Two-by-Two Matrices
Can everything be made easier with two questions and four boxes? Fraser, Nick and Peter explore the undying appeal of 2×2 matrices, and ask how they can help us prioritise tasks, classify information and choose an analytical approach.
From the Eisenhower matrix to known unknowns, the team discusses what makes a useful matrix, how to choose its axes and why an empty quadrant can prompt an unexpected insight. They also consider when matrices go wrong, the risks of oversimplification, and why you should never trust a man with a cube. Finally, Nick shares some of his most illustrious matrix moments.
Quote Investigator on the 'Eisenhower Matrix': https://quoteinvestigator.com/2014/05/09/urgent/
Cognitive Engineering episode about personality tests: https://podcast.alephinsights.com/episode/personality-tests/
This podcast uses the following third-party services for analysis:
Podtrac - https://analytics.podtrac.com/privacy-policy-gdrp
Transcript
Hello and welcome to the Cognitive Engineering Podcast brought to you by Aleph Insights and produced by me, Fraser McGruer.
I'm here with Peter Coghill and Nick Hare of Aleph Insights.
On this podcast, we look at a wide range of topics from an analytical viewpoint.
And today we're discussing two by two matrices.
Nick, I can sense the excitement, Excitement just fizzing from your direction.
Tell us.
Go for it.
Speaker B:Well, I feel like you're being ironic, but I love 2x2 matrices and.
And by the end of this podcast, our listeners will too.
They're absolutely awesome.
They are essentially tools for classifying or helping decide which decision to make in all kinds of different contexts.
And they essentially ask you two questions.
Is it A or B?
And then is it C or D?
They are your two.
They are two options for each axis and that puts you into one of four boxes.
And hey, presto, job done.
Speaker A:Yeah.
Speaker B:Right, so do you want to know some famous examples of.
Speaker A:I couldn't want anything more, by the way.
No, I wasn't being ironic at all, because I know you love a 2x2 matrix.
Speaker B:They are so useful.
And I'll give some examples towards the end of two by two matrices that I've created and used.
Speaker A:Brilliant.
Speaker B:Some of which are in use by the government as we speak.
Yeah.
Speaker A:Wow.
Speaker B:Yeah, Okay.
I mean, there's no.
Fine.
There's no finer compliment really for a 2x2 matrix man than to have his 2x2 matrix actually find its way into government guidance.
So classic examples of 2x2 matrices.
I think probably the most famous is the Eisenhower matrix, which is a bit of a misnomer because it's highly disputed whether Eisenhower had anything to do with.
With it at all.
But it is a tool for prioritizing tasks.
And you go to yourself, well, I've got this thing I need to do.
Is it urgent or not urgent?
And is it important or not important?
And that then enables you to decide, well, if it's.
If it's urgent and important, I'll do it.
If it's not urgent but important, I'll schedule it.
If it's urgent but not important, I'll delegate it.
And if it is neither urgent nor important, I just won't do it.
I'll eliminate it from my to do list.
And it's now.
So that's a classic example of, I think quite a good two by two matrix.
Gives you a kind of just a way of structuring your to do list.
And if we just let tasks come at us and we just deal with them using instinct, we're going to probably misprioritize.
This is the kind of thing you can just do quite easily and go, well, I've got these 20 things I need to do.
I'm going to rank them all.
First of all, it quite easy.
Is it urgent or not urgent and is it important or not important?
You're not choosing at this point between the four things.
You're not thinking, what should I do about this?
You are literally just asking a question of each thing which is easy to answer and then you look at the answers and you go, right, now I can see here's my.
There's actually only five in the top, right?
They're the things that I'm going to do now and then I can deal with the other stuff as appropriate, you know.
So that's a classic example of a really useful two by two matrix.
It's easy to put into operation.
It's actually decision relevant.
It's helpful, you know, if you're the kind of person who's constantly besieged by tasks.
Speaker A:Before you go and Nick, I just want to say I really like this.
I'm going to surprise you.
I'm not a big matrix guy, but I wish I were.
Speaker B:Yeah.
Speaker A:And I'm open to this, to being educated.
I can see the benefits immediately.
Right?
Speaker B:Yeah.
Speaker A:And what I love about this is our podcast, right?
The intro that I do analysis and decision making.
Well, boom, here we are right at the heart of it.
Speaker B:So we're in the little bit of.
Speaker A:Decision making process right in the middle.
Speaker B:Of that Venn diagram.
So a few others which people might be familiar with, there's a sort of simplified Myers Briggs 2x2 matrix which is for classifying people.
Well, personality types and the first two letters of the Myers Briggs type indicator.
We have done a episode about the Myers Briggs type indicator.
It's either introversion or extroversion.
Which one of those are you?
And then are you a sensing type or an intuition type or an intuitive type?
And that actually turns out from our, you know, the research we did in the podcast about Myers Briggs turns out to tell you an awful lot about someone.
So it's like, well here, here we've got.
It's not so much a decision support tool, but it's a really good classifying tool because if you, if you know those two things about someone, you can infer quite a lot of other stuff about them.
And I know our listeners are, you know, know they're intelligent people and that's a lot of them will be saying no Myers Briggs is just astrology.
Well, it's not actually, it turns out to be to be quite informative.
So there's that.
We've got the Ansoff matrix, which is about business strategy.
And you say, right, is this market that I'm trying to sell to, does it exist already or is it new?
And the product that I'm trying to sell, is that, does that already exist or is it a new one?
And that then tells you, well, what kind of activity should you be, should you be doing?
Should you be focusing on market penetration, product development, diversification?
There is a bit of a classic the risk matrix, which is widely used.
Impact.
Is it high impact or low impact?
Is it high probability?
Low probability.
And that tells you how scary risk is going to be.
So they're all over the place, two by two matrices.
They have a terrible reputation because consultants like me love them and squeeze them into every available opportunity.
But I think we want to talk about, well, what you know, what, what exactly are they for?
How do they work, how are they, what makes them good?
How do you go about making a two by two matrix?
When should you do it?
Whole bunch of things.
Speaker A:Peter, weigh in on any one of those things.
Speaker C:I'm add my favorite, which is the one that Donald Rumsfeld sort of slightly fumbled.
The known unknowns and the unknown unknowns.
So the two axes are your knowledge of something, you either know it or you don't know it.
And your awareness of that knowledge, your.
Speaker B:Knowledge of the knowledge.
Speaker C:Knowledge of the knowledge.
You're either unaware that you've got the knowledge or you're aware you've got a knowledge.
So you've got known knowns, which are things you obviously know about.
You've got the unknown unknowns, which things you have no idea about at all, not even thought about them at all.
You got the known unknowns, that is the things that you know, you don't know enough about.
So you need to go and find out more about them.
The interesting square I think is the one that he missed out, which is this, the unknown knowns.
So in a big organization there lots of people in it, people might have the answer to something, but you as the sort of the brain of the organization don't necessarily know that you know the answer.
Speaker B:And I think it is a phenomenon that can be said to be true of people at various times as well that you, you sort of think that something's the case and it turns out that you actually know that it's the case that you acquired that information, that belief that you had, you acquired it using, using a reliable method.
And so you can be said to.
But you actually forgot how you found it out, you know, so you kind of have instinct that something is the right answer, but you don't actually know that it's knowledge.
Yeah, yeah, it's a good great one, the Rumsfeld matrix.
Speaker A:Yeah.
Anything more, Peter?
Speaker B:Yeah, Peter must have some other cool ones.
Speaker C:Yeah, the matrix is the one, the war.
So it's slightly overstating.
It didn't, it didn't win the war.
It was a key product of when, during World War II, when radar was new and they needed ways to understand not only the technology, but they were interested in the, the interplay between the operators of the radar and the radar itself.
And it was very difficult to distinguish.
Well, how good is this radar actually when you have to have people operating it?
They came up with a two by two matrix which is the truth matrix.
So where the two states are, the truth states about the world.
Is there a plane or is there not a plane?
And the operator's assessment of the, the screen is yes, there is a plane.
No, there is not a plane.
Speaker A:Okay.
Speaker C:So you can be in the state where you get a hit, which there is a plane.
And the operator says, yes, you get a miss where there is a plane, but the operator says there isn't a plane.
You get a false alarm where there is no plane but the operator says there is.
And you get a correct rejection when the operator says there isn't one and there isn't actually a plane.
So this matrix came out of World War II radar research and has subsequently popped up everywhere.
Speaker B:So it's where we get.
Presumably this is where we get type one and type two.
Speaker C:This is type one and type two error.
So it's all over statistics, it's all over medicine.
It's how.
It's the two by two diagnostic table.
You get it in machine learning.
It's the confusion matrix.
You get it in eyewitness identification.
It's used by police to judge the accuracy of eyewitnesses.
So it's literally everywhere.
But it's not something everyone, everyone's got.
Everyone has an intuitive understanding of it and has probably come across it.
But it's not something that sort of everyone can know where it came from.
Speaker A:Yeah.
Speaker B:And I can imagine people saying, well, it's bloody obvious.
What's the point of turning that into a 2?
Well, because what it does is it reminds you that in these various places you have the same fundamental issue.
You know, how many things do we want in each of these boxes, like what's the right number of type 1 and type 2 errors?
And it turns what might be a thousand specific problems into one, you know, general problem.
And to which we have a sort of a common approach.
Speaker A:I mean, I quite agree.
And what I like about this is, as, you know, as I said, I've never really thought about, you know, 2x2 matrices that much.
And in one sense, yes, intuitively myself and others are using them all the time, but there's actually a real value in being able to know that and label it and understand that you're using a matrix.
But also what I like is, or what's really valuable is what you've said, Pinnick, which is that it's a kind of simplification process.
And it's not a decision making process in itself, but it's a tool to aid that.
Because once you've simplified that information and sort of characterized it, and off the back of that it sounds like there goes your analysis and decision making off the back of a really nice simplification process, essentially.
Speaker B:Have I got it about right?
I mean, shall we, shall we dive into how do you, how do you do it?
Right, so how would you go about creating a two by two matrix?
So first of all, just, you know, what, why would you.
So the whole point of this is, you know, we've got a large number of data points in any given context.
This might be people, it might be people's beliefs, it might be objects, whatever it is, we've got a large number of potential data points.
They have lots and lots of features.
So there's lots of things that are true about a person.
And what we're going to want to do is boil that down to two things, right?
Situations you're in tasks, we want to boil them down to just two questions.
Two kind of, essentially, yes, no questions.
So why would you want to do that?
Well, for obvious reason that it massively saves.
Once you've done that work of designing the matrix, it massively saves you having to do loads of information gathering and analysis and future.
I mean, if you, if it's a good two by two matrix, it tells you what to care about and you don't need to care about the other stuff.
Right, so the work goes into the design of the matrix.
What is that work?
Well, so there's two sort of broad families of approach here which we can think of.
Well, essentially this is the language drawn from machine learning, but feature selection, right, where we have a bunch of features already and we Want to pick the two that are most informative?
What do we mean by informative?
Well, basically, which two kind of spread things out as much as possible.
Right?
Which, which we might sort of think of it intuitively as how can we kind of divide people up in a way that's most predictive of all the other features, like which two questions.
When I are, when I answer those two questions sort of more or less answer the rest of it anyway, that's, that's what we're trying to find out.
And obviously there are statistical methods of doing that.
And there's another approach, which is feature extraction, which one of the most common methods for that is principal component analysis, where instead of using one of the features you've got already, you kind of build several features together into one new feature which you give a name to.
And so things like, say, the political compass, for example, has these two dimensions, which are authoritarianism and libertarianism.
Now, they're not something you can just generally go and ask someone, how libertarian are you?
What you have to do is ask a bunch of instruments, you've got to ask a bunch of questions first.
You know, how, how important is it that government regulates what size people's hedges are, those kinds of things.
And that then gives you an insight into where that you then construct this sort of artificial idea of this guy's a libertarian versus an authoritarian.
And that's your axis.
Right.
So the idea, the fundamental idea here is we want it to be informative ultimately about the decision we're going to make.
Speaker A:Exactly.
Informative about our aim, about the thing.
Speaker B:We're trying to achieve.
Right.
So in other words, which two questions can we ask which will most reliably put this into one of the four, if you like, responses that we have to make.
So, yeah, essentially that is what you should do.
Look at the axes you've got and sort of say, well, which two best correlate with all the other stuff?
Which two are going to give me the most insight into all the other stuff?
There you go, you've got your two axes.
Then another thing you probably are going to have to do is discretization.
So, yeah, a lot, well, a lot of.
A lot of axes are actually continuous.
Speaker A:So is it where.
So I know you're about to explain, but is it how you kind of separate it from the chat?
Speaker B:Are you a tall man or a short man?
Well, that's actually a number.
But if we're trying to think about, you know, if we're trying to design a two by two matrix for tailoring Services.
We might want to just say we've got a tall men's department and a short man's department and we've got to have a cutoff.
So we're going to just define that arbitrary.
And then that gives us one of the four rooms that they're going to go to.
They've got the sort of.
The short extrovert men over here and we've got the tall introvert men.
Speaker C:Loud trousers.
Speaker B:Yeah, the tall introvert men.
They, they want to have something very dark and unobtrusive, you know, so you got, that's, that's.
You got to decide what you mean by those things.
Speaker A:Also, I like the idea of mixing and matching axes as well.
I'm sure that has all sorts of fun results.
I don't know if you see what I'm driving at.
Speaker B:I do, I think.
Well, I mean, of course, if, if, if it's the case that really there are sort of four fundamental types of clothing which are about height and extroversion.
Are they bright and tall?
Tall, yeah.
Are they sure.
Are they dark?
If that's the case.
And I've got no means, I'm not a clothing guy, so I've got no means of telling you that it isn't.
Speaker A:Right.
Speaker B:But if that is the case, then this is a perfect example of where you want a two by two matrix.
Speaker A:Right.
Speaker B:We've got, we've got to classify these things.
We can't have one shop for everyone because then it would be really inefficient.
We'd have dark clothes sitting next to long bright clothes.
And everyone knows that you never run a clothes shop along those lines.
So yeah, you've got to have your two by two matrix.
And so the question is, well, what's the best way to slice this up?
And this, this approach is basically what you do.
Speaker A:Yeah.
I guess at the heart of this is a word that you mentioned there.
We're involved in designing a classification exercise.
Exactly.
That's what we're doing and we're trying to what.
Speaker B:And so you've got it right when the classifications line up, when you carve nature at the joints, as it were, when your classifications then do a lot of other work.
So now I'm not a massive fan of the political compass as it's normally presented, but actually it does.
It is still good for predicting all kinds of other things.
Like if you find out that someone has a lot of respect for the police and that they, but that they also think that, you know, it's really important to, to share Things fairly.
If one person's got a lot of stuff they should share it with other people.
Then that's putting them into the kind of left wing authoritarian camp.
And you might then predict, well, like, you know what they like communism and stuff.
And that means there's a lot of other things they probably wear, probably live in North London.
They probably live in.
They probably wear a colorless grey shirt.
They probably like going on marches.
They almost certainly have facial hair.
If they're a man.
There's.
You can predict a lot of things.
Yeah, people are very, very predictable.
And you know, it turns out that just sticking someone into one of these axes is very informative.
So that's why it works.
It works because it's a good.
Because it work.
It works because you've carved the world up in a way that the world actually is carved up.
Speaker A:Nice.
Peter.
Speaker C:Another.
Another quick selling point that it goes beyond just classification and then automatically giving you a.
What does it.
What to do about it.
It can be a surprise generator.
So it can be so.
And particularly in the count, the counterintuitive corners off on the off diagonal.
So kind of high, high, low, low.
They.
They're often, they're often like no brainers.
What you do in those situations is in the.
When one situation is high and the other is low on the off diagonal, it's often more interesting.
eph lufton Harrington Ingram,:Plots how known to yourself against how known to others.
Certain things about you or that you know are.
So you've got the two dimensions.
Known to self, not known to self, known to others, not known to others.
Speaker B:Like what, what kind of thing?
Speaker C:Well, things like the secrets.
Right.
So a secret is a hidden thing and that's not known to others but known to you.
Speaker B:Right.
Speaker A:So yeah, give us a concrete example.
Speaker C:So note to others what clothes you're wearing.
And known to you.
That's trivial, boring.
Not known to others, not known to anyone.
The mysteries of the world.
Things that you.
None of it.
No one, no one knows.
But then the two.
The interesting corners are the hidden thing, the secrets.
Speaker B:Right.
Speaker C:And the blind spots.
So things that are known to others and not known to you.
The fact that your flies are open, those are the kind of.
Those are the things that are interesting.
Speaker B:I assume it isn't actually generally used to work out whether your flies are open.
What sorts of things do they.
Speaker A:Yeah, give us, give us a specific example.
So I'm still not quite understanding it.
Speaker B:Maybe because maybe you're really annoying in parties.
Speaker C:Yes.
Speaker B:That's kind of got bad breath or something like that.
Speaker C:It's a means of sort of introspection, is if you can put things down on this matrix, then you can't.
Speaker B:Right.
You'd have to ask other people.
Speaker C:Yeah, yeah.
Speaker B:So how does it work?
Speaker C:I don't know.
I've not looked into that.
Speaker A:I mean, I'm still confused, but.
Speaker C:Well, I think.
Speaker A:Should we just leave my confusion there?
Speaker B:I tell you what, we.
I think what we would do is I would.
You would write 10 things you think are true about yourself, I would write 10 things I think are true about you, and then we would find the things that you've written down, but I haven't, and vice versa.
So, you know, you might have written down that you're really excited by butterflies, and I wouldn't know that because you've never told anyone because you're ashamed for some reason.
I don't know why, but you just are.
Whereas I've written down, you know, Fraser is just incredibly annoying to be around.
And you didn't realize that.
Well, that's a useful exercise.
Speaker A:Yeah.
Speaker B:We've learned something about you.
Speaker A:And I can see how it immediately maps out to those four quadrants.
You know, the things I say, but you don't say, the things you say but I don't say, and then the things that both of us say and things that neither are.
Speaker B:And actually, I think.
I think Peter.
Speaker A:But the unknown is the other things that neither of us say.
Speaker B:But anyway, well, well, right, but I mean, but actually, see, Peter said they're the mysteries of the world.
I don't think that's.
They're things that aren't true of you, I think.
I mean, with the best one in the world.
You're not the world's most reliable person, you know that?
I know that.
So Fraser being reliable is in that bottom left hand corner.
Yeah, yeah, I guess, sort of.
Speaker A:Yeah, exactly.
Yeah.
Yeah.
Speaker B:Anyway, but I think Peter's right.
This has now prompted a discussion, and he's absolutely right.
When you create one of these matrices, normally you can populate two or three of the boxes and then you go, well, what's that one?
Yeah.
And like, is there such a thing as a.
As an unknown known?
And that's a really good question.
And then you start going, well, hang on, actually, what would that look like?
Yeah, So I mean, another one that we used an awful lot in the mod and subsequently is, you know, you know, a SWOT analysis.
Speaker A:Yeah, Right.
Speaker B:So you got your strengths Weaknesses, opportunities and threats.
Now it's not always widely known that that's actually secretly a two by two matrix.
And what you're really doing is asking for every feature of your, you know, of what it is you're looking at.
Is it good or bad?
Does it tend to promote the outcomes you want or does it tend to work against them?
And then is it in your control or out of your control gives you the other thing?
So that if it's positive but out of your control, it's an opportunity.
You know, if it's.
If it's in your control and it's negative, then it's a weakness.
So you've got.
And that's a really good.
But then, you know, actually just being able to ask those questions, you then start thinking, well, actually I'm.
It's really easy to come up loads of strengths.
It's really easy to come up with loads of threats.
But then you start going, well, actually, what are the things that are in my control but are actually bad for me?
I wouldn't have maybe thought about doing that, you know, but now I've got this box I need to fill in.
Speaker A:Yeah.
So yeah, okay.
Speaker B:Man, I love two by two.
Yeah, I don't know if that's coming over.
Yeah, yeah.
Speaker A:And you know, I'm rapidly being drawn into your cult.
I like this something.
I think we want to move on to Peter.
I've noticed it down wrong, but four by three, the magic number.
Am I onto something here?
Speaker B:Well, Peter's 4 by 3 by 7.
Speaker C:Matrix, obviously I want to stretch it and try, you know, what else can we do?
You know, can we make.
Can can we go beyond the four boxes that we have?
Speaker A:Let's do a matrix, see if we can.
Speaker B:I would say no, but Peter's about to prove that we can.
Speaker C:Yeah, no, I'm about to say that you probably can't.
So it relates.
This relates.
It relates to Conwyn's magic number.
So famously you can only hold seven things in your head is apparently a real limit.
Okay, it's not actually.
That's kind of like a very much an upper bound.
It's actually more like four or five things.
Speaker A:Some of us.
It's about time.
What did you call it?
Speaker B:Conlon's magic number.
Speaker C:Conwan Ko Wan's magic number.
Speaker B:Oh, it's not.
It's George Miller, magic number seven, plus or minus two.
Speaker C:Okay.
Yeah.
He's another guy from:Behavioral and brain science.
Speaker B:Lying bastard.
This is from the: Speaker C:He's next.
Yeah, yeah, yeah.
Magic number seven.
Yeah, but actually Ko Wang builds on that, so.
No, actually it's more like four.
Speaker B:Ah, he must be a matrix guy.
Speaker C:He's a matrix guy.
Speaker A:Well, tell us, tell us more.
Speaker C:Yeah, so your, your kind of working memory can only really hold four according to Conwan and he four complex concepts at once.
You can probably hold more similar simple things.
So maybe you can hold seven short numbers or seven colors in your head.
But as soon as the numbers get too long or the thoughts, the ideas that represent your categories get too big, 4 becomes a sort of natural, natural limit.
Speaker B:I'm absolutely buying it and not least because I think, and it's something that we discuss a lot, your visual images, your visual cortex is basically two dimensional.
Speaker C:Yeah.
Speaker A:So how does this feed into what we're talking about?
Speaker C:So what this means, what this means is that the 2x2 is kind of already simple though it is a bit of an upper bound.
So I mean it would be tempting to do a couple of things but it tends to say, well, why not make it a three by three?
Why not have like this sort of middle layer?
What that ends up being though is a sort of an excuse to just park things in the middle layer because you're too lazy or don't want to make a black and white call about the extremes on things.
So it often gets overpopulated.
So it kind of, it loses its value.
Speaker A:Yeah, I mean I can visualize a two by two matrix quite easily and I feel that I can work with that.
Three by three or whatever, you know, anything more than, you know, I start to go, oh my God, there's quite a lot going on.
Speaker B:Nearly 10.
That's nearly double digits in terms of the number of boxes.
Speaker A:Yeah.
Speaker B:Your brain as we know.
Speaker A:Yeah.
One I can use if that's on a good day.
Speaker B:Yeah.
You know, I think, I think and I think this is the, this is, this is where if, if you start feeling that pull that temptation to start adding boxes, it could be a sign that your problem is wrong.
For a two by two matrix.
Now I have a, I've got a, I've got a checklist.
You can ask yourself to find out whether or not your problem is amenable to it.
Speaker C:Can we?
Yeah.
So another way you might be to expand it is to add a third dimension to have a two by two by two.
So you could represent three continuum of decision.
Now we've talked about why you can't do that with your brain capacity.
But also you start running into problems of display technology.
You can't Your paper in front of you is two dimensional.
And to have two try to spread it out onto two dimensions would just be messy and become more complicated.
Speaker A:But also, I mean, I'm not whatever the academic area is that does this stuff.
I don't know if it's math, philosophy, I mean, who knows?
But you don't need a two by two by two.
You could just do a two by two and then do another two.
Speaker B:It's.
Exactly.
Which is equivalent to it.
Speaker C:This is equivalent.
Speaker B:Yeah.
Speaker A:But you're maintaining that simplification simple process.
Speaker B:There's also actually his a bit of a secret rule which your listeners might want to take account of.
If you meet someone, anyone who's some sort of analyst or thinker, and they start telling you about something they've come up with and it's a cube, get the hell out of town.
Speaker A:Oh, really?
Speaker B:Yeah.
They're a crank.
Speaker C:Yeah.
Speaker B:Any cranks love cubes?
Speaker C:Yeah.
Speaker B:Right now, I mean, secretly I've got some cubes that I'm working on, but I will never tell anyone else about them.
Yeah.
Cubes are the sign of an analytical crank.
Speaker A:Just to say at one level I know what a cube is.
Speaker B:Yeah.
Speaker A:On another level I don't.
What are you talking about?
What's a cube?
Speaker B:Well, a 2x2x2 matrix is a cube with eight little sub boxes.
Speaker A:Yeah, yeah, yeah.
Speaker C:Okay.
Okay.
Speaker A:So steer clear of those guys.
Speaker B:Yeah, yeah, yeah.
The cube men.
Stick with two dimensions and you're gonna.
You're on solid ground.
Yeah, yeah.
Speaker A:Is there anything to round off what you're saying, Peter?
Speaker C:So, yeah, your visual field and your display technology just doesn't support it very well.
You can't manipulate a 3D object on screen very easily and you haven't got enough, you haven't got enough slots in your brain to hold eight things quite.
So stick with two.
Speaker B:Yeah.
Speaker A:Good.
I want to come in with Nick just before I do, as is always the case.
There's so much here that sort of reminded me of other sort of podcasts we've done and other episodes.
It makes me think of that beautiful episode we did on models.
Because models, as we talked about, I think is a kind of a simplification process.
Right.
To help you understand the world and, you know, decisions sort of.
Right.
It also makes me think about, you know, extrapolation we talked about in chess.
Okay.
And you know, restrictions that we have and holding stuff in our head, holding information, knowledge in our head.
It sounds there's some sort of overlap there as well, I feel.
Speaker B:Yeah.
Well, well, I mean, one of the ways I think we probably characterized models, which is absolutely the correct way of characterizing them or a way of characterizing them is as compression.
Yeah, that is the, this process of identifying two axes out of all of your potential features that you could use, this process of picking your 2 is basically compression.
And the idea of saying, well, okay, which two questions can I ask of this person that will enable me to predict whether they've got a dog or a cat merely by finding out whether they like whether they have respect for military personnel?
That's compression.
Because it turns out people and their beliefs are quite compressible.
Mine aren't, but most people's are.
And if you've done that compression properly, then you literally.
This is a model.
It's a model which nevertheless gives you the same amount of information as something with 100 features, you know, because it turns out those features are compressible.
Which brings me on to Peter's talked about some potential consultancy failure modes and I've certainly seen that.
Speaker A:Great.
Okay, so look, we're most of the way through this.
We're sort of steering our way towards the end here.
Okay, let's sort of move.
Yeah, help us move towards that conclusion.
It sounds like you're about to talk about failings that there can be.
And when matrices go wrong, is that where you're edging towards?
Speaker B:I would say, I mean, so if you put together your matrix and you find yourself tempted to add a third box, God forbid.
Speaker C:Or a null bucket.
Speaker B:A null bucket.
Or a third dimension or some other extra thing.
Oh, I tell you what, let's have color coding as well.
We'll write some of these in red and some of the.
But no, no, no, that's another dimension.
Stop doing that.
You're only allowed two dimensions.
Right, but it might be a sign not that you're not doing a good job, but that the problem is not amenable to a two by two matrix.
Speaker A:Okay, well, let's talk about that.
Are there some problems, issues that are not amenable to two by two matrices?
Speaker B:Well, and so basically I've got a two by two matrix to help you decide whether or not your problem is amenable to a two by two matrix?
Right.
So the first one is quite straightforward, really.
Discrete versus continuous.
So what we want is things that are categorizable where there's meaningful categories.
You know, authoritarian versus libertarian.
Some people are in the middle, there's no doubt about it.
But it's a meaningful difference.
It's not just a number like between 0 and 10.
Similarly, if the reason you're using this thing is to inform a level of something like how much should I spend on something, how much should I care about something?
It's not going to be as useful to try and turn it into a matrix.
The whole point of this is you've got a small number of decision like categorically distinct decisions to make.
Do I do it now?
Do I delegate it?
Do I.
You know, and so that's the first thing is, is your problem kind of discreet?
Like is, are the features that you're looking at and the decisions you've got to make sort of discrete and category categorizable or are they all sort of continual where there's no natural break points?
So it needs to be discreet.
And secondly, really it's about actually compressibility.
So is it true that these features are compressible?
So are a lot of the things you're looking at kind of correlated?
So what you're looking for is.
Well a lot of these features are correlated with each other.
So you know, either I can kind of create my own feature which captures that or I can just pick one which seems to do that job already, you know, so is it.
So that's my, that's, you know what I.
Speaker C:In stats big.
Is it amenable to principal components?
Speaker B:Yeah, kind of thing.
Exactly.
Speaker A:Is it?
Speaker B:Well, or at least how much information do you get if you were to line your, line up your features in terms of informativeness, do the first two do a lot of the work.
If the information is spread out, if the things are very complex and can't easily be described with two dimensions, it's not going to work.
Speaker A:So can you give me an example where it's not going to work?
Speaker B:Yeah.
Speaker C:So something like how much time should I spend thinking about this particular purchase?
Speaker B:That's an example of a kind of discrete, sorry a continuous variable, an example of a data set or a problem space which is probably not very compressible into two dimensions.
We'll be something like types of food.
Right.
Food has a lot of features and they are compressible but they're not going to be compressible into two dimensions.
Which is why, you know, when you get things like the food pyramid, it's kind of not, it's not a nice two by two matrix.
It'd be nice to have high fat, low fat, green, non green or something.
But food is just got, you know, like dairy food for example has a whole bunch of categories which it sort of shares a little bit with carbohydrates and shares a little bit with fats and you know, so, so like types of food just don't, are not compressible to two dimensions, by and large.
So that's the, that's the, that's an example of a problem space where if you tried to do that, you'd be missing information that you really need to inform your decision.
Right.
So there we are.
Speaker A:Yeah.
Speaker B:So you want, you want kind of categorizable problem space and you want the information to be highly concentrated in a small number of features.
So it needs to be compressible.
Speaker A:And again, but the, the, that's the kind of thing where to make it valid as a two by two matrix.
If you're talking about food, it depends on the, the information that you're looking to get out of it at the end, right?
Speaker B:Ultimately, yes, asking the right questions.
If it is simply what, for example, what, what.
I'm on a diet and I want to kind of be satisfied and have, you know, not eat that many calories.
You might do kind of high calorie foods, low calorie foods, and you might do satisfying foods and unsatisfying foods and you might put spinach in the bottom.
Right.
That might be unsatisfying and low calorie.
And what you want to do is find out, well, what things are in that highly satisfying low calorie box.
And it might be things like, I don't know, porridge, eggs, that kind of stuff.
Yeah.
You know, so, so that's.
If it's, if it's like, actually you've only got kind of one decision to make.
That's, that's great.
But generally when it comes to, so what we, what we're trying to categorize foods for, it's going to be, it's going to be a problem.
The kinds of decisions you're gonna have to make are more complex than just, you know.
Speaker A:Yeah.
And this will aid you making the right decision for the right reasons.
Yeah, that's it.
Yeah.
Okay, look, we need to, we could.
Speaker B:Now do a tour through the other boxes, but I'm not gonna.
Yeah, that's left as an exercise for the reader.
So, you know, if you have, well, they're highly compressible, but they are, you know, irreducibly continuous, then what you want is a heat map, for example, that's, then you're gonna get a nice, a nice heat map.
Various.
I mean, the bmi, you know, height and weight is a really good example of a.
We don't just have Fat, thin, tall, short.
It makes much more sense.
It's highly compressible.
Tells you a lot about someone and what health problems they're gonna have.
But it's not really reducible to categories, so we have to leave them as continuous axes.
But.
Yeah, so that's an example of where you, you know, you're.
Yeah, yeah.
And so on.
Speaker A:As much as we love them and notice I say we 2x2 matrices are not the only game in town.
Speaker B:They're not the only game in town.
Speaker C:But they're.
Speaker B:But they're.
Speaker A:But they're great game.
Speaker B:When they're good, they're really good.
Speaker A:Okay.
So talking about when they're good and when they're really, really good and when they're bad, they're horrid.
But we need to sort of more or less draw to conclusion.
I think a great way to do that might be some of your proudest moments in matrices formulation.
Speaker B:I've left behind me in my professional life a trail of two by two matrices.
Speaker A:Yeah, yeah.
Speaker B:I've scattered it like Johnny Appleseed.
Speaker A:Yeah.
Speaker B:Through the world of analysis, scattering two by two matrices behind me.
Speaker A:Yeah, I know, Quite.
So let's.
This feels like a good note on which to finish.
Speaker B:Right, Peter, have you got some as well you'd like to.
No, none that spring to mind.
Speaker C:None that spring to mind.
No, Nothing original to me that I can remember.
Speaker B:I think Peter's.
I think Peter's being modest.
Speaker A:Yes, exactly.
Speaker C:I'm being forgetful.
Speaker B:Yeah.
Speaker C:Is more accurate.
Speaker B:Right, because.
Because you're modest, whereas I'm massively egocentric and I've remembered all.
Exactly.
Speaker A:Well, look, we've had to turn it to postage.
Speaker B:Yeah.
Speaker C:And you hand them out a party.
Speaker B:I certainly do.
Speaker A:Yeah.
Well, let's sort of.
As much as I would want to hear all of them.
Yeah, let's hear two or three of them, perhaps, and.
Yeah, go for it.
Tell us.
Speaker B:So I think one of my reasons, one of my recent successes, and I actually did put this on Facebook quite a long time ago.
,:It was after the Brexit vote.
And this is, this goes back to my slight issue with the, with the, with the political compass, because the political compass has, has authoritarianism and libertarianism as one of its axes and it has economic left, economic right as another axis.
Speaker A:Now I can see why with this break.
This would break down that matrix for Brexit.
I think I know where you're going with this.
Speaker B:Go for it.
So I would like.
I'm broadly happy with the economic one.
I think essentially that's capitalist versus socialist.
I would say sort of like do we think the state should manage the distribution of resources or not?
And how much?
Like if you just think, well no, where should a minimal state, not taxing anyone, shouldn't be any welfare state.
You're on the extreme capitalist end versus the socialist end, which is like, well yeah, we all need to just.
We should have 95% tax rates and a very extensive welfare state.
I'm happy with that.
That's kind of the economic left right wing.
But I think a better axis for libertarianism versus authoritarianism is actually order versus progress.
And see the problem here is that libertarianism interferes with economic left right because economic left right is very closely correlated with how free you think people should be from government interference.
Whereas order versus progress is more about do we need to be changing?
Right.
So now actually, and here you actually end up with a much more informative model of the modern political landscape, which I think in a lot of ways has sort of prefigured the big political changes we've seen.
So for example, this gives you two boxes for where we would have just thought, well they're all the Tories, for example.
But actually there's a big difference between the kind of businessy libertarian Tories, the kind of David Cameron types and the old fashioned sort of, you know, conservatives, the Alf Garnet types.
And it's the Alf Garnet types who have been, you know, reasserting their voice in politics and in fact have common cause with the old fashioned sort of, you know, left wing order.
Speaker C:They can do a deal.
Speaker B:Traditional working class.
Speaker A:Yeah, exactly.
Speaker B:And so I was quite pleased with that, as I said.
Speaker A:Well, I love, you know, I like that one, Nick.
And because what I like about it, I'm starting to see the truth, which I really knew there was truth there of if what I like about is how your two axes are just so different from one another.
Yeah, right.
And they offer that sort of, that, that sort of sufficient distance from one another which in its.
Which then offers clarity from a new perspective.
Speaker B:That's right.
I mean if, if your two axes.
We didn't really talk about it.
If your two axes are actually themselves highly correlated, what you want, what you've got is a one by one matrix.
Yes, we've really got, or rather a two by one matrix.
You know, you've got a continuum, you just got a line, you can put things on.
A line.
Speaker A:Yeah, yeah.
Speaker B:All of your data kind of forms a line and that's boring, obviously, too easy.
Give us another right I suppose this is the one that has had the most impact, probably.
But my question analysis matrix for analyzing a question, in comes a question.
Here it comes.
Fraser, you ask two questions about that question.
Don't worry, it's not going to keep spawning questions.
There's only two.
Is it about the present or is it about the future?
That's easy.
Is it open or closed?
Is it a yes, no question, or is it a what, who, how kind of question?
Right.
And with those two, you then immediately have a whole family of analytical approaches that you can then just draw down.
So, for example, if you have a close.
Is this the case now?
You're going to use a whole load of, you're going to gather information, you're going to analyze stuff.
You're not.
There's not a great deal of uncertainty.
You only have to worry about measurement, uncertainty.
It really becomes an act of measurement and inference.
But if I said, well, how might Russia respond to the death of Vladimir Putin?
Well, now you've got to do a whole different bunch of stuff.
You've got to think of potential scenarios.
There's lots of potential answers out there.
It's not a yes, no question.
And then you've got to, for each of those, you've got to start building, for example, in the case of something you're looking at in the future, you've got to start building a kind of timeline and looking for indicators and building a model of the evolution of the world.
So they're totally different sets of facts, but actually the analytical process you would use for each of those quadrants is pretty similar.
So, you know, if you've got a closed future question, actually, all of those are similar approaches.
Speaker A:So give us a very specific example then of, you know, a question.
I know there was one in there.
Speaker B:But will North Korea conduct a nuclear test in the next three months?
And so that's a yes, no question.
So you can start by saying, well, let's, let's assume they do.
Speaker A:And we're not analyzing the answer to that question, we're analyzing the question itself.
Speaker B:We would go, what analytical method should we use to answer that question?
Speaker A:So give us the four quadrant.
Give us the two axes and future and present.
Speaker B:Closed.
Speaker A:Future and present.
Open and closed.
Speaker B:Okay, so we've got, will North Korea conduct a nuclear test in the next three months?
It's future.
Speaker A:Yeah.
Speaker B:And it's closed because it's a yes, no question.
Speaker A:Yeah.
Speaker B:So then you've got a bunch of scenario evaluation methods which you can then say.
So that.
Anyway, that is in government Analysis guidance.
And I can.
This.
The process of designing that was kind of different.
I mean, I had about 10 different little sub questions and I started out with a big, you know, flowchart like, is it this?
Is it that?
And it was really complicated.
And gradually I kind of boiled it down and boiled it down until I thought, well, I've got.
I've got these two axes and they are, they are open and closed.
That was a big one.
And then they were factual and counterfactual.
And my friend Matt Jolly at Government Analysis Legend came in and I said to him, I think I've got this thing.
I think it might be useful.
I think this kind of does quite a good job of it.
And he said, counts factual, counterfactual.
I'll have to.
That'll be really complicated to explain.
And I told him what it was and he said, well, it's basically, it's present versus future.
Yeah, brilliant job done.
And, you know, and it was like a Friday.
Took me a Friday to do that.
And when it was done, and I hope that our listeners, when they go about designing their little two by two matrices, which I hope will now happen, they will get the same sense of this works.
Speaker A:Yeah, yeah, yeah, yeah.
I think, I mean, we'll draw to a conclusion there.
But I think that's where this gets really interesting, I think, and I think it's a very interesting creative exercise, endeavor in, in formulating these.
Speaker B:There's a reason I love them so much.
Speaker A:Yeah, yeah, I can see why it sparks your brain.
And, you know, I, I tell you what, I feel like I've not been converted.
Right.
Because I was ready for this.
This is what I've been looking for,.
Speaker B:You know, all your life.
Speaker A:Exactly.
And here it is.
You've sort of, you've, you've laid it forth.
Speaker B:I would love, I would love to hear about.
Because I feel like, you know, particularly you and me, Fraser, have a tendency to sort of dissolve a little bit, to be a bit overwhelmed by things to have.
And these kinds of things are really, really handy.
Speaker A:Yeah.
Speaker B:And, oh, I've got.
I've got, you know, these seven things I need to do to my house.
What am I going to do next?
Well, let's, you know, how can I classify them?
Speaker A:Yeah, well, yeah, it's a lovely simplification of inputs and, you know, I feel this, I can feel it already bubbling away that my life is changing as we speak.
So, yes, not just me, but all.
Speaker B:Our listeners as well.
Yeah, hopefully.
Speaker A:Yeah, yeah, great.
Okay.
All right, we'll stop there.
We'll wrap up there.
So you've been listening to the Cognitive Engineering Podcast brought to you by Aleph Insights and produced by me, Fraser McGruer.
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