
(21:05):
we create something that that that that that corresponds to
the natural world so well that it allows us to
control it. Or is it something that we discovered. Did
we discover, you know, in Galileo's words, the language of God,
the language of the universe. Is this? Is it a
human creation or a human discovery? Now? Both both possibilities
(21:27):
are equally awesome and and humans wind up looking pretty
good both equations because because either we're just you know,
either we are just so awesome that we created something
that that the universe corresponds to and and unlocks the
hidden mysteries of the universe, or we discovered like we
it's like under uncovering the bones of God in your
backyard and saying, look what I found. It enables me
(21:49):
to understand And it was always there, whether or not
you noticed, right, whether or not. That's the other way
of looking at it. Does math exist independently of humans? Like,
is a planet out there that we've never we we
don't even know about, we haven't heard, we haven't discovered,
we haven't been there. Does math exist there? Okay, So
that's where I see parallels with like the Copernican principle, right,
(22:12):
which basically says that humans are not privileged observers of
the universe, Like the universe is going to sit out
there and exist regardless of whether or not our gaze
is directed at the universe, which I think is pretty interesting.
And I think that you know, math is inherently on
the one on that one side existing and it's for
us to discover. On the other hand, the human brain,
(22:34):
it's obviously has obviously developed to a point where it
is hardwired to make these observations, right, Like we know
that the neo cortex is a new thing for at
least the mammalion brain. It was lumped on there on
on top of the reptilian brain, and it deals with
these higher cognitive functions um like spatial reasoning, like logarithmics.
(22:59):
So it's kind of a chicken egg proposition to me, Yeah,
and uh and and as will continue to discuss here,
you can you can sort of go with both sides. Now,
my power analogy definitely sort of lends itself more to
the idea that we build something and it's a human creation.
But but on the other hand, is was pointed out
to me by actually by a DJ by the name
(23:20):
of the d J Eric, who actually is a has
a PhD in mathematics. I've interviewed him recently on the blocks.
You can look that up. But he pointed out that
U two hydrogen atoms floating beside two other hydrogen atoms,
can still be called four hydrogen atoms, regardless of you know,
I fear on Earth in another galaxy that there there
is a there is a there's a number system at
(23:41):
work in the universe, just an inherent intrinsic number system. Yeah.
To to actually throw in, uh, you know, the words
of to invoke the words of Plato, who and this
is actual Plato, not a DJ named Plato, um argue.
He argued that method is this is a discovery system,
discoverable system that underlines the structure of the universe, all right,
So in other words, the universe has made a math,
(24:02):
and the more we understand this vast interplay of numbers,
the more we can understand nature itself. So math exists
to the observer. But then you know, then the of course,
the other side again is that math is a man
made tool, um, and that and that it's an abstraction
it's free of time and space and merely corresponds with
the universe. Uh, and that and and not. It doesn't
(24:24):
always correspond, you know, completely, like a consider elliptical planetary orbits. Uh.
An elliptical trajectory provides astronoers with a close approximation of
a planet's movement, but it's not a perfect one. Okay.
See what I love about that is again you get
into this sort of gray area that yes, you've got.
Math is an elegant uh thing unto itself. It's very straightforward,
it's universal, and yet there it doesn't provide all the answers.
(24:48):
The mystery still remains the logistic theory. There are a
number of theories about this, which I'm not going to
mention all of them. But the logistic theory holds that
math is an extension of human reason and a lot
so again, it's the the idea, that's the system. It's
an extension of our our problem solving abilities, and it's
just the extension of that that allows us to candle
(25:10):
even larger problems. It's just an extrapolation of our own
cogitating minds. Okay, yeah, and then then there's the instant
the intuitional theory, which defines math is a system of
purely mental constructs that are internally consistent. So the reason
math works so well is because it's internally consistent. That
the system itself works well. And then it but it
(25:31):
happens to correspond to nature, So you're intuiting pattern recognition. Right.
The the extrapolation of of the intuitional theory and one
that is less accepted as one called fictionalist theory, which
says that math is essentially a fairy tale. Uh success
that are just scientifically useful fictions, which is uh. And
(25:52):
again this is an extreme version, but it helps eliminate
this whole idea of math is a human creation. It's
it's kind of the idea that you have outgo biblical
for a second. So you have Jesus setting around on
a log, right, I don't know why it's on a log,
but he he's telling parables. Right. There are no like
fancy seats, right, and the parables that he's telling in
this situation, they're not true stories. Uh, there're you know,
(26:15):
some some story about someone's kind of like subs fables, right.
The subs fables are not real stories. They didn't actually happen,
but there's a truth to them that that resonates throughout
human culture, you know. So it's kind of that idea
of math. It's like math is an internally consistent story
(26:36):
that is not true, but it's real. Okay. And and
did we talk about formalist theory yet, because I want
to talk about that one and then and then I
want to sort of see if we can locate if
it's possible dark matter in one of these Okay, I
don't know, just as like a little quiz for us,
which um, just a fun game. But the formalist theory,
(26:58):
and this is from your article, argues that mathematics boils
down to the manipulation of man made symbols. In other words,
these theories propose that math as a kind of analogy,
um that draws a line between concepts and real events.
And I thought it was interesting because I began to think,
what is the line between art and math? Then, because
you're communicating through a system of symbols some sort of experience, right,
(27:22):
So I find I find that really fascinating for for
that aspect of it. But I began to think about
the fictionalist theory, and I'm begin to think about dark matter,
and and I don't want to call it a fairy tale.
I don't want anybody to to misconstrue that. But I
did think that if even though we've got the mathematical
model that sets one plus one equals too it is,
it may not necessarily be a true statement, right, because
(27:46):
it's still an unknowable quantity. It's still a mystery to
a certain degree. I don't know. Yeah, I think that's valid.
The when when you take this even farther though, you
get into question of okay, regardless of whether math is
something we created or discovered, like how far does it go?
(28:06):
What are the limits of mathematics? Um, there's a cosmologist,
contemporary dude by the name of Max teg Mark. Yes,
he has a website and everything, so you know he's yes,
string theory guy. So this is the idea of of
math is the ultimate, like like, yeah, math is the
universe and math is the understanding of the universe, and
and hey, we can probably figure it out in time. Well,
(28:26):
I think that's fascinating because, uh, in the neuroscience field,
they're trying to figure out a theory of the brain,
which is very similar to the theory of everything right,
it's very difficult to figure out how the brain works,
the one cohesive theory of the brain. But we know
because we've we've researched this before that there's the Blue
Brain project, in which they're trying to re engineer the
(28:48):
human brain, essentially map it's one trillion synapses and to
get some sort of understanding of how it works, much
like the universe. Because if what they're saying to what
they're proposing is that the universe is the brain, it
is a construct of the brain. So let's just imagine
(29:10):
that these these you know, side by side, they are
going down the same rails, and then within ten years
we'd be able to answer this question. I mean, what
would we just vaporize with, you know, because we've we've
reached some sort of final end of the meaning you know,
it's like the semantic apocalypse. Like we've discussed before, the
idea that if you explain the way the magic trick,
(29:32):
then it's no longer a magic trick, and that and
we are the magic tricks. So um. Then but then
there's also something we call Godal's first incompleteness theorem, and
this is the work of Austrian mathematician Kurt Godel, and
he basically said in this theorem that any theory that's
(29:52):
based on self evident but unprovable proofs is incomplete or inconsistent.
So the the implication here is that um and and
this is something that this is something that also this
is what keeps us from vaporizing. Yeah. Yeah, So so
basically the idea here is that mathematics is inexhaustible. All right,
no matter how many problems we solve, we're inevitably going
to encounter more unsolvable problems within the existing rules. Um
(30:17):
So this would seem to discount the idea of of
a of a theory of everything, because math is is
this system that whether we created it or or discovered it,
it goes on forever. It's like the how many to
what decimal point can we carry out pie? Uh? You know,
you can carry it out to the billions, you can
carry it out to the trillions, But can you carry
(30:38):
it out to the end. No, because it's infinite, because
there is no end. Well, but that's what's so interesting too.
You know, if if the Blue Brain Project does have
some sort of breakthrough about our understanding of the hum
mbringing and if string theory begins to prove itself out
in a more concrete way, then does it just spiral
other questions that we need to answer into the you know,
(31:00):
into the effor um or you know, which is probably
the case, right. I don't think it just closes down
our understanding and we finally say we are complete, we
know it all. Yeah, it's like we get new you know.
It's it's like it's like life. You you solve one problem,
there's going to be another one. You. You know, if
you're you see that one item in the store, that
(31:20):
one game, that one book you you know you really need,
and you finally get it, and it's just gonna be
another one you you end up setting your heart on.
So yeah, and at the end today, it's not going
to actually make me become a scrabble champ. I don't think.
I don't know. Maybe maybe we could take some theories
of the brain and in some string theory and we
(31:41):
should do something of scrabble. Sometimes it's pretty yeah, word
freaking well, Hey, there you go. So that's math. Um.
You know, from a very broad level, it's like like
math is a city and we're flying over it at
a fairly high altitude and trying to make out as
much as we can of it through the clouds. That's right,
we're we're just tourists of math cool. I have a
(32:03):
couple of listener mail here for us and nonmath related,
because it would be impossible for someone to respond to
the podcast that you just record. I don't know, multi
versus maybe stream theory um. This first one comes from
a listener by the name of Peyton, and Peyton says, hey,
Robert and Julie, this is Peyton from Hendersville, North Carolina.
I lived just up the road apiece from you guys
(32:25):
in Atlanta. Actually it's more it's about three hours away.
I just wanted to say that I enjoyed the Nuclear
Fallout podcast and it actually reminded me of a very
funny episode of The Office from a few years ago.
It was the one where Pam's old boyfriend Roy comes
into the office and attacks Jim. Fortunately, Dwight quickly Pepper
sprays him, and everyone in the office has immediately bent over,
coughing and rubbing their eyes. A similar thing would happen
(32:47):
in the case of a nuclear strike. It's true that
only one concentrated area would receive the full destruction of
the bomb, but its effects would be felt all over
the world. Just that i'd share the analogy with you guys,
keep up the great podcast. So, yeah, this is the
example he's he's bringing up here is a small application
of um of fluid dynamics. The way um these particles
(33:10):
of pepper spray, uh, particles of pepper or whatever would
would distribute through a closed environment in moving air and
moving fluid and then nuclear fallout. As we discussed in
the previous podcast, A lot of that depends on you know,
how is how is air, how is this fluid moving on,
you know, around the globe, in a local area, in
(33:33):
an urban environment, et cetera. I just like the fact
that in this analogy, Dwight, it's kind of like the
enriched uranium. I think that's appropriate. Yeah, we received another
one here. This is from Eric, and Eric writes in
about the dog podcast that's my dogs really loved me
that we did and uh, actually he's responding to an
email with most of respond he's actually responding to a response.
(33:56):
He says, he says, Hey, you had an email from
a dog owner who felt that maybe his dog had
Stockholm syndrome, having adopted more than one rescue dog. I've
noticed many dogs who have been abused are very skittish
at first, but when they realized they will no longer
be a hit, they showed quite a lot more love.
My current dog than Austie, named Ghost, was very skittish
at first. If you reached down to give him a rub,
(34:17):
he'd always he'd always flinch. Uh. He was also always
very skittish around new people. We started having all the
HouseGuests give him a treat when they arrived. Last week,
while walking him off leash, we came upon another couple
walking their dogs. Ghost walk right up to them for
a rub. Personally, I think this this person's dog was
simply afraid of him at first, but soon realized his
(34:38):
new owner was okay. Uh. It's something whether there's an
account of dogs. I don't know if it's love, but
you know it certainly it shows that dogs are able
to get over trauma a lot easier to humans. Yeah.
But do you think Ghost has something to do with
with maybe being a most skittish I mean the names Ghost.
He occured to send us a picture but did not.
(34:59):
I'm not, you know, questioning the existence of the dog. Yeah,
or even that the name choice. I'm just wondering, don't
ever know what dogs really understand. I think i'd be
a little skinnish if I was name ghost I did.
I think that's a lot to put it on the
naming of the dog, I know, but still I have heard, um,
I have heard the argument that the name you give
(35:19):
the dog does have a huge play a role in
how that dog is, Like it's just about like how like, um,
I forget which dog expert this was, but they pointed
out that if you have a big, scary pit bull
and you name it Kujo, then you're already, as you know,
ascribing a certain energy to that animal, you know, and
uh and and you're like, I'm just a subconscious level,
(35:43):
you're already making the dog the scary thing that you're
going to be submissive to. And is is you know,
maybe not your friend, that's the so psychologically on the
part of that the person who's perceiving the dog, right,
maybe it's kind of I don't know if it actually
crosses up like human names as well, because you've heard
like if you if you name a child like Eggberg
or something, it's not really a name like Cuban Hubert
(36:05):
or Hubert. That's kind of you're kind of setting them
up to be, you know, a bookish nerd, I guess.
And if you're kind of call them brutus or something,
then there they've kind of been. They're kind of destined
to be on the football team, right, unless they're taking
some sort of like classical like antiquities interpretation from that,
you know, I don't know. Yeah, it's certainly not the
only factor. But you know, you wonder to what extent
(36:27):
you're you're you're you're forecasting their their future. You're gonna
have to check in with Apple in a couple of
years see how that's working for her. Gwyneth paultrows kid, right,
that's right, Yeah, that's all I got. All Right, Well, hey,
if you guys have anything to share with us, you
want to check out what we're into. You can find
(36:47):
us online. We are blow the Mind on both Twitter
and Facebook, and do check out how stuff Works dot com.
You can find that math article we talked about, um,
how math works. You can find the Fibonacci of Nassis
numbers article, and uh, there's also some really cool stuff
about fractals. Right, Yeah, we have an incredible Fractal Image Gallery, um,
(37:08):
which is I mean, if you would like to see
math is interpreted in in these um incredible figures, then
you should check that out. It's on our homepage and
it's definitely worth a look. Um. It's not something that
we were able to get to today, but Mandel brought
set one of the fractals is just amazing. Yeah, and
we and if you don't know what fractals are, guess what.
They have an article about how fractals work as well,
(37:30):
and it's excellent. And yeah, if you want to drop
us line, please do so at blow the Mind that
has to Works dot com. For more on this and
thousands of other topics, visit how stuff Works dot com.
To learn more about the podcast, click on the podcast
icon in the upper right corner of our homepage. The
How Stuff Works iPhone app has a ride. Download it
(37:52):
today on iTunes
Welcome to Stuff to Blow your mind from how Stuff
Works dot Com. Robert Lamb and I'm Julie Douglas, and listeners,
do not run away. We are we are talking about
math in this episode, but we're not going to talk about, um,
you know, a whole bunch of rat We're not gonna
rattle off a bunch of equations and talk about, um,
(00:25):
you know, the the inner workings of Alderbar geometry or calculus,
because if you're like me, you probably never really got
into mathematics in school and you're not particularly good at it.
And uh, anytime a math question comes up, you try
and force it on other people. And you absolutely cannot
go to a bowling alley that does not have automated
score keeper right right, Or you always say something like
(00:47):
I'm an English major yeah to the response of what's
seven times three or something ridiculous like that, But I
will say yes, stick around absolutely, because nobody has more
anxiety about math and I do, and nobody's less of
a mathlete than I am. And yet I find this
question that we're going to pose to you into ourselves
absolutely fascinating. Yeah, we're getting into the philosophical area of
(01:10):
mathematics to a certain degree and just talking about what
it is and uh and indeed the question is mathematics
a human creation, a human invention, or is it a
human discovery? So think think about that. Mathematics this thing
that powers everything pretty much everything that we do, uh
that from the device that you're listening to this podcast
(01:32):
on right now to the the science that has enabled
civilization to reach the point that it has reached. But
what is math? Right? Yeah, what is math? We should
back up. We're gonna back up. We're gonna we're gonna start.
You know, we're not gonna really go back into the
history books and talk about like who invented this in
that because a lot of mathematics is pretty ancient to
(01:53):
the point where we can't really place uh, you know,
attributed to one particular individual or another. But we can
back up to birth to you, when you were a
baby and you were just you know, spit out on
the world, uh gleaming with with goog um. Even then,
(02:13):
your brain had some mathematics and you didn't even know it. Yeah,
a minor mathlete at least. Yeah, because you were you
were born with something that we call number since all right, Um,
and a number. Just to to break it down, a
number is a word and a symbol representing a count. Okay, uh,
(02:34):
Like that's the basic though you may call it too,
you may attribute it with the numeral two, or you
may have some other system of referring to it um.
For instance, in China they have they have small they
have shorter words for their numbers, which is one of
the reasons they're supposedly better at at mathematics because there's
s less just you know, it's kind of like cutting
(02:54):
a penny off of every transaction. It adds up and
that allows everything to to move. You don't have to
have a new word for two hundred um. You just
well anyway, we won't get into that math system. But
it's pretty cool. But but this is necessary because it's
imagine yourself in the wild and you encounter a dog,
like a wild dog that's barking at you. And then
(03:15):
and then you were to encounter two wild dogs barking
at you. Being able to differentiate between the two is essential.
It's it's all about navigating a world full of multiple
objects and moving objects. You know, there are a lot
of like if you're just walking around the forest, there
are a lot of trees, there are um wild dogs
moving around, There may be other humans. I mean, just
(03:35):
think all the things in your life that are in flux,
and you have to be able to navigate that world.
And that is what mathematics helps us do well. And
this is your brain in action, right, I mean, when
you enter a room, of what you are seeing is
not coming in through your eyes, it's actually what your
brain is inferring. And so we're pointing to here is
(03:57):
our brain structures and this idea that we might be
hardwired to to spatially differentiate as much as possible. That's
what you're talking about. Right, When you come into a room,
you're looking at the height whether or not you know
you're looking at the height of the walls. You're you're
sort of creating this pattern in your brain of pattern recognition, right,
And other animals do this too. But but those other animals,
(04:20):
like the gooey infant that you once were, uh, they
have wiped that off actually after a while. Yea, all
the infants on encounter gooey, some of the adults are
gooi um. But such a child will have no grasp
of the human number system. They are not going to
know what two is, or what three is, or what
three times eight is. Those are things are going to
(04:41):
come with in time via education, but they still have
that number. Since then they can identify changes in quantity
and this basically equates to something called logarithmic counting. And
neuroimaging research is actually studied the brains of infants and uh,
I mean scientists have studied the brains of infants through
(05:02):
near imaging research and they've they've registered these, uh the
mental activity going on as they identify integral increases in
physical quantity. So like a baby, for instance, wouldn't be
able to tell that much difference between five and six
heady bears, but five and ten they'll definitely see because
there there's a definite um logarithmic increase in quantity. Yeah,
(05:27):
and I thought this is really fascinating. Um uh To
that point, there's an article from futurity dot org and
it's called babies can compt before they can communicate, And
what they say is our findings indicate that humans use
information about quantity to organize their experience of the world
from the first few months of life. Quantity appears to
be a powerful tool for making predictions about how objects
(05:50):
should behave And what I think is really important about
that is predictions because that is what math is about
at the end of the day. Right If I'm sitting
there adding one in one, then then I'm trying to
predict what the following number is going to be. And
that's at the most basic level. I mean, we know
this is applied throughout physics, throughout every single field that
you can think of, in order for us to try
(06:10):
to make sense and categorize our lives and predict future outcomes.
Even chaos theory is an attempt to predict the unpredictable.
Now here's the thing, though, and this is where math begins,
because we're not even really dealing with math yet. We're
dealing with numbers. We're dealing with with numbers. Since but
as we're navigating this environment around us, um, the the
(06:34):
higher the higher the math gets, the more the larger
the numbers become, the harder it is for us to
to to to process it like even um like humans
are systematically slower to compute four plus five than they
are to compute two plus three. Like when I was
going over that in my notes, I could actually notice
(06:55):
it since I'm not good at math. I mean I
could actually feel the difference in in computing four place,
you could feel the brain power. Yeah. But but this actually,
this is something that everyone experiences, everybody because we are
not evolved to do arithmetic, higher arithmetics, certainly not geometry
or anything. But I do think this is actually started
looking through some information about autism UM, in particular savants
(07:18):
UM and ten percent of autistic population is savant, by
the way, and estimated one percent of non autistic population
is a savant. But when you think about that, and
the reason I bring it up is because it's clear
in those instances that the brain is working at a
much higher cognitive function level than than what we would
(07:40):
normally be used to, right. So that's why you've got
someone like Daniel Talmot. He's an autistic savant UM And
from the Guardian article Genius explains Talmont, they say that
Talmot broke the European record for recalling pie the mathematical
constant to the furthest decimal point to twenty two thousand,
five hundred and fourteen decimal places. He yes, I mean,
(08:02):
you know what I'm saying, and we most of us
can just say three point one, four and then yea
two decimal points right right. Um, So he says that
he found it easy because he didn't even have to think.
To him, pie is an abstract set of digits. It's
a visual story. Um. It's almost like a film projected
in front of his eyes. So in that case, we
know that he has a brain that is hardwired for
(08:25):
this kind of thinking. Um, and this really complex level. Right.
But even he, even someone is is gifted uh for numbers,
UM has has to turn to an outside system. They
have to augment their their number since even if it's
particularly phenomenal one And that's where mathematics begins to play. Well, actually,
(08:46):
even before mathematics really becomes into play, we have we
was we've discussed in our five Fingered Evolutionary podcast. We
start using our fingers. That's why we are so much
of our our number system is based on us on
units of five, tune or twenty, because that's what the
tools that we had. It's like, you know, you can
easily imagine this ancient and you know, prehistoric individual doing
(09:08):
mathemis like, well goodness, I'm having a hard time processing
numbers beyond like three or four in my head, What
can I turn to to help me? Oh, look at
these things? And uh, and you know, starts using his fingers,
starts using his toes. From there starts using other things rocks, twigs.
Uh and before long you have a an emerging mathematical system.
(09:29):
And yeah, and that's why we have these like ten
based twenty based mathematics decimal system or the other twenty
is of vegesimal system twenty base right. Yeah, even our
even our numerals um, like the the Phoenician symbols that
are number numbers are are based on those were in
their original archaic forms, which are our current system is
(09:50):
derived from. If you look back at the the the
ancient versions of it, the number um, you could tell
what the number was by the number of angles in
the symbol. I remember this from your article how math works. Yeah,
And a lot of it doesn't stack up because like
our nine is a lot different from the the ancient
Phoenician nine. Take the number zero. Zero zero has no
(10:11):
angles in it because it is nothing. The numeral one
has one angle in it, right because it is one.
Two has two angles in it in the arcade version,
et cetera. So that that's that's fascinating. But that's another
example of of you know, the human brain can only
do so much and you have to build outward. It's
like that the trailer that one is building onto and
(10:31):
creating all these additional rooms. Um, we're the trailer and
we've begin building the system and out from ourselves to
help us to better compute the world around us. Well.
And again it's this idea of symbols and abstraction, which
is pretty fascinating, right because math becomes something that's much
more than just you know, trigonometry or even one plus one.
It is a system of symbols that we use to
(10:55):
you know, extrapolate our existence in a sense. But I
did I didn't want to talk a little bit about
pattern recognition. I know we've already brought it up, but
I wanted to say a little bit more about the
brain and the fact that we're pretty much pattern recognition machines. Um.
So you know, you all have all these causal connections
between A and B. And this is from a Scientific
(11:16):
American article called Turn Me On, dead Man. We can
talk about that TI if you want to. Um, But
they say that as when our ancestors. Uh so, the
causal connection between A and B are like when our
ancestors associated the seasons with the migration of game animals.
We are skilled enough at it to have survived and
passed on the genes for the capacity of association learning.
(11:39):
So again, what we're doing is attributing some sort of
symbol to these associations, these patterns that we see to
document our world and try to navigate it in a
better way. Yeah, And I mean that's why pattern recognition
is one of the pillars of artificial communication. Yeah, I mean,
(11:59):
and that's why I um, that's and that's why pattern
recognition is one of the pillars of artificial intelligence, like
being able to instill that in a machine, which incidentally
is essentially made out of math. Yeah, right, And because
it's a it's a type of communicating right um. And
and AI we know was sort of based on the
way that we think, right um. And even I was
(12:20):
thinking even like morse code, something like the sort binary code.
These are again attempts to communicate ideas, um. And there's
this idea that that math is fundamentally universal. Right, So
what you end up with is basically a tower of mathematics,
which we're going to discuss, right after this quick break.
(12:45):
This presentation is brought to you by Intel Sponsors of Tomorrow,
and we're back a tower of mathematics. Now, hang with
me on this particular analogy, um, which I came up
with for the out Stuff Works article how Math Works,
which is a broad, um, you know, a broad look
(13:07):
at what math is for generally, you know, for people
who are not super into math. It's you know, more
about the philosophy of and what it is and the
kind of stuff we're discussing here. Um. I was really
proud of this analogy until I realized that other people
had also developed it years before. Your intuition, your pattern recognition, right, yeah, exactly, So, yeah,
you can think of math is this tower that we've built.
(13:29):
Imagine a human standing on a plane, all right, a
big grassy plane. He can only see so far he
or she he, I don't know, she whatever, whatever the gender,
This human can only see so far. Given there there
their natural born height and the site. Now, if they're
going to see better, they're gonna want to climb on
(13:49):
top of something, right, climb a tree or something. There
no trees around, so they need to build something, and
they build a tower, all right. So and in this analogy,
the natural born height equates to one's natural born limited
mathematical abilities. And then the tower that we build is
the system of mathematics. Each level of the mathematical tower
(14:11):
enables humans to see farther and achieve more UM. And
this this tower like just as a structured you know,
physical tower is built of materials and systems. You know,
you would you would, you know, have the guys bring out,
you know, some stone for it, some woold et cetera.
And then you have you know, you probably need plumbers,
(14:32):
electricians and other various uh specialists. I'll come out to
build the systems that make up the tower. Well, our
tower of mathematics would be made of of integers, would
be made of rational numbers, irrational numbers, complex numbers, um,
real numbers, and these are explained in that article that
I reference to how math works. You would also have
(14:53):
such systems as arithmetic, algebra, geometry, trigonometry, calculus. Uh. In
each of these you can think of as a different
level of complexity. Yeah, building block building on the last.
And the higher the tower gets, the more humans are
able to achieve to they you know, they reached the
point where they're able to use mathematics to better navigate
(15:13):
the physical world. They're able to use it to better
navigate and understand the world beyond our planet, to build
artificial machines and artificial intelligences, and create the computer world
that we have today. All of these things become possible
by building building this tower, working on the backs of
(15:35):
other geniuses, as we can sending on the shoulders of giants, right.
And I think that's really interesting, even like you're talking
about using this system to to get outside of ourselves, right,
to get outside of our our particular planet, our universe. Um.
And we can see that proven out through math managed
throughout history, right. And I was thinking at the very
(15:57):
basic level, and we began to understand, uh, you know,
pattern recognition in nature. You know, something like the Fibonacci sequence,
which you have an excellent article on as well. Um.
And if for those who are not familiar with it,
Fibonacci sequences essentially like a number wherein each number is
that some of the previous two? Yeah, and they in
(16:19):
this number sequence is not It's not like the secret
code of everything, like it doesn't it doesn't correspond with everything,
but it corresponds with the alarming number of things from
like propagation numbers in various uh uh species. You know,
the number of rabbits for instance of the classic example,
like if you can predict how many rabbits will be born, right,
and how the population will grow based on that growth
(16:40):
points and trees, pedal counts, sunflower seed arrangements. Uh. They're
just expressed in multiple ways in nature. And this is
called the golden ratio to write this number. Um. And
what I thought is when, of course, when us vain humans,
when we apply to ourselves, we can see it, right, Um.
We can see this um in the number of body
(17:00):
parts that we have, the way that our body parts
are arranged in spaced they all follow this golden ratio.
So there's there's that aspect of math. You know that
it it helps us understand the world. It helps us,
um predict things in nature that we haven't actually observed
yet or proven. Um. You know, certainly when it comes
(17:21):
to things like dark matter. Well in dark matter is
this problematic thing, right, um? And what I think is
interesting about math it's contribution to physics is that we
again we arrive at this understanding because we have this
universal language and many different uh, epochs of time, people,
cultures have all contributed to this. So we have this understanding.
(17:44):
But then you get to something like dark matter, and
it is purely a result of math. And if I'm
understanding it correctly, our computational models of the universe weren't
really washing and it was cosmologists who finally figured, you know,
via math, that in order are for the mathematical models
to make sense, there had to be some sort of
matter not seen, known or measured really to us that
(18:09):
was occupying the space of the universe. And this is
dark matter. It's like an accountant looking at the books
for a business and saying, hey, we've got some money
missing here. Somebody's embezzling, you know, But in this case
the embezzler it's the universe itself, which apparently has the
right to embezzle. And then it's just figuring out, well,
what does that what where does this money go? What
is it paying for? Well? And I love this idea
(18:31):
of dark matter um as an example of what what
are the limits of our knowledge? You know? What's noble
because it's still very much a mystery, but now it's
a known mystery, right, It's a known quantity of mystery
and um. It furthers us to the edge of understanding,
just as the theory of relativity did and every other
mental constract that helped us to define something like say,
(18:54):
quantum mechanics that now we are beginning to use in
a very concrete way, right Like you've got the Hadron
large clider, and we're hoping to answer some really fundamental
questions about physics through that. Here's the other thing about math.
Look back through the history books and show me one
war that was waged over disagreements about mathematics. You know.
(19:16):
It's it's like, mathematics is the is like the one
thing that we have where everybody's like like, yeah, yeah,
we can agree. I mean, you can get into disagreements
about certain things with with mathematical theory or mathematical philosophy,
and you know, you'll have scholarly debates and I'm sure
in some cases some bitter rivalries among math mathematicians. But
(19:37):
for the most part, this is the thing that we
we all understand and we can agree on. And while
we may use it to uh, you know, to to
prove or or or dictate science, which can at times,
as we we know, can can become a little problematic
and uh, and there'll be disagreements about things that are scientific,
but the mathematics you cannot. You can all you can
(19:58):
argue with mathematics, but the reason behind it, the mathematics
itself is pure. It's an elegant system, right, and it's
not saddled with and I don't know, as far as
I can tell, it is not saddled with um a
lot of the problems that we have culturally, right and
in communicating, because it is universal. So in every single culture,
(20:19):
this number system is going to represent the same thing
um and maybe just a little bit differently, but you know,
certainly and where we are in history right now, it's
widely used. And so to your point, you know, it's
how can you sit there and argue about the following
equation when it is bearing out at least in theory.
(20:42):
So we come to the inevitable, inevitable question about mathematics.
We've talked about this, this thing that composes the tower
by which we achieved everything we've achieved. You know, our
our culture, also our science, everything rests on it. Our
ability to command as much of the physical world as
we seem to be able to command. It comes down
to mathematics. So is this something that we created. Did
(21:05):
we create something that that that that that corresponds to
the natural world so well that it allows us to
control it. Or is it something that we discovered. Did
we discover, you know, in Galileo's words, the language of God,
the language of the universe. Is this? Is it a
human creation or a human discovery? Now? Both both possibilities
(21:27):
are equally awesome and and humans wind up looking pretty
good both equations because because either we're just you know,
either we are just so awesome that we created something
that that the universe corresponds to and and unlocks the
hidden mysteries of the universe, or we discovered like we
it's like under uncovering the bones of God in your
backyard and saying, look what I found. It enables me
(21:49):
to understand And it was always there, whether or not
you noticed, right, whether or not. That's the other way
of looking at it. Does math exist independently of humans? Like,
is a planet out there that we've never we we
don't even know about, we haven't heard, we haven't discovered,
we haven't been there. Does math exist there? Okay, So
that's where I see parallels with like the Copernican principle, right,
(22:12):
which basically says that humans are not privileged observers of
the universe, Like the universe is going to sit out
there and exist regardless of whether or not our gaze
is directed at the universe, which I think is pretty interesting.
And I think that you know, math is inherently on
the one on that one side existing and it's for
us to discover. On the other hand, the human brain,
(22:34):
it's obviously has obviously developed to a point where it
is hardwired to make these observations, right, Like we know
that the neo cortex is a new thing for at
least the mammalion brain. It was lumped on there on
on top of the reptilian brain, and it deals with
these higher cognitive functions um like spatial reasoning, like logarithmics.
(22:59):
So it's kind of a chicken egg proposition to me, Yeah,
and uh and and as will continue to discuss here,
you can you can sort of go with both sides. Now,
my power analogy definitely sort of lends itself more to
the idea that we build something and it's a human creation.
But but on the other hand, is was pointed out
to me by actually by a DJ by the name
(23:20):
of the d J Eric, who actually is a has
a PhD in mathematics. I've interviewed him recently on the blocks.
You can look that up. But he pointed out that
U two hydrogen atoms floating beside two other hydrogen atoms,
can still be called four hydrogen atoms, regardless of you know,
I fear on Earth in another galaxy that there there
is a there is a there's a number system at
(23:41):
work in the universe, just an inherent intrinsic number system. Yeah.
To to actually throw in, uh, you know, the words
of to invoke the words of Plato, who and this
is actual Plato, not a DJ named Plato, um argue.
He argued that method is this is a discovery system,
discoverable system that underlines the structure of the universe, all right,
So in other words, the universe has made a math,
(24:02):
and the more we understand this vast interplay of numbers,
the more we can understand nature itself. So math exists
to the observer. But then you know, then the of course,
the other side again is that math is a man
made tool, um, and that and that it's an abstraction
it's free of time and space and merely corresponds with
the universe. Uh, and that and and not. It doesn't
(24:24):
always correspond, you know, completely, like a consider elliptical planetary orbits. Uh.
An elliptical trajectory provides astronoers with a close approximation of
a planet's movement, but it's not a perfect one. Okay.
See what I love about that is again you get
into this sort of gray area that yes, you've got.
Math is an elegant uh thing unto itself. It's very straightforward,
it's universal, and yet there it doesn't provide all the answers.
(24:48):
The mystery still remains the logistic theory. There are a
number of theories about this, which I'm not going to
mention all of them. But the logistic theory holds that
math is an extension of human reason and a lot
so again, it's the the idea, that's the system. It's
an extension of our our problem solving abilities, and it's
just the extension of that that allows us to candle
(25:10):
even larger problems. It's just an extrapolation of our own
cogitating minds. Okay, yeah, and then then there's the instant
the intuitional theory, which defines math is a system of
purely mental constructs that are internally consistent. So the reason
math works so well is because it's internally consistent. That
the system itself works well. And then it but it
(25:31):
happens to correspond to nature, So you're intuiting pattern recognition. Right.
The the extrapolation of of the intuitional theory and one
that is less accepted as one called fictionalist theory, which
says that math is essentially a fairy tale. Uh success
that are just scientifically useful fictions, which is uh. And
(25:52):
again this is an extreme version, but it helps eliminate
this whole idea of math is a human creation. It's
it's kind of the idea that you have outgo biblical
for a second. So you have Jesus setting around on
a log, right, I don't know why it's on a log,
but he he's telling parables. Right. There are no like
fancy seats, right, and the parables that he's telling in
this situation, they're not true stories. Uh, there're you know,
(26:15):
some some story about someone's kind of like subs fables, right.
The subs fables are not real stories. They didn't actually happen,
but there's a truth to them that that resonates throughout
human culture, you know. So it's kind of that idea
of math. It's like math is an internally consistent story
(26:36):
that is not true, but it's real. Okay. And and
did we talk about formalist theory yet, because I want
to talk about that one and then and then I
want to sort of see if we can locate if
it's possible dark matter in one of these Okay, I
don't know, just as like a little quiz for us,
which um, just a fun game. But the formalist theory,
(26:58):
and this is from your article, argues that mathematics boils
down to the manipulation of man made symbols. In other words,
these theories propose that math as a kind of analogy,
um that draws a line between concepts and real events.
And I thought it was interesting because I began to think,
what is the line between art and math? Then, because
you're communicating through a system of symbols some sort of experience, right,
(27:22):
So I find I find that really fascinating for for
that aspect of it. But I began to think about
the fictionalist theory, and I'm begin to think about dark matter,
and and I don't want to call it a fairy tale.
I don't want anybody to to misconstrue that. But I
did think that if even though we've got the mathematical
model that sets one plus one equals too it is,
it may not necessarily be a true statement, right, because
(27:46):
it's still an unknowable quantity. It's still a mystery to
a certain degree. I don't know. Yeah, I think that's valid.
The when when you take this even farther though, you
get into question of okay, regardless of whether math is
something we created or discovered, like how far does it go?
(28:06):
What are the limits of mathematics? Um, there's a cosmologist,
contemporary dude by the name of Max teg Mark. Yes,
he has a website and everything, so you know he's yes,
string theory guy. So this is the idea of of
math is the ultimate, like like, yeah, math is the
universe and math is the understanding of the universe, and
and hey, we can probably figure it out in time. Well,
(28:26):
I think that's fascinating because, uh, in the neuroscience field,
they're trying to figure out a theory of the brain,
which is very similar to the theory of everything right,
it's very difficult to figure out how the brain works,
the one cohesive theory of the brain. But we know
because we've we've researched this before that there's the Blue
Brain project, in which they're trying to re engineer the
(28:48):
human brain, essentially map it's one trillion synapses and to
get some sort of understanding of how it works, much
like the universe. Because if what they're saying to what
they're proposing is that the universe is the brain, it
is a construct of the brain. So let's just imagine
(29:10):
that these these you know, side by side, they are
going down the same rails, and then within ten years
we'd be able to answer this question. I mean, what
would we just vaporize with, you know, because we've we've
reached some sort of final end of the meaning you know,
it's like the semantic apocalypse. Like we've discussed before, the
idea that if you explain the way the magic trick,
(29:32):
then it's no longer a magic trick, and that and
we are the magic tricks. So um. Then but then
there's also something we call Godal's first incompleteness theorem, and
this is the work of Austrian mathematician Kurt Godel, and
he basically said in this theorem that any theory that's
(29:52):
based on self evident but unprovable proofs is incomplete or inconsistent.
So the the implication here is that um and and
this is something that this is something that also this
is what keeps us from vaporizing. Yeah. Yeah, So so
basically the idea here is that mathematics is inexhaustible. All right,
no matter how many problems we solve, we're inevitably going
to encounter more unsolvable problems within the existing rules. Um
(30:17):
So this would seem to discount the idea of of
a of a theory of everything, because math is is
this system that whether we created it or or discovered it,
it goes on forever. It's like the how many to
what decimal point can we carry out pie? Uh? You know,
you can carry it out to the billions, you can
carry it out to the trillions, But can you carry
(30:38):
it out to the end. No, because it's infinite, because
there is no end. Well, but that's what's so interesting too.
You know, if if the Blue Brain Project does have
some sort of breakthrough about our understanding of the hum
mbringing and if string theory begins to prove itself out
in a more concrete way, then does it just spiral
other questions that we need to answer into the you know,
(31:00):
into the effor um or you know, which is probably
the case, right. I don't think it just closes down
our understanding and we finally say we are complete, we
know it all. Yeah, it's like we get new you know.
It's it's like it's like life. You you solve one problem,
there's going to be another one. You. You know, if
you're you see that one item in the store, that
(31:20):
one game, that one book you you know you really need,
and you finally get it, and it's just gonna be
another one you you end up setting your heart on.
So yeah, and at the end today, it's not going
to actually make me become a scrabble champ. I don't think.
I don't know. Maybe maybe we could take some theories
of the brain and in some string theory and we
(31:41):
should do something of scrabble. Sometimes it's pretty yeah, word
freaking well, Hey, there you go. So that's math. Um.
You know, from a very broad level, it's like like
math is a city and we're flying over it at
a fairly high altitude and trying to make out as
much as we can of it through the clouds. That's right,
we're we're just tourists of math cool. I have a
(32:03):
couple of listener mail here for us and nonmath related,
because it would be impossible for someone to respond to
the podcast that you just record. I don't know, multi
versus maybe stream theory um. This first one comes from
a listener by the name of Peyton, and Peyton says, hey,
Robert and Julie, this is Peyton from Hendersville, North Carolina.
I lived just up the road apiece from you guys
(32:25):
in Atlanta. Actually it's more it's about three hours away.
I just wanted to say that I enjoyed the Nuclear
Fallout podcast and it actually reminded me of a very
funny episode of The Office from a few years ago.
It was the one where Pam's old boyfriend Roy comes
into the office and attacks Jim. Fortunately, Dwight quickly Pepper
sprays him, and everyone in the office has immediately bent over,
coughing and rubbing their eyes. A similar thing would happen
(32:47):
in the case of a nuclear strike. It's true that
only one concentrated area would receive the full destruction of
the bomb, but its effects would be felt all over
the world. Just that i'd share the analogy with you guys,
keep up the great podcast. So, yeah, this is the
example he's he's bringing up here is a small application
of um of fluid dynamics. The way um these particles
(33:10):
of pepper spray, uh, particles of pepper or whatever would
would distribute through a closed environment in moving air and
moving fluid and then nuclear fallout. As we discussed in
the previous podcast, A lot of that depends on you know,
how is how is air, how is this fluid moving on,
you know, around the globe, in a local area, in
(33:33):
an urban environment, et cetera. I just like the fact
that in this analogy, Dwight, it's kind of like the
enriched uranium. I think that's appropriate. Yeah, we received another
one here. This is from Eric, and Eric writes in
about the dog podcast that's my dogs really loved me
that we did and uh, actually he's responding to an
email with most of respond he's actually responding to a response.
(33:56):
He says, he says, Hey, you had an email from
a dog owner who felt that maybe his dog had
Stockholm syndrome, having adopted more than one rescue dog. I've
noticed many dogs who have been abused are very skittish
at first, but when they realized they will no longer
be a hit, they showed quite a lot more love.
My current dog than Austie, named Ghost, was very skittish
at first. If you reached down to give him a rub,
(34:17):
he'd always he'd always flinch. Uh. He was also always
very skittish around new people. We started having all the
HouseGuests give him a treat when they arrived. Last week,
while walking him off leash, we came upon another couple
walking their dogs. Ghost walk right up to them for
a rub. Personally, I think this this person's dog was
simply afraid of him at first, but soon realized his
(34:38):
new owner was okay. Uh. It's something whether there's an
account of dogs. I don't know if it's love, but
you know it certainly it shows that dogs are able
to get over trauma a lot easier to humans. Yeah.
But do you think Ghost has something to do with
with maybe being a most skittish I mean the names Ghost.
He occured to send us a picture but did not.
(34:59):
I'm not, you know, questioning the existence of the dog. Yeah,
or even that the name choice. I'm just wondering, don't
ever know what dogs really understand. I think i'd be
a little skinnish if I was name ghost I did.
I think that's a lot to put it on the
naming of the dog, I know, but still I have heard, um,
I have heard the argument that the name you give
(35:19):
the dog does have a huge play a role in
how that dog is, Like it's just about like how like, um,
I forget which dog expert this was, but they pointed
out that if you have a big, scary pit bull
and you name it Kujo, then you're already, as you know,
ascribing a certain energy to that animal, you know, and
uh and and you're like, I'm just a subconscious level,
(35:43):
you're already making the dog the scary thing that you're
going to be submissive to. And is is you know,
maybe not your friend, that's the so psychologically on the
part of that the person who's perceiving the dog, right,
maybe it's kind of I don't know if it actually
crosses up like human names as well, because you've heard
like if you if you name a child like Eggberg
or something, it's not really a name like Cuban Hubert
(36:05):
or Hubert. That's kind of you're kind of setting them
up to be, you know, a bookish nerd, I guess.
And if you're kind of call them brutus or something,
then there they've kind of been. They're kind of destined
to be on the football team, right, unless they're taking
some sort of like classical like antiquities interpretation from that,
you know, I don't know. Yeah, it's certainly not the
only factor. But you know, you wonder to what extent
(36:27):
you're you're you're you're forecasting their their future. You're gonna
have to check in with Apple in a couple of
years see how that's working for her. Gwyneth paultrows kid, right,
that's right, Yeah, that's all I got. All Right, Well, hey,
if you guys have anything to share with us, you
want to check out what we're into. You can find
(36:47):
us online. We are blow the Mind on both Twitter
and Facebook, and do check out how stuff Works dot com.
You can find that math article we talked about, um,
how math works. You can find the Fibonacci of Nassis
numbers article, and uh, there's also some really cool stuff
about fractals. Right, Yeah, we have an incredible Fractal Image Gallery, um,
(37:08):
which is I mean, if you would like to see
math is interpreted in in these um incredible figures, then
you should check that out. It's on our homepage and
it's definitely worth a look. Um. It's not something that
we were able to get to today, but Mandel brought
set one of the fractals is just amazing. Yeah, and
we and if you don't know what fractals are, guess what.
They have an article about how fractals work as well,
(37:30):
and it's excellent. And yeah, if you want to drop
us line, please do so at blow the Mind that
has to Works dot com. For more on this and
thousands of other topics, visit how stuff Works dot com.
To learn more about the podcast, click on the podcast
icon in the upper right corner of our homepage. The
How Stuff Works iPhone app has a ride. Download it
(37:52):
today on iTunes
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