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