So I was actually just back in Connecticut
at my high school for the first time in years recently,
and chatting with some of my successors about where I made my way in life,
and what I really didn't do, actually, in high school.
In fact, I gave a talk about all of the studies
that I didn't discover when I was back in high school.
Because I still remember wandering around the hallways
when I was last there, looking in on various classrooms
where I'd spent a lot of time, that there was one in particular
that I spent no time in.
And that was the computer science lab.
I still vaguely remember peeking through the glass of the window
when some of my friends were taking their introductory computer science
classes, but I had no interest in it, honestly.
I just assumed it was all about programming, and like C++ or Java,
whatever those were.
But it just didn't seem all that interesting to me.
And any time I did look in, all my friends had their heads down,
typing away, doing whatever it was they were doing.
And so I focused on history, and English,
and constitutional law was my favorite class in high school.
And so when I got to Harvard some years later, I kind of just
stuck with where I was comfortable.
I felt like, well, I hadn't studied CS in high school,
so all the other students who are taking CS here surely have a leg up
and know way more than me.
So I figured, ah, I thought of it too late.
And there was this core CS50 my first year here.
And it had this alluring reputation.
There were a lot of students in it.
But it really didn't seem like it was for me.
I wasn't really a computer person in that way.
And I felt like I was behind.
I didn't want to hurt my GPA by taking something so unfamiliar to me.
And so I stayed within my comfort zone, and I took more history, and government
classes, and I declared my major to be-- or concentration to be government.
And it wasn't until sophomore year when I finally got up the nerve to shop,
so to speak--
Sit in on a class before you officially register-- this class called CS50.
And I only got up the nerve to register for it
officially because the professor at the time let me sign up for pass-fail.
So no harm to the GPA.
I was really able to explore really well beyond my comfort zone.
And honestly, within weeks, I realized for the first time in like 18 years
that homework can actually be fun.
And if you find the field that's of interest to you, whether it's
CS or anything else, by exploring things that you're not familiar with right
now, you might have the same experience I did of going home on a Friday night.
The problem set or homework assignment had just
been released at like 7:00 PM every Friday night.
And I would spend the entire evening on my laptop working on CS50's programming
assignments.
Because I finally realized what it was.
And programming itself is not the ends of a course like this.
It really is just about problem-solving.
And so quickly did I realize, wow, I can use these kinds of ideas
to go solve problems in other courses, to be more efficient,
to be more creative in my extracurriculars.
I realized, wow, I can now build some application
to now make processes more easily accessible
on campus, like the intramural sports program.
I was able to overhaul just with a little bit of computer science.
And if we distill today what took me all too long to discover,
problem-solving really is kind of a picture
like this, where you have some inputs, and the goal
is to achieve some outputs.
And that, in some sense, really is computer science.
And programming, and a lot of the particulars
that you learn in the classroom, are really just deeper
dives into this very simple idea.
But how do you get to that point of actually solving problems?
Well, I eventually realized that you needed to do two things.
One, you needed to represent these inputs and these outputs.
That is, we just all have to agree how to do it.
And then you actually have to do something with those inputs
to get those outputs.
And therein lies the problem-solving.
And so how do you go about representing information?
Well, I could represent information--
all I need is some kind of input.
And here's the power cord to my laptop.
And honestly, even if you have no idea how your computer works,
odds are, you appreciate that this is pretty integral,
having somehow electricity, some physical input come into the computer.
And if you unplug it, it's off.
If you plug it in, it's on.
And batteries, of course, can persist this here too.
But off and on maps really cleanly to what you all probably generally know
to be true of computers, in that they only speak what language?
AUDIENCE: Binary.
DAVID MALAN: Yeah, binary.
"Bi" meaning two, mapping to this concept of off and on,
or as a computer scientist would say, 0 or 1.
That's why we have 0s and 1s at the end of the day,
because the simplest thing to do electrically
is to either turn the power on or turn the power off.
1 or 0.
We could have called it A and B, but we call it 1 and 0.
But if all you have in a computer is the ability to turn it on or turn it off,
or to store some value-- kind of like a light switch goes on or off--
how can you possibly do anything interesting or solve problems?
Well, let's just consider like a simple light bulb here.
This has some power.
It happens to have a battery.
And if this thing is off, we'll just call it a 0.
And if this thing is on, we'll call it a 1.
So now we have a single switch, or what's
known in computing as a transistor.
In fact, inside of your computer are lots and lots-- millions of transistors
that just turn things on and off.
Well, if I have just one of these, I can only do 0 or 1.
That's not all that interesting.
That would seem to give us two problems total to solve.
So how can we count higher than just 0 or 1?
Well, I might take two of these, or three of these,
and maybe start doing things a little more methodically.
So I could do 1, 2, 3.
So now I can clearly count as high as three.
But that would seem to be it as well.
But no.
Computers are a little smarter than that,
and we can actually adopt patterns of on and off.
So this now, I'll claim is 0.
All three of these light bulbs are off.
Let me turn on this one on, thereby representing
what I'm going to call a 1.
But you know what?
Now I'm going to go ahead and claim that that's how a computer would store a 2.
It would turn a different light switch on, the second one.
And you know what?
If it turns the first one back on, this is how a computer stores a 3.
And now just take a guess, if I do this--
uncomfortably-- what is the computer perhaps now storing?
AUDIENCE: 4.
DAVID MALAN: 4.
This happens to be 6.
This is now 7.
Why?
How did I choose those particular patterns?
Well, it turns out this is something that all of us
are probably really familiar with.
If you think about our grade school understanding of numbers, if I draw
something on the screen quite simply--
like this pattern of symbols.
1, 2, 3.
This is, of course, 123.
But why?
Because all of us just pretty instantaneously did
the mental arithmetic of this being the ones place, this is the tens place,
this is the hundreds place.
And then what did you probably do in that split second?
Well, you did 100 times 1 plus 10 times 2 plus 1 times 3, which of course gives
you 100 plus 20 plus 3, or 123.
Now, that's a bit of a circular argument because that's kind of where I started,
but now these symbols--
these curves on the screen, 1, 2, 3--
actually have now meaning that we've all agreed represents the human number 123.
So computers are actually fundamentally the same thing.
And in some sense, they're even simpler than us humans in the following way.
If you have the same number of placeholders, and we write down--
with great difficulty-- if we write down, say,
three places, or three light bulbs, if you will, but doing it now textually,
and I write down, for instance, 0, 0, 0, you
can probably guess that in the world of computers,
if you've got three switches that are all off, this represents the number 0.
And if I turn one of these light bulbs on, so to speak, this of course--
as before-- is going to be the number that I called 1.
Well, if I now do not just change this one, but change this to a 0--
and this is where maybe my light bulb patterns got a little non-obvious--
why is this 2?
Well, it's the same mental arithmetic but just with different places.
A computer doesn't use powers of 10, so to speak--
10 to the 0, 10 to the 1, 10 to the 2--
but powers of 2.
So this is 2 to the 0, or the ones place.
This is 2 to the 1, or the twos place.
This is 2 to the 2, or the fours place.
And so you just need to turn these light bulbs on and off
based on this kind of pattern to get whatever number it
is you're interested in.
So this is 2 because it's 4 times 0 plus 2 times 1 plus 1 times 0.
Why is this three when I turned two light bulbs on earlier?
The same reasoning.
And what's the highest I can count with just three light bulbs, or three
0s and 1s?
7, just because you got a 4 plus a 2 plus a 1, and so forth.
And what would happen, then, if I wanted to count as high as 8, would you think?
AUDIENCE: [INAUDIBLE]
DAVID MALAN: Yeah, you need to add another place.
Or really, you need more physical hardware.
And this is why your computer can only count so high
or store so much information.
You need an additional light switch-- or another transistor, if you will--
to actually store additional information.
So that, then, is binary.
If you've just known intuitively computers only speak 0s and 1s, why?
Well, that's because they start with electricity as their physical input.
We humans have just all agreed to represent values
in this way using binary by just having these patterns of 0s and 1s.
But that pretty much makes for a very expensive calculator,
if all you have are numbers.
So how do you get from numbers and from electricity to now,
letters, say of the alphabet?
What could we do?
How do we now enable spreadsheet programs, and word processors,
and text messaging, and email clients, and the like?
What can we all do if our only input is electricity, or in turn, 0s and 1s?
AUDIENCE: [INAUDIBLE]
DAVID MALAN: Say again?
AUDIENCE: Assign number values to letters?
DAVID MALAN: Yeah, we can just assign number values to letters.
So you know what we could go ahead and do,
and if we want to represent letters of the alphabet,
as before, the only goal at hand is to just agree
on how to represent that information.
So let's pick a few letters of the alphabet.
A, B, C, D, E, F, G, H, I. We could just say, you know what?
Let's just agree to represent A as 1, and B as 2, and C as 3.
Doesn't really matter, so long as we all agree to do that.
But it turns out, some years ago, humans decided
that A is actually going to be 65, and B is 66,
and C is 67, 68, 69, 70, 71, 72, 73, and so forth.
This is known as ASCII or Unicode.
It's just a system that humans agreed decades ago
shall be used by computers to represent letters of the alphabet
just by storing numbers, and those numbers in turn
are just the result of the computer turning
little switches known as transistors on and off in these certain patterns.
And let me, with the wave of a hand, assure sure
that we can represent colors, and sounds,
and videos in very similar ways.
But we need to actually just agree on how to do this.
So in fact, there's an opportunity here perhaps
to write a message in exactly the same way that a computer could.
If you could humor me, maybe, with eight volunteers?
Could we get some eight volunteers up on stage?
OK, 1, 2.
Let me look a little harder.
3, 4.
Can I go a little farther?
I see no hands in the back.
OK.
There we go.
5.
6 over there.
I see someone pointing at someone else.
Come on, 7.
And let's go 8, over here.
Come on down.
And I just need you to go ahead, if you could,
and stand beneath these placeholders here on the slide, which
I've gone ahead and rotated just so that they fit a little more
visibly on the screen.
Come on over.
What's your name?
AUDIENCE: Matt.
DAVID MALAN: Matt.
Come on over and stand under the 128.
What's your name?
AUDIENCE: Mira.
DAVID MALAN: Mira.
David.
AUDIENCE: Hey.
DAVID MALAN: David.
Nice to meet you.
Hello.
David.
Nice to meet you.
AUDIENCE: Anesha.
DAVID MALAN: Anesha, David.
And Monica.
Nice to meet you.
And what was your name?
AUDIENCE: Chris.
DAVID MALAN: Chris.
Nice to meet you as well.
So each of these guys is going to have to scooch a little closer
to each other.
And you know what?
If this isn't too much effort, could we actually get eight more volunteers now
that you know what you're vol--
OK, now everyone's hand goes up.
OK.
1, 2, 3, 4, 5, 6, 7, 8, if you could.
Come on down.
We'll do this round more quickly.
And what you'll notice now that we have a bytes' worth of volunteers here.
What is a byte?
A byte is just 8 bits.
It's a more useful unit of measure than just a 0 or 1.
And notice the terminology here too.
A bit-- a 0 or 1-- is a binary digit.
There's the etymology of just that simple phrase.
And a quick hello to AJ.
AUDIENCE: AJ.
DAVID MALAN: David.
Jay.
AUDIENCE: Hi.
DAVID MALAN: David.
Nice to meet you.
AUDIENCE: Bianca.
DAVID MALAN: David, and nice to meet you as well.
Here we have our second byte of humans.
And--
AUDIENCE: [INAUDIBLE]
DAVID MALAN: What's that?
AUDIENCE: We have seven right here.
DAVID MALAN: We have a seven right here?
1, 2, 3, 4, 5, 6, 7.
1, 2, 3, 4, 5, 6, 7, 8.
We have a bug.
Here we go.
Come on up.
Thank you.
Thank you very much.
In computer science, that's an off-by-one error.
What's your name?
AUDIENCE: Helen.
DAVID MALAN: Helen.
David.
Nice to meet you.
Go ahead and join, I guess, this group right here in the middle, if you could.
So these folks here hopefully do have cell phones on you.
Key detail I probably should have mentioned earlier.
That's OK if you don't.
That's OK.
We're going to recover.
Whoever doesn't have a cell phone is now going to get a flashlight.
OK.
Let's do this.
OK.
Key detail.
Sorry, you can go ahead and turn that off.
Going to cross my fingers here that we have enough light bulbs.
Hang on.
Let's go ahead now and turn on, if you could, three light bulbs here.
So you don't have your phone?
Here is a nice iPhone XS.
OK.
[LAUGHTER]
1, 2, 3, 4.
Let's go ahead and turn yours on.
Can you swap phones for a moment?
So we have two light bulbs there, and we don't need anyone else's phone
on just yet.
Could you turn your light bulb on?
And could you turn your light bulb on?
And we need just one light bulb here, if you could turn that on.
So let me step out of the way.
And you'll see that we have someone in the 64s place whose light is
on, in the 8s place, then again in the 64s place and the 8s place,
and lastly, the 1.
So if a computer indeed had some 16 switches or transistors inside of it
and turned on those switches in this particular order,
what message are these humans here representing at the moment?
AUDIENCE: Hi.
DAVID MALAN: So it's indeed hi.
Why?
Because the mapping we arbitrarily chose but globally decided on is that 72 is H
and 73 is I.
Well, let's try one more further.
At the moment, we're just using two bytes of humans, if you will.
Two units of eight.
But suppose that we didn't just draw an imaginary line in between them
and count only up to the ones place through that 128s place.
But suppose that we treated everyone as one
much bigger value so that we could count much higher.
So now, these humans are taking on the value of a 128s place,
but then the 256, 512, 1024.
All I'm doing is multiplying by 2.
I'm going to need one more volunteer, and I'll take on this role over here.
If I were to be at the very end here, I'd now have 17 bits on stage.
17 switches or transistors.
Let me go ahead and turn on just some of these, if we could.
Most of them, we might have to borrow a couple of phones.
Let's go ahead and give-- if you could turn your phone on.
Here.
Your flashlight.
Let me-- that's technically yours.
Can we borrow your phone for a moment?
OK.
Your phone is going over here to the 32,000s place.
We need to turn yours on.
OK, I'll turn mine on over there.
So we need 1, 2.
Can we give you 3, 4 on?
Can we borrow that?
3, 4.
Can we-- keep the phones coming.
[CHUCKLING]
3, 4.
So 1, 2, 3, 4.
And then we skip 1.
And then we need you two to be on, if that's OK.
And then over here, thankfully, we need just one light bulb on.
So now it's your chance.
If a computer were using this many bits--
16 bits.
And if I stand in place now, 17 bits, where I represent 65,536,
and our volunteers all the way on the end represents the number 1,
and you do this math, what number are we all representing?
OK, no one's going to get this right.
It's 128,514.
What might that message say?
Well, there's not nearly enough clues in mine, but it's actually this.
So if you've sent today or recently an email or a text message with an emoji,
you might have sent this one--
Face with Tears of Joy.
So that's its official name.
But it's not an image per se.
It's actually a character.
And in fact, you might know that you have so many emojis these days,
and that's because computers and humans who
use them have started using way more than 8 bits.
Way more than 16 or 17 bits.
Sometimes 24 or 32 bits, which gives us so many darn possible permutations
of 0s and 1s, or switches being turned on or off, that frankly, it's
just become kind of a cultural thing that we
have so many darn possibilities, let's start using some of them
for more silly reasons, if you will, like emojis.
So if you ever receive today or hereafter a face with tears of joy,
what your friends have really sent to you is a pattern of 0s
and 1s somehow implemented with electricity or wavelengths of light
that represents, rather mundanely, 128,514.
So if we could, a round of applause for our human volunteers here.
[APPLAUSE]
Let me borrow this.
Thank you.
If you'd like to step off stage, we have a little something for each of you.
So we have just one last question to answer.
Thank you all so much.
We have just one other question to answer,
which is, if problem-solving ultimately boils down
to representing inputs and outputs, what is
the process that we pass those inputs through in order to get those outputs?
What is it you learn, ultimately, in a course on computer science?
Well, it's perhaps best explained by way of a problem.
So here is an old-school problem where you
have a whole bunch of names and numbers alphabetically sorted from A through Z,
and you want to find someone.
And even though this is pretty old-school,
it's honestly the same thing as the address book or the contacts app
that you have in your own iPhone or Android
phone, or any particular device.
If you scroll through your contacts, odds
are they're A through Z, alphabetized by first name or last name.
So this is just representative of the same problem
that you and I solve any time we look someone up in our phone.
Well, if I want to look up an old friend-- someone like Mike Smith,
last name starting with S--
I could certainly just start at the beginning of this book
and do 1, 2, 3, 4.
And that's a step-by-step process, otherwise known as an algorithm.
And is that algorithm correct?
Will I find Mike Smith?
AUDIENCE: Yes.
DAVID MALAN: Yeah.
I mean, it's a little tedious, and it's a little slow, but if Mike is in here,
I'll eventually find him.
But I'm not going to do that.
I know he's going to be roughly at the end.
So maybe a little more intelligently or efficiently,
I could do 2, 4, 6, 8, 10, 12, and so forth.
It's going to fly me through the phone book twice as fast.
And is that algorithm or step-by-step process correct?
AUDIENCE: [INAUDIBLE]
DAVID MALAN: A literal contention.
It's almost correct, except if I get unlucky and might
get sandwiched between two pages because I'm a little aggressively flying
through the phone book.
But no big deal.
If I maybe hit the T section, I could maybe double back one or few pages
and fix that.
But none of us are going to do that.
What's a typical person going to do?
And really, what's a computer going to do, be it in your phone or a laptop
these days?
AUDIENCE: [INAUDIBLE]
DAVID MALAN: Yeah.
It's going to go roughly maybe to the middle, or a little biased
toward the right, because you know S is a little alphabetically later
than most letters.
And I look down, for instance, here, and I see, oh, I'm in the M section.
And so I know that Mike is not this way.
He's definitely this way.
So both metaphorically and literally, can I tear a problem like this in half?
This is actually not that hard vertically.
I can tear the problem in half, and now I'm
left not with 1,000 pages with which I began, but maybe 500.
And I can do it again, and whittle myself down to like 250 pages.
And again, down to 125.
And again and again and again until I'm left with, hopefully,
just one or so page.
But what's powerful about, honestly, that intuition that odds are you
had when you walked in this door is that, in just 10 or so steps,
can you find Mike Smith in a phone book?
In just 10 or so steps, can iOS or Android find someone in your contacts
by dividing and conquering, dividing and conquering?
Whereas the other algorithms might have taken,
gosh, like 1,000 steps, 500 steps, almost as many pages as there are.
And so that's an algorithm, and that's what's
inside this proverbial black box.
It's the sort of secret sauce.
And the idea is that you learn not just to learn along the way,
but learn to harness in your own human intuition.
And so I wish I had discovered that far earlier for myself,
knowing that computer science is not about programming per se.
It really is about problem-solving, and just formalizing, and cleaning up
your thought process, and introducing you to ideas like this
that you can then apply in so many different ways.
So that there, say, is just a taste of computer science.
Allow me to conclude with a taste of this one course, CS50,
by way of the point of view of one of our very own students.
[VIDEO PLAYBACK]
[MUSIC - PORTUGAL.
THE MAN - "LIVE IN THE MOMENT"]
- (SINGING) My home is a girl with eyes like wishing wells.
I'm not alone, but I'm still lone-- lonely.
Those days are done, but I'm still glowing.
Ooh, la, la, la, la, la, let's live in the moment.
Come back Sunday morning.
Oh my, oh well.
When you're gone, goodbye, so long, farewell.
Ooh, la, la, la, la, la, let's live in the moment.
Come back Sunday morning.
Got soul to sell.
When you're gone, goodbye, so long, farewell.
My home is a girl who can't wait for time to tell.
God only knows we don't need history.
Your family swinging from the branches of a tree.
God only knows we don't need ghost stories.
Ooh, la, la, la, la, la, let's live in the moment.