WHEN IS REASONING VISUAL? GEORGE STINY MIT Abstract. How to stop counting and start seeing. My line of thought I’d like to take a stab at the following question from the point of view of someone who thinks about design. I’m mostly interested in how I can come up with something new when I calculate with shapes. How creative can I possibly be if I use rules? Am I any more creative if I don’t? I won’t say anything else about this, but keep it in mind. My question right now has to do with seeing: (1) When is reasoning visual? That I come from MIT where the motto is ‘Minds and Hands’ — I’m told this means theory and practice — may put me at something of a disadvantage when it comes to original thinking about minds and eyes. Anyone who has seen MIT knows instantly that no one there pays much attention to how things look, even with a distinguished architectural tradition including Aalto and today Siza, Maki, Gehry, and Correa. MIT is not a visual place. I’m going to try and see anyway. I’m not daring enough to attack question (1) directly. My first thought was to tackle two additional questions and to take a route through their answers that appeared to me more clearly marked: (2) When is calculating visual? (3) Does reasoning include calculating? If the answer to question (3) is a solid yes and I can answer question (2), then I can use visual calculating as a working model to understand visual reasoning. This is reasoning by inference — from the properties of a part to the properties of the whole. And this is how everything is related 1G. STINY ��������� ���������������� ���������� ����������� ����������� if it all fits together the way it’s supposed to. But the longer I looked at my neat little diagram — is this visual reasoning? — the more I thought about which way the inclusions should go. Maybe the relationships are really like this ���������������� ����������� ������������������ ��������� so that reasoning and calculating are merely special cases of visual reasoning and visual calculating. In fact, I’m sure each of my diagrams is correct in its own way, and have already established the underlying equivalencies for calculating by counting and alternatively by seeing. (Counting is the standard model. I’ll return to the idea that calculating is normative later on.) Some of you may be familiar with the details. They involve the algebras of shapes Ui j U0 0 U0 1 U0 2 U0 3 U1 1 U1 2 U1 3 U2 2 U2 3 U3 3 and whether basic elements in shapes are points with dimension i = 0, or lines, planes, or solids with dimension i > 0. And then there are a number of technical devices including, for example, analytic descriptions of basic elements and their boundaries, canonical representations of shapes using maximal elements, and reduction rules to compare shapes and combine them. But right now, I’d like to take a more leisurely, conversational approach. There’s no reason to insist on rigor in Bellagio on Lake Como in the summer. 2WHEN IS REASONING VISUAL First I show that calculating is part of reasoning, and then by analogy — how many kinds of reasoning are there anyway? — conclude that visual calculating is part of visual reasoning. And I go on to present some of the evidence I’ve found for visual calculating. My plan is the same. What I glean from visual calculating will tell me what I need to know about visual reasoning. This is a discursive process that runs by logic or desultory rambling. I’m not too fond of logic and avoid it if I can. So I’m apt to ramble aimlessly. Roaming around to see what’s what is a more effective way (procedure) to get new and useful results. But the ambiguity of this process — sometimes logic and sometimes not — isn’t wasted. It shows better than anything I can say why visual calculating and so reasoning are important. They’re the only way I know to deal with ambiguity and novelty, and not give up on calculating as a creative part of thought. This is the key if calculating is to model visual reasoning. Some of you may have already decided that my line of thought is only engineering. It may be practical to use models and the like, but it’s unlikely to lead to fresh insights of the kind you have come to hear. I won’t argue that I’m not doing engineering. I’m more confident about calculating than I ever will be about reasoning. I can point to examples of calculating — including one or two of my own invention — but I’m never sure about reasoning. My own reasoning when it goes beyond calculating is as suspect as any. If I think I’ve got a really good argument, someone soon comes along and pokes holes in it. And it’s the same if I try to follow the reasoning of others. I go from thinking I’m thinking to thinking I’m not. This is the sort of abstruse game philosophers like to play. It’s hard, and it goes on and on forever. I’m no philosopher. I’m a lot happier with the more accessible pleasures of engineering. I like to calculate and to get sensible results. But what about fresh insights? Everybody is always on the lookout for something new. Is there any reason to buy into my three questions if it’s not going to go anywhere new and different? I’m always surprised at how much more there is to calculating than I expect at the beginning. What surprises me the most is that the best surprises don’t come from clever ways of counting or complicated coding tricks that take real brain power — from what’s valued and encouraged in calculating — but straight from seeing. Let’s see just how visual calculating works. I can’t be sure before I show you, but I’m almost positive that you’re going to be surprised at how much there is to visual reasoning if it’s like visual calculating. 3G. STINY Does reasoning include calculating? I want to show that reasoning includes calculating. Most of the people I’ve asked agree that it does, but only as a narrow kind of process among many other kinds of greater scope that contribute more to thinking. Even so, I need to show this to go on: I need an account of reasoning that’s like calculating, so that I can explain visual reasoning in terms of visual calculating. I won’t