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In this section, we are going to consider the perennial trade-off between simplicity

and complexity.

So we've already made reference to the world being a very complex place.

Now, other things equal, we dislike uncertainty.

If I ask you to describe the world, let's consider, a simple binary choice.

Is the real world, a, nice, simple and easy, or b, big, horrible and complicated.

Well, clearly, it's the latter, that being b.

However, it will be much nicer for us if it was nice, simple and

easy i.e., option a.

So whenever we try to understand the real world around us,

what we would like to try and do is to simplify things as much as possible.

Because there's an inherent appeal for simplicity over complexity.

We like things to be as easy as possible for us to follow and to understand.

So within a sort of learning environment,

we're not necessarily restricted to say statistics.

We could extend this to mathematics, economics,

finance and no doubt I'm sure, many qualitative disciplines as well but

our goal is to try and model the real world.

So what is a model?

Perhaps, many definitions we could offer here.

But a version I like is to say, a model is a deliberate simplification of reality.

Such that we are trying to model some real world phenomenon,

whereby a good model is one which catches the most important features of

the real world and ignores some less important, some trivial details.

So do keep in mind that a model does not equal reality.

However, a good model is one which is very close to reality.

So, the real world, highly complex, we dislike it.

So if we work with a model, we gain simplicity, so we reduce the complexity,

improve the simplicity, as we go from the real world to a model.

But of course, that model is a departure from reality so

we do lose a little bit of realism.

So the question is, is this trade-off acceptable and

how do we sort of resolve this trade-off.

Well, ideally, we would like the benefit i.e., that gain in simplicity to be enough

to offset the slight loss of reality that we inevitably get with a model.

So, as an interesting example, I'll offer you the London tube map.

This is an iconic map, whether or not you've visited London before,

you may well have seen a snapshot of the world famous tube map.

Now arguably, I could have chosen any metro system around the world for

this example.

They will all have similar maps which people use, but

this is the University of London, so let's be London-centric for a moment.

So is this a good model?

Well, let's revisit my definition of a model,

a deliberate simplification of reality.

So is this a good model or a bad model?.

Well, arguably, the answer to this question is, it depends.

It depends who we are and what we wish to use this model for.

Now if you are let's say a tourist visiting London,

I offer this up as an excellent example of a model.

So, what do we see on the tube map?

Well, we see different colors representing the different London underground lines.

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Now if your goal is simply to get from point A to point B, and provided you're

not color blind and can read the station names, this Tube map is excellent for

achieving that simple objective, from point A to point B.

Why?

Because this map offers the need-to-know information for achieving that objective.

It tells you the order of stations on a particular line.

You have the different colors, to distinguish the different lines.

And it also shows the points of intersection,

where you would change from one London underground line, to another.

And frankly, if you're goal is to get from point A to point B,

that's the essential information you need to know.

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Now I know I'm sure how familiar you are with the London underground map but

those different colors do represent different lines.

Let's just pick one of them, the yellow line.

Now this is called the Circle line.

Now I'm sure you all know what a circle is, something like that.

And if you have a look at the London underground map, you will see that the so

called Circle line is in fact a lie, because the line is not a true circle.

Yes, all it does go around in a bit of a loop, but it's not an exact

geometric circle that you would've been familiar with from school maths.

And nonetheless though,

it is a simplification of what we observe in reality.

And you see that loop, and circle seems a reasonable enough name.

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Perhaps to pick another one, the red line.

This is the Central line, passing through really the main part of Central London,

roughly from east to west.

Now if, let's say, you look at the center of the central line,

you will see a straight red line on that London underground map.

And you'll also see, according to the map,

that those stations are equidistant from one another.

The gap from one station to another seems to be exactly the same.

Well, if any of you have been on the London underground line or

any of those lines, I'm sure you can attest

to these tunnels not being dead straight under the streets of London.

Indeed, I often have to hold on to the handrail as the train

meanders through these sort of curved tunnels under the streets.

So the map does not clearly represent those features.

That straight part of the red line there,

the Central line is simply used to simplify reality.

And frankly, if your goal is simply to go from point A to point B, do you

really need to know exactly how that tunnel meanders underneath the streets?

Clearly not.

So in that map, for let's say, a tourist,

someone just visiting London is indeed fit for purpose.

It tells you the essential information that you need to know.

But of course, it is not a perfect representation of the real world.

Indeed, we know those tunnels do sort of move in curves and

there are many bends along the way.

Also not represented on the map would be the depth of those tunnels,

some indeed actually are on ground level, some of them very deep underline.

Indeed they are the black line,

the Northern line I believe is the deepest of the London underground lines.

Now depth is not presented on that map, but frankly

to get from point A to point B you don't need to know that piece of information.

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On the other hand, if you were, let's say, an engineer, you are responsible for

maintaining the tunnel network, maybe doing some repairs to the rails, say.

Think really, that tube map would not be fit for purpose.

You would need to know the exact distance between the stations,

which is typically not equidistant as the map seems to suggest.

You will need to know where the actual access points are,

you will need to know exactly how that tunnel bends around under the streets.

You will need to know the depth information and other things as well.

So depending on who you are and what you need that map for,

you could argue it's a good model, or it's a bad model.

But of course, we know it as this well famous or iconic map, but mainly for

it's use not by those engineers but for sort of the general public, and

tourists visiting London.

So in that sense, I uphold this as a great example of a model.

It retains the most important features that one needs for decision making, i.e.,

how to get from point A to point B and ignores less important details.

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However, it can be a little bit misleading.

So you will also find access through this MOOC course to what I call the real

London underground map which is, in fact, more geographically accurate.

So perhaps as a take away exercise for yourselves is for

you to compare the familiar-looking tube map with those nice,

straight lines, very easy for people to interpret with

the geographically accurate tube map and see a comparison of the two.

Now both are examples of models.

Even the geographically accurate one still omits some information.

For example, the depth of those tunnels,

you can't see those on that geographically accurate representation.

Now perhaps there is a question, an open question to you to consider,

is of those two maps, both are models, they're clearly different models.

One geographically accurate,

the other not, which one of those is the better model?

I'll give it as an open-ended question,

I would perhaps offer maybe a subjective answer here.

Namely, it depends.

There's clearly a trade-off between these two models.

The geographically accurate one has the advantage of being geographically

accurate.

And it's perhaps using that one it's clearer to see

the relative distances between your one point and another and

to perhaps decide on the optimal route in terms of the quickest route to undertake.

Whereas the more familiar looking tube map is geographically inaccurate and

can give very misleading indications as to the distance between stations.

Just as perhaps a simple example of that, if you compare say Edgware Road

station with Marble Arch across these two maps, and judge for

your yourselves what might be the optimal route to take from one point to the other.

I'll give you the answer here.

In fact, the quickest thing to do is to actually walk it.

But these are both models.

There is a trade-off.

Geographically accurate is a good thing but you might see looking at it,

it's a little bit more confusing to use than the more familiar form.

So potentially, we could offer that up as an explanation for why transport for

London, the transport authority here for getting people from A to B through public

transport, opts for that more iconic map than the geographically accurate version.

So I'm not saying these are academic models, but are familiar things,

which really emphasize the point about what a good model should try and

be, namely a deliberate simplification of reality.

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