A blind man is dwelling in a cave. He is not confined to the cave. He can come and go as he pleases. He lives in the cave because he has found it to be a rather congenial place, a place of shelter from the extremes of weather. Yet he is by no means a hermit or a loner. He enjoys his frequent walks to the nearby town where he can socialize with others. He is an avid radio listener, and he uses the radio to keep himself well up to date on the local and national goings on.
Nor is the blind man without modern conveniences. He has persuaded the electrical utility company to provide him with an electrical connection to his cave. He frequently uses one of the electrical outlets to recharge his battery operated computer. His life is significantly helped by the computer, with its talking voice system that can report what he is unable to see on the screen. These days he uses the computer as his most effective tool for making notes, since he can enter data at the keyboard far faster than would be possible with his Braille writer.
The cave itself is quite large. Perhaps this is one of the reasons that the blind man finds it so congenial. But, without the use of his eyes, he cannot tell what is the shape of the cave. He has a rough idea of the ground level of the cave, because he often walks around feeling the surfaces. But he cannot tell how high it is, nor can he tell what is the shape of that part of the cave which is so high as to be beyond his reach.
Finding the shape of the cave has become something of an obsession with the blind man. And why not, since it is the place he calls home.
He has, of course, tried the obvious method for determining the shape of his cave. He has invited some of his sighted friends, and asked them to describe it to him. But their descriptions have been most unsatisfactory. In describing the cave, his sighted friends like to point to and talk about a feature that they can see “over there.” But pointing is of little value to the blind man. And when he reminds his friends of this, they find themselves lost for words, unable to come up with ways of describing the cave which do not depend on their visual intuition.
In spite of his physical handicap, it happens that the blind man is a skilled craftsman. He had acquired his skills as a child under the tutelage of his devoted father, himself a skilled artisan. And the blind man has worked to maintain his skills, for it is those skills that have given him a degree of independence that is unusual for one suffering from total blindness.
The blind man is not one to sit around and brood about his fate in life. Unable to get useful assistance from his sighted friends in satisfying his obsession, he decides to act for himself so that he can discover what is the shape of the cave. So he heads to the local hardware store, and orders some steel bars (angle iron) that he could use to erect a scaffolding within the cave. He also orders suitable bolts that he can use in his construction.
On the next day, when the delivery truck arrives with the steel bars and bolts, the blind man sets about erecting his scaffolding. As he moves a bar into place, he attaches a Braille label to it. Next, he carefully inserts the bolts, and tightens up the nuts so that the bar is rigidly in place. Then he goes to his computer, and records where in the structure the new bar was bolted. That is, he records which bar was connected to which. Since the bars are not all of the same length, he also records the length of the bar measured between the centers of the bolt holes that were used for connecting it into the structure. It is his intention that, by the time he has finished, his computer will contain a precise description of the scaffolding, a complete set of rules which define the shape and structure of the framework he has erected.
The blind man expects that it will take him several weeks to finish the construction of his scaffolding. He cannot be sure quite how long it will take, and he cannot be sure how many additional steel bars he will need to order before he can complete the task. But he is in no hurry. He can work on the scaffolding while he is listening to the radio. His project has given him something to do with his spare time.
The reason that the blind man cannot be sure how long the construction will take, and how many steel bars he will require, is that he has no complete design planned out for the structure. He has a systematic methodology, but not a design. He could not have a design, for to have one would require knowing the shape of the cave, and that is what he does not know. His methodology is to build the scaffolding so that it will be rigid and strong enough to support his weight. Then, during the construction, he can climb onto the structure, and reach out to feel how close it is to the sides of the cave, and to the roof of the cave. If the distance is so great that he cannot reach the stone surface of the cavern, he knows that he will have to further extend his scaffolding in that direction. His intention is to eventually erect a scaffold which will be a close fit to the shape of the cave.
By now four weeks have passed since the blind man began his project. The scaffolding is complete. It is a framework which fills out the cave. The outer perimeter of the structure is never more than a few inches from the surface of the cave. And the blind man has the complete specifications of the scaffold recorded in his computer.
The shape of the cave
Because he carefully labeled all of the steel bars in the scaffolding, the blind man has a way of designating locations on that structure. He can use the symbol M3A7 to denote the vertex where the bar M3 is bolted to the bar A7. But he can also use M3A7 to denote the point on the wall of the cave nearest to that vertex. Using the construction parameters he has recorded in his computer, he can quickly calculate the distance between M3A7 and G1H6. Technically, this is the distance between two vertices of the scaffolding. But because these vertices are very close to the cave wall, it is also a close approximation to the distance between two points on the cave wall.
As a result of his methodical work, the blind man can now truly say he knows the shape of the cave. He knows it in far more detail than did any of his sighted friends when they tried to describe the cave. The scaffolding that he had constructed was a framework that he could use to help him find the shape of the cave. The labels he assigned to parts of the scaffolding have become part of a conceptual framework he can now use to describe the shape of the cave.