372-applied-math.vtt

WEBVTT

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- Everyone out there on YouTube, hello, Vince.


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Hey, Garant.


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- Hi.


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- Hi.


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- It's good to have you here on YouTube


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and the podcast in just a moment.


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Make sure you're patient as we're getting started.


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I know some of you were waiting for the live stream to start


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so very nice to have you here.


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Now, let's kick this off, guys.


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- Thanks to anyone who's here.


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- Yeah, thanks for being here


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and if you have any thoughts or questions,


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please put them in the live chat


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if you're here watching live.


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Vince Garant, welcome to Talk Python to Me.


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- Thanks, Michael.


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Thank you very much for having us.


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Thank you.


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- Yeah, thanks.


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Nice to be here.


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- Yeah, it's great to have you.


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Vince, I guess it's welcome back for you, right?


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- Yeah, I was on the show a while ago


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and I'm a big listener, love the show.


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Yeah, I came here a long time ago


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to discuss one of the game theoretic libraries I work on.


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So yeah, thanks for having me again.


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- Yeah, you bet.


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I love game theory, it's amazing.


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We'll touch on that a little bit.


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We're gonna do kind of a survey


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of a bunch of different areas of applied math


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and how Python and compare that


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with how R might solve those problems.


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Some of the libraries involved,


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some of the techniques involved.


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So lots of fun things.


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I'm looking forward to diving into them with you.


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- Awesome, awesome.


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- But before we do,


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maybe we'll kick it off with Garen.


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You're new, tell people quickly about how you got


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into programming, Python, math.


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How'd you end up here on this show?


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- So I'm a lecturer at Cardiff University


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in the School of Mathematics.


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So I learned to program while I was doing my PhD.


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And Vince here was actually my PhD supervisor.


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So I essentially learned programming


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from Vince during that time.


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- Nice.


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Yeah, and I think during my PhD, I sort of realized


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or I learned that everything that we'd been able to learn


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during my like masters and stuff,


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it was all completely doable in open source software.


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And that's kind of where I focused my PhD on then.


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I sort of, one of my main projects during my PhD


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was building a library to be able to do some of this stuff.


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And then, yeah, I passed.


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- That's what general area was your PhD in?


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I know math, but what specifically?


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- Discrete event simulation was where I specialized


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in my PhD, but like in conjunction with some


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of the other techniques, stuff like Markov chains


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and queueing theory, which all sort of are different ways


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of solving the same sort of problem.


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And that's where I sort of specialized in.


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- Fun, very, very cool.


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- We have a running joke with Garrent


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that one of his sub topics in his PhD


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that he became hyper specialized in as PhDs go is deadlock.


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And so there's a tweet came up about a question


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about deadlock and all these jokes that come up.


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We got very excited.


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Well, I got very excited.


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Like, "Garrent, someone's joking about your work."


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- That's fantastic.


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Vince, you've already told your story.


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Maybe just a quick update.


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What have you been up to in the last couple of years?


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- Yes, in the last couple of years,


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having the pleasure of working with Geraint now,


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now that he's a colleague of mine,


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but otherwise continuing my work on the Axtra library,


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which is the library we were chatting about just now.


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And yeah, I'm still a mathematician at Cardiff,


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where the best part of my job is getting to teach people


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how to program.


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And that's, I think mathematics is such a cool subject,


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but in a way you're only ever a theoretical mathematician


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until you can program the stuff you're doing.


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Even the applied stuff is quite theoretic.


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And then it's once you can code these things


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that are so powerful,


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it really kind of releases the magic of mathematics


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for want of a less cringy type of way of saying it.


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So that's kind of what I really enjoy doing


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and what I keep doing.


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Kind of what we're going to be talking about today.


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- Yeah, absolutely, we're gonna touch on a bunch


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of different manifestations of that basically.


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Cool, I wanna put out a quick disclaimer.


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So we're gonna be talking about math things,


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obviously Python things as well on the Python show here.


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The disclaimer is, I have some degrees in math,


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but I have not done anything with them for 20 years.


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And therefore, I know just enough to ask bad questions


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and make poor assumptions.


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So you all are gonna have to keep me on track


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and just tell me, no, no, no, Michael,


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you are totally misremembering that


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from your courses 20 years ago.


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- The real problem is we might just be


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on just the other side of that boundary


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where we could confidently give you bad answers.


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That's the--


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(laughing)


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- Look, if you say it confidently, I'm sure--


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- Yeah, exactly, confidently giving bad answers


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is the problem.


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- Yeah, sure, all right, cool.


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- Well, let's kick this off by just talking about


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what is applied mathematics.


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Because one of the final courses I took,


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it very much confused me,


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both in the content and just purely in its title.


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This was a course at UCSD in the PhD program there.


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The course was titled Applied Abstract Algebra.


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- Right.


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(laughing)


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- I'm distracted.


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(laughing)


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- Why is it applied?


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Because I really don't, I just, so let's just start out.


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We're gonna be talking about solving applied math problems.


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Like what the heck is applied math versus like,


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what am I doing, a calculus class


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where I'm solving a bunch of like formulaic type of problems


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versus real analysis where I'm chaining theories


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to derive new ideas or maybe it's a numerical analysis


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or stats, like what, where are we in the math world?


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- Yeah, I think applied mathematics


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is an interesting kind of like term


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because in a way it's become a,


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it's come destroyed from its meaning


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in a lot of cases in that there's a whole area


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of applied mathematics as a subfield of mathematics.


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That's not necessarily applied in any realistic sense.


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I don't know what you think, Gav.


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- Yeah, yeah, so I think traditionally


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what applied mathematics was when I was doing my undergrad was these sort of physics models


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where they assume no gravity and they assume no friction and stuff like that which doesn't seem


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very realistic to me at all. Whereas when me and Vince have been talking about applied


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mathematics sometimes that goes under another name called operational research or operations research


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that we call it applied mathematics because we're applying various techniques in mathematics


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to a situation, a real situation. Right. So that they are and I do think not necessarily by


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definition but just in general different techniques that apply to the more physicsy problems to the


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more management style problems maybe that is yeah but not by definition it doesn't have to be like


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that. It's just that's what people find useful. Yeah, in a way a lot of these labels in terms of


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the mathematical subfields and things are not terribly helpful because they create barriers


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between these fields. There's this problem I studied in my PhD where it's in a pure enumerative


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combinatorics trying to count these types of matrices. Really neat problem actually,


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'cause a whole other series of conversations.


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And the most elegant proof that came for this conjecture


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came from statistical mechanics, whatever that means,


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but it's a field of mathematical physics,


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and it's where like all these boundaries from fields


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not always are helpful,


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whereas really the techniques are the helpful ones


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and knowing when to apply them.


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Yeah, so I think the definition that we would use


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for the purpose of what we're talking about today


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in terms of applied mathematics are just,


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without necessarily going to an incredibly high level


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of mathematics where you're talking about the stuff


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that they do at CERN that is certainly applied,


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you know, there's some very low hanging fruit.


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I don't know if that's the right word.


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Low hanging fruit of where mathematics can vary much.


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- Like day to day trumps, yeah.


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- Exactly, day to day.


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And it's where you take these ideas of, you know,


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in high school where you're told,


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oh, matrices are important because computers


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can do mathematics really quickly with them,


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but you don't do it with a computer.


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So, you know, who cares, right?


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- Yeah, exactly.


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- But I'm happy with the matrix.


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- They tell you how to do it with computers


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and then you, yeah, then you proceed to do it by hand


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for the next two weeks, yeah.


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- Exactly, two weeks if you're lucky.


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- I wish I could tell you.


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I wish I could tell you that, but yeah, exactly.


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You're like, well, I could tell you


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whether this matrix is singular or not,


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but I have no idea why I would do that, right?


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So this is sort of the next step, like,


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well, what would you, if you had that knowledge,


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that kind of knowledge, what would you do with it?


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Like what kind of problems could you answer?


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And some of the examples that you all cover in this book


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that we're gonna highlight a little bit


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are things like if you have two businesses


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that are competing, what choices might they make?


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Or if, no, I know this is extremely theoretical


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and it's never gonna happen,


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but what if there was like a pandemic


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and there were people who were sick?


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(laughing)


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- Probably not that fun to be in.


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(laughing)


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We're using it to make weird trade-offs about society, like should we shut everybody in a basement?


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Should we make them behave in different ways?


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What's the cost versus benefit analysis?


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And those kinds of things, right?


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And all these things that you can, without needing too much high-level mathematics,


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you can describe them mathematically relatively simply.


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And then just with a little bit of code, you can really do cool stuff with it.


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It doesn't take much code, you know,


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and that's where Python really comes in.


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- Yeah, for sure.


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One of the things that we'll see throughout here


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is there's a bunch of different examples


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across these different areas of math


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and these different types of problems


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in different libraries that apply to solving them.


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But the thing that's cool is every one of those solutions


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fits within a couple of pages on the long ones, right?


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For Jupyter Notebooks that have the solutions


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plus have some of the output of the answer, right?


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It's not a ton of code, is it?


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- No, no, exactly.


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And that's, this kind of touches on something else


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that we were gonna talk about is the idea


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that a lot of the time when these things are taught,


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they're taught with specific pieces of software,


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mostly commercial pieces of software.


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And then the topic itself is kind of not separated


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from the software used to attack the topic.


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we often go into meetings with industrial partners for research products,


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and they talk about the tool as opposed to the idea.


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And that's a pity because that makes the idea much more complicated than it is,


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because all of a sudden you have to take apart this really complex idea.


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But often with open source software, or with Python and R,


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which are the two examples that we've used,


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it's like three lines of code to find out the effect of a pandemic or other things.


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- I also think it demystifies things a little bit


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because if what you do is you go to some expensive


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polished piece of software like Maple or something


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and you can say, you say, well, I could ask this


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expensive, complex, huge piece of software a question


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and it can magically give me the answer.


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- Yeah.


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- And it's great that you know you have this


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very fancy tool, but it doesn't necessarily reveal


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a ton of understanding because of it, right?


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- Yeah.


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- Yeah, cool.


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- Yeah, and an idea that's beginning to form in my head,


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I was just saying this to Gary,


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I just haven't fully formed,


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I think there's a blog post that no one's gonna read


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that I wanna write one day about,


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you know, the ethics of it,


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about teaching these fancy commercial softwares,


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why these great companies give out these educational software is that


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they immediately have lots of users of the software that don't know how to use anything


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else. And I wonder if ethically as educators if that's okay. I think we should make more of an


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effort to separate the concept from the software. And I was kind of like saying like I don't think


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I don't think we should teach any commercial software.


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Geraint, you made a good point.


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- Yeah, I don't really have a problem


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with teaching a particular topic through commercial software


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as long as we teach it in a separated way


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so that you know, once you've formulated the concepts


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and the ideas mathematically,


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you can use whatever software you want.


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But in the classroom, we happen to have


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this expensive license, we're gonna use this.


00:13:40.040 --> 00:13:41.700
But outside of the classroom,


00:13:41.700 --> 00:13:43.540
there are other things you can use.


00:13:43.540 --> 00:13:47.140
- Yeah, well, I think there's a couple aspects here.


00:13:47.140 --> 00:13:50.380
One, Vince, you spoke about the ethics of it.


00:13:50.380 --> 00:13:51.660
Is it the right thing to do


00:13:51.660 --> 00:13:53.900
to basically reinforce this loop?


00:13:53.900 --> 00:13:56.020
- Exactly, exactly.


00:13:56.020 --> 00:13:58.060
- That entrenches some of these.


00:13:58.060 --> 00:14:02.260
The other part is, if you're in the UK


00:14:02.260 --> 00:14:06.320
or if you're in the US and you say to your student,


00:14:06.320 --> 00:14:08.060
probably especially if you're in the US,


00:14:08.060 --> 00:14:10.540
they're used to getting paid so much.


00:14:10.540 --> 00:14:12.580
I just paid for both my daughters to go through college.


00:14:12.580 --> 00:14:20.960
So I'm aware that here you pay a lot for the actual tuition, but many places you'll say


00:14:20.960 --> 00:14:22.880
to students, what is it in the UK?


00:14:22.880 --> 00:14:25.600
Is there, how is college, what's the affordability?


00:14:25.600 --> 00:14:29.160
I know in Germany and other places, but I don't know what that was.


00:14:29.160 --> 00:14:36.000
- So it's a touchy subject in that tuition fees have just come in.


00:14:36.000 --> 00:14:40.800
And so cost of universities here are equivalent,


00:14:40.800 --> 00:14:43.780
not far off to in-state tuition


00:14:43.780 --> 00:14:45.880
in public universities in the United States.


00:14:45.880 --> 00:14:48.700
I think they're not far off.


00:14:48.700 --> 00:14:52.880
But then we get to charge, and I'm saying we,


00:14:52.880 --> 00:14:54.840
very, very not talking about me,


00:14:54.840 --> 00:14:57.120
but we get to charge whatever we want


00:14:57.120 --> 00:15:00.000
to a certain extent to people from the European Union


00:15:00.000 --> 00:15:02.800
and then even more to people from outside of that.


00:15:02.800 --> 00:15:03.920
Actually, I don't even know if that's true


00:15:03.920 --> 00:15:08.640
about the European Union because of recent events anymore.


00:15:08.640 --> 00:15:09.480
But yeah.


00:15:09.480 --> 00:15:13.840
So yeah, there is a cost.


00:15:13.840 --> 00:15:14.680
- Sure, okay.


00:15:14.680 --> 00:15:18.920
So going back though, my point about the ethics was,


00:15:18.920 --> 00:15:21.820
it's one thing to be in the US or places in Europe


00:15:21.820 --> 00:15:24.960
where we have a decent amount of money.


00:15:24.960 --> 00:15:27.200
It's another to say to somebody,


00:15:27.200 --> 00:15:31.400
you have to pay $500 for this software


00:15:31.400 --> 00:15:33.260
to learn the subject, right?


00:15:33.260 --> 00:15:37.620
where 500 US dollars might be the yearly income


00:15:37.620 --> 00:15:39.620
for an employed person and their student.


00:15:39.620 --> 00:15:47.540
It seems like there's a lot of good would be done


00:15:47.540 --> 00:15:52.320
by building up maybe the missing gaps


00:15:52.320 --> 00:15:53.840
that force or encourage people


00:15:53.840 --> 00:15:55.600
to go to this commercial software,


00:15:55.600 --> 00:16:00.220
building that up rather in the form of SciPy libraries


00:16:00.220 --> 00:16:05.220
and the Python data science stack in general.


00:16:05.220 --> 00:16:07.980
So that it's free, open source and all those things.


00:16:07.980 --> 00:16:10.300
- I think that would apply for all subjects.


00:16:10.300 --> 00:16:14.020
I think really close to what we're talking about here


00:16:14.020 --> 00:16:19.020
is with mathematics, I think it's really frustrating


00:16:19.020 --> 00:16:22.740
'cause maybe I'm thinking too purely now,


00:16:22.740 --> 00:16:25.580
but I mean, pure of heart, not pure mathematics.


00:16:25.580 --> 00:16:28.660
In terms of like, mathematics is just such a clean


00:16:28.660 --> 00:16:30.860
and minimalistic subject.


00:16:30.860 --> 00:16:33.500
You need a pen and a paper to do it.


00:16:33.500 --> 00:16:34.900
And if all of a sudden we're teaching people


00:16:34.900 --> 00:16:36.540
to use a pen and paper to do mathematics


00:16:36.540 --> 00:16:38.660
and saying like, oh, but you can only do it


00:16:38.660 --> 00:16:41.380
with a pen made by a BIC.


00:16:41.380 --> 00:16:44.620
But don't worry, BIC is--


00:16:44.620 --> 00:16:46.580
- Long pen is the only one that can do calculus.


00:16:46.580 --> 00:16:47.700
- Exactly, right?


00:16:47.700 --> 00:16:49.940
And then once you graduate,


00:16:49.940 --> 00:16:52.580
if you want to write down this idea again,


00:16:52.580 --> 00:16:54.100
you have to use a BIC pen,


00:16:54.100 --> 00:16:55.300
but you have to pay for it yourself.


00:16:55.300 --> 00:16:57.100
And I really do think mathematics,


00:16:57.100 --> 00:17:03.260
evolution of mathematics and a lot of science, I would argue, is into computing, right? Is


00:17:03.260 --> 00:17:09.420
into getting computers to do it. And that extension of using the pen now is to use code.


00:17:09.420 --> 00:17:10.420
And yeah, it's...


00:17:10.420 --> 00:17:17.420
I do think, I think, for me at least, I think one of the important things is our separation


00:17:17.420 --> 00:17:23.580
of mathematical concepts to software. Because it's a lot less of a problem, but there's


00:17:23.580 --> 00:17:30.620
still a problem going, the only way you can do this is by using free open software. There


00:17:30.620 --> 00:17:35.260
are some places, unfortunately, that are not allowed to use open software because they


00:17:35.260 --> 00:17:39.020
think there's security problems and stuff. So if you've only taught open software, then


00:17:39.020 --> 00:17:45.180
certain, like the NHS, for example, I know they discourage using open software. So maybe


00:17:45.180 --> 00:17:49.100
you think then, think, "I can't do this maths thing anymore." But if you've separated the


00:17:49.100 --> 00:17:53.900
concept from the software, at least you know the concept and you know you've got choices.


00:17:53.900 --> 00:18:01.100
Yeah, absolutely. I think that's very true. Separating the concept from the software is key


00:18:01.100 --> 00:18:07.900
where possible and I think perhaps we don't always do a good job of that. And here I am speaking as


00:18:07.900 --> 00:18:12.940
an industry, I think sometimes we often... I've been to conversations where people have said,


00:18:12.940 --> 00:18:16.620
"I need to use MATLAB. Can you help me with MATLAB?" And it turned out they wanted to know


00:18:16.620 --> 00:18:20.460
how to numerically solve a differential equation. They didn't want to do math lab. They just wanted


00:18:20.460 --> 00:18:24.700
to solve a numeric equation. They just did not know that that's what they were doing.


00:18:24.700 --> 00:18:38.540
I do want to move off of this so we can dive into the applied math aspects. But I think one other


00:18:38.540 --> 00:18:47.860
final thing on this is I feel like professors, especially as they get older, they've taught


00:18:47.860 --> 00:18:51.260
a certain way with a certain set of tools for 20 years.


00:18:51.260 --> 00:18:52.260
And you know what?


00:18:52.260 --> 00:18:56.700
That course they wrote, they already have the materials and the exercises and all of


00:18:56.700 --> 00:18:57.700
that.


00:18:57.700 --> 00:19:01.300
And the idea of saying, "Well, we're going to now throw out this and grab some new open


00:19:01.300 --> 00:19:02.300
source library."


00:19:02.300 --> 00:19:08.020
I mean, there's 350,000 libraries on PyPI and they're always changing and turning and


00:19:08.020 --> 00:19:09.520
and something new is coming along.


00:19:09.520 --> 00:19:13.700
And it's maybe a lot to ask,


00:19:13.700 --> 00:19:16.320
but also maybe not too much to ask to say,


00:19:16.320 --> 00:19:18.560
look, you should keep up with these things.


00:19:18.560 --> 00:19:21.640
And if there's a new way to present it to your students,


00:19:21.640 --> 00:19:24.080
not because even some of the ethics stuff,


00:19:24.080 --> 00:19:26.760
but you might be doing a disservice to your student


00:19:26.760 --> 00:19:29.520
to say, look, the only way that you can solve these problems


00:19:29.520 --> 00:19:30.720
is with say Fortran,


00:19:30.720 --> 00:19:31.560
or the only way you can do


00:19:31.560 --> 00:19:35.000
is with a $2,000 toolbox extension to MATLAB.


00:19:35.000 --> 00:19:37.040
That's the way that you have to go to solve this.


00:19:37.040 --> 00:19:40.960
here's this super well-respected professor telling you that's how you do it.


00:19:40.960 --> 00:19:41.960
Well, that's not actually how you do it.


00:19:41.960 --> 00:19:43.560
That's how they've done it for 20 years.


00:19:43.560 --> 00:19:46.920
And so there's a lot of inertia there, right?


00:19:46.920 --> 00:19:53.120
I'm really new at being a lecturer, so maybe I'm being really naive here, but


00:19:53.120 --> 00:19:58.920
it is an effort to keep up with all this stuff, but that's our job.


00:19:58.920 --> 00:20:01.280
Our job is to keep up with the latest maths.


00:20:01.280 --> 00:20:05.280
Anyway, if I was still using, if in 30 years time, I was still using the same


00:20:05.280 --> 00:20:08.280
math that I'm using today, I wouldn't be doing my job properly.


00:20:08.280 --> 00:20:10.560
So why is the same true with software?


00:20:10.560 --> 00:20:21.800
Yeah, I think it actually, frankly, comes back to ethics in that it's unethical to not make the effort to update your training.


00:20:21.800 --> 00:20:29.600
And if we were talking about doctors and surgeons, they do need to learn new things as the science evolves.


00:20:29.600 --> 00:20:36.160
I think it could probably with lecturers, professors, higher education, it comes back


00:20:36.160 --> 00:20:43.160
to that dichotomy between research and teaching and how teaching is viewed.


00:20:43.160 --> 00:20:44.160
But yes, absolutely.


00:20:44.160 --> 00:20:45.160
I think, yeah.


00:20:45.160 --> 00:20:51.240
In a way, I would be disappointed if at the end of my career, I'm still teaching Python.


00:20:51.240 --> 00:20:53.200
In a way, I also hope I have.


00:20:53.200 --> 00:20:54.200
in a way.


00:20:54.200 --> 00:20:55.200
Yeah, yeah.


00:20:55.200 --> 00:21:00.600
Well, but not 2020 Python, but 2050 Python or whatever it is, right?


00:21:00.600 --> 00:21:01.600
Absolutely.


00:21:01.600 --> 00:21:02.600
Yeah, exactly.


00:21:02.600 --> 00:21:03.600
Oh, Python's already on.


00:21:03.600 --> 00:21:08.040
I started teaching Python 2, and then I had to figure out how to teach both.


00:21:08.040 --> 00:21:09.040
Yeah, exactly.


00:21:09.040 --> 00:21:10.040
Yeah, yeah.


00:21:10.040 --> 00:21:11.040
Sorry to cut you off.


00:21:11.040 --> 00:21:15.360
So you started teaching Python 2, and then now you've moved on.


00:21:15.360 --> 00:21:19.800
And then I had to figure out how to deal with Python 2 and 3, and now I just teach Python


00:21:19.800 --> 00:21:20.800
3, and yeah.


00:21:20.800 --> 00:21:21.800
Yeah.


00:21:21.800 --> 00:21:24.440
I can't believe that transition took so long,


00:21:24.440 --> 00:21:26.040
but well, there it is.


00:21:26.040 --> 00:21:29.360
All right, well, let's dive into some of the problems.


00:21:29.360 --> 00:21:33.120
And we're gonna, more specifically,


00:21:33.120 --> 00:21:36.240
I'm gonna take this book that you all created


00:21:36.240 --> 00:21:39.200
and use it to sort of guide our exploration


00:21:39.200 --> 00:21:40.640
of both some of these problems,


00:21:40.640 --> 00:21:42.520
how we might solve them with Python,


00:21:42.520 --> 00:21:44.920
and some of the libraries that make it possible.


00:21:44.920 --> 00:21:47.720
I guess one of the things that struck me about that journey


00:21:47.720 --> 00:21:52.280
is that there's not that many external packages


00:21:52.280 --> 00:21:53.680
that are required.


00:21:53.680 --> 00:21:56.360
It's not like, well, this one takes 10 to solve this problem.


00:21:56.360 --> 00:21:58.400
This one takes these complex, these five.


00:21:58.400 --> 00:22:00.320
If you put them together just right, you get the answer.


00:22:00.320 --> 00:22:01.780
So that'll be fun.


00:22:01.780 --> 00:22:04.600
But tell us a bit about this book,


00:22:04.600 --> 00:22:06.940
Applied Mathematics with Open Source Software.


00:22:06.940 --> 00:22:12.840
- Yeah, so publisher, this is an academic publisher,


00:22:12.840 --> 00:22:15.760
which amongst other things means


00:22:15.760 --> 00:22:17.720
the book is really too expensive.


00:22:17.720 --> 00:22:21.840
But they often just send out emails to people saying,


00:22:21.840 --> 00:22:23.400
hey, could you write a book?


00:22:23.400 --> 00:22:26.060
It's not necessarily a source of flattery.


00:22:26.060 --> 00:22:30.040
But we got one of these emails


00:22:30.040 --> 00:22:35.040
and Geraint actually had just given a talk at PyCon UK.


00:22:35.040 --> 00:22:36.400
I don't know if you want to say a little bit


00:22:36.400 --> 00:22:39.120
about the talk you gave, Geraint.


00:22:39.120 --> 00:22:42.400
- Yeah, so it was very much a precursor to this book


00:22:42.400 --> 00:22:45.820
where I had given an introduction


00:22:45.820 --> 00:22:48.260
to the field of operational research,


00:22:48.260 --> 00:22:52.940
which is how we label this certain type


00:22:52.940 --> 00:22:54.380
of applied mathematics


00:22:54.380 --> 00:22:56.780
and all the different problems that could occur.


00:22:56.780 --> 00:22:58.580
And I think the title of the talk was,


00:22:58.580 --> 00:22:59.780
there's a library for that,


00:22:59.780 --> 00:23:02.620
because every sort of problem that we could come up with,


00:23:02.620 --> 00:23:04.220
you could pip install a library


00:23:04.220 --> 00:23:07.380
and in a function or two solve the problem,


00:23:07.380 --> 00:23:08.940
which was a neat little,


00:23:08.940 --> 00:23:10.380
oh, there it is, it's a neat little.


00:23:10.380 --> 00:23:11.220
- Is this it?


00:23:11.220 --> 00:23:12.060
- Yeah, yeah.


00:23:12.060 --> 00:23:15.980
- If I could just interrupt the call for proposals


00:23:15.980 --> 00:23:18.060
for PyCon UK closes on Saturday.


00:23:18.060 --> 00:23:21.940
So if you're thinking of talking, please submit a talk.


00:23:21.940 --> 00:23:26.980
- So yeah, and it was just really neat


00:23:26.980 --> 00:23:30.220
that we had these, like what we call standard problems.


00:23:30.220 --> 00:23:33.220
It was essentially our postgraduate MSC course


00:23:33.220 --> 00:23:35.740
that we teach, but instead of teaching the maths,


00:23:35.740 --> 00:23:39.020
there was one or two Python functions that solved it for you


00:23:40.500 --> 00:23:44.320
And then, yeah, that eventually evolved into this book


00:23:44.320 --> 00:23:45.860
where instead of each little topic


00:23:45.860 --> 00:23:47.440
being a couple of functions,


00:23:47.440 --> 00:23:49.760
we filled out chapters on some of the theory,


00:23:49.760 --> 00:23:53.460
and again, tried to separate the maths and the programming,


00:23:53.460 --> 00:23:55.700
emphasizing that by introducing another language,


00:23:55.700 --> 00:23:57.900
which was R, to show that you can do it


00:23:57.900 --> 00:23:58.740
in two different ways,


00:23:58.740 --> 00:24:01.380
and the software is independent of the problem.


00:24:01.380 --> 00:24:02.660
- Yeah. - Yeah.


00:24:02.660 --> 00:24:05.060
- And we kind of, I think you and I have described it,


00:24:05.060 --> 00:24:07.220
'cause every now and then as we were writing the book,


00:24:07.220 --> 00:24:09.980
we kind of stop and go, "Wait, who's the book for?"


00:24:09.980 --> 00:24:14.060
And as we were making decisions about how exactly to do something, we're like, "Wait,


00:24:14.060 --> 00:24:16.940
who's the before and after?"


00:24:16.940 --> 00:24:17.940
I won't necessarily...


00:24:17.940 --> 00:24:19.540
Well, maybe we should talk about that.


00:24:19.540 --> 00:24:26.540
But I think we've written a book that's meant to be useful to people wanting to get started


00:24:26.540 --> 00:24:34.780
either with the mathematical field problem or with how to actually do it with the code.


00:24:34.780 --> 00:24:37.520
And so every chapter has got the same kind of structure


00:24:37.520 --> 00:24:39.000
that describes a problem.


00:24:39.000 --> 00:24:42.800
Then it describes the basics ideas


00:24:42.800 --> 00:24:44.900
between behind the theory of the problem


00:24:44.900 --> 00:24:46.080
or the mathematical tools,


00:24:46.080 --> 00:24:47.360
the theory behind the mathematical tools.


00:24:47.360 --> 00:24:48.840
But again, not going into too much depth,


00:24:48.840 --> 00:24:50.440
kind of what I said before about,


00:24:50.440 --> 00:24:52.600
you don't need to understand


00:24:52.600 --> 00:24:55.460
all of Newton and Leibniz's calculus


00:24:55.460 --> 00:25:00.460
to be able to kind of predict the outcome of a pandemic.


00:25:00.460 --> 00:25:04.600
And then it just solves the problem.


00:25:04.600 --> 00:25:09.400
original problem, it solves it in two separate ways, the R and the Python, using R and Python.


00:25:09.400 --> 00:25:16.080
And the final kind of section, every chapter is pointing at a bunch of literature on it,


00:25:16.080 --> 00:25:17.080
which should be useful.


00:25:17.080 --> 00:25:21.360
Yeah, and more broadly, you might be able to, these types of problems appear and what


00:25:21.360 --> 00:25:23.600
you might be able to do with them.


00:25:23.600 --> 00:25:27.320
But the really cool stuff with the publisher is that we had an ongoing kind of conversation


00:25:27.320 --> 00:25:28.320
before the start.


00:25:28.320 --> 00:25:32.480
Garren and I were both like, well, the book has to be open.


00:25:32.480 --> 00:25:36.080
And so they've agreed, like all--


00:25:36.080 --> 00:25:38.880
there's not a PDF floating around online of the book.


00:25:38.880 --> 00:25:40.680
But all the source files are there.


00:25:40.680 --> 00:25:42.720
So all the LaTeX files are there.


00:25:42.720 --> 00:25:45.400
All the Jupyter notebooks are there with the code.


00:25:45.400 --> 00:25:47.840
We haven't quite gotten all our Markdown files up yet,


00:25:47.840 --> 00:25:50.320
but they are theoretically all there.


00:25:50.320 --> 00:25:55.720
And so the book is very open, which we're happy about.


00:25:55.720 --> 00:25:57.640
Yeah, that's great.


00:25:57.640 --> 00:25:59.400
- It is very shiny new.


00:25:59.400 --> 00:26:01.040
It still has that new book smell.


00:26:01.040 --> 00:26:05.000
It was released just almost exactly a month ago, right?


00:26:05.000 --> 00:26:07.040
- That's right, that's right.


00:26:07.040 --> 00:26:07.880
Yeah, yeah.


00:26:07.880 --> 00:26:11.560
Keep on saying I've got to have Garent over to celebrate,


00:26:11.560 --> 00:26:13.360
but we don't have enough doing that.


00:26:13.360 --> 00:26:17.180
- I have to sign a copy for my nan.


00:26:17.180 --> 00:26:19.760
(all laughing)


00:26:19.760 --> 00:26:24.840
- All right, now before we dive into the various problems


00:26:24.840 --> 00:26:28.280
on the Python side, while we're still kind of talking


00:26:28.280 --> 00:26:31.440
a little bit high level, this is,


00:26:31.440 --> 00:26:33.660
one of the interesting aspects here is the Python


00:26:33.660 --> 00:26:36.960
and R aspect.


00:26:36.960 --> 00:26:39.360
So when you go through each chapter,


00:26:39.360 --> 00:26:40.840
which is, I think I agree with you


00:26:40.840 --> 00:26:44.320
that it's pretty approachable, even if you don't have a,


00:26:44.320 --> 00:26:45.960
you don't have to have like a master's in math


00:26:45.960 --> 00:26:48.020
or specialize in that area for it to make sense.


00:26:48.020 --> 00:26:50.080
It doesn't have, if you don't really want to see


00:26:50.080 --> 00:26:53.160
a ton of formulas, yeah, it's not super intense.


00:26:53.160 --> 00:26:55.220
- I think that's our first official review, Michael.


00:26:55.220 --> 00:26:57.120
Pretty approachable, it's fantastic to hear.


00:26:57.120 --> 00:26:59.400
(laughing)


00:26:59.400 --> 00:27:00.800
- Well, like I said, my math,


00:27:00.800 --> 00:27:04.480
while I study a ton of it is highly rusted


00:27:04.480 --> 00:27:07.760
and it was pretty approachable for me, so there's that.


00:27:07.760 --> 00:27:12.760
But maybe just talk about putting R and Python side by side


00:27:12.760 --> 00:27:14.560
for solving a set of different problems.


00:27:14.560 --> 00:27:15.960
What are some of the takeaways


00:27:15.960 --> 00:27:17.360
either of you got from that?


00:27:17.360 --> 00:27:22.160
- Yeah, so one thing I wanna say,


00:27:22.160 --> 00:27:24.440
- Yeah, I'm sorry, I'm interrupting you there,


00:27:24.440 --> 00:27:27.280
but one thing we wanted to do here,


00:27:27.280 --> 00:27:30.360
'cause we would, well, I would certainly describe myself


00:27:30.360 --> 00:27:33.040
as a Python person, not an R person.


00:27:33.040 --> 00:27:35.960
I know R, I write R, I've written a book in R,


00:27:35.960 --> 00:27:37.080
but I would certainly describe myself


00:27:37.080 --> 00:27:38.640
as a Python person in that.


00:27:38.640 --> 00:27:40.600
- If you're gonna sit down and write something,


00:27:40.600 --> 00:27:41.840
you would pick Python first.


00:27:41.840 --> 00:27:44.160
- I would pick Python, exactly.


00:27:44.160 --> 00:27:47.400
But also, I'm embedded in the Python community,


00:27:47.400 --> 00:27:52.040
I listen to some good Python podcasts,


00:27:52.040 --> 00:27:57.040
I'm a Python person and I can look at some Python code


00:27:57.040 --> 00:28:01.400
and the joyous, that looks very Pythonic, right?


00:28:01.400 --> 00:28:04.760
I can tell you that.


00:28:04.760 --> 00:28:07.200
And so we were kind of aware that we didn't want


00:28:07.200 --> 00:28:11.440
to translate the Python to R when we were writing this.


00:28:11.440 --> 00:28:16.440
We wanted to write this as close to R people as we could.


00:28:16.440 --> 00:28:20.160
I don't know if we managed that,


00:28:20.160 --> 00:28:21.880
but that was something as well that we were aware of.


00:28:21.880 --> 00:28:24.720
It's not just translating languages.


00:28:24.720 --> 00:28:25.560
Geraint, did you--


00:28:25.560 --> 00:28:28.420
- In Python, yeah, in Python we have the word


00:28:28.420 --> 00:28:30.400
Pythonic for idiomatic Python.


00:28:30.400 --> 00:28:32.800
Do you all know, is there a word for that in R?


00:28:32.800 --> 00:28:35.320
Or is it just idiomatic R?


00:28:35.320 --> 00:28:37.640
- I don't know, I don't know, yeah.


00:28:37.640 --> 00:28:38.840
- I don't either.


00:28:38.840 --> 00:28:41.700
Geraint, you were gonna say something, jump in here.


00:28:41.700 --> 00:28:44.280
- So I was gonna say, as we were writing the book,


00:28:44.280 --> 00:28:47.240
we noticed that there were certain problems


00:28:47.240 --> 00:28:50.900
which the R and the Python lined up exactly,


00:28:50.900 --> 00:28:53.260
not from design, just from,


00:28:53.260 --> 00:28:56.020
if we were gonna approach these independently,


00:28:56.020 --> 00:28:59.280
it is pretty much exactly the same way to solve it.


00:28:59.280 --> 00:29:01.500
There were some problems where


00:29:01.500 --> 00:29:04.340
we had to reformulate the mathematics


00:29:04.340 --> 00:29:07.120
because the way to do it in R


00:29:07.120 --> 00:29:10.340
was so different to the way you do it in Python.


00:29:10.340 --> 00:29:11.660
That doesn't mean the math's changed,


00:29:11.660 --> 00:29:14.140
we just had to reformulate it, re-communicate it


00:29:14.140 --> 00:29:16.540
so that we could write it down in R.


00:29:17.700 --> 00:29:20.880
And then there were some problems again


00:29:20.880 --> 00:29:23.000
where we have to use different mathematics


00:29:23.000 --> 00:29:24.300
to solve it in Python and R


00:29:24.300 --> 00:29:26.700
because of the availability of libraries and stuff.


00:29:26.700 --> 00:29:28.540
So I thought that was really, really neat.


00:29:28.540 --> 00:29:30.980
And I think that emphasizes again,


00:29:30.980 --> 00:29:34.300
the separation of concept to software


00:29:34.300 --> 00:29:37.020
because sometimes you did have to do very different things


00:29:37.020 --> 00:29:38.640
in different softwares.


00:29:38.640 --> 00:29:41.620
- My favorite chapter on this is the one


00:29:41.620 --> 00:29:44.360
that is your specialty, Darren,


00:29:44.360 --> 00:29:47.140
the discrete event simulation chapter


00:29:47.140 --> 00:29:51.300
where I forget the name of the two


00:29:51.300 --> 00:29:54.940
theoretic ideas about discrete event simulation,


00:29:54.940 --> 00:29:58.060
process-based and what's the other one?


00:29:58.060 --> 00:30:00.540
- Yeah, so there's process-based


00:30:00.540 --> 00:30:02.620
and there's the event scheduling approach.


00:30:02.620 --> 00:30:05.140
There's two different ways of approaching


00:30:05.140 --> 00:30:06.740
discrete event simulation


00:30:06.740 --> 00:30:11.740
and the standard library in R to do it is process-based


00:30:11.740 --> 00:30:16.900
and I don't wanna call it the way to do it in Python,


00:30:16.900 --> 00:30:18.740
The way we've said in Python to do it


00:30:18.740 --> 00:30:22.700
is by using the Q libraries, CIW library.


00:30:22.700 --> 00:30:24.620
- The only reason Gerard doesn't want to say


00:30:24.620 --> 00:30:25.460
it's the way to do it in Python


00:30:25.460 --> 00:30:26.740
is because it's using his library,


00:30:26.740 --> 00:30:29.260
the library that he's the maintainer of.


00:30:29.260 --> 00:30:31.860
(laughing)


00:30:31.860 --> 00:30:32.700
- Yeah, nice.


00:30:32.700 --> 00:30:37.700
- Both those libraries, I'm pretty sure that underneath,


00:30:37.700 --> 00:30:40.100
well, I know how Q works underneath,


00:30:40.100 --> 00:30:42.700
but the Simmer, which is the R version,


00:30:42.700 --> 00:30:46.540
I'm pretty sure underneath they work very, very similarly.


00:30:46.540 --> 00:30:49.260
There's not many ways you can do different ways


00:30:49.260 --> 00:30:50.800
of discrete dimensionalization,


00:30:50.800 --> 00:30:54.260
but the way you formulate the problem is very different.


00:30:54.260 --> 00:30:58.780
And going through that in the book and going in Python,


00:30:58.780 --> 00:31:02.000
you have to take like an overhead worldview


00:31:02.000 --> 00:31:03.580
where you look at the system,


00:31:03.580 --> 00:31:06.460
whereas in R you have to take a sort of,


00:31:06.460 --> 00:31:09.500
you have to put yourself mind in the, sorry,


00:31:09.500 --> 00:31:11.500
put yourself in the mind of the customer and go,


00:31:11.500 --> 00:31:13.260
what is the customer doing right now


00:31:13.260 --> 00:31:15.260
rather than from a systems point of view


00:31:16.140 --> 00:31:17.740
in order to formulate the problem


00:31:17.740 --> 00:31:20.080
before you could just then go and solve it.


00:31:20.080 --> 00:31:21.500
I just thought it was very, very interesting


00:31:21.500 --> 00:31:25.780
that the way to do it in each language was so different


00:31:25.780 --> 00:31:26.980
and yet probably underneath


00:31:26.980 --> 00:31:28.180
it's doing exactly the same thing.


00:31:28.180 --> 00:31:29.540
You get the same answers out.


00:31:29.540 --> 00:31:31.520
You just got to formulate it in a different way.


00:31:31.520 --> 00:31:34.140
- I think that's such a nice example where diversity,


00:31:34.140 --> 00:31:35.060
and I'm using diversity


00:31:35.060 --> 00:31:37.940
from the way that languages do things.


00:31:37.940 --> 00:31:40.200
I think that's the best chapter in the book, frankly.


00:31:40.200 --> 00:31:42.140
I think that's the best chapter in the book


00:31:42.140 --> 00:31:45.180
because you not only do things differently


00:31:45.180 --> 00:31:46.140
from a programming point of view,


00:31:46.140 --> 00:31:47.580
but because you do things differently


00:31:47.580 --> 00:31:48.860
from a programming point of view,


00:31:48.860 --> 00:31:52.060
the theoretic discussion allows you to kind of,


00:31:52.060 --> 00:31:54.220
yeah, give a really good understanding


00:31:54.220 --> 00:31:55.860
of these two ways of doing this.


00:31:55.860 --> 00:31:58.500
- Yeah. - Yeah.


00:31:58.500 --> 00:32:00.860
- Yeah. - Something else


00:32:00.860 --> 00:32:03.660
that's kind of worth mentioning about the Python in R bit.


00:32:03.660 --> 00:32:07.900
I don't know if this is a terrible address,


00:32:07.900 --> 00:32:09.620
but I like tests.


00:32:09.620 --> 00:32:11.180
I don't like trusting any code.


00:32:11.180 --> 00:32:13.020
I like writing tests all the time.


00:32:13.020 --> 00:32:14.820
And we came to this immediate thing


00:32:14.820 --> 00:32:16.700
So we wanted the book to be tested.


00:32:16.700 --> 00:32:18.260
We wanted to know the code was correct in the book,


00:32:18.260 --> 00:32:22.340
but we wanted to have these two different languages.


00:32:22.340 --> 00:32:24.300
And we didn't want to kind of use the standard


00:32:24.300 --> 00:32:26.940
doc test notation for the Python.


00:32:26.940 --> 00:32:28.220
And then we wanted to find something that would work


00:32:28.220 --> 00:32:29.180
for the R, et cetera.


00:32:29.180 --> 00:32:34.180
So we actually wrote a little language of Gnostic doc tester


00:32:34.180 --> 00:32:37.940
that basically runs through and tests all the code


00:32:37.940 --> 00:32:39.100
in the book for us.


00:32:39.100 --> 00:32:41.260
And theoretically, when we write the second edition,


00:32:41.260 --> 00:32:42.420
when we add Julia as well,


00:32:42.420 --> 00:32:44.380
it will be able to handle that as well.


00:32:44.380 --> 00:32:45.860
(laughing)


00:32:45.860 --> 00:32:47.260
- Yeah, I guess Julia is another option


00:32:47.260 --> 00:32:50.140
that could have possibly shown up in here.


00:32:50.140 --> 00:32:53.360
Pretty interesting.


00:32:53.360 --> 00:32:56.740
I guess it's worth pulling this up.


00:32:56.740 --> 00:33:00.980
It's probably worth pulling up the Stack Overflow trends


00:33:00.980 --> 00:33:04.220
and you're putting those in there.


00:33:04.220 --> 00:33:05.800
- Yeah.


00:33:05.800 --> 00:33:10.800
- Right, so we have R, we've got Julia.


00:33:10.800 --> 00:33:13.620
I don't know where these all lie right now,


00:33:13.620 --> 00:33:16.780
but I would imagine the graph,


00:33:16.780 --> 00:33:21.360
the graph looks a little bit different across these.


00:33:21.360 --> 00:33:23.360
Just for people listening, I would say,


00:33:23.360 --> 00:33:25.880
you know, R is certainly growing.


00:33:25.880 --> 00:33:28.320
It's actually growing pretty healthily


00:33:28.320 --> 00:33:31.040
compared to many, many programming languages.


00:33:31.040 --> 00:33:35.360
And it's not going crazy, but it's going across.


00:33:35.360 --> 00:33:38.520
You've got Python, which if anyone's looked


00:33:38.520 --> 00:33:39.400
in the last couple of years,


00:33:39.400 --> 00:33:43.480
it's just done insane stuff in terms of popularity


00:33:43.480 --> 00:33:45.480
- Over there, so there's that.


00:33:45.480 --> 00:33:48.480
And then Julia is, it's, I don't know,


00:33:48.480 --> 00:33:50.240
I can't really read it.


00:33:50.240 --> 00:33:55.240
It's like 0.01% versus say like 2% for Julia,


00:33:55.240 --> 00:34:01.680
for R, excuse me, and then for 16% for Python.


00:34:01.680 --> 00:34:04.360
And there is something to be considered


00:34:04.360 --> 00:34:07.800
about choosing not just a language,


00:34:07.800 --> 00:34:10.200
'cause the language has a cool way of doing async


00:34:10.200 --> 00:34:11.480
or its generators are beautiful,


00:34:11.480 --> 00:34:14.680
but choosing a language for its ecosystem as well.


00:34:14.680 --> 00:34:15.520
- Yeah.


00:34:15.520 --> 00:34:20.040
- And I think that's where it touches on this here, right?


00:34:20.040 --> 00:34:23.200
- But also for the community that's already there,


00:34:23.200 --> 00:34:28.200
I think, at least in the area of mathematics


00:34:28.200 --> 00:34:30.480
that me and Vincent are in,


00:34:30.480 --> 00:34:34.080
I think R and Python are quite prevalent,


00:34:34.080 --> 00:34:34.920
but they're also used-


00:34:34.920 --> 00:34:37.000
- Maybe they're people there, right?


00:34:37.000 --> 00:34:37.840
- Yeah.


00:34:37.840 --> 00:34:41.640
- But I think that also used in different ways,


00:34:41.640 --> 00:34:43.120
would you agree Vince?


00:34:43.120 --> 00:34:44.900
I would say Python's very,


00:34:44.900 --> 00:34:50.240
because of PyPy, things like out of the box,


00:34:50.240 --> 00:34:54.120
there's one library to do this and it's their way to do it.


00:34:54.120 --> 00:34:58.280
Whereas with R, people tend to write their own stuff


00:34:58.280 --> 00:35:00.760
and then upload it.


00:35:00.760 --> 00:35:01.600
- Yeah.


00:35:01.600 --> 00:35:05.840
- So you might get lots and lots of different ways


00:35:05.840 --> 00:35:07.040
of doing the same thing,


00:35:07.040 --> 00:35:09.460
but each one might specialize slightly in a different way.


00:35:09.460 --> 00:35:13.620
Whereas with Python, I feel like there's one library


00:35:13.620 --> 00:35:15.380
that does it really, really well.


00:35:15.380 --> 00:35:18.380
I think people just use the ecosystems in different ways.


00:35:18.380 --> 00:35:20.580
- Yeah, both those two things are often talked as


00:35:20.580 --> 00:35:22.140
strengths of either library, right?


00:35:22.140 --> 00:35:24.740
The fact that Python has that one way to do things,


00:35:24.740 --> 00:35:27.660
and then the seven different ways to do string formatting


00:35:27.660 --> 00:35:28.780
conversation comes up.


00:35:28.780 --> 00:35:33.580
Then the fact that R is kind of like


00:35:36.020 --> 00:35:37.100
closer to the science.


00:35:37.100 --> 00:35:38.500
I don't know if that's even accurate,


00:35:38.500 --> 00:35:40.700
but that's the feeling I guess.


00:35:40.700 --> 00:35:42.060
It's also a strength, right?


00:35:42.060 --> 00:35:44.340
- Yeah, the reason there's lots and lots of libraries


00:35:44.340 --> 00:35:46.620
to do the same thing is 'cause they've each specialized


00:35:46.620 --> 00:35:49.220
in something which a new academic


00:35:49.220 --> 00:35:50.420
has just written a paper on.


00:35:50.420 --> 00:35:52.260
And that's why there's lots of different ways of doing it.


00:35:52.260 --> 00:35:53.100
- Yeah.


00:35:53.100 --> 00:35:53.920
- All right, sure.


00:35:53.920 --> 00:35:56.660
And maybe, you know, like out in the audience,


00:35:56.660 --> 00:35:59.500
the ninja says, "R is really powerful


00:35:59.500 --> 00:36:02.460
"when it comes to things like analytics and so on."


00:36:02.460 --> 00:36:05.100
So maybe there's certain areas where...


00:36:05.100 --> 00:36:06.260
- Yeah.


00:36:06.260 --> 00:36:07.780
- You know, there's the libraries you can pick,


00:36:07.780 --> 00:36:08.820
there's definitely better.


00:36:08.820 --> 00:36:10.940
Okay, now we talked about the book.


00:36:10.940 --> 00:36:12.340
The book also, as you pointed out,


00:36:12.340 --> 00:36:17.340
has an open version where you can find it on GitHub,


00:36:17.340 --> 00:36:20.480
which obviously we'll link to.


00:36:20.480 --> 00:36:23.440
And in here for each one of these,


00:36:23.440 --> 00:36:27.660
you've got some examples which are basically the,


00:36:27.660 --> 00:36:29.900
at least for the Python side,


00:36:29.900 --> 00:36:33.060
the Jupyter Notebook examples here.


00:36:33.060 --> 00:36:36.860
So I thought maybe we could sort of talk through a little bit


00:36:36.860 --> 00:36:39.460
of what is the problem and then,


00:36:39.460 --> 00:36:42.020
maybe really first quick,


00:36:42.020 --> 00:36:44.780
quickly introduce what this area is.


00:36:44.780 --> 00:36:49.540
And then we can talk about the problem,


00:36:49.540 --> 00:36:50.820
the example problem you put out there


00:36:50.820 --> 00:36:53.660
and some of the libraries and techniques there.


00:36:53.660 --> 00:36:54.500
- Sure.


00:36:54.500 --> 00:36:59.000
So the chapter two, which you're looking at right there,


00:36:59.860 --> 00:37:04.860
uses is about a mathematical concept called Markov chain.


00:37:04.860 --> 00:37:11.820
So it's this probability model that you loosely go that


00:37:11.820 --> 00:37:17.900
as the system changes over time,


00:37:17.900 --> 00:37:19.780
the system is in a particular state


00:37:19.780 --> 00:37:22.520
and then you go with a given probability


00:37:22.520 --> 00:37:24.260
of being in that state to another state


00:37:24.260 --> 00:37:26.780
and you can go around like that.


00:37:26.780 --> 00:37:28.380
That's not the best explanation I've ever given.


00:37:28.380 --> 00:37:32.140
I've explained that many times, that was probably one of my worst explanations.


00:37:32.140 --> 00:37:39.500
But Markov chains can be used to model queues. And there's a whole field of mathematics called


00:37:39.500 --> 00:37:45.980
queuing theory, and that is often used as a very applied problem. And so the problem we got here


00:37:45.980 --> 00:37:52.460
is, imagine you've got a barber, and the barber has kind of two decisions, how many chairs they


00:37:52.460 --> 00:38:00.660
have to cut hair in and how many chairs they have to keep people waiting for a chair.


00:38:00.660 --> 00:38:04.460
And obviously that has an impact on the queue, right, of how long people have to wait to


00:38:04.460 --> 00:38:05.900
get their hair cut.


00:38:05.900 --> 00:38:11.780
And you can use Markup Change to build up a model and find the probability of having


00:38:11.780 --> 00:38:14.100
to wait relatively simply.


00:38:14.100 --> 00:38:18.460
I don't know if you want to clean up what I just said.


00:38:18.460 --> 00:38:20.040
(laughing)


00:38:20.040 --> 00:38:21.400
- No, yeah, so I think,


00:38:21.400 --> 00:38:29.140
the model then would be the set of states


00:38:29.140 --> 00:38:31.180
and the probabilities of going between each states


00:38:31.180 --> 00:38:32.320
from the state you're in.


00:38:32.320 --> 00:38:35.140
And that can be written as a matrix.


00:38:35.140 --> 00:38:36.900
And the neat thing then is there's loads and loads


00:38:36.900 --> 00:38:38.460
of linear algebra techniques,


00:38:38.460 --> 00:38:41.660
which at this point you don't really need to know about,


00:38:41.660 --> 00:38:43.460
but there are linear algebra techniques,


00:38:43.460 --> 00:38:45.860
which stuff like NumPy can just do for you,


00:38:46.900 --> 00:38:49.060
which if you know which techniques to use,


00:38:49.060 --> 00:38:50.880
you know how to interpret that


00:38:50.880 --> 00:38:54.840
as a real life interpretation.


00:38:54.840 --> 00:38:57.960
So for example, there's one certain set of equations


00:38:57.960 --> 00:39:00.480
you can solve using our Markov chain,


00:39:00.480 --> 00:39:01.920
sorry, using our matrix,


00:39:01.920 --> 00:39:04.520
which will give you the long run probabilities


00:39:04.520 --> 00:39:05.760
of being in each state.


00:39:05.760 --> 00:39:08.520
There's another certain linear algebraic technique


00:39:08.520 --> 00:39:10.360
which will give you something else.


00:39:10.360 --> 00:39:12.040
And that's what this is.


00:39:12.040 --> 00:39:13.840
- Nice.


00:39:13.840 --> 00:39:16.760
- Yeah, the problem is essentially comes down


00:39:16.760 --> 00:39:19.800
of solving a matrix equation,


00:39:19.800 --> 00:39:21.420
which you can write down and understand


00:39:21.420 --> 00:39:23.780
with basic mathematical knowledge.


00:39:23.780 --> 00:39:26.260
And then that can be solved.


00:39:26.260 --> 00:39:27.580
This goes back to what you told me in high school,


00:39:27.580 --> 00:39:28.420
that matrices are great


00:39:28.420 --> 00:39:29.480
'cause computers can do them fast,


00:39:29.480 --> 00:39:30.820
but then you never actually get to do that.


00:39:30.820 --> 00:39:33.060
You just write down equations.


00:39:33.060 --> 00:39:35.340
But it's just a call to NumPy's,


00:39:35.340 --> 00:39:39.780
the NALS library can just solve it immediately for you.


00:39:39.780 --> 00:39:40.620
- It's amazing.


00:39:40.620 --> 00:39:43.700
Yeah, so the problem here to make this applied


00:39:43.700 --> 00:39:46.580
or more operational, I guess,


00:39:46.580 --> 00:39:48.780
that you all put out there says you have a barber shop


00:39:48.780 --> 00:39:52.060
and the shop notices that there's a lot of customers


00:39:52.060 --> 00:39:55.180
who are, they come and the shop is full


00:39:55.180 --> 00:39:57.000
and the waiting room is full and people just leave.


00:39:57.000 --> 00:40:00.540
And I, you know, since COVID I've just decided


00:40:00.540 --> 00:40:01.420
I'm cutting my own hair.


00:40:01.420 --> 00:40:03.940
I can't, it took too long to find a barber


00:40:03.940 --> 00:40:04.780
or anything that worked.


00:40:04.780 --> 00:40:05.940
And then after that, I kind of figured it out.


00:40:05.940 --> 00:40:07.880
But there used to be this place I would go to


00:40:07.880 --> 00:40:09.320
and boy, did it need this problem.


00:40:09.320 --> 00:40:10.780
It would be, you would go there


00:40:10.780 --> 00:40:13.100
and it'd be like an hour and a half wait.


00:40:13.100 --> 00:40:16.440
And you know, you just, all the time.


00:40:16.440 --> 00:40:20.200
And you never knew, so they would solve it by giving away free beer to people while they


00:40:20.200 --> 00:40:22.560
wait, which was nice.


00:40:22.560 --> 00:40:27.120
But this one wants to solve it more in a more formal business way where they would have


00:40:27.120 --> 00:40:28.800
people just wait less.


00:40:28.800 --> 00:40:33.360
So it says you have two barber chairs, there's room for four people in the waiting room,


00:40:33.360 --> 00:40:40.000
there's about 10 customers an hour, and it takes about 15 minutes to serve a customer.


00:40:40.000 --> 00:40:45.000
How can we minimize or how do we change things


00:40:45.000 --> 00:40:48.360
so that we don't have customers leaving


00:40:48.360 --> 00:40:50.040
'cause they come in and see a full waiting room


00:40:50.040 --> 00:40:51.080
and take off, right?


00:40:51.080 --> 00:40:53.040
Yeah.


00:40:53.040 --> 00:40:55.360
- So instead of knocking down a wall


00:40:55.360 --> 00:40:57.960
and building a bigger waiting room


00:40:57.960 --> 00:41:01.040
or spending a lot of money on an extra barber chair


00:41:01.040 --> 00:41:02.360
and just seeing the effect


00:41:02.360 --> 00:41:04.820
and maybe five years later trying the other way,


00:41:04.820 --> 00:41:06.740
you can just mathematically model this.


00:41:06.740 --> 00:41:08.040
And this is a good example of, I think,


00:41:08.040 --> 00:41:09.940
what we've described as applied mathematics


00:41:09.940 --> 00:41:13.660
so that you can answer these cool questions.


00:41:13.660 --> 00:41:14.500
- So you could say,


00:41:14.500 --> 00:41:16.460
well, maybe we need a bigger waiting room


00:41:16.460 --> 00:41:18.140
or maybe we need more barber chairs


00:41:18.140 --> 00:41:19.320
or something like that, right?


00:41:19.320 --> 00:41:22.060
And then you can make that trade off.


00:41:22.060 --> 00:41:25.620
Yeah, so let me find the,


00:41:25.620 --> 00:41:34.260
this is the numpy, numpy.linalg magic.


00:41:34.260 --> 00:41:35.660
And so basically you set it up


00:41:35.660 --> 00:41:39.860
so that you set up all these scenarios in these constraints


00:41:39.860 --> 00:41:43.660
And then you just say, "NumPy, solve it," right?


00:41:43.660 --> 00:41:45.220
- That's pretty much it, yeah.


00:41:45.220 --> 00:41:51.220
Mathematically, you write down this matrix A


00:41:51.220 --> 00:41:52.360
and another vector B,


00:41:52.360 --> 00:41:55.140
and you're solving an equation AX equals B.


00:41:55.140 --> 00:41:59.380
Most of the code is just getting the matrix set up


00:41:59.380 --> 00:42:00.740
and the B set up.


00:42:00.740 --> 00:42:03.100
Actually, most of the code is the doc strings.


00:42:03.100 --> 00:42:06.860
And then, yeah, you just use the linalg.leastSquares.


00:42:06.860 --> 00:42:08.900
That's one of many ways you can do it.


00:42:08.900 --> 00:42:12.980
least squares is actually getting an approximate solution


00:42:12.980 --> 00:42:16.280
to the linear algebraic equation.


00:42:16.280 --> 00:42:18.300
And there's various reasons why that's a better idea


00:42:18.300 --> 00:42:19.620
than solving it directly.


00:42:19.620 --> 00:42:22.680
And yeah, it's just basically one line.


00:42:22.680 --> 00:42:27.340
- Well, I think one of the neat things about this then


00:42:27.340 --> 00:42:30.660
is all that maths you sort of learn in school


00:42:30.660 --> 00:42:32.620
or even first year university where you're doing


00:42:32.620 --> 00:42:36.060
sort of row operations and stuff.


00:42:36.060 --> 00:42:38.660
That's not the mathematics that matters here.


00:42:38.660 --> 00:42:42.540
The mathematics of math is, what is the matrix you need to do that to?


00:42:42.540 --> 00:42:45.500
And once you've done it, how do you interpret the result?


00:42:45.500 --> 00:42:47.620
That is the mathematics.


00:42:47.620 --> 00:42:53.340
It's not the actual operations that you spent so long doing in first year university.


00:42:53.340 --> 00:42:56.220
That's such a good point, Garen.


00:42:56.220 --> 00:42:59.980
That's such a good point, Garen, because I think what is mathematics is an interesting


00:42:59.980 --> 00:43:00.980
question, right?


00:43:00.980 --> 00:43:05.460
And is it being able to differentiate a whole bunch of quadratics really fast?


00:43:05.460 --> 00:43:07.340
Or is it knowing which quadratic


00:43:07.340 --> 00:43:08.780
you need to differentiate, right?


00:43:08.780 --> 00:43:12.620
And I would argue that it is that, you know,


00:43:12.620 --> 00:43:15.700
it's knowing what, really knowing what the problem is


00:43:15.700 --> 00:43:17.380
so that, okay, then the actual specific


00:43:17.380 --> 00:43:20.020
mathematical technique, well, who cares, right?


00:43:20.020 --> 00:43:20.860
- Sure.


00:43:20.860 --> 00:43:22.740
Well, Vince, people so often say,


00:43:22.740 --> 00:43:24.340
oh, I'm never gonna use that.


00:43:24.340 --> 00:43:26.100
I'm never gonna do these things.


00:43:26.100 --> 00:43:28.460
I can do that with a calculator, or I can do that,


00:43:28.460 --> 00:43:30.980
you know, and I think a lot of that might be


00:43:30.980 --> 00:43:32.220
slightly misplaced.


00:43:32.220 --> 00:43:33.260
I'm not gonna say misplaced,


00:43:33.260 --> 00:43:37.300
a somewhat misplaced focus on some of these things, right?


00:43:37.300 --> 00:43:38.460
Like if you could say, well,


00:43:38.460 --> 00:43:40.700
spend a little time showing you how to differentiate,


00:43:40.700 --> 00:43:44.240
then we'll show you how to actually solve problems


00:43:44.240 --> 00:43:46.520
with that instead of just getting, you know,


00:43:46.520 --> 00:43:50.300
more and more complicated techniques that you can apply,


00:43:50.300 --> 00:43:52.780
I guess, integrations more of a pick and choose


00:43:52.780 --> 00:43:55.860
or I like to find which thing applies, but still,


00:43:55.860 --> 00:43:59.060
you know, instead of going deep, deep, deep, deep,


00:43:59.060 --> 00:44:02.260
deep into that on the first year stuff, yeah.


00:44:02.260 --> 00:44:03.100
- Yeah, absolutely.


00:44:03.100 --> 00:44:05.420
You had someone on the show a little while ago


00:44:05.420 --> 00:44:06.660
called Allen Downey.


00:44:06.660 --> 00:44:07.660
- Yeah.


00:44:07.660 --> 00:44:11.180
- And he writes a lot of really great books.


00:44:11.180 --> 00:44:15.100
And I remember what he said on your show was about,


00:44:15.100 --> 00:44:17.560
he likes to think of teaching these things in the other way


00:44:17.560 --> 00:44:19.740
that code allows you to do these things immediately.


00:44:19.740 --> 00:44:22.540
So instead of waiting through and waiting


00:44:22.540 --> 00:44:25.440
and having to have faith that there's gonna be used to it,


00:44:25.440 --> 00:44:27.420
you can just flip that around, you know,


00:44:27.420 --> 00:44:29.260
and understand what it is.


00:44:29.260 --> 00:44:30.660
I think there's also a lot of that


00:44:30.660 --> 00:44:33.380
in what we should be doing.


00:44:33.380 --> 00:44:34.460
- Yeah, that's a very good point.


00:44:34.460 --> 00:44:36.060
I totally agree.


00:44:36.060 --> 00:44:37.500
All right, wrap this one up.


00:44:37.500 --> 00:44:40.340
You were able to find that it would be better


00:44:40.340 --> 00:44:42.460
to increase the number of barbers by one


00:44:42.460 --> 00:44:46.220
than increase the waiting room capacity by two.


00:44:46.220 --> 00:44:48.060
'Cause I think the chance of the shop being full


00:44:48.060 --> 00:44:50.660
is like 23% if you had--


00:44:50.660 --> 00:44:51.980
- Something like that, yeah.


00:44:51.980 --> 00:44:55.180
- Yeah, yeah, versus like 8%, you know,


00:44:55.180 --> 00:44:56.020
those kinds of things.


00:44:56.020 --> 00:44:57.580
And those are really concrete numbers


00:44:57.580 --> 00:45:00.500
that you could go to a business and say,


00:45:00.500 --> 00:45:02.840
you hired us to analyze these things.


00:45:02.840 --> 00:45:04.780
We gathered all the necessary information


00:45:04.780 --> 00:45:08.420
like average time, how much that might vary


00:45:08.420 --> 00:45:10.020
and those kinds of things.


00:45:10.020 --> 00:45:11.180
And here are your choices


00:45:11.180 --> 00:45:14.060
and here are what are the rough expected outcomes.


00:45:14.060 --> 00:45:17.620
Like that's really, really valuable information.


00:45:17.620 --> 00:45:22.620
And I am very sure that most barbershops


00:45:22.620 --> 00:45:25.380
even chains don't do this kind of analysis.


00:45:25.380 --> 00:45:27.180
- Not enough linear algebra going on in barbershops.


00:45:27.180 --> 00:45:29.340
That's an interest, that's a bold thing.


00:45:29.340 --> 00:45:31.840
- I know. (laughs)


00:45:31.840 --> 00:45:36.580
- And this question, so a lot of the research


00:45:36.580 --> 00:45:38.220
Geraint and I do is within healthcare.


00:45:38.220 --> 00:45:40.940
So we work with hospitals solving essentially


00:45:40.940 --> 00:45:43.580
very similar problems to the one that we've just discussed.


00:45:43.580 --> 00:45:46.320
We're keen to avoid too much healthcare


00:45:46.320 --> 00:45:47.920
because that's what we do so much of.


00:45:47.920 --> 00:45:52.660
But yeah, if you get rid of the idea of a barber shop,


00:45:52.660 --> 00:45:54.740
you talk about a ward, how many beds are on the ward,


00:45:54.740 --> 00:45:57.380
how big's the parking lot for ambulances to wait in,


00:45:57.380 --> 00:46:00.260
et cetera, et cetera, that becomes very important


00:46:00.260 --> 00:46:04.860
and very powerful and not something you need to spend


00:46:04.860 --> 00:46:09.220
thousands of pounds or dollars on licenses for,


00:46:09.220 --> 00:46:13.020
not necessarily even have a huge understanding


00:46:13.020 --> 00:46:14.620
of underlying mathematics.


00:46:14.620 --> 00:46:15.700
It's all right there.


00:46:15.700 --> 00:46:18.260
It's all right there available to anyone.


00:46:18.260 --> 00:46:20.500
- Yeah, but there's way more at stake


00:46:20.500 --> 00:46:24.300
in a hospital and healthcare than there is for--


00:46:24.300 --> 00:46:25.580
- Of course, of course.


00:46:25.580 --> 00:46:26.900
- A haircut. - Of course.


00:46:26.900 --> 00:46:28.900
- Yeah, of course.


00:46:28.900 --> 00:46:33.180
- Okay, let's go on to the next one.


00:46:33.180 --> 00:46:36.780
So the next topic is discrete events.


00:46:36.780 --> 00:46:39.640
So I'll find my way over to that one.


00:46:39.640 --> 00:46:47.020
And you'll introduce this one, discrete event simulation.


00:46:47.020 --> 00:46:49.220
This sounds like this might be somewhat


00:46:49.220 --> 00:46:51.460
in your wheelhouse, Garin.


00:46:51.460 --> 00:46:56.460
- Yeah, so I think discrete event simulation


00:46:56.580 --> 00:46:59.620
is probably, if you're used to programming,


00:46:59.620 --> 00:47:01.940
this is probably the one that probably makes the most sense


00:47:01.940 --> 00:47:04.620
because it's moving virtual things


00:47:04.620 --> 00:47:06.620
around the place essentially.


00:47:06.620 --> 00:47:07.460
- Yeah.


00:47:07.460 --> 00:47:11.180
- So the question we're asking here


00:47:11.180 --> 00:47:12.940
is very similar to the question


00:47:12.940 --> 00:47:16.180
we just answered with Markov chains.


00:47:16.180 --> 00:47:19.220
But sometimes things are too complicated


00:47:19.220 --> 00:47:21.900
to be able to formulate that correct matrix


00:47:21.900 --> 00:47:23.420
or the matrix doesn't quite work


00:47:23.420 --> 00:47:26.100
because the situation is a bit too complicated.


00:47:26.100 --> 00:47:30.140
But what we can do is build a virtual representation


00:47:30.140 --> 00:47:31.460
of our system.


00:47:31.460 --> 00:47:34.060
And by sampling random numbers,


00:47:34.060 --> 00:47:37.500
we can move virtual people around that barbershop


00:47:37.500 --> 00:47:41.580
and look at what would happen, right?


00:47:41.580 --> 00:47:44.900
Just observe, collect data, crunch that data.


00:47:44.900 --> 00:47:47.060
And this is what discrete event simulation is.


00:47:47.060 --> 00:47:49.900
It's building a virtual representation of the system,


00:47:49.900 --> 00:47:52.340
using random numbers to play


00:47:52.340 --> 00:47:54.220
that virtual representation system,


00:47:54.220 --> 00:47:58.620
and then collect some data about what just happened virtually.


00:47:58.620 --> 00:47:59.120
Right.


00:47:59.120 --> 00:47:59.740
OK, excellent.


00:47:59.740 --> 00:48:01.780
So this one-- let me set the problem that you all


00:48:01.780 --> 00:48:02.420
laid out here.


00:48:02.420 --> 00:48:05.140
This is a bicycle repair shop.


00:48:05.140 --> 00:48:10.380
And there's a set of gates or actions or, I guess,


00:48:10.380 --> 00:48:15.220
events, you might say, that it flows through.


00:48:15.220 --> 00:48:22.020
So a bike arrives randomly at a rate of 15 bikes per hour.


00:48:22.020 --> 00:48:23.660
They show up and they say, hey, there's


00:48:23.660 --> 00:48:25.100
something wrong with my bike.


00:48:25.100 --> 00:48:29.180
And the staff member looks at it and helps them.


00:48:29.180 --> 00:48:31.060
That takes about three minutes.


00:48:31.060 --> 00:48:32.900
But it turns out about 20% of the time,


00:48:32.900 --> 00:48:33.980
the bikes don't need repair.


00:48:33.980 --> 00:48:35.660
There's like, did you know that there's a thing


00:48:35.660 --> 00:48:36.900
to just twist here and tighten it?


00:48:36.900 --> 00:48:38.140
All right, go away.


00:48:38.140 --> 00:48:39.900
You're fixed, you're cured.


00:48:39.900 --> 00:48:41.700
But 80% of the time, there's something wrong,


00:48:41.700 --> 00:48:43.980
flat tire, broken chain, whatever.


00:48:43.980 --> 00:48:47.100
And that gets put into a place


00:48:47.100 --> 00:48:48.420
where they're waiting to work on it.


00:48:48.420 --> 00:48:50.580
And that takes about six minutes, right?


00:48:50.580 --> 00:48:51.940
And then you've got to collect it back.


00:48:51.940 --> 00:48:59.040
The question is, I guess the difference that I see here is there's not an uncertainty of


00:48:59.040 --> 00:49:02.400
whether or not you want a haircut when you show up at a barbershop.


00:49:02.400 --> 00:49:05.880
There's just amount of time and where the people are and actions they might take if


00:49:05.880 --> 00:49:06.880
it's too full.


00:49:06.880 --> 00:49:11.520
But here you may show up and you may need help or you may not need help and so on.


00:49:11.520 --> 00:49:13.680
So is that the difference?


00:49:13.680 --> 00:49:20.640
>> I suppose that is the difference between these two problems.


00:49:20.640 --> 00:49:24.640
but that's not the reason we would use simulation over Markov chains.


00:49:24.640 --> 00:49:32.800
In fact, the situation we're looking at here could be formulated as a Markov chain.


00:49:32.800 --> 00:49:36.640
The difference I see is that in this situation,


00:49:36.640 --> 00:49:39.680
you could have an infinite amount of bicycles in your bicycle shop.


00:49:39.680 --> 00:49:45.200
So if we were to formulate that as a Markov chain, we'd have an infinite matrix,


00:49:45.200 --> 00:49:47.360
which is not terrible to deal with,


00:49:47.360 --> 00:49:49.520
but you wouldn't be able to deal with it in the way we just did.


00:49:49.520 --> 00:49:52.040
- Got it, okay.


00:49:52.040 --> 00:49:52.880
- Yeah.


00:49:52.880 --> 00:49:54.880
- There's also, sorry, Gary.


00:49:54.880 --> 00:49:56.360
- No, go on.


00:49:56.360 --> 00:49:58.840
- There's also, talking about the states


00:49:58.840 --> 00:50:02.200
that I did kind of awkwardly in the previous chapter,


00:50:02.200 --> 00:50:04.920
it's just how many people are in the shop.


00:50:04.920 --> 00:50:06.580
So there's three people in the shop.


00:50:06.580 --> 00:50:08.200
Well, there's a probability that the next thing


00:50:08.200 --> 00:50:09.940
that happens is four, or the probability


00:50:09.940 --> 00:50:11.360
that the next thing that happens is two.


00:50:11.360 --> 00:50:16.360
So it's a very straightforward set of states


00:50:16.360 --> 00:50:18.160
that is finite, as Garen said.


00:50:18.160 --> 00:50:21.540
Here, there's two things to keep track of.


00:50:21.540 --> 00:50:23.920
There's the number of bikes waiting to be seen


00:50:23.920 --> 00:50:25.320
by the inspector, the number of bikes waiting


00:50:25.320 --> 00:50:26.760
to be seen by the repair shop.


00:50:26.760 --> 00:50:29.560
And that just immediately, the fact that now you've got


00:50:29.560 --> 00:50:32.020
these two dimensions that can change,


00:50:32.020 --> 00:50:34.000
just again adds to the complexity and the fact


00:50:34.000 --> 00:50:35.400
that it's an amount of them.


00:50:35.400 --> 00:50:38.060
- Yeah, okay.


00:50:38.060 --> 00:50:38.900
- Yeah.


00:50:38.900 --> 00:50:42.140
- So the reason we would use, no.


00:50:42.140 --> 00:50:44.760
So the reason we would use simulation for this


00:50:44.760 --> 00:50:47.800
is because it's a more complicated situation


00:50:47.800 --> 00:50:51.040
for a variety of reasons than what we had before.


00:50:51.040 --> 00:50:53.980
It would take a really, really big,


00:50:53.980 --> 00:50:56.680
if not infinite matrix to be able to solve this.


00:50:56.680 --> 00:50:58.960
So why would we go to that effort


00:50:58.960 --> 00:51:00.400
when we can get quick, easy answers


00:51:00.400 --> 00:51:02.820
just by virtually playing the system?


00:51:02.820 --> 00:51:04.920
- Right.


00:51:04.920 --> 00:51:07.480
- And these two chapters are paired.


00:51:07.480 --> 00:51:08.920
Sorry, Michael, I'm, please.


00:51:08.920 --> 00:51:10.920
- No, please go.


00:51:10.920 --> 00:51:12.480
- These two chapters are paired,


00:51:12.480 --> 00:51:14.400
and actually there's this,


00:51:14.400 --> 00:51:16.640
all the chapters are paired in the book


00:51:16.640 --> 00:51:23.880
the reason that they are kind of the two similar types of problems from opposite angles and


00:51:23.880 --> 00:51:27.360
correct me, Garen, if you don't agree, but I think that the two opposite angles about


00:51:27.360 --> 00:51:35.640
numerical tractability, how much you can do with an exact method, which is what the previous


00:51:35.640 --> 00:51:41.080
chapter was, versus a more approximative method.


00:51:41.080 --> 00:51:44.600
And it's not always easy to say exactly what you should use one or the other.


00:51:44.600 --> 00:51:47.520
Sometimes it's absolutely clear, but sometimes it's not.


00:51:47.520 --> 00:51:52.240
But there's these pairs of chapters that kind of reflect the size of the problem, for want


00:51:52.240 --> 00:51:53.920
of a better word.


00:51:53.920 --> 00:51:54.920
Very interesting.


00:51:54.920 --> 00:52:01.920
Okay, the fundamental Python bit here is the CIW, or you pronounce that Q?


00:52:01.920 --> 00:52:05.920
Yeah, I call that Q.


00:52:05.920 --> 00:52:10.680
CIW, Q, it's the Welsh word for Q, Q-U-E-U-E.


00:52:10.680 --> 00:52:14.480
It's the Welsh word for that, and that's why I call it the library, though.


00:52:14.480 --> 00:52:16.280
- Yeah, fantastic.


00:52:16.280 --> 00:52:19.160
All right, and so the idea is basically


00:52:19.160 --> 00:52:23.400
you state the problem in terms of


00:52:23.400 --> 00:52:25.520
the arrival rate of events,


00:52:25.520 --> 00:52:29.280
the inspection or the service distributions


00:52:29.280 --> 00:52:31.880
in terms of how those flow through there,


00:52:31.880 --> 00:52:33.960
the number of things that can be servicing it,


00:52:33.960 --> 00:52:35.560
and the routing and so on.


00:52:35.560 --> 00:52:40.160
You create a network with the Q library


00:52:40.160 --> 00:52:45.120
and then you could just ask it questions, right?


00:52:45.120 --> 00:52:48.360
You can tell it to run a simulation,


00:52:48.360 --> 00:52:50.820
you can run it for some amount of time,


00:52:50.820 --> 00:52:53.220
like eight seconds or so on.


00:52:53.220 --> 00:52:57.380
And it's interesting that it simulates it,


00:52:57.380 --> 00:53:00.180
that it doesn't exactly solve it, right?


00:53:00.180 --> 00:53:06.260
- Yeah, so that's the point of simulation,


00:53:06.260 --> 00:53:08.920
not the point, but like one of the uses of simulation


00:53:08.920 --> 00:53:12.760
is that we can quite easily simulate something


00:53:12.760 --> 00:53:15.800
that's too complicated to solve exactly,


00:53:15.800 --> 00:53:17.760
or would take too long to solve exactly,


00:53:17.760 --> 00:53:19.600
but we can quite easily simulate it.


00:53:19.600 --> 00:53:21.680
The trade-off then is,


00:53:21.680 --> 00:53:23.920
because assimilation is essentially


00:53:23.920 --> 00:53:26.320
streams of random numbers that we do things to,


00:53:26.320 --> 00:53:30.920
you could get extreme values, you could get flukes.


00:53:30.920 --> 00:53:35.920
So you lose accuracy, but you gain efficiency.


00:53:37.680 --> 00:53:40.320
Yeah, so the idea is you run it over and over and over again


00:53:40.320 --> 00:53:44.680
with the randomness playing out there.


00:53:44.680 --> 00:53:47.640
And then you just say, well, what is the most common set


00:53:47.640 --> 00:53:50.800
of outcomes look like?


00:53:50.800 --> 00:53:52.480
Yeah, yeah, essentially, yeah.


00:53:52.480 --> 00:53:55.120
Nice.


00:53:55.120 --> 00:53:55.960
Very cool.


00:53:55.960 --> 00:53:58.040
So what did we learn from this one?


00:53:58.040 --> 00:54:04.440
That we could add an extra inspector at the front,


00:54:04.440 --> 00:54:08.000
or we could add an extra repairer.


00:54:08.000 --> 00:54:11.160
And what was the better outcome here?


00:54:11.160 --> 00:54:15.720
- So we were measuring was the maximum amount of time


00:54:15.720 --> 00:54:17.920
a bicycle spends in the shop.


00:54:17.920 --> 00:54:20.480
We wanted to get bicycles out as quick as possible.


00:54:20.480 --> 00:54:25.480
So if we added an extra bicycle inspector,


00:54:25.480 --> 00:54:29.400
we would reduce our time,


00:54:29.400 --> 00:54:31.240
maximum time in the shop by quite a lot.


00:54:31.240 --> 00:54:33.840
But if we added an extra repairer,


00:54:33.840 --> 00:54:36.000
we'd reduce it, but not quite so much.


00:54:36.000 --> 00:54:37.740
So we essentially found that the bottleneck


00:54:37.740 --> 00:54:40.140
was the inspection desk and not the repairing.


00:54:40.140 --> 00:54:42.060
- How interesting.


00:54:42.060 --> 00:54:44.940
And I suspect, maybe this is not true,


00:54:44.940 --> 00:54:47.440
but I feel like if I was a business,


00:54:47.440 --> 00:54:50.420
knowing that would not just help me hire the right person,


00:54:50.420 --> 00:54:53.680
but I think having an inspector type of person


00:54:53.680 --> 00:54:55.960
would be easier to get, right?


00:54:55.960 --> 00:54:58.480
You don't have to have as great of a skillset


00:54:58.480 --> 00:55:02.120
to actually be the mechanic that does the repairs.


00:55:02.120 --> 00:55:07.120
So that's really valuable as somebody who runs a bike shop.


00:55:07.120 --> 00:55:10.120
I will also throw out another statement here


00:55:10.120 --> 00:55:11.360
that's probably true.


00:55:11.360 --> 00:55:15.080
I also suspect bike shops don't employ these techniques


00:55:15.080 --> 00:55:15.920
but should.


00:55:15.920 --> 00:55:18.500
(all laughing)


00:55:18.500 --> 00:55:21.560
- Oh, they can now.


00:55:21.560 --> 00:55:23.860
- They can, well, and they can now, honestly.


00:55:23.860 --> 00:55:27.920
- I believe larger companies probably would.


00:55:27.920 --> 00:55:30.640
Stuff like supermarkets and airports probably would


00:55:30.640 --> 00:55:34.080
a team of people behind them doing this, but smaller shops probably not.


00:55:34.080 --> 00:55:38.560
Yeah. Oh gosh, I don't remember the name.


00:55:38.560 --> 00:55:45.360
Not always, right, would be a little caveat. We certainly know of lots of examples of big


00:55:45.360 --> 00:55:53.680
entities, companies, things that make very expensive decisions without doing these sorts of


00:55:53.680 --> 00:55:57.040
investigations. Yeah.


00:55:57.040 --> 00:56:01.080
- Yeah, well, you mentioned grocery stores and stuff.


00:56:01.080 --> 00:56:05.240
I had the folks from Kroger, which I think, if not,


00:56:05.240 --> 00:56:09.000
is the largest, one of the largest chains in the US.


00:56:09.000 --> 00:56:12.300
They have basically an analytics and data science


00:56:12.300 --> 00:56:15.320
subsidiary called 8451.


00:56:15.320 --> 00:56:19.440
They employ 200 data scientists who do R and Python.


00:56:19.440 --> 00:56:24.520
That's not joking around in terms of,


00:56:24.520 --> 00:56:25.780
where do the bananas go?


00:56:26.760 --> 00:56:28.680
Yeah, all those types of things, right?


00:56:28.680 --> 00:56:28.880
There.


00:56:28.880 --> 00:56:29.840
So you're right.


00:56:29.840 --> 00:56:33.120
The larger companies definitely, definitely invest in that.


00:56:33.120 --> 00:56:38.400
It's interesting thing about what is data science, right?


00:56:38.400 --> 00:56:43.600
So my data scientists, in that, are they looking at historic


00:56:43.600 --> 00:56:46.760
data and identifying things?


00:56:46.760 --> 00:56:50.000
And I suspect there's no answer to my question here as well.


00:56:50.000 --> 00:56:52.200
I suspect different data scientists do different things.


00:56:52.200 --> 00:56:56.120
Um, but when you hear a data science department, that doesn't necessarily


00:56:56.120 --> 00:57:03.080
mean they're doing this type of work? It might be, absolutely might be. But they might be diving


00:57:03.080 --> 00:57:08.600
into the data and understanding and observing as opposed to necessarily modeling. It's possible.


00:57:08.600 --> 00:57:16.120
Right. It could be AI, it could be AI and ML, it could be data ETL, just bringing in data,


00:57:16.120 --> 00:57:21.160
just getting into system. Yeah, there's all these different aspects. I wonder more about the data


00:57:21.160 --> 00:57:31.640
science on when do I go from being somebody that uses say Python for computation to becoming a data


00:57:31.640 --> 00:57:37.160
science right when do I where would you cross the boundary from being a mathematician or a biologist


00:57:37.160 --> 00:57:44.600
to becoming a data scientist that has some understanding of biology for example. I would


00:57:44.600 --> 00:57:48.440
argue it kind of goes back to what we were saying earlier about what is an applied mathematician and


00:57:48.440 --> 00:57:51.280
And at what point are these labels helpful


00:57:51.280 --> 00:57:53.540
and at what point are they not, right?


00:57:53.540 --> 00:57:55.920
- Yeah, yeah, exactly.


00:57:55.920 --> 00:57:57.840
Out in the audience,


00:57:57.840 --> 00:57:59.360
Preetam says, "Yeah, data science


00:57:59.360 --> 00:58:00.880
is such a catch-all phrase right now."


00:58:00.880 --> 00:58:02.480
I would agree, also a buzzword.


00:58:02.480 --> 00:58:03.760
So if you're looking for a job,


00:58:03.760 --> 00:58:05.680
so it's a good one to employ for that.


00:58:05.680 --> 00:58:06.520
All right.


00:58:06.520 --> 00:58:08.720
Let's go on to another one.


00:58:08.720 --> 00:58:10.880
We'll get through as many of these as we can.


00:58:10.880 --> 00:58:13.360
And then we have time for anyway.


00:58:13.360 --> 00:58:18.360
So those two problem areas were paired together.


00:58:18.360 --> 00:58:19.200
- Yeah.


00:58:19.200 --> 00:58:20.400
- The next area that you focused on


00:58:20.400 --> 00:58:24.280
is fairly different with differential equations.


00:58:24.280 --> 00:58:27.000
- Yeah, so those two areas that we were just in,


00:58:27.000 --> 00:58:29.520
the book's got parts and there's two chapters in every part


00:58:29.520 --> 00:58:31.020
and that was in the probabilistic modeling


00:58:31.020 --> 00:58:31.860
is what we'd call it,


00:58:31.860 --> 00:58:34.520
modeling these probabilistic type situations.


00:58:34.520 --> 00:58:37.400
And here in the dynamical systems section


00:58:37.400 --> 00:58:39.100
and so specifically here,


00:58:39.100 --> 00:58:40.080
we're looking at a problem


00:58:40.080 --> 00:58:42.400
where differential equations can be used.


00:58:42.400 --> 00:58:45.040
And we wrote, we started writing this book


00:58:46.120 --> 00:58:50.000
before the world changed, before COVID.


00:58:50.000 --> 00:58:55.120
And I remember coming into one of our writing sessions,


00:58:55.120 --> 00:58:57.440
I have to say I really enjoyed writing the book.


00:58:57.440 --> 00:59:00.320
Very glad to have it finished, but I enjoyed writing the book


00:59:00.320 --> 00:59:02.160
and I said to Garren, Garren,


00:59:02.160 --> 00:59:04.280
do we need to change this chapter?


00:59:04.280 --> 00:59:08.080
Because this chapter is, there's a disease going around,


00:59:08.080 --> 00:59:09.460
I think we call it a cold.


00:59:09.460 --> 00:59:13.400
Yeah, everyone's caught a cold in a small community.


00:59:13.400 --> 00:59:14.240
There's a cost to not being able to work.


00:59:14.240 --> 00:59:16.000
- It's a point now to have a cold.


00:59:16.000 --> 00:59:16.840
Right?


00:59:16.840 --> 00:59:19.040
And the cost, financial cost associated


00:59:19.040 --> 00:59:20.720
with not being able to work,


00:59:20.720 --> 00:59:23.840
financial costs with a possible cure


00:59:23.840 --> 00:59:26.880
that would double the rate at which you get better


00:59:26.880 --> 00:59:28.320
from the cure.


00:59:28.320 --> 00:59:30.600
Is it worth, from the cold, pardon me,


00:59:30.600 --> 00:59:35.600
is it worth financially to get this cure was the problem.


00:59:35.600 --> 00:59:39.960
And yeah, we were like, should we make this about COVID?


00:59:39.960 --> 00:59:43.280
You know, should we just essentially all the graphs


00:59:43.280 --> 00:59:45.300
we spent so long looking at that was on the news


00:59:45.300 --> 00:59:52.500
the time, this is it. This is essentially the same thing. Should we make it about COVID?


00:59:52.500 --> 01:00:00.420
We decided not to, didn't we, Garry? We decided to just keep it somewhat abstract. But yeah,


01:00:00.420 --> 01:00:10.940
that's the problem here. And the model is a textbook, for want of a better word, a textbook


01:00:10.940 --> 01:00:16.860
model that's often taught when you start learning about systems of differential equations called


01:00:16.860 --> 01:00:25.420
the SIR model. And the SIR model has a population in three groups, susceptible people.


01:00:25.420 --> 01:00:28.220
Sorry, Vint, I think you're talking about a different chapter.


01:00:28.220 --> 01:00:34.060
I am talking about the wrong chapter. Thank you. Sorry, I went off on that one. Thank you.


01:00:34.060 --> 01:00:35.180
That's the next chapter.


01:00:35.180 --> 01:00:38.700
They're similar. Yeah, they're similar.


01:00:38.700 --> 01:00:39.980
Very similar.


01:00:39.980 --> 01:00:44.980
- This one, you can write down a differential equation


01:00:44.980 --> 01:00:47.440
that dictates not a system,


01:00:47.440 --> 01:00:50.240
but just the number of people that are infected over time.


01:00:50.240 --> 01:00:52.240
And so you can write that down, that differential equation,


01:00:52.240 --> 01:00:54.140
you can get a solution for it.


01:00:54.140 --> 01:00:57.640
Sorry, thank you, Geraint, thank you.


01:00:57.640 --> 01:01:01.160
- Yeah, no worries.


01:01:01.160 --> 01:01:03.560
This one actually uses an interesting library


01:01:03.560 --> 01:01:06.460
that I am just fascinated with.


01:01:06.460 --> 01:01:07.660
- Awesome library, yeah.


01:01:08.840 --> 01:01:12.240
- Yeah, I just had the folks on back in May,


01:01:12.240 --> 01:01:13.960
not too long ago for this one,


01:01:13.960 --> 01:01:17.440
Andre and Aaron for this.


01:01:17.440 --> 01:01:21.440
I did not expect this from Python


01:01:21.440 --> 01:01:25.040
because I expected NumPy


01:01:25.040 --> 01:01:27.720
and the linear algebra type things,


01:01:27.720 --> 01:01:32.560
but not, here's the integral of this solution


01:01:32.560 --> 01:01:34.200
of this differential equation.


01:01:34.200 --> 01:01:36.200
And here were the steps that I took to get there.


01:01:36.200 --> 01:01:37.080
It is so neat.


01:01:37.960 --> 01:01:41.040
SimPy is an incredible library that just gives you


01:01:41.040 --> 01:01:43.840
so much of what in mathematics is thought


01:01:43.840 --> 01:01:45.200
to have to be commercial


01:01:45.200 --> 01:01:48.440
in that you can have all your symbolic stuff.


01:01:48.440 --> 01:01:51.840
So, if you wanna know what is X plus X,


01:01:51.840 --> 01:01:55.880
you don't need to tell the computer what value X has.


01:01:55.880 --> 01:01:58.480
With SimPy, the computer can just understand the concept


01:01:58.480 --> 01:02:01.680
that X is this mathematical idea, and it's incredible.


01:02:01.680 --> 01:02:04.400
And it's a fantastic, fantastic library.


01:02:04.400 --> 01:02:09.400
I think it was when I started teaching programming


01:02:09.400 --> 01:02:11.940
through our first year cohort,


01:02:11.940 --> 01:02:13.560
I actually taught SageMath


01:02:13.560 --> 01:02:15.240
and SageMath is built on top of SimPy.


01:02:15.240 --> 01:02:19.320
But at some point I decided to just teach with SimPy.


01:02:19.320 --> 01:02:20.440
And so that's what we use here.


01:02:20.440 --> 01:02:21.280
That's what we use here.


01:02:21.280 --> 01:02:25.560
We build up the actual numeric solution


01:02:25.560 --> 01:02:26.640
for the differential equations.


01:02:26.640 --> 01:02:29.320
We find the expression that if you put it


01:02:29.320 --> 01:02:31.160
into this differential equation,


01:02:31.160 --> 01:02:34.320
that would be the solution.


01:02:34.320 --> 01:02:36.080
So again, the exact solution here.


01:02:36.080 --> 01:02:38.840
- Yeah.


01:02:38.840 --> 01:02:39.760
It's pretty wild.


01:02:39.760 --> 01:02:42.420
You say, the way you set it up,


01:02:42.420 --> 01:02:44.160
I mean, everything about Senpai is wild,


01:02:44.160 --> 01:02:47.040
but the way you set it up here is you say,


01:02:47.040 --> 01:02:51.320
I'm gonna create some symbols like time T


01:02:51.320 --> 01:02:54.860
or a constant alpha or so on, or initial conditions.


01:02:54.860 --> 01:02:56.280
And then you say, I'm gonna have a function.


01:02:56.280 --> 01:02:57.360
You don't say what the function is.


01:02:57.360 --> 01:03:00.120
You say there is a function called I.


01:03:00.120 --> 01:03:03.240
And then what you define for the thing you're going to work with is you say,


01:03:03.240 --> 01:03:06.200
uh, sim dot equation.


01:03:06.200 --> 01:03:10.920
And you say the equation is going to be given the derivative of this function


01:03:10.920 --> 01:03:13.920
and, of T and T.


01:03:13.920 --> 01:03:16.600
And then it has this, this expression in there.


01:03:16.600 --> 01:03:16.940
Negative.


01:03:16.940 --> 01:03:20.560
I guess that's probably the, you, what you're specifying here is this is the


01:03:20.560 --> 01:03:25.040
derivative, not the equation itself, which is negative alpha times I have T.


01:03:25.040 --> 01:03:25.320
Right.


01:03:26.080 --> 01:03:31.300
This is one of those parts of SymPy that when we teach this to our first years, it allows


01:03:31.300 --> 01:03:35.880
us to help identify misunderstandings about the mathematics.


01:03:35.880 --> 01:03:40.760
I think programming can often help you understand mathematics better and likewise and vice versa,


01:03:40.760 --> 01:03:47.100
but people often come to study mathematics and don't know the difference between a formula


01:03:47.100 --> 01:03:49.680
and an equation, and an equation has two sides.


01:03:49.680 --> 01:03:52.200
An equation has an equal side in the middle.


01:03:52.200 --> 01:03:58.680
And so what you're creating here is sim.eq takes two variables, a left-hand side and


01:03:58.680 --> 01:03:59.680
a right-hand side.


01:03:59.680 --> 01:04:01.240
That's actually the name of the parameters.


01:04:01.240 --> 01:04:03.880
So the left-hand side is the derivative of i.


01:04:03.880 --> 01:04:10.400
So it's saying that the speed at which the number of infected people changes over time,


01:04:10.400 --> 01:04:14.360
that's the left-hand side of your equation, is equal to, and then the right-hand side


01:04:14.360 --> 01:04:19.760
of your equation, some constant alpha minus some constant alpha, sorry, times the number.


01:04:19.760 --> 01:04:21.240
So the speed is related to the number.


01:04:21.240 --> 01:04:25.240
And that's really the relationship that defines the differential equations.


01:04:25.240 --> 01:04:26.240
Right.


01:04:26.240 --> 01:04:31.480
And in this scenario, you can change the alpha, the rate of recovery by providing medicine


01:04:31.480 --> 01:04:35.240
or just letting people do their thing, you know?


01:04:35.240 --> 01:04:37.240
Naturally recover, yes.


01:04:37.240 --> 01:04:38.800
Yeah, yeah, exactly.


01:04:38.800 --> 01:04:42.560
So in here you say, you know, given these constants, we're going to, you know, get the


01:04:42.560 --> 01:04:45.240
equation and then you solve it.


01:04:45.240 --> 01:04:50.240
You come up with the actual symbolic solution, which is always, always blows my mind.


01:04:50.240 --> 01:04:52.180
- And then when you say sim.dsolve,


01:04:52.180 --> 01:04:54.980
like does that solve the differential equation?


01:04:54.980 --> 01:04:56.180
I'm guessing you give it the equation


01:04:56.180 --> 01:04:58.260
and the initial conditions and stuff,


01:04:58.260 --> 01:05:01.320
and you're like, where the initial condition is,


01:05:01.320 --> 01:05:06.980
we defined a function i, we didn't say what it is, really.


01:05:06.980 --> 01:05:09.740
What we said at zero, it's the initial condition


01:05:09.740 --> 01:05:10.900
of like how many people are sick


01:05:10.900 --> 01:05:13.420
or whatever that turned out to be, which is just amazing.


01:05:13.420 --> 01:05:14.660
- All of which is simple.


01:05:14.660 --> 01:05:16.340
Everything here is just an idea.


01:05:16.340 --> 01:05:17.580
Nothing's a number.


01:05:17.580 --> 01:05:18.420
Everything is just an idea.


01:05:18.420 --> 01:05:20.300
- Yeah, yeah, we don't know anything about it.


01:05:20.300 --> 01:05:23.580
We just know that these are the constraints of the equation


01:05:23.580 --> 01:05:28.380
and out it gives you, let's see.


01:05:28.380 --> 01:05:34.260
You get the solution and it says an equation.


01:05:34.260 --> 01:05:35.900
Let's see, I gotta go further down.


01:05:35.900 --> 01:05:36.740
- So that's it.


01:05:36.740 --> 01:05:38.860
- Yeah, so it gives you the actual solution


01:05:38.860 --> 01:05:40.740
and then you start plugging in like the numbers,


01:05:40.740 --> 01:05:43.820
the different conditions and it gives you the answers, right?


01:05:43.820 --> 01:05:45.140
- Exactly.


01:05:45.140 --> 01:05:47.740
- Yeah, you plug in the numbers at the end.


01:05:47.740 --> 01:05:49.420
- Yeah.


01:05:49.420 --> 01:05:53.400
So we get the cost if you were to purchase the cure


01:05:53.400 --> 01:05:57.300
would be 700 and the cost without purchasing the cure


01:05:57.300 --> 01:05:58.140
would be 500.


01:05:58.140 --> 01:06:01.060
And since the overall costing into account productivity


01:06:01.060 --> 01:06:04.620
offsetting all the impacts of, you know,


01:06:04.620 --> 01:06:06.900
the similar type of decisions that have been,


01:06:06.900 --> 01:06:09.020
you know, governments all over the world have been making.


01:06:09.020 --> 01:06:11.180
And in this particular case, for this cold data is,


01:06:11.180 --> 01:06:13.780
no, it is not worth getting the cure.


01:06:13.780 --> 01:06:14.620
(laughing)


01:06:14.620 --> 01:06:16.300
- Don't tell that to the people who are suffering


01:06:16.300 --> 01:06:17.500
with a fever or whatever.


01:06:17.500 --> 01:06:19.180
- It's a cold.


01:06:19.180 --> 01:06:20.020
- It's a little like, yeah, yeah, it's a cold.


01:06:20.020 --> 01:06:22.460
- This is not like a common cold, this is a cold.


01:06:22.460 --> 01:06:24.700
(laughing)


01:06:24.700 --> 01:06:28.620
- Well, this chapter, I think was,


01:06:28.620 --> 01:06:30.460
we found this chapter really, really neat


01:06:30.460 --> 01:06:33.980
because when we started doing exactly the same thing,


01:06:33.980 --> 01:06:35.940
going, how do we solve this in R,


01:06:35.940 --> 01:06:39.700
we realized we had to use a completely different approach.


01:06:39.700 --> 01:06:42.260
- Well, you know what, you skip,


01:06:42.260 --> 01:06:43.980
skipping a step, right? - It was a bad choice.


01:06:43.980 --> 01:06:46.460
- Yeah, 'cause, sorry, again,


01:06:46.460 --> 01:06:55.580
Sorry. So we went looking in R for an equivalent symbolic mathematics package in R. And there


01:06:55.580 --> 01:07:05.820
is one, but really it's a wrapper for Python's SymPy. And so we found ourselves writing strings


01:07:05.820 --> 01:07:11.900
of Python that you pass to R that R passes to SymPy. And yeah, sorry.


01:07:11.900 --> 01:07:13.220
- Yeah, I think that's--


01:07:13.220 --> 01:07:16.540
- That doesn't sound like really like solving it in R.


01:07:16.540 --> 01:07:17.380
You know?


01:07:17.380 --> 01:07:18.220
- Exactly, exactly.


01:07:18.220 --> 01:07:20.780
So then, so we decided, well, no,


01:07:20.780 --> 01:07:23.460
if we were just to solve this in R, how would you do it?


01:07:23.460 --> 01:07:26.860
And as there is no symbolic library,


01:07:26.860 --> 01:07:29.780
a library for doing symbolic mathematics in R,


01:07:29.780 --> 01:07:30.900
we solved it numerically.


01:07:30.900 --> 01:07:34.660
And that just shows like exactly the same problem.


01:07:34.660 --> 01:07:36.460
We get exactly the same answers out,


01:07:36.460 --> 01:07:39.460
but the bit in the middle, the solution steps,


01:07:39.460 --> 01:07:42.100
were completely different in both Python and R


01:07:42.100 --> 01:07:47.100
for those reasons, which I think is really neat.


01:07:47.100 --> 01:07:51.980
I think that shows that you're concentrating


01:07:51.980 --> 01:07:55.140
on the problem rather than the solution steps.


01:07:55.140 --> 01:07:57.340
Yeah, I like that.


01:07:57.340 --> 01:07:59.740
- Yeah, absolutely.


01:07:59.740 --> 01:08:04.340
And what you've learned here is that this function


01:08:04.340 --> 01:08:07.780
that expresses the cost of people being sick,


01:08:07.780 --> 01:08:11.360
IFT that we talked about is 100 for a hundred people sick.


01:08:11.360 --> 01:08:15.560
E to the negative alpha of T, which is, it's pretty awesome.


01:08:15.560 --> 01:08:17.820
I mean, there's never,


01:08:17.820 --> 01:08:22.680
there's almost always a reason to marvel at the number E.


01:08:22.680 --> 01:08:26.460
Have you all read the book, E, the story of a number?


01:08:26.460 --> 01:08:28.460
- I don't think I have, no.


01:08:28.460 --> 01:08:33.440
- This, this book is so good.


01:08:33.440 --> 01:08:36.200
It just goes back to the history literally of just,


01:08:36.200 --> 01:08:38.820
- Oh yeah, I totally can recommend it.


01:08:38.820 --> 01:08:39.660
So people can check that out.


01:08:39.660 --> 01:08:41.980
- E is a ridiculously cool number, right?


01:08:41.980 --> 01:08:43.940
In terms of, I know pi gets all the press,


01:08:43.940 --> 01:08:45.580
but E is a ridiculously cool number.


01:08:45.580 --> 01:08:46.840
- It's way cooler than pi.


01:08:46.840 --> 01:08:48.060
It's way cooler than pi.


01:08:48.060 --> 01:08:51.980
I mean, pi is cool, but if you are into


01:08:51.980 --> 01:08:54.660
the change of anything, differential equations,


01:08:54.660 --> 01:08:58.620
integrations, like, there's nothing like it, yeah.


01:08:58.620 --> 01:09:00.420
- Recommendation, I haven't heard about that one.


01:09:00.420 --> 01:09:02.360
- We are going pretty long on time here,


01:09:02.360 --> 01:09:05.340
so I wanna be respectful of your time and everything.


01:09:05.340 --> 01:09:07.980
So maybe, is there any other of the problems


01:09:07.980 --> 01:09:10.060
or areas or libraries that you've made?


01:09:10.060 --> 01:09:11.940
Actually, let me pick one here.


01:09:11.940 --> 01:09:16.940
Which chapter is the game theory one?


01:09:16.940 --> 01:09:19.760
(laughing)


01:09:19.760 --> 01:09:24.100
Wait for it, no, it's nine.


01:09:24.100 --> 01:09:25.980
- Just one before that, yeah.


01:09:25.980 --> 01:09:27.820
- Yeah, or yeah, no, it was one before that.


01:09:27.820 --> 01:09:28.980
Yeah, got it, yep.


01:09:28.980 --> 01:09:32.540
The missing one is the linear programming one.


01:09:32.540 --> 01:09:34.380
All right, game theory.


01:09:34.380 --> 01:09:37.980
And the reason I want to pull this up is we talked about Q,


01:09:37.980 --> 01:09:41.300
Grant's library and his application.


01:09:41.300 --> 01:09:42.380
How about some Nash pie?


01:09:42.380 --> 01:09:46.100
I mean, there was John Nash won the Nobel Prize in economics


01:09:46.100 --> 01:09:51.140
for coming up with basically proving in every game


01:09:51.140 --> 01:09:56.180
there was an equilibrium position, which is insane.


01:09:56.180 --> 01:09:59.780
- In a 17 page PhD thesis.


01:09:59.780 --> 01:10:00.800
Yeah, incredible.


01:10:00.800 --> 01:10:03.780
- Not bad, not bad.


01:10:03.780 --> 01:10:07.140
So, quick game theory, what is it?


01:10:07.140 --> 01:10:10.580
People maybe have heard of it, but they don't really know,


01:10:10.580 --> 01:10:11.940
or maybe they do know.


01:10:11.940 --> 01:10:14.740
I know I fumbled through the previous one,


01:10:14.740 --> 01:10:17.220
but it probably makes sense for me to take this one.


01:10:17.220 --> 01:10:17.940
Yeah, yeah, sure.


01:10:17.940 --> 01:10:18.440
Right.


01:10:18.440 --> 01:10:25.700
So game theory is the study of emergent interactions,


01:10:25.700 --> 01:10:30.260
of if you can kind of make some decisions,


01:10:31.140 --> 01:10:37.860
Describe a system at the lower level, how individuals interact, what happens at the


01:10:37.860 --> 01:10:43.700
higher level. That's the study of game theory. It's interactive decision-making. A lot of the


01:10:43.700 --> 01:10:50.020
time you can think of decision-making, for example, with that barbershop problem we discussed at the


01:10:50.020 --> 01:10:56.180
first stage of, well, if I had this many chairs or this much waiting room, what's the best thing for


01:10:56.180 --> 01:11:02.420
me, but there you're the only thing that your decision gets hit back with. If you think of a


01:11:02.420 --> 01:11:06.340
game of tennis, it's playing against a wall, it's playing against that probability. Game theory is


01:11:06.340 --> 01:11:10.660
just taking it to a slightly different dimension where you have two barbershops. What if you had


01:11:10.660 --> 01:11:14.660
two barbershops and if one does this and the other does that, where are the customers going to go?


01:11:14.660 --> 01:11:20.260
Right. Both barbershops could say expand their waiting room. Both barbershops could hire more


01:11:20.260 --> 01:11:23.780
barbers or one could say, "You know what? If you hire barbers, I'm getting a bigger waiting room."


01:11:23.780 --> 01:11:24.180
Yeah.


01:11:24.180 --> 01:11:27.380
- Right, it's like that trade-off, yeah.


01:11:27.380 --> 01:11:29.900
- Exactly, a very famous problem in game theory


01:11:29.900 --> 01:11:31.300
is the prisoner's dilemma.


01:11:31.300 --> 01:11:34.260
Two prisoners are,


01:11:34.260 --> 01:11:37.560
two criminals are convicted


01:11:37.560 --> 01:11:39.460
and are separated and are questioned,


01:11:39.460 --> 01:11:43.380
and they can give evidence about the other prisoner.


01:11:43.380 --> 01:11:46.820
If they both stay quiet, they both give no evidence,


01:11:46.820 --> 01:11:49.500
the police won't have enough evidence


01:11:49.500 --> 01:11:52.020
to send them to prison for a very long time.


01:11:52.020 --> 01:11:54.300
they'll have to stay for a very short amount of time.


01:11:54.300 --> 01:11:55.540
So that's in their interest,


01:11:55.540 --> 01:11:57.340
but the police offer me a deal.


01:11:57.340 --> 01:12:00.060
And if I give evidence about Geraint,


01:12:00.060 --> 01:12:02.340
then I'll go free and Geraint will go to prison


01:12:02.340 --> 01:12:03.540
for far longer.


01:12:03.540 --> 01:12:05.060
Geraint gets offered the same deal


01:12:05.060 --> 01:12:06.940
and that immediately creates a dilemma


01:12:06.940 --> 01:12:09.340
that we will both end up getting to prison for a long time


01:12:09.340 --> 01:12:11.220
because we will both give evidence one about the other.


01:12:11.220 --> 01:12:14.340
And so that's a very simple model.


01:12:14.340 --> 01:12:16.020
And that's actually what I came on the show


01:12:16.020 --> 01:12:18.220
a long time ago to talk about was that actual model


01:12:18.220 --> 01:12:20.820
and all the interesting stuff you could do with that.


01:12:21.780 --> 01:12:27.060
But this game theoretic chapter is paired with another chapter


01:12:27.060 --> 01:12:29.860
called agent-based modeling. It's again one of those points


01:12:29.860 --> 01:12:32.980
where labeling is interesting because for some, agent-based


01:12:32.980 --> 01:12:35.220
modeling is a subset of game theory. In a way, it doesn't


01:12:35.220 --> 01:12:38.820
really matter. And so this chapter is all about emergent


01:12:38.820 --> 01:12:44.260
behavior. If we can define how decision makers in our system


01:12:44.260 --> 01:12:47.860
interact, what happens based on what they do, and they being


01:12:47.860 --> 01:12:54.900
plural, then what is the emergent behavior that you can measure? And so the game that


01:12:54.900 --> 01:13:04.740
we model in this chapter is there are two taxi firms that serve a community, again, a small town,


01:13:04.740 --> 01:13:15.300
and they get to decide how many taxis they're going to have. And the town wants to incentivize


01:13:15.300 --> 01:13:19.100
these two taxi firms, essentially not to collude.


01:13:19.100 --> 01:13:24.320
They want to incentivize the taxi firms to give better service to the population.


01:13:24.320 --> 01:13:29.360
And so we create the game that allows the taxi firms to decide how many taxis they're


01:13:29.360 --> 01:13:33.220
going to have, one, two, or three.


01:13:33.220 --> 01:13:41.380
And we build a little model that describes what happens if each taxi firm has one taxi,


01:13:41.380 --> 01:13:44.420
what happens if one has one, the other has two, what happens if one has one, the other


01:13:44.420 --> 01:13:47.620
as three, et cetera, et cetera.


01:13:47.620 --> 01:13:51.060
And then we obtain what is called the Nash equilibrium,


01:13:51.060 --> 01:13:54.380
which is a measure of if both tax firms know all this


01:13:54.380 --> 01:13:57.080
and act rationally, what would we expect to happen?


01:13:57.080 --> 01:14:03.020
- It's just amazing how these outcomes,


01:14:03.020 --> 01:14:04.740
it's just so clear, you know,


01:14:04.740 --> 01:14:08.440
if what's the likelihood of the other person doing


01:14:08.440 --> 01:14:12.460
or the other player participant taking this particular


01:14:12.460 --> 01:14:15.260
choice and if I take this choice,


01:14:15.260 --> 01:14:18.740
what are they most likely to do and where are things going to settle in?


01:14:18.740 --> 01:14:22.540
It's really neat how this all sets up here.


01:14:22.540 --> 01:14:25.620
Let me find the section.


01:14:25.620 --> 01:14:30.260
Yeah. So what you do is you create


01:14:30.260 --> 01:14:39.900
a NumPy array that represents one of the participants outcomes and choices.


01:14:39.900 --> 01:14:43.200
And this one, I guess it's a, what is this?


01:14:43.200 --> 01:14:44.480
A zero sum game?


01:14:44.480 --> 01:14:45.320
'Cause you can--


01:14:45.320 --> 01:14:46.160
- Not quite, not quite.


01:14:46.160 --> 01:14:48.000
It's not zero sum, it's symmetric.


01:14:48.000 --> 01:14:48.840
So--


01:14:48.840 --> 01:14:50.000
- Oh, symmetric, okay.


01:14:50.000 --> 01:14:52.200
So you can pass in the transpose of that,


01:14:52.200 --> 01:14:53.500
which says, here's the other player.


01:14:53.500 --> 01:14:56.600
They get basically the opposite of that.


01:14:56.600 --> 01:15:00.880
And then you just say, Nash.game, and off you go, right?


01:15:00.880 --> 01:15:03.200
- Yeah, Nash.game creates this game.


01:15:03.200 --> 01:15:05.760
It creates the game object, and in the game object,


01:15:05.760 --> 01:15:09.560
the Nash Pi library has all sorts of different algorithms


01:15:09.560 --> 01:15:11.400
that could be used and the one we use


01:15:11.400 --> 01:15:13.400
is something called support enumeration,


01:15:13.400 --> 01:15:18.400
which is essentially the basic by definition idea.


01:15:18.400 --> 01:15:23.640
And the thing that we do do here is we say,


01:15:23.640 --> 01:15:27.040
okay, if we are the town hall trying to decide


01:15:27.040 --> 01:15:29.900
how to let these two tax firms compete,


01:15:29.900 --> 01:15:33.520
is we essentially are deciding not how we regulate them,


01:15:33.520 --> 01:15:35.000
but how we incentivize them.


01:15:35.000 --> 01:15:38.020
So what game should we make the two taxi firms play?


01:15:38.020 --> 01:15:40.740
And we do that by essentially saying,


01:15:40.740 --> 01:15:42.980
I guess we will tax you slightly less


01:15:42.980 --> 01:15:45.220
if you put on this amount of taxis


01:15:45.220 --> 01:15:47.780
or give you an extra bonus if not.


01:15:47.780 --> 01:15:51.420
And the idea is to, what is the smallest amount


01:15:51.420 --> 01:15:54.940
that the city hall has to kind of guarantee


01:15:54.940 --> 01:15:58.660
to the taxi firms to ensure that their rational behavior


01:15:58.660 --> 01:16:01.400
would be to give best service to the population?


01:16:01.400 --> 01:16:03.220
- Yeah. - So yeah,


01:16:03.220 --> 01:16:04.140
then it's just those three lines


01:16:04.140 --> 01:16:04.980
you got on the screen right there,


01:16:04.980 --> 01:16:05.800
it's a little while loop


01:16:05.800 --> 01:16:07.540
where it just increments that offset.


01:16:07.540 --> 01:16:14.540
Yep, and you just say, you know, get the equilibrium from it and off it goes.


01:16:14.540 --> 01:16:16.540
Yeah, very nice.


01:16:16.540 --> 01:16:18.540
Okay.


01:16:18.540 --> 01:16:22.540
This is really great and I guess it's worth pointing out.


01:16:22.540 --> 01:16:24.540
I've heard of the guy.


01:16:24.540 --> 01:16:25.540
Yeah, that's me.


01:16:25.540 --> 01:16:26.540
I should say that.


01:16:26.540 --> 01:16:34.540
The Nash Pi Library is myself and a former undergraduate.


01:16:34.540 --> 01:16:36.540
Actually, they went on to start their PhD


01:16:36.540 --> 01:16:38.540
at the School of Mathematics.


01:16:38.540 --> 01:16:40.540
We started this library,


01:16:40.540 --> 01:16:44.540
and it's grown quite nicely now.


01:16:44.540 --> 01:16:46.540
To be honest, probably the part of the library


01:16:46.540 --> 01:16:48.540
I'm the most proud of is the documentation.


01:16:48.540 --> 01:16:50.540
There's arguably a game theory textbook in there,


01:16:50.540 --> 01:16:52.540
if anyone's interested,


01:16:52.540 --> 01:16:54.540
as well as all the functionality


01:16:54.540 --> 01:16:56.540
for two-player games. >> Yeah, fantastic.


01:16:56.540 --> 01:16:57.540
[laughter]


01:16:57.540 --> 01:16:59.540
Yeah, it looks really great. I'm a big fan of game theory.


01:16:59.540 --> 01:17:02.540
I think it's very simple,


01:17:02.540 --> 01:17:09.500
and yet it reveals pretty amazing answers and behaviors. So, you know, as opposed to something


01:17:09.500 --> 01:17:13.900
like partial differential equation, which can also reveal amazing answers, but the journey to get


01:17:13.900 --> 01:17:20.860
through it is extremely long versus this. You could sit down in an afternoon and explain it to somebody,


01:17:20.860 --> 01:17:24.860
you know, like that prisoner's dilemma and so on. We could all kind of relate to a lot of what's


01:17:24.860 --> 01:17:31.180
happening there. I mean, to be honest, if you, this is one of those things, right, you know, you


01:17:31.180 --> 01:17:34.220
you wonder, you realize that you're aging.


01:17:34.220 --> 01:17:36.940
But I remember when I first started teaching game theory,


01:17:36.940 --> 01:17:39.100
everyone had seen the movie "A Beautiful Mind."


01:17:39.100 --> 01:17:40.620
But if people listening


01:17:40.620 --> 01:17:42.260
and haven't, are slightly interested in game theory


01:17:42.260 --> 01:17:43.300
and haven't seen "A Beautiful Mind,"


01:17:43.300 --> 01:17:44.660
I'd definitely recommend it.


01:17:44.660 --> 01:17:46.700
It's a Hollywood movie,


01:17:46.700 --> 01:17:49.780
so have the correct level of expectations.


01:17:49.780 --> 01:17:52.380
But it's a really nice movie.


01:17:52.380 --> 01:17:54.540
It's Russell Crowe plays John Nash.


01:17:54.540 --> 01:17:57.500
And it's more about the,


01:17:57.500 --> 01:17:59.900
not necessarily about the mathematics,


01:17:59.900 --> 01:18:02.140
about his life, which is incredibly interesting.


01:18:02.140 --> 01:18:04.340
And there's a couple of scenes in that movie


01:18:04.340 --> 01:18:07.660
that arguably if you just spend a little bit of time


01:18:07.660 --> 01:18:09.140
talking about a couple of scenes in that movie,


01:18:09.140 --> 01:18:11.140
you could explain most of the game theory.


01:18:11.140 --> 01:18:15.660
- Yeah, absolutely.


01:18:15.660 --> 01:18:18.060
All right, well, I get the sense we're a tad bit over time,


01:18:18.060 --> 01:18:21.760
which is fine, but maybe we should wrap it up here.


01:18:21.760 --> 01:18:24.720
There's a bunch of other areas that we haven't covered


01:18:24.720 --> 01:18:27.100
that are lots of fun that you go into.


01:18:27.100 --> 01:18:30.500
So yeah, very, very neat.


01:18:30.500 --> 01:18:32.580
But let's kind of wrap it up.


01:18:32.580 --> 01:18:36.940
Maybe we'll ask you the final two questions


01:18:36.940 --> 01:18:37.780
and then we can--


01:18:37.780 --> 01:18:38.900
(laughing)


01:18:38.900 --> 01:18:40.340
- I want to thank you for having us,


01:18:40.340 --> 01:18:42.020
but I know that you got these two questions coming.


01:18:42.020 --> 01:18:43.260
So like, oh, do I thank you now?


01:18:43.260 --> 01:18:44.100
Do I thank you later?


01:18:44.100 --> 01:18:46.460
But no, I really do appreciate you having us on, Mike.


01:18:46.460 --> 01:18:47.420
I really do appreciate it.


01:18:47.420 --> 01:18:49.020
- Yeah, you're very welcome.


01:18:49.020 --> 01:18:50.180
It's been great to talk about it.


01:18:50.180 --> 01:18:52.580
All right, now maybe a lightning round.


01:18:52.580 --> 01:18:54.660
Vint, if you're gonna write some Python code,


01:18:54.660 --> 01:18:56.740
what editor are you using these days?


01:18:56.740 --> 01:18:57.580
- I use Vim.


01:18:57.580 --> 01:18:58.400
I use Vim.


01:18:58.400 --> 01:19:00.880
- Vim, right on.


01:19:00.880 --> 01:19:02.460
Grant?


01:19:02.460 --> 01:19:03.820
- I use Sublime.


01:19:03.820 --> 01:19:07.680
I really like having no features.


01:19:07.680 --> 01:19:09.240
I just like typing.


01:19:09.240 --> 01:19:10.080
I don't want features.


01:19:10.080 --> 01:19:10.900
- Right on.


01:19:10.900 --> 01:19:13.560
Perfect.


01:19:13.560 --> 01:19:17.000
And then a notable PyPI package that you've come across


01:19:17.000 --> 01:19:20.040
that you're thinking is worth giving a shout out to?


01:19:20.040 --> 01:19:21.480
- I was thinking about this before,


01:19:21.480 --> 01:19:25.680
and the one I'm gonna suggest is one called Python Ternary.


01:19:25.680 --> 01:19:26.960
You've got it on the screen there.


01:19:26.960 --> 01:19:31.960
Yeah, Python Ternary is a library for plotting on simplexes.


01:19:31.960 --> 01:19:35.480
So for plotting on triangles, want a better word.


01:19:35.480 --> 01:19:37.280
It's type of plots you draw a lot


01:19:37.280 --> 01:19:40.640
in evolutionary game theory, as well as other things.


01:19:40.640 --> 01:19:43.280
Actually a collaborator on another project of mine


01:19:43.280 --> 01:19:44.360
that maintains this.


01:19:44.360 --> 01:19:45.520
And it's a very nice library


01:19:45.520 --> 01:19:48.320
for plotting different looking plots.


01:19:48.320 --> 01:19:53.080
- Yeah, there's some, I'm sure people think about,


01:19:53.080 --> 01:19:54.640
well, you could have these different plots


01:19:54.640 --> 01:19:59.640
on triangle surfaces or how much are you,


01:19:59.640 --> 01:20:02.160
how close are each three different states


01:20:02.160 --> 01:20:03.400
or something like that.


01:20:03.400 --> 01:20:04.240
- Yeah.


01:20:04.240 --> 01:20:05.880
- You've got, some of these are really amazing,


01:20:05.880 --> 01:20:08.680
like this M cherry one on there where it's got


01:20:08.680 --> 01:20:11.480
kind of crawling graphs through these triangle


01:20:11.480 --> 01:20:12.760
different states and so on.


01:20:12.760 --> 01:20:16.200
Yeah, I haven't seen any one like that before.


01:20:16.200 --> 01:20:17.040
- It's very cool.


01:20:17.040 --> 01:20:17.880
It's very cool.


01:20:17.880 --> 01:20:19.000
And it's built on top of MapPlotLib.


01:20:19.000 --> 01:20:24.000
So it's essentially the layer to do all the correct scaling


01:20:24.360 --> 01:20:26.300
and things like that is there for you.


01:20:26.300 --> 01:20:29.560
So yeah, Python ternary is really cool.


01:20:29.560 --> 01:20:31.840
- Yeah, fantastic.


01:20:31.840 --> 01:20:32.680
Grant.


01:20:32.680 --> 01:20:36.920
- So I think the library I would choose is,


01:20:36.920 --> 01:20:38.340
it's called Traces.


01:20:38.340 --> 01:20:39.980
It's a small library.


01:20:39.980 --> 01:20:42.920
I don't know if you've heard of it before.


01:20:42.920 --> 01:20:43.920
I got the link here.


01:20:43.920 --> 01:20:51.080
It's one thing, yeah, it does one thing and one thing good.


01:20:51.080 --> 01:20:55.760
it takes moving averages over irregular time intervals.


01:20:55.760 --> 01:20:58.080
And it was a problem which I thought I had


01:20:58.080 --> 01:21:00.400
until I found this, and then it just made life easier.


01:21:00.400 --> 01:21:01.880
I liked it.


01:21:01.880 --> 01:21:02.840
- Yeah, very cool.


01:21:02.840 --> 01:21:03.680
Okay.


01:21:03.680 --> 01:21:05.960
- I think it's the next link.


01:21:05.960 --> 01:21:07.360
- Fantastic.


01:21:07.360 --> 01:21:08.280
This one right here?


01:21:08.280 --> 01:21:09.360
Not that one.


01:21:09.360 --> 01:21:10.400
This one?


01:21:10.400 --> 01:21:11.240
- There it is.


01:21:11.240 --> 01:21:13.600
- Yes, the uneven time series.


01:21:13.600 --> 01:21:14.440
Yeah, perfect.


01:21:14.440 --> 01:21:15.880
Okay.


01:21:15.880 --> 01:21:17.340
Oh yeah, that's great.


01:21:17.340 --> 01:21:20.200
- It does one thing quite well.


01:21:20.200 --> 01:21:21.200
Yeah.


01:21:21.200 --> 01:21:24.360
And yeah, that's often just what you need.


01:21:24.360 --> 01:21:26.920
Put a link to both of those in the show notes.


01:21:26.920 --> 01:21:29.200
Thank you so much.


01:21:29.200 --> 01:21:34.440
So people, people are interested in your book or maybe exploring some of these problems.


01:21:34.440 --> 01:21:36.440
What do you tell them?


01:21:36.440 --> 01:21:38.400
Where do they go?


01:21:38.400 --> 01:21:42.320
I think if they're interested in the book, that's, that's great.


01:21:42.320 --> 01:21:47.680
I think I, I, I'd more kind of emphasize just, just mathematics is so incredibly powerful


01:21:47.680 --> 01:21:50.400
And it really, really is.


01:21:50.400 --> 01:21:55.400
And it's kind of like, I feel that code, open source code,


01:21:55.400 --> 01:22:00.400
Python, kind of an order of how important each other is,


01:22:00.400 --> 01:22:03.400
with mathematics really, really gives you superpowers.


01:22:03.400 --> 01:22:07.720
And so, I'd encourage people to investigate those things


01:22:07.720 --> 01:22:09.440
and you can do amazing things with mathematics


01:22:09.440 --> 01:22:10.340
and a bit of code.


01:22:10.340 --> 01:22:12.960
That'd be mine.


01:22:12.960 --> 01:22:14.800
I don't know what you think, Gary.


01:22:14.800 --> 01:22:17.000
- No, no, yeah, I second that.


01:22:17.000 --> 01:22:20.760
I think my main message is the maths and the software


01:22:20.760 --> 01:22:25.000
are separate things and they complement each other


01:22:25.000 --> 01:22:27.280
really, really well, but they are separate things.


01:22:27.280 --> 01:22:29.520
- They are separate things, yeah, that's the thing.


01:22:29.520 --> 01:22:31.400
- Yeah, fantastic.


01:22:31.400 --> 01:22:34.400
All right, like I said, your book is on GitHub,


01:22:34.400 --> 01:22:37.600
so people can go poke around some of the examples


01:22:37.600 --> 01:22:40.680
and some of the notebooks and see what we're talking about.


01:22:40.680 --> 01:22:41.660
Make it a little more concrete.


01:22:41.660 --> 01:22:43.620
Make it a little more applied, maybe.


01:22:43.620 --> 01:22:45.400
- Yes.


01:22:45.400 --> 01:22:47.820
(laughing)


01:22:47.820 --> 01:22:49.660
- All right guys, thanks for being here.


01:22:49.660 --> 01:22:50.500
Thanks for sharing your work.


01:22:50.500 --> 01:22:51.320
- Thank you so much.


01:22:51.320 --> 01:22:52.160
- It's been a lot of fun.


01:22:52.160 --> 01:22:53.000
Yeah.


01:22:53.000 --> 01:22:53.820
- Thank you very much.


01:22:53.820 --> 01:22:54.660
- Thank you.


01:22:54.660 --> 01:22:55.500
- You bet.