DAVID MALAN: So odds are you know someone who is or perhaps are

yourself a computer person.

But what does that mean?

Well I propose that a computer person is simply

someone who's really good at computational thinking.

Thinking methodically, or more formally, thinking algorithmically,

whereby you take inputs to some problem, you solve that problem

and produce output, but you do so step by step by step, along the way

defining any of the terms or ideas that you

need to use so that anyone else following along

can understand exactly what it is you're doing.

Computer science itself is really about computational thinking, then.

It's not about programming, with which it's

often conflated, although programming is a wonderfully useful tool with which

you can solve problems, but computer science itself

is about solving problems themselves.

And it can be in any number of domains, whether it's

software or hardware or artificial intelligence or machine learning

or data science or beyond.

That's the wonderful thing about computer science--

it's just so wonderfully applicable to other fields.

It's all about equipping you with a mental model,

so to speak, a set of concepts, as well as

some practical skills via which you can bring to bear solutions

to problems in other domains entirely.

Now what, though, does it mean to solve a problem?

I propose that we think about problem-solving quite simply as this.

If you've got some problem to be solved, you have an input.

And the goal is to solve that problem and come up with some solution, which

we'll call simply our output.

And in between those inputs and outputs hopefully

are the step-by-step instructions via which we can solve that problem.

Now how we're going to solve that problem we'll have to come back to.

For now we'll consider it to be the proverbial black box.

So we don't quite know or need to know right now just how it works,

but that it can work, and we'll come back to this soon.

But for now, we do need a way to represent these inputs,

and we do need a way to represent our outputs.

Right now I happen to be speaking English

and you happen to be hearing English, and so we've sort of

tacitly agreed that we'll represent our words using this particular language.

Now computers tend not to use English, they have their own system,

if you will, with what you might be familiar even if you don't quite

speak it yourself, and indeed, there are different ways

you can represent information.

For instance, let's consider the simplest of problems-- for instance,

counting the number of people in a room.

I could do this old-school.

I don't need computers or English, I can simply use my physical hand and say,

I'm starting with zero people and now I'll

count one, and then two, and then three, and then four, and then five,

and then--

I'm out of fingers, but I can at least employ my other hand, maybe

a couple of feet and get as high as 10, maybe even

20 using this physical system.

This is pretty equivalent, actually, to just keeping

score counting the old-school way with hash marks.

Right now we've not counted anything, but as soon

as I start drawing some lines, I might represent the number 1,

or 2 people in the room, or 3, or 4.

Or by convention I can draw a slash just to make super clear that this is now

representing 5, and then I can do another five of those

to count up the 10 and beyond.

Now these systems of hashes, as well as this system of counting on my fingers,

actually has a name.

That of unary notation.

Uno implying one, simply signifying that I only have one digit--

pun not intended-- via which I can count things.

This takes the form of my fingers on my hand or these hash marks on the screen.

But it doesn't get me very far, because of course

on my one hand with five fingers, I can only count up to five total.

And even on the board it feels pretty inefficient, because for every number

I want to count higher, I have to draw yet

another line on the screen, which just continue to accumulate.

But suppose we were a little more clever about this

and we thought about this problem from a different angle.

Maybe I could take into account not just the number of fingers

that I've raised, but the order in which I've raised them

or the pattern via which I've permuted them rather than just taking

into account how many of them are up.

If I take that approach, maybe I can actually count even higher than five

on just one hand before resorting to another hand or feet.

Now how could I do that?

Well instead of counting up 0 to 1 to 2 to 3 to 4

to 5, why do I instead start with some patterns instead?

So I'll still start with 0, I'll still start with 1, but now for 2,

I'm not just going to raise the second finger,

I'm instead going to go from 0 to 1 to 2,

putting down that first finger or thumb, simply representing 2

with this one finger.

And when I'm ready to represent the number 3,

I'll bring that finger back up.

And so using just two fingers now have I represented four possible values--

0, 1, 2, and 3.

From 0 to 3, of course, is four total values,

and so I've counted as high as 3 now using not three fingers, but only two.

How, though, can I count higher than 3?

Well, I just need to raise an additional finger.

And so let's start at 0, to 1, to 2, to 3, to 4-- whoops--

to 5, to 6, and now to 7.

And if it didn't hurt so much, I could continue counting as high as 8 and 9

and 10 and beyond by simply permuting my fingers in different ways.

So how high can I now count on this one hand?

Using unary notation with fingers just up or down, I can count as high as 5--

from 0 to 5.

But with these same five fingers, if I instead use not unary,

but let's call it binary notation where we're actually

taking into account whether the fingers are up or down and the pattern thereof,

well now it would seem that each of these fingers

can be in one of two possible states or configurations.

They can either be up or they can be down, or just one of them can be up

or can be down, or just one other can be up or down.

So if there's two possible states or configurations for each of these five

fingers, that's like 2 times 2 times 2 times 2 times 2,

or 2 to the power of 5 for five fingers, which is actually 32 possible patterns.

Which is to say with my one human hand, now can I

count using not unary, but binary from 0 to 31, which is 32 possible values.

Now what's the goal at hand?

It's quite simply to represent information.

Because if we have inputs and outputs, we

need to decide a priori how we're going to represent those values.

Now it turns out in computers, binary is wonderfully well-suited.

Because after all, what's the one physical input to any computer

you have, whether it's your laptop or desktop or these days,

even a phone in your pocket?

Well odds are, at the end of the day-- or even perhaps earlier in the day--

you need to physically plug that device into the wall and actually recharge it.

And somehow or other there's electricity or electrons

flowing from the wall that are stored in the battery in your device

if it has a battery, and that is the input that drives your entire machine's

operation.

And so if that's the only possible input,

it's pretty straightforward to imagine that you might have your computer

plugged in or not, power is flowing or not,

you've got a charge in your battery or you don't.

And so this binary world where something can be in two possible states--

on or off, plugged in or not--

is wonderfully conducive to now using binary in the context of computers

to represent information.

After all, if I want to represent a number,

I might simply turn on the lights.

And so my phone here has a light built in, and right now that light is off,

but if I consider this then to be off, we'll call it a 0.

And if I turn this flashlight now on, I can be said to be representing a 1.

And so simply with a simple light bulb can I represent two possible values

just like my finger can be up and down.

But computers don't necessarily use lots of little light bulbs,

they use something else that's called a transistor.

A transistor is a tiny little switch, and that switch, of course,

can be either on or off-- letting electricity in or not.

And so when you have a computer, inside of which

is a motherboard and CPU and bunches of other pieces of hardware,

one of the underlying components ultimately

are these things called transistors.

And computers today have millions of them inside, each of which

can be on or off-- so far more than my five fingers,

and that's ultimately how a computer can go about representing information.

So long as it has access to some physical supply of electricity can

it use that electricity to turn these switches

on or off in distinct patterns, thereby representing 0, 1, 2, 3, 4,

all the way up to 31 or even millions or billions or beyond.

And so computers use binary.

Computers speak binary-- only 0's and 1's or off and on,

because it's so wonderfully well-conducive to the physical world

on which they're ultimately based.

We humans, meanwhile, tend to communicate

not only in English and other spoken languages,

but in a numeric system called decimal.

So decimal, dec meaning 10, has 10 digits at its disposal--

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, whereas binary has just two--

0 and 1-- and unary, you might say, has just one--

1, the hash mark that I drew on the board.

But if I only have 0's and 1's at my disposal, how can

I possibly count to 2 or 3 or beyond?

Well, we need some way of mapping these 0's and 1's to the more familiar

numbers that we ourselves know.

So how can we go about doing this?

It's one thing to describe it in terms of patterns on your fingers,

but again, a device just has switches that it can turn on and off.

Well it turns out even if you don't yet speak binary

or have never really thought about doing so,

turns out that it's not all that dissimilar to the system of numbers

with which we grew up.

In fact, in grade school, you and I probably

grew up learning how to represent numbers in rather the same way.

For instance, consider this--

clearly the number 123.

But why is that?

It's not inherently the number 123.

Really, this is just three symbols on the screen.

We of course immediately recognize them as 1 and 2 and 3,

and we infer from that, oh, this is the number 123, but why is that exactly?

Well if you're like me, you probably grew up

representing numbers in the following way,

even if it's been quite some time since you thought about it like this.

With the symbol here, 1, 2, and 3, if you're like me,

you probably grew up thinking of this rightmost digit

as being in the ones place, and this middle digit

is being in the tens place, and this leftmost digit

as being in the one hundredths place.

And if it were a longer number, you'd have

the one thousandths place and ten thousandths place and beyond.

Now how do we get from 1, 2, 3 to 123?

Well, the arithmetic we were taught says to do 100 times 1, and then 10 times

2, and then 1 times 3, and then add all three of those products

together, giving us, of course, 100 plus 20 plus 3, which of course is 123.

Now that actually doesn't feel like much progress, because we started at 123

and we got to 123, but that's not quite that.

We actually started with the pattern of symbols--

1, 2, 3, like a pattern of fingers, and ultimately ascribe mathematical meaning

to those symbols as 123.

And it turns out computers, even though they speak binary and therefore only

have 0's and 1's at their disposal-- no 2 or 3 or 4 or 5 or 6 or 7 or 8 or 9,

they count in exactly the same way, and they represent inputs and outputs

in fundamentally the same way.

Consider this.

Suppose that I have 3 bits at my disposal, 3 switches or light bulbs,