Melvyn Bragg and his guests discuss imaginary numbers

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## Comments

There should have been a warning before this programme. I have never been so BORED by a BBC Radio 4 programme in my life. This is a specialist subject that many (or most) listeners will have no connection with. I listen to many Radio 4 programs where I know little or nothing about the topic, but get educated & interested as the programme moves along. This particular programme is a WASTE OF RADIO 4 AIR TIME!

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Come on Melvin. Normally I'm pretty tolerant of your departures but, to someone tuning in midway through the programme, this would have sounded like someone talking in numbers, which it was. Utterly detached programming

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It does not have to be a specialist subject - it's being badly presented as such. I've got a degree in Pure Maths and I can barely follow it.

Marcus is enthusiastic and engaging, Ian Stewart I would venture to suggest is very intelligent but not a great communicator, the other panellist the same.

The idea of the square root of -1 could be presented as philosophically challenging and engaging - particularly as it is tagged with the word imaginary. Try telling a 15 year old kid with a decent grasp of maths/arithmetic that -1 has a square root and they'll tell you where to go.

When you square a number you get a positive number eg 4x4 = 16 but hang on -4x-4 is also 16. Try again -10x-10 = 100 (*not* -100). You simply can't get to a negative number by squaring. Or can you? I think there's a real intellectual challenge here and I was really looking forward to this programme but when I heard Ian Stewart was on...

And when Michael Gove advocates that only graduates with 2:2 or better can become teachers you might like to remember this programme :-)

As I started this comment they'd just got on to Fourier transforms. Now that's specialist.

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What a great programme! Although a long-ago A-level maths student with a an aging brain, I have never lost my love of maths. I found the topic well explained by the experts and I now understand much much more about imaginary numbers, their point and their practical uses. Thank you.

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I could hardly disagree more than with MS.

The thing that I like (a lot) about this series is that Melvyn Bragg does try to tackle science and maths (as well as other quite esoteric topics) that other programmes shy away from. If you are not willing to open your mind to that then don't listen - and no prior warning should be necessary. If it does go over some listeners' heads that is not the fault of the presenter who is by his own admission no expert in science and maths.

Can I suggest another topic? (MS be warned, it probably will not be to your taste; re-tune to Radio 1 now.) It's another difficult one, but I would hope this would be a chance to make it more accessible.

Recently one of the most significant problems in Computer Science has been solved. It has been proved that P /= NP. Could Melvyn get some articulate Computer Scientists in to explain what that is and why it is such an important result?

It means that encrypted internet communications with my bank do remain secure, after all - among other things.

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It must be Autumn today as Melvyn is back with the beautiful 'In Our Time' and kicking off with this important and unreal concept. It was only when I learnt about complex numbers that I realised how easy my 'O' & 'A' level Maths would have become had I known about this elegant symbol 'i' as a teenager struggling with lengthy formulae.

If you want to know more and aren't worried about a few equations then read Paul Nahin's book 'An Imaginary Tale - The Story of i'

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Good programme, you might have mentioned that i numbers are known as j numbers in electrical enineering.

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Technical Point

I also though that Marcus, who I like, with reservations, as a communicator, missed a trick when talking about

e^i*pi=-1

A much more aesthetic formulation is

e^i*pi+1=0

an equation connecting the fundamental numbers i, pi, e, 1, and 0 (zero); the fundamental operations +, x and exponentiation; the most important relation = ; and nothing else.

Taken from http://mathworld.wolfram.com/EulerFormula.html

Frankly if you're interested in that sort of thing that is God at work - actually forget I said that :-)

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Surely the real pleasure of this programme was the subtle inclusion of a piece of unresolved dramatic tension - who missed out on the apple? Or did he/she get an imaginary one?

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Well done Melvyn Bragg for being willing to have a go at describing complex mathematical theory on talk radio. This was easily one of the clearest explanations of the subject I have heard and as a physicist I still got a couple of new ways of looking at things from the discussion.

I'm grateful we have a radio station that is willing to engage with science at a serious level and help open it up.

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Quote from angry loner, above

“The idea of the square root of -1 could be presented as philosophically challenging and engaging - particularly as it is tagged with the word imaginary. Try telling a 15 year old kid with a decent grasp of maths/arithmetic that -1 has a square root and they'll tell you where to go.”

Not so. I came across “I” when as a very mature but immature student aged 34 I did a London External degree. One subject was Maths and the lecturer introduced sq rt of -1, “we’ll call it I he said” I said it was cheating but he replied “why not, it works”. Years later I was a teacher in an FE college when they were real colleges and had classes of BT apprentices when the nationalised company had apprentices. Hundreds of them.

They all took to the idea of j and alternating current………..no-one told me where to go. They actually enjoyed maths.

And Gove is an idiot. Alan Turing had to be dismissed as a teacher, he felt kids who did not understand ideas which to him were obvious were being obdurate.

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This has enormous potential: mathematicians quizzed by a non mathematician (someone like me). I am sure there is a basic physiological wiring difference here: those that endlessly think about numbers and those that doze off at the very prospect. And there must be a crossover group who strive endlessly.

I found the program both fascinating and frustrating. M de S can speak very quickly in his enthusiasm and MB can get lost on the followup question. But this is still very worthwhile and the web site links has me clicking on links for complex numbers. I would not normally consider doing this.

But here is an idea. Not everyone is able to see the website but for those of us who can why not have a "white board" that could be written on in real time so that those of us who are listening (and this could be linked to the podcast) as a way of illustrating complex abstract ideas as they are being spoken about? Or notes that could be downloaded BEFORE the broadcast. But then you can always listen again. However maddening these are please IOT do not stop the attempt at bridging the gap.

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Great program, but not a good idea to choose 3 maths professors. They had, perhaps unsurprisingly, little idea of where complex numbers might be useful in real life. The BBC would still exist without them, and we'd still have AC mains. Here are a few of the obvious things we wouldn't have without complex numbers:

1 - pretty much any modern semiconductor device, since you can't design or build diodes or transistors without complex numbers. No computers, no mobile phones, no engine management systems. We could build valve radios and wartime-era computers, but that's about it.

2 - Digital communications. You can do this without complex numbers, but it's not until you do the maths properly that you realise that there's a way to do it 100 times (literally) better. No DSL telephone lines; no digital radio or television; no satellite comms; no GSM or 3G telephones.

In fact, it's probably fair to say that almost none of the technology developed since the 40's would exist today if we didn't have an understanding of complex numbers.

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Although I understand the purpose of imaginary numbers, especially the j notation which we used on the telecommunications course I took, I was taken aback when one of the two male contributors stated that "complex numbers generate waves"!? and added that if it were not for the work of Gauss and Argan "our voices would not be piping into the listeners home via the radio"!?

This is of course total nonsense.

Mathematics is a 2 dimensional tool for scientists and others to describe events and phenomena in the 4 dimensional universe - and calculate the end products. However, Radio 4 broadcasts come to us, not through the work of those eminent mathematicians, but through the work of the scientists Maxwell, Faraday, and others and finally the engineer Signor Marconi.

It wouldnt matter how many times Albert Einstein wrote his famous equation e = mc squared on a blackboard it would not produce anything louder than a squeaking of chalk!

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Re David Nichoslon

"They all took to the idea of j and alternating current………..no-one told me where to go."

I'm sorry if what I wrote wasn't clear: What I meant was that, to some at least, the idea of the square root of a negative number can be "challenging" even repellent, separate from its utility.

I've tried to introduce the idea of sqrt -1 to a few more able kids, and they don't like it. By that I mean it upsets their pretty solid and dearly held ideas of what numbers are. Their reaction is similar to the Babylonians(?) who if I'm right gave up and ignored it because they didn't like it. *I think this is a good thing.* (Not the ignoring!) I'm not complaining that they tell me where to go. Far from it. Like I said, I think that introducing i upsets a few preconceived ideas, and the outraged, negative reaction is an initial defence against that.

As a pupil/student where I went from there was accepting it and using it, but never really understanding it. What is i? I've never really had that satisfactorily explained. I suppose I'm approaching it philosophically rather than practically.

Maybe everyone understands j, whereas i remains a total mystery :-)

Throughout this discussion I've been thinking about Quantum Mechanics: similarly simultaneously practically useful and philosophically incomprehensible.

I've been familiar with i for 30 years or so but I'm still not sure what it is, and this programme didn't help. That was a disappointment.

I'd say the aim of the programme should have been to inform, educate, and entertain the interested lay person. This subject should not be beyond the scope of that remit. The fact that there were nervous jokes about incomprehensibility from presenter and continuity announcer to me shows they failed, badly.

Like I said I think i could be a rich source of (sometimes hostile) debate. This programme was a wasted opportunity.

My two penn'orth.

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