Structure and Interpretation of Computer Programs

I'd like to welcome you to this course on computer science. Actually, it's a terrible way to start. Computer science
is a terrible name for this business. First of all it's not a science. It might be engineering... or it might be art...
Or we'll actually see that computer... so-called 'science' actually has a lot in common with magic. We will see that in this course.

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And it's not about computers in the same sense that... that physics is not really about particle accelerators...
and biology is not really about microscopes and Petri dishes. and it's not about computers in the same sense that geometry
is not really about using surveying instruments. In fact there is a lot of commonality between computer science and geometry.
Geometry first of all is another subject with a lousy name. The name comes from 'Gaia' meaning the earth and 'Metron' meaning to measure.
Geometry originally meant measuring the earth... or surveying. And the reason for that was that thousands of years ago


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the Egyptian priesthood developed rudiments of geometry in order to figure out how to restore the boundaries of fields that were destroyed
in the annual flooding of the Nile. And to the Egyptians who did that the geometry really was the use of surveying instruments.
Now, the reason that we think that computer science is about computers is pretty much the same reason
that the Egyptians thought geometry was about surveying instruments. and that is when some field is just getting started and

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it's very easy to confuse the essence of what you're doing with the tools that you use. And indeed on some absolute
scale of things we probably know less about the essence of computer science than the ancient Egyptians
really knew about geometry. Well, what I mean by the essence of computer science, what I mean by the essence of geometry...
See, it's certainly true that these Egyptians often used surveying instruments. But when we look back on them

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The important stuff they were doing was to begin to formalize notions about space and time. To start a way of talking about...
mathematical truth formally that led to the axiomatic method, that led to... sort of all of modern mathematics.
Figuring out a way to talk precisely about so-called 'declarative' knowledge - 'what is true'. Well, similarly, I think in the future
people will look back and say, yes, those primitives in the twentieth century were fiddling around with these gadgets called computers,


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but really what they were doing is starting to learn how to formalize... formalize intuitions about... process...
how to do things. Starting to develop a way... to talk precisely about 'how to' knowledge, as opposed to geometry
that talks about 'what is true'. Let me give you an example of that. Let's take a look... Here is a piece of... a piece of mathematics.

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The square root of X is the number Y such that Y squared is equal to X and Y is greater than zero. Now that's a fine piece of mathematics,
but just telling you what a square root is doesn't really say anything about... about how you might go out and find one.
Let's contrast that with a piece of imperative knowledge. Right? How you might go out and find the square root.
This in fact also comes from Egypt. Not ancient-ancient Egypt. This is an algorithm due to Heron of Alexandria


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called how to find a square root by successive averaging.