[MUSIC PLAYING]
Hi.
I'm Dianna.
You're watching "Physics Girl," and I'm here
with Zach Weinersmith, who is the author and mastermind
behind SMBC Comics.
ZACH WEINERSMITH: Yes.
Saturday Morning Breakfast Cereal.
I've seen your comics like all over the internet,
before I knew that they were yours.
And I'm sure this is pretty common.
Yeah.
You Have this one comic that's about a math teacher.
ZACH WEINERSMITH: I was surprised
about how well that did it, because it was kind of mean.
Well, it was funny-- that was one
where I got a whole lot of math teachers,
and I was surprised, like math teachers who were still working
were like, this is exactly it.
And I was like, mm.
Oh, Zach.
I know, right?
Oh, that's so--
oh, poor children.
Thank you so much for--
the real reason that you're here is
to answer some physics riddles.
Yes.
OK, good.
Yeah.
OK, I'm going to start with a warm-up, which
is more of like a physics trivia question.
OK.
And I didn't get it right.
So, good luck.
What are the base SI units?
ZACH WEINERSMITH: Oh, like the most fundamental?
DIANNA COWERN: Yes.
Pause here if you want to think about the answer first.
ZACH WEINERSMITH: Grams.
I'm going to give you the point for gram,
but it's actually kilograms.
A kilogram is weirdly defined off of a physical object--
a cylinder kept in France called the Big K.
ZACH WEINERSMITH: Meters, obviously.
[DING]
This is such an evil question for someone
who hasn't studied physics for a long time.
Yeah, I'm just trying to think what--
I mean, because there are obviously
all the bigger aggregate units.
Like does joules count as fundamental?
No.
Well, then there would be seconds, of course.
[DING]
DIANNA COWERN: Yes.
The second is defined off of the frequency of light
from energy-level transitions in a cesium 133 atom-- so weird.
And there's more.
OK, well, there must be a charge unit, right?
So that's also one that I guessed.
I thought the coulomb was a base SI unit.
Right.
Why not?
I don't know why not.
It's probably a historical reason.
I just want you to know that you've
got all the ones that I got.
And the rest of them are weird.
What else do you need to describe what's
going on in the universe?
[LAUGHING] We've got a practicing physicist over here,
like dying to answer do you know what they are?
Yeah, what is it?
LLOYD: I think there's one for light.
It's either lumens or candela.
[DING]
DIANNA COWERN: Yeah!
Yeah!
That's some of the weird ones.
I never would have guessed.
It's the candela, which has to do
with the light from a candle.
LLOYD: Amp, is it?
DIANNA COWERN: Amp, yeah.
[DING]
ZACH WEINERSMITH: OK, explain amps-- yeah.
DIANNA COWERN: It turns out the amp is a base
unit for historical reasons.
It was historically easier to measure the force
on wires with current than to measure individual charges.
ZACH WEINERSMITH: And then-- but coulombs are not--
huh.
We should write a letter.
[BOTH LAUGHING]
You should write a comic about this.
Yeah, yeah.
OK so there are-- yeah, there are two more.
LLOYD: Mole.
[DING]
DIANNA COWERN: It's related to temperature.
ZACH WEINERSMITH: There's kelvin.
DIANNA COWERN: Yeah.
And there's kelvin, too.
[DING]
That was just the warmup to let you know how mean
I would be with these riddles.
Yeah.
So the actual riddle-- the real riddle.
Yes?
There is a group of prisoners.
Do you want to pick a number?
ZACH WEINERSMITH: 100.
DIANNA COWERN: 100 prisoners.
ZACH WEINERSMITH: Yeah.
DIANNA COWERN: A city with a lot of crime.
The evil warden decides she wants to play a sadistic game.
And so she tells all of the prisoners the night before,
the next day she's going to line them up and put hats on them,
one of two colors.
Do you want to pick the colors?
ZACH WEINERSMITH: Ooh.
Purple and green.
DIANNA COWERN: Purple and green.
You've got purple and green hats randomly on the prisoners.
It's going to be a random number of purple or green hats.
You don't have necessarily 50 purple and 50 green.
What she says to the prisoners she's going to do
is line them up all facing the same direction.
For example, the prisoner in the back is looking forward
and can see all of the prisoners in front of him.
And then the next prisoner can see just
all the ones in front of him.
The prisoner at the front can only see the wall.
Got it.
So then she's going to go from the back
and ask the prisoner the color of her hat.
If she guesses correctly, she gets to live.
If she guesses incorrectly, she dies a silent death.
And then she goes to the next prisoner.
Imagine that I'm behind you.
OK.
And you're facing that way.
Yeah.
And the warden comes to me and is like,
what color is your hat?
And I'm going to make my guess, or my educated guess,
and be like, green.
That's all you hear.
And then I will either die or not.
But you won't know.
Yeah.
And then she'll come to you, and you'll make your guess.
Is there a strategy that prisoners can come up with
to maximize the number of prisoners
that are going to live?
So they can meet before, like the night before.
ZACH WEINERSMITH: But they can't like look at each other's hat
and say.
DIANNA COWERN: No.
She lines them up, then puts the hats on of different colors.
They can't see their own hat.
They can only see the hats in the prisoners in front of them.
ZACH WEINERSMITH: Do they get to pick
how they line up in any way?
They're just randomly--
DIANNA COWERN: Just randomly, and then randomly given hats.
And can they-- they can't interact after they're lined
up?
The only thing they can say is--
guess the color of their hats.
So they can talk to each other?
They can talk to each other to come up with a strategy
the night before.
But not the day of.
Uh.
I'm not--
It's a hard one.
Yeah.
Try and maximize the number of survivors.
Right.
Not necessarily maximize--
Right.
Can you hear the person behind you when they guess?
Yes, you do.
[BOTH LAUGHING]
I mean, yeah, so the other thing you can do
is guess the same thing or guess the opposite thing,
but I don't see how that--
Well, the person behind you can see your hat.
Oh, OK.
So you should always guess what the next person
is going to say.
So only one person dies, right?
Well, let's think through that.
OK, so everyone can see all of the hats in front of them.
ZACH WEINERSMITH: Right, right.
So the next person who's going to be up,
you should just say whatever their hat is.
DIANNA COWERN: And then how many does that guarantee will live?
Like the strategy you're saying, right, it's like you--
you say the--
the hat of the person in front of you?
Yeah.
Say it's like green, purple, green, purple, green, purple.
Then everybody dies if you just say the hat in front of you.
ZACH WEINERSMITH: Oh, because-- right, of course,
because they could die because they gotta say the right thing.
DIANNA COWERN: Exactly.
ZACH WEINERSMITH: I see.
Yeah, you're right.
You're right-- yeah.
If it's lined up green, purple, green, purple,
and like every other person says the hat in front of them,
the worst loss for that one would be 50%.
Yeah, but you could say it in a different pitch
to tell the next person whether you're lying or not.
That should be your strategy.
Wasn't banned by the rules, I think, right?
It was not banned by the rules.
If every other person says the hat in front of them,
then you guarantee 50%.
Right.
Other than the cheat.
Was that-- was that your guess?
LLOYD: Yeah.
Is there a way to get better than that?
Not counting my cheating method?
So the first person could say something
about the total group with one word.
But like-- so you could-- the first person
could say what the majority is.
Is that--
Or something like that?
Or something like that.
Ooh!
Shoot.
I went through this struggle silently in my room.
And I made you do it on camera.
On camera.
This is a hint for you.
You have to figure out this thing
that you could look forward, see a whole group,
then decide something binary.
Right.
Like either it's this or it's that of the group.
So I've tortured you--
Yes.
--with a physics trivia question and a really hard
riddle.
Yes.
Do you want to ask me your riddle,
so I'm suffering while you--
That's a great idea.
OK.
Yeah, OK, so this is-- this is a Ray Smullyan riddle.
This is something I guess he did at a lecture.
He-- it was at a math lecture, and he called some poor guy up.
And he said, I want to make a deal with you.
And the deal is, I'm going to give you two $10 bills,
and then I'm going to make a statement of some kind, just
any kind of logical statement.
And if the statement is false, you
give me back one of the $10 bills.
And if the statement is true, you keep both.
So would you agree to this?
It's a good deal, right?
You either get $10 or $20.
And so the guy says yes.
And then he says, OK-- and this is-- this is not the statement.
But he says, I'm going to say something,
and then you're going to owe me $1,000.
And the question is, what can he say
that will result in him being owed $1,000.
Raymond Smullyan would get $1,000.
It's just a statement.
The other guy doesn't interact anymore at this point.
But does-- does the other have $1,000?
Those
Well, that's his problem.
He's gotta cough it up.
[BOTH LAUGHING]
OK, so he may go into debt.
Now you're suffering, too.
[BOTH LAUGHING]
[MUSIC PLAYING]
Is it something like, in order for you to figure out
whether this statement is true, you need to give me $900?
In the sense that that's like a logic statement,
it's that sort of structure, but it's not even that complicated.
It's not even that complicated.
No, no.
I feel like I'm getting nowhere.
Yeah, yeah.
Is it something like a qualifier, where--
is it something like, either you will keep $10
and give me back $1,010, or you will keep $20
and give me back $1,020?
Money
No, because then you could just not do it,
and the statement would be false,
and you'd only have to give back $10.
Yeah, I've though that that might be a-- a fly
in my ointment.
Yeah.
[LAUGHING] Yeah, yeah.
There's-- there's a condition where you can escape.
Ugh!
[BOTH LAUGHING]
I think-- I think that I'm done.
All right, let's--
In the time--
in the time allotted--
[LAUGHING]
I'm ready.
For the answer?
Yeah.
The answer is he will say, you will either
give me $1,000 or $10.
You have to think for a second about why this is true, right?
So--
DIANNA COWERN: Yeah.
ZACH WEINERSMITH: So if he--
DIANNA COWERN: Oh!
ZACH WEINERSMITH: Right?
So, yeah, he can't give him the $10, because then the statement
is false.
DIANNA COWERN: OK.
ZACH WEINERSMITH: [LAUGHING] Yeah.
DIANNA COWERN: I get it.
That's what I was trying to get, was
like there's something in the statement that guarantees
that it's either true or false.
ZACH WEINERSMITH: Right.
DIANNA COWERN: And that's the "you
will give me $10," is what contradicts the statement.
ZACH WEINERSMITH: Right.
DIANNA COWERN: Because if it's $10, then it's false.
But then he is doing what the thing is.
Right.
So it can't be false.
It has to be true.
Yes.
Ugh!
That was a great riddle.
Yeah, I like that one.
OK, are you ready?
Yes.
So the solution that guarantees
the most survivors does have to do with odds and evens.
OK.
If the person in the back says purple,
that means there's an odd number of purple hats ahead.
OK.
And-- and then the next person will know what they are.
So the person in the back will say either green or purple
and determine the total--
like, of the rest of the hats, is there
an odd number of purple hats or an even number of purple hats?
OK.
And they're telling everybody that.
So then the next person can see the rest of the hats
and sees, OK, well--
Dammit!
That's it.
That's beautiful.
You guys both, at the same time, you're like, oh!
Oh, that's great.
Isn't it nice?
Yeah, that's really good.
[LAUGHING]
Yeah, so if you look down the line and you know it's odd,
and there's an equal number of other kinds of hats,
you know you must be the odd man out-- the odd person out.
Yes.
And if it's not, then you know you must
align with the missing spot.
Yes.
And so now you have an answer to your--
[LAUGHING AND CLAPPING]
That's-- that's really-- that's really irritating.
You and I both like got right up to that last step.
Yes.
You got so close.
Thank you so much.
Thank you for having me.
This is-- this is such a coincidence.
I happened to be in London and going to BAHFest.
BAHFest.
Just one last thing.
(BOTH) Happy physics-ing.
That was the best first try ever.
I nailed it.
I was so good at that.
Yeah.
Bam.
Yes.
Hey, one last thing.
It's that time of year again--
Christmas!
Just kidding.
PBS Digital Studios is running a survey.
And basically, they'd like to hear from you
what you'd like to see more of on YouTube and in the world.
So, it's a quick survey.
There's a link to the description and in the card.
And 25 random participants are going to get a PBS T-shirt,
so sounds worth it.
That's all.
Thanks.