The BBC Horizon series will show a programme about “Infinity” some time in the first half of 2010. Last Thursday I spent a long hard day with the team making the programme. Here are a few impressions of the filming. If I get any visual material I will post some here.
I arrived at the Mathematics building at about 7:45; the crew were just arriving in a car and a van. Karen had managed to work some magic and arrange a permit from security to allow them to leave the vehicles right outside the building, which saved a lot of trouble.
It was a beautiful morning, with the sun lighting up the 60s concrete of the building. The cameraman and soundman, who were obviously very much in love with their job, enthused over the sight, and immediately got out their kit and started filming.
We went into the building. Some readers of this will know what the inside of my office looks like; I made a half-hearted attempt to get them to use a different room, but they were so struck with the sun shining in the window and onto the whiteboard in my office that they wouldn’t look at anything else. Later on, they took atmospheric shots of me over a pile of papers or books.
While the light lasted, I had to go over the fact that there are as many even numbers as whole numbers several times while they filmed it from different angles, with different lighting. So the pattern of the day was set.
At 10:30 we had to break to drive to the Grange City Hotel near Tower Hill to film there. This was a sequence to illustrate Hilbert’s hotel, an idea dreamed up by Hilbert to illustrate the point I had just been making:
Suppose that an infinite hotel is full, and someone walks in and asks for a room. No problem: the manager asks each guest to move into the next room, freeing up the first room for the new arrival.
What happens if infinitely many people arrive? Still no problem. Simply move the guest in room number n into room 2n. Then all the odd-numbered rooms are freed up to accommoodate the newcomers.
The conceit was to be that the infinitely many new guests would be infinitely many clones of me. So I had to be filmed checking in many times; this will be edited to make it look like infinitely many arrivals. After this (the girl doing the dummy check-in was quite an accomplished actor by the end of it), we went upstairs to a rather grand room with a stunning view over the Tower and Bridge, backlit by the sun. I had to sit on the bed and explain the idea to the camera (and have closeups of testing the firmness of the bed). Finally, we had the use of a corridor, so I had to be filmed coming in and out of doors and tracked walking down corridors.
Then back to Queen Mary. The light had completely changed; it was overcast and night was falling, since we had taken longer than budgeted in the hotel. We had to get some pictures of me reading a book, some conversation about various things related to infinity (questions which all participants will be asked), and finally explain Cantor’s discovery that there are more real numbers than natural numbers (several times from different angles again.)
We had been going for twelve hours with hardly a break by the time we were finished; the security man was about to lock the gates. A hard day’s work!
I had to learn a few things about filming. I am not at all sure how well I learned them; and you won’t be able to judge from the finished programme because hopefully all the glitches will be edited out.
- First, and rather obviously, I must not look at the camera, even if what I am looking at is in the same direction.
- Anything I say must be self-contained. If I am asked a question, I must turn it round into a statement and say it before going on to comment or amplify. Moreover, I must wait until the question is finished before beginning my reply, to leave room for the editorial scissors.
- It must be self-contained in another way. Even if we have just been talking about something, I shouldn’t refer to it; that might be later in the finished programme, or even edited out completely.
- In particular, I should always say “infinity”, not “it”, even if I have just been talking about infinity.
- I mustn’t mention the word “set” since that will be introduced quite late in the programme. (I didn’t always succeed with this.)
- I must also give up my teacher’s habit of explaining the same thing in several different ways. They may be filming this bit for the third or fourth time, but I must keep the explanation the same, so that they can cut between takes if necessary.
What didn’t we cover? There are a couple of things that I think are important about infinity, one of which we attempted:
- Infinity is simpler than a large finite number, because it is less structured. The line we took on this is that, for example, the question “Is the number of elementary particles in the observable universe odd or even?” is meaningful (modulo some physical assumptions), but much too hard to answer, whereas the question “Is infinity odd or even?” doen’t have any meaning, since this concept does not apply to infinity.
- Undecidable questions in set theory such as the Continuum Hypothesis seem to lead to different kinds of mathematics, using the same logic but different assumptions about the foundations. I think it is possible that these questions will be answered in an unexpected way. We might change our view of the foundations of mathematics, and build it up in a completely different way, which will actually resolve these questions.
We didn’t talk much about the layperson’s view of infinity either. At one point the director led me briefly onto the topic of mysticism, as direct perception of infinity; I didn’t really say much worth remembering. But there is a view of infinity which for me is captured well by Bob Dylan in Visions of Johanna:
Inside the museums, infinity goes up on trial.
Voices echo, “This is what salvation must be like after a while.”
The infinity of space and time pushes us into insignificance, but is also infinitely tedious if we have to experience it.
Finally, I have to say: a very different day, but what an enjoyable day working with intelligent professionals who love their job and pick up so quickly the point I am trying to make (and even suggest better ways of putting it across).
For example, I thought that it might be worth explaining a bit about decimals in the segment about Cantor’s proof, and even thought it would be possible to do this while writing down the list of numbers. But I was told not to worry: people who don’t understand decimals won’t be watching this programme!