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Speaker 1: Welcome to tech Stuff, a production from I Heart Radio.

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Speaker 1: Hey there, and welcome to tech Stuff. I'm your host,

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Speaker 1: Jonathan Strickland. I'm an executive producer with I Heart Radio.

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Speaker 1: And how the tech are you. I'm not doing so

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Speaker 1: great myself right now. I'm running a low fever. I'm

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Speaker 1: hoping that I just have like a stomach bug or

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Speaker 1: something and that it's not a second case of COVID,

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Speaker 1: because I don't want to be that guy. Uh. And

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Speaker 1: that's a good reminder that if you are in an

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Speaker 1: area where the COVID numbers have not really slacked off,

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Speaker 1: still a good idea to wear a mask, you know,

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Speaker 1: limit your exposure to other folks. Seriously, this is no fun.

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Speaker 1: You don't want to go through it if you can

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Speaker 1: avoid it. So yeah, just you know, I care about

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Speaker 1: you guys, so take care of yourself. Also, you know

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Speaker 1: that means that I'm not really able to write a

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Speaker 1: new episode because I can't read good when I got

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Speaker 1: a fever. So we're gonna have a little bit of

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Speaker 1: a rerun. I apologize for that. I wish I could

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Speaker 1: avoid it, I really do. But I also feel like

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Speaker 1: this is an episode that is timeless. It's one that

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Speaker 1: is important. It's called what Is an Algorithm? Which originally

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Speaker 1: published last year on July twenty one, And the reason

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Speaker 1: why I think it's important is that a lot of

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Speaker 1: people know the word algorithm, but they don't have a

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Speaker 1: deeper appreciation of what that actually means. We almost just

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Speaker 1: use it as a placeholder. It might as well be magic, right.

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Speaker 1: The Facebook algorithm determines what you see and what you

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Speaker 1: don't see, but that doesn't really explain what an algorithm is.

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Speaker 1: So I hope that you find this episode interesting and

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Speaker 1: if you would like to leave a suggestion for an

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Speaker 1: episode topic for me in the future. There are a

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Speaker 1: couple different ways of doing it. One is you can

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Speaker 1: go over to the I Heart Radio podcast app, which

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Speaker 1: is free. You can just navigate over to the tech

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Speaker 1: stuff page and there is a little microphone icon which

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Speaker 1: allows you to leave a talk back message up to

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Speaker 1: thirty seconds in length, so you can always leave me

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Speaker 1: a message if you like. You can indicate if I

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Speaker 1: could use the audio in an upcoming episode, which would

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Speaker 1: be a lot of fun. But I'm not gonna just

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Speaker 1: assume that you're cool with that. You'll have to tell me.

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Speaker 1: And um, A lot of people have been doing that.

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Speaker 1: They've been leaving messages. It's been great. You've all been

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Speaker 1: so kind and so enthusiastic, and I love it. Keep

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Speaker 1: them coming. Also, if you don't want to use the app,

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Speaker 1: I totally get it. You can always leave me a

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Speaker 1: message on Twitter. The handle for the show is tech

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Speaker 1: Stuff hs W. Now let's get to this episode that

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Speaker 1: originally published July twenty one, two thousand twenty one. What

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Speaker 1: is an algorithm? I frequently speak about algorithms on the show.

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Speaker 1: I talked about them all the time, about Facebook's algorithm

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Speaker 1: or YouTube's algorithm. We talk about search algorithms and recommendation

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Speaker 1: algorithms and tons of others. But I haven't really spent

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Speaker 1: a ton of time talking about what algorithms actually are.

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Speaker 1: Like it kind of become shorthand for do not look

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Speaker 1: behind the curtain, right, It doesn't really help you if

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Speaker 1: you don't know more about it. Uh. I might go

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Speaker 1: as far as to say it's a set of rules

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Speaker 1: or instructions to carry out a task, but that's pretty

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Speaker 1: reductive and it doesn't really help you understand what algorithms

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Speaker 1: actually do. So today I thought we'd talk a little

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Speaker 1: bit about algorithms and what they do in general, and

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Speaker 1: then maybe chat about a few famous examples and some fun,

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Speaker 1: little quirky stuff. So before I dive into this, we

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Speaker 1: do need to establish a few things, and arguably the

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Speaker 1: most important of those things is that I am not

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Speaker 1: a mathematician. I am not a computer scientist. I'm a

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Speaker 1: guy who loves tech, and I'm decent at research, and

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Speaker 1: I do my best to communicate topics in an informative

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Speaker 1: and you know, on a good day and entertaining way.

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Speaker 1: So with that in mind, I fully admit that this

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Speaker 1: is a subject that is outside of my narrow expertise,

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Speaker 1: and so my descriptions and explanations will be from a

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Speaker 1: very high level. Uh. And you might even be able

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Speaker 1: to get something like this just by glancing at a

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Speaker 1: pamphlet that's about a computer science introductory course. So for

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Speaker 1: all you folks out there who are deep in the

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Speaker 1: computer sciences, this is going to be like a children's

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Speaker 1: story book for you, possibly one where you don't like

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Speaker 1: de illustrations very much. Another thing that I need to

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Speaker 1: establish is that algorithm itself is a very broad term,

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Speaker 1: you know, in that sense, it's kind of like the

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Speaker 1: word program or app or software, and that these words

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Speaker 1: are categories that can have a wide variety of specific instances.

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Speaker 1: For example, let's just take a look at software. If

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Speaker 1: I'm talking about software, I could be talking about a

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Speaker 1: very simple program that serves as a basic calculator that

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Speaker 1: can add and subtract and divide and multiply. That could

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Speaker 1: be a piece of software, be a very simple one.

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Speaker 1: Or I might talk about something a little more complicated,

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Speaker 1: like a word processing program. Or I could talk about

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Speaker 1: an advanced three D shooter video game, or an incredibly

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Speaker 1: complicated computer simulation program, or anything in between. All of

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Speaker 1: those could fall into the realm of software well. Algorithms

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Speaker 1: similarly come in a wide variety of functions and complexity.

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Speaker 1: There are some that are elegant in their simplicity, and

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Speaker 1: there are some that when I look at them written

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Speaker 1: out in in what is clearly well defined terminology, uh,

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Speaker 1: I'm just left wondering what the heck it is I

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Speaker 1: just saw. They might as well be hieroglyphics to me.

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Speaker 1: In other words, but let's start off by talking about

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Speaker 1: the word algorithm itself. Now, unlike a lot of words

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Speaker 1: that we use specifically in English, algorithm does not have

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Speaker 1: its roots in Latin vocabulary. There are words in Latin

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Speaker 1: that are like al gore and things like that, but

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Speaker 1: that's not where algorithm comes from. Instead, it's a Latinized

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Speaker 1: version of an Arabic name. Algorithm comes from algorithmic, which

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Speaker 1: is the name that Latin scholars gave to a brilliant

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Speaker 1: man named al Ka Ritzmy and my apologies for the

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Speaker 1: butchering of the pronunciation of that name. No disrespect is intended.

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Speaker 1: It's merely American ignorance anyway. This particular mathematician philosophers scholar

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Speaker 1: served as a very important astronomer and librarian in Baghdad

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Speaker 1: in the ninth century. His work in mathematics was truly foundational,

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Speaker 1: so much so that we get the word algebra from

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Speaker 1: a work that he published. He treated algebra as a

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Speaker 1: distinct branch of mathematics, when before it was just kind

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Speaker 1: of lumped in with other stuff. And he did a

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Speaker 1: lot of work and showing how to work various types

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Speaker 1: of equations and how to balance equations. And on a

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Speaker 1: personal note, this was something that I used to love

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Speaker 1: to do in my mathematics courses. I could really see

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Speaker 1: the beauty in determining if two sides of an equation

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Speaker 1: truly were equal. It was like an elegant puzzle, and

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Speaker 1: I really love that. But again, just to be clear,

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Speaker 1: my love of algebra and trigonometry is pretty much where

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Speaker 1: math and I parted ways, because when calculus came along,

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Speaker 1: I was I was pretty much done. So at that

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Speaker 1: point it was it was beyond my ken as they say. Anyway,

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Speaker 1: back to our Arabic scholar, he highlighted the importance and

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Speaker 1: effectiveness of using a methodical approach towards the solution of problems,

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Speaker 1: and that kind of gets at the heart of what

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Speaker 1: our gorhythms actually are. The basic definition, which I kind

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Speaker 1: of alluded to earlier is quote a process or set

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Speaker 1: of rules to be followed in calculations or other problems

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Speaker 1: solving operations, especially by a computer. End quote that's from

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Speaker 1: Oxford Languages. But you know this can apply to all

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Speaker 1: sorts of stuff. For example, if you've ever seen anyone

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Speaker 1: who can solve Rubics cubes, those those puzzles that are

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Speaker 1: in cube form where you've got all the little, uh

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Speaker 1: different colors of squares and your job is to make

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Speaker 1: each side of the cube the same color. Well, there

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Speaker 1: are people who can solve Rubik's cubes in in a

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Speaker 1: fraction of like, like less than a minute. It's it's

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Speaker 1: amazing to watch them go. It's so fast and it's

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Speaker 1: hard to keep up with what they're doing. They are

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Speaker 1: essentially following algorithms, these processes that will get to a

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Speaker 1: dependable and replicable outcome based on what you're doing. Um So,

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Speaker 1: an algorithm is really just a way for us to

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Speaker 1: problem solve. Let's say we have a particular outcome that

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Speaker 1: we want to achieve. The algorithm is the recipe that

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Speaker 1: we followed to go from whatever our starting condition is

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Speaker 1: our starting state. In order to get to the outcome

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Speaker 1: we want to our target state, it needs to be

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Speaker 1: well defined. Algorithms have to be well defined because computers

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Speaker 1: are not really capable of implementing vague instructions. It needs

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Speaker 1: to have a pretty solid approach so that the computer,

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Speaker 1: when following the algorithm quote unquote, knows exactly what to

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Speaker 1: do based upon the current state of the problem. It

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Speaker 1: also needs to be finite. Computers are not capable of

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Speaker 1: handling infinite possibilities, so the algorithm has to work within

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Speaker 1: certain parameters, and those parameters depend upon the nature of

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Speaker 1: the problem you're trying to solve. And the equipment that

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Speaker 1: you have to solve it with. So let's take a

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Speaker 1: problem that computers typically struggle to achieve, and that is

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Speaker 1: random number generation or r in G. Now you would

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Speaker 1: think that creating a random number would be easy. I mean,

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Speaker 1: we can do it just by throwing some dice for example, Right,

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Speaker 1: you can throw a die and and whatever the number

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Speaker 1: comes up, that's your random number. But computers have to

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Speaker 1: follow specific instructions and execute operations that by definition need

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Speaker 1: to have a predictable and replicable outcomes. So computers find

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Speaker 1: random number generation really tricky. Typically, the best we can

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Speaker 1: hope for when it comes down to this sort of

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Speaker 1: thing is pseudo random numbers. So these are numbers that,

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Speaker 1: to an extent, appear to be random, right Like, on

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Speaker 1: casual observation, it looks like the computer is generating random numbers. However,

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Speaker 1: if you were to really seriously dig down into the process,

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Speaker 1: you might discover that they are not really really random

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Speaker 1: at all. But we just need them to be random enough, right.

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Speaker 1: We need it to be close enough to seeming to

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Speaker 1: be random for it to fulfill the function we need

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Speaker 1: if it's not truly random. For a lot of applications

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Speaker 1: that ends up being, you know, negligible. On a related note,

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Speaker 1: there are some types of mathematical problems that have many

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Speaker 1: degrees of freedom lots of variables, for example. So a

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Speaker 1: problem that does have a lot of variables could have

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Speaker 1: a lot of potential solutions, and so it could be

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Speaker 1: a challenge for computers to solve. We need algorithms to

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Speaker 1: tackle these sorts of problems, to go at them in

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Speaker 1: ways that go beyond deterministic computation, which I guess I

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Speaker 1: should define that. So, deterministic computation refers to a process

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Speaker 1: in which each successive state of an operation depends completely

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Speaker 1: on the previous state. So what comes next always depends

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Speaker 1: upon what came just before. And I'll give you an example.

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Speaker 1: Let's say I give you a math problem, and I

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Speaker 1: say you need to add these two numbers together. And

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Speaker 1: let's say it's like, uh, five and six, and then

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Speaker 1: from the sum of those numbers you have to subtract four. Well,

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Speaker 1: you would first add those two numbers together, so five

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Speaker 1: plus six you got eleven, and then you would subtract

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Speaker 1: four from that number, and so eleven minus four equal seven.

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Speaker 1: And this process is deterministic because I gave you those

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Speaker 1: specific instructions that computers do really well with deterministic processes.

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Speaker 1: These are pretty easy to follow. These sorts of processes

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Speaker 1: are by their nature replicable. So in other words, if

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Speaker 1: I ask you to do that same operation, if I

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Speaker 1: tell you add five and six together and then subtract four,

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Speaker 1: it doesn't matter how many times you are you do

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Speaker 1: that that process, right, You're always going to come out

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Speaker 1: with the same answer. It's always going to come back

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Speaker 1: no matter what you do, You're gonna always of seven

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Speaker 1: as your answer, just based on that same input. So

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Speaker 1: there are a family of algorithms that collectively get the

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Speaker 1: name Monte Carlo algorithms, and they're named after Monte Carlo,

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Speaker 1: the area of Monaco that is famous for being the

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Speaker 1: location of lots of high end casinos have been there.

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Speaker 1: It's not really my jam, but it is pretty darn flashy.

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Speaker 1: So the reason these algorithms get the name Monte Carlo

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Speaker 1: algorithms is that, like gambling, they deal with an element

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Speaker 1: of randomization. So gambling is called gambling because you're taking

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Speaker 1: a risk. You're gambling, you're betting that you're gonna beat

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Speaker 1: the odds in whichever game it is that you're playing.

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Speaker 1: And that you're going to achieve an outcome that's favorable

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Speaker 1: to you, which you experience as a payout. So, whether

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Speaker 1: it's throwing dice or playing a card game, or placing

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Speaker 1: bets at a roulette wheel or playing a slot machine,

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Speaker 1: you are engaged in an activity in which there is

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Speaker 1: some element of chance, at least in theory if the

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Speaker 1: game is honest, and what you're hoping for is that

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Speaker 1: chance lands in your favor. Similarly, Monte Carlo algorithms often

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Speaker 1: focus on chance and risk assessments such as what are

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Speaker 1: the odds that if I do this one thing, I'm

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Speaker 1: gonna totally regret doing it later? But you know, more

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Speaker 1: of the a computational problem and not a lifestyle choice. Well,

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Speaker 1: back in ninet, scientists at the Los Alamos Scientific Laboratory,

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Speaker 1: including John von Neumann, uh stand All Lam and Nick

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Speaker 1: Metropolis propose what would become known as the Metropolis algorithm,

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Speaker 1: one of the Monte Carlo algorithms, and the purpose of

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Speaker 1: this algorithm was to approximate solutions two very complicated mathematical

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Speaker 1: problems where going through a deterministic approach to find the

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Speaker 1: definitive answer just wasn't feasible. So In other words, for

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Speaker 1: certain complicated math problems, figuring out the quote unquote real

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Speaker 1: answer would really just take too long, perhaps to the

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Speaker 1: point where you would never get there within your lifetime.

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Speaker 1: So you need a way to kind of get a

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Speaker 1: ballpark solution that hopefully is closer to being correct than incorrect.

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Speaker 1: Doesn't sound like the sort of thing that computers would

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Speaker 1: be particularly good at doing right off the bat, right.

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Speaker 1: In fact, the algorithm allows computers to mimic a randomized process,

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Speaker 1: so it's not truly random, but it's random ish if

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Speaker 1: you like, and it uses this to approximate a solution

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Speaker 1: to whatever the problem is that you're trying to solve

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Speaker 1: that falls into this category. I once saw a simulation

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Speaker 1: of a randomized process using the Monte Carlo method that

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Speaker 1: I thought was pretty nifty, and it was determining what

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Speaker 1: is the value of pie. Let's say that you don't

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Speaker 1: know the value of pie and you're just trying to

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Speaker 1: figure it out. So and by the way, I mean

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Speaker 1: pie is in p I not as in the delicious

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Speaker 1: pie dessert treat. So here's the scenario. Imagine that you've

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Speaker 1: got a table and the tables like, I don't know,

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Speaker 1: three ft to a side, and positioned over this table

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Speaker 1: is a robotic arm. And this robotic arm can pick

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Speaker 1: up and drop large ball bearings onto the table, and

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Speaker 1: the arm can just move over the entire region of

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Speaker 1: the table, so it's got a three ft by three

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Speaker 1: ft range of motion. And in on this table you

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Speaker 1: set down two containers. You've got one that's that's a

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Speaker 1: circular container and one that's square. And the square container

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Speaker 1: measures six inches to a side. The radius of the

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Speaker 1: circular container is also six inches, so that means it's

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Speaker 1: got a twelve inch diameter. Right, So those are your containers,

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Speaker 1: and you've got your situation with your your robot arm

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Speaker 1: above this three ft square table. So the robotic arms

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Speaker 1: job is to pick up ball bearings and then from

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Speaker 1: a random que will drop that ball bearing somewhere above

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Speaker 1: the table. So some of those balls are going to

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Speaker 1: fall into the square container, some of them are going

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Speaker 1: to fall into the round container, some of them are

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Speaker 1: not going to fall in either. And if the process

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Speaker 1: is truly random, meaning there's an equal chance that it

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Speaker 1: will drop a ball bearing over any given point of

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Speaker 1: that table, over time, we would expect to see more

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Speaker 1: ball bearings fall into the round container because it has

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Speaker 1: a greater area and there's more space for a ball

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Speaker 1: bearing to fall into one of these. At the end

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Speaker 1: of repeating this process many, many times, we should be

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Speaker 1: able to take these two containers and then count the

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Speaker 1: number of ball bearings in each of them. And if

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Speaker 1: we divide the number of ball bearings in the circular

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Speaker 1: container by the number of ball bearings that fell into

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Speaker 1: the square container, we're gonna get results that should be

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Speaker 1: really close to pie. And you might think, wait, why

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Speaker 1: why would the number of ball bearings in one container

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Speaker 1: versus another, and then dividing those why would you get pie? Well,

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Speaker 1: if you have a process that is uniformly random across

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Speaker 1: an area, like our hypothetical three ft square table, the

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Speaker 1: probability that a dropped ball bearing will land in one

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Speaker 1: of those two specific containers is proportional to that specific

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Speaker 1: containers area or cross section. So then we just ask, all, right, well,

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Speaker 1: how do we define area? Well, with the square, it's

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Speaker 1: really simple, right. We take one side of a square

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Speaker 1: in this case, it's six inches, and we multiply it

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Speaker 1: by itself six times six. Because all sides of a

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Speaker 1: square are equal, we know that the length and the

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Speaker 1: width are each going to be six inches. We multiply

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Speaker 1: those together. We get thirty six square inches. That is

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Speaker 1: the area or cross section of our square container. But

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Speaker 1: for our circular container, we take the radius, which again

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Speaker 1: this case, the radius is six inches, and we square

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Speaker 1: it and then we multiply that number by pie. So

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Speaker 1: area for the circular container is six times six squared

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Speaker 1: times pie. And if we divide the cross section of

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Speaker 1: the circular container by the cross section of the square container,

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Speaker 1: the two six squared you know, the two elements the

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Speaker 1: squared elements cancel each other out, and so all we're

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Speaker 1: left with is pie. So the end result is that

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Speaker 1: when we count up these ball bearings that have landed

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Speaker 1: randomly in these containers, that that difference, the division that

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Speaker 1: we get that should be a close approximation of pie.

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Speaker 1: Now it's not going to be precise. Chances are the

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Speaker 1: number of ball bearings in the two containers will just

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Speaker 1: get you close to pie. But it illustrates how a

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Speaker 1: randomized process can help you get to a particular solution

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Speaker 1: that might otherwise be difficult to ascertain. There are videos

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Speaker 1: on YouTube that show this particular simulation. It's kind of

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Speaker 1: a famous one. So you can actually watch and get

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Speaker 1: kind of an understanding of what I said to you

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Speaker 1: makes no sense whatsoever. There are other options for you

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Speaker 1: to look into that might help, And that is a

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Speaker 1: great example. But what are the actual algorithms that fall

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Speaker 1: into the Monte Carlo methods spectrum? What are they used

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Speaker 1: to do well? They can be used to simulate things

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Speaker 1: like fluid dynamics, or cellular structures or the interaction of

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Speaker 1: disordered materials. So in other words, these are all processes.

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Speaker 1: They have a lot of potential variables at play, and

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Speaker 1: you can think of variables as representing uncertainty, something that

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Speaker 1: computers typically don't do well with. You know, from a

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Speaker 1: general stance, computers excel at specific instances rather than potential instances.

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Speaker 1: So algorithms like the Metropolis algor rhythm would lead computer

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Speaker 1: scientists to develop methodologies to kind of work around the

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Speaker 1: limitations of computers and leverage computational power and tackling very

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Speaker 1: difficult problems in that way. In the Monte Carlo family

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Speaker 1: of algorithms, we typically assume that the results we get

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Speaker 1: are going to have a potential for being wrong, like

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Speaker 1: there'll be a small percentage of error that we have

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Speaker 1: to take into account, and so keeping that in mind,

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Speaker 1: we need to frame results as being again approximations of

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Speaker 1: an answer, rather than the definitive answer to whatever problem

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Speaker 1: it is we're trying to solve. For me, this was

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Speaker 1: one of those things that was very difficult to grasp

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Speaker 1: for a long time because I was equating it to

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Speaker 1: math class, where you're supposed to get the answer. Now,

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Speaker 1: when we come back, we'll talk about a few more

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Speaker 1: famous algorithms and what they do. But first let's take

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Speaker 1: a quick break. Now. In our previous section, I talked

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Speaker 1: about a family of algorithms that trace their history back

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Speaker 1: to nineteen and so does the next one I want

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Speaker 1: to talk about, which was created by George Dantzig, who

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Speaker 1: worked for the Rand Corporation. And Danzig created a process

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Speaker 1: that would lead to what we call linear programming. So

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Speaker 1: at its most basic level, linear programming is about taking

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Speaker 1: some function and maximizing or minimizing that function with regard

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Speaker 1: to various constraints. But that is super vague, right, I mean,

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Speaker 1: it's not terribly helpful. It feels like I'm talking in

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Speaker 1: a circle. But this is one that's really important for say,

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Speaker 1: business developers. So let's talk about a slightly more specific

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Speaker 1: use case. Let's say that you are launching a business

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Speaker 1: and you're trying to make some you know, big decisions

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Speaker 1: as you're going to do this, and you're going to

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Speaker 1: manufacture and sell a product of some sort, some physical thing. Now,

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Speaker 1: your whole goal as a business is to make money

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Speaker 1: from the work you do, and to do that, you

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Speaker 1: need to figure out what your costs are going to

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Speaker 1: be and how you cannot just offset these costs but

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Speaker 1: make enough money to actually profit from it, so cover

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Speaker 1: all your costs plus some extra. So in this case,

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Speaker 1: what you're trying to do is figuring out how you

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Speaker 1: can minimize costs and maximize profits. Right. The constraints come

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Speaker 1: into play as you start to look at specifics, like

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Speaker 1: maybe you're gonna partner with a fabrication company, and maybe

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Speaker 1: you've actually got a few choices. You've got different companies

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Speaker 1: that you could go with. Well, these choices could represent

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Speaker 1: constraints in your approach. Perhaps one is more expensive than

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Speaker 1: the others, but it can produce a greater volume of product,

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Speaker 1: so you'd be able to get more product out to

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Speaker 1: market in less time. Or maybe you've got one that's

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Speaker 1: more expensive but it's also less likely to have fabrication errors,

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Speaker 1: and errors can be both costly and time can assuming

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Speaker 1: to address. So you have to quantify all these variables

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Speaker 1: and use them as constraints to start figuring out your

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Speaker 1: men maxing approach. Here, linear programming simply looks for the

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Speaker 1: optimum value of a linear expression, and depending on the

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Speaker 1: problem you're trying to solve, like maximizing profit versus minimizing costs,

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Speaker 1: you're either looking for the highest value being optimum or

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Speaker 1: the lowest value being optimum. Like with costs, you want

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Speaker 1: that to be the lowest, and you have to look

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Speaker 1: at what constraints are at play with any given expression.

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Speaker 1: So Danzing's approach to linear programming, called the simplex method,

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Speaker 1: was efficient and elegant and far more simplified than other

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Speaker 1: methodologies attempting to kind of do the same thing around

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Speaker 1: that time. But it also had some limitations, and that's

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Speaker 1: because the real world isn't as simple as math tends

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Speaker 1: to be. Like math tends to be pretty, you know,

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Speaker 1: firm in the grand scheme of things in the world

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Speaker 1: is a little more wibbly. Doubly, so, a linear programming

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Speaker 1: solution only works if the various relationships between the different

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Speaker 1: elements like the requirements and the restrictions and constraints that

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Speaker 1: you've set up with this problem. It only works if

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Speaker 1: all of those relationships are linear, or, in other words,

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Speaker 1: for a given change in one variable, we see a

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Speaker 1: given change in other variables. And that is super vague,

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Speaker 1: So we're going to talk about two variables. Will reduce

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Speaker 1: it down to that. So we'll use the classic X

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Speaker 1: and Y as our variables. Those can stand in for

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Speaker 1: all sorts of different values. And let's say that we

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Speaker 1: see there's a relationship between X and Y, and that

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Speaker 1: if the value of X changes from one to two,

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Speaker 1: we then see that the value of Y goes from

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Speaker 1: three to nine. Well, that doesn't tell us anything on

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Speaker 1: its own, right, We just know that if x is one,

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Speaker 1: y is three. If x is two, y is nine.

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Speaker 1: If we then see that if x is three, then

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Speaker 1: why is fifteen? And when x is four, why is

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Speaker 1: twenty one? We start to see a linear relationship because

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Speaker 1: each time X increases by one, why increases by six.

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Speaker 1: The rate of increase for each variable is linear. It's

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Speaker 1: it's not like the rate of increase doesn't change. So

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Speaker 1: we've got this linear relationship here. We can contrast this

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Speaker 1: with exponential relationships, in which we see not a constant increase,

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Speaker 1: but a constant ratio in successive terms in one variable

433
00:26:36,800 --> 00:26:39,920
Speaker 1: when you change another. So in this case, let's say

434
00:26:39,920 --> 00:26:42,879
Speaker 1: that we find out then, when X is one, why

435
00:26:43,000 --> 00:26:47,080
Speaker 1: is three? When X is two, why is nine? When

436
00:26:47,200 --> 00:26:50,760
Speaker 1: X is three, why is twenties seven? Now we see

437
00:26:50,800 --> 00:26:54,560
Speaker 1: that why is not increasing by six each time. We're

438
00:26:54,560 --> 00:26:59,280
Speaker 1: seeing that the value of why is multiplied by three

439
00:26:59,720 --> 00:27:02,320
Speaker 1: each time X goes up once. So we're seeing there's

440
00:27:02,320 --> 00:27:06,439
Speaker 1: a constant ratio of change with why with regard to X.

441
00:27:06,920 --> 00:27:11,200
Speaker 1: This gets into an exponential relationship. So when someone describes

442
00:27:11,280 --> 00:27:15,679
Speaker 1: something is having exponential growth, what this is supposed to

443
00:27:15,720 --> 00:27:20,560
Speaker 1: mean is that you should see a rate of growth

444
00:27:20,760 --> 00:27:25,399
Speaker 1: that is increasing by some exponent for given unit of time.

445
00:27:25,760 --> 00:27:29,000
Speaker 1: So it's not just that the thing is growing. In fact,

446
00:27:29,040 --> 00:27:32,240
Speaker 1: it's not even that the thing is growing quickly. It's

447
00:27:32,320 --> 00:27:35,880
Speaker 1: that the thing is growing faster as time goes on,

448
00:27:36,040 --> 00:27:39,800
Speaker 1: so that you would say today it's growing, you know,

449
00:27:39,880 --> 00:27:42,240
Speaker 1: say twice as fast as it was growing yesterday, and

450
00:27:42,280 --> 00:27:44,359
Speaker 1: tomorrow it will grow twice as fast as it was

451
00:27:44,440 --> 00:27:48,280
Speaker 1: growing today. And a lot of people use this phrase incorrectly.

452
00:27:48,840 --> 00:27:52,919
Speaker 1: We often really just mean yo, that thing is growing

453
00:27:53,000 --> 00:27:57,200
Speaker 1: wicked fast, but we don't necessarily mean yo, that thing

454
00:27:57,280 --> 00:27:59,840
Speaker 1: is growing wicked fast, and the rate of growth increases

455
00:27:59,840 --> 00:28:05,120
Speaker 1: by a constant amount over time, So you know, it's

456
00:28:05,240 --> 00:28:09,040
Speaker 1: it's an important distinction to make. Anyway, that was a

457
00:28:09,080 --> 00:28:11,840
Speaker 1: bit of a tangent to say that linear programming works

458
00:28:11,960 --> 00:28:15,680
Speaker 1: if the relationships between all the variables is in fact linear.

459
00:28:16,160 --> 00:28:19,560
Speaker 1: But if if it's not, If the relationship, say is

460
00:28:19,640 --> 00:28:24,639
Speaker 1: exponential or logarithmic or anything like that, linear programming doesn't apply.

461
00:28:25,280 --> 00:28:28,600
Speaker 1: And the real world is pretty darn complicated. So linear

462
00:28:28,640 --> 00:28:31,960
Speaker 1: programming relies on sort of kind of dumbing down what's

463
00:28:32,000 --> 00:28:34,760
Speaker 1: really going on in the real world. Two. Again, more

464
00:28:34,800 --> 00:28:37,840
Speaker 1: of an approximation, and the solution that you arrive at

465
00:28:37,960 --> 00:28:40,760
Speaker 1: might not be the ideal solution, but it might be

466
00:28:40,920 --> 00:28:43,479
Speaker 1: good enough, depending upon what it is you're trying to do.

467
00:28:44,200 --> 00:28:47,680
Speaker 1: Another limitation of linear programming is that as you add

468
00:28:47,720 --> 00:28:51,000
Speaker 1: more variables to a problem, This is specific to the

469
00:28:51,040 --> 00:28:54,920
Speaker 1: simplex method. As you add more variables, well, it grows

470
00:28:54,960 --> 00:28:59,000
Speaker 1: more difficult to lay out in a linear fashion. You're

471
00:28:59,040 --> 00:29:04,280
Speaker 1: you're adding more uncertainty, and the methodology has trouble dealing

472
00:29:04,320 --> 00:29:09,560
Speaker 1: with additional uncertainty. Perhaps ironically, the complexity of the linear

473
00:29:09,640 --> 00:29:14,160
Speaker 1: function would grow exponentially as more variables joined a problem.

474
00:29:14,200 --> 00:29:18,440
Speaker 1: So this process would be unsuitable for certain subsets of

475
00:29:18,520 --> 00:29:21,719
Speaker 1: computational problems because they just would get so complex that

476
00:29:21,760 --> 00:29:24,160
Speaker 1: even the most advanced computers in the world wouldn't be

477
00:29:24,160 --> 00:29:28,320
Speaker 1: able to handle them. Later on, other mathematicians would propose

478
00:29:28,400 --> 00:29:32,320
Speaker 1: algorithms that could compensate for this particular limitation of the

479
00:29:32,360 --> 00:29:37,680
Speaker 1: simplex method. For example, there are polynomial time algorithms. We're

480
00:29:37,680 --> 00:29:41,040
Speaker 1: gonna leave that for the time being, because ain't no

481
00:29:41,120 --> 00:29:44,440
Speaker 1: way I'm going to get that right anyway. I wanted

482
00:29:44,440 --> 00:29:48,400
Speaker 1: to talk about those two algorithms, in particular, the Metropolis

483
00:29:48,440 --> 00:29:52,200
Speaker 1: algorithm and the simplex method, because they are the foundation

484
00:29:52,320 --> 00:29:55,080
Speaker 1: for a lot of work that's been done in computer science.

485
00:29:55,120 --> 00:29:59,479
Speaker 1: But let's get some really basic ideas in with the

486
00:29:59,520 --> 00:30:04,080
Speaker 1: next one. Let's talk about sorting. Sorting is all about

487
00:30:04,160 --> 00:30:07,600
Speaker 1: arranging a list of things in order with regard to

488
00:30:07,680 --> 00:30:13,520
Speaker 1: some specific feature of those things. That seems pretty basic, right,

489
00:30:13,560 --> 00:30:16,320
Speaker 1: I Mean, there's a real world example that I think

490
00:30:16,360 --> 00:30:18,280
Speaker 1: most of us have had in the past, which is

491
00:30:18,320 --> 00:30:21,640
Speaker 1: that let's say you're looking at an online store and

492
00:30:21,680 --> 00:30:26,720
Speaker 1: you're searching for a specific product or specific type of product.

493
00:30:26,800 --> 00:30:29,320
Speaker 1: Let's say it's a blender, because I had to do

494
00:30:29,400 --> 00:30:32,880
Speaker 1: this recently, right, So you go to some online store

495
00:30:32,920 --> 00:30:35,840
Speaker 1: and you're searching for blenders and you get results, Well,

496
00:30:35,880 --> 00:30:38,040
Speaker 1: you might actually want to sort those results by a

497
00:30:38,080 --> 00:30:40,240
Speaker 1: specific way. Maybe you want to sort it by price,

498
00:30:40,360 --> 00:30:42,400
Speaker 1: and you want to go low to high because you

499
00:30:42,440 --> 00:30:44,479
Speaker 1: have a specific budget, so you just want to look at,

500
00:30:45,000 --> 00:30:47,600
Speaker 1: you know, blenders that are an x price or less.

501
00:30:48,440 --> 00:30:51,160
Speaker 1: Maybe you want to sort it by high price too

502
00:30:51,200 --> 00:30:53,760
Speaker 1: low because maybe you're a fat cat tycoon type and

503
00:30:53,760 --> 00:30:55,840
Speaker 1: you're just thinking, I want whatever is the most expensive.

504
00:30:56,600 --> 00:30:59,360
Speaker 1: Or maybe you want to sort the results by customer

505
00:30:59,440 --> 00:31:03,520
Speaker 1: review because we know rice and quality don't always go

506
00:31:03,640 --> 00:31:06,400
Speaker 1: hand in hand. Maybe you just want to look at

507
00:31:06,440 --> 00:31:08,920
Speaker 1: all the blenders in alphabetical order, or maybe you want

508
00:31:08,920 --> 00:31:11,920
Speaker 1: to look at them in a reverse alphabetical order. You

509
00:31:12,000 --> 00:31:15,720
Speaker 1: do you. Sorting is one of those most basic functions

510
00:31:16,160 --> 00:31:19,880
Speaker 1: and heavily studied concepts within computer science, so much so

511
00:31:20,040 --> 00:31:25,640
Speaker 1: that a lot of programming language libraries have sorting functions

512
00:31:25,640 --> 00:31:29,240
Speaker 1: built into them. But it's still one of those things

513
00:31:29,240 --> 00:31:31,640
Speaker 1: that people look at to see if there are better

514
00:31:31,680 --> 00:31:36,240
Speaker 1: ways to sort various types of data, particularly as you

515
00:31:36,280 --> 00:31:42,200
Speaker 1: get into a larger number of of sortable features um

516
00:31:42,240 --> 00:31:45,440
Speaker 1: and it becomes really important. So let's take Google's search

517
00:31:45,480 --> 00:31:49,680
Speaker 1: algorithm for example. Now, that name suggests that the algorithm

518
00:31:49,720 --> 00:31:52,600
Speaker 1: we're talking about is related to the process of searching

519
00:31:52,640 --> 00:31:55,720
Speaker 1: the web for pages that relate to a given search query,

520
00:31:55,960 --> 00:31:58,600
Speaker 1: and in fact, Google does have a search algorithm that

521
00:31:58,680 --> 00:32:01,440
Speaker 1: does this. But most of the time I hear people

522
00:32:01,480 --> 00:32:05,760
Speaker 1: talking about the search algorithm, they actually mean that the

523
00:32:05,840 --> 00:32:10,280
Speaker 1: algorithm that Google relies upon to determine what the order

524
00:32:10,440 --> 00:32:13,280
Speaker 1: of search results are going to be that a person

525
00:32:13,320 --> 00:32:15,680
Speaker 1: sees when they search for, you know, whatever it might be.

526
00:32:16,600 --> 00:32:20,840
Speaker 1: This is critically important because multiple studies have shown that

527
00:32:20,880 --> 00:32:23,840
Speaker 1: most people never bother to go beyond the first page

528
00:32:23,880 --> 00:32:27,400
Speaker 1: of search results, which means that Google really needs to

529
00:32:27,400 --> 00:32:30,480
Speaker 1: do its best to make sure that the most relevant

530
00:32:30,600 --> 00:32:35,000
Speaker 1: results to any given search query show up toward the

531
00:32:35,040 --> 00:32:38,520
Speaker 1: top of this list, because most people are never going

532
00:32:38,560 --> 00:32:41,480
Speaker 1: to bother going any further than that. And if those

533
00:32:41,480 --> 00:32:44,560
Speaker 1: people decide that Google search results just aren't any good,

534
00:32:45,040 --> 00:32:48,200
Speaker 1: they could conceivably use some other search engine. And let

535
00:32:48,200 --> 00:32:53,440
Speaker 1: me tell you. Google hates that idea. So Google's goal

536
00:32:53,800 --> 00:32:56,960
Speaker 1: is to present to users search results that are most

537
00:32:57,040 --> 00:33:00,400
Speaker 1: likely going to meet whatever their needs are based on

538
00:33:00,560 --> 00:33:03,800
Speaker 1: their search criteria. And way back in the day, Google

539
00:33:04,160 --> 00:33:08,560
Speaker 1: relied pretty much solely on an algorithm called page rank,

540
00:33:09,760 --> 00:33:13,040
Speaker 1: and from what I understand, Google still relies on page rink,

541
00:33:13,080 --> 00:33:17,280
Speaker 1: but also makes use of several other algorithms to augment

542
00:33:17,720 --> 00:33:21,760
Speaker 1: page drink. But the page rank algorithm would take a

543
00:33:21,800 --> 00:33:25,800
Speaker 1: ton of stuff into account in the process of determining

544
00:33:26,440 --> 00:33:29,960
Speaker 1: where within a list of search results any given example

545
00:33:30,040 --> 00:33:35,400
Speaker 1: should appear. So let's say that I'm searching for blenders

546
00:33:35,440 --> 00:33:41,080
Speaker 1: on Google for some reason, and the search algorithm has

547
00:33:41,120 --> 00:33:43,959
Speaker 1: gone out and indexed a ton of web pages that

548
00:33:44,240 --> 00:33:47,920
Speaker 1: deal with blenders. Let's say that one of those results

549
00:33:48,640 --> 00:33:52,080
Speaker 1: is in a blog post that isn't that old, it's

550
00:33:52,120 --> 00:33:56,480
Speaker 1: fairly recent, but from a mostly unknown source, and very

551
00:33:56,520 --> 00:34:01,680
Speaker 1: few other documents are linking into this blog. Well, chances

552
00:34:01,720 --> 00:34:05,800
Speaker 1: are that search result would appear really far down on

553
00:34:05,840 --> 00:34:09,400
Speaker 1: the list, probably pages and pages and pages down on

554
00:34:09,440 --> 00:34:12,719
Speaker 1: the results. But then let's say that there's another web

555
00:34:12,760 --> 00:34:16,359
Speaker 1: page that belongs to an established entity, one that has

556
00:34:16,400 --> 00:34:19,319
Speaker 1: a good reputation that's been around for a while, and

557
00:34:19,360 --> 00:34:22,600
Speaker 1: there are a ton of other pages that link to

558
00:34:22,880 --> 00:34:27,120
Speaker 1: this particular website, well, that one would probably rank fairly

559
00:34:27,239 --> 00:34:31,920
Speaker 1: high on the list. So the page rank algorithm essentially

560
00:34:31,920 --> 00:34:36,040
Speaker 1: assigns a score to each search result, and the value

561
00:34:36,080 --> 00:34:39,040
Speaker 1: of that score depends upon lots of stuff I mentioned,

562
00:34:39,040 --> 00:34:42,240
Speaker 1: as well as tons of other variables, and these variables

563
00:34:42,239 --> 00:34:45,120
Speaker 1: can either boost a score higher or it can knock

564
00:34:45,239 --> 00:34:48,480
Speaker 1: some points off. And then page rank would take all

565
00:34:48,520 --> 00:34:52,760
Speaker 1: these different search results and order them based upon those scores.

566
00:34:53,120 --> 00:34:57,880
Speaker 1: Essentially really oversimplifying here, but the idea was that the

567
00:34:57,920 --> 00:35:02,239
Speaker 1: more reliable and therefore real event results would likely be

568
00:35:02,360 --> 00:35:06,000
Speaker 1: the ones that were the most popular, So all those

569
00:35:06,080 --> 00:35:08,600
Speaker 1: links that aimed at a page would count for a lot.

570
00:35:09,360 --> 00:35:13,320
Speaker 1: If you happen to run the definitive page on blenders

571
00:35:13,360 --> 00:35:17,160
Speaker 1: and everyone was linking to you, that would boost your

572
00:35:17,160 --> 00:35:21,800
Speaker 1: page links score significantly. Now, clearly, just because something is

573
00:35:21,840 --> 00:35:27,560
Speaker 1: popular doesn't necessarily mean it's the most relevant or valuable thing,

574
00:35:27,760 --> 00:35:33,839
Speaker 1: but it's generally more true than it isn't true. It

575
00:35:33,920 --> 00:35:37,320
Speaker 1: might not always be the absolute best result, but it

576
00:35:37,440 --> 00:35:40,880
Speaker 1: might be reliably relevant, and that was what was important

577
00:35:40,920 --> 00:35:44,360
Speaker 1: to Google and to Google's users. Again, it just needs

578
00:35:44,400 --> 00:35:48,279
Speaker 1: to be good enough. So the page rank algorithm was

579
00:35:48,400 --> 00:35:51,960
Speaker 1: using a pretty complex sorting method to determine which results

580
00:35:52,000 --> 00:35:55,840
Speaker 1: should be the most visible. You can, of course, page

581
00:35:55,880 --> 00:35:59,240
Speaker 1: through search results. You don't have to go with whichever

582
00:35:59,320 --> 00:36:03,319
Speaker 1: one's are on page one, And in theory, if you

583
00:36:03,480 --> 00:36:07,560
Speaker 1: keep on scrolling through, going to page after page after

584
00:36:07,600 --> 00:36:12,000
Speaker 1: page of search results, then over time you should see

585
00:36:12,040 --> 00:36:15,160
Speaker 1: that the results you're getting are not as relevant as

586
00:36:15,200 --> 00:36:18,520
Speaker 1: those that appeared earlier on the list, assuming everything is

587
00:36:18,520 --> 00:36:24,319
Speaker 1: working properly. Again, this doesn't always happen, but generally it's oh,

588
00:36:24,480 --> 00:36:28,839
Speaker 1: it holds true, and yeah, I'm drastically oversimplifying. You could

589
00:36:28,840 --> 00:36:33,080
Speaker 1: teach an entire computer science course on the page rink

590
00:36:33,120 --> 00:36:36,440
Speaker 1: algorithm and how it works. We're not going to do that.

591
00:36:36,560 --> 00:36:40,200
Speaker 1: I would just get it wrong anyway. Speaking of search, however,

592
00:36:40,480 --> 00:36:43,960
Speaker 1: let's talk about a much simpler form of search that's

593
00:36:44,000 --> 00:36:47,880
Speaker 1: based on a basic algorithm, and this is called binary search.

594
00:36:48,600 --> 00:36:51,120
Speaker 1: This is a process that's meant to decrease the amount

595
00:36:51,120 --> 00:36:54,280
Speaker 1: of time it takes to search for a specific value

596
00:36:54,880 --> 00:36:59,440
Speaker 1: within a sordid array of values. Alright, so let's say

597
00:36:59,440 --> 00:37:03,480
Speaker 1: that you've got a really big array or list of

598
00:37:03,840 --> 00:37:08,359
Speaker 1: entries right, and it's massive, and you're searching for a

599
00:37:08,440 --> 00:37:13,520
Speaker 1: specific target that has a specific value associated with it,

600
00:37:14,200 --> 00:37:19,160
Speaker 1: and a computer could go through this list item by item,

601
00:37:19,160 --> 00:37:22,399
Speaker 1: comparing it with your target right and look to see

602
00:37:22,440 --> 00:37:24,440
Speaker 1: if there's a match. If there's not a match, you

603
00:37:24,440 --> 00:37:26,480
Speaker 1: can go to the next item on the list and

604
00:37:26,560 --> 00:37:30,120
Speaker 1: do that. But if you're talking about a truly huge list,

605
00:37:30,320 --> 00:37:33,120
Speaker 1: this could take ages because if it happens to be

606
00:37:33,160 --> 00:37:34,680
Speaker 1: at the bottom of that list, you have to wait

607
00:37:34,719 --> 00:37:38,280
Speaker 1: for the computer to go through every single other entry

608
00:37:38,360 --> 00:37:43,000
Speaker 1: before it gets there. So a binary search cuts this short.

609
00:37:44,000 --> 00:37:48,360
Speaker 1: It takes a value that's in the middle of the array,

610
00:37:48,520 --> 00:37:52,280
Speaker 1: so like halfway down the list. Essentially it just pulls

611
00:37:52,360 --> 00:37:55,480
Speaker 1: that value and it compares it against your target, the

612
00:37:55,480 --> 00:37:58,759
Speaker 1: thing that you're searching for. And if the array is

613
00:37:58,800 --> 00:38:01,879
Speaker 1: a hundred thousand trees long, it's essentially looking at entry

614
00:38:01,960 --> 00:38:06,160
Speaker 1: number fifty thousand and one. It compares this to your search.

615
00:38:06,560 --> 00:38:09,839
Speaker 1: And let's say the value target of your of your

616
00:38:09,880 --> 00:38:14,600
Speaker 1: search query is lower than the entry that appeared at

617
00:38:14,640 --> 00:38:18,359
Speaker 1: fifty thousand and one. Well, now the binary search just

618
00:38:18,440 --> 00:38:22,560
Speaker 1: tosses everything that's fifty and one or higher on the

619
00:38:22,640 --> 00:38:25,040
Speaker 1: list because the values are only going to go up

620
00:38:25,080 --> 00:38:28,240
Speaker 1: from there, so it can get rid of half the list.

621
00:38:28,840 --> 00:38:33,120
Speaker 1: Right there, You're left with fifty thousand items in this array,

622
00:38:33,200 --> 00:38:37,000
Speaker 1: and the algorithm repeats this process. It goes for an

623
00:38:37,160 --> 00:38:40,320
Speaker 1: entry smack dab in the middle of the array, compares

624
00:38:40,360 --> 00:38:43,600
Speaker 1: it to the target. If the target's value is lower

625
00:38:44,200 --> 00:38:49,960
Speaker 1: than the middle entry of this array, then you you

626
00:38:50,040 --> 00:38:53,960
Speaker 1: dump everything that's at a higher number than that if

627
00:38:54,000 --> 00:38:57,040
Speaker 1: it's lower or its higher. Rather, if the target value

628
00:38:57,040 --> 00:38:59,279
Speaker 1: is higher than the middle entry, then you would get

629
00:38:59,360 --> 00:39:01,840
Speaker 1: rid of all the previous ones, like one through twenty

630
00:39:01,880 --> 00:39:05,000
Speaker 1: five thousand. For example, Let's say that you know your

631
00:39:05,040 --> 00:39:07,840
Speaker 1: your target value is higher than the middle entry of

632
00:39:07,880 --> 00:39:11,480
Speaker 1: twenty and one. It's gonna dump everything from one to

633
00:39:12,040 --> 00:39:15,040
Speaker 1: thousand and start over again and half it again again.

634
00:39:15,080 --> 00:39:17,960
Speaker 1: I'm kind of oversimplifying here, but the idea of binary

635
00:39:18,000 --> 00:39:21,080
Speaker 1: search is that rather than go through every single entry,

636
00:39:21,200 --> 00:39:25,360
Speaker 1: it keeps cutting this array in half, comparing it with

637
00:39:25,440 --> 00:39:29,080
Speaker 1: the target, and doing it again, which reduces the number

638
00:39:29,120 --> 00:39:33,200
Speaker 1: of times it takes to find the specific answer. Uh.

639
00:39:33,360 --> 00:39:35,640
Speaker 1: You might have thought of the like the the experiment

640
00:39:35,680 --> 00:39:39,680
Speaker 1: where you think about you're given two pennies on day

641
00:39:39,680 --> 00:39:42,440
Speaker 1: one and the next day, you're given four pennies or

642
00:39:42,480 --> 00:39:45,120
Speaker 1: cents if you prefer two cents. The next day you

643
00:39:45,120 --> 00:39:47,280
Speaker 1: get four cents. The next day you get eight cents,

644
00:39:47,320 --> 00:39:50,680
Speaker 1: and it doubles, and pretty quickly you see how that

645
00:39:50,800 --> 00:39:53,440
Speaker 1: doubling can actually start to amount to what we would consider,

646
00:39:53,600 --> 00:39:56,359
Speaker 1: you know, like quote unquote real money, same sort of thing.

647
00:39:56,400 --> 00:40:00,319
Speaker 1: By by having an array over and over again, you

648
00:40:00,520 --> 00:40:03,279
Speaker 1: very quickly whittle down the stuff you have to go

649
00:40:03,360 --> 00:40:05,759
Speaker 1: through and it speeds up the process of searching for

650
00:40:05,800 --> 00:40:11,720
Speaker 1: a specific value within a huge UH data list. Binary

651
00:40:11,760 --> 00:40:14,680
Speaker 1: search is just one form of search for for various

652
00:40:14,760 --> 00:40:18,600
Speaker 1: data constructs. There are lots of others. For example, there's

653
00:40:18,680 --> 00:40:23,200
Speaker 1: depth first search and breadth first search. I won't get

654
00:40:23,239 --> 00:40:25,960
Speaker 1: too deep into this but because it gets really technical,

655
00:40:26,040 --> 00:40:28,640
Speaker 1: but I can describe what's what's happening here from a

656
00:40:28,719 --> 00:40:32,800
Speaker 1: high level. So these search functions are used for data

657
00:40:32,840 --> 00:40:37,200
Speaker 1: structures that are that consists of nodes. And this is

658
00:40:37,239 --> 00:40:40,520
Speaker 1: easier to understand if we use an analogy, and I

659
00:40:40,560 --> 00:40:43,000
Speaker 1: want you to think of a choose your own adventure

660
00:40:43,160 --> 00:40:46,440
Speaker 1: book in case you're not familiar with those. These are

661
00:40:46,480 --> 00:40:49,120
Speaker 1: books where you would read a page and at the

662
00:40:49,200 --> 00:40:51,520
Speaker 1: end of the page, you would actually be given a choice,

663
00:40:51,600 --> 00:40:55,160
Speaker 1: like you could choose what the character you're reading about

664
00:40:55,160 --> 00:40:58,120
Speaker 1: would do next. So you might get to the end

665
00:40:58,160 --> 00:41:00,880
Speaker 1: of the first page of like a mystery book, and

666
00:41:01,360 --> 00:41:05,400
Speaker 1: the instruction might say, if you want your protagonists to

667
00:41:05,440 --> 00:41:08,279
Speaker 1: go down the hall, turn to page eight. If you

668
00:41:08,320 --> 00:41:11,359
Speaker 1: want her to shut a door and walk away, turn

669
00:41:11,440 --> 00:41:13,920
Speaker 1: to page twenty three, and you would make your choice,

670
00:41:13,960 --> 00:41:16,239
Speaker 1: turn to that page and continue the story that way.

671
00:41:16,320 --> 00:41:21,200
Speaker 1: And so the story branches, and you've got these branching pathways. Well.

672
00:41:21,239 --> 00:41:26,880
Speaker 1: Depth first and breadth first searches explore nodes in different ways.

673
00:41:27,000 --> 00:41:31,960
Speaker 1: A depth first search follows each branched path all the

674
00:41:32,000 --> 00:41:35,120
Speaker 1: way down from start to the end of that one branch,

675
00:41:35,719 --> 00:41:39,359
Speaker 1: before moving on to look at a different branch. So

676
00:41:39,400 --> 00:41:41,880
Speaker 1: in our example, would the Choose your Own Adventure book,

677
00:41:42,160 --> 00:41:45,239
Speaker 1: a depth first search would go to page eight to

678
00:41:45,400 --> 00:41:50,440
Speaker 1: follow your protagonists down the hall. Then whatever the options

679
00:41:50,440 --> 00:41:52,040
Speaker 1: were at the end of that, it would go with

680
00:41:52,080 --> 00:41:55,440
Speaker 1: the first option, continue and doing this all the time

681
00:41:55,760 --> 00:41:58,239
Speaker 1: until you get to the end of that pathway. Then

682
00:41:58,280 --> 00:42:01,040
Speaker 1: it would come back up to the next most recent branch,

683
00:42:01,160 --> 00:42:02,919
Speaker 1: follow that all the way to the end, and so

684
00:42:03,000 --> 00:42:07,279
Speaker 1: on until it had searched through every possible pathway in

685
00:42:07,360 --> 00:42:10,920
Speaker 1: this this uh this graph, that's what we would call it.

686
00:42:12,000 --> 00:42:17,920
Speaker 1: Breath search instead progresses equally across all possible paths. So

687
00:42:18,040 --> 00:42:21,920
Speaker 1: breath search would mean that you would go to page eight,

688
00:42:22,840 --> 00:42:24,759
Speaker 1: and let's say at the end of page eight, it

689
00:42:24,800 --> 00:42:27,560
Speaker 1: says you can then turn to page seventeen or page

690
00:42:27,560 --> 00:42:29,719
Speaker 1: fifty two to make your next choice. But instead of

691
00:42:29,760 --> 00:42:32,920
Speaker 1: continuing down that pathway, you back up to your starting

692
00:42:32,920 --> 00:42:35,720
Speaker 1: position and then you go down to page twenty three.

693
00:42:35,760 --> 00:42:37,520
Speaker 1: You know, the other option where you would close the

694
00:42:37,520 --> 00:42:40,120
Speaker 1: door and walk away. You would read that maybe at

695
00:42:40,120 --> 00:42:42,400
Speaker 1: the end of that page it says you can choose

696
00:42:42,400 --> 00:42:45,600
Speaker 1: to either go to page three or to page forty six. Well,

697
00:42:45,800 --> 00:42:48,160
Speaker 1: then you would go back to your your first branch.

698
00:42:48,200 --> 00:42:52,640
Speaker 1: You would go down the list of pages seventeen and

699
00:42:52,719 --> 00:42:55,960
Speaker 1: fifty two and three and forty six, maybe those all

700
00:42:56,040 --> 00:42:59,040
Speaker 1: end in different choices. You would then do all of

701
00:42:59,040 --> 00:43:01,680
Speaker 1: those across the board. Next you're you're searching across the

702
00:43:01,760 --> 00:43:06,200
Speaker 1: width of the graph the breadth of it. Both are

703
00:43:06,320 --> 00:43:09,760
Speaker 1: valid forms of searching, and the method used typically depends

704
00:43:09,840 --> 00:43:12,239
Speaker 1: upon the type of data being searched and what you're

705
00:43:12,239 --> 00:43:15,040
Speaker 1: trying to do. We've got a lot more to cover

706
00:43:15,080 --> 00:43:19,000
Speaker 1: with algorithms, but I feel like I'm gonna have to

707
00:43:19,080 --> 00:43:23,080
Speaker 1: give you guys a break, So let's do that really quick,

708
00:43:23,160 --> 00:43:26,680
Speaker 1: and I'll just give you a very short example following,

709
00:43:27,200 --> 00:43:29,760
Speaker 1: and then we'll pick up back up with algorithms again

710
00:43:29,840 --> 00:43:32,400
Speaker 1: in a future episode. But first let's take this quick break,

711
00:43:33,040 --> 00:43:43,279
Speaker 1: all right. I know I've waxed poetic about algorithms so

712
00:43:43,360 --> 00:43:46,399
Speaker 1: much so that this episode is running longer than I anticipated.

713
00:43:46,440 --> 00:43:52,640
Speaker 1: I have a whole extra section to talk about with algorithms,

714
00:43:52,640 --> 00:43:56,040
Speaker 1: including things that are related to algorithms but aren't necessarily

715
00:43:56,160 --> 00:44:00,520
Speaker 1: specifically algorithms, stuff like hashing and Markov models and things

716
00:44:00,560 --> 00:44:03,600
Speaker 1: of that nature. But I want to finish up with

717
00:44:03,680 --> 00:44:06,239
Speaker 1: one that I think is kind of fun. And this

718
00:44:06,320 --> 00:44:09,479
Speaker 1: is called the Doomsday rule. And to be be fair,

719
00:44:09,560 --> 00:44:12,200
Speaker 1: this is not just a computational algorithm. This is something

720
00:44:12,239 --> 00:44:14,440
Speaker 1: that you can do in your head if you learn

721
00:44:14,560 --> 00:44:16,960
Speaker 1: the rule. I'm not saying I could do it. I

722
00:44:16,960 --> 00:44:21,319
Speaker 1: haven't really committed this to a memory process yet, but

723
00:44:21,400 --> 00:44:26,000
Speaker 1: it is possible. And the Doomsday rule sounds pretty ominous, however, right.

724
00:44:26,120 --> 00:44:29,400
Speaker 1: I mean, it's basically to figure out what day of

725
00:44:29,440 --> 00:44:33,839
Speaker 1: the week any given date is So if you were

726
00:44:33,880 --> 00:44:36,880
Speaker 1: an expert with the doomsday rule and I asked you, hey,

727
00:44:37,080 --> 00:44:41,279
Speaker 1: what day of the week does June five fall on?

728
00:44:41,920 --> 00:44:44,160
Speaker 1: You could use that rule and say, oh, that's gonna

729
00:44:44,160 --> 00:44:46,920
Speaker 1: be a Thursday. That also, by the way, happens to

730
00:44:46,920 --> 00:44:50,399
Speaker 1: be the day I'll turn fifty. Yikes, man, we're coming

731
00:44:50,440 --> 00:44:53,400
Speaker 1: up on that one. All right, So where did this

732
00:44:53,560 --> 00:44:56,520
Speaker 1: rule come from? And what the heck is this doomsday

733
00:44:56,520 --> 00:44:59,080
Speaker 1: stuff about? Well, the doomsday thing is kind of just

734
00:44:59,120 --> 00:45:02,520
Speaker 1: a cheeky name, and there's all these different ways we

735
00:45:02,520 --> 00:45:06,920
Speaker 1: could describe that. But during any given year, there are

736
00:45:07,000 --> 00:45:09,879
Speaker 1: certain dates that will always share the same day of

737
00:45:09,920 --> 00:45:12,160
Speaker 1: the week, which is no big surprise, right. I mean,

738
00:45:12,719 --> 00:45:17,120
Speaker 1: you might notice that Christmas, that is December, falls on

739
00:45:17,160 --> 00:45:19,680
Speaker 1: the same day of the week as New Year's Day

740
00:45:19,880 --> 00:45:22,439
Speaker 1: for the following year that happened, you know, January one.

741
00:45:22,480 --> 00:45:26,040
Speaker 1: It always is that way. But with the doomsday rule,

742
00:45:26,600 --> 00:45:31,120
Speaker 1: the dates for that are called doomsdays. Are things like

743
00:45:31,239 --> 00:45:36,040
Speaker 1: April four or four four, June six that's six six,

744
00:45:36,520 --> 00:45:40,160
Speaker 1: August eight that's eight eight, and you know, so on

745
00:45:40,200 --> 00:45:46,000
Speaker 1: like October tenth, that's ten ten. The anchor day are

746
00:45:46,080 --> 00:45:51,200
Speaker 1: called these are anchor days. They're called doomsdays, um they

747
00:45:51,280 --> 00:45:55,200
Speaker 1: change with each year or with leap years. The anchor

748
00:45:55,280 --> 00:45:58,759
Speaker 1: day actually leaps a year, but once you know that day,

749
00:45:58,920 --> 00:46:01,120
Speaker 1: you know it's the same for all of those dates.

750
00:46:01,440 --> 00:46:07,120
Speaker 1: So for one, as I record this, this year's doomsday

751
00:46:07,440 --> 00:46:10,160
Speaker 1: is or anchor day is a Sunday. So that means

752
00:46:10,200 --> 00:46:12,520
Speaker 1: every Doomsday is going to be a Sunday. So I'm

753
00:46:12,520 --> 00:46:17,600
Speaker 1: recording this in July with our next doomsday being on

754
00:46:17,760 --> 00:46:23,640
Speaker 1: August eight, so that means August eight should be a Sunday.

755
00:46:23,680 --> 00:46:26,399
Speaker 1: And if you look at the calendar, you'll see that yes,

756
00:46:26,560 --> 00:46:30,160
Speaker 1: August day is a Sunday. That means that October ten

757
00:46:30,560 --> 00:46:35,200
Speaker 1: should be a Sunday, that December twelve should be a Sunday.

758
00:46:35,280 --> 00:46:37,600
Speaker 1: So the doomsday rule involves a little bit more than

759
00:46:37,680 --> 00:46:40,960
Speaker 1: just this, but not much more. And this means that

760
00:46:41,120 --> 00:46:44,319
Speaker 1: if you learn the doomsday rule and you have a

761
00:46:44,360 --> 00:46:48,560
Speaker 1: general idea of what the anchor day is for each year,

762
00:46:49,120 --> 00:46:52,319
Speaker 1: you can calculate what in what day of the week

763
00:46:52,560 --> 00:46:57,239
Speaker 1: any given date will fall on, including past years. The

764
00:46:57,239 --> 00:47:00,000
Speaker 1: guy who came up with this was a mathematician named

765
00:47:00,239 --> 00:47:04,360
Speaker 1: John Conway, and reportedly he could give you an answer

766
00:47:04,440 --> 00:47:06,560
Speaker 1: in less than two seconds if you gave him a date,

767
00:47:06,600 --> 00:47:08,080
Speaker 1: he could tell you what day of the week it

768
00:47:08,120 --> 00:47:11,760
Speaker 1: was going to fall on in two seconds or less. Sadly,

769
00:47:11,840 --> 00:47:15,239
Speaker 1: he passed away last year at the age of eighty

770
00:47:15,280 --> 00:47:20,000
Speaker 1: two after he contracted COVID nineteen. But that doomsday rule

771
00:47:20,080 --> 00:47:21,799
Speaker 1: is one that I think is super cool. I've seen

772
00:47:21,840 --> 00:47:23,600
Speaker 1: people who can do this where you give them a

773
00:47:23,680 --> 00:47:25,719
Speaker 1: date and they're just able to tell you what day

774
00:47:25,719 --> 00:47:28,120
Speaker 1: of the week that falls on, and you can go

775
00:47:28,160 --> 00:47:30,520
Speaker 1: and check it and sure enough they're right. Well, this

776
00:47:30,600 --> 00:47:33,239
Speaker 1: is one process where you can do that. It's not

777
00:47:33,280 --> 00:47:35,960
Speaker 1: the only one, by the way, there are other algorithms

778
00:47:36,040 --> 00:47:39,360
Speaker 1: that also can help you determine what day of the

779
00:47:39,400 --> 00:47:42,680
Speaker 1: week a specific date will fall on. But the doomsday

780
00:47:42,760 --> 00:47:46,000
Speaker 1: rule is is one that works. And again I don't

781
00:47:46,040 --> 00:47:49,040
Speaker 1: have it, um. I don't have an expertise in this.

782
00:47:49,200 --> 00:47:51,759
Speaker 1: I haven't practiced it at all, so I can't do it.

783
00:47:52,239 --> 00:47:53,840
Speaker 1: If you came up to me and say, hey, Jonathan

784
00:47:54,400 --> 00:47:57,640
Speaker 1: May first, nineteen, what day of the week was that,

785
00:47:57,680 --> 00:48:01,279
Speaker 1: I'd be like, I don't know. Probably really a it's

786
00:48:01,320 --> 00:48:04,840
Speaker 1: probably a fine day. I don't I don't know because

787
00:48:04,840 --> 00:48:07,240
Speaker 1: I haven't done this yet. But I think it's really cool.

788
00:48:07,280 --> 00:48:10,960
Speaker 1: I gets. It illustrates how for certain types of problems

789
00:48:11,360 --> 00:48:14,560
Speaker 1: you can come up with a mathematical approach to solving

790
00:48:14,560 --> 00:48:18,600
Speaker 1: those problems, and it just is applicable for all problems

791
00:48:18,640 --> 00:48:21,880
Speaker 1: that fall into that category. And that's really the elegant

792
00:48:21,920 --> 00:48:24,439
Speaker 1: and cool thing about algorithms. Also the other cool things

793
00:48:24,520 --> 00:48:26,960
Speaker 1: that people are coming up with new ones all the time,

794
00:48:27,719 --> 00:48:31,120
Speaker 1: and they might be trying to refine earlier algorithms to

795
00:48:31,200 --> 00:48:34,400
Speaker 1: make them even more efficient and effective, or they might

796
00:48:34,400 --> 00:48:36,279
Speaker 1: be trying to come up with all new algorithms to

797
00:48:36,320 --> 00:48:41,320
Speaker 1: take advantage of emerging technology stuff like quantum computing. I

798
00:48:41,400 --> 00:48:44,560
Speaker 1: hope you enjoyed that episode. Like I said, it originally

799
00:48:44,560 --> 00:48:48,080
Speaker 1: published last year in two thousand twenty one, and hopefully

800
00:48:48,160 --> 00:48:51,239
Speaker 1: tomorrow I'll be back in shape and I'll be able

801
00:48:51,280 --> 00:48:54,920
Speaker 1: to do another news episode. We'll have to wait and see.

802
00:48:55,040 --> 00:48:56,799
Speaker 1: Like I said, I'm really hoping that this is just

803
00:48:57,400 --> 00:49:00,120
Speaker 1: a stomach bug thing that I'm dealing with and not

804
00:49:00,400 --> 00:49:04,120
Speaker 1: like round two of COVID. I do have a test

805
00:49:04,280 --> 00:49:06,480
Speaker 1: that literally I think just arrived at my door, so

806
00:49:06,560 --> 00:49:08,879
Speaker 1: I will check and make sure, because obviously I want

807
00:49:08,880 --> 00:49:11,200
Speaker 1: to be responsible and safe for all of my fellow

808
00:49:11,280 --> 00:49:13,920
Speaker 1: human beings. Out there. I hope all of you are

809
00:49:13,920 --> 00:49:17,080
Speaker 1: well and staying safe and healthy, and that you're having

810
00:49:17,360 --> 00:49:20,839
Speaker 1: a great summer so far. Uh you know, I plan

811
00:49:20,880 --> 00:49:24,040
Speaker 1: on having a great summer once I feel better. For now,

812
00:49:24,120 --> 00:49:27,719
Speaker 1: I'm just having a kind of grouchy summer because that's

813
00:49:27,920 --> 00:49:29,839
Speaker 1: I mean, that's my go to mood for pretty much

814
00:49:29,920 --> 00:49:33,680
Speaker 1: any situation, but particularly when I'm not feeling well. Anyway,

815
00:49:34,239 --> 00:49:37,680
Speaker 1: take care and I will talk to you again really soon.

816
00:49:43,560 --> 00:49:46,600
Speaker 1: Text Stuff is an I Heart Radio production. For more

817
00:49:46,680 --> 00:49:50,040
Speaker 1: podcasts from my Heart Radio, visit the i Heart Radio app,

818
00:49:50,200 --> 00:49:53,320
Speaker 1: Apple Podcasts, or wherever you listen to your favorite shows.