Hi Sal.
>> Hey Brit.
>> How are you?
>> Good, it looks like you have a game going on here.
>> Not a game, yeah, kind of a challenge question for you.
What I did is I put one grain of rice in the first square.
>> That's right.
>> There's 64 squares on the board.
>> Yep.
>> And in each consecutive square I doubled the amount of rice.
>> Mm-hm.
>> How much rice do you think would be, on this square?
>> On that square.
So let me, let me think about it a little bit.
Actually I'm going to take some [SOUND].
So here you have 1.
And we multiply that times 2.
So this is going to be 2 times.
2 no, no 2 times 1, what am I doing?
Now this is 2 times that 1, so this is 2 times 2.
Now this 2 times that so this is okay,
we're starting to get a lot of 2s here, multiplying them together so this is 2
times 2, I'm trying to write sideways times 2.
So this one is going to be five 2s multiplied together.
This is going to be six 2s multiplied together.
This is gonna be seven twos multiplied together.
>> Mm-hm.
>> Eight 2s multiplied together.
So nine 2s, 10, 11, 12, 13.
So 2, all, all of this stuff multiplied together 8,192 grains of rice.
Is what we should see right over here.
>> You know I had fun last night, I was up late, but there you go.
>> Did you really count out 8192 grains of rice.
>> More or less.
>> Okay let's just say you did.
>> What if we just went four steps ahead, how much rice would be here?
>> Four steps ahead, so we're gonna multiply by 2, multiply by 2 again.
Then multiply by 2 again, then multiply by 2 again.
So this number times, let's see 2 times two is 4, times 2 is 8 times 2 is 16.
So it's gonna get us like a 120, like 120,000 or around there.
>> 131,672.
You had a lot of time last night.
>> We're not even halfway across the board yet.
>> We're not.
>> We, I mean this is, this is a lot of,
that's a lot of rice there, that, you could throw a party.
>> What about the last square, this is 63 steps.
>> We're gonna take, we're gonna take 2 times 2, and we're gonna do 63 of those.
So this is going to be a, a huge number and
actually, it would be neat if there was a notation for that.
>> I, I didn't, I didn't count this one out, but
it is the size of Mount Everest, the pile of rice.
>> Hm.
>> And it would feed 485 trillion people.
>> But I have got a question.
I mean [INAUDIBLE] this was a little bit of a,
of a pain, for me to write all of these twos.
>> So is this.
>> If I were the mathematical community.
>> Mm-hm.
>> I would want some type of notation.
>> You kind of got on it here.
I, I like this dot, dot, dot and the 63.
This, you know, I understand this.
>> Yeah, you could understand this.
But, this is still a little bit.
Little bit too much, what if instead you just wrote.
>> Mathematicians love being efficient right they want, they're lazy.
They have things to do they have to go home and count grains of rice.
>> Right.
>> [LAUGH] Yeah so that is 63 twos and multiply them all together.
>> This is the first square on our board, we have one grain of rice.
And when we double it, we have two grains of rice.
>> Yup.
>> And we double it again, we have four, and I'm thinking,
this, this is similar to what we were doing, it's just represented differently.
>> Yeah, well I mean this one, the one you were making, right, every time you,
you're kind of adding these more, these Popsicle
sticks you're kind of branching out, you know, one.
Popsicle stick now becomes two popsicle sticks, and then you keep doing that.
One Popsicle stick becomes 2, but now you have 2 of em.
So here you have 1, now you have 1 times 2.
Now each of these two branch into 2, so now
you have 2 times 2 or you have four Popsicle sticks.
Every stage, every branch you're multiplying by 2 again.
>> I, I just basically continue splitting just like the tree does?
>> Yup.
Now, I can really see what 2 to the power of 3 looks like.
>> And, that's what we have here.
1 times 2 times 2 times 2, which is 8.
This is 2 to the third power.
>> And, when I see 2 to the power of something, let's just say n.
>> Mm-hm.
>> N could also be number of steps up this tree.
I could think about it that way.
>> Yeah, you could do, I guess one way to think about it is
how many times you branched, but that one, that tree there's actually even more.
>> I don't think this counts because, again,
this branch is four times of each branch.
>> Well, I guess, why not.
Well.
I mean, its It's different, it's not gonna be 2 anymore.
So this, the first one we haven't branched yet.
This is gonna be 4 to the 0 power, you've had no branches yet.
This you branched once, so this is 4 to the 1st power, you have 4 branches now.
>> Oh, I like this.
>> And now each of those,.
So now you've branched twice, so this is 4 to the second power.
So yeah, the base, or what is called the base, when
you're dealing with an exponent is four right over here, this
is how many times, how many new branches each of the
new branches turn in to at each of these new junctions.
>> Let's call them junctions.
>> Junctions.
You haven't branched yet, here you branch once and here you branch.
>> This is interesting.
This is also why when I look at a tree,
you know, there's thousands of leaves, but just one trunk.
And when you actually go up, and you look inside
the tree, it only branches you know, three or four times.
>> And that shows the power of exponential growth.
>> Yes.
[LAUGH]