Problem Statements

You've probably all had some problem you've worked at. And you keep going at it, and you keep going at it... Nothing seems to work. You go away. Suddenly, the next day you think, 'What problem? It's easy!' It's something I said I've certainly had, and I'm sure you've encountered. And psychologists and other people studying creativity have looked at these kind of issues – why it is that we get to these impasses and how it is that we break out of them.

*Fixation* is one of the keywords that psychologists use here: the way in which when you start to deal with a problem, you have some sort of approach, some sort of way of dealing with it, and it's incredibly hard to stop just continuing with that same way. Once you've got that original idea, that original approach, it's very hard to go to a new one. And sometimes – you know – an approach that might work for one problem doesn't work for

another, but of course if you're stuck in that approach, you can't try other ones. This can get worse depending on how you encounter the problem. And this is sometimes used in sort of trick questions to get you thinking down the wrong track and then it's very hard to get down the right one. And this is sometimes called – if I can say it right! – the *Einstellung effect* which is about being fixed in a position.

These guys called Luchins and Luchins back – I think – in the 1940s did experiments with water jars. And you've probably seen this sort of puzzle. You've got a number of jars, and the idea is they're different sizes and you're trying to get, say... two pints of water and you've got a 17-pint jug and a 3-pint jug and you've got to pour water back and forth. And there sometimes are really complicated solutions where you have to like fill one up from another, and then what's left in this one is some nice magic amount.

So, if you've got a 3-liter jug and a 7-liter jug and you fill the 7-liter one and you pour it into the 3-liter jug and then throw the three liters away, you've got four liters in your 7-liter jug. And you have these complex solutions. So, what Luchins and Luchins did was they gave people a number of examples which they worked through which required that kind of complex solution. And then they gave them four more. But the four more they gave them were ones where you could actually solve it very, very simply. You know – possibly just filling up two and pouring them into another.

So, some subjects were given that; some were just given the four easy problems. The ones who were just given the four easy problems solved it in the easy way. The ones who *started off with the complex ones applied the same complex heuristics* to the easier problems and took *much longer* to do it. So, they got so stuck in their ways having been introduced to this set of problems. One that I encountered myself, and this gives you an opportunity to laugh at me if you want to,

because you'll probably, most of you I'm guessing might find this easy, but I was in university and I was once given this puzzle. And the puzzle starts off – and there is this stage where you're driven down the wrong path – anyway, so I'm giving you a hint by telling you that. So, you often get these puzzles where you're supposed to chop things up into identical pieces. So, I've got a square up there, and obviously you can chop a square into four identical

smaller squares. Or you can chop it into four triangles. So, the triangles are all the same shape as each other, the same size as each other. In mathematical terms, they are *congruent to* each other. But they're not necessarily squares. I've got some triangles, and we can chop the triangles into four; they're different kinds of triangles in different ways. And on the right I've got one of the ones you sometimes see as a trick puzzle in books; and – or sometimes actually cut out pieces as a sort of trivia-type puzzle.

And the idea there is to have four pieces that will make up that 'L' shape. And certainly there may be other ways of doing it, but the way I've always seen is with these four pieces like that. So, they're all 'L' shapes themselves and they fit together. How about cutting things into three? Well, obviously, the 'L' shape is an easy one, and things that start off with three degrees of similarity like a triangle or hexagon are relatively straightforward.

So, the crucial question is, can you chop a square into three pieces that are congruent with one another? Not all squares, but some shape – they could be triangular; they could be more complex – that are each identical. Can you do it? Now, my guess is you've probably already thought of how to do it and you'll be right. It took me three days to solve this because I was a mathematician and the whole thing was framed in geometry, mathematics,

and I was trying to apply really complex mathematics. And despite numerous hints, it took me three days to solve this. If you haven't solved it, you're probably a budding mathematician. So, *fixation is a problem*. There's also – fixation is more about the methods you use to apply things, but there's also *bias* – when you *evaluate* things. When we look at them, we have tendencies to see things in one way or another. And that's about all sorts of things.

That can be about serious personal issues. It can be about trivial things. Often, the way in which something is *framed* to us can actually create a *bias* as well. A classic example, and there are various ways you can do this, is what's called *anchoring*. So... if we're asked something and given something that *suggests a value* even if it's told that it's just there for guesswork purposes or something,

it tends to hold us and move where we see our estimate. So, you ask somebody, 'How high is the Eiffel Tower?' You might have a vague idea that it's big, but you probably don't know exactly how high. You might ask one set of people and give them a scale and say, 'Put it on this scale. Just draw a cross where you think on this scale, from 250 meters high to 2,500 meters high, how high on that scale? And people put crosses on the scale – you can see where they were, or put a number.

But alternatively, you might give people, instead of having a scale of 250 meters to 2,500 meters, you might give them a scale between 50 meters and 500 meters. Now, actually the Eiffel Tower falls on both of those scales: the actual height's around 300 meters. But what you find is people don't know the answer; given the larger, higher scale, they will tend to put something that is larger and higher even though they're told it's just a scale.

And, actually, on the larger scale it should be right at the bottom. Here it should be about two thirds of the way up the scale. But what happens is – by framing it with big numbers, people tend to guess a bigger number. If you frame it with smaller numbers, people guess a smaller number. *They're anchored by the nature of the way the question is posed.* So, how might you get away from some of this fixation? We'll talk about some other things later, other ways later. But one of the ways to actually break some of these biases and fixations is to

*deliberately mix things up*. So, what you might do is, say you're given the problem of building the Eiffel Tower. And the Eiffel Tower I said is about 300 meters tall, so about a thousand feet tall. So, you might think, 'Oh crumbs! How are we going to build this?' So, one thing you might do is say, 'Imagine, instead of being 300 meters tall, it was just *three* meters tall. How would I go about building it, then?' And you might think, 'Well, I'd build a big, perhaps a scaffolding or 30 meters tall.

I might build a scaffolding and just hoist things up to the top.' So, then you say, 'Well, OK, can I build a scaffolding at 300 meters? Does that make sense?' Alternatively, you might, say, perhaps it's *300,000 miles tall* – basically reaching as high as the Moon. How might you build that now? Well, there's no way you're going to hoist things up a scaffold – all the workers at the top would have no oxygen because they'd be above the atmosphere. So, you might then think about hoisting it up from the bottom, building it,

building the top first, hoisting the whole thing up, building the next layer, hoisting the whole thing up, building the next layer. You know... like jacking a car and then sticking bits underneath. So, *by just thinking of a completely different scale*, you start to think of *different kinds* of *solutions*. It forces you out of that fixation. You might *just swap things around*. I mean, this works quite well if you're worried about – that you're using some sort of racial or gender bias;

you just swap the genders of the people involved in a story or swap their ethnic background, and often the way you look at the story differently might tell you something about some of the biases you bring to it. In politics, if you hear a statement from a politician and you either react positively or negatively to it, it might be worth just thinking what you'd imagine if that statement came to the mouth of another politician that was of different persuasion; how would you read it then? And it's not that you change your views drastically by doing this, but it helps you to

perhaps expose why you view these things differently, and some of that might be valid reasons; sometimes you might think, 'Actually, I need to rethink some of the ways I'm working.'

The big question – *why design with data?* There are a number of benefits, though,  to quantitative methods. We can get a better understanding of our design issues  because it's a different way of looking at the issues. So, different perspectives  often lead to better understanding. If you're working in project teams or within  organizations who really don't have

a good understanding of *qualitative methods*, being able to supplement those with quantitative research is very important. You might be in a big organization  that's very technology-focused. You might just be in a little team that's technology-focused,  or you might just be working with a developer who just doesn't get qualitative research. So,  in all of these cases, big, small and in between, having different tools in your bag is  going to be really, really important. We can get greater confidence in our  design decisions.

Overall, that means that we are making much more *persuasive  justifications* for design choices.