Is administering a Covid-19 test on yourself difficult, or are the instructions just confusing? How should we explain complexity and is there a limit to how much we can simplify things?

In our latest podcast, we discuss different ways of simplifying information, how to judge the right level of detail for a given context, and whether reductionism is always a useful concept. We look at how simplification can help or hinder understanding, examining some of the consequences of oversimplification.

A few things we mentioned in this podcast:

• Reddit: Explain Like I’m Five
• Shannon information and Kolmogorov complexity

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 Peter Coghill and Nick Hare of Aleph Insights and this week we're talking about how easy, or not, it is to test yourself for Covid. Okay, Peter, you've been testing yourself, hopefully just for Covid. So, yeah, tell us, talk us through. Was it easy? Was it complicated? Were you confused? You look a bit confused.

Well, this is the thing, right, so the background is a couple of weeks ago my partner and I both came down with colds. The symptoms weren't Covid symptoms, they were just like a normal cold, but we were planning to go and visit parents and things that weekend, so we prudently thought, well, let's get some tests. So, I had already previously got some of the peak flow, that's the thing that you breathe into, lateral flow, that's it. So, I'd already got some lateral flow tests. So, I took one of those and Rosie sent off for one of the kind of rapid post by test things you can get. So, they send you a kit and you do the test and you post it back and you get a result within overall a couple of days or so. And so, these tests are obviously doing something fairly complicated. You've got to be able to get an unsoiled sample into a little vial and then you mix it up with a bit of solvent and on the lateral flow test you squirt it into a little hole and it does a little bit of sort of chromatography type, some sort of cleverness goes on and it gives you an indication. And with the send away jobs, you put the sample into a tube and put it in a bag and send it off. Now, to make sure that you get an unsullied sample that doesn't reduce the quality, reduce the accuracy of the test, there's quite a lot of sort of little steps you have to go through, like washing your hands and putting things out and laying things out and putting A into B and putting things in the bag and doing everything basically in the right order so you maximise the chance of getting a good test. Now, that ends up being a sort of 20-step process or something. This sounds right up your street, but anyway, go on. Which, if you do more than once, you probably get it, but you only really get one chance, certainly with the post test, the send off test. So, on the basis of it, it's quite complicated and I could imagine there'd be some people who would struggle with this. Their ability to read the booklet and keep up with it might not be so strong and they could really struggle. So, it got me thinking about explaining difficult things to people or complex topics or complex processes or complex concepts. Is there a sort of limit to how simple you can make things? And is there a sort of inherent limit to understanding that we can have in our little human, fleshy human brains? So, yeah, I just thought it was an interesting thing. You've got a complex thing. Can you boil it down? Could you boil down quantum dynamics, quantum mechanics, so that a three-year-old

could understand it? Okay. When we first started discussing what topics we would do, this one jumped out at me. I like the look of this one. I think the reason why is because I think an ongoing theme we have is me... Finding the limits of Fraser's knowledge and understanding. Well, that too. But more like I have a tendency to simplify things, to oversimplify some might say. And I think we did a podcast where I was basically arguing everything's really simple and you guys were saying, no, it's not. And what it boiled down to was just because there's a decision to be made, which might be a simple decision, let's say it's a binary decision, doesn't necessarily mean that everything underneath it is simple. Now, this is a little bit different to that. Can complicated things be simplified and explained? Is that more or less the question we're asking? Is that right? Or how far can it be? And what are the limits of it?

Yeah. I mean, so for example, the way I think about it is that you can, most things can be simplified to any degree. I think you can sort of take any concept and break down into lots of little axioms that once you get the axioms, once you've got the sort of taxonomy of axioms that help you understand something, understand things, you could explain anything. However, I think there are some concepts that are just so inherently complicated that it would take kind of longer than the lifetime of the universe to explain it using basic axioms. You have to sort of, you build concepts on other concepts. So once you've got the basics of one plus one equals two, and lots of other sort of little logical things, you build up concepts to become shortcuts to a whole bag of those axioms. I feel like, I think Peter might be

Using analogies would fall into the exact analogy and metaphor and all that kind of stuff,

right? Well, yeah. So so this is I think the exact this reminded me of that joke. Now, I know I can't tell jokes. I'm not going to I'm not going to try. But the one about do you know the one about the prisoners who are all saying numbers to each other? Heard that one? No. This guy goes to prison and he gets in there, you know, he's kind of on the with a bunch of life, you know, lifers. And they're all say one of them says 13 and they all start laughing. The other one says 56 and they all start killing themselves laughing. And he says, what's going on? And one of the prisoners says, oh, it's just that we've told the same joke so many times that now we just remember them all by numbers. So you just say the number and, you know, people remember the joke and laugh. And so this new guy thinks, oh, we'll have a go at that. And he shouts 36. And there's an awkward silence. And his cellmate says, oh, well, it's the way you tell them. But I mean, that's that's the kind of I think that's the kind of thing we're talking about with reference based is sort of, you know, if you have a shared set of information that you can refer to, then, you know, then then then actually it looks like you're simplifying, but you're not. You're just you're really referring to existing information. And I suspect that nearly all information hugely relies on there being a

shared pool of info. And this sort of goes back, I think, yeah, as you were saying, that that third one, I think is pretty ubiquitous side of thought. And that's what they talk about. And for example, of culture. Well, that's what culture is, really. But also when they talk about, you know, culture, you know, animals have their own cultures. And it's essentially learned, you know, it's group learning and goes to different generation anyway.

Well, I just did. So maybe I need to qualify my question slightly. So then if you what I'm trying to get at, is there is there a way of explaining quantum mechanics to a five year old or a three year old in such a way that they can still then advance the science so they still have a working useful knowledge? Because, yeah, you could explain quantum mechanics in such a way that it fit in 100 words and was really simplified, but they wouldn't be sort of in any sort of they don't maybe understand kind of, it's a thing, but they wouldn't have any, they wouldn't have a working knowledge of it sufficient that they could then advance it. I don't think I think quantum.

Why would you want to be explaining quantum mechanics to a five year old?

Well, just say, just assume, just assume that we're trying to do this. Yeah, for some five year old who's joined our research group. And he's about to go into a lab. We don't we can't

go with him. He's got to go into the lab and perform an experiment that's going to potentially change the world. But he has to do it by himself. No, I don't think I actually think quantum mechanics is is not is a good example for one aspect of this, which is a thing that you know, that we don't really there aren't any intuitive analogies. There's very little shared information. I mean, none almost with quantum mechanics, as far as I understand it, which is not very far, but you know, that actually the concepts involved are not ones that have intuitive analogies, you know, that with so it's almost like just a set of, you know, concepts that only relate to one another. You can't really say, okay, well, a quark is a bit like, you know, an apple. Yeah, it just, you know, they don't work like that. I wonder if there's helpful results

of an unfilled terminology, like spin and charge and things you don't actually don't, they are similar or the same as other mechanical process sort of phenomena, but they're not they're

completely different. They don't. So I think I would say that it's a really good example of compression quantum mechanics, because it feels like it probably explains a huge number of things with a small number of concepts. But I reckon the kind of extreme opposite of something like that might be organic chemistry or something where there's just, you know, millions and thousands of different things. Exactly. You know, and that's, I feel like you'd have an easier job explaining quantum mechanics to a five year old because they

don't need as much. Okay, well, let's pick a different example. So explaining quantum mechanics, yeah, they're almost like a whole set of things you need to know mechanics that you need to understand that sit outside of anything else. But what about something like explaining the why the Middle East is so complex, explaining Israel and why it's so sort of complicated to a five year old who's got to make a policy decision about something that will affect Israel. So I mean, that's, yes, you could boil that down to like, one sentence. But you know, that's not useful that that kind of that amount of knowledge is not useful. You need much more detail on top of that to actually make a sort of make contribution. Well, I think I'm not sure you'd kick off with

Palestinians and Israelis and stuff like that. I feel like you'd explain it in terms of someone someone found a ball, then somebody else found the ball later on and somebody else took that ball. That would be a terrible way to explain it. No, but I think if you want to explain it to a five year old, it'd be very difficult to do that in a way that wasn't perhaps importing some some kind of narrative bias. No, but you can't. I mean, look, as a kid, I didn't have a clue what politics was, but I understood what it was like, you know, to be annoyed with someone who had taken your stuff. And I feel like understanding that is probably more of a key to understanding, you know, and the extent to which, you know, two people feel like they have a claim on the same object or the same item or the same piece of land and both feel that those claims are entirely justified. You know, like, that's that's the key. That's the key thing you need to get here. Maybe you are. And I think a kid could understand that. But I mean, obviously, you're reducing information then, aren't you? It's a kind of

information reduction exercise. OK, look, I'm not quite sure where we are. I mean, I don't think we've sort of done anything groundbreaking here. But but one thing to say, I think there's something missing as well, which is it's kind of it's it's the vessel through which this stuff is explained. Right. Because, for example, you might have let's say you've got your flat pack furniture arrived from a certain Swedish store. Yeah. Then, you know, you've got your instructions there. Right. Written instructions. Right. But let's say you want to explain to your kid about the news and what's going on, you know, in Israel, for example, then. Well, it's it's it's it's you. You're effectively a teacher. So, yes, you've got these different modes that you described, Nick, and that might be one way to put it. I just think we're missing that as well. I mean, look, maybe I'm biased. I used to be a teacher. So, you know, and you get good teachers, you get bad teachers. So there's that element of as well. I mean, is that relevant? I don't know. Where are we? What do we what do we want to say? Because we're sort of about two thirds the way through.

Well, I think I reckon I've got a sort of schema that you can apply to ask yourself how how simplifiable is this? So a schema is, but I'm with you. Keep going. It's a simplification. OK, so what's a simplification? So I think a framework and I think actually in general, like, so I'm about to give you a what might what I think is a framework for understanding simplification and frameworks, I would say are, you know, they fall into that category if they're good. And Peter and I are always talking about two by two matrices because they're so ubiquitous in business, you know, business consultancy. I think frameworks are really good if they are lossless, if you like, if they losslessly compress the space of phenomena that they're trying to help you explain. And they're bad if they if they don't carve it up into, you know, informatively different. So in other words, if they don't distinguish between things that they ought to distinguish between. And so I'm about to give you one of these frameworks. Brilliant. Just so I think sort of three questions you can ask yourself about whether can this thing be simplified is, first of all, how predictable are the information is the information you're giving, right? So that's about compressibility. Yeah. How once you've got it going, once you've started the explanation, you know, how, how, how compressible isn't it? If you've got to do the same things 30 times, don't list that out as 30 separate instructions. Just say, do this one thing 30 times, right? Then there's about the utility function. Now, some things I think is probably the issue with a COVID test. Some things absolutely have to be all done. You know, if the COVID test isn't done exactly right in order, then it's worthless, right? So utility function is, is really narrow. You, you either do everything right and it's, and it's useful, or you get one thing wrong and it breaks. But, you know, the extent to which someone can, someone could be more or less, find the information you're giving more or less useful, depending on what you miss out, right? So, so, you know, if it's, if it's yes, there's sort of a falling off of information value that there's, you know, some really important things that they've got to get right, but the rest they can get right. And some of it, well, they could. And then finally, how much shared info is there? And if you, if, you know, if you share a lot of information with that person, then you can, you can obviously simplify a lot more. And thinking back to, you know, my life as a former civil servant, that was really a key. One of the, one of the things that you would, usually the kinds of things people would write, you know, would be, would have too much useless information in. So I'm thinking about sort of ministerial submissions, is they would, they would contain too much useless information, but they also assume much more shared information as well. They would, they would try to rely on things that they assume that the minister would care about or know about, you know, to do with their particular weapons program or something. And actually, you know, you almost always, you'd want to be saying, okay, you've really got to explain all of these things that you think the minister knows about because they don't, they've got no idea. But also, you know, you've got way too much stuff in here, which isn't, you know, doesn't pass the so what test. Okay. I'm sure

that was a really good framework, but I've kind of forgotten which one of the things were.

Informativeness, so predictability, utility, and shared information.

Right. The first, I get third, I get the second, I need to work on a little bit, but let's leave that. Let's leave that. That's fine. I think the other element of this equation, as we talk about is the needs or even the how useless or not the person is that is trying to understand stuff. I think that's, that's, that is, that's kind of, yes, but I think that's subsumed. Yes, exactly.

Yeah. I think that's subsumed. Like if they, if they, if they're really not knowledgeable at all, you're going to have to put in is the what, what's tomato, isn't it, Peter? We have this, we've invented this handy shorthand for people who, you know, where you, you've got to start your explanation several, several chapters earlier, because, you know, they say, well, how did you make this delicious spaghetti bolognese? And you say, well, okay, first, you've got to get your shit, you know, peel your tomatoes, get a water. Yeah. And then they say, what's a tomato? And you're like, oh, okay. Quite a lot of the time, you know, when you're talking to someone about something fairly abstract, you're in a tomato situation where you've got to sort of explain, okay, well, this guy doesn't know what probability is.

So I'm gonna have to start. This is really good, because this leads me onto a question I want to ask. However, before I ask that question, is anything either of you want to sort of wrap up

on? Because I do have a question. But yeah, go Peter. Yeah, I mean, I was maybe we won't get onto it today. Maybe it's another, maybe it's part two. But I was wondering, it got me wondering, what are the limits of human understanding? And it's a thought experiment. So you create an AGI, super intelligent AGI, that's many millions of times more in clever than all the humans put together in one box. And you give it, you give it just the time to go and think about itself, think about the universe by itself for a couple of minutes. And it comes back with what amounts to maybe like a million years worth of human progress in, say, physics or something, and tries and then wants to explain that concept to you. Is it just a question of well, well, you die before it finished explaining it to you? Or is there a way that it could boil that down to something simple that would get the full thing across to you with all the complexities and subtleties?

I reckon there's an answer to this, which is about compressibility. Because you know, you know how there's, there's a kind of famous theorem? Well, it's not even a theorem. It's a really obvious thing, really, which is the pigeonhole principle, which says that you can't have a lossless compression algorithm that works on everything. It's just not possible, because, you know, you never know. Well, essentially, you can't reduce something if you if you imagine, you know, a 10 digit number, trying to reduce that to a five digit number using some purported compression algorithm. Well, there are simply more 10 digit numbers than there are five digit numbers, you know, like 100,000 times more of them. And so the pigeonhole principle says, you know, if you've got 10 pigeons and nine holes, you can't get you can't get all of the pigeons into their own holes. The thing is, there's no, you have to actually know about the thing, you've got to know how what that thing is like, now, it could be the universe is highly compressible. And I feel like the laws of physics have been a process of compression, you know, so we go through the sort of Keplerian laws of motion, which are three things. And then you get to, you know, the Newtonian laws, and then it's like, Okay, well, now it's only one thing that explains the planets and stuff. And then you realize that that fits in with other laws, and you get Einstein simplifying it a bit further. You know, and so I feel like we don't know if we knew the answer to Peter's question, then we'd already have solved it. You know, like, it could be that there's one equation, it might just spit out one equation, and we go like, oh, duh. Or it might be something

really hideously complicated. Well, look, this is getting very close, again, to what I want to ask, which is as follows. Let's see if you think it's a good question or not. What's the most complex thing that you've ever had to explain to someone or some people? But also one that you found difficult, or that you maybe weren't even successful in explaining? What do we reckon to

that? Yeah, I know exactly what that is. Brilliant. Do you want to go first, Peter? Go for it, Peter. Well, people. I still don't get them. They're just too bloody messy and complicated, and I'd like to live as far away from them as possible. And I've failed on a number of occasions. We feel the same, Peter. Let alone, let alone explain why people behave in any particular way to anybody else.

But let's be serious a moment. Why do you think that is, Peter? Because I don't feel the same, and perhaps most people don't feel the same. Why do you think you are like that? I don't know. I

think I'm too obtuse and not empathetic enough. But I don't think that's true. I think when I try, I can be pretty empathetic. Okay. It's just that you just can't rely on people to be predictable

in any kind of way. So yeah, he doesn't like the lack of compressibility in people's behaviour. I don't know. I feel like, certainly as an economist, like people are really, really predictable, like more predictable than they think, especially en masse.

Yeah, but their emotions are, you know, when they get upset about stuff, and then when they take offence to things that you say, they take offence then won't explain why. And then you find out later that there's some thing in their history, in their past. It's like, well, why don't you just tell me that you didn't like what I said, and I'll apologise and I'll learn from it, rather than like hiding it and making it obscure. I feel a little bit like I'm having a conversation with

a robot or something. But also it reminds me of once I was moaning to a mate of mine about the people with whom I worked. And I was going, oh, this person's terrible, and that person's terrible, and this one's terrible as well. And he said, well, look, something that someone once said to me was that, you know, if you think everyone is a wanker, maybe they're not the wankers. Right? And I'm not trying to be rude, Peter, but maybe it's you.

You just called Peter a wanker. We can read between the lines there.

Even I picked up on that phrase.

No. Okay, nice. Nick?

Well, I come across this a lot, actually, which is this problem. Actually, you know, well, the reason our company is called Aleph Insights is, you know, it was named after the short story by Borges, The Aleph, which is about this point in the universe which contains all the other points in the universe in one place. And the reason we chose that is because, you know, basically, the stuff we do is to take lots of problems that people think of as hugely separate. You might be dealing with the future of space travel or, you know, what's going to happen in the Middle East or understanding, you know, a particular armed group or something. And actually, from an analytical point of view, really, they're all explained by the same kind of underlying processes and concepts. And you're like, well, you know, if you want to analyze stuff, you get data and you generate hypotheses and test them, you know, assign probability to the hypotheses of interest. And this affects your decision in the same way. You know, all of those problems really look the same when you understand this. The problem is, it's really hard to get that over to people who haven't been doing it for as long as we have. And I think one of those things is, you know, I find trying to explain how probability works and what it means is really challenging, because actually, it's really sort of quite simple on one level and, you know, in its connection to information theory in the way that data and probability link together and stuff, there's a really nice, sort of quite simple, elegant relationship there. But it's really hard to explain to someone who thinks of probability as something to do with, you know, dice and chance and, you know, randomness. Really hard to kind of, because so many other concepts you've got to dig,

it's a real sort of tomato situation. It's not just like referencing things, you've got to dig out the old references and replace them with the correct one. So yeah, I still haven't found

a really satisfying way of, and I can tell, you know, you can tell when it hasn't worked, because if it has worked, there will be a kind of light bulb moment. And you know, when you're trying to explain something to someone, and there isn't a light bulb moment, you're like, look, I know you're not getting this, because otherwise you'd be like, oh, I see now, I see all this stuff is

actually related. Yeah, yeah, yeah. What's yours, Frase? Well, so my one is a number of years ago, I think my daughter was about three, in the garden, we found a dead bird, okay. And so she said, oh, what, you know, what's going on here? What's this? What's happened to it? Sort of thing. And I felt 100% equipped to answer this question, because one, I used to be a teacher, as I say, and two, I've got a background in theology. So I thought, right, I know exactly what I'm doing here. And also, but I wanted to be careful and like not upset her and that kind of thing. So I didn't want to just say, oh, it's dead, you know, and that's that. And I said, well, you know, this bird has died. But although it's, why I went down this avenue, I do not know. And I said, but like I said, I was just worried about her getting upset. So I said, I started talking about heaven and souls and that kind of stuff. God knows why, because I don't believe in any of that rubbish.

But also, but the particular feature of that bird was that it wasn't in the sky, but on the ground, which is quite unusual for birds.

Well, yes. And not moving. Yeah. Yeah. And anyway, so I got into this quite long, complicated thing. And I could see her getting more and more confused as we were going along. And me thinking, why, why, why, why did I do this? And at the end of all, she's just said, no, I think it's just dead. And so I sort of thought, okay, yes. And I said, yeah, you're right. And so then from then on, and actually I'd already made, you know, mentally, I'd already kind of made this commitment previously, but then I really did. I thought, right, anything else like this in the future, I'm just going to say, I'm just going to tell it as it is. I maybe went too far with that, you know? So I remember one of my sons asking me what happens, you know, when we die. No, I remember asking if he was going to die. And if I was going to die and I'd get, yep, you die. I die. Yep. We all die. At which point he just burst into tears and said, I don't want to be died. But maybe, yeah. So that's sort of my policy now is just like forthright. Brutal honesty. I hope you corrected him on his grammar at that point. I did indeed. Okay, good. Right. We'll stop there. We'll stop there. As always, thanks for listening. If you've got any thoughts or suggestions for topics, you can email us at podcast.alephinsights.com. We'd love to hear from you. If you've enjoyed the podcast, what should people do, Peter?

Make it as simple as possible. They should, they should write us a letter and we'll send them a gift pack that explains how they can subscribe and like the podcast. You said it,

that's it. Thank you as always for listening. I'm Fraser McGruer, being here with Nick Hare and Peter Coghill of Aleph Insights. Until next time, goodbye.