The Impossible Number

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Last episode of the current run. On the script, I've written the word intor

because every time I try to write the word intro, it comes out as intor. Does it? Yeah.
Do you have words that you just always type out wrong? Oh, yeah. What's your

soldier?

How do you type it? Oh, God. Every time I'm like, I just don't know what.

S, and then I basically don't know what's next.

I did um so my thesis back in the day was on the development of the retina.

So that required writing the word retina a few times. Not a single time in the last 25 years have I written the word retina without first writing retian.
Really?

I've

put an autocorrect on. Oh, you know what, actually? So I did have one in my thesis, but it was viscous.
My thesis was all about viscous fluids. A lot of them were vicious.

That could have really serious implications. It did, it did.
Consider a vicious fluid. Okay.
Yeah.

Anyway, that's nothing to do with the programme that you're about to hear, the final episode in this run, which is one of those ones where Hannah's extraordinarily overexcited.

What I will say is that I just asked our producer to cut out some of my squeals.

She did. I hope he doesn't.
I hope he doesn't. You're about to find out.
I insist that he does.

After our major maths nerd out in the pie episode from last series, loads of you wrote in to ask for some more maths. Did they though? Yes, they did, Adam.
Yes, they did.

This is what the listeners want. And you know what? I know you're going to enjoy this by the end.
Will I? You enjoyed the pie episode by the end. I did.
You did.

And today, we're venturing into extra weirdness because, you know, pie, ultimately, it's just a number that's slightly bigger than three. So, yeah,

it's interesting, but it's not that weird and wonderful.

Quite easy to grasp. Today, Adam, we are going to go for stuff that are much stranger, much more difficult to conceptualize, and yet numbers that are indispensable in maths, engineering, and physics.

Today, Adam, we're talking about imaginary numbers. Oh, for heaven's sake.

Really?

Yes, we are. 30 minutes, buckle up, strap in.
Okay, wait, wait, wait. Let me...
You know the number 9, right? What's the square root of 9? 3. Correct.
What's the square root of minus 9?

Minus 3. Right? Well, it can't be.
The square root of minus 9 can't be minus 3 because, yeah, minus 3 times minus 3 is 9. I have an answer for you.

The square root of minus 9 is there isn't one.

Well, that is what people thought for a long time. Sensible people.

But people also thought that you couldn't divide one number over the other. People thought that there wasn't a zero for a really long time.

And so mathematicians don't like the idea of having a question without an answer.

And it turns out that there is an answer to what is the square root of minus nine, but you can only do it if you know what the square root of minus one is. And that, my friend, is the topic of today.

Right. Okay, well, listener Peter Scott did ask in an email, should you have a program on the square root of minus one?

Well, Peter, I'm going with no, but it may be that I've already lost this battle.

Indeed you have because the answer is yes and we have got two fellow maths nerds to help us navigate through this weird landscape. We've got Dr.
Michael Brooks author of The Math That Made Us. And Dr.

Eleanor Knox, a philosopher of physics from King's College London, currently a visiting fellow at the University of Pittsburgh and you last heard her on the Pi programme.

Okay well listen. Michael we'll start with you.

We've established that the square root of minus one is a... it's an impossible concept.
Who first came up with this nutso idea and what were they up to?

So it's a guy called Jerome Cardano who was working in Italy in the 16th century and he was solving some cubic equations like you do and he discovered that basically in the middle of his calculations he had a root square root of minus 15 to deal with and it sort of stopped him in his tracks and he said that's not right you know you can't do that he knew that you can't have the square root of a negative number and he sort of said this seems like it's an impossible case, was what he wrote down.

So he said, you know, this is arithmetic subtlety, or there's something odd about all of this. But he went on to kind of, you know, work out a sort of sidestep.

He basically carried on with the calculation and got to an answer that worked in the end. So it was fine.

But he did at least acknowledge that this was actually a real thing that was really there in the maths, which previous mathematicians, like Heron of Alexandria, had said,

oh, I've just got something wrong and scrubbed out the negative.

Which is, I would have gone with Heron of Alexandria if I knew anything about him. Him? A bird? Is that a Heron?

He was a man.

Not an actual Heron. Thank you.
That's useful information. So, Cardano then, so he doesn't ignore this.

He recognises that it's a real thing, but also acknowledges that it's a slightly quirky concept. What happens next? He basically says it's too hard for him to deal with.

So he kind of talks about it, writes a bit about it, and then sort of moves on.

And he's working with his student, Ludovico Ferrari, to kind you know advance the frontiers of maths and and so he just doesn't want to get distracted so he just leaves it.

You know how you said that just doing some cubic equations as though it's like a standard thing that you do on a Wednesday afternoon, right?

I mean I know that not everyone has as an exciting a life as I do

but around this time, the Renaissance, there's a lot of this going on, isn't there? Yeah, because these things are really important.

So if you can solve, you know, first of all, quadratic equations, so x squared, and then the cubic with x cubed, x to the power of 3, and then the quartic, quartic, x to the power of 4.

If you can solve these things, you work out ways to solve them, you can make a lot of money from it.

First of all, because all the financiers want to employ you, because it helps them to calculate good rates of interest.

So as today, you know, the mathematicians just got hoovered up by all the bankers and finance institutions.

No calculators, of course. No calculators, not even algebraic notation.
So everything's written out in words, literally like words describing what we would see as an equation. And also,

you can get university teaching posts by solving equations that other mathematicians can't solve.

So if you know the solution to a cubic equation, you can challenge somebody who's got a job you want, challenge them to a mathematical duel in the street where you set each other 30 problems and people watch you try and solve them.

And you lose or win a job on the basis of this. Whoa, whoa, did this happen? Did this really happen? This is a real phenomenon.

Yeah, so Cardano nearly got tangled up in one, except that he, so there was a guy called Niccolò Tartaglia who wanted to challenge him because he said that cardano had published a solution that tartaglia owned so um it was wild so he got very upset and challenged cardano to a duel after lots of nasty letters maths duel maths duel and um and cardano said i'm not doing that but but the his student ferrari said i'll do it and took him on and because uh ferrari had worked out the solutions to the quartic equations and tartaglia hadn't ferrari just sent him 30 30 questions that were just like quartic that he knew how to solve and the other guy didn't.

And Tartalia didn't even turn up. I'm deeply in favour of bringing this back.

I think next Prime Minister, right, what we should do is get them in Downing Street, give them blackboards each and just set them off and go. Wow.
It would be amazing. But people used to watch this.

This was like a public spectacle. Right.
But you also used to hang people as public spectacles. I don't know whether that was.
And there wasn't maybe much entertainment as well.

I don't know whether that's in the plus column or the negative column. But then this idea, when does it become imaginary rather than impossible? So Cardano doesn't do anything with it.

And then a couple of decades later, Raphael Bombelli sort of works out the maths of doing complex numbers with imaginary parts and real parts.

But then nobody really does much with it for really a couple of centuries.

So then Descartes turns up, calls them imaginary in a kind of very derogatory kind of way, like, you know, what's the point of these?

So, okay, Descartes was essentially just throwing some 18th century shades on this, which is fine.

But the thing is, is that you shouldn't get sidetracked, Elinor, should you, by uh, by thinking of them as imaginary, even though they are technically different from real numbers. Shall we is it?

Do you think that we can

load Adam's brain with the difference between the two?

So, real numbers are the ones that we're usually pretty familiar with.

You start off with the integers and you start off counting, and then you learn about fractions, and eventually, you have a long line, right? All of the numbers that you're familiar with and

from school, 11's a real number, 42, 2.34 is a real number. It's going to take a really long time if we go through all of them, Adam.

23, that's not a real number, is it?

Look, I mean, 0 is also a real number, and minus 10 is a real number, too. So they're not quite just the numbers that you use to count blocks in your kid's toy box.

All right. How should we think of this? Adam wants to say impossible.
I say perfectly, perfectly fine number. Well, I mean, you could think of

i as just something that we've made up. That's terribly, terribly useful, right? You need some solutions to some equations.

You wanted to know what the square root of a negative number was, and we just kind of made up this number and popped it in. And all of a sudden, a lot of things become a lot easier.

And that's sometimes how maths works.

You know, just making, you can't make up numbers. You can't just make up numbers to make your equations work.
You can't. You can't.
There are numbers, you can't just make them up. Zero.
Yeah.

Where is it?

It's

no things. Can you see it?

No.

Can you hold it? Is this a song?

It should be. I'm going to to release it as a B-side.

But just, you know, these mathematical conveniences because your equations don't work. Yeah.
Yeah. That's why they're imaginary.
It's not imaginary. No, no.

But it gets weird because, you know, they turn out to be useful. So you have this thing that you make up to solve an equation and it turns out to do lots of other things too.
All right. Okay.

I feel like I need a recap just for my own purposes here. So I...

which is the imaginary number that we're talking about. The square root of minus one.

The square root of minus one, which is invented, doesn't exist, is impossible to conceptualize, but it does follow certain rules.

And we know that it came about from people like Cardano and the Heron guy who just ignored it to solve some pointless equations.

And it

and it and at some point in history it switched from being an impossible number to an imaginary number, which is my homoceptic voice.

Thank you very much, Adam. That's a

what a wonderful summary. We appreciate it.
But you know what, though?

Okay, all of this stuff about being pointless, this number actually turns out to be wildly, wildly useful because here is Professor Jeff O'Connell from Aloney College in California to tell us why.

Being a teacher of mathematics, I've always found it interesting that we teach imaginary numbers to algebra students, but

there's never an application.

And it isn't until you get into talking about things like differential equations and physics where imaginary numbers become this fantastic tool that we use in order to solve problems.

And it isn't that the problem starts off with imaginary numbers or even ends with imaginary numbers, but all of the tools that we use in the middle, imaginary numbers, are very much a part of that.

For example, when you are modeling maybe the suspension of a car, that is what we call a spring mass system.

When you're driving, you go over a bump and the car oscillates a little bit to kind of absorb the shock of that bump and give the people in the car a smooth ride.

So when we create the equations to model that behavior, the equation doesn't have any imaginary numbers in it. And then the answer doesn't have any imaginary numbers in it.

But in the middle, getting from the equation to the answer, many times we have to use imaginary numbers in order to get to that answer. Adam's pulling a face.

Eleanor, help me unpack that a little bit though, because Jeff was talking about using I, using imaginary numbers in modeling things that oscillate, so you know, bouncing springs or pendulums.

Tell us why it's useful in oscillations. So it turns out that you can use these numbers to think about anything that's got to do with angles and circles and periodic motion.

And to give you a little bit of an idea about how that might work, I need you to go back and imagine our real number line again.

So all the way going down to the negative numbers, up into the positive numbers, lay your normal numbers out on a line. Now, stick another axis on through the zero, going vertically this time.

So we're going to turn this into a pair of axes, and the vertical axis is going to go all the way up into positive multiples of i, and all the way down into negative multiples of i.

So once we've got our two axes, our real axis and our imaginary axis, I want you to think of every single point on that plane, on those axes, as representing a number.

And now those numbers, we're going to call them complex numbers. Adam may like this title better than imaginary or impossible.

Complex numbers are basically a mix of a real number and an imaginary number. Yeah, so okay, I can deal with that.

So on the anything which is an interaction between the real numbers and the imaginary numbers is called a complex number. Exactly, right? So 3 plus 2i or 11 minus 6i.

It's sort of the coordinates on that plane, where you find yourself.

Now I want you to imagine putting four big red dots on plus one, minus one, plus i, and minus i, and drawing a big circle all the way around your axes.

It's going to turn out that that circle, which has radius one,

has a very special relationship to the angle.

The points on that circle have a special relationship to the angle. And that's closely related to the nature of these complex numbers.

And once you start to understand that, you get the opportunity to use these complex numbers, these things with a real bit and an imaginary bit, to model anything that has to do with angles and circles.

And it turns out that springs and waves and all of the beautiful things in partial differential equations in physics are a bit like that. You get this tool that is just spectacularly useful.

Many, many hundreds of years after people try and solve these funny equations and invent this number I. Okay, here's the thing, Adam.
I know, I know, I can read your expression.

I've worked with you long enough. I know exactly what's going on in your head.
I know you're not happy.

But here is the thing, you know how mathematicians describe kind of moving around, doing mathematics like you're in a very thick thicket and you can't see where you are and it's all like messy and unusual.

And then there's a moment where you turn a corner and in front of you, you see this beautifully landscaped garden and everything is absolutely perfect. And you can see completely where you've been.

And this new perspective shows you how all of these things are completely connected.

What Eleanor has just described there is circles, it's imaginary numbers, it's real numbers, it's triangles, it's angles, it's exponentials, it's just hiding in there, you can't quite see it.

It's pi is in there, all of them together form this unbelievably beautiful equation, which is e to the i pi plus 1 equals zero.

And

you're just going to have to believe me.

A few weeks ago, we did a program about aphantasia and the inability for some people to be able to imagine things in their head.

All I can think of now is the garden you just described. Yeah.
Everything else you just said sounded like this.

Okay, so you're in the garden, right? You're in the garden. Euler is standing in this garden and he's looking around.
Is the heron there? The heron?

I don't think the heron was invited.

The heron's in my garden.

The heron's back in the thicket.

Disinvited himself by ignoring the important clues.

But, you know, he's standing in this garden and he looks around and he's got pi in one corner, right? Love that number. Great number.
He's got imaginary numbers I in another corner.

He's got zero, he's got one, and he's got...

exponential e the exponential number and he looks around and he's like holy moly these are the five most beautiful extraordinary numbers in mathematics and there is one equation which links them all together it's ridiculous, isn't it?

It is ridiculous. Michael looks really excited about this as well.
I'm feeling less confused because this garden is quite a peaceful place. It's a beautiful garden.
There's only five things in it.

You've all said something interesting, which is, and the clip from Jeff's also said that, that having to use imaginary numbers in order to solve equations which have real-world applications,

the input are real numbers and the output are real numbers, obviously, because the imaginary numbers aren't real.

But in the middle, you're using imaginary numbers in order to get from... So it's like going from London

to Birmingham via a wormhole. Kind of.

Yeah. In that it takes you into another dimension, you know, which is what Eleanor was talking about.
That axis that goes away from the normal number line.

Imagine it just going into another dimension, but you come back again in a very useful place.

Do you know what, honestly, your wormhole idea is actually pretty good. It sort of is, isn't it, Eleanor? Well, you need imaginary numbers to model a wormhole, that's for sure.
Oh, come on.

Come on. I was doing so well there.

Okay, but here's the thing. We've talked about this sort of theoretical connection, this wormhole that you get to go into.
But the thing is, is that there might...

That makes it sound like it's a maths trick.

But those weird properties that imaginary numbers have don't just turn out to be useful for nice, fancy maths gardens, because you can actually also you can also use imaginary numbers in order to make quite a lot of money.

Right. I mean,

imaginary money is,

this is not an unproblematic concept. How does this work? It's real money.
You can make money, but you just use imaginary numbers. And this is the entire basis of the 20th century electronics industry

comes from actually a guy called Charles Proteus Steinmetz.

Proteus was his nickname because when he was growing up he was so clever that all his mates at school thought that if they just touched him, like you used to touch the Greek god Proteus, he would impart wisdom to them.

So they said he was just so amazing. So he grew up in Prussia.
He came over to America in 1889, somewhere around then.

And he came right at the time when everyone was trying to work out how to electrify America. So how to build all the electrical infrastructure, like generators,

the electrifying houses and cities and how you do all of this.

And there was a big debate going on between Edison and Tesla at the time about whether it should be alternating current, AC, or direct current, DC. Edison was DC.
Tesla was AC.

And there were sort of problems with both in some ways. But

what they couldn't do with AC, which was really difficult, was modeling how circuits would behave.

So the mathematical model of a circuit, you know, going from the generator all the way through to your light switch to your light bulb, was actually really difficult with AC because alternating current varies all the time, which means you have to build in a sort of time variation into your equations.

And then you add in components like capacitors and inductors, and they add a phase shift to all those waves. So, it gets really messy.

And Steinmetz came in and said, Oh, it's easy, you just use complex numbers.

No one just got excited about that.

You did get really excited there for

Tesla was AC? Tesla was AC. Ellison was DC? Yeah.
And what was Angus Young's position?

I can't really contribute much to this conversation, to be perfectly honest. The thing is, though,

alternating current, positive, negative, positive, negative, positive, negative. It's that oscillation.

And if you think about something spinning around in a circle, if above the line you are positive and below the line, you're negative,

it's the same thing. It's all the same story.
It's all the same thing. It's sort of, when you look at it like that, you think, why didn't anybody see this before?

But Steinmetz came in and just said, oh, you know, I I can solve all of these problems, gave them the complex maths that would do it.

And all of a sudden, all the electrical engineers were like, oh, we can do this. And AC just won, like, won the day immediately.

Because all of a sudden, you could use really easy equations to model AC.

And AC has the advantage that you can transmit it from the generator to where you're using it without much loss or with much less loss than with DC. So Edison was sort of out at that point.

And imaginary numbers are absolutely crucial to working out the modelling of AC for this. Absolutely crucial if you want something you can actually manage.

Well, I'm slightly persuaded by that argument. Tell him the Dave Packard story as well.
Tell him the story.

So the amazing thing is that so you go from there, and it's like, oh, we just electrified America really easily, basically, using Tesla's stuff, all his hardware, and Steinmetz's brilliant maths.

So you get the birth of radio, you get everything sort of taking off at that point. And then people are doing electrical engineering degrees.

And you've got this guy called Bill Hewlett, who does a master's degree in electrical engineering and he uses imaginary numbers and Bill Hewlett takes this to his friend Dave Packard who hold on a minute exactly David Packard has a garage that they can build this thing that that Hewlett has kind of designed which is an audio oscillator basically a sound generator and and they so they start building it in David Packard's garage they formed this company called Hewlett-Packard

they bring out their first sort of electronics box which they called the HP 200A 200A, so that people didn't think that they just, like, that was their first invention.

So they wanted to make it sound like they were, you know, they'd been on the production line for ages and ages.

And then,

so then when they got the HP 200B going, the Walt Disney company bought eight of them, used them in the first broadcasting in cinemas of Fantasia to recreate that amazing sort of symphony sound, all built on the back of imaginary numbers.

But what are they actually, what is the

HP200B? The HP 200B is basically a way of generating sound. So Walt Disney were looking for something that would faithfully recreate the sound of a symphony orchestra in a cinema.

So they had to, it was basically the first proper, decent sound system with what Hewlett Parkard did. Do you know what sound is, Adam?

Oscillating waves.

Now you're talking about films. Now I can get on board.
I'm beginning to be persuaded by this. Well, that's it, because anything, anything that rotates or oscillates.

So helicopter blades, all of the sound stuff. I mean, this is everywhere that you look where there's anything rotating or oscillating.

And that includes, Adam, I think we're going to get you on this last one. That includes things that are fundamental to our universe, doesn't it, Eleanor? Yes, it does.

So we're going to get to quantum mechanics and that probably terrifies everyone.

But I'm going to give Adam

a little bit of support here. So I'm going to push back for you, Adam, right here, on this wave stuff.

It is mathematically extraordinary and beautiful and incredible that all this stuff ends up connected.

And then we can describe currents and sound waves and water waves using complex numbers but I'm going to make you feel better because you don't absolutely have to use complex numbers for any of those things we can do without it's not as nice thank goodness for that

it's not as nice we'd have struggled to electrify America but you know

If you want to do clunkier mathematics, less beautiful mathematics, there are ways to describe oscillations without having to use a complex number.

We We can just use our old-fashioned angles and our sines and cosines and things that we knew. If you don't care about beauty.
Yes. Well, that's really interesting.

So

the imaginary numbers are, they simplify the complexities of actually making calculations, which are pretty hard to do. Yeah.
So it's a mathematical convenience. Yes.

Yes. Until we get to quantum mechanics.
I've got bad news. So I was going to throw you a bone, but now I'm going to take us back in the other direction.

So early in the 20th century, people are puzzling about how to model really small stuff, atoms, electrons,

atomic structure, etc.

This is the birth of quantum mechanics and what we do know by that point is that those things behave exceedingly oddly and that the physics we're going to have to use to describe those things is going to look nothing like all of our nice previous physics which is often going to be wavy physics for example

And a whole bunch of people are working on this in the sort of 1920s.

There's one version of it come up with by Heisenberg called matrix Mechanics that looks pretty alien to everything physicists are used to.

But at the same time, Erwin Schrödinger is working on shoehorning quantum mechanics into a really comforting, familiar form. So he wants to make it look like a wave equation.
And he manages to.

He manages to write down Schrödinger's equation, which looks like a wave equation.

And when you teach this stuff to undergraduates, right, you kind of pull the wool over their eyes and you show them this equation. You go, it's fine.

You know how to solve wave equations using complex numbers, this is just the same thing.

And to some extent it is.

But Schrödinger's wave equation doesn't just use complex numbers to solve for a wave, it gives you a wave with a complex value, with an imaginary value. or its amplitude.

So my water wave, right, its amplitude is like how far off from the middle it is, how high my wave is. And if that's five feet, right, five is a nice real number.

The waves that get involved in quantum mechanics, their amplitudes are given by multiples of I, complex numbers.

And that

looks like an application of imaginary numbers that we can't just get rid of.

I'm doing the face again. I mean,

I got on board with the ACDC in America. I got on board with the general rotating things, but the amplitude of a quantum state is not a whole number like the amplitude of a

water wave is, it's an imaginary number. Yes, I mean, Schrödinger was unhappy too.

Oh, well, that makes me feel much better.

And as a result, he put a cat in a box, and now the cat's dead.

Exactly. I mean, the piece and the cat is alive and dead are pretty intimately related to these pesky complex numbers.

But it's now pretty widely accepted that in quantum mechanics, you just have to have states of the system that are directly described by complex numbers.

Now of course that means that we don't have nice, neat, easy ways of interpreting that state. That's part of why we get so puzzled by quantum mechanics.
But it doesn't look like we can change it.

Essentially, Adam, these things cannot be imaginary only. They are in there embedded in the fundamental state of the universe.
They are not a mathematical convenience.

They are not just a made-up answer to an equation that no one else can solve. They are totally and completely integral and they're there in the garden forever.
Yes. We're back in the garden.

We've just discovered them effectively. So they're not impossible, they're not imaginary, they are real things.

Absolutely. You're all nodding enthusiastically, like I've had an epiphany.
We've got him in the end. We've got him.
Well, you know what, on that note, I think it's time to thank our guests.

Thank you to Dr. Eleanor Knox and Dr.
Michael Brooks for joining us and having me persuade Adam.

So, Dr. Rutherford, when it comes to imaginary numbers, can we say case closed? No, Professor Fry, I'm still not very happy.
That wasn't the question, I asked if we could say case closed. Eh, well.

Okay, you know what? I'm gonna do it because we can, yes, because imaginary numbers were created to solve a problem. And called imaginary by Descartes as an insult.

But they are wildly useful in anything that oscillates or rotates.

Is it? Say it. And found in fundamental equations that describe the universe and therefore are not imaginary but are very much real.
Thank you. Imaginary.

I mean,

yes, I am persuaded. Obviously, it's important.
I did do math say levels and I sort of know what an imaginary number is. But the history is really interesting.
Sorry about the garden thing.

Sorry about the heron thing. I'm really sorry about the ACDC joke, which I think only 4% of the audience will get.
Hang on, Adam, are you saying...

Are you saying that this podcast is like a performance? Are you saying this?

Are you saying you're not always absolutely completely and totally true to your real character i'd say that that uh i mean i do you know we've talked about this many times before i do find this stuff conceptually

glorious no fantastic no beautiful and i can see you doing that and that makes me more

anxious and weirded out and but at the same time i don't want to be

You know, I value scholarship and academia and expertise. And I don't want to be the guy going, oh, oh, you people are not in the real world and your stuff is completely made up.

And at the same time, I'm looking at it going, I'm taking a lot of what you're saying on trust.

Well,

I mean, you can if you want to, but you can just go into the garden yourself.

It does sound like a nice garden. Such a lovely garden.
Is that a real metaphor that has already existed?

I think I'm not the first to use it, but I wouldn't say it was exactly official.

This could be. You know, the thicket, the overgrown thicket.
There's quite a lot of thickets.

You did say a thick thicket.

Oh, yeah, let's go with that. It's a little bit of tautology.

Anyway, thank you. I enjoyed that.

I really enjoyed that. I did, too.
And it's one of those things where I'll attempt to explain it to someone in four days' time and go, well, it's because it's like, you know,

there's a tape, there's two axes, and if you draw it on the axes, there's a heron on one, and there's a Ferrari on the other, and

money is based on it, and so are printers.

And there's a crowd watching people solve equations. Exactly.
When he started, when Michael started talking about Hewlett Packard,

I was listening, following him like a panther,

slightly thinking about the job that I had at Hewlett Packard when I was 17, which was just soldering, so it wasn't very technical at all.

But also I was thinking, oh, mate, does that explain why printers never work?

Tell you what, though, actually, talking about numbers, I was actually having a little look through the numbers of downloads for our episodes, right?

And would you like to know, Adam Rutherford, what the most popular episode that we've ever released is the most downloaded.

Hundreds and hundreds of thousands of people have downloaded this and listened to it. Was it

was it Infinity? Nope.

Was it

oh, I know, the hairy, the hair, like, really in the first series when we had Alice on and she was really rude. Nope.
Should I tell you? What? It was your ASMR track. Shut.

Yes. By quite a long way.
My one. Your one.
What was I doing?

You have got way more than double

the number that I got for mine. Way over double.
Well, we were making a drink. Yes.

And with the sound, the special microphones that picked up the

room. Yes.
Well, and I was making an old-fashioned cocktail. Hundreds and hundreds of thousands of people have downloaded that, Adam.
How weird. Why?

I don't know, maybe you're a big star in the ASMR world. Oh, man, there's money to be made there.
ASMR cocktails by me.

Yeah, I can only make one cocktail. Symptomic.
No, old-fashioned.

I think it was a mojito, wasn't it? No, you made a mojito. Oh, what did you make? An old-fashioned.
Okay.

Oh, you shouldn't have told me that.

This is like last week when you told me that Stephen Soderberg had been reading our book. I got really overexcited.
That's what this section of the podcast is for, Adam. It's just to stroke your ego.

Things that I get very excited about. Okay, so for the hundreds of millions of, that's what I heard when you said this: the hundreds of millions possibly don't.

You want to put it on your spreadsheet and email it around to your device. I'm going to do that.
For people who downloaded that noise, can I just say to them?

Thank you.

Right. Correspondent? Let's do correspondent.
Okay.

So a couple of weeks ago, we did the episode on magnets and how do they work? Conclusion, don't know.

Magic.

Well,

so one of the things that I asked was we were talking about what is the

thing that carries the magnetic field. Because I was doing that ultra-rational thing that I do again, which is to say, stop making stuff up.
There has to be a physical property here.

What is the particle that carries the magnetic field? Okay. Mm-hmm.

And the particle is photons, they said. But the thing is, is that people tend to think that photons are equal to light, right? And a lot of people wrote in because they were quite baffled

when they said that.

Excuse me, how come magnets work in the dark? That's a perfectly reasonable question.

Where you start laughing and go, wait a minute.

Hang on a second. So our physicist, Felix Flicker, got an answer for us.

Now,

you need to bear in mind, right, this is still quantum magic, but here you go, because he emailed us with this very cool fact. He said, the short answer is that magnets generate their own light.

Exclamation mark. That should have been a terabang, maybe.

Remember that light is electromagnetic radiation and not all light is visible.

If you see, if you set a magnet spinning so that it completes a fugal turn once per second, the changing magnetic field will generate a one hertz radio wave.

To generate visible light, you would need to spin the magnet about a quadrillion times per second. That's 10 to the 15 times per second.
A 1 and 15 zero.

Is that a possible thing to do? Let's try it.

That's not the correct answer at all, isn't it?

A reason I was asking that stupid way is because when you say numbers like 10 to the whatever it was, quadrillion made-up number, then quantum physicists go, oh yeah, yeah, we do that all the time.

That's what these bogey quantum things do. They rotate at that all the time.
So it was a genuine question. Can we rotate things at 10 to the whatever the number you said times?

I don't know why you're asking me, mate.

I've got genuinely no idea. And let's say probably not.
They said probably not. I was more...

So after the Magnets episodes, and we put it up on Twitter, and

my friend, the children's author, Anthony McGowan,

expressed dismay that we hadn't asked him on the program as a magnet expert. He's a children's author.
Okay. Excellent award-winning children's author.

So he put up a list of magnet facts, hashtag magnet facts, on Twitter. I just want to read a few of them out.
Please do.

So some archaeologists believe that Stonehenge functioned as a giant electromagnet.

Okay, are those the archaeologists who have Netflix series? I'll keep going.

Technically, the Crown owns all of the magnets in Great Britain, but not Northern Ireland. It was at this point I was thinking, are these real facts?

Let me keep going. Magnets can be used in place of fire extinguishers by sucking the magnetically charged oxygen from the flames.
Probably just about to get away with that one.

It's a myth that magnets always point north, magnet fact. Some do, but many others don't and can point anywhere.

These are great magnets. I think there's a whole book.

Chimpanzees have been observed attempting to use magnets to extract termites from their nests. It didn't work.

What I want to know is, was he he just tweeting these into a void? Was he getting any engagement on them? I'm having a look now. No retweets.
Apart from me.

Although difficult, it is possible to magnetise wood.

Magnetic bras were popular in the Soviet Union.

Here's one which could definitely be.

This is the time when you think this might work. In 1851, a man in the US state of Oklahoma legally married his magnet.

Amazing.

How is his career going?

He's a multiple award-winning, Carnegie Medal award-winning author.

I think that is enough magnet facts. Wait, we've got one more.
We've got one more. Well, maybe this one's slightly more of a real magnet fact.

Not casting any aspersions

on that list that you've extensively shared. We had this message in from Dr.
Richard Hill.

We were talking also about levitating magnetically. And Richard said, at Nottingham University, we routinely do experiments in which we magnetically levitate water.

The magnetic susceptibilities of the various types of soft biological tissues are approximately all the same around that of water. Bone, however, has a different susceptibility.

And the upshot is that the magnet would levitate the soft parts of the person, which would be approximately weightless, whereas bones would still feel the force of gravity, and the bones would hang down within the flesh, in other words, which is the other way around from the normal situation situation of the skeleton supporting the rest of the body.

This,

I mean, that just sounds like one of Anthony McGowan's magnet. Hashtag magnet facts.
But let me keep going. Until 1922, the Catholic Church banned the use of magnets on Fridays.

Right, let's do Curie of the Week.

Week

Strong case for Anthony McGowan to be Curio of the Week after

that exceptional entry. I'm sure he'd be delighted.
But actually, we do have a different magnet-themed Curio of the Week this week. Adrian Glasser made a machine.
So I'm going to look at this video.

So we've got the video up here, and

if we press play,

it looks like a bit of sort of

Raspberry Pi circuitry on top of a computer with a screen with an oscillating wave on it. What are we looking at? Let's have a little listen.
Let's have a little listen.

Do you know what it is? What? It's a rotating magnet. And do you know what that does, Adam?

Beautifully and succinctly. It ties together both the magnet episode and the complex number episode.
Oh, God.

Oh,

no.

Do I have any vetoes left? No, they're all gone. This is the end of the season.
Thank you very much. Thank you very much for doing my job.

He says, I was inspired by your magnets program to build this machine that I've been thinking about. This is the Arduino Nano microcontroller driving a DC motor.
Okay, yeah, yeah, yeah, yeah.

At relatively slow speed, there are eight magnets in the 3D printed octagonal part that rotates around the top of the motor shaft, and the magnets are spinning around on top of the motor shaft.

Absolutely fantastic.

I mean, I'm just going along with it. You get a pass from me.
Hannah looks absolutely delighted. That is the end of the current series.

We will be back, although we're not sure in what form,

when,

how,

or why.

I don't think we've ever known why, have we? Anyway, send in your questions as ever to curiouscases at bbc.co.uk, and we will see you soon. Are you fed up with

the news? In the last few minutes, I've been talking to Michael Goat. Its snake-like mouth quivered and slapped like wet leather.
The skewer. The skewer.
The skewer. The news chopped and channeled.

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