SPEAKER 1: Well at the end of the day, computers
are using what is their input, really just electricity, right?
Probably the only thing all of us do every day or every couple of days
with our laptop or desktop or phone is either make sure it's still plugged
in or to plug it in so as to charge it.
So the only physical input to our devices
these days is electricity in some form.
And we don't have to get into the nuances of what electricity is,
but I think it's about electrons flowing into the device so as to charge it.
So it suffices for our purposes to know that there's
some physical input to the device, these computers and phones that we use,
but that's it.
And so if we harness this electricity, maybe we
can start to represent information with it.
For instance, here is a light bulb, this old ghost lights in the theater here
that's currently off.
But it has the ability to turn on.
We just need to plug it in or throw on a switch.
And if that's the case, what's really quite
compelling about the metaphor of using lights
is that right now this light bulb is currently off.
But as soon as I allow electricity to flow
as by plugging it in or maybe throwing a switch, now it's of course, on.
And if I unplug it or throw the switch again, it's off.
Or if I plug it back in, it's on.
And the implication of this very simple idea
is that we can take a physical device, like a single light bulb
and by plugging it in or unplugging it, we can represent information.
What did I just do?
I represented the light bulb being off or on.
But we can just call off and on something else.
We can call them zeros and ones.
And so this really is the germ of an idea
that gave us computers and with it, their use of the binary system.
If at the end of the day all they have is physical input is electricity,
well, let's just use that to harness and keep track of information.
Let's store a little bit of electricity when we want to represent a one
and let's let go of that electricity in some sense
when we want to represent a zero instead.
And so because the input to computers is so simple
thus gives us the zeros and ones that we now use.
But we seem to have created a problem for ourselves.
If we only have one light bulb or one switch, if it's off, it might be zero.
If it's on, it might be a one.
But how do I count higher than one?
That problem still fundamentally remains.
Well, I could, of course, use more light bulbs.
So let me ask this.
If we were to use three light bulbs, how high could we count?
So with one light bulb, we can count from zero to one, two possibilities.
But with three light bulbs, how high could we count?
Well, let me go ahead and ask this question here on the screen.
In just a moment, you'll see on your side
this particular question via which you can respond on your device.
How high can you count with three light bulbs?
So instead of one, I give you three.
Each of which can be on or off.
How high can we perhaps count?
So you'll see on the screen here the answers coming in.
We have a lot of folks thinking 60 plus percent
that it's 8 is the highest you can count.
A lot of you think it's 7.
And some of you also think it might be 3 or 2.
So that's actually an interesting range of answers.
And let's see what might actually be the case.
Well, let me cut back over to three actual light bulbs here, all of which
are off.
And most naively, I think if we were to turn these light bulbs
on if they currently represent zero, obviously I could turn one on
and we could call it one.
Then I could turn the second one on, and call it two.
Turn on the third one, and now with all three on, we could say now,
we're representing three.
But we're not really being clever enough just
yet if we're only counting as high as three
because I'm just turning them on in this story left to right.
But what if we were a little more clever.
Maybe we turn them on right to left, or maybe we kind of permuted them
in different directions.
That is we took into account not just how many bulbs are on
or how many fingers are in the air but rather the pattern of on
and off light bulbs that we've created.
So let's just count this up.
So let me somewhat systematically turn some of these bulbs on here
albeit virtually.
Here might be one.
Here might be two.
Here might be three.
But then we're kind of done with that story.
So how might we do it a little better?
Well, start again at zero.
Here might be one.
Why don't we call this two?
Why don't we call this three?
Why don't we call this four?
Call this five, this six, and this seven.
Now, it's fine if you didn't quite see what pattern I was following.
But take my word for it that was a unique pattern of light bulbs
eight total times.
I started at off, off, off, and I ended at on, on, on.
But along the way, there were indeed eight.
But how high can I count?
Well, it kind of depends on what number you start counting from.
And just as we thus far have been doing, computer scientists do all the time.
Computer scientists, and in turn computer programs
typically start counting from zero just because it makes sense
because when everything is off, you might as well call that zero.
So if we start counting at zero, and we have eight possible patterns
that we just saw pictorially, well, that would
allow us to count as high as seven.
So from zero to seven, so seven is the highest
we can count with three light bulbs.
So those of you who propose that seven was the answer, 36% of you
were indeed correct.
57% of you who said eight are correct if you assume we start counting at one,
and that's fine, but at least in the computing world now,
we'll generally by convention start counting from zero.
But you are correct to say that there's eight such possibility.