Opposites are one of the first things we teach children: big-small, short-long, happy-sad. But how universal is the idea of opposites? What's the opposite of a banana for example?

In our latest podcast, we take an in-depth look at the concept of opposites. We attempt to define opposites, exploring whether they are based on categorical or quantifiable features, or some intuitive interpretation of context. Finally, we examine how they can be used to help us navigate our environment, supporting rapid analysis and decision-making. And if you're interested in knowing what the opposite of a banana is, Nick will reveal the analytical output of his opposite-generator model. You may find the answer surprising or predictable, rigorous or widely speculative.

A few things we mentioned in this podcast:

• Concepts and Categories: A cognitive neuropsychological perspective
• Kaggle: Countries of the World Dataset
• U.S. Department of Agriculture: Food and nutrient database for dietary studies
• Overtly prompting people to “think in opposites” supports insight problem solving
• Principal Component Analysis: a review and recent developments

For more information on Aleph Insights visit our website https://alephinsights.com or to get in touch about our podcast email [email protected]

Hello and welcome to the Cognitive Engineering Podcast produced by me, Fraser McGruer for Aleph Insights. In this series of podcasts, we take a look at interesting topics and discuss what we think they tell us about analysis and decision making. I'm here with Sara Nonu, Chris Wragg and Nick Hare of Aleph Insights, and this week we're discussing what is the opposite of a banana? Nick, you're our in-house resident banana-ologist. What is the opposite of a banana? Well, this is a question posed actually to us by a loyal listener and one-time guest, Mikey, who was involved in a conversation in which he suggested something which someone found preposterous and they said, that's bananas. And Mikey said, no, it's the opposite of bananas. And apparently they then had a big discussion about what the opposite of bananas actually was. Now, they did come to an answer, which I won't reveal until the end, but I thought this was an interesting question, actually, because opposites are one of those things which we all understand. We all have a kind of very intuitive understanding that a cat is in some sense the opposite of a dog, that dark is the opposite of light, that cold is the opposite of hot. And when you come to try and ask exactly what is going on here, you realise it's not actually very straightforward to say how all this works. And so I thought we could try and unpick this and work out how we could calculate the opposite of anything. Yeah. I mean, in the first place, as you say, I think we need to investigate this concept of opposite and really what is that, what's that all about? Who wants to jump in, Sarah or Chris? Yeah, well, I mean,

I think for me, the answer to that question, what is the opposite of a banana is an apple, right? Obviously. But I think that answer or my intuitive answer gives me a sort of insight into what I think of in terms of opposites. And it's noticeable that I picked a fruit, right? I didn't pick something else. So I've actually picked something that is quite similar to a banana, right? But I claim it's the opposite. So what's that about? And I think for me, opposites are sometimes actually, if you look at them in a multidimensional sense, they are quite similar. But what makes them distinct is polarity on a particular thing. And I suppose in my mind, if you've got bananas, the other common fruit that you will see is apple. Apple's a different shape and a different colour. So that sort of narrowing it down gives you an opposite. And it's about picking one thing. You can't have multiple opposites. It's about picking one dimension and deciding what is on the other end of the spectrum on that dimension. But hold on.

But is it sometimes the case that there's not an opposite? Because, I mean, what's the opposite of cold, right? What's the opposite of good, right? What's the opposite of ugly? Fine. All those are fine. What's the opposite of an apple? Or what's the opposite of banana? What's the opposite of

meningitis? I mean, I don't know. Sarah? I just, that's kind of how I, when I looked at this topic and I was researching it, the more I was looking into it, I was like, it's hard to find what actually a true opposite is. Because yes, if you take the case of banana and apple, they're still both fruits. So you're looking at characteristics and it's kind of how you think about objects and how you define them. And I think it's somewhat to do with helping us process and categorise information. But I definitely agree with you, Fraser, on what you've just said. What is it? What is an opposite? I mean, what's the opposite of Nick? I mean,

is it Chris? Peter? Well, I think I'm more the opposite of Nick than Peter is. Maybe, maybe. Sorry. Can you have more and less opposites? Because I just actually used that. I said, I think I'm more the opposite of Nick than Peter. That's it, right? Things are essentially on a

scale looking at, like, you're hot and you're cold, right? It's one end of the spectrum. In the middle somewhere, there's warm, there's not warm. It's somewhat hard to kind of define it to be like, this is precisely one thing and this is the opposite of something. Who was I talking to recently? Maybe it was yesterday and I was talking to Tom about this podcast and we were having the discussion looking at, you know, well, if you think about human beings, people would say the opposite of a man is a female. But really,

we're just variations of the same thing. Yeah, it should be like a female ant or something. Yeah, yeah. So what is really an opposite? Yeah, so I just want to put forward, I think this is all really good, but before we get into more detail about actually how this works, I had a quick, I want to put forward a theory about what the point of this is, right? Because we all get it, the idea of opposites. And I had an idea, this is just a hypothesis, highly speculative, that the reason that opposites are something important that we think about is that if there's an object that has a certain set of characteristics, and what I should do with that object is some action or other, like, I don't know, eat it or be nice to it. If I identify that another object is the opposite of that thing, like is different on all kinds of characteristics, then by and large, that should mean I should not eat it or I should be nasty to it. So I sort of feel like actually what we're doing here is trying to work out the relevant rules that should affect our behaviour towards things. I suspect that's what's at the root of this kind of understanding of opposites, that if you should eat an apple, then you should definitely not eat the opposite of an apple, which would be poison or something, you know? Anyway, I just thought I'd get that out there. But there's a few things, which people have said. So let's distinguish, to begin with, between categorical features and quantitative features. So with categorical features, these are things that aren't orderable as such. You can't sort of say that a male isn't sort of 50% more than a female or something. They're just different. And quite a lot of things are like that. The shape that something is, you could say, well, you know, a circle and a square and a triangle are just different shapes. Then a triangle isn't a particularly sort of square circle or something. They're just different things. Now, it feels to me like we can intuitively understand the opposite of a binary variable. So we have a category where it's either one thing or it's another. The opposite is the other thing. But could you imagine a concept of a sort of troposite, a trinary opposite, where you don't just have one opposite, but for everything you are, for that particular feature, you have two opposites. But let's just say that when you have a variable that is categorical and has more than two values, the concept of opposites becomes problematic. It becomes quite hard to say. As you said, what's the opposite of meningitis is a really good example, because, you know, it probably has a whole range of characteristics which are not orderable. Just the other thing, quantified. So if it's quantified, it feels a bit easier, right? So the opposite of a high number is a low number. But problematic. What's the opposite of two? Is it minus two or is it a half? Or is it four? Or is it four? Because if there was a population which was generally, the average was three, and you had one which was two, the opposite

of that might be a four. Or you could say it's 536. Because 536 is a high number. So even with quantitative variables, it's not totally straightforward. But I think key to opposites is context, right? And this stems from what you were saying, Nick, about it affecting behaviour, right? So generally, you know, a number in itself is abstract, right? But if you attach it to a value of something, so let's say you equate it to heat energy, right, and you make it a temperature, then the opposite of cold is hot, you know, the existence of a high level of heat energy.

Well, no, sorry, sorry, just to stop it. Because as far as the way that we model heat energy, right, is, is it's a scale from zero to infinity. So we might go around saying that minus 200 Kelvin is, is, is cold. But if you were in the middle of the deep space, that would be boiling. And similarly, like the sun, we might think that 10,000 degrees was hot, but the sun might go, well, that's nothing, you should see, you know, Antares, it's incredibly hot there. But I think, again, it comes

down to context and, and interpretation about what you're trying to do with it. So if you look at something like distance, right, if you look at, you know, short distance versus a long distance, it doesn't actually tell you something objectively about the number itself. So if you, if I said, well, they, they threw the ball a long way, right, you'd have in your mind some something, you know. But if I said, it's a short walk to the shops, right, you wouldn't think the short walk to the shops was less distance than the long, the long ball throw, right. So it's very true, the context in which you interpret the thing. And if you look at most of the, most of the things we present opposites, you know, like we teach children opposites, it was one of the first things you do, big, small, you know, little, little, large, Canada ball, all of the great comedy duos. But you, who incidentally, usually are opposites of one another in some way. Indeed, I think we're tapping into something quite important here. We teach this, but it's usually in a simplistic form. And it's driven by context. So they'll show you, you know, two pictures of a, of a small person and a large person or a thin person and a fat person and, and attach the words to them. And what you're not thinking is, oh, wait a minute, you know, one of them's a man and one of them's a woman, or, you know, you're focusing in on one particular thing that you are, you are interested in. And that's because that's driving some sort of decision making at that point, like you're trying to pick some trousers for them or something, you know. So I think it's very context specific, what an opposite is.

Yeah. Sorry, you were about to come in, but I think what you were saying there, Chris, is I think you're absolutely right. Because actually, you know, opposites, in effect, it's a, it's, it's really a language, it's a vocabulary that we all use. And we use it like an analogy to, to explain something, to explain the way the world works. And so maybe- But I wonder if it's more important. But hold on, Nick, but, but maybe it falls apart when you start to unpick it, because the thing itself is used to explain stuff. So then when you start to go, well, how about, you know, if we use it for that, it, by definition, it starts to fall apart. And I think Chris's point about context is important, because, yes, we all, everyone recognises the short and long will change meaning and context. But everyone understands that intuitively, because we're using it as a function to understand the world. So when you start asking these questions, so maybe we're using it in the wrong way and say, ah, but what if we want to do an opposite of an apple? Well, why would you? Why would you want to do that? Unless you're, unless you're Mikey Lear in some weird argument. Sarah, you were going to say something.

I just think opposites help us to navigate the world, essentially. Like we're, we're, we're creating assumptions, we're making comparisons that are making it easy for us to think about things, classify them, to make those decisions quickly. So whether or not something, you know, is a short walk to, to the shops, well, you can easily say yes or no, I'll go for a short walk, I don't actually know how short that short walk is, but instead it's short compared to a long walk. So I just think it's about how, it's a way that we can quickly navigate through the world and our thinking processes by having, having these concepts of opposites, even though, as you say, when we unpick them, it turns into a bit of a mess.

Yeah, I think that's it. I think it boils, it really quickly boils down to the salience of, of, of something, what you, what you care about in that particular context. I've got a quick question I wanted to ask Sarah to see if, see if this, this works. I was going to ask you, what's, what's the opposite of New Zealand?

I already have the answer I want to say straight away, but I might be wrong.

Yeah, yeah, yeah. That's the one I want. Say Australia.

I was going to say Australia.

Right, exactly. Right. So here we go.

But we're not opposite, we're so similar. Yeah. Right. To me, I'm like Australia.

So this is, this is why I wanted to ask that question, because I think it gets to the heart of, of opposites, right? Which is that, you know, Australia and New Zealand are objectively, you know, pretty similar in terms of histories, geographical location, language they speak, you know, lots of the cultural references. I know the accents are different, but they're, they're speaking the same language and, you know, lots of people do get the accents confused. So, but yet, you know, you, you pick them as an opposite. And why do you, why do you pick them as an opposite? What, what, what is it that you think is different about Australia and New Zealand?

I have, like, the more I think about it, the more I kind of like go into a spiral, because I actually don't know. I just think it's because it's proximity and it's the one thing that's closest to us. So I'm like, well, they're essentially very similar to us. But for me, I'm, they're the opposite to us. Yeah. So I'm wondering if it's because, thinking about it in context, like, we are all the way on the other side of the world, just us in Australia, really. So does that mean straight away that, well, the opposite to us has to be them, because that's all that there is in our part of the world? Like, if I asked you, what is the, what is the opposite to the UK? What would you say?

I'd probably say France.

Oh, well, okay, so this is fun, because I'd go for Japan. Because, because Japan is very similar in a lot of ways. It's an island off the, off the edge. It's even shaped similarly off, off the, or a collection of islands off, off the coast of a massive continent, with its kind of quite distinct culture and a history of the feudal system. Yeah, but the point is, everything else is different, like the whole content, the content. So the, if you like, the container is similar, but the content is, is, is, is sort of unrecognisable. So I can't, I, yeah, it's really interesting. I guess we have, what we've done is pick different dimensions as the key ones. But I see, when you were talking about language, it made me think, well, actually, the concept of opposites is not just something you can do with language, but absolutely fundamental to how you learn it in the first place. In that, you know, you, in order to show that you've understood a word, you have to be able to show which words, which things it excludes. You know, not, you can't just be picking things that it includes, you've got to show that you understand it, you've got to show which things aren't that, aren't covered by that word. And anything where there's a word can be more or less true of something implies, already implies an opposite, which is the thing that it's least true of. So I, you know, it could be that this is a really fundamental kind of concept. Yeah, sorry, but I just think, just, sorry, just, I don't know if we can come up with rules as to what criteria are up for grabs, what things, like why, why it is that this Australia, New Zealand problem, why there has to be a certain amount of similarity, a bit like cat and dog, right? Because, you know, really, if you're going to try and list every single feature and take the opposite of it, you'd have, you'd pick something that doesn't exist. You'd have to, because New Zealand at the very least exists. We can all agree on that. And so it's opposite, surely, it doesn't exist. No, I haven't, not with my own eyes. So, so being non-existent, non-country of some sort, you know, and so that, that's, that's the issue really. I wonder if, if, you know, there is a way of, of trying to narrow that down or really, really just, you know, it's always context. I want to move us on a little bit. Nick, I believe that you have developed an opposite emitter, if I have termed that correctly. Is this the time to introduce this to the discussion? I will, I just will say one more thing though, just a quick one, which is something really interesting about, so when I, in fact, it's related because when I was doing, so I decided to create a couple of oppositometers based on where I could easily get data. And, and so I got some data about fruits and, well, foods actually, big pile of foods, all kinds of data about their nutritional content and all that kind of stuff. And I also got one on countries, which is things like their population and surface area and all of that kind of stuff. And, and, and so I've worked out a way of identifying the thing that's most opposite just in terms of ranking. So if you're in the top 10% of in one thing, you're looking for a country, which is in the top bottom percent of that thing as being your opposite, but it made me think, well, okay, so the thing is the criteria I'm doing the opposites of criteria, but those are criteria that are in the dataset, which made me think that well, is there something, some neural or some cognitive correlate of things being in your data set, which in order to count as an opposite, they have to somehow be stored in the same data set. So, so which makes me think, well, okay, we have a data set for animals and it's got a snake and an ant and a cat and a dog. And, you know, so the opposites have to somehow be in that data set. But if the data set was just mammals, then that will be a different set of data. And the interesting thing is that actually, you know, there is evidence that we have sort of distinct cognitive categories for things. So for example, we have, you know, people, people have, there are particular kinds of brain damage where people will forget, you know, about fruits and vegetables, but not about animals, for example. So there are like, actually it does seem to be the case that we store data about different types of thing in discrete chunks like that. So, so yeah, I just thought that was quite interesting because it felt a bit like what I was doing. I was like saying, well, I'm finding the opposite in this data set, but I'm not trying to find the opposite of any, you know, of a fruit by looking in a data set about, you know, rocks. I think I'm with you. I'm thinking that said, yeah. The other thing it might be, I just, it's interesting to think about the way principal component analysis works, which is something we've done on a few projects recently. But what that does essentially is you take your data, you take your data points and your data points all have different, you know, values for all of their features. So you, you know, your, you know, your features might be height and weight and, you know, IQ and gender or whatever. And so you're, you know, you have all your data points and, and principal component analysis essentially says, how can we separate these data points as much as possible, which, which things separate these data points as effectively as possible, and then comes up with a kind of, you know, set of things that will pull them apart as much as possible. And it just occurs to me that really fundamentally that's trying to do this job of saying, well, if we were trying to find the opposites of things, what would those, what would the opposites be? If you could get these things to be as far apart as possible,

which things would be opposite ends of that? And I feel like principal component analysis is almost the opposite of doing opposites in practical terms, because what it does is it collapses multidimensional space, you know, and looks at separating things on a bunch of things. Whereas I think actually, you know, like the classic example is like rivalries, you know, people say, oh, like Alain Prost and Ayrton Senna, right? They say they were two complete opposites. Well, no, they weren't. They were both Formula One drivers for a start, right? You know, but yet people have picked one thing about them, you know, to do with their sort of their level of flair and preparedness and decided that is, you know, that makes them, you know, completely sort of antinomical to one another. And so and I feel like, you know, by picking lots of things and pushing them apart, you lose the meaning, you think you're gaining meaning, but you actually

lose meaning. Talking of doing that, that's what I've done with my absurd omitters. So I say it's no longer an opposite, an opposite, an opposite omitter. It's now an absurd omitter. Well, what it what it does, we're going to have a play with it. Yeah. So what it does is it essentially, it's all rather arbitrary, because as we've said, there's no there's sort of there is an objective component to this, but it but certainly it's very subjective at the same time. What it does is you put in the thing you're you're interested in comparing and it gives you the thing that is at the opposite end of the scale the most on all of these scales kind of thing. And what's nice is I can see you've wheeled it out there. Yeah. And I like the bells you've put on it. And I presume you just pull that lever and it spits it out, right? Yeah. So we've got so the country omitter, let's start with that. We've got the surface area, population, GDP, share of economy, which is agriculture, international trade, urban population, all kinds of stuff in there. Few countries excluded, because the data isn't there. But yeah, if you want to, you know, give me a country, I can tell you the opposite of that country, Georgia, the country of Georgia. The opposite of Georgia is Azerbaijan. Oh, it's the right next door. That's weird. That's weird. That Okay, well, let's, let's go on. Let's shall we try if I try New Zealand, someone else? Yeah, let's put in New Zealand. It's apparently Swaziland. Which is interesting, because that's got Zealand in it as well. But it's interesting, like intuitively, immediately, when you say the opposite of New Zealand is Swaziland, everyone would just go, what, really? And yet the data says that it's true. So yeah, I mean, I mean, well, yeah, the opposite of the United Kingdom is allegedly Guinea Bissau. The opposite of Japan, the opposite of Japan is Rwanda. I like that. That feels like that kind of sort. Yeah. And Russia, Russia, the opposite of Russia is Suriname. Yeah. Yeah, Chris, Sarah, any more for countries you want to randomly shout out?

Australia. Why not just go? Oh, yeah. Okay. So the opposite of Australia. I'm going to try and guess I'm going to try and guess what the opposite to Australia is. I'm gonna say the opposite to Australia is going to be something like Liechtenstein. You're gonna love this, Sarah.

It's actually Samoa. Really? Yeah. What do you think of that? It's only a only just a couple of thousand miles away across the Pacific. It's not very far away. No, but I think Australia is big and Samoa is small. Yes. I think population wise, there's probably quite a distinction, but also economic urban population. I mean, Australia has got quite a high urban population, isn't it? I don't know about Samoa, but. Is it always locked? As in, if you were to do the opposite of Samoa, would it would it always be? No, no, no. So let's see. Let's put that in. It's Argentina, the opposite of Samoa. Well, you could just keep going around the world. Well, I see if you think about what it's doing is it's sort of trying to find the closest point to where the opposite ought to be. So so it's saying, well, the opposite ought to be here. But actually, there isn't any country there. So we'll find a close point. But then if you take the opposite of that, there might be a country that's closer than the place you started, sort of mean. But do you want to do food as well? Yeah. OK, so right. So now we have to. There are thousands of foods in the database. I mean, there's about seven thousand foods. Right. Could you say lettuce? Yeah. So so if you if that's the best way of doing it, if you say if you say food, I will find it. But you've got to decide whether you want a butter head lettuce, cause or remain lettuce, green leaf, let's cause lettuce. OK, so the opposite of lettuce is cured strips of pork, which is correct. It feels right, doesn't it? What is the opposite of a banana? No, well, I tell you what, let's save that to the end. Yeah. Should we should we see what the opposite of whiskey is? Oh, is it? No, hold on. What do you think it's going to come out? Well, it can't be a drink. Is this in the drinks category or just in food consumables in general? It's a really specific. It's a weirdly, really specific one. And it's so perfect. Is it like celery or something like that? No, it's actually Kellogg's Special K. Makes sense. You have it at a different time of the day, the opposite end of the day. It's good for you instead of bad for you. Yes. You know, it's one's fun. One's no fun. Yeah. Sorry. Is there one that you've got? Espresso coffee. So the opposite of an espresso is apparently a whole dried egg. A whole dried. And what is the opposite of a whole dried egg? Oh, that's a good one.

Wait a minute. What is it? What is a dried egg? You mean like a powdered egg? Yeah, I guess so.

The opposite of a whole dried egg is honey, raw honeydew melons. When would you cook a honeydew melon? Well, you would cook an egg. Of course, you wouldn't cook honey. Oh, I see. Why would it be raw? I don't know. Like maybe melon juice or something. OK, we should. We could be here for hours doing this. What's the opposite of a doughnut? The opposite of a doughnut. OK, that's a good one. Let's have a look. So we've got yeast, leavened cake type French crullers, glazed, glazed, glazed. This this category actually includes, I must inform you, includes honey buns. OK, the opposite of those is raw Brussels sprouts. Correct. This is great. This is really good. I'm going to claim a victory. Much better than the country. Yeah, there's more things. So I think. So let me. Shall we answer the question once and for all and go for bananas? Yes. So here we go. Let's wait. So we need super pause. So wait, wait, wait. So raw bananas. By the way, did you know there's a kind of banana? There are many times about many types of bananas, of which one is an apple banana. But anyway, do you want to guess before I before I give you the answer? Is it going to be. Remind

me what the dimensions are again? Oh, it's about it's about that long. Oh, God, about that wide.

There's about there's about 40 different. Are they curved in the middle? Yeah. The amount of alpha carotene, ash, beta-crypsoanthin, the amount of carbohydrate, cholesterol. It's everything.

So is it is it. But it's it's constituents of the food is. Yeah, it's the kind of the percentage,

I guess, of that stuff in the food. It's going to be some kind of synthetic banana. Right.

So something with minus potassium. I think it's going to be

some kind of processed food. I don't know. I can't think. Oh, spam. I was thinking ham. Well, I'm going to call that correct because it's actually breakfast items, biscuit with egg and sausage. So I think what that is is sort of like imagine, I guess, like a kind of McMuffin or something. Yeah. Yeah. So, you know, that is the opposite. Like if you had a banana for breakfast one day, you might fancy the biscuit with egg and sausage the next day. Yeah. So there we are. So I think this is a revelation. I think even the data driven approach seems to produce interestingly plausible answers. But anyway, shall I tell you what Mikey's answer was? Yeah, this was about to ask, what did he say was the opposite? So they decided. Yeah. And I think it's rather good. So the opposite of bananas is Uluru. Isn't that the name for Ayers Rock? Yeah. Right. So it's big instead of small. It's brown instead of yellow. It's made of rock instead of made of fruit. And but crucially, it has the same sort of vowel pattern as banana. So there's a nice similarity there. So anyway, I think that's quite a good answer. But obviously, Mikey's got more. He's more relaxed with which features he's varying. Whereas here, we're really just looking for foods. Yeah, I think we've answered it. The data driven answer is a biscuit with egg and sausage. The opposite ometer has spoken. Yeah.

Oh, they mean an American biscuit, don't they? Yeah, they mean one of those one of those crumbly,

like scone. Yeah. Yeah. Wow. Brilliant. I think we need to stop. I think we need to stop. We've cracked it. Yeah. Yeah. When I say we, I mean, Nick and his soon to be copyrighted. Yeah, no, this is awesome. I just put in for fun, put in a Domino's pizza, pepperoni pizza, and it came out with corn on the cob. So I, this is correct. As far as I'm concerned, we've got a data driven answer. And it's it's American style biscuits, egg and sausage. It's rare that we really can definitively answer one of the questions that we get asked. But I feel like we've done it. We've done it. We've done it. Seriously, I want to next time I come around to you, Nick, we can sort of play on this all day. Play with this. Yeah. Yeah. Okay. All right. Thank you, as always, for listening. If you've got any thoughts or suggestions for topics, you can email us at podcast at alephinsights.com. We'd love to hear from you. If you've enjoyed the podcast, what should people do? Anyone jump in? What should people do? Hit the dislike button.

That's right. It's opposite. Maybe. Yeah. Do the opposite of that.

Thanks, as always. I'm Fraser McGruer. We've been here with Sara Nonu, Chris Wragg and Nick Hare of Aleph Insights. Until next time. Hello.