Marie don't have to know much mathematics.

You don't need to know a lot about numbers you don't need to know about differential stuff.

No integration, no matrices.

It's a branch of mathematics, can pick up from scratch all by itself and actually come up with interesting results and understand what's going on.

People then often asked, What about not?

Is there something practical I cannot think of something that's really practiced in the terms off the shoe laces Or so when they still believed that our universe is filled with some ether Ether was that medium that would transport, you know, light waves since on.

And then I think it was Lord Kelvin and others that believed that the atoms are just different knots.

So the simplest possible act, um, say hydrogen, maybe just the a knot.

And then maybe helium is the next.

More complicated not.

And so that's the trifle not, and then you go down the periodic system.

And of course it was a beautiful and tempting way off bringing order into the periodic table, except it was just plain wrong.

I mean, pretty soon, people found out that is no.

And of course, also, people found that actually, atoms break apart into into particles in some way.

There's more structure to it, and they're clearly not not there more, more like little planetary system and said that was the end of that.

On the other hand, not actually now play a role in advanced physics in a trance chemistry and in advanced biology.

You on physics, even with string theory and and similar things there in statistical mechanics that suddenly they use some off the things that could prove is not.

That seemed to apply there in chemistry there now building molecules that are deliberately not in complicated ways.

They're also people working these nano particles that seemed to find material to have interesting properties when the or the elementary elements at the small scale are not it.

And finally, in biology, you probably have millions off knots in your body.

It turns out many bacteria, but even in your cell, some of the D N A strands are actually close loops, and some of them are actually happen to be.

Not that if you have so very close D n a strand that maybe not that, and you can see in this case there may be a particular group exposed, and it can undergo some chemical interaction with other molecules.

But then, if this thing can, it folds up in different way.

That part may no longer be available, but something else may pop out and then that can interact.

So as part of the regulation of what goes on inside a cell, some of these strands may recoil and change their shape and turns out that even can change.

They're not amiss because there actually are some enzymes and these ensigns they can essentially come along and snip, restrained and essentially that another slant pass through and then reconnect it some because mathematics competitions would never do it, because that that's totally against what you're allowed to do in not theory.

So that's their knots.

Play a role in very advanced fields, athlete challenges for you here, tipping it kind of exercises you want to do, and you could start that.

This knot theory is you look at something that you might draw arbitrarily, you know, having over under crossings in some way.

And then the question is What?

Not this this And now you may want to go and take your pipe, cleans or wires and try to carefully lay out this particular not over and under.

Crossings carefully observed, fused the ends together.

And now the question is lucky.

Which enough is it?

I'm just counting here.

It's going to be 1234 crossing.

So you think Oh, must be before crossing?

Not it must be the figure eight Not true or not true.

Let's take this loop that's of hangs down and just kind of flip it up.

Right?

So now somehow this thing goes up there, makes a loop and comes back down and then goes into this, not this loop up.

There can be untwist ID and it goes away.

But then we're just left.

Is this part?

Is this closing back onto itself?

Have you know what that is?

That's a trefoil.

So here we see an example, but you have something that looks likely more complicated.

It's relatively easy to unravel this and figure out okay, this is just a trifle not well.

Things can get worse.

What's not?

Is this now?

Yeah.

I can do a lot of mental exercise.

I think I could take this whole loop and kind of flip it over on.

Then I can actually pull it through here.

And similarly, I can take this loop here and flip it around the back to the other side.

I'm pretty sure that this not we'll get simpler when you try to unravel it.

I think you should really lay this out, try it with some wire or pipe clean and figure out what not buddies.

You making.

People don't want no more difficult.

Homework Year is yet another.

Not 1234566 crossings.

No problem.

I mean, I can try to mentally flip these loops around or so and nothing comes of it.

So I'm probably stuck.

Now.

I go back to the not table that we had before.

Can we figure out this six trusting?

Not which one of those three of these and you may want to do a lot of deforming and probably will get very frustrated because you may not be able to find anything.

And he said, Wait a minute.

Them sort of fourth different.

Kind of not, not really.

Mathematicians call this a composite not it's really to trifle not stuck together.

You can see from here to there.

It's clearly a trefoil now, and we can take this loop and kind of flip it down.

And then we'd have another trifle not.

And it's couple to this one beasties to links.

So any time you can take one complicated, not and cut it open somewhere.

So to strand, stick out another complicated, not cut it open summer to slant stick out.

You put it together.

Essentially, get a compound.

Not, and that's not so.

No, it's that's that doesn't fit into a table of well, it would make things much, much more complicated, so this allows to simplify things.

Now, all off the knots that you see in here are called prime knots.

They cannot possibly be reduced to something simpler.

They're really on their own, as complicated as ticket.

But there many, many complicated knots that can be taken apart like a complicated number can be taken apart into prime factors.

But once you ever prime factory can no further simplify it.

So all the not table does is give you only prime knots that they're not themselves compound.

But now you can take 73 and taking or 63 snippet open here so they could open their sticking together.

And you make something that has on the order off seven plus six crossings.

But it's not a 13 crossing, not it's it's this compound.

Not that it's a craft.

You've dropped a bomb on May.

So if he didn't do that, you know, then they're not stable.

Would become totally unwieldy.

Okay, Now would explode even even more quickly and even faster.

You actually are on the other side, and then you have to go once through Maur through the roller coaster until you come back to where you started.

So it's just one long string, essentially tied together.