By Jamie Everitt, Collections Development Manager of Norfolk Museums & Archaeology Service

Enrico Fermi (1901-1954) was a pretty smart chap, as you would expect from nuclear physicist. He worked on the first nuclear reactor, contributed to the development of quantum theory and particle physics, and along with Robert Oppenheimer lead the development of the atomic bomb.

He also had an enviable reputation amongst his colleagues for being able to estimate accurately quantities from very limited information. At the first atomic test in the Nevada Desert in 1945, Fermi was based at the control site ten miles from the explosion. He dropped six small pieces of paper and observed how far they were blown by the blast. He used these to estimate the explosive force at 10,000 tons of TNT (10 kilotons) – modern analysis suggests that the actual force was 18 kilotons. Quite an impressive result from such limited data.

Fermi used to ask his physics students at ChicagoUniversity to estimate how many piano tuners there were in Chicago. The usual first response was bewilderment or wild guesses, but he would go on to show them how they could use a few known facts and some reasoned assumptions to arrive at an answer reasonably close to the truth. These kinds of questions have become known as ‘Fermi questions’. They are often inaccurate but can give a good indication of the true answer; the results may be out by a factor of two or three but rarely more.

I tried out a Fermi question for myself, asking “how many piano tuners are there in Norwich?” If you would like to have a go, my reasoning and the answer are at the end of this article. Remember, you can’t just guess but have to used reasoning and assumptions – it might help you to know that there are roughly 180,000 people in the greater Norwich area, but I’m saying no more than that!

So, what has all this got to do with the Shine A Light project? Well, I was reminded of Fermi questions when trying to work out how much additional storage space we would need. Several years ago Norfolk Museums Service had to vacate one of its rented stores. The collections were packed into 24 wooden storage crates which have been stored at Gressenhall ever since. Each crate was originally packed very carefully to maximise the number of objects which could be fitted in, and they have proved a very efficient but very inaccessible means of storage.

Our chosen solution to making these collections more accessible is to install a mezzanine in the store, enabling us to put the smaller, lighter objects on shelves on the upper floor with larger collections (such as the Norwich snapdragons and the Colman’s mustard stamps) and other choice, interesting items on the ground floor. The public will have access to the ground floor during tours and will be able to get up close to the objects.

Most of the objects in the crates are destined for the new mezzanine. In an ideal world we would wait until the Shine A Light team had processed every crate, assessing, photographing and measuring each object as they went. We would then assess which objects we were going to retain in the collections and which we needed to find new homes for. At the end of this process we would know exactly what we had to find storage for, and could work out how much extra storage space we need.

Trouble is, life isn’t like that. Generous though the funding from the Esmee Fairbairn Foundation is, we don’t have enough time to assess all the collections before working out the design for the mezzanine, placing the order, and getting it installed by the end of the project. This is where estimating and calculated assumptions come in.

Each crate has a known internal volume (4.36m^{3}, to be precise). Looking at half a dozen opened crates, and talking to Dayna and Wayne about how representative they were of others they had already looked at, I was able make an overall estimate of how well-packed the crates were. After adding an allowance to be on the safe side, my final estimate was that on average the crates are about five-sixths full.

Next, how many objects will we retain in the collections? “How long is a piece of string?” was my first thought but, like Fermi’s students, I took a step back and thought about what evidence we had. Helen and John Renton had already assessed nine of the crates, and I was able to measure the objects they had selected for re-homing. They totalled just over one-sixth of the volume of the nine crates.

So, of the 24 crates I could estimate that about one-sixth was empty space, and guess that another sixth consisted of objects which would be rehomed. This gave me the total volume of collections for which we would need to find shelving space – it worked out at 80m^{3}. But that is for objects packed tightly into crates. When they are unpacked, laid on shelves and made more accessible the space they need will expand. How to work this out?

I looked at objects on shelves elsewhere in the store, measured a representative selection (again adding a margin of error) and calculated their total volume. I then compared this to the total space occupied by the shelves they sat upon – it turned out that we would need to add 50% to the volume of collections. So that gave me the total amount of shelving space required, from which it was a relatively straightforward process to work out how many shelving units we need, add another margin of error, and thus arrive at the size of mezzanine needed to accommodate all the shelves. Simple!

In theory, that is. We won’t know how it will work in practice until we actually start unpacking the crates onto the shelves. And it was small consolation to hear the very experienced representative from the mezzanine company agree that this was so. What happens if the objects start to use up the space more quickly than anticipated? We have a contingency plan – there is space on the large mobile racking in the other half of the store, and we already have spare shelves and brackets ready for installation.

Will it work? I think so – I have left generous margins of error in all my measurements and calculations, but only time will tell. Personally, I won’t be happy until nearly all of the objects are sitting on their new shelves!

**How many piano tuners in Norwich?**

Here is my reasoning. Firstly, how long does a piano take to tune? I don’t know, but 1½ – 2 hours seems like a reasonable assumption. This means that a tuner could tune 2-3 pianos a day – so let’s say two pianos a day as there will be times when the average tuner is not fully booked. Assuming every tuner works a five day week for 50 weeks in the year (we must allow them a holiday), they will each be able to tune 2 x 5 x 50 = 500 pianos every year.

Next, how many people in Norwich have pianos? Again, I have no idea but from a rough tot up of my friends and acquaintances I guess that about 1 in 50 of them have pianos. This is a big assumption – I haven’t been in all their houses, the people I know are mainly adults, middle aged and middle class, and some may keep their piano playing a closely guarded secret – but I don’t have much else to go on. If there are 180,000 people in Norwich, that translates into 3600 pianos. 3600 pianos divided by 500 per year gives seven piano tuners hard at work.

Using the latest sophisticated search techniques (i.e. typing “Norwich piano tuners” into Google!) gives us… five piano tuners in and just outside the greater Norwich area, a number confirmed by the phone book. And there may be others not advertising at all, so I was within the normal bounds of a Fermi question. How did you do?