6.001 Structure and Interpretation of Computer Programs. Copyright o 2004 by Massachusetts Institute of Technology Slide 9.1.10 Whose number is it? then here is the key question. What actual number does this Suppose we pick up the following object object represent? This may sound odd, as after all, it is just a complex number. But suppose this is a complex nu 1+「 by Bert. Then what number would this represen( amber made What number does this represent 0O1 sIcP Slide 9.1.11 Whose number is it? In that case, we know that the first part of this list represents the real part of the number, and the second part of the list represents uppose we pick up the following object the imaginary part. Thus, in this case, this number would correspond to the vector or point shown on the diagram What number does this represent? 4 Whose number is it? Slide 9. 1.12 Suppose we pick up the following object On the other hand, if this were a complex number made by Ernie, we know that the first part of the list is the magnitude and is the angle of the vector. In that this number represents the red vector or point shown on the Thus, we have a problem. Depending on who made the complex number we found, we get a different answer to the question of What number does this represent? what number this is so how do we tell who made it? That is exactly the problem we are raising. Given what we have shown OI SICP "designer"complex numbers let's have the designer of eachate so far, we can't tell. Fortunately the solution is easy. Let's crea kind of complex number sign his work on the back. That means we will have each creator of complex numbers but a label on the object that either says this is a"Bert"or Cartesian number, or this is an"Ernie"or polar number6.001 Structure and Interpretation of Computer Programs. Copyright © 2004 by Massachusetts Institute of Technology. Slide 9.1.10 .. then here is the key question. What actual number does this object represent? This may sound odd, as after all, it is just a complex number. But suppose this is a complex number made by Bert. Then what number would this represent? Slide 9.1.11 In that case, we know that the first part of this list represents the real part of the number, and the second part of the list represents the imaginary part. Thus, in this case, this number would correspond to the vector or point shown on the diagram. Slide 9.1.12 On the other hand, if this were a complex number made by Ernie, we know that the first part of the list is the magnitude and the second part of the list is the angle of the vector. In that case, this number represents the red vector or point shown on the diagram. Thus, we have a problem. Depending on who made the complex number we found, we get a different answer to the question of what number this is. So how do we tell who made it? That is exactly the problem we are raising. Given what we have shown so far, we can't tell. Fortunately the solution is easy. Let's create "designer" complex numbers, let's have the designer of each kind of complex number sign his work on the back. That means we will have each creator of complex numbers but a label on the object that either says this is a "Bert" or Cartesian number, or this is an "Ernie" or polar number