We paired up Britain's most celebrated scientists to chat about the big issues: the unity of life, ethics, energy, Handel – and the joy of riding a snowmobile

Sir David Attenborough, 84, is a naturalist and broadcaster. He studied geology and zoology at Cambridge before joining the BBC in 1952 and presenting landmark series including Life On Earth (1979), The Living Planet (1984) and, recently, Life. Richard Dawkins, 69, was educated at Oxford, later lectured there and became its first professor of the public understanding of science. An evolutionary biologist, he is the author of 10 books, including The Selfish Gene (1976), The God Delusion (2006) and The Greatest Show On Earth (2009). He is now working on a children's book, The Magic Of Reality.

What is the one bit of science from your field that you think everyone should know?

David Attenborough: The unity of life.

Richard Dawkins: The unity of life that comes about through evolution, since we're all descended from a single common ancestor. It's almost too good to be true, that on one planet this extraordinary complexity of life should have come about by what is pretty much an intelligible process. And we're the only species capable of understanding it.

Where and when do you do your best thinking?

DA: I've no idea. All I know is if I'm stuck with something and go to bed, I wake up with the answer.

RD: That's a fascinating phenomenon, isn't it?

DA: That's if I find the answer at all.

RD: Very few people say, "I think I'll have an hour's thinking now."

DA: Mathematicians do. I had an uncle who was a mathematician, and one of his students said, "How long can you think for?" He said, "I sometimes manage two or three minutes." And this young man said, "I've never managed more than 90 seconds." Of course, that's abstract thinking, and by and large I'm not an abstract thinker.

What distracts you?

RD: The internet.

DA: I used to work to music, but I can't now. Music is too important not to give it my full attention.

What problem do you hope scientists will have solved by the end of the century?

DA: The production of energy without any deleterious effects. The problem is then we'd be so powerful, there'd be no restraint and we'd continue wrecking everything. Solar energy would be preferable to nuclear. If you could harness it to produce desalination, you could make the Sahara bloom.

RD: I was thinking more academically: the problem of human consciousness.

Can you remember the moment you decided to become a scientist?

RD: I only became fired up in my second year of a science degree. Unlike you, I was never a boy naturalist, to my regret. It was more the intellectual, philosophical questions that interested me.

DA: I am a naturalist rather than a scientist. Simply looking at a flower or a frog has always seemed to me to be just about the most interesting thing there is. Others say human beings are pretty interesting, which they are, but as a child you're not interested in Auntie Flo's psychology; you're interested in how a dragonfly larva turns into a dragonfly.

RD: Yes, it's carrying inside it two entirely separate blueprints, two different programmes.

DA: I couldn't believe it! I remember asking an adult, "What goes on inside a cocoon?" and he said, "The caterpillar is totally broken down into a kind of soup. And then it starts again." And I remember saying, "That can't be right." As a procedure, you can't imagine how it evolved.

What is the most common misconception about your work?

RD: I know you're working on a programme about Cambrian and pre-Cambrian fossils, David. A lot of people might think, "These are very old animals, at the beginning of evolution; they weren't very good at what they did." I suspect that isn't the case?

DA: They were just as good, but as generalists, most were ousted from the competition.

RD: So it probably is true there's a progressive element to evolution in the short term but not in the long term – that when a lineage branches out, it gets better for about five million years but not 500 million years. You wouldn't see progressive improvement over that kind of time scale.

DA: No, things get more and more specialised. Not necessarily better.

RD: The "camera" eyes of any modern animal would be better than what had come before.

DA: Certainly... but they don't elaborate beyond function. When I listen to a soprano sing a Handel aria with an astonishing coloratura from that particular larynx, I say to myself, there has to be a biological reason that was useful at some stage. The larynx of a human being did not evolve without having some function. And the only function I can see is sexual attraction.

RD: Sexual selection is important and probably underrated.

DA: What I like to think is that if I think the male bird of paradise is beautiful, my appreciation of it is precisely the same as a female bird of paradise.

Which living scientist do you most admire, and why?

RD: David Attenborough.

DA: I don't know. People say Richard Feynman had one of these extraordinary minds that could grapple with ideas of which I have no concept. And you hear all the ancillary bits – like he was a good bongo player – that make him human. So I admire this man who could not only deal with string theory but also play the bongos. But he is beyond me. I have no idea what he was talking of.

RD: There does seem to be a sense in which physics has gone beyond what human intuition can understand. We shouldn't be too surprised about that because we're evolved to understand things that move at a medium pace at a medium scale. We can't cope with the very tiny scale of quantum physics or the very large scale of relativity.

DA: A physicist will tell me that this armchair is made of vibrations and that it's not really here at all. But when Samuel Johnson was asked to prove the material existence of reality, he just went up to a big stone and kicked it. I'm with him.

RD: It's intriguing that the chair is mostly empty space and the thing that stops you going through it is vibrations or energy fields. But it's also fascinating that, because we're animals that evolved to survive, what solidity is to most of us is something you can't walk through. Also, the science of the future may be vastly different from the science of today, and you have to have the humility to admit when you don't know. But instead of filling that vacuum with goblins or spirits, I think you should say, "Science is working on it."

DA: Yes, there was a letter in the paper [about Stephen Hawking's comments on the nonexistence of God] saying, "It's absolutely clear that the function of the world is to declare the glory of God." I thought, what does that sentence mean?!

What keeps you awake at night?

DA: Worrying about things I worked at too late in the evening.

RD: I have the same problem.

What has been the most exciting moment of your career?

DA: One would be when I first dived on a coral reef and I was able to move among a world of unrevealed complexity.

RD: Something to do with a puzzle being solved – things fall into place and you see a different way of looking at things which suddenly makes sense.

DA: We are living in the most exciting intellectual time in history. In my lifetime we have discovered such profundities, such huge principles. When I was an undergraduate, I went to the professor of geology and said, "Would you talk to us about the way that continents are drifting?" And he said, "The moment we can demonstrate that continents are moving by a millimetre, I will consider it, but until then it's sheer moonshine, dear boy." And within five years of me leaving Cambridge, it was confirmed, and all the problems disappeared – why Australian animals were different – that one thing changed our understanding and made sense of everything. When I made Life On Earth, we had to start with really complex organisms because the ecology of the very first oceans was not known. But you're doing a child's book? Tell me about it.

RD: It's about science more generally. Each chapter begins with the myths, so in the sun chapter, for instance, we have an Aztec myth, an ancient Egyptian myth, an Aboriginal myth. It is called The Magic Of Reality and one of the problems I'm facing is the distinction between the use of the word magic, as in a magic trick, and the magic of the universe, life on Earth, which one uses in a poetic way.

DA: No, I think there's a distinction between magic and wonder. Magic, in my view, should be restricted to things that are actually not so. Rabbits don't really live in hats. It's magic.

RD: OK, but what if you took a top hat and all you can see inside is some little boring brown things, and then one splits and out emerges a butterfly?

DA: Yes, that's wonderful. But it's not magic.

RD: OK. Well, you're rather dissing my title...

DA: The wonder of reality? But that's rather corny.

RD: Yes, it's a bit like "awesome".

Who is your favourite fictional scientist?

RD: The one I can think of is Conan Doyle's Professor Challenger, but he was a very irascible character and not a good role model.

DA: I don't read fiction.

What is the most difficult ethical dilemma facing science today?

DA: How far do you go to preserve individual human life?

RD: That's a good one, yes.

DA: I mean, what are we to do with the NHS? How can you put a value in pounds, shillings and pence on an individual's life? There was a case with a bowel cancer drug – if you gave that drug, which costs several thousand pounds, it continued life for six weeks on. How can you make that decision?