I want to show you how to fill a climb bottle.

Can a client probably filled?

Does the client bottle have volume?

Yes, a mathematician.

And they'll say, Well, a Klein bottle doesn't really have any volume.

It's a tope logical shape.

This doesn't have value, but wait a second.

Looks like it has volume.

Well, if you ask apologised Does a measuring cup have volume?

They'll probably tell you no.

Does a sphere have volume?

Yep.

No matter how hot.

You know, you know, four pi r cubed whatever.

It has a volume.

It divides the universe into an outside and it inside.

And no matter how you stretch and contort it in the A, shrink it if you make it bigger, it'll always have a volume.

Oh, a piece of paper.

I can make it into sort of a cup somehow or another, but I'll always occupied very little valuable, you know, in the limit.

None.

Likewise.

A bag right.

I can put stuff in and put stuff into it.

I even put stuff that has volume into it.

But it doesn't divide the universe.

It doesn't divide the universe into two parts.

If I were in outer space.

All of these grape would float out a bag doesn't divide our universe into two parts.

This is related closely to a two dimensional problem called the Jordan Curve Problems, which asks a cool question of Is there a difference between that curve and this other curve this encloses in area This doesn't enclose an area turns out to be a surprisingly difficult thing to prove.

And the mathematician Camille Jordan, who finally solved it.

It was a real smart character in the same way to ATT.

Apologised.

The question is, does something divide the universe into the outside?

In the inside Klein bottle, even a three dimensional Klein bottle, an immersion like this?

Well, the air on the inside of it can easily escape to the outside sort of this cup, this measuring cup, which says, Oh, 500 mill liters over here.

Ah, physical volume to it apologised.

They just melt it down, flatten it out and say, Oh, this is home.

You morph IQ to a disk.

It has no volume.

A disc has no value.

So be careful when you talk to mathematicians in the kitchen.

Don't don't, don't don't let them near your recipe book.

Having said that, you know, Sphere has a volume.

A doughnut.

A tourist has a volume, but Klein bottle doesn't have a mathematical value.

Got that?

What about a physical volume?

Well, it's obviously you put no in America.

It's possible to put 16 ounces of water in it.

Everywhere else in the world, you could put 500 milliliters into it.

Got there.

So if a claim bottle doesn't have a mathematical volume doesn't have a physical value.

Well, the way make these the answer is, well, sort of.

Yes, you can fill a Klein bottle with water and throw some dye in it.

Also, you can't pull that out.

Well, yeah, I can pour it out.

Let's pour some water out.

Go through here.

But look, glug glug.

Pour it out.

Out it goes.

Drop by drop.

Essentially, it's vapor locked.

It won't.

So Yep, I can get water in.

I can get water out, so I like the measuring cup.

Your Klein bottle in the real world only has volume depending on its orientation and gravity.

That's right.

Another way of thinking of it is this.

Measuring cup depends on gravity toe hold, Hold water theat absence of gravity.

Or if the gravitational field is inverted, it doesn't hold water anymore.

Bright Got that?

Likewise declined bottle, but a sphere.

Hey, this is you Put water in here.

It'll stay in there no matter what.

So how do you feel a client bottle?

Oh, step one for me.

I'll put a drop of food coloring in dip, which is way more than you need a little bit of water in a few drops.

It'll go right through.

Noticed my fingers have already been died.

It's okay.

I got some.

Got some water in there.

Problem is, every time, pour water into vapor locks and I don't get sort of this much water in.

So come on over.

I'll dunk it underwater and show you how to fill a Klein bottle with water along with a little bit of blue in it.

Don't get underwater and wiggle it around.

Each time a bubble of air comes out and with each bubble of air, a little bit of water comes in.

Let's get a bubble of here and held underwater long enough.

So you're doing like, a sort of a 360 you to get the bubble.

Yeah, And if each bubble is about a mill leader or two eventually with each bubble leaving conservation of something tells me that Ah, bubble size bit of water is going in.

Yeah.

Oh, come on, It's not slow.

This is fast compared to the age of the universe.

This is speed compared to even something as rapid as global warming.

This is fast stuff here, not just fast, but, you know, compared to the rate it takes to make a Klein bottle, it's enormously fast.

Um, you could use an aquarium pump.

You could use a water pump and so on.

But here's a Klein bottle that's completely filled with water, and if I lift it up that first, it'll noticed.

Now, when I take my hand off the bottom, a little bit dribbles out, but not too much.

Can you put water into Klein bottle?

You bet you in our physical universe problem, of course, is water can also be taken out.

Riel problem though this once you get water in there, Yeah, you can get almost all of it out by tilting it and sort of doing the opposite of what you did before.

Tilt and poor tilt and dribble out.

Yeah, that works.

So you get water in kind of shake it out.

The problem is the last few drops of water.

Oh, there's not much air circulation inside of a physical Klein bottle.

As a result, the last few drops of water that surface tension holds there.

I have an example, probably not very visible in the video, but there's droplets of water in here you can.

Well, Getting the last few drops out means overcoming surface tension.

Hard to do so to remove the last few drops, I'll let the sit in a distance strain for, oh, an hour or three.

Little bit of water will collect there.

I'll pour it out then two, you know, get it nice and dry on the outside.

A little bit of water still in there.

I'll either pour acid tone in, swish it around, pour it out, then let the acid Tony evaporate.

Pour alcohol in.

That'll work or intubated with an aquarium air pump and pump air through it.

Let the water evaporates.

This, they says, isn't this the same thing?

That's why you do the astronomy.

After all, it's not gonna make you rich.

It's not gonna make you famous.

It's not going to get Your girls didn't work for me.

What it does do is it gets you closer in touch with the universe.