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visit MIT OpenCourseWare at ocw.mit.edu. ANA BELL: All right. Let's begin. As I mentioned
before, this lecture will be recorded for OCW. Again, in future
lectures, if you don't want to have the
back of your head show up, just don't sit in
this front area here. First of all, wow,
what a crowd, you guys. We're finally in 26-100. 6.0001 made it big, huh? Good afternoon and welcome to
the very first class of 6.0001, and also 600, this semester. My name is Ana Bell. First name, Ana. Last name, Bell. I'm a lecturer in
the EECS Department. And I'll be giving some
of the lectures for today, along with later on in the term,
Professor Eric Grimson, who's sitting right down there, will
be giving some of the lectures, as well. Today we're going to go over
some basic administrivia, a little bit of
course information. And then, we're going
to talk a little bit about what is computation? We'll discuss at
a very high level what computers do just
to make sure we're all on the same page. And then, we're going to dive
right into Python basics. We're going to talk a little bit
about mathematical operations you can do with Python. And then, we're going to
talk about Python variables and types. As I mentioned in my
introductory email, all the slides and code that I'll
talk about during lectures will be up before
lecture, so I highly encourage you to download
them and to have them open. We're going to go through some
in-class exercises which will be available on those slides. And it's fun to do. And it's also great if could
take notes about the code just for future reference. It's true. This is a really
fast-paced course, and we ramp up really quickly. We do want to position you
to succeed in this course. As I was writing
this, I was trying to think about when
I was first starting to program what helped
me get through my very first programming course. And this is really a good list. The first thing was I just
read the psets as soon as they came out, made sure that
the terminology just sunk in. And then, during
lectures, if the lecturer was talking about something
that suddenly I remembered, oh, I saw that word in the pset
and I didn't know what it was. Well, hey, now I
know what it is. Right? So just give it a read. You don't need to start it. If you're new to programming, I
think the key word is practice. It's like math or reading. The more you practice,
the better you get at it. You're not going to
absorb programming by watching me write programs
because I already know how to program. You guys need to practice. Download the code
before lecture. Follow along. Whatever I type,
you guys can type. And I think, also,
one of the big things is if you're new to
programming, you're kind of afraid that you're
going to break your computer. And you can't really do that
just by running Anaconda and typing in some commands. So don't be afraid to
just type some stuff in and see what it does. Worst case, you just
restart the computer. Yeah. That's probably the
big thing right there. I should have probably
highlighted it, but don't be afraid. Great. So this is pretty much a
roadmap of all of 6.0001 or 600 as I've just explained it. There's three big things we
want to get out of this course. The first thing is the
knowledge of concepts, which is pretty much true of
any class that you'll take. The class will teach you
something through lectures. Exams will test
how much you know. This is a class in programming. The other thing we want
you to get out of it is programming skills. And the last thing,
and I think this is what makes this
class really great, is we teach you how
to solve problems. And we do that
through the psets. That's really how I feel
the roadmap of this course looks like. And underlying all of
these is just practice. You have to just type some
stuff away and code a lot. And you'll succeed in
this course, I think. OK. So what are the things we're
going to learn in this class? I feel like the things we're
going learn in this class can be divided into basically
three different sections. The first one is related to
these first two items here. It's really about
learning how to program. Learning how to
program, part of it is figuring out what
objects to create. You'll learn about these later. How do you represent knowledge
with data structures? That's sort of the
broad term for that. And then, as you're
writing programs, you need to-- programs
aren't just linear. Sometimes programs jump around. They make decisions. There's some control
flow to programs. That's what the second
line is going to be about. The second big
part of this course is a little bit more
abstract, and it deals with how do you write
good code, good style, code that's readable. When you write code, you
want to write it such that-- you're in big company,
other people will read it, other people will
use it, so it has to be readable and
understandable by others. To that end, you
need to write code that's well organized,
modular, easy to understand. And not only that, not
only will your code be read by other people,
but next year, maybe, you'll take another
course, and you'll want to look back at
some of the problems that you wrote in this class. You want to be able
to reread your code. If it's a big mess, you might
not be able to understand-- or reunderstand--
what you were doing. So writing readable
code and organizing code is also a big part. And the last section is going
to deal with-- the first two are actually part of the
programming in Introduction to Programming and
Computer Science in Python. And the last one deals mostly
with the computer science part in Introduction to Programming
and Computer Science in Python. We're going to talk about,
once you have learned how to write programs
in Python, how do you compare programs in Python? How do you know that one program
is better than the other? How do you know
that one program is more efficient than the other? How do you know
that one algorithm is better than the other? That's what we're going to
talk about in the last part of the course. OK. That's all for the
administrative part of the course. Let's start by talking at a high
level what does a computer do. Fundamentally, it
does two things. One, performs calculations. It performs a lot
of calculations. Computers these days
are really, really fast, a billion calculations per
second is probably not far off. It performs these
calculations and it has to store them somewhere. Right? Stores them in computer memory. So a computer also has
to remember results. And these days, it's not
uncommon to find computers with hundreds of
gigabytes of storage. The kinds of calculations
that computers do, there are two kinds. One are calculations that
are built into the language. These are the very
low level types of calculations,
things like addition, subtraction,
multiplication, and so on. And once you have
a language that has these primitive calculation
types, you, as a programmer, can put these types
together and then define your own calculations. You can create new
types of calculations. And the computer will be able
to perform those, as well. I think, one thing
I want to stress-- and we're going to
come back to this again during this entire
lecture, actually-- is computers only know
what you tell them. Computers only do what
you tell them to do. They're not magical. They don't have a mind. They just know how to
perform calculations really, really quickly. But you have to tell them
what calculations to do. Computers don't know anything. All right. We've come to that. Let's go into the
types of knowledge. The first type of knowledge
is declarative knowledge. And those are things
like statements of fact. And this is where my
email came into play. If you read it all
the way to the bottom, you would have entered a raffle. So a statement of fact
for today's lecture is, someone will win a
prize before class ends. And the prize was
a Google Cardboard. Google state-of-the-art
virtual reality glasses. And I have them right here. Yea. I delivered on my promise. That's a statement of fact. So pretend I'm a machine. OK? I don't know anything
except what you tell me. I don't know. I know that you tell
me this statement. I'm like, OK. But how is someone going
to win a Google Cardboard before class ends, right? That's where imperative
knowledge comes in. Imperative knowledge is
the recipe, or the how-to, or the sequence of steps. Sorry. That's just my
funny for that one. So the sequence of steps
is imperative knowledge. If I'm a machine,
you need to tell me how someone will win a Google
Cardboard before class. If I follow these
steps, then technically, I should reach a conclusion. Step one, I think we've
already done that. Whoever wanted to
sign up has signed up. Now I'm going to open my IDE. I'm just basically
being a machine and following the steps
that you've told me. The IDE that we're using in
this class is called Anaconda. I'm just scrolling
down to the bottom. Hopefully, you've installed
it in problem set zero. I've opened my IDE. I'm going to follow the
next set of instructions. I'm going to choose a random
number between the first and the nth responder. Now, I'm going to actually
use Python to do this . And this is also an
example of how just a really simple
task in your life, you can use computers or
programming to do that. Because if I chose
a random number, I might be biased
because, for example, I might like the number 8. To choose a random number,
I'm going to go and say, OK, where's the list of responders? It starts at 15. Actually, it starts at
16 because that's me. We're going to choose a
random number between 16 and the end person 266. Oh, we just got-- oh. OK. OK. I'm going to cut
it off right here. 271. OK. 16 and 271. Perfect. OK. I'm going to choose
a random number. I'm going to go to my IDE. And you don't need to
know how to do this yet, but by the end of
this class, you will. I'm just going to use Python. I'm just going to get the random
number package that's going to give me a random number. I'm going to say random.randint. And I'm going to choose a random
number between 16 and 272, OK. 75. OK. Great. I chose a random number. And I'm going to find the
number in the responder's sheet. What was the number again? Sorry. 75. OK. Up we go. There we go. Lauren Z-O-V. Yeah. Nice. You're here. Awesome. All right. That's an example of me
being a machine and also, at the same time, using
Python in my everyday life, just lecturing, to
find a random number. Try to use Python
wherever you can. And that just
gives you practice. That was fun. But we're at MIT. We're MIT students. And we love numbers here at MIT. Here's a numerical
example that shows the difference between
declarative and imperative knowledge. An example of
declarative knowledge is the square root of a number
x is y such that y times y is equal to x. That's just a statement
of fact It's true. Computers don't know
what to do with that. They don't know what to
do with that statement. But computers do know
how to follow a recipe. Here's a well-known algorithm. To find the square
root of a number x, let's say x is originally
16, if a computer follows this algorithm, it's going
to start with a guess, g, let's say, 3. We're trying to find
the square root of 16. We're going to calculate
g times g is 9. And we're going to
ask is if g times g is close enough to x, then
stop and say, g is the answer. I'm not really happy with
9 being really close to 16. So I'm going to say,
I'm not stopping here. I'm going to keep going. If it's not close
enough, then I'm going to make a new guess
by averaging g and x over g. That's x over g here. And that's the
average over there. And the new average is
going to be my new guess. And that's what it says. And then, the last step
is using the new guess, repeat the process. Then we go back to the beginning
and repeat the whole process over and over again. And that's what the
rest of the rows do. And you keep doing
this until you decide that you're close enough. What we saw for the
imperative knowledge in the previous
numerical example was the recipe for how to
find the square root of x. What were the three
parts of the recipe? One was a simple
sequence of steps. There were four steps. The other was a flow of
control, so there were parts where we made decisions. Are we close enough? There were parts where
we repeated some steps. At the end, we said,
repeat steps 1, 2, 3. That's the flow of control. And the last part of the
recipe was a way to stop. You don't want a program
that keeps going and going. Or for a recipe, you don't want
to keep baking bread forever. You want to stop at some point. Like 10 breads is enough, right? So you have to have
a way of stopping. In the previous example,
the way of stopping was that we decided
we were close enough. Close enough was maybe
being within .01, .001, whatever you pick. This recipe is there
for an algorithm. In computer science speak,
it's going to be an algorithm. And that's what we're going
to learn about in this class. We're dealing with computers. And we actually want
to capture a recipe inside a computer, a computer
being a mechanical process. Historically, there were two
different types of computers. Originally, there
were these things called fixed-program computers. And I'm old enough to
have used something like this, where there's
just numbers and plus, minus, multiplication,
divide, and equal. But calculators these days
are a lot more complicated. But way back then, an example
of a fixed-program computer is this calculator. It only knows how to do
addition, multiplication, subtraction, division. If you want to plot
something, you can't. If you want to go on the
internet, send email with it, you can't. It can only do this one thing. And if you wanted to create a
machine that did another thing, then you'd have to create
another fixed-program computer that did a completely
separate test. That's not very great. That's when stored-program
computers came into play. And these were machines
that could store a sequence of instructions. And these machines could execute
the sequence of instructions. And you could change the
sequence of instructions and execute this different
sequence of instructions. You could do different
tasks in the same machine. And that's the computer
as we know it these days. The central processing unit is
where all of these decisions get made. And these are all
the peripherals. The basic machine architecture--
at the heart of every computer there's just this
basic architecture-- and it contains, I
guess, four main parts. The first is the memory. Input and output
is the other one. The ALU is where all of
the operations are done. And the operations
that the ALU can do are really primitive operations,
addition, subtraction, and so on. What the memory contains
is a bunch of data and your sequence
of instructions. Interacting with the Arithmetic
Logic Unit is the Control Unit. And the Control Unit
contains one program counter. When you load a sequence
of instructions, the program counter starts
at the first sequence. It starts at the sequence,
at the first instruction. It gets what the instruction
is, and it sends it to the ALU. The ALU asks, what are we
doing operations on here? What's happening? It might get some data. If you're adding two numbers,
it might get two numbers from memory. It might do some operations. And it might store
data back into memory. And after it's done, the
ALU is going to go back, and the program counter
is going to increase by 1, which means
that we're going to go to the next sequence
in the instruction set. And it just goes linearly,
instruction by instruction. There might be one
particular instruction that does some sort of test. It's going to say, is
this particular value greater or equal to or the same
as this other particular value? That's a test, an
example of a test. And the test is going to
either return true or false. And depending on the
result of that test, you might either go to
the next instruction, or you might set
the program counter to go all the way back to
the beginning, and so on. You're not just
linearly stepping through all the instructions. There might be some
control flow involved, where you might
skip an instruction, or start from the
beginning, or so on. And after you're done,
when you finished executing the last
instruction, then you might output something. That's really the basic
way that a computer works. Just to recap, you have
the stored program computer that contains these
sequences of instructions. The primitive operations
that it can do are addition, subtraction,
logic operations, tests-- which are something equal
to something else, something less than, and so
on-- and moving data, so storing data, moving data
around, and things like that. And the interpreter goes
through every instruction and decides whether you're going
to go to the next instruction, skip instructions, or repeat
instructions, and so on. So we've talked
about primitives. And in fact, Alan Turing, who
was a really great computer scientist, he showed that
you can compute anything using the six primitives. And the six primitives are move
left, move right, read, write, scan, and do nothing. Using those six instructions
and the piece of tape, he showed that you
can compute anything. And using those
six instructions, programming languages
came about that created a more convenient
set of primitives. You don't have to program
in only these six commands. And one interesting thing, or
one really important thing, that came about from
these six primitives is that if you can compute
something in Python, let's say-- if you write a
program that computes something in Python, then,
in theory, you can write a program that
computes the exact same thing in any other language. And that's a really
powerful statement. Think about that today when
you review your slides. Think about that again. That's really powerful. Once you have your
set of primitives for a particular language, you
can start creating expressions. And these expressions
are going to be combinations of the primitives
in the programming language. And the expressions are
going to have some value. And they're going up some
meaning in the programming language. Let's do a little bit of
a parallel with English just so you see what I mean. In English, the
primitive constructs are going to be words. There's a lot of words
in the English language. Programming languages-- in
Python, there are primitives, but there aren't
as many of them. There are floats,
Booleans, these are numbers, strings,
and simple operators, like addition,
subtraction, and so on. So we have primitive constructs. Using these
primitive constructs, we can start creating, in
English, phrases, sentences, and the same in
programming languages. In English, we can say
something like, "cat, dog, boy. That, we say, is not
syntactically valid. That's bad syntax. That's noun, noun, noun. That doesn't make sense. What does have good syntax in
English is noun, verb, noun. So, "cat, hugs boy" is
syntactically valid. Similarly, in a
programming language, something like this-- in
Python, in this case-- a word and then the number five
doesn't really make sense. It's not syntactically valid. But something like operator,
operand, operator is OK. So once you've created these
phrases, or these expressions, that are syntactically
valid, you have to think about the static
semantics of your phrase, or of your expression. For example, in English, "I
are hungry" is good syntax. But it's weird to say. We have a pronoun, a verb,
and an adjective, which doesn't really make sense. "I am hungry" is better. This does not have
good static semantics. Similarly, in
programming languages-- and you'll get the
hang of this the more you do it-- something like
this, "3.2 times 5, is OK. But what does it mean? What's the meaning to have
a word added to a number? There's no meaning behind that. Its syntax is OK,
because you have operator, operand, operator. But it doesn't really make
sense to add a number to a word, for example. Once you have created
these expressions that are syntactically correct and
static, semantically correct, in English, for example, you
think about the semantics. What's the meaning
of the phrase? In English, you can
actually have more than one meaning to an entire phrase. In this case, "flying
planes can be dangerous" can have two meanings. It's the act of flying
a plane is dangerous, or the plane that is in
the air is dangerous. And this might be
a cuter example. "This reading lamp
hasn't uttered a word since I bought it. What's going on?" So that has two meanings. It's playing on the
word "reading lamp." That's in English. In English, you
can have a sentence that has more than
one meaning, that's syntactically correct and
static, semantically correct. But in programming languages,
the program that you write, the set of instructions that
you write, only has one meaning. Remember, we're coming
back to the fact that the computer only does
what you tell it to do. It's not going to
suddenly decide to add another variable
for some reason. It's just going to execute
whatever statements you've put up. In programming languages,
there's only one meaning. But the problem that comes into
play in programming languages is it's not the meaning
that you might have intended, as the programmer. That's where things
can go wrong. And there's going
to be a lecture on debugging a little
bit later in the course. But this is here
just to tell you that if you see an error
pop up in your program, it's just some text
that says, error. For example, if we do
something like this, this is syntactically correct. Incorrect. Syntactically incorrect. See? There's some angry
text right here. What is going on? The more you program,
the more you'll get the hang of
reading these errors. But this is basically
telling me the line that I wrote is
syntactically incorrect. And it's pointing to the exact
line and says, this is wrong, so I can go back and
fix it as a programmer. Syntax errors are actually
really easily caught by Python. That was an example
of a syntax error. Static semantic
errors can also be caught by Python as long as, if
your program has some decisions to make, as long as you've
gone down the branch where the static semantic
error happens. And this is probably going to
be the most frustrating one, especially as
you're starting out. The program might do
something different than what you expected it to do. And that's not because the
program suddenly-- for example, you expected the program
to give you an output of 0 for a certain test case, and
the output that you got was 10. Well, the program
didn't suddenly decide to change
its answer to 10. It just executed the
program that you wrote. That's the case where
the program gave you a different answer
than expected. Programs might crash, which
means they stop running. That's OK. Just go back to your code and
figure out what was wrong. And another example
of a different meaning than what you intended was
maybe the program won't stop. It's also OK. There are ways to stop
it besides restarting the computer. So then Python
programs are going to be sequences of
definitions and commands. We're going to have expressions
that are going to be evaluated and commands that tell the
interpreter to do something. If you've done
problem set 0, you'll see that you can type
commands directly in the shell here, which is
the part on the right where I did some really
simple things, 2 plus 4. Or you can type commands up in
here, on the left-hand side, and then run your program. Notice that, well, we'll
talk about this-- I won't talk about this now. But these are-- on the
right-hand side, typically, you write very simple
commands just if you're testing something out. And on the left-hand
side here in the editor, you write more lines and
more complicated programs. Now we're going to start
talking about Python. And in Python, we're going
to come back to this, everything is an object. And Python programs
manipulate these data objects. All objects in Python
are going to have a type. And the type is going to tell
Python the kinds of operations that you can do
on these objects. If an object is the
number five, for example, you can add the number
to another number, subtract the number, take it
to the power of something, and so on. As a more general example,
for example, I am a human. So that's my type. And I can walk, speak
English, et cetera. Chewbacca is going
to be a type Wookie. He can walk, do that
sound that I can't do. He can do that, but I can't. I'm not even going
to try, and so on. Once you have these
Python objects, everything is an
object in Python. There are actually
two types of objects. One are scalar objects. That means these are very basic
objects in Python from which everything can be made. These are scalar objects. That can't be subdivided. The other type of object
is a non-scalar object. And these are objects that
have some internal structure. For example, the
number five is a scalar object because it
can't be subdivided. But a list of numbers,
for example, 5, 6, 7,8, is going to be
a non-scalar object because you can subdivide it. You can subdivide it into--
you can find parts to it. It's made up of a
sequence of numbers. Here's the list of all of
the scalar objects in Python. We have integers, for example,
all of the whole numbers. Floats, which are all of
the real numbers, anything with a decimal. Bools are Booleans. There's only two
values to Booleans. That's True and False. Note the capitalization,
capital T and capital F. And this other thing
called NoneType. It's special. It has only one
value called None. And it represents the
absence of a type. And it sometimes comes in
handy for some programs. If you want to find
the type of an object, you can use this special
command called type. And then in the
parentheses, you put down what you want to
find the type of. You can write into
the shell "type of 5," and the shell will tell
you, that's an integer. If you happen to want to convert
between two different types, Python allows you to do that. And to do that, you
put the type that you want to convert to
right before the object that you want to convert to. So float(3) will convert the
integer 3 to the float 3.0. And similarly, you can convert
any float into an integer. And converting to an
integer just truncates. It just takes away the
decimal and whatever's after it-- it does not round--
and keeps just the integer part. For this slide, I'm
going to talk about it. But if you'd like if
you have the slides up, go to go to this exercise. And after I'm done
talking about the slide, we'll see what people
think for that exercise. One of the most
important things that you can do in basically
any programming, in Python also, is
to print things out. Printing out is how you
interact with the user. To print things out, you
use the print command. If you're in the shell, if
you simply type "3 plus 2," you do see a value here. Five, right? But that's not actually
printing something out. And that becomes apparent
when you actually type things into the editor. If you just do "3 plus 2," and
you run the program-- that's the green button here-- you see
on the right-hand side here, it ran my program. But it didn't actually
print anything. If you type this
into the console, it does show you this
value, but that's just like peeking into the
value for you as a programmer. It's not actually
printing it out to anyone. If you want to
print something out, you have to use the print
statement like that. In this case, this is actually
going to print this number five to the console. That's basically what it says. It just tells you it's an
interaction within the shell only. It's not interacting
with anyone else. And if you don't
have any "Out," that means it got printed
out to the console. All right. We talked a little
bit about objects. Once you have objects, you can
combine objects and operators to form these expressions. And each expression is
going to have a value. So an expression
evaluates to a value. The syntax for an
expression is going to be object, operator,
object, like that. And these are some operators
you can do on ints and floats. There's the typical ones,
addition, subtraction, multiplication, and division. If, for the first
three, the answer that you get-- the type of
the answer that you get-- is going to depend on the
type of your variables. If both of the variables of
the operands are integers, then the result you're going
to get is of type integer. But if at least one of
them is a float, then the result you're going
to get is a float. Division is a little
bit special in that no matter what the
operands are, the result is always going to be a float. The other operations you can
do, and these are also useful, are the remainder,
so the percent sign. If you use the percent
sign between two operands, that's going to give you the
remainder when you divide i by j. And raising something to
the power of something else is using the star star operator. And i star stars j is going
to take i to the power of j. These operations have
the typical precedence that you might expect
in math, for example. And if you'd like
to put precedence toward some other
operations, you can use parentheses to do that. All right. So we have ways of
creating expressions. And we have operations
we can do on objects. But what's going to be useful
is to be able to save values to some name. And the name is going to
be something that you pick. And it should be a
descriptive name. And when you save
the value to a name, you're going to be able
to access that value later on in your program. And that's very useful. To save a value to a variable
name, you use the equal sign. And the equal sign
is an assignment. It assigns the
right-hand side, which is a value, to the
left-hand side, which is going to be a variable name. In this case, I assigned
the float 3.14159 to the variable pi. And in the second
line, I'm going to take this expression,
22 divided by 7, I'm going to evaluate it. It's going to come up
with some decimal number. And I'm going to save it
into the variable pi_approx. values are stored in memory. And this assignment
in Python, we say the assignment binds
the name to the value. When you use that name
later on in your program, you're going to be referring
to the value in memory. And if you ever want
to refer to the value later on in your code,
you just simply type the name of the variable
that you've assigned it to. So why do we want to give
names to expressions? Well, you want to reuse the
names instead of the values. And it makes your
code look a lot nicer. This is a piece of
code that calculates the area of a circle. And notice, I've assigned
a variable pi to 3.14159. I've assigned another variable
called radius to be 2.2. And then, later on in my
code, I have another line that says area-- this
is another variable-- is equal to-- this
is an assignment-- to this expression. And this expression is referring
to these variable names, pi and radius. And it's going look up
their values in memory. And it's going to replace
these variable names with those values. And it's going to do
the calculation for me. And in the end, this
whole expression is going to be
replaced by one number. And it's going to be the float. Here's another exercise, while
I'm talking about the slide. I do want to make a note
about programming versus math. In math, you're often
presented with a problem that says, solve for x. x plus y is equal to
something something. Solve for x, for example. That's coming back to the
fact that computers don't know what to do with that. Computers need to
be told what to do. In programming, if you
want to solve for x, you need to tell the computer
exactly how to solve for x. You need to figure
out what formula you need to give the
computer in order to be able to solve for x. That means always in programming
the right-hand side is going to be an expression. It's something that's going
to be evaluated to a value. And the left-hand side
is always a variable. It's going to be an assignment. The equal sign is
not like in math where you can have a lot
of things to the left and a lot of things to the
right of the equal sign. There's only one thing to
the left of the equal sign. And that's going
to be a variable. An equal sign stands
for an assignment. Once we've created expressions,
and we have these assignments, you can rebind variable
names using new assignment statements. Let's look at an
example for that. Let's say this is our memory. Let's type back in the example
with finding the radius. Let's say, pi is equal to 3.14. In memory, we're going to
create this value 3.14. We're going to bind it
to the variable named pi. Next line, radius
is equal to 2.2. In memory, we're
creating this value 2.2. And we're going to bind it
to the variable named radius. Then we have this
expression here. It's going to substitute
the values for pi from memory and the value
for radius from memory. It's going to calculate the
value that this expression evaluates to. It's going to pop
that into the memory. And it's going to
assign-- because we're using the equal
sign-- it's going to assign that value
to that variable area. Now, let's say we rebind
radius to be something else. Radius i is bound
to the value 2.2. But when we do this line, radius
is equal to radius plus 1, we're going to take
away the binding to 2.2. We're going to do
this calculation. The new value is 3.2. And we're going to rebind that
value to that same variable. In memory, notice
we're still going to have this value,
2.2, floating around. But we've lost
the handle for it. There's no way to get it back. It's just in memory
sitting there. At some point, it might
get collected by what we call the garbage collector. In Python, And it'll
retrieve these lost values, and it'll reuse them for new
values, and things like that. But radius now points
to the new value. We can never get back 2.2. And that's it. The value of area-- notice,
this is very important. The value of area
did not change. And it did not change because
these are all the instructions we told the computer to do. We just told it to change
radius to be radius plus 1. We never told it to
recalculate the value of area. If I copied that line down
here, then the value of area would change. But we never told it to do that. The computer only does
what we tell it to do. That's the last thing. Next lecture, we're going
to talk about adding control flow to our programs, so
how do you tell the computer to do one thing or another? All right.
