students tend to see equal sign as kind of a command now you are a calculator someone is pressing a button on your forehead and telling you all right it tell me 7 plus 2 once you've sort of gotten used to the language of algebra that's not how you read that you're just supposed to kind of let them sit there and read them as pieces of language bringing play and fun into it is
probably a better way to teach especially kids right what students love in math is when they feel powerful the power of math is not your power to out compete someone it's your power to seize control over a weird question and pin it down and find an answer when a meth gets their hands on a problem they just obsess until it is solved well hello everyone it's Jim oan
with another episode of infinite Loops I have been very excited to chat with today's guest who is Ben Orland for a lot of reasons uh first off he's going to school me on mathematics as he's a graduate a suuma Kum L graduate from Yale University but I love the double major of math and psychology that's very very cool you are a math lover extraordinaire you've
written four books on the power of mathematical ideas your most recent one is coming out in September and it's uh titled math for English Majors a human take on the universal language well Ben I was a economics major so I'm probably even more up uh in terms of that concern but my first question it's just a super easy one for you Ben just to get us started why is the answer
to the question like the universe and everything 42 yeah well well thanks much for having me on Jim and starting with you know the easiest question of all you know the question that in Douglas Adam's book it takes supercomputers Millennia to to devise the answer that question let's see so y 42 I think they debate it right in the in the hitchiker books as to Y 42
and they consider they they realize that they haven't figured out what the question of the life the universe and everything is so they know the answer is 42 um I think they they debate whether it might be six time seven you know is that the question um which to be fair I think that's a great that's a great question because it's you know two times 3times seven you got three prime factors
I don't know that's like that's a pretty cool question to ask but maybe a little too too trivial um and then right they settle on uh how many roads must a man walk down before you can call him a man and the answer being 42 for me why why 42 it's a good it's a good question I don't know I think I think it might just be six times seven I think maybe we've
been running around trying to find meaning and much more complex places when really really the secret to the universe is just yeah what what is six time seven yeah and uh that's a great answer um and I was doing a little research uh before uh recording with you and I found from Adams himself he goes I made the number up which I find really really funny well
in your own words you say a mathematician is hardly a reasonable person more like a pharoh philosopher or logician gone Rogue I love that which made me kind of contemplate Pythagoras Archimedes uid and I started with the help of AI started to say okay like what common characteristics personality type psychological background would these people share and I thought the answer
was pretty reasonable it came back with well here's what they share they are all obsessively curious they are all intellectually stubborn they are all eccentric they are all have a sense of wonder and awe and they all have the courage challenge existing norms and I I thought that was a pretty good summation of what like drives I myself am only a
Layman I love math but uh unlike you I'm I'm not trained in it I'm self-trained um do you think that's right do do you think those are drivers for great mathematical Minds yeah I think so I mean I think give it another year or two and you're just going to be having this conversation with the AI you won't need me uh because I think that the first word when you mention those names I was
think okay what are the what are the traits that Unite mathematicians the one that always comes to mind for me is obsessiveness um there's something and it's something that I actually don't share I'm I I don't know I see glittery ideas and I'm always drawn in 70 different directions and my books really show that because I'll do chapters on everything um but the the research
mathematicians that I know they're obsessive um and obsessive about everything you know they get excited about a mathematical idea and that'll be three years or they get excited about a card game and they become the best in the world at that card game um very one very typical example or well extreme but typical um is I'm blanking on her name
but uh see Swiss biker I think I think maybe she was just working swiland anyway but from the from the Tokyo Olympics the ones that were delayed from 2020 to 2021 and she's just a she studies partial differential equations she's a mathematician who you know trained herself to be a fast biker and went won the Olympic gold medal and not just won it but like in the opening
moments of the race zipped off into the distance so that the people who' been training together and kind of knew the field and knew the world when they finish second thought that they'd won not realizing she'd finish minutes ahead she's just flown away um and I don't know there's something when when a mathematician gets their gets their hands on a problem they they just obsess
until it is solved um yeah that that's something that I think yeah across you look across history and you look across different kinds of mathematics and and and there's such Variety in mathematicians as there is in any uh any discipline but yeah obsessiveness is definitely something they share yeah and and I would add the Curiosity after the obsessive right I think that yeah
obsessively curious people have always fascinated me and uh so I find when when I'm kind of like looking into various people's biographies or autobiographies the number of mathematicians like that show up are are is like very high um and and I was thinking about your book Ma's language uh my own experience in that regard I was not formerly trained math
at all um but I became really interested when I was in my early 20s with onum physics right so I went through all of the Layman you know books and DOW physics and all that kind of stuff and and then I wanted to learn more and I bought some books that had equations in them that literally I like closed the book I'm like I am so I'm not going to be able to figure this out but
then I had the Insight that you have which is what if I just looked at math as a language as opposed to you know scary symbols and and everything else so let's start let's start with the the idea behind teaching l math as a language understanding math as a language and how that really opens the aperture of uh the student be they a child or an adult uh to to being able to
grock math better yeah yeah I think this the language idea it's funny because it's it at once sort of unnatural for students and unnatural for teachers and experts in mathematics but for very different reasons um so for experts they don't tend to think about math as a language because they already speak it fluently um and like you and I don't we
don't think of ourselves as having like oh look at all the English words we're using in this conversation look look at all the sentences we're constructing it's like we're thinking about content not form um and so and so that's how math is for mathematicians you know like they makeable about bad notational choices or they might say uh you know
actually I would use this definition not that definition yeah but but like they're not really thinking about the language they're thinking about what's being conveyed through it um and for students it's sort of unnatural because it's not like any language that they know I me you can you can walk into math classroom trilingual but none of the three languages you speak are very much
like mathematics it's so specialized and sculpted for these certain purposes um it has such strange featur and in particular it's it's developed in this way where these little there these little notational dances you do you know you expand across the parenthesis and what is that about that's not that English doesn't work that way you don't have these little routines these little
you know sort of notational sub routines where you kind of move the symbols around the page and somehow that accomplishes something um so there's there's just weird features to mathematical language so it's it's weird for students and it's weird for teachers but I think it is it's it's sort of the key thing um yeah that that mathematics is both a set of ideas and a set of
linguistic inventions for talking about those ideas and you've kind of got to learn them both in parallel you got to move back and forth between them as you go um so that's there a lot of things I was doing yeah and working on this last book but language kept kind of rising to the surface for me as this is the way to unify that alienating student experience
where you're like I don't know I just do these 17 things in the right order and then I get 100% And I don't really know what it means or what's going on I'm like you know I'm like the person the thought experiment John S the uh you know the the Chinese room where you're being handed slips of paper and you're copying things out of books and handing them back under the door and it's like
you're pantomiming some kind of linguistic process you have no idea what any if it means um and mathematicians for whom that's totally alien because they're just they're just talking you know they're just communicating about ideas um and it's yeah it's Mastery of that that language and its form that is the difference I think that's the Gap another way that I used to think about
math uh when I was trying to get younger people interested in it in my own family was as a you know a musical score because math and music to me at least are are so inherently linked to one you know defining the other uh but let's let's go through what you say so you say that if you think of numbers as nouns and adjectives and you think of verbs as
calculations and grammar as algebra why not you're going to be able to understand you're going to be able to understand it a lot better so teach me teach me something uh using that construct yeah sure yeah yeah so um the pivot point I think is is the equal sign and is the move from thinking about essentially arithmetic equations to algebraic equations um so from the right
perspective this is barely a jump at all it's just it's just NE stepping stone um from a student's perspective it is not um and the difference I think is students tend to see equal sign as kind of a command so 7 plus 2 equals like bam now there's like you are a calculator someone is pressing a button on your forehead and telling you all right tell me seven plus two um and once you've
sort of gotten used to the language of algebra that's not how you read that um in fact 7 plus two and I talk about this in the book when you're first learning it it's it feels like a verb right the plus is an action I need to combine these two piles um but once you are sort of an expert user of mathematics it's not a verb it's actually more like a
preposition sort of like a seven and two seven with two so a conjunction or a preposition or something um because you don't need to add the seven and two you can just call it seven plus two and nine is sort of a synonym it's a paraphrase of seven plus two but it's not uh it's not a necessary action so that seems like just kind of a I don't know a little linguistic pedantry um but it
turns out to be crucial uh because when you run into X Plus y or any algebraic sum you can't there's nothing to do with xos Y is the way people find algebra so frustrating they sort of look at the equation like well what what am I supposed to do right like 19 plus 4 I know I'm supposed to write 23 I'm supposed to add them but X Plus y like is it XY and like no that's actually not
XY that's something else um and you just need to let it sit there you just need to not do anything with it uh which is really hard when you've gone through a decade of math education already and every single day it was like do do do right like follow this exercise take these steps and then suddenly you run into to algebraic expressions and you're
just supposed to kind of let them sit there and read them as as pieces of language um and so yeah the equal sign I see as kind of the pivot here because you need to stop seeing it as kind of the call to action um or call like a drum roll preceding the answer um and you need to see it as as sort of the Workhorse verb of mathematical language which is just it's it's the to be verb
it's is equal to so 9al 7 plus 2 is just the statement that those things are the same um and so math the language becomes this very weird repetitive discourse because almost every sentence is just well this is the same as that and this is the same as that and when you see a page of equations it's just a bunch of statements that things are the same as
each other uh but it turns out that's that's a really powerful way of thinking about the world indeed it also led me to kind of think about uh Mr Orwell's 1984 where one of the primary ways that they try to break down a person's ability to trust their own perceptions and logic is to get them to say 2 plus 2 equals 5 and and I always found that to be like
more profound than many people think because to me at least it it's signaling a totalitarian government's attempt to basically negate and control base reality if you can get people to believe 2 plus 2 equals 5 right I mean am I Wrong Am my off base no no no no I know I like yeah that's that's something I read about a little bit in the book in my chapter on Edition
that like that's the thing when Orwell is trying to reach for what is the what is the deepest base truth what is the thing that if a totalan government can reach that they've got everything yeah it's it's your your basic perceptions of number um and addition and equality that those are it's funny because they're they're both Universal right like two
plus two should equal four for everybody um but because they're Universal that makes them sort of the deepest most personal thing that you have your ability to perceive that like that's your that's your deepest possession and if someone can take that from you then they've taken everything yeah and I guess in new speak would the the party would find that double plus good right double plus
good but it also made me start thinking about L Carroll who as you know is the logician and Charles Dodson his real name and I I I got obsessed when I was young with this very brief what the tortoise said to Achilles because essentially what he is doing in the piece is he's got the Taurus challenging Achilles to justify logical inference right and so he says if a the premise
and B another premise are true then Z the conclusion must be true and achilles keeps adding prepositions and the toris keeps rejecting them he keeps going yeah no I don't believe you I don't believe you and then I think the point and you can correct me because your knowledge of this is far greater than mine but the point I took away from it is that
logical reasoning no matter how far you dig down ultimately res uh requires mean you to accept that and agree on the rules of logic and the reason I bring it up is because I was just trying to think of like one of your main objections is or uh with what you're doing is to try to get people to get excited by math to like show how really cool it is and then
and then you come up with this in a grip is trilemma and all of that kind of stuff and I find that stuff fun but yeah no yeah me too no no I love I love the the story of achillas and the and the Tortoise right I think it was probably um probably an intro philosophy class where I where I ran into that first um yeah and it's it's this uh there's this strange set of features that math has
and people have been wrestling with it for ages right I mean there's a reason leis Carroll in the 19th century put this in the mouth of figures from Deep Antiquity because these are the same questions you know ever since we could ever since we started recording things on paper um some of the same questions about the philosophy and the the theory of math have been recurring um so that
one yeah they right to to like draw it out a little more the Achilles and the Tortoise I think it's right it's riffing on the idea of them running the race and so obviously Achilles is going to win the race when they run and I think as Le Caroll tells it the tortoise is like wait okay yeah we could run in just a minute but just before we do that I'm
just I'm just puzzling out this logical dilemma that I'm having so you know is something is true say a the statement is true and and a implies B so can we therefore include conclude B and achilles is like yeah yeah yeah let's go let's get let's get move let's run um and like okay that seems that seems right I want to conclude B but isn't there kind of another rule you're using
there you're using this rule that if a is true and a implies B then be is true isn't that like that whole statement kind of its own Rule and it's sort of like yeah just like the just the idea that you can you can apply a logical inference right that you can you can move from premise to conclusion I guess that is kind of its own rule so Achilles grants that and
says okay fine there's one more rule we write that down and then we're okay um but then the tortoise yeah just keeps saying well but we still can't quite conclude B can we because isn't that whole thing you just wrote down isn't that a rule um and so I I don't know I don't know enough uh mathematical log to know how um you know how modern logicians would would sort of resolve
that or refute that um but yeah it gets it something about math which is I don't know sort how do you get anywhere with math if we're just working with pure ideas that were were're certain are true um yeah there's sort of this question of how how do you get anywhere Bron Russell has a line where he says mathematics is the subject where we only study
statements of the form a implies B right if this than that and we never really ask if a is true it's all it's all hypothetical it's all conditional um which is a very modern perspective on math that's not how you know I don't know if Achilles the mythical figure knew much math um but certainly it's not how Talis or or uclid would have seen math they would viewed it as preceding
even even through the 17th century I think maans viewed it as like no no we proceed from things that are absolutely certain self-evident that we know are true and that's not how modern mathematicians see it they like well make assumptions and an assumption is an assumption we don't it doesn't it doesn't really matter if it's true it's just a logical starting point and then
we reason from there um which makes the field in its modern form so flexible and so powerful um and and like often alienating for other people it's like what do you mean we don't know if any of it is true you're just you're just doing these little thought experiments and you're not like give me give me something real give me something true it's that's not that's not math doesn't
do that kind of truth it's it's a different kind of Truth which is one of the reasons I'm so fascinated by it because of its flexibility ility um and its ability uh to to be conducted that way and and one of the things that I've always thought is that and it's a question for you uh I think uh people who understand abstractions get math much better than people who are much
more you know kind like concrete thinkers and we we had a a pretty large societal change in my opinion right around the beginning of the 20th century where where if you look at um the the fellow Flynn who did the uh paper on why are IQs going up and and one of his conclusions was because he and he looked at not traditional Stanford Benet IQ
tests but you know those types of tests of the late 1800s and and he found that one of the big changes in people was the people from the late 19th century really thought in very concrete and specific terms right like they would be baffled by the why is the bare white riddle right and and then then through a variety of things like uh you know Innovations in physics video games a
variety of things he found that that we were getting better and better at abstractions H how how would you as a teacher like how would you get somebody who's much more of a literal thinker to you know kind of fall in love with math yeah yeah yeah math has a funny relationship between between the concrete and the abstract um you know every every discipline has its kind of
concrete examples in every in every discipline as you kind of move through schooling you're sort of moving from very concrete experience into this more abstract academic study um and in math I don't know if that's accelerated or something or if we just go five layers more abstract is kind of the nature of the subject um but yeah it's oh it's
it's such a big question I mean often the what students need is experience of those concrete particulars that are going to generalize you know leaping straight into generalities just doesn't really get you anywhere it means that you kind of wind up pushing symbols around a page um or concepts around your mind which is kind of amounts to the same thing it's sort
of like but it's all it's all game of chest if you don't know what any of it stands for or or how it cashes out um it's hard to find much meaning in it and so uh I can't remember who I'm quoting here but there's someone um maybe one of the 17th 18th century great mathticious who says that uh to study math is about finding the example that contains the seed of generality it's about finding
that that concrete instance which is going to grow into the the beautiful full abstraction um and so yeah I mean like right you kind of pick any topic and it's um it is it's about you know for for helping students meet a topic it's about what's that specific example that specific problem that's going to get you into that that's why you we
teach probability dice are great because you know six sides is like kind of enough you can you can think about it you can handle it you can you can write out all the possibilities but then you can start to see some surprising results and and start to start to see where your intuition is going to lead you astray and and you can you can actually roll the dice or simulate it in the
spreadsheet and see what what is the truth here and that brings me to uh the other thing that really appeals to me about your work is is the idea that bringing play and fun into it is probably a better way to teach especially kids right I love the idea I used to uh I play a game with kids that I knew um as Korean Dice and it it's played with five die and it your
objective is to get uh the lowest score possible and three is equal to zero and so you have to roll the dice and you can take as many Die away as you want so if you've got five die in your hand and you roll all three you win you get a zero and you could take all of them but you also must take one die away before you roll so if you roll all sixes right you got to take one away if you go
above nine you bust and if you want to continue to play the game anyone who busts have to double the pot if there is no winner and and I found that like that generated such interesting a fun everyone really enjoys it and has a really good time we played with we played with play money Monopoly money uh but it also really was a springboard for like tons of questions
about probabilities about probability Theory do do you have any do you have any other methods you can share with us on on how like you could play a game and use that game to illustrate mathematical Concepts and thinking yeah yeah that's a that's a great game for one thing I gotta make make a note after our conversation because I've got my my third book was a book of games um
including some dice games well that that's a really nice one sort of yti style rrolling but I like the way that the um having to set aside one die kind of creates a gradual pressure on you it's like you can't you know you're sort of forced into some into some bad choices potentially um yeah one thing I love to do with games right so so I did
I did this book on games um and I went out of my way not to pick games that felt like classroom games you know a couple of them come from teachers but those are the ones that that you play in the classroom they don't really feel like classroom math I I didn't want to half like oh and kids will never play outside of the classroom right yeah exactly yeah yeah you can do your last
polinomial flash cards like that's not really a game it's that's a math exercise dressed up as a game um so yeah so di games like that are great I think the way to extract kind of the best mathematical conversations and thinking from that is to view those games as kind of puzzle engines they're just constantly every move they're generating a new puzzle for you and sometimes it's
an easy puzzle as you said if you roll all threes and three is the lowest like okay then that's a very easy puzzle the thing to do is set them all aside um and sometimes it generates a hard puzzle so you know say roll all twos how many twos do you set aside two is better than average is it I'd have to think about that right so that that that's kind of interesting question so
to me when I when I do you know classroom visits or when I'm using them in my own classes that I teach uh I like to kind of find a good moment and hit pause like okay here's the scenario here's what we're doing what should we do um and just in any kind of simple game like that you'll suddenly get really rich Concepts that you need to be able to evaluate the situation because
you'll need to consider sort of what are all the possible outcomes and now you're starting to think about distributions and you need to say okay well which is the likeliest outcome and so you're thinking about probability and you might want to say well you know there's a five and six chance that something kind of bad happens but a one in six chance you
win the game right there um and so you need to start thinking about expected value too and how do you you know how do you take a weighted average of different outcomes um so like one that I like there's a simple game dice game to play with a 10-sided die um or yeah you can generate it on Google dice um where it's a 5x5 grid and you're rolling this 10 side a die and just writing the number
somewhere in your grid um and you score points by having adjacent numbers be the same so two sevens next to each other is worth 14 or three sevens in a row is worth 21 uh so it's really simple and it's so simple that you think like well isn't everyone just going to kind of have roughly the same grid um and I've done the game with a room of 50 people and
the answer is no like people do not have the same grid like everybody quintilian of ways to arrange the numbers so even trying to accomplish the same objective with the same numbers people will will do it differently um and that's a great one for generating puzzles because you get down to the last two or three spaces left and it's like oh do I put this number here you know
that's next to a 10 so it'll score whatever I've got a one and I can put it next to the 10 where it'll score two points by being next to another one but maybe I want to leave that Space Blank because if a 10 comes up that's tons of points for me um so sometimes you'll sort of need to sacrifice a little bit but also do you want to maximize
expected value or do you want to maximize your chance to win which are which are different things I'm sure you sort of get similar similar dilemas in finance where it's like are you trying to maximize expected value even if what that means is there's a one in a 100 chance of having a huge you know Venture Capital style payoff um or or do you just want to maximize kind of your your
median outcome um or even you know minimize the the bottom outcome so I sort of like avoid disaster um sort of look for an insurance policy anyway these these are all like I don't know these are things that run deep through through gamling and through Finance um and you can get there just with a you know a simple dice game um it's sort of there's enough structure there to to
cast off some interesting puzzles yeah and it also makes me wonder why people who are engaged in teaching math don't like do that take that path more often like one of the things that I found specifically in finance was trying to get people to understand base rates right and and there was a great experiment uh I can't remember who did it um and I I didn't put it in my notes
I'm just thinking of it as I'm listening to you now but yeah I wonder if this is one of the kerski ones yeah yeah yeah it might be so the experiment is you take a random sampling of people you tell them the following things there is a town of 100,000 people 70,000 of them are lawyers 30,000 of them are Engineers when you randomly select just names and
give them the names the majority of people say well if my objective is to get the most right I'm going to say they're all lawyers because I'll get 70% right and most people actually do that but then they add meaningless descriptive information to the name and it's like uh you know Jim is 64 years old and uh has the hair which he has left is gray uh you know Mary is 22 and
likes to walk when they had the meaningless descriptions people largely begin to abandon the underlying base rate of 70,000 and 30,000 right and and then the Clincher they add stereotypical information Frank is 42 years old wears glasses likes mathematical puzzles and doesn't like going out on Saturday night and like literally everyone no matter
how sophisticated they are say I don't care if it was 99 999,000 lawyers and one engineer he's an engineer yeah no I I I love that yeah I love that that line of experiments yeah yeah definitely it's something Conan writes about at some point um it wouldn't surprise me if those were those were some some studies he did um yeah it's funny there there's so much there
yeah I think statistics is a very unnatural process for us right you love talk about the the human operating system and it's not built to look at spreadsheets right that's not that's not what our that's not what we're about right we can learn that because we're very malleable um but we're about details we're about looking at the world and seeing all the richness of detail
and about the social world and and kind of drawing quick social assumptions and calculations about people so you tell me like this person likes sidoku and I'm like the lawyers don't like sedu that's an engineer right there it doesn't matter right the city is 99% lawyers which right interesting city where it's 99% lawyers maybe maybe beheaded there
in some sense for for the future um but but yeah like I'm just you know I ignore the base rate I can't like base rates what what are base rates right like in in in ordinary everyday life you never know the base rate you just know what you see and you got to go by what you see um so it's really hard one of the things I think of that math asks of us and it's often very tough is to
disregard many forms of knowledge that we have um and it doesn't mean disregard them forever but disregard them for the moment while you're doing the calculation there's a lot you need to throw out um yeah the one that came off this I was teaching an interest statistics course um and a student let's see what was it she she had missed a few days um family emergency and so I was
trying to get her caught up on on what we've done in the meantime and it was just the basic idea that if you want to know something about a big population take a sample find the average of your sample and that's your best guess now for for the average of the population right you sort of can't do better than that especially if you've got a nice random sample um but even that requires
turning off some knowledge so the example I started with I was okay say say you're running a business what business do you want to run do you want to run a tea business you know do fun bubble tea I was like okay so you got a new flavor you don't know how much people are going to like it so you go out and ask 50 people and their average score is seven out of 10 um so what do
you think it'll be for all of St Paul the whole city and she was like well probably a little higher than seven actually I said well why higher than seven it was because she has lots of knowledge about Boba and she was picturing a specific flavor and she pictur the people she knows so it's like oh I I activated all this knowledge for you that you actually you need to hold
that in suspension need to that um the example that she liked made more to to why you hold that say there's new of animal that's just been discovered not going to tell you anything else about it but my assistant is down there outside the building and has a hundred of these things so let's bring one in and let's see what it weighs okay it weighs 10 pounds what do
you think is the average weight and that one she was like okay well I don't know anything about this animal and she could have maybe been like well I know animals kind of range from you know you don't get animals more than about 10 tons you know animals smaller than tardigrades or something but that's a pretty big range so so she was willing to accept that it's like
okay I don't I don't have any knowledge I can bring to bear 10 pounds that's the that's the guess for the average um but it was funny I had to construct an example for her that prompted her to ignore other information um because it's it's really unnatural like like in math um it's such this a purified form of reality it's it's so narrow the information that makes it into a
calculation uh and that's what makes it powerful but that's also can make it unnatural it feels feel like why why would I forget all the things I know um like I know a lot about the world you want me to leave that all aside like yeah actually while while you're doing while you're doing the math you leave it on the side and then you bring it back
in that's a great way of doing it um and because I often think about why people have such a difficulty with understanding the law of large numbers vers the small sample right they they don't intuitively understand that the small sample is going to have much wider deviations right and you ask them like uh if hospitals in general give birth to you
know five boys and five girls where would you guess that a hospital that gave birth the nine Boys on one night was located in in St Paul or in Manhattan or New York City as with all the buroughs and and they always picked New York City with all the Burrows do you think that that what do you think that that's in intuitive thing that messes up the way to think about it yeah I I was
thinking about this a lot most recent time I was teaching statistics because I think the way we naturally tend to think about samples is almost exactly backwards um so right I think you're totally right about sample size that and with coins that's that's the way we maths always try to explain it you say okay think about coins you flip 10 coins you can get nine heads that's not crazy
you wouldn't be you wouldn't be like slapping your face be like wake me up I'm in a dream if if you flip nine out of 10 heads if you flip 900 out of a thousand like you should be like you're in a simulation you're dreaming the coin has is like biased like there's no way that happens that does not happen right that would be the weirdest event in the
history of Earth if you flip 900 out of a thousand heads um and that would yeah so with coins and I don't know people can see that to varying degrees to some extent think it's important to have just like a gut feel for I don't know for coins for numbers there's a few things like building that intuition is not always so easy um but the other thing
that happens with sampling that's tough is um the only thing you really need to worry about when it comes to random sampling there sample size is an issue but it's bias in sampling like you know ask any statistician like statistics is all about handling the random error in sampling and like we've got great ways of putting constraints on that and and sort of knowing how much error might
arise um but if your sample's biased you're screwed right there's the famous story of the beginning of G polling I think this was the was it the 1936 election when FDR was up for re-election and you know Readers Digest had a huge circulation and they pulled their readership and on the basis of like two million you know in a country I don't know 100 million like they pulled tons
of the population um and they're like okay you know Landon is going to beat uh Roosevelt and then Gallup you know got a thousand people tiny tiny fraction um it was a few thousand and said it's going to be FDR he's going to win the re-election uh and it was the difference between a huge huge buy a sample which doesn't really tell you that much and a
small random sample which does um and that's I don't know for students I find for people learning it approaching samples from the outside you just get they get it backwards they think that they think that the bias doesn't really occur to them they don't worry about bias in a sample um but they're always worried about random error you know you
pull 50 people it's like oh well what if we just got 50 people who really really like Boba or 50 people who hate Boba it's like well that wouldn't happen randomly like you know 50 maybe but like but that's actually not that's not really the thing you need to be worried about thing you need to be worried about is if you went out and asked your friends because your friends are not
random um like that that's biased and but it's not if you actually could just pull random people from St Paul you'd be fine I mean 50 is a great a great sample if it's actually random yeah and that's one of my little hobby horses or soap boxes that I like to be on uh self- selected samples right like at the challenge that I have is a getting people to understand what a
self-selected sample is and not to beat up on anyone but like the book The Millionaire Next Door right so so this book sold millions and millions of copies and I read it and I'm like this is all utter and and I just started thinking about it and I'm like well wait a minute like what kind of millionaire will devote two days or whatever the amount of time it was to
answering this very deep detailed questionnaire right for $1,000 right and and the answer is that guy exactly they have nothing in common with real millionaires in my opinion right and so it's pervasive through culture though it's like whenever I read something like science says or you know according to I immediately kind of like okay where are the Planet axioms here is
this a self- selected sample or is this a Reader's Digest sample right people don't intuitively go okay what type of person might subscribe to Reader's Digest right that end of itself is is like a biased group right and then your example of your friends like that's a super biased group how how do you disambiguate that how do you get people to understand that it's I I I wish I
knew I mean to me that's like one of the great epistemological problems that we all face is you go around the world and you just you don't get a random experience of the world you get your little slice you get the people you know who are probably very similar to you in lots of ways um yeah no I think about this a lot because you um just like the
kind of questions that we all care about but you don't get data on you know like how do people act when they're in Conflict you know when they're fighting with each other or like what what makes a good relationship or um I don't know how people approach death you know um like you don't get a random sample of this I don't I don't know how the world approaches this I know how my very
particular demographic World approaches this um it's really hard to break out of I think the first thing you can do and I think math helps with this is just to see that that's the problem that you're seeing this tiny tiny little slice that's very um biased to be like you you know that like the the world around you is going to resemble you a little bit
the the exercise I like um is Al ask a class uh think about Wikipedia uh what fraction of pages do you think have pictures like what what percentage of pages if you pick a random Wikipedia page what percentage of pictures and it's like I never go to a Wikipedia page without a picture you know like John travolto yeah they've got pictures of John Travolta it's like not you know
there there pictures everywhere so I've never seen anybody guess below 90% maybe one kid who didn't use Wikipedia very much guessed like 80% or something um but everybody thinks it's gonna be 95 plus a lot of people think it's going to be effectively 100 um and then you say okay everybody in the room go go find couple Wikipedia pages and report back
and so you know they'll go find the Wikipedia page for chicken it's like oh yeah there's a picture of a chicken right there um and they come back and yeah 100% in the sample um and you say okay great now Wikipedia The reason I use Wikipedia not Instagram or or you know Tik Tok for some equivalent thing is social media doesn't give you a random button but Wikipedia is this
beautiful Human Institution here in the 21st century it's built to be accessible and transparent and so they've got a random button so click random article do it 10 times and come back can tell me how many have pictures um and so you know room of 20 kids you get 200 examples and it's a about half uh because what you realize is when you look at Wikipedia you see you know you
go to the page for uh I don't know the Oppenheimer movie and then you go to the page for the Barbie movie it's like yeah they have pictures of both of those but if you click random article you get the 2010 National swimming championships in bellus or you get a train station in Sri Lanka or you get you know a midterm election in Ireland in 1997 like you get
you get stuff that you don't think of that's not the pages you're thinking to go to and you realize like oh I'm just going to the big famous Pages I'm getting I'm getting these very biased glimpses of reality and if you can really randomly sample it you see that so much is missing from your your daily experience um like we we all see the big
stuff we all see the famous stuff um there's there's stuff that's visible and shows up all over and over again and then there's the invisible kind of dark matter of of every population um and so I hope right we were talking ear about concrete examples I'm hopeful that Wikipedia as a as a real concrete example where like we know how many pages are on Wikipedia we know how many
we've looked at um can start to plant a seed if you have the conversation afterwards like and that's that's everything you know um it might seem like everybody on social media is a famous influencer you see famous influencers they're famous they're influencers like they show up a lot people have very few followers on social media that's just that's just how most accounts are you
just don't see them because nobody's following them I love that example and again you also hit on my absolute favorite function of Wikipedia which is the random button every day every morning I go to Wikipedia and hit the random button and it's just so fun because like lots of times it's it's as you say you know Irish elections in 1938 and you know well sh the see and omali
were having at it right no pictures but there are a a significant number of times where like it's something so cool that I'd never thought about and then it just like that ruins that day because like I go down that rabit hole and but um that that is that's a great that's a great habit I'll to start doing that yeah it's really fun and because you know you just never know and and it uh
it helps with uh a lot of things if you just are like really really curious about things but it's it's also you're talking about like the the epistemological challenges and I'm also like really interested in those right because it language for example I do do you think that people's native language influences how well they Gro math H yeah it's a good question there's a
little bit of research on counting that I know of I'm not not an expert in this in this research area but yeah that so Mandarin which I don't speak um apparently has a more regular pattern for naming numbers than English does particularly through the teens right we have this weird funky Legacy of Anglo sax and whatever so you get you know 10 and 11 and 12 and then the teens and
it's a little weird it's not the same pattern as 2122 23 um but apparently in Mandarin it's you know it's more like the equivalent of 101 10 two 10 three 10 four they get to two t and one and two t and two and two tens and three um and apparently yeah kids like like my daughter's five right now kids at that age learn to count a little faster if
Mandarin is their is their native language um and actually even even slow they they compared English to Mandarin I think for bilingual speakers maybe or I can't remember exactly where the study was done and they also compared English to Welsh um and at least in Old Welsh so so I love I talk about this in the book because I Welsh was so cool I was hiking in Wales and came across this plaque
that just lists the numbers um and they look pretty similar to English you can kind of see the parallels until you get to 15 which is I don't know how to pronounce it something like pin and then 16 is 15 and one like unarm P and then 17 is two and 15 and 19 to jump ahead is four and 15 but 18 is not three and 15 18 is two nines which is like a really cool name
for 18 that's like that's a great way to think about 18 mathematically um but also yeah like kids who are learning count in Welsh they learn it a little slower um so so there's at least some evidence that yeah that the language you're speaking and how um you know how easy it is to grasp the naming system is going to affect your the way you learn counting um and the speed with which you
learn how to count to 100 um you know I suspect that after that lots of cultural factors will swamp the specifics of the language that would be my guess um but it's funny the right the super War hypothesis is the the language that that people have for this spr the hypothesis that you're the you know the language in which you speak and think about the
world really shapes how you see the world um and it's funny because it's one that my understanding is when psychologists really try to test it it does you know the predictions don't tend to cash out you know there tend to be faint effects but it's not like it's actually not really the case that our our thinking is totally constrained by our language as as far as they can
test uh and yet thinker philosophers and thinkers of all kinds keep coming back to the idea because it just feels there there's sort of an intuitive appeal to it and and I don't know I I'm one of those people who finds it intuitively appealing um it doesn't seem like a lot of a lot of learning mathematics as an individual is finding the right language
to pin down ideas and even research mathematics can be that you know maths will often be kind of lost and searching in a space but then if you can just pin down the right definition uh just saying what the thing is that you're looking at in just the right way um imato the uh the philosopher calls them um proof sharpened definitions so it's a definition that's
that's sharpened by your exploration and now you're putting a name on it um yeah I it seems to me that naming can be very powerful I think did I drift away from your question I don't feel like I no no I'm I'm just fascinated to listen to your response I I I agree it actually makes me think of like you know if if if you let's let's go way way way back to ancient Sam area right and you know the
the temple priests were had like very arduous tasks because the people would bring these offerings of grain and they had to like account for it they're like well there goes our week and and I'm going to give them an honorable mention be because of that because we have the tablets uh for for the discovery of zero but it really belongs over in India I
think um and yeah yeah that's my understanding yeah I started thinking about it though and and I want to get your read on it because zero is such a profoundly important not just number but concept and and it's not just mathematically important it is also philosophically important it is also important by the way you view the cosmos like it also like gives birth to the
idea of hey you know the void and so so chat to me a bit about like a concept like that how would you teaching the concept of zero like it leads to limits and infin decimals all of those things without zero right we're kind of screwed yeah yeah no it's it's true and it it's uh yeah so Charles Cy I know has a or C I'm not sure pronounce his name
has has a book on on zero s of bi graphy of zero um and yeah it's funny it always I I feel when I look at zero it's almost like the rabbit duck illusion you know where you can see it two different ways because from one angle you're like were they idiots in the past like yeah if there's nothing there there's nothing there that's zero things like it just feels so obvious um and then from
another angle which is the one you you were eloquently laying out like it is is this incredible leap of intuition to imagine zero as number to think that anything could be gained from calling it a number um because like you know the Greeks even like in Greek mathematics one wasn't always considered a number one was like the unit it was like a thing but you didn't like number should
have more to it than that even two was sometimes a little ambiguous as whether that was a number because a number should kind of have a beginning and a middle and an end so three is kind of your first number number um and they they had a very concrete geometric way of conceiving of number right uid avoids multiplying more than three numbers together um he could do it
computationally right he knew like you know in his proof that they're infinite prime numbers you could have need to effectively multiply together arbitrarily many numbers um but he wouldn't do more than three on the page because you know one number measures a length and two numbers multiplied together gives you an area and you multiply by a third number now you have
a volume but like four numbers multiplied together what's that that's that's nonsense like there no there's no fourth spatial Dimension um so yeah so like I like trying to inhabit those other ways of seeing number because it makes you realize Even in our what feels like a very simple concept there's lots of different perspectives one can have on it um okay so I'm drifting away
though circling back to zero right so what what makes zero compelling and and weird um I think it's not so hard to get the idea that you can label nothing as zero um what's weird is folding zero into your system of computation right what's weird is the idea you can do arithmetic with Zer you can add zero and subtract zero and even multiply by zero
um and that's weird because it's sort of like it doesn't it's not interesting with a res right zero times anything is zero it's sort of the attractor point of multiplication uh so it it it's kind of a leap to be like okay something is going to be gained by that um but it turns out it it is um there's a a very general long-term Trend in thinking about number um because exping the last
several centuries at least but going back to to origins of zero um of moving away from a sort of natural way of thinking about number which is as labels for quantities you know like okay there's two cups on the table that's two there's three cups on the table that's three um and to thinking about them instead as things you operate with or sort of solutions to equations even um
and so you kind of need to expand your notion of what a number is for zero to make sense um this is even more Vivid with negative numbers where like there's no there's not negative three ducks in the pond that doesn't like I don't know what that would mean it's like little chasms of emptiness where a dock should be like like you can't negative3 doesn't
do the things that we like numbers to do um and so there's a strict sense in which negative3 isn't really a number at all it's something else but I guess there's sort of number definition one and that's the one you kind of grasp first when you're learning math the counting numbers and then number definition two which is sort of we can extend that system of
number and and suddenly it becomes less about labeling quantities in the world and more about patterns and letting our patterns propagate and extend um yeah think a lot about this recently not with zero but with negative times a negative being a positive um which like you learn in I I've talked to sixth graders um people hate it people hate it for for good reason because it doesn't make any
sense it's like there's no actually no concrete physical reason why a negative time a negative is a positive it's just if you basically it's the distributive property if you want to make the distributive property king of your multiplication and addition and how they relate then you need negative times a negative to be a positive uh but that's
a very that's a very intellectually Inside Out reason for most people as they approach math um and zero has some of the same flavor to say oh yeah zero divided by something that's still zero something divided by zero no no don't do that it's not that kind of number can't can't divide with with it um not not not the dividing kind of number um yeah so you sort of you need to
embrace of uh yeah a version of math and a way of seeing math that lots of very very smart people throughout history have not embraced right that they you know Archimedes didn't really think of negative numbers that way um and like I'm not smarter than Archimedes I'll tell you that much but I live I live in a different culture that's given me a
different inheritance and so I I can I can manipulate of numbers in a way that that he wouldn't have wanted to he would have seen that as as nonsense you know I love that way of looking at it too because we often forget that we as Newton is alleged to have said which I think he actually did as a dig on Leb nits where he said that if he's seen further it only because he uh stood on
the shoulders of giants and of course leet was warar oh I wonder was it hook maybe I think labet was might have right that's right hook I think yeah I think somebody says in a in a letter to hook yeah and apparently apparently it's a it's like a it was a common phrase before that um they're like but it's um it something about the the phrase prior
to that was like a dwarf standing on the shoulder of Giants and when Newton applies to himself he just kind of leaves out the part where the guy on the shoulders is supposed to be shorter than other people he's like oh just yeah right um and and what's funny to me though getting back kind of zero and negative numbers right so it negative numbers make zero sense until you have
until you have zero then it's like if you and I are going mountaineering uh I can say yeah it's 300 we got to climb 300 feet we certainly don't want to fall 300 feet right and and that kind of makes it a practical like holy that negative 300 I'm dead don't fall 300 feet right yeah no that's right yeah I think what what negatives let us do is they're the
mathematical language of opposites they let us unify opposite quantities and opposite directions and and opposite ideas as if they all belong to the same Continuum um so I mean you can think of altitude is a really good one and then debt of course is kind of that's really the one that clinches I think the the meaning of negative numbers when I when I teach middle schoolers that's what
I've done a few years now but that dead is the one that gets to them it's like you owe four bucks it's like oh that's real that's like you know and it's it's ni money is a sort of magnificent fiction we've created but I owe somebody four bucks that that's like that's a that's a very Vivid social reality um I owe four bucks and I owe that guy five
bucks like oh my gosh I owe nine bucks like and then then then like negatives take on a real a real meaning yeah I love that uh my friend Annie Duke uh also says that you can help people understand math better if you challenge them to think of everything as a bet in other words like you're doing with the oh holy I I owe that guy three I owe that guy seven I owe oh I don't want
to even talk to him I owe him 20 uh and it becomes much more visceral right and and it made me think about like when I when I've had so I've got six grandkids and I love math I want them to get excited about it and I'm showing a book here for people who are listening as opposed to watching and it's about the golden ratio why do my personal opin is
that I think one reason people love things and non-math people with like zero interest in math they still know about Fibonacci right and and if they do a little bit of homework because the Fibonacci sequences are beautiful and they describe so much you know spiral galaxies sea shells Etc so the ubiquity of their explanatory power is really interesting and I find that you know
this is a book that has really pretty pictures and it also ties in art with Matt and like I find that that's like very helpful when you're able to say Okay so let's look at this you don't even bring up math right and then and then they get it and they're like huh so 1 + 1al 2 2+ 1 equals right they do this Fey yeah and then you bring in five right you're like what would you think
about about a ratio that like shows up all over architecture and everything do you think there's a validity to that kind of way of teaching just to edify me because if it's wrong I I'll do something else sure yeah yeah no I think um yeah they definitely people love beauty it turns out um people don't necessarily love worksheets um I you know in my teaching career I've probably
used more work sheets that I've used Beauty but that maybe that isn't me doing it doing it right um yeah I feel like we have a very many of us have a very alienating experience of math in school um you know and I I think it's easy and sometimes I do it to blame teachers and including myself and like the way we the choices we make in presenting it um and
you can blame other aspects of the educational system what I tend to think of it as is um it's an extraordinary project we're attempting right like Mass education on the level in this society that we're attempting it it's huge right like you can go back through the years and like you know how many people were getting a four-year college degree 100 years ago you know 7% of the population
that may be only the male population you know okay go back further how many people are finishing high school or even you know up up to World War II how many people are finishing High School like not that many um so so the idea of this Mass education where it's like okay you know a quarter of the population is Gonna Learn calculus that is a hugely
ambitious undertaking and may we could maybe Target our ambition a little more um a little more intelligently sometimes um but okay so like what what happens when you do that you just have the system of mass schooling it's a huge bureaucracy and like huge bureaucracies are not known for exciting people's sense of wonder and curiosity um that's like no it's not
the thing they do best um so what do you need as a teacher is you need you need to do that like you're the human in the room um and it's tough because you have all these bureaucratic pressures on you um but one of the duties you have is you do have to awaken their sense of curiosity um and it is it's it's about Awakening it or igniting it because there I mean the fuel is all there
people have a fascination with number um and with pattern uh and with shape and the fact that all those things turn out to be related you know that numbers are a way of talking about patterns and shapes can be a language of number and number can be a language of shapes like that's cool that's weird that's that's a weird facet of this existence we happen
to find ourselves in um and so any doorway into that I think is is great um yeah I you know a lot of math lessons inevitably in a good math education you know they look they look pretty down toe you know you're you're working on a certain kind of question you're wrestling with different sides of it you're practicing a technique maybe you know like not every lesson will look
like that a lot will but the you know the fairly small percentage of lessons that are about that are explicitely about like we're just we're just having fun today we're exciting some curiosity those are really important lessons um you know not every day of your life is equally impactful and not every day of your math education is equally impactful so those days even if it's not
90% of days when you're seeing something Vivid and electrifying and and glimpsing the patterns of the cosmos it doesn't have to be 95% of days if you do that on 5 per of days that's actually that's pretty solid that's better than we tend to do in math education yeah and then it's the linking them to the more practical aspects that I'm still struggling with right like I use metal
BRS uh chaotic uh diagrams because they're beautiful they show pen R tiles and you know kind of explain why they're important but then like linking them back right I I what yeah know that's right no this I I I struggle with this too no I mean my I something I think a lot about with this fourth book that I was working on because um you know I sort of like I'm a math teacher
but also a math popularizer right and what's the way you popularize math is you don't talk about school math you talk you talk about cooler stuff you talk about mandet you talk about fractals you talk about yeah a periodic tilings Penrose tiling the new the new a periodic TI that they've discovered um you talk about knots you like there's
lots of great stuff there's great fodder um you know my first book I talk about lottery tickets I talk about the geometry of the Death Star triangles and architecture you know so there's great stuff out there there's lots of beautiful math that actually people can get excited about um but factorize X S Plus 5x plus 6 that's not that's that's hard harder to get excited about um so
and and yet that that core you learn in school we don't always teach a great we could probably make some trimming here and there there there are topics that you know I don't know conic sections I don't think really need necessarily to be taught in in N for 2 then you we could all make a little little uh they trim a little bit of fat here and there
um but there's a lot of math I'm sure as you know this from your your quantitative work like there's a lot of math that just to access it you do need that core of algebra um you need you need a good sense of proportion which is a lot of what's taught in middle school math you need a good command of the operations and what they mean in different settings and that's Elementary
School math um ratio and fractions like just just a good grasp of that um and so that that's a dilemma like I think it's beautiful that math has so many different sides that there's the artistic beautiful side and there's the really concrete practical side um but how to how to weave them all together for students and and get them get them excited about the parts that are maybe
less naturally beautiful um yeah is tricky um the the thing the thing I think about like the word that I come back to always is power or powerful um that what students love in math is when they feel powerful um when they feel capable and unfortunately given the way that our education system works we have a room full of kids who are all the same age all doing kind of the same work
every day and somebody probably finishes first and it's usually the same kid every day who finishes first the the thing that makes people feel powerful in math is is being better than others at it like that just as a descriptive matter that tends to be how it goes is that uh you know if you feel like you are good at math then you will probably like it and if you feel like you are
slow or bad at math then you probably won't like it um and so what we need to do and it's hard but is to give a different sense of the power of math um that the power of math is not your power to out compete someone it's your power to seize control over a weird question and pin it down and find an answer um you know an answer that that's more elegant than you could have guessed or
or to a question that you never would have thought you could you could manage given the tools you have uh yeah it's those sens that sense of like the the power of math is I think the only way to really make it get through to to all students that's very abstract though like how do you get kids to get excited about quadratics um you gota you need a
good relationship with the kids so they trust you and think like okay this is worth this is I guess this is worth learning this this guy I trust says it so okay we're gonna we're gonna go along for the red yeah one thing I always on that note uh one thing I tried was to look historically at what empowered certain cultures and civilizations and we're back to the Sumerians now right
what empowered certain cultures to rise become powerful Etc and there's always math lurking yeah yeah yeah especially in um agriculture you know that like you want to go to agriculture you need to know the seasons you want to know the seasons it turns out there's this weird coded set of dots in the sky that are going to tell you how the seasons are changing
and what's going on and give you this this notion of deep time that very hard to get here in the terrestrial realm um and so yeah you get you know the Mayas the the right civilizations inan Indian subcontinent right incredible astronomy um with really sophisticated mathematical thinking um and all all for that purpose yeah for for kind of command of the sky or being able to
predict what's what's going to happen in the night sky yeah and like I was fascinated by that the connection between like the Babylonians and the clay tablets and why Babylonia Rose but then I found like a story that really interested me and it dismayed me a little actually and it was that the Babylonians like were kind of first on the scene with cing and
figuring out how to collect it and add and subtract and all that kind of stuff and you know the rest of Samaria just want weren't having like yeah whatever our gods are more powerful than your Gods so what actually made Babylonia become one of the central city states of suaria was they were like okay we have a new God and they literally invented a new mythology where
their God was the god that tore the uh the known universe as we would call it in half he threw half up this way and created the sky and he threw the other half down and created The Flat Earth and he was the god who created everything ER go we the but the the the ultimate thing was probably the map and and I just wonder like I what metaphors would you find particularly
attractive like you note power uh for for kids are there are there other that get him excited that get him like oh wow maybe I should be interested in this yeah yeah I'll have it's not a period of History I know I think about but the guy ripping the world in half that's a pretty good I feel like that's hard to imagine a seven-year-old being like Oh
yeah I don't care about anybody ripping in the world in half that's not you you you don't have my interest right now um yeah I like that to actually somehow it's this it's got a funny rhyme you know thousands of years later with Newton um and his the the falling apple right which like who knows if that happened but he told the story a lot loved to tell that story of like he sees
the Apple falling and suddenly he realizes like apple moon gravity it's Universal it's one thing the sky up there like this ancient Babylonian God apparently tore it in half and put half up there and half down here and then it took Newton to put them back together it's ah it's actually universal gravitation you know unites them both um yeah for kids I mean kids love games
games are great for kids you know so so dice games and number games and Counting games um you know yeah you mentioned right drawing and art and shapes um um there's a reason there's a lot of geometry in how kids like to approach math right just you know corners and edges and how many ways can you connect things um and and puzzles and riddles too um you
know the one of the strange features of math is that what it does as a discipline is it takes these really fun open-ended curiosity provoking riddles and just beats them down with a mallet until they're totally flat and you can do a hundred of them and they're all kind of the same um it's a very great service as a discipline right that's what makes say computers possible
because you can have routine algorithmic calculations um you do want to give people an experience though of the problem before it's been smashed with a mallet um and to see you know so where I mentioned quadratics earlier this is older than the the kind of age you're talking about um but you can frame problems in in quadratics factoring problems or or solving a quadratic
equation as a interesting oneoff puzzle right you can pick one that has just the right features where it's like oh you can almost guess what those numbers are if you can guess what the first one is you can maybe figure out the second one um and so you can frame them as puzzles and then eventually you're going to find a routine way to solve them all um but
breaking off one and giving one problem space to breathe I think that's often enticing for students um it's got to be one they can get a handle on right you can't give them something that they're totally clueless on if they right just like I throw a partial differential equation at well I mean at me much less at a ninth grader like that's I don't know how to
solve it so you're just not gonna get anywhere but but if you you know and this is this is the art of teaching right the science of teaching is is finding that problem where they can get a handle on it and they're going to be able to dive in and start exploring um I think that puzzles pull people in I mean there's like millions of people who wake up every day and sidoku um they don't
wake up every day and solve a system of linear equations except for they do actually like soku is is some more fan to a system of lar C so like you know they kind of are um so if you can find find the puzzle in the math I think I think that pulls people in that's what games are too right games are like I said they're they're puzzle engines they're sort of every move is
generating a new puzzle for you yeah if you were gonna create like a mathematical escape room like you're in danger and you've gotta solve this puzzle to get in that safe room what would it look like oh my gosh that sounds fun um I I have I have to go through like we got friends who are really good with the manipulatives and have all the cool um ah yeah different
right my daughter play with magnatiles um there got be something fun you could build out of magne tiles build a platonic solid out of magneet tiles um one thing comes to mind like good for an escape room is uh the 15 puzzle um you know right there you know there's 15 tiles in a 4x4 grid so there's one empty space you've probably seen them in you
know gift shops um they have like picture versions um but it was apparently when this came out in uh it was just about 100 years before the Rubik's Cube actually was like 1880s um it was like a huge National craze people lost their minds over the 15 puzzle it was like like the New York Times was doing like fad piece articles on it you know so so a 15 puzzle where you have to
rearrange may maybe you know for an escape room you've only got an hour usually so maybe a maybe an eight puzzle you know 3x3 inste 4x4 to be a little more manageable um like I say were you and you arrange it and if you if you get the picture then you can press it down and open it up um I guess I'm assuming I've got a decent budget for to hire a an architect or an engineer to build
some cool math stuff for me um I don't know yeah I mean like yeah I mean to some extent like our reality is a mathematical escape room so so you there there's lots of lots of material there I love that line what do you think Matt's greatest mystery is wow that's a good question I don't know do you can I throw it back at you do you have a a mystery
that a mathematical mystery or has to be on me okay it's on you you're the mathematician here yeah right funny I mean there there's there's so many open questions internal to math right you know still open questions about the behavior of the prime numbers um I think the the biggest mystery though and like the one that we'll never quite solve it's not quite solvable um is the one
that I think Einstein probably put most simply which is like why is the world comprehensible um why do we live in a world that's that's patterned and lends itself to thought um and to to solutions to problems um and not a world of like formless chaos which like you can it's hard to imagine but you can almost imagine well maybe just a world where
like nothing follows patterns and it's just it's just Madness everywhere um and you can maybe answer that with sort of an anthropic argument that like in such a world we couldn't frame such a question um but but I think that's like why does math work I think is sort of the fundamental question about math you know MTH just love to talk about these
Cycles you get where someone takes a um there's like a concrete problem you're trying to solve and so you go off you try to find a solution and then it leads to other weird weird fanciful math that has nothing to do with anything and the math she can spend a century just like kind of lost in a closet over there exploring their own little ideas that have nothing to do with anything and
then they come out of the closet and the scientists like oh good that's just what we needed to solve protein folding I wait how they they were working on protein folding they had never seen a protein they were just working in the closet like no actually like you know something about the the nature of logic and and pattern means that we get Cycles
like that in in mathematics um yeah I think that you know in the simplest form why does math work um or in even simpler form why why does thinking work um as a way of understanding the world uh yeah that that to me is probably the the big the ongoing mystery of math which of course brings us back to Charles Dodson as leis Caroll right like I wrote a ter paper in college about Allison
Wonderland essentially being his questioning why the hell does all this stuff work what if what if it didn't work and I'm fascinated with that story and and him himself I I I think he was kind of asking and getting after the same type of question as the answer you just gave right like why yeah and if I remember the title of paper correctly was something like the neoclassical era
through the looking glass or something like that M and and like when you when you do that deep dive it's really interesting because when you put him in his set and setting right Victorian England like there were so many weird things about Victorian England like they were the most prudish right on the surface but they had the greatest number of brothel in London than at kind of
like any other time and so there were all of these discontinuities and these paradoxes and he himself like if you read his stuff more as like logic and philosophy like it's a really a trip because it it he's he's really good at it which also kind of leads me to Tesla right tesor was obsessed by 36 and n and and I was kind of like trying to figure that out why was Tesla the man
obsessed with it and so I did a little research and like wow is that a rabbit hole like I don't I don't know anything about Tesla well yeah what what why 36 and9 so he one of his great quotes was to understand everything about the universe think in terms of amp uh what was it uh one quote is 36 and9 and then so I feed that in and I start looking at books about it and you
know you gets you into numerical patterns Vortex mathematics energy weapons like I had no idea that Tesla Tesla had was obsessed by scalar weights and he concocted what he called a death ray he didn't build it thank God but but like just this this like seeing Tesla and reading his really I very few people have seen it because it's not broadly in publication it's
very very thin autobiography uh I got kind of obsessed with all this kind of stuff and then the 3 six and nine and suddenly you're reading about energy weapons and scal waves and all this kind of stuff and so it's like he must have been on to something and yeah yeah but possibly both onto something and on something exactly but like he he fascinates me because like again like we
were talking about uh Pythagoras and and uid and everyone else he too was like his story is am it's cinematic almost right like this was a guy who was inarguably a genius and and like he didn't care he just didn't care the only thing he cared about was learning more figuring more stuff out right and that gets back to that insatiable curiosity and like uh George westing house totally
screwed him he uh uh he had an agreement with George Westinghouse he had arguably the keys to a fortune in his patents and Westinghouse is like in this battle with Edison and so Westinghouse comes and says to Tesla dude like I really need you to not get your share of this and that's like yeah whatever ripped up the contract died in poverty right and and
yet I'm fascinated by guys like him because like they all do come back to math in many instances right and and so it leads me another question I have specifically for you because you're right about it obviously the title of this podcast infinite loops and and you have you have h a very specific notion which I agree with by the way uh but about how people
think about the infinite help us help us there yeah yeah yeah right well before before we get into that I love learning about the biographies with mathematicians obviously um but I especially love when you have a thinker we don't think of as mathematical or or a figure we don't think of as mathematical but if they're sufficiently curious that Curiosity will have led
them at some point to mathematics and how the role that math plays in their worldview and in their their understanding of things is always always fascinating um yeah Lincoln being one of my favorite examples loved uclid and so for him like mathematical logic and argument was really Central I think to how he thought about constitutional law much less about about math um anyway but
going back to to Infinity um yeah it's well it's it's real hard to think about Infinity um it's very attractive right it's it's like it's it's it's compelling it's the thing you know if you want to mention a uh you know a mathematical topic and have an eight-year-old really dig in and just wanna want to think about it and wrap their hands around
Infinity is probably the one um you know it is I'm I'm not I'm obviously not the originator at this point but that Infinity we can only really think of it by negating what we know right that Infinity is is that which does not end I think Dave Foster walls has a line like this he wrote a book on on mathematical concepts of infinity um and he talks about how like the defining feature of
our existence is its finiteness right it's like it's our mortality um and so there's something attractive and Elusive and and Impossible about Imagining the infinite um and then what's what's wild about math is you know for the last 150 years or so we've actually had a really good well-developed theory of infinity um before that it was meth mostly had to
Sid step it you know there was a lot of talk about the difference between a potential infinity and an actual Infinity um the Aristotle introduces that distinction and and to varing degrees it's important in in later thinkers um but then uh Jor caner comes along and it's like no okay it it sets we got it like set theory Bam um and then lays out this beautiful and insane
theory of and that logically airtight theory of different levels of infinity um and right what you know all the intuitions you have to give up in order to grasp the infinite are are numerous um there's a lot of things that are true of finite numbers that cease to be true of infinite numbers um yeah but so I mean as as someone with mathematical
training right caner is my like that's that that's what Infinity is I guess um and there are other ways of conceiving of it but that's still it's such a such a beautiful and weird one that he gave us uh that that for me that's still like when I think the infinite rather than try to think Unthinkable thoughts get lost in the like the bottomless well of
imagination I tend to be like it sets it's power sets I love that um and the idea that I I I I'm still I still struggled to try to like another thing that I use a lot is I love Bach right and so uh generally speaking during a work day like today unless I'm doing an interview bak's but um and and I I think back getting back to Douglas Adams again uh he had a quote that went something a lot
of the lines it's not a very nice quote because I like all of these musicians that he is uh referencing uh but his quote was something like Beethoven's music teaches you what it's like to be Beethoven Mozart's music teaches you what it's like to be a human box language teaches you what it's like to be the universe and I know he kind of met it as a a joke he loved he loved
music but I've always thought of B that way I've always thought of Bach as like the I'm just like since I was a kid and accidentally right like what 5-year-old says oh this is great well I had was lucky enough to have a father Who Loved music and he had Bak on one day and he came upon me and this is not my memory this is him telling me about it apparently I was five and he said he
found me on a couch just like with this my eyes closed with this kind of sublime little smile on my face and he said Jim what what what are you doing and apparently my dad told me I looked at him and I said what is this magical music do you do do you think I mean like I don't I don't want to get like really woo woo here but like like the The Music
of the Spheres all of the the ideas that really tie mat into music am I just being F no I mean Douglas hoffstead be the one asked right he wrot gerle ler Bach the the book that unifies the right the great modern mathematician and and the the great artist and and one of my one one of my favorite books actually but what a slog like I'm not smart enough and like literally read a page
Turn the Page and then go I had no idea what was on a page that I just read and go back yeah definitely very very ambitious book um yeah I mean laet has a quote that's something to the effect of um yeah music is the soul calculating without knowing that it calculates oh I love that you know I didn't want I'm familiar with yeah I maybe botching the trans whatever he didn't say in English
so I can translate it over want um uh no I think there's I don't know there's there's something deep in in music I guess this right you mentioned I majored in math and psychology um and like I I came to psychology first and then and then yeah I was always taking a little bit of math but it really sort of like my last year in college I just loaded up
on math classes so I could get the major and and you know be qualified to go be a teacher of it um but Psychology was sort of my first Passion in in college just like how how do people think what are people like who who how does how does this bizarre Machinery operate um and music is music is there very much to the heart I love Oliver Sach has the book
music ailia um yeah you know about the and and there's something really really deep about music in how we think and and math is the same I think they maybe braided together down there um like my my my younger daughter is one now um almost one and a half and she's just started getting into music and she's into it like it'll be like I I set the timer for my older daughter and the
timer went off I was just playing it's little like like gentle beeping noises and my one-year-old just starts dancing she's like oh wow you know like I'm listen if I'm watching her while I'm listening to a podcast and then the podcast outro music starts to play again she'll just like she'll start dancing it's just like there's something like
she knows music is playing um I actually played her a pop song the other night and she's like went ballistic like oh my gosh I didn't know music could be this good I thought I thought it was just timers and podcast outro music I didn't know you could be like this um so there's like I don't know it's in the body and the Brain there's something really deep about music um and yeah Bach
I I don't know music theory well enough at all to I know zero to comment on on what's woven into Bach um but yeah the the patterns are are really rich um and even just you know how we hear right like just just to take sound waves and turn them into that experience we have is sort of like a fascinatingly mathematical process um I've Heard lots of math ticians talk very fondly about
the weird puzzles of of tuning right of like out as an Ive work um and you sort of you get stuck with ir rational numbers because you just want to have you know go from a c to a c and the next octave up and you want to do it in eight steps because that's an octave actually you sort of you need you need an irrational number because you want with
kind of the 12th root of two or something like that being the the way to do these half steps um yeah so I can't can't speak to box but that's great Douglas Adams line though yeah and that also gets back to Tesla because he said amplitude and frequency see like they were everything right under understand and and then of course there are all these Urban myths right I don't you're
too young but Dan Rather who used to do the evening news for CBS yeah had this bizarre instant in in Manhattan where these two guys came up to him and started costing it literally good look at Wikipedia and and type in what is the what is the frequency K oh I know the RM album yeah so you know the RM Apple but it's a wild story and just check it out check
out what is the frequency kenet because okay have a couple hours because it's a really deep Rabbit Hole way deeper than I understood because I knew the song too uh but I remember I remember the incident when it happened like everyone thought rather was like crazy it turns out no no no these were two real guys and then we don't have enough time and it's not a math subject really but what
happens to these two guys everything's a math subject in the end that's true that's true uh what happens to these two guys though is like really interesting um I'm getting the hook from my nanny here I would go on forever and ever and that's why her job is so important uh then uh well if you if you uh well first off the book out in September where it's
going to be available everywhere yeah yeah it should be anywhere you like to buy books um yeah should be around yeah math for English majors and yeah subtitle is a human take on the universal language yep and we will have links to um any preference you have to where people might want to buy it um and uh all will'll link to your other books as well because they're all fun I I love
your stuff on drawing for example a mathematician who loves drawing and cannot draw I can't draw either um but uh we our final question on the show is is uh uh the the following we're gonna wave a magic wand and we're going to make you the emperor of the world um you can't kill anyone you can't put anyone in a re-education camp you can't insist
that they endlessly do math or or or flash cards for mat yeah but we're going to give you a magical microphone and you can say two things into it and if you're familiar with the movie Inception uh you're going to be able to incept the entire population of the world and everywhere whenever their morning is everyone's going to wake up and say you
know what unlike all the other times I got two great ideas and never acted on them I am going to act on these two ideas starting today what you going to accept in the world Ben yeah well first I I should have thought about this more deeply I heard you asked this question bunch of times I'm always curious do people do people ever try to go for the re-education camp or the or the mass
murder is that you're very careful to give that cave has that come up before or something said well what I would do is I actually you're the first person to ask me that question and when I was trying to think of like what should I uh ask people final question that would be fun and that like would get people thinking I started talking to a bunch of friends and one particular friend
s he shall remain okay yeah quiet quiet ruthlessness there it's funny right you're I mean your guests always seem so genial and friendly I don't none of them seem like the re-education camp types but I guess you know you never know you never know until until it happens well it's my little specific piece like we were talking about earlier right do not
take this sample as being legitimate in any way other than to make me add those two exclusions right right so that so that nobody has them yeah uh yeah well there I mean I think I'll go back to the beginning of our conversation I think my two will be uh first be curious right like ask questions no more um and these are the nice thing about these also is these
will work if I if I could just remember these myself and wake up and and really drive through on these um because they're so the the world is so complex there's so much one could be here ious about it can almost be like it's just so much noise you just shut down you're like I don't know there's too many questions I have no idea how any of this works so I'm just going to give up but
if you can just kind of carve off piece and just be curious and keep asking and keep asking and like okay well I didn't get an answer there but you know I'm gonna come back tomorrow and ask more questions um that's I I don't know that's what humans are are best at when when we can get the ball rolling um so I say number one be curious uh and number
two uh be obsessive uh not about like not don't a stalker or something um but like be obsessive about what you're making what you're building um because that the the best moments of my creative work right the the moments when I feel like I'm making the best things that I can make is is when I vanish into them um it's not it's not all the time it sort of can't be all the time you know
it's like when I'm really deep into a book um and I need to have all those parts moving around in my brain uh and but it but like obsessiveness yeah just gives gives you um I don't know enlists these powers that humans have that we're not always using um and in some ways those those two kind of Point different directions right to be curious is to sort of be
open to lots of different possibilities to you know hit the random article on Wikipedia um and then to be obsessive is to go five miles deep once you find a good random article that you're that you're excited about um but yeah so that those would be my two I think be curious and then once your curiosity catches on something be be obsessive let yourself obsess I absolutely love those for very
sympatico when I was doing the first version of what works on Wall Street I didn't really kind of realize that I was behaving ridiculously obsessively like my wife looked at me and she's like you you you you didn't realize and of course this is in the 90s when computer monitors were this big right and the towers right and she goes Jim when we used to take the kids to n Tucket I had
to plan the packing just really carefully you brought three computers with you so that you could be continually running the tests on the comput set dat and I went and you and you find that obsessive do it's only three I yeah that was my point that was my point yeah right fewer than there are people on the trip it's exactly that's right that's right well
Ben this has been really delightful and fun uh we'll have to and you know as many as often happens to me I had a bunch of other stuff here uh but maybe we maybe we'll have a chat again uh on another episode because like this is just an infinitely interesting topic to me and like I'm no met let's let's be really clear I make no claims to being a mathematician I'm sure I think I think
I'm sure I'm sure you're under selling a lot of your your quantitative skills I'm sure I think I think the things you know are are it's a vast set of things I don't know so that's why that's what makes what makes conversation fun that's exactly right Ben thank you so much for joining me and uh I really really enjoyed the conversation as did I cheers Ben