416: Multi-Dimensional Numbers

About this Episode

Joël discusses the challenges he encountered while optimizing slow SQL queries in a non-Rails application. Stephanie shares her experience with canary deploys in a Rails upgrade. Together, Stephanie and Joël address a listener's question about replacing the wkhtml2pdf tool, which is no longer maintained.

The episode's main topic revolves around the concept of multidimensional numbers and their applications in software development. Joël introduces the idea of treating objects containing multiple numbers as single entities, using the example of 2D points in space to illustrate how custom classes can define mathematical operations like addition and subtraction for complex data types. They explore how this approach can simplify operations on data structures, such as inventories of T-shirt sizes, by treating them as mathematical objects.

• EXPLAIN ANALYZE visualizer
• Canary in a coal mine
• Episode 413: Developer Tales of Package Management
• Docs for media-specific CSS
• Episode 386: Value Objects Revisited: The Tally Edition
• Money gem

Transcript:

STEPHANIE: Hello and welcome to another episode of The Bike Shed, a weekly podcast from your friends at thoughtbot about developing great software. I'm Stephanie Minn.

JOËL: And I'm Joël Quenneville. And together, we're here to share a bit of what we've learned along the way.

STEPHANIE: So, Joël, what's new in your world?

JOËL: I've recently been trying to do some performance enhancements to some very slow queries. This isn't a Rails app, so we're sort of combining together a bunch of different scopes. And the way they're composing together is turning out to be really slow. And I've reached for a tool that is just really fun. It's a visualizer for SQL query plans.

You can put the SQL keywords in front of a query: 'EXPLAIN ANALYZE,' and it will then output a query plan, sort of how it's going to attempt to do the work. And that might be like, oh, we're going to use this index on this table to join on this other thing, and then we're going to...maybe this is a table that we think we're going to do a sequential scan through and, you know, it builds out a whole thing.

It's a big block of text, and it's kind of intimidating to look at. So, there are a few websites out there that will do this. You just paste a query plan in, and they will build you a nice, little visualization, almost like a tree of, like, tasks to be done. Oftentimes, they'll also annotate it with metadata that they pulled from the query plan. So, oh, this particular node is the really expensive one because we're doing a sequential scan of this table that has 15 million rows in it. And so, it's really useful to then sort of pinpoint what are the areas that you could optimize.

STEPHANIE: Nice. I have known that you could do that EXPLAIN ANALYZE on a SQL query, but I've never had to do it before. Is this your first time, or is it just your first time using the visualizer?

JOËL: I've played around with EXPLAIN ANALYZE a little bit before. Pro tip: In Rails, if you've got a scope, you can just chain dot explain on the end, and instead of running the query, it will run the EXPLAIN version of it and return the query plan. So, you don't need to, like, turn into SQL then manually run it in your database system to get the EXPLAIN. You can just tack a dot explain on there to get the query plan.

It's still kind of intimidating, especially if you've got a really complex query that's...this thing might be 50 lines long of EXPLAIN with all this indentation and other stuff. So, putting it into a sort of online visualizer was really helpful for the work that I was doing. So, it was my first time using an online visualizer. There are a few out there. I'll link to the one that I used in the show notes. But I would do that again, would recommend.

STEPHANIE: Nice.

JOËL: So, Stephanie, what's new in your world?

STEPHANIE: So, I actually just stepped away from being in the middle of doing a Rails upgrade [chuckles] and releasing it to production just a few minutes before getting on to record with you on this podcast. And the reason I was able to do that, you know, without feeling like I had to just monitor to see how it was going is because I'm on a project where the client is using canary deploys. And I was so pleasantly surprised by how easy it made this experience where we had decided to send the canary release earlier this morning.

And the way that they have it set up is that the canary goes to 10% of traffic. 10% of the users were on Rails 7 for their sessions. And we saw a couple of errors in our error monitoring service. And we are like, "Okay, like, let's take a look at this, see what's going on." And it turns out it was not too big of a deal because it had to do with, like, a specific page. And, for the most part, if a user did encounter this error, they probably wouldn't again after refreshing because they had, like, a 90% chance [chuckles] of being directed to the previous version where everything is working.

And we were kind of making that trade-off of like, oh, we could hotfix this right now on the canary release. But then, as we were starting to debug a little bit, it was a bit hairier than we expected originally. And so, you know, I said, "I have to hop on to go record The Bike Shed. So, why don't we just take this canary down just for the time being to take that time pressure off? And it's Friday, so we're heading into the weekend. And maybe we can revisit the issue with some fresh eyes." So, I'm feeling really good, actually. And I'm glad that we were able to do something that seems scary, but there were guardrails in place to make it a lot more chill.

JOËL: Yay for the ability to roll back. You used the term canary release. That's not one that I'm familiar with. Can you explain what a canary release is?

STEPHANIE: Oh yeah. Have you heard of the phrase 'Canary in the coal mine'?

JOËL: I have.

STEPHANIE: Okay. So, I believe it's the same idea where you are, in this case, releasing a potentially risky change, but you don't want to immediately make it available to, like, all of your users. And so, you send this change to, like, a small reach, I suppose, and give it a little bit of a test and see [chuckles] what comes back. And that can help inform you of any issues or risks that might happen before kind of committing to deploying a potentially risky change with a bigger impact.

JOËL: Is this handled with something like a feature flag framework? Or is this, like, at an infrastructure level where you're just like, "Hey, we've got the canary image in, like, one container on one server, and then we'll redirect 10% of traffic to that to be served by that one and the other 90% to be served by the old container or something like that"?

STEPHANIE: Yeah, in this case, it was at the infrastructure level. And I have also seen something similar at a feature flag level, too, where you're able to have some more granularity around what percent of users are seeing a feature. But I think with something like a Rails upgrade, it was nice to be able to have that at that infrastructure level. It's not necessarily, like, a particular page or feature to show or not show.

JOËL: Yeah, I think you would probably want that at a higher level when you're changing over the entire app. Is this something that you had to custom-build yourself or something that just sort of came out of the box with some of the infrastructure tools you're using?

STEPHANIE: It came out of the box, actually. I just joined this client project this week and was very delighted to see just some really great deployment infrastructure and getting to meet the DevOps engineers, too, who built it. And they're really proud of it. They kind of walked us through our first release earlier this week. And he was telling me, the DevOps engineer, that this was actually his favorite part of the job, is walking people through their first release and being their buddy while they do it. Because I think he gets to also see users interact with the tool that he built, and he had a lot of pride in that, so it was a very delightful experience.

JOËL: That's so wonderful. I've been on so many projects where the sort of infrastructure side of things is not the team's strong point, and releasing can be really scary. And it's great to hear the opposite of that.

We recently received a question for Stephanie based on an earlier episode. So, the question asks, "In episode 413, Stephanie discussed a recent issue she encountered with wkhtml2pdf. The episode turned into a deeper discussion about package management, but I don't think it ever cycled back to the conclusion. I'm curious: how did Stephanie solve this dilemma? We're facing the same issue on a project that my team maintains. It's an old codebase, and there are bits of old code that use wkhtml2pdf to generate print views of our data in our application.

The situation is fairly dire. wkhtml2pdf is no longer maintained. In fact, it won't even be available to install from our operating system's package repositories in June. We're on FreeBSD, but I assume the same will be eventually true for other operating systems. And so, unless you want to maintain some build step to check out and compile the source code for an application that will no longer receive security updates, just living with it isn't really an option.

There are three options we're considering. One, eliminate the dependency entirely. Based on user feedback, it sounds like our old developers were using this library to generate PDFs when what users really wanted was an easy way to print. So, instead of downloading a PDF, just ensure the screen has a good print style sheet and register an onload handler to call window dot print. We're thinking we could implement this as an A/B test to the feature to test this theory. Or two, replace wkhtml2pdf with a call to Headless Chrome and use that to generate the PDF. Or, three, replace wkhtml2pdf with a language-level package. For us, that might be the dompdf library available via Composer because we're a PHP shop."

Yeah, a lot to unpack here. Any high-level thoughts, Stephanie?

STEPHANIE: My first thought while I was listening to you read that question is that wkhtml2pdf is such a mouthful [laughs]. And I was impressed how you managed to say it at least, like, five times.

JOËL: So, I try to say that five times fast.

STEPHANIE: And then, my second high-level thought was, I'm so sorry to Brian, our listener who wrote in, because I did not really solve this dilemma [chuckles] for my project and team. I kind of kicked the can down the road, and that's because this was during a support and maintenance rotation that I've talked a little bit about before on the show. I was only working on this project for about a week.

And what we thought was a small bug to figure out why PDFs were a little bit broken turned out, as you mentioned, to be this kind of big, dire dilemma where I did not feel like I had enough information to make a good call about what to do. So, I kind of just shared my findings that, like, hey, there is kind of a risk and hoping that someone else [laughs] would be able to make a better determination.

But I really was struck by the options that you were considering because it was actually a bit of a similar situation to the bug I was sharing where the PDF that was being generated that was slightly broken. I don't think it was, like, super valuable to our users that it be in the form of a PDF. It really was just a way for them to print something to have on handy as a reference from, you know, some data that was generated from the app. So, yeah, based on what you're sharing, I feel really excited about the first one. Joël, I'm sure you have some opinions about this as well.

JOËL: I love sort of the bigger picture thinking that Brian is doing here, sort of stepping back and being like, wait, why do we even need PDF here, and how are our customers using it? I think those are the really good questions to ask before sinking a ton of time into coming up with something that might be, like, a bit of a technical wonder. Like, hey, we managed to, like, do this PDF generation thing that we had to, like, cobble together so many other things. And it's so cool technically, but does it actually solve the underlying problem? So, shout out to Brian for thinking about it in those terms. I love that.

Second cool thing that I wanted to shout out, because I think this is a feature of browsers that not many people are aware of; you can have multiple style sheets for your page, and you can tag them to be for different media. So, you can have a style sheet that only gets applied when you print versus when you display on screen. And there are a couple of others. I don't remember exactly what they are. I'll link to the docs in the show notes.

But taking advantage of this, like, this is old technology but making that available and saying, "Yeah, we'll make it so that it's nice when you print, and we'll maybe even, you know, a link or a button with JavaScript so that you could just Command-P or Control-P to print. But we'll have a button in there as well that will allow you to print to PDF," and that solves your problem right there.

STEPHANIE: Yeah, that's really cool. I didn't know that about being able to tag style sheets for different media types. That's really fascinating. And I like that, yeah, we're just eliminating this dependency on something, like, potentially really complex with a, hopefully, kind of elegant and modern solution, maybe.

JOËL: And your browser is already able to do so many of these things. Why do we sort of try to recreate it? Printing is a thing browsers have been able to do for a long time. Printing to PDF is a thing that you can do for a long time. I will sometimes use that on sites where I need to, let's say I'm purchasing something, and I need some sort of receipt to expense, but they won't give me a download, a PDF download that I can send to the accounting team, so I will print to PDF the, like, HTML view. And that works just fine. It's kind of a workaround hack.

Sometimes, it doesn't work well because the HTML page is just not well set up to, like, show up on a PDF page. You get some, like, weird, like, pagination issues or things like that. But, you know, just a little bit of thought for a print style sheet, especially for something you know that people are likely going to want to print or to save to PDF, that's a nice touch.

STEPHANIE: Yeah. So, good luck, Brian, and let us know how this goes and any outcomes you find successful. So, for today's longer topic, I was excited because I saw, Joël, you dropped something in our topic backlog: Multidimensional Numbers. I'm curious what prompted this idea and what you wanted to say about it.

JOËL: We did an episode a while back where we talked about value objects, wrapping numbers, wrapping collections. This is Episode 386, and we were talking about tallying, specifically working with collections of T-shirt sizes and doing math on these sort of objects that might contain multiple numbers. And a sort of sidebar from that that we didn't really get into is the idea that objects that contain sort of multiple numbers can be treated as a number themselves.

And I think a great example of this is something like a point in two-dimensional space. It's got an x coordinate, a y coordinate. It's two numbers, but you can treat sort of the combination of the two of them together as a single number. There's a whole set of coordinate math that you can do to do things like add coordinates together, subtract them, find the distance between them. There's a whole field of vector math that we can do on those.

And I think learning to recognize that numbers are not just instances of the integer or the float class but that there could be these more complex things that are also numbers is maybe an important realization and something that, as developers, if we think of these sort of more complex values as numbers, or at least mathematical objects, then that will help us write better code.

STEPHANIE: Cool. Yeah. When you were first talking about 2D points, I was thinking about if I have experience working with that before or, like, having to build something really heavily based off of, like, a canvas or, you know, a coordinate system. And I couldn't think of any really good examples until I thought about, like, geographic locations.

JOËL: Oh yeah, like a latitude, longitude.

STEPHANIE: Yeah, exactly. Like, that is a lot more common, I think, for various types of just, like, production applications than 2D points if you're not working on, like, a video game or something like that, I think.

JOËL: Right, right. I think you're much more likely to be working with 2D points on some more sort of front-end-heavy application. I was talking with someone this week about managing a seat map for concerts and events like that and sort of creating a seat map and have it be really interactive, and you can, like, click on seats and things like that. And depending on the level of libraries you're using to build that, you may have to do a lot of 2D math to make it all come together.

STEPHANIE: Yeah. So, I would love to get into, you know, maybe we've realized, okay, we have some kind of compound number. What are some good reasons for using them differently than you would a primitive?

JOËL: So, you mentioned primitives, and I think this is where maybe I'm developing a reputation about, like, always wanting value objects for everything. But it would be really easy, let's say, for an xy point to be just an array of two numbers or maybe even a hash with an x key and a y key.

What's tricky about that is that then you don't have the ability to do math on them. Arrays do define the plus operator, but they don't do what you want them to do with points. It's the set union. So, adding two points would not at all do what you want, or subtracting two points. So, instead, if you have a custom 2D point class and you can define plus and minus on there to do the right thing, now they're not pairs of numbers, two values; they're a single value, and you can treat them as if they are just a single number.

STEPHANIE: You mentioned that arrays don't do the right thing when you try to add them up. What is the right thing that you're thinking of then?

JOËL: It probably depends a little bit on the type of object you're working with. So, with 2D points, you're probably trying to do vector addition where you're effectively saying almost, like, "Shift this point in 2D space by the amount of this other point." Or if you're doing a subtraction, you might even be asking, like, "What is the distance between these two points?" Euclidean distance, I think, is the technical term for this.

There's also a couple of different ways you can multiply values. You can multiply a 2D point by just a sort of, not by another point, but by just an integer. That's called scaling. So, you're just like, oh, take this point in 2D space, but make it bigger, make it five times bigger or five times further from the origin. Or you can do some stuff with other points. But what you don't want to do is turn this into, if you're starting with arrays, you don't want to turn this into an array of four points. When you add two points in 2D space, you're not trying to create a point in 4D space.

STEPHANIE: Whoa, I mean [laughs], maybe you're not.

JOËL: You could but -- [laughter]

STEPHANIE: Yeah. While you were saying that, I guess that is what is really cool about wrapping, encapsulating them in objects is that you get to decide what that means for you and your application, and --

JOËL: Yeah. Well, plus can mean different things, right?

STEPHANIE: Yeah.

JOËL: On arrays, plus means combining two arrays together. On integers, it means you do integer math. And on points, it might be vector addition.

STEPHANIE: Are there any other arithmetic operators you can think of that would be useful to implement if you were trying to create some functionality on a point?

JOËL: That's a good question because I think realizing the inverse of that is also a really powerful thing. Just because you create a sort of new mathematical object, a point in 2D space, doesn't mean that necessarily every arithmetic operator makes sense on it. Does it make sense to divide a point by another point? Maybe not. And so, instead of going with the mindset of, oh, a point is a mathematical object, I now need to implement all of arithmetic on this, instead, think in terms of your domain. What are the operations that make sense? What are the operations you need for this point?

And, you know, maybe the answer is look up what are the common sort of vector math operations and implement those on your 2D point. Some of them will map to arithmetic operators like plus and minus, and then some of them might just be some sort of custom method where maybe you say, "Oh, I want the Euclidean distance between these two points." That's just a thing. Maybe it's just a named instance method on there. But yeah, don't feel like you need to implement all of the math operators because that's a mistake that I have made and then have ended up, like, implementing nonsensical things.

STEPHANIE: [laughs] Creating your own math.

JOËL: Yes, creating my own math. I've done this even on where I've done value objects to wrap single values. I was doing a class to represent currency, and I was like, well, clearly, you need, like, methods to, like, add or subtract your currency, and that's another thing. If you have, let's say, a plus method, now you can plug it into, let's say, reduce plus. And you can just sum a list of these currency objects and get back a new currency. It's not even going to give you back an integer. You just get a sort of new currency object that is the sum of all the other ones, and that's really nice.

STEPHANIE: Yeah, that's really cool. It reminds me of all the magic of enumerable that you had talked about in a previous conference talk, where, you know, you just get so much out of implementing those basic operators that, like, kind of scales in handiness.

JOËL: Yes. Turns out Ruby is actually a pretty nice system. If you have objects that respond to some common methods and you plug them into enumerable, and it just all kind of works.

STEPHANIE: So, one thing you had said earlier that I've felt kind of excited about and wanted to highlight was you mentioned all the different ways that you could represent a 2D point with more primitive data stores, so, you know, an array of two integers, a hash with xy keys. It got me thinking about how, yeah, like, maybe if your system has to talk to another system and you're importing data or exporting data, it might eventually need to take those forms.

But what is cool about having an encapsulated object in your application is you can kind of control those boundaries a little bit and have more confidence in terms of the data types that you're using within your system by having various ways to construct that, like, domain object, even if the data coming in is in a different shape.

JOËL: And I think that you're hitting on one of the real beauties of object-oriented programming, where the sort of users of your object don't need to know about the internal representation. Maybe you store an array internally. Maybe it's two separate instance variables. Maybe it's something else entirely. But all that the users of your, let's say, 2D point object really need to care about is, hey, the constructor wants values in this shape, and then I can call these domain methods on it, and then the rest just sort of happens. It's an implementation detail. It doesn't matter.

And you alluded, I think, to the idea that you can sort of create multiple constructors. You called them constructors. I tend to call them that as well. But they're really just class methods that will kind of, like, add some sugar on top of the constructor. So, you might have, like, a from array pair or from hash or something like that that allows you to maybe do a little bit of massaging of the data before you pass it into your constructor that might want some underlying form. And I think that's a pattern that's really nice.

STEPHANIE: Yeah, I agree.

JOËL: Something that can be interesting there, too, is that mathematically, there are multiple ways you can think of a 2D point. An xy coordinate pair is a common one, but another sort of system for representing a point in 2D space is called the polar coordinate system. So, you have some sort of, like, origin point. You're 0,0. And then, instead of saying so many to the left and so many up from that origin point, you give an angle and a distance, and that's where your point is. So, an angle and distance point, I think, you know, theta and magnitude are the fancy terms for this.

You could, instead of creating a separate, like, oh, I have a polar coordinate point and a Cartesian coordinate point, and those are separate things, you can say, no, I just have a point in 2D space. They can be constructed from either an xy coordinate pair or a magnitude angle pair.

Internally, maybe you convert one to the other for internal representation because it makes the math easier or whatever. Your users never need to know that. They just pass in the values that they want, use the constructor that is most convenient for them, and it might be both. Maybe some parts of the app require polar coordinates; some require Cartesian coordinates. You could even construct one of each, and now you can do math with each other because they're just instances of the same class.

STEPHANIE: Whoa. Yeah, I was trying to think about transforming between the two types as well. It's all possible [laughs].

JOËL: Yes. Because you could have reader-type methods on your object that say, oh, for this point, give me its x coordinate; give me its y coordinate. Give me its distance from the origin. Give me its angle from the origin. And those are all questions you can ask that object, and it can calculate them. And you don't need to care what its internal representation is to be able to get all four of those.

So, we've been talking about a lot of these sort of composite numbers, not composite numbers, that's a separate mathematical thing, but numbers that are composed of sort of multiple sub-numbers. And what about situations where you have two things, and one of them is not a number? I'm thinking of all sorts of units of measure. So, I don't just have three. I have three, maybe...and we were talking about currency earlier, so maybe three U.S. dollars. Or I don't just have five; I have five, you know, let's say, meters of distance. Would you consider something like that to be one of these compound number things?

STEPHANIE: Right. I think I was–when we were originally talking about this, conflating the two. But I realized that, you know, just because we're adding context to a number and potentially packaging it as a value object, it's still different from what we're talking about today where, you know, there's multiple components to the number that are integral or required for it to mean what we intended to mean, if that makes sense.

JOËL: Yeah.

STEPHANIE: So yeah, I guess we did want to kind of make a distinction between value objects that while the additional context is important and you can implement a lot of different functionality based on what it represents, at the end of the day, it only kind of has one magnitude or, like, one integer to kind of encapsulate it represented as a number. Does that sound right?

JOËL: Yeah. You did throw out the words encapsulation and value object. So, in a situation maybe where I have three US dollars, would you create some kind of custom object to wrap that? Or is that a situation where you'd be more comfortable using some kind of primitive? Like, I don't know, maybe an array pair of three and the symbol USD or something like that.

STEPHANIE: Oh, I would definitely not do that [laughter]. Yeah. Like I, you know, for the most part, I think I've seen that as a currency object, and that expands the world of what we can do with it, converting into a lot of different other currencies. And yeah, just making sure those things don't get divorced from each other because that context is what gives it meaning. But when it comes to our compound numbers, it's like, without all of the components, it doesn't make sense, or it doesn't even represent the same, like, numerical value that we were trying to convey.

JOËL: Right. You need both, or, you know, it could be more than two. It could be three, four, or five numbers together to mean something. You mentioned conversions, which I think is something that's also interesting because a lot of units of measure have sort of multiple ways of measuring, and you often want to convert between them. And maybe that's another case where encapsulation is really nice where, you know, maybe you have a distance object. And you have five meters, and you put that into your distance object, but then somebody wants it in feet somewhere else or in centimeters, or something like that. And it can just do all the conversion math safely inside that object, and the user doesn't have to worry about it.

STEPHANIE: Right. This is maybe a bit of a tangent, but as a Canadian living in the U.S., I don't know [laughs] if you have any opinions about converting meters and feet.

JOËL: The one I actually do the most often is converting Celsius to Fahrenheit and vice versa. You know, I've been here, what, 11 years now? I don't have a great intuition for Fahrenheit temperatures. So, I'm converting in my head just [laughs] on a daily basis.

STEPHANIE: Yeah, that makes sense. Conversions: they're important. They help out our friends who [laughs] are on different systems of measurement.

JOËL: There's a classic story that I love about unit conversions. I think it's one of the NASA Mars missions.

STEPHANIE: Oh yeah.

JOËL: You've heard of this one. It was trying to land on Mars, and it burned up in the atmosphere because two different teams had been building different components and used different unit systems, both according to spec for their own module. But then, when the modules try to talk to each other, they're sending over numbers in meters instead of feet or something like that. And it just caused [laughs] this, like, multi-year, multi-billion dollar project to just burn up.

STEPHANIE: That's right. So, lesson of the day is don't do that. I can think of another example where there might be a little bit of misconceptions in terms of how to represent it. And I'm thinking about time and when that has been represented in multiple parts, such as in hours and, minutes and seconds. Do you have any initial impressions about a piece of data like that?

JOËL: So, that's really interesting, right? Because, at first glance, it looks like, oh, it's, like, a triplet of hour, minute, seconds. It's sort of another one of these sort of compound numbers, and I guess you could implement it that way. But in reality, you're tracking a single quantity, the amount of time elapsed, and that can be represented with a single number.

So, if you're representing, let's say, time of day, what would show up on your clock? That could be, depending on the resolution, number of, let's say, seconds since midnight, and that's a single counter. And then, you can do some math on it to get hours, minutes, seconds for a particular moment. But really, it's a single quantity, and we can do that with time. We can't do that with a 2D point. Like, it has to have two components.

STEPHANIE: So, do you have a recommendation for what unit of time time would best be stored? I'm just thinking of all the times that I've had to do that millisecond, you know, that conversion of, you know, however many thousands of milliseconds in my head into something that actually means [laughs] something to me as a human being who measures time in hours and minutes.

JOËL: My recommendation is absolutely go for a single number that you store in your, let's say, time of day object. It makes the math so much easier. You don't have to worry about, like, overflowing from one number into another when you're doing math or anything like that. And then the number that you count should be at the whatever the smallest resolution you care at.

So, is there ever any time where you want to distinguish between two different milliseconds in time? Or maybe you're like, you know what? These are, like, we're tracking time of day for appointments. We don't care about the difference between two milliseconds. We don't need to track them independently. We don't even care about seconds. The most granular we ever care about things is by the minute. And so, maybe then your internal number that you track is a counter of minutes since midnight. But if you need more precision, you can go down to seconds or milliseconds or nanoseconds.

But yeah, find what is the sort of the least resolution you want to get away with and then make that the unit of measure for a single counter in your object. And then encapsulate that so that nobody else needs to care that, internally, your time of day object is doing milliseconds because nobody wants to do that math. Just give me a nice, like, hours and minutes method on your object, and I will use that. I don't need to know internally what it's using.

Please don't just pass around integers; wrap it in an object, especially because integers, there's enough times where you're doing seconds versus milliseconds. And when I just have an integer, I never know if the person storing this integer means seconds or milliseconds. So, I'm just like, oh, I'm going to pass to this, like, user object, a, like, time integer. And unless there's a comment or a constant, you know, that's named something duration in milliseconds or something like that, you know, or sometimes even, like, one year in milliseconds, or there's no way of knowing.

STEPHANIE: Yeah. That makes a lot of sense. When you kind of choose a standard of a standard unit, it's, like, possible to make it easier [laughs].

JOËL: So, circling back to sort of the initial thing that sparked this conversation, the previous episode about T-shirt inventories, there we were dealing with what started off as, like, a hash of different T-shirt sizes and quantities of T-shirts that we had in that size, so small (five), medium (three), large (four). And then, we eventually turned that into a value object that represented...I think we called it a tally, but maybe we called it inventory.

And this may be wrong, so tell me if I'm wrong here, I think we can kind of treat that as a number, as, like, one of these compound numbers. It's a sort of multidimensional number where you say, well, we have sort of three dimensions where we can have numbers that sort of increase and decrease independently. We can do math on these because we can take inventories or tallies and add and subtract them. And that's what we ended up having to do. We created a value object. We implemented plus and minus on it. There are rules for how the math works. I think this is a multidimensional number with the definition we're working on this show. Am I wrong here?

STEPHANIE: I wouldn't say that you're wrong. I think I would have to think a little [laughs] more to say definitively that you're right. But I know that this example came from, you know, an application I was actually working on. And one of the main things that we had to do with these representations [laughs], I'm hesitant to call them a number, especially, but we had to compare these representations frequently because an inventory, for example, in a warehouse, wanting to make sure that it is equal to or there's enough of the inventory if someone was placing an order, which would also contain, like, a representation of T-shirt size inventory.

And that was kind of where some of that math happened because, you know, maybe we don't want to let someone place an order if the inventory at the warehouse is smaller than their order, right? So, there is something really compelling about the comparison operations that we were doing that kind of is leaning me in the direction of, like, yeah, like, it makes sense to me to use this in a way that I would compare, like, quantities or numbers of something.

JOËL: I think one thing that was really compelling to me, and that kind of blew my mind, was that we were trying to, like, figure out some things like, oh, we've got so many people with these size preferences, and we've got so many T-shirts across different warehouses. And we're summing them up and we're trying to say like, "How many do we need to purchase if there is a deficit?"

And we can come up with effectively a formula for this. We're like, sum these numbers, when we're talking about just before we introduce sizes when it's just like, oh, people have T-shirts. They all get the count of people and a count of T-shirts in our warehouse, and we find, you know, the difference between that. And there's a few extra math operations we do.

Then you introduce size, and you break it down by, oh, we've got so many of each. And now the whole thing gets really kind of messy and complicated. And you're doing these reduces and everything. When we start treating the tally of T-shirts as an object, and now it's a number that responds to plus and minus, all of a sudden, you can just plug those back into the original formula, and it all just works. The original formula doesn't care whether the numbers you're doing this formula on are simple integers or these sort of multidimensional numbers. And that blew my mind, and it was so cool.

STEPHANIE: Yeah, that is really neat. And you get a lot of added benefits, too.

I think the other important piece in the T-shirt size example was kind of tracking the state change, and that's so much easier when you have an object. There's just a lot more you can do with it. And even if, you know, you're not persisting every single version of the representation, you know, because sometimes you don't want to, sometimes you're really just kind of only holding it in memory to figure out if you need to, you know, do something else. But other times, you do want to persist it. And it just plugs in really well with, like, the rest of object-oriented programming [laughs] in terms of interacting with the rest of your business needs, I think, in your app.

JOËL: Yeah, turns out objects, they're kind of nice. And you can do math with them. Who knew? Math is not just about integers.

STEPHANIE: And on that note, shall we wrap up?

JOËL: Let's wrap up.

STEPHANIE: Show notes for this episode can be found at bikeshed.fm.

JOËL: This show has been produced and edited by Mandy Moore.

STEPHANIE: If you enjoyed listening, one really easy way to support the show is to leave us a quick rating or even a review in iTunes. It really helps other folks find the show.

JOËL: If you have any feedback for this or any of our other episodes, you can reach us @_bikeshed, or you can reach me @joelquen on Twitter.

STEPHANIE: Or reach both of us at hosts@bikeshed.fm via email.

JOËL: Thanks so much for listening to The Bike Shed, and we'll see you next week.

ALL: Byeeeeeee!!!!!!

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