The Importance of Multiplication in Math

If you're in the market for bicycle shorts, Joël's got you. Stephanie just returned from RubyKaigi in Japan and shares details of her trip.

Recently at thoughtbot, there have been conversations around an interesting data modeling exercise. Joël and Stephanie discuss the following:

• Value Objects vs. Hashes
• Doing Math on Compound Numbers
• Monoids and Folding
• Naming Concepts in Code

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• Ruby Kaigi
• Google Translate Lens
• Video on city parks
• Enumerable#tally
• Hash#merge
• Monoids
• Enumerable#all?
• Value of specialized vocabulary
• Gist with Joël’s code solution

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 little bit of what we've learned along the way.

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

JOËL: I've made an unusual purchase this week. I went out and bought a pair of bicycle shorts. And, for those who are not aware, these are special shorts that have padding built into them. Typically, they're, like, skin-tight, but I got, I guess, what are called mountain biking shorts. So, they kind of look more like the cut of a normal short. But they've got this, like, built-in padding for biking.

STEPHANIE: So. Just to confirm, you did get these shorts for biking purposes, right?

JOËL: Yes. I purchased these shorts for biking purposes.

STEPHANIE: Okay. [laughs]

JOËL: And I got these because I was talking to a friend about this and mentioning that this was, like, probably the most ambitious cycling thing I've ever done in my life. And they recommended if you have not done bike shorts, you really should get them. They make a big difference.

STEPHANIE: Wow. Okay, I have two thoughts here. First of all, you prefaced this saying that this was an unusual purchase. So I thought maybe that you bought these bike shorts for some other purpose. [laughs] But I am excited to talk about this because I've also been curious about trying bike shorts.

I bike a lot in Chicago in the summer, and I've been doing, like, longer rides on the Lakefront trail. And one of my goals, actually, this summer is to do a bikepacking trip. But I have not been super comfortable on longer rides. And I was just thinking that this might be something really helpful to make them a little more enjoyable.

JOËL: So, is the kind of biking that you're doing closer to what might be considered commuting?

STEPHANIE: Yeah, mostly commuting. But also, just, like, going on long rides on the weekends, in addition to this, hopefully, forthcoming bikepacking trip up to a state park. So not too long, maybe, like, 60 miles, but definitely long enough to start getting a little uncomfy on your seat.

JOËL: Yeah, is 60 miles, like, in one day?

STEPHANIE: Yeah, exactly.

JOËL: That's a lot. Yeah, the friend who recommended biking shorts to me told me that pretty much anything over maybe 10 miles is worth getting shorts.

STEPHANIE: Wow, okay. I clearly have been suffering [laughs] for way too long, then. Tell me more about your cycling trip.

JOËL: So this is a bikes plus beer trip. Basically, I plotted a bunch of breweries in Belgium on a map and constructed an itinerary that could hit a bunch of them while keeping fairly short rides between towns. And the goal is to do maybe 30-35 miles in a day. And so I'll be going probably, like, cycling in the morning, and then exploring and drinking in the afternoon and evening.

STEPHANIE: That sounds amazing. That's really cool to do a little bit of a tour of the area and then also traveling by bike.

JOËL: Yeah, I'm excited because other modes of transport really just give you the origin and the destination, whereas cycling, you kind of get all of the in-between places. You get a much better feel for the area that you're in. And you can make all these unexpected stops if you want. You can make detours. So I feel like you get the sort of being in the moment, being in the place effect that you would have as a pedestrian but with a much longer reign.

STEPHANIE: Yeah, absolutely. That's exactly what I was going to say. I love cycling. And there's something really special about being able to be present in your surroundings and seeing people on the street or a cool building as you're going. But also going at a speed where it feels very fun and very freeing to just be cycling through a town and making stops when you want to, and traveling greater distances than you could be able to on foot.

JOËL: So I just received these bike shorts yesterday in the mail. So today, at the end of the day, I'm going out for a bike ride, and I'm going to see if they perform as advertised.

STEPHANIE: That's exciting. Keep us posted [laughs] on if you end up liking them or not.

JOËL: Yeah, yeah. The next episode or two, I'll have to report bike shorts; yay or nay?

STEPHANIE: Yeah, The Bike Shed will now become bike gear reviews.

JOËL: The name will actually line up, then with what the people googling, it might think it actually is. Stephanie, what's new in your world?

STEPHANIE: Speaking of vacation, I just got back from a two-and-a-half-week trip myself. I mentioned on the podcast a couple of episodes ago, I think, that I was traveling to Japan for RubyKaigi, an international Ruby Conference over in Japan. And then I spent another week in Taiwan, just on my own time. So, yeah, I had a really big, long trip, and it was really great. It was my first time going abroad in a really long time. It was my first time being somewhere where I didn't speak the language.

So, in Japan...I don't speak any Japanese. And it was both challenging and also, like, not too bad. I found my way around through a lot of gesturing and smiling, and nodding. [laughs] And, hopefully, people were able to understand what I was trying to communicate. Also, pointing at menus, I highly recommend going to places that have pictures of the food, and then you can just point when you want to order. [laughs]

JOËL: So, did you find that English was not particularly useful then in Japan as a tourist?

STEPHANIE: Yeah, I would say so. The next thing was that most signs were translated. So we ended up taking public transportation a lot. And that was quite easy to navigate, especially since I have kind of navigated subways in other cities before, and reading the signs is no problem. But when you're trying to communicate with locals, that was a little harder.

JOËL: Did you use any, like, apps on your phone or anything like that to help navigate kind of the different language?

STEPHANIE: Yeah, the Google Translate Lens app. I can't remember exactly what it is. But this was my first time really using it. And I was really impressed by how it was able to translate things that you're using your camera to take pictures of, or just, like, having your camera view. I did feel a little silly, like, holding my phone up to everything and trying [laughs]...so I could understand what I was reading. But for menus that did not have pictures, that was my backup strategy. [laughs]

JOËL: Did you ever have to have your phone translate something and then just show your phone to someone else?

STEPHANIE: No, I didn't have to go that far. Though I do think that it has a feature where you can have someone speak into the phone, and it will translate that into your native language. And then you respond by speaking into it and then playing the sound for them, which, you know, I bet really works in a pinch. But I think that required a little more investment into the interaction [laughs] with the other person than I was ready for. Like I said, the gesturing served me quite well.

JOËL: I got the experience of being on the other side of that a while back. So, here in Boston, I was just walking down the street, and someone stopped me and just holds up their phone. And they've typed something in Chinese on there. And they hit a button, and it comes in English.

STEPHANIE: [laughs]

JOËL: And they're asking for directions. And I think I typed a sentence back on their phone in English, and then they hit the translate button and got it back in Chinese. We went back and forth a few times. And eventually, I think he got what he wanted, and we went our separate ways. And I was kind of amazed that this whole interaction happened.

STEPHANIE: Yeah, that's really cool.

JOËL: Yeah, kudos to that person for having the courage to stop someone on the street when you don't speak their language.

STEPHANIE: Yeah, absolutely. I think even when I was struggling to communicate with someone because of the language barrier, I could tell from their gesturing in return that we were, like, willing to help each other out. And that, like, there was still an ability to find some kind of connection, even though, you know, we didn't completely understand each other. And that was definitely one thing that I really enjoyed was being in a place with, you know, people different from me and having that exposure. It's been a really long time since I've got to experience that, and that was really valuable.

JOËL: So, other than the conference, what would you say are some highlights of the trip for you, maybe one from Japan and one from Taiwan?

STEPHANIE: So one of my favorite things about being in Tokyo was all the green space that was around. I ended up walking a lot just to explore the neighborhoods. And I always just stumbled across a local park or even a shrine that had really great nature around it, a lot of big trees. You know, some, like, water features, maybe like a pond, and a lot of really fun plants that I got to learn about.

And, yeah, that was really nice, especially in such a dense urban area, like, coming across green space to just sit for a little while. And it was such a nice relief from the density and busyness of a big city. That was just one thing that I was really impressed by being in Japan.

JOËL: That's really cool. I think that really speaks to the quality of their urban planning. I know that the stereotype of Tokyo that I have in my mind is that it's, like, you know, ultra-modern, ultra-urban, you know, it's the largest city in the world. So the idea that they've taken the time to set up all these little parks everywhere is really endearing.

Particularly, I think the idea of smaller parks at the neighborhood level where you don't need, you know, something massive like, let's say, New York's Central Park, which is, you know, really cool. But having just a little green space in your neighborhood where you can, like, stop by, I think it's a wonderful upgrade to local people's quality of life.

I was recently listening to a video on YouTube from a city planning channel talking about just all the thinking that goes behind city parks, and having them at different scales, and how that impacts the residents of different areas. So it's really cool to hear that Tokyo has done a great job with that.

STEPHANIE: Yeah, absolutely. I think part of the joy of just stumbling upon it was that you know, even when I wasn't seeking it out, it would just come along during my walks. And, yeah, it really was very refreshing.

JOËL: What about Taiwan?

STEPHANIE: So, in Taiwan, what I really enjoyed about it it's a bit of a smaller island. And so you can actually get to a lot of places within a few days. And a lot of folks take day trips out to the coast from Taipei. And I was able to do a two-day trip to another county that had some hot springs, and I got to enjoy an outdoor hot springs in the rain. And that was really nice because it was, like, surrounded by trees.

And it happened to be raining that morning, but, you know, we were all kind of already getting wet, so it didn't really matter. And it was just, like, this really serene and gorgeous experience being able to enjoy that. And I think that was another place where I was in a very urban area, and then being able to escape a little bit was really nice.

JOËL: That sounds like a magical moment. Have you visited hot springs before, or was this your first time going to a hot spring?

STEPHANIE: I have been to a few in the U.S. before. I like to take road trips to national parks. And there are some really great hot springs in the U.S. as well. And so this was kind of something that I really wanted to do somewhere else just to experience it elsewhere. And, yeah, I'm really glad to have checked that off my bucket list.

JOËL: That's really cool. I've never been to a hot spring, and it sounds like a fun thing to do. So it's on my kind of greater bucket list. It's maybe not a top-five thing to do, but definitely, something I want to do one day.

STEPHANIE: Cool. Love it. That was vacation talk from Joël and Stephanie. [laughs]

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JOËL: So recently at thoughtbot, we've been having conversations around this really interesting data modeling exercise, where let's say this is a company, and you want to purchase T-shirts for everyone at the company. You have already some T-shirts on hand because you've done this kind of thing before in a couple of different warehouses. And you need to know how many new T-shirts you need to order in order to have enough for everyone.

So as long as you keep things simple, the math is pretty easy because you sum the number of people at your company, and then you sum the number of shirts across all of your warehouses, and that gives you the T-shirts that you need, the T-shirts that you have. You get the difference between those two numbers, and that tells you how many new T-shirts you need to order. Where things get more complicated is once you start introducing T-shirt sizes, and that's where the fun data modeling comes in.

If everyone at your company has a T-shirt size that they want and then at your warehouses, you store...the object that represents a warehouse stores a hash of sizes and how many of each size you have. Now, how do you do all this, like, summing across things? And it's not really just a single number that you want. Now you need to know how many small, mediums, and larges.

And, sometimes, you've got a hash. Sometimes you've got just symbols on a user, and you've got a sum across hashes. Maybe do some differences across hashes. And it gets kind of tricky to work with. So that's sort of the problem as it's initially presented. And we've been having a really interesting conversation around different ways to try to solve it in a way that's really kind of clean and nice.

STEPHANIE: Yeah, that's interesting because what you described sounds like the first iteration of solving the problem is, oh, the warehouse stores this information as a hash. So maybe I will create a new hash for the counts of T-shirt sizes that I need and then do the comparison on those two hashes. It sounds like maybe there was some unwieldiness or maybe even some duplicated code there. Is that what you think you all were trying to solve by modeling this differently?

JOËL: I think we kind of quickly hit some limitations with hashes. One thing that is fun before we start trying to combine a bunch of hashes is that some of the data exists as a hash on the warehouses. But to get the T-shirts that we need, all we have are an array of users and a size on all of them.

And we can use this fun method from Enumerable called Tally to give us a kind of Tally hash that is just a mapping of size, two counts of that size in the array. And so that's a really fun method. You don't get to bring it out that often in Ruby. And it's nice because that hash format happens to match the same format as the hashes stored on the warehouse objects.

STEPHANIE: Right. So now you're comparing apples to apples. But it sounds like maybe this hash representation does hold some kind of significance.

JOËL: Yeah. I guess, for me, I tend to see anytime you're doing fancier operations on a hash more than just reading in and out; it probably wants to be some kind of value object. And, in this case, we kind of want to do math on hashes. I think the equation is kind of still the same thing. We're trying to get the difference between the two, between the want versus have, but you can't just subtract one hash from another directly.

There's some things that you can do with the hash merge method that allows you to pass a custom block and do some things there. But we're going to have to do this sort of repeatedly. And now we're kind of leaking some of that knowledge a little bit. So it feels like something where you might want to actually name this concept and make it an object of its own that can then have its own kinds of domain operations as methods on it.

STEPHANIE: Yeah, I like that a lot. Because even just as I was thinking about it when you are storing data like that in just a hash, what do you call it? Like, what do you name it? I think I've seen things like that named, like, T-shirt data, or, like, warehouse data, or warehouse T-shirt counts, or T-shirt counts. You know, that is when it starts to diverge, and you end up maybe seeing the same, like, data represented, but it being named different things in different parts of the code. And I, in experience, have found that very painful.

JOËL: Yeah, because I guess you could have, like, T-shirts on hand from your warehouse; that's one hash. But the hash generated from the users might get called something like user preferences. And if you're reading through that code and you see a hash, and you're like, okay, do these two hashes that I'm looking at, maybe in a test, just kind of coincidentally have the same keys? Or are these kind of fundamentally the same thing? Or is the idea of, like, T-shirts on hand like a stock different from, like, a preference? And do they represent different things that just happen to be similar in this particular scenario?

STEPHANIE: Right. And especially if then there are methods where you're passing that data structure that really represents the same thing. But you're passing it as arguments, and then, suddenly, one variable name, user preferences, or user T-shirt preferences becomes, you know, T-shirt count. That has been really confusing for me before.

JOËL: One thing that does get, I think, clunky very quickly is that you have all of these warehouse objects that have that hash of, like, stock on hand on them. And what you really want is a kind of aggregate object that tells you not what's the stock on hand for one warehouse but across all warehouses. So you've got to go through, I guess, that array of warehouses and somehow kind of aggregate all of those hashes together. And because they're already tallies, you can't just do Enumerable Tally on it anymore. You've got to find some way to combine them together, and that gets tricky really quickly.

STEPHANIE: Right. I can see they're starting to be, like, nested loops, especially if you're just working with primitives.

JOËL: I think some initial implementations that we saw ended up doing either, like, some kind of reduce block or each_with_object, or something like that, which are, I think, fine solutions here. But what lives inside of those blocks is what gets complicated. And I don't know about you, but I feel like if I'm reading through some code and then all of a sudden I see a reduce block, and it's, like, ten lines of logic with maybe some, like, nested things, like, maybe some nested loops or some conditions inside of it, that's kind of intimidating. Reduce is not a super easy method to wrap your head around, especially when the block has got a lot of logic.

STEPHANIE: Yeah, that's a really good point. It definitely gives me pause. And I have to, like, you know, commit to reading the method in its entirety to fully understand [laughs] what's going on.

JOËL: Sometimes, like, really pause and, like, annotate with comments and all this stuff.

STEPHANIE: So, what did you end up thinking about in terms of solving that problem of aggregating the sums of all the different T-shirt sizes for each warehouse?

JOËL: So I think, for me, oftentimes, it's easier to make the problem a little bit smaller, solve that smaller problem, and then try to kind of scale up back up again and particularly when you're dealing with something like reducing or aggregating a large collection. Like, forget about dealing with a collection. Just how could I combine two items of this type? So if I had two of these hashes. And forget about fitting it for an array. But if I have two of these hashes, how could I combine them together?

And you could do this with hash merge. I wanted to do things a little bit more encapsulated. And because I also knew that we're building some more logic around these, I actually wrote a custom object. I called it a tally, maybe inspired by that Enumerable method, and implemented an operator plus on this tally object. So a tally object can plus another tally object. And the response from that is you get a third tally object that's gone through all of the keys and summed them together. So it's kind of an aggregate sum.

STEPHANIE: This is a cool example of a method that's a verb also representing a noun to name the return value, right? So the Tally method on Enumerable returns a hash, which we have been talking about for a while as, like, a data structure that's, you know, perfectly fine, but maybe we can leverage turning it into like you said, a value object to give it more meaning or to make it easier to work with. And it seems like the naming part just kind of fell into your lap.

JOËL: Yeah, tally is interesting in that it is both a noun and a verb in English. I'm not sure what the grammatical term for that kind of word is.

STEPHANIE: So, once you extracted this new class out, what insights or observations did you have about this problem?

JOËL: What becomes really cool about this is that once you have a way of combining two objects together, reduce is a way to just kind of scale that up to an arbitrary number. And so, just like you can sum an array of numbers by reducing plus over the array. Because I have plus on my tally object, I can reduce plus operator over an array of tally objects. And they all just kind of sum together in a single tally that's the combination of all of them. So this is really cool.

What used to be an intimidating reduce block, the intimidating logic gets moved into a plus method, which I think is much more approachable. Because I can go in the context of an object and say, okay, I've got this tally object, and I'm trying to add it to another tally object. And we're just going one key at a time, adding them together. Simple enough.

And then in the place where we're reducing, all we're saying is list of tallies reduce plus. And I know that pattern already because I do it with integers to sum them together. And so now I've just got this really simple one-line in the scary part. And the actual complex logic is much more approachable.

STEPHANIE: That is very cool. I found it really interesting that this came about because we were trying to do math on these two hashes. So it seems like, you know, a tally because it represents a score or, like, a number. Like, we were able to implement those plus operators and get to a simple solution because we're working with numbers.

JOËL: Yeah, I think it might be fair to describe it as maybe a compound number is the term that I use. I don't know if that's mathematically correct. Oftentimes, when you're dealing with things that represent a number or something that's represented numerically but that might have more than one number involved in it. But you still want to do math with this kind of compound, multi-number value anyway.

And one example that you might have is, let's say, a point in 2D space. You have an X coordinate and a Y coordinate. And you can do math on points. In fact, there's a whole field of math to deal with that kind of thing. That's an important thing that you have to do. You might want to be able to add or subtract points. You might want to do certain types of multiplication on them. And so just because something has more than one number associated to it doesn't mean that it can't be used for math. In fact, oftentimes, that's where the fancier math does come into play.

But when we treat them as primitives, and we just have, let's say, our XY pair was a hash, or, like, a two-element array, then we lose the ability to do math nicely. If we create, let's say, a point class that has an X and Y, and then we define plus, we define minus, we define scalar and vector multiplication, things like that, now we can do all those operations. And we can treat it like math, even though it's not just a simple integer anymore.

STEPHANIE: Yeah, I like that a lot because we do end up working with data, you know, maybe even from our database. But then, inevitably, we want to, like, learn something about it. And so I was thinking about how frequently I use GROUP BY in MySQL queries and how, oftentimes, I care about counts, or, like, number of records.

And perhaps this is why we see, like, the hash primitive used so frequently in codebases that then become pretty complicated once we're trying to, like I mentioned, like, learn something about it or, like, compare things or whatever logic that we need to do. And transforming them into objects that then know how to do math on themselves [laughs] is very cool.

JOËL: Hashes are interesting because they're pretty much just basic data structures. And I think, very often, they're sort of pre-objects. They're things that want to eventually become objects. And, oftentimes, what I find is that hashes get passed around a system. And various other classes or subsystems all have bits of logic that act on the hash because the hash can't own that.

And so you end up with the logic around the concept of whatever the hash represents kind of scattered and maybe duplicated across three or four places in the application. And then, all of a sudden, if you give that a name, if you create a class for it, you can pull all of that logic into one place. And, all of a sudden, it probably cleans up all of the surrounding places because now they don't have to care about the implementation of exactly what operating on the hash is.

But, also, it means that these operations generally have, like, nice domain names. And, in the case of a complex number, you might even have that represented through math operations, like, plus or minus. And that allows your code to read really nicely.

STEPHANIE: Right. Which gets me thinking about how I mentioned, like, tally as a noun, and, you know, you implemented your custom class. But do you think there's any value in the idea of a tally being specifically like a hash-like thing with a number as the value for each key, like, that existing as a more general class for people to use?

JOËL: Oh, that's interesting. So, in my personal implementation, I hard-coded values for small, medium, and large because those were the T-shirt sizes from the example. But you're talking about some sort of generic tally object that maybe would be a gem or something like that that people could use that represents counts of arbitrary things or multiple counts of arbitrary things that might then implement some common math operators so that you could add or subtract them.

STEPHANIE: Yeah, exactly. Because I was just thinking, you know, like I mentioned, I often represent that when I count number of records in my database. Or even I can recall a problem that I encountered previously where I had to figure out the number of orders for an e-commerce store based on the location. And I held that in a hash data structure, but really, it's a tally. [laughs] And so, yeah, I think that maybe we've kind of stumbled across a very useful representation of very common problems.

JOËL: Yeah, I can see there being use for a generic version of this. Maybe that's your chance to go out and create some open source, or maybe this already exists. We should maybe research that first.

STEPHANIE: Yeah, if any one of our listeners know, [laughs] send us an email.

JOËL: So something that was really interesting to me about all of these changes, introducing the value object, cleaning up the reduce, all that stuff, is that, in the end, once the...there was this object that represented the sort of aggregate compound value, the tally, then the equation stayed the same. And I can just slot in those variables as before.

Whereas previously, when we switch from just a single count to this, like, we need to take into account sizes that, like, broke the initial implementation of the code. So it's funny how you sort of go from a simple implementation and then a new requirement, which breaks it. But then just changing the hash to be an object all of a sudden made the original code, which didn't really need to change; it just worked again.

STEPHANIE: Hmm. That's really interesting because it makes me think about how maybe the primitives were perfectly fine, you know, in the first set of requirements, and not until, like, an additional complexity or something new emerged that we needed to reach for an object that could support the change.

JOËL: Yeah. And I think I'd argue that if you're doing just raw T-shirt count, an integer is probably the right value to use there. But if you're doing counts broken out by T-shirt size, then having an object that's a single thing that responds to plus and minus so that you can use it in the same equation where you're saying sum up all of these things from the warehouse, and then do a difference with the T-shirts that we need that becomes really nice.

STEPHANIE: Do you think there was some value in going through the hash implementation first, though, and then arriving at using a more custom object? I'm curious, kind of, like, what that journey was like.

JOËL: It's hard to say. I would say maybe yes. But I could also see someone who's done this a lot, who's built the sort of heuristics, the instincts around this could immediately be like, oh, wait, we're trying to sum hashes here. Clearly, these need to be objects. Clearly, what we need is something that implements a plus operator that we can reduce.

STEPHANIE: Yeah, I like that a lot. Because part of, you know, knowing what to reach for is having seen it enough times and seeing patterns, right?

JOËL: This reminds me of a particular pattern that comes from the world of functional programming. It has a kind of scary-sounding name. It's monoid, not monad, monoid. And the idea in the context of Ruby is it's some kind of object that implements a plus method. So two of these objects can combine each other. And typically, you also have some sort of empty version of this object or some sort of, like, zero value.

And there's a few rules that go around, like, kind of how this object has to behave. Like, you can't just put any implementation you want in that plus method. Certain requirements that have to be met for it to be considered, like, a valid plus method in this pattern. But if you do meet those requirements, then arrays of this type of object are just inherently reducible because you can just reduce plus over them.

And so I think anytime you're trying to aggregate some sort of unwieldy data structure, that's probably a useful pattern to have because, you know, wait, as long as I have a way to combine two items together and potentially some way to generate an empty state, I can aggregate this whole list.

STEPHANIE: I'm curious, does that also apply to non-numerical values?

JOËL: Yes, any kind of aggregation combination, whatever. So maybe what you're doing is you're combining strings together.

STEPHANIE: Got it.

JOËL: String concatenation is a form of combination. And so you could be reducing some kind of concatenation over an array of strings, and you end up with one aggregate string that's the combination of all of them. Sometimes, though, you're not just taking values and putting them next to each other so that what you have is kind of all of them at the same time. You might instead do some kind of comparison.

An example here might be Boolean values. You might say the way that I'm sort of, quote, unquote, "aggregating" two values, two Boolean values is with the operator AND. And so you have two Boolean values, and you get a new sort of combo value out of them, that is, are both of these values true?

STEPHANIE: Whoa, that's blowing my mind right now. Because I had never thought of the, like, AND operator on Booleans, essentially aggregating them into a single true or false value. [laughs]

JOËL: It's kind of weird, right? But I guess we do the same thing with numbers. One plus one doesn't give us 11 unless you're writing JavaScript.

STEPHANIE: [laughs]

JOËL: You know, we get a new number too, that is some sort of, like, combination of the two. So, similarly, it kind of makes sense that two Booleans might combine to create a new sort of third Boolean value. Where it gets really interesting, though, is that once you have this sort of combination, if you try to reduce AND over an array of Booleans, what you effectively have created is Ruby's Enumerable all method that checks to say, are all values in this array true?

STEPHANIE: Interesting. But really, the way that's implemented is just, like, a definition of what aggregate means for Booleans, right?

JOËL: Right. But it's taking that idea of aggregating two values and scaling it up to an array of many values. So we know Boolean AND. Another way to think about it is, are both of these values true? Is the question it's trying to answer. And then we're scaling that out to say, is both of these values true for everything? So are all of these values true? Because we're going from two to many.

STEPHANIE: Cool. So maybe the takeaway for some of our listeners could be, like, next time they find themselves having to deal with a collection or an Enumerable and, you know, using a reduce or, like, trying to break it down to compare two of those elements first, and figuring out how they want that interaction to work. Does that sound right?

JOËL: Yeah, absolutely. Once you have a way to combine two elements together, if you want to scale it up to n elements, you just plug it into reduce, and it does the rest of the work for you.

My big takeaways from this exercise were one: the value of creating custom objects. Wrapping primitives like hashes in an object and adding a few domain methods on them made such a difference in my final implementation.

Secondly, I think it's what you're saying, this whole thing about breaking down complex reduce problems by figuring out how to combine two items and then just using reduce to scale it to an array.

And then, finally, I think this is a point that we've mentioned on this podcast before, the value of specific vocabulary - being able to name things and patterns. And so knowing some of the details of this monoid pattern and having a name for it means that now I start seeing it in places. And so the moment I see, oh, wait, we're aggregating values; we're combining two values together and then doing this in a reduce, immediately, my mind goes, wait, that feels like monoid. And then, I can explore that with my custom object to try to make the code better.

STEPHANIE: Yeah. And even if you don't remember the monoid part specifically, the idea of Tally, like, that is something that I think is really cool and really applicable to a lot of codebases.

JOËL: So, for those who are interested in more practically what this code looks like, I've put this all in a Gist, and I'll link to it in the show notes. This was a really fun exercise for me because I used sort of two development techniques to help sort of build this out.

One, I went with a kind of literate programming approach, where I had just a Ruby file and would have put in some big comment blocks talking about what the setup was, what I was trying to do, and then describing how I'd like to use the code, and then try to write code that made that happen. And then, for the actual objects that I was using under the hood, I used TDD to test drive and build them out.

So you've got all of that in the Gist. We've got the tests and that sort of literate programming script that almost reads like a mini blog post, except it's executable Ruby. So, if you're curious to see about that, the link is in the show notes.

STEPHANIE: That's a very cool format. I'm excited to take a look.

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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