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SPEAKER 1: Well at the
end of the day, computers

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are using what is their input,
really just electricity, right?

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Probably the only thing all of us
do every day or every couple of days

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with our laptop or desktop or phone
is either make sure it's still plugged

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in or to plug it in so as to charge it.

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So the only physical
input to our devices

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these days is electricity in some form.

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And we don't have to get into the
nuances of what electricity is,

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but I think it's about electrons flowing
into the device so as to charge it.

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So it suffices for our
purposes to know that there's

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some physical input to the device,
these computers and phones that we use,

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but that's it.

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And so if we harness this
electricity, maybe we

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can start to represent
information with it.

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For instance, here is a light bulb, this
old ghost lights in the theater here

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that's currently off.

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But it has the ability to turn on.

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We just need to plug it
in or throw on a switch.

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And if that's the case,
what's really quite

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compelling about the
metaphor of using lights

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is that right now this
light bulb is currently off.

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But as soon as I allow
electricity to flow

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as by plugging it in or maybe throwing
a switch, now it's of course, on.

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And if I unplug it or throw
the switch again, it's off.

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Or if I plug it back in, it's on.

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And the implication of
this very simple idea

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is that we can take a physical
device, like a single light bulb

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and by plugging it in or unplugging
it, we can represent information.

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What did I just do?

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I represented the light
bulb being off or on.

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But we can just call off
and on something else.

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We can call them zeros and ones.

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And so this really is
the germ of an idea

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that gave us computers and with
it, their use of the binary system.

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If at the end of the day all they
have is physical input is electricity,

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well, let's just use that to harness
and keep track of information.

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Let's store a little bit of electricity
when we want to represent a one

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and let's let go of that
electricity in some sense

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when we want to
represent a zero instead.

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And so because the input
to computers is so simple

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thus gives us the zeros
and ones that we now use.

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But we seem to have created
a problem for ourselves.

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If we only have one light bulb or one
switch, if it's off, it might be zero.

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If it's on, it might be a one.

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But how do I count higher than one?

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That problem still
fundamentally remains.

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Well, I could, of course,
use more light bulbs.

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So let me ask this.

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If we were to use three light
bulbs, how high could we count?

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So with one light bulb, we can count
from zero to one, two possibilities.

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But with three light bulbs,
how high could we count?

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Well, let me go ahead and ask
this question here on the screen.

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In just a moment,
you'll see on your side

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this particular question via which
you can respond on your device.

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How high can you count
with three light bulbs?

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So instead of one, I give you three.

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Each of which can be on or off.

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How high can we perhaps count?

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So you'll see on the screen
here the answers coming in.

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We have a lot of folks
thinking 60 plus percent

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that it's 8 is the
highest you can count.

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A lot of you think it's 7.

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And some of you also
think it might be 3 or 2.

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So that's actually an
interesting range of answers.

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And let's see what might
actually be the case.

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Well, let me cut back over to three
actual light bulbs here, all of which

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are off.

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And most naively, I think if we
were to turn these light bulbs

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on if they currently represent
zero, obviously I could turn one on

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and we could call it one.

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Then I could turn the second
one on, and call it two.

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Turn on the third one, and now with
all three on, we could say now,

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we're representing three.

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But we're not really
being clever enough just

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yet if we're only
counting as high as three

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because I'm just turning them
on in this story left to right.

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But what if we were
a little more clever.

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Maybe we turn them on right to left,
or maybe we kind of permuted them

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in different directions.

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That is we took into account
not just how many bulbs are on

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or how many fingers are in the
air but rather the pattern of on

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and off light bulbs that we've created.

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So let's just count this up.

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So let me somewhat systematically
turn some of these bulbs on here

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albeit virtually.

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Here might be one.

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Here might be two.

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Here might be three.

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But then we're kind of
done with that story.

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So how might we do it a little better?

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Well, start again at zero.

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Here might be one.

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Why don't we call this two?

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Why don't we call this three?

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Why don't we call this four?

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Call this five, this
six, and this seven.

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Now, it's fine if you didn't quite
see what pattern I was following.

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But take my word for it that was
a unique pattern of light bulbs

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eight total times.

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I started at off, off, off,
and I ended at on, on, on.

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But along the way,
there were indeed eight.

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But how high can I count?

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Well, it kind of depends on what
number you start counting from.

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And just as we thus far have been doing,
computer scientists do all the time.

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Computer scientists, and
in turn computer programs

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typically start counting from
zero just because it makes sense

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because when everything is off,
you might as well call that zero.

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So if we start counting at zero,
and we have eight possible patterns

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that we just saw
pictorially, well, that would

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allow us to count as high as seven.

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So from zero to seven,
so seven is the highest

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we can count with three light bulbs.

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So those of you who propose that
seven was the answer, 36% of you

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were indeed correct.

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57% of you who said eight are correct
if you assume we start counting at one,

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and that's fine, but at least
in the computing world now,

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we'll generally by convention
start counting from zero.

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But you are correct to say that
there's eight such possibility.

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