Do You Think You're Clever? (10 page)

(Economics, Cambridge)

As the author Anthony Powell said, ‘Growing old is like being increasingly penalized for a crime you haven’t committed’. After decades of hard labour and long service to the government in the form of taxes, you finally start to get ready for a deserved rest – and what happens? Your body starts to play up and your senses start to weaken – and you can only sleep properly in the middle of a conversation. To add insult to injury, some people start to say that you are placing a burden on the health service. No wonder you might begin to mutter bitterly every now and then!

Of course, there is a serious point here. Old people are as deserving of health resources as anyone, if not more so, because they have paid their tax contributions all their lives. The ethos of the NHS is that it provides free health care for all, and old people should not be exceptions to this policy. It’s quite simple; if they are ill, they should be treated.

Unfortunately, the NHS does not always live up to this ideal. A recent survey by the British Geriatric Society of British doctors suggested that more than half would be
worried about how they might be treated when they were older – because of the way they see old people being treated now. Most doctors surveyed believe that older people are much less likely to have symptoms properly investigated. When old people feel ill, there is a tendency to assume that the problem is ‘just old age’ rather than examining them properly for signs of a treatable illness. Three-quarters of the doctors asserted that older people are less likely to be properly treated and referred to the right specialists.

Of course, many of the health problems faced by older people are an inevitable part of growing old. But this does not mean they cannot be treated in any way. Old people may also respond less well to treatment for some ailments than younger people do. It is therefore sometimes suggested that limited NHS resources should be steered towards younger people where they can give more obvious improvements to quality of life. Indeed, there is some evidence that this how the NHS does indeed respond, often treating old people as second-class patients. There are much longer waits, for instance, for hip and knee replacements, which affect primarily old people, than for other operations. Women over 70 are not automatically invited for breast screening as younger women are. And older women with breast cancer are less likely to receive the full range of cancer therapy than younger women.

In 2005, NICE, the body that produces guidelines on drug policy for the NHS, put the cat among the pigeons when it produced a report saying that, ‘When age is an
indicator of benefit or risk, age discrimination may be appropriate’. It fired an angry response from Help the Aged, who retorted: ‘Assumptions that the life of an older person is somehow worth less, or that it is not important if someone who is nearing the end of average life expectancy receives less attention than people in their twenties or thirties, have been widespread. The [NICE] guidelines would run the risk of reinforcing such prejudice.’

It is perhaps understandable that this happens. On the face of it, it seems so much more worthwhile to pour the best (and most expensive) resources the medical profession can offer into treating a nineteen-year-old with all their life ahead of them, if the treatment is effective, than into treating an 89-year-old who is less likely to thrive, and likely to have only a short time of health before some other ailment strikes. Managers and doctors facing a heavy workload and limited resources may argue that choices have to be made and that such prioritising, though undesirable, is simply unavoidable. There is often an attitude, too, that old people have had their ‘fair share’. More poignantly, sometimes doctors who treat old people with all the skill and dedication they would devote to younger patients are forced to accept that they are fighting a losing battle – that they will not be able to keep their patient alive, let alone restore them to good health. When, then, do they stop fighting?

But there is a problem with too much ‘pragmatism’. The NHS is an ideal – the ideal of the best available treatment free to all, no matter who – and it’s an ideal that should not
be sacrificed lightly. For each and every patient and their loved ones, it’s their health and their life that is precious. The ideal of the NHS means we should not be making choices between one person’s health and another’s. Every patient should be treated to the best of doctors’ abilities. If this principle is compromised, it begins to undermine the important and reassuring comfort of knowing that we will always be treated when we are ill; it also begins to place a very difficult burden on doctors to choose who should be treated and who shouldn’t.

Yet the NHS budget is rising by the year and the UK has a population that is ageing. Already over 20 million (more than a third of) British citizens are over 50 years old, and old people are more prone to illness. 55 per cent of 75–84-year-olds have some illness or disability and two-thirds of those over 85 do. It is argued therefore that this increasingly aged population will place more and more strain on the NHS’s limited resources – and the ability of younger people to fund it – and that we need to start recognising this before catastrophe strikes. What this argument fails to recognise, however, is that the old people of today are much, much more healthy than those of former years. That is exactly why we have so many old people. And if there are numerically many more frail 90-year-olds now dependent on the NHS than in earlier times, there are also many, many more very fit people in their 60s still actively contributing to society economically, socially and intellectually. More importantly, a society that fails to look after its old people and hold them in any less than the utmost respect may be said to be sick and in need of treatment.

(Mathematics, Oxford)

This problem comes up in the movie
Die Hard with a Vengeance
. At the bidding of the monstrous Simon Gruber (aka Peter Krieg) (Jeremy Irons), John McCain (Bruce Willis) and Zeus (Samuel L. Jackson) are forced to solve this problem in order to disarm a bomb. They succeed just in time. They did it like this (using gallons rather than litres): First they fill the 5-gallon jug. Then they empty 3 gallons from the 5-gallon jug into the 3-gallon jug, leaving 2 gallons in the 5-gallon jug. Then they empty the 3-gallon jug and add the last 2 gallons from the 5-gallon jug. Then they fill the 5-gallon jug and fill up the 3-gallon jug, using just 1 gallon and leaving 4 gallons in the 5-gallon jug.
Et voilá
!

This problem is so simple that you can see the solution straight away, and the writers were clearly looking for a riddle that most of the audience would be able to work out or at least understand for themselves. But it’s an age-old arithmetical problem based on the subtraction of relative prime numbers. Relative prime numbers are numbers where the only whole number that both can be divided by is 1. That doesn’t mean that either is a true prime number,
just that they can both be divided only by 1. Thus 15 and 16, although not primes, are both relative primes, whereas 15 and 21 are not, because they can both be divided by 3.

Euclid found a way to solve relative prime number problems like the
Die Hard
riddle 2,300 years ago. The proof is complex, but the arithmetic relatively simple, and it allows us to solve any similar problem, such as how you would get a 13-minute egg from a 5-minute and a 9-minute egg timer.

(You ‘calibrate’ the 5-minute timer to 4 minutes, by starting them both off together, stopping when the 5-minute timer runs out – leaving 4 minutes on the 9-minute timer – starting both off together again and stopping when the 9-minute timer runs out, leaving just a minute on the 5-minute timer. You can then cook your egg for exactly 13 minutes by starting with the 9-minute, then reversing the 5-minute timer for the remaining 4 minutes.)

All these solutions can be expressed by mathematical equations. If one of the measures you have is
p
and the other is
q
, you can find the solution you need,
k,
with the following equation. In this,
m
is the number of times you need to fill or empty
p,
and
n
is the number of times you need to fill or empty
q
.

If
m
or
n
is negative, it means emptying the jug (or egg timer); if
m
or
n
is positive it means filling the jug. In the
case of the
Die Hard
jugs,
p
is 3 and
q
is 5. So you would get
k
is 4 if
m
is plus 3 and
n
minus 1.

That means filling the 3-gallon jug three times and emptying the 5-gallon jug once. Alternatively, you could go with
m
as minus 2 and
n
as plus 2, i.e. emptying the 3-gallon jug twice and filling the 5-gallon jug twice.

Both of these are different solutions from John McCain’s and require a third large jug as a reservoir, but they are equally valid solutions.

(Land Economy, Cambridge)

The idea that our past needed protecting by law from the ravages of modernisation first emerged in the mid-nineteenth century. As mass industrialisation and urbanisation swept away age-old ways of life, many believed something valuable was being lost – not just old and often beautiful things but our whole connection to the past, intangible, fragile but immensely precious. It’s no coincidence that the first great strides into the modern urban, industrial world
coincided with the revival of the Gothic style of architecture, the medievalism of the pre-Raphaelite art movement and the emphasis on traditional skills of the Arts and Crafts movement.

The preservation movement began with the scheduling of Ancient Monuments in 1882 to protect important ancient archaeological and historical sites. In 1947, the realisation that unique old buildings needed protection too against demolition or simply being ruined by modernisation led to the idea of ‘listing’ buildings. Then conservation areas came in during the 1960s; battlefields, historic parks and gardens were placed on registers in the 1980s; and, most recently, marine archaeology has been given protection.

Conservation areas recognise that not just stately homes, ancient castles and quaint medieval cottages are part of our heritage but so too are whole neighbourhoods of ‘ordinary’ historic houses. The idea is to preserve the special historic character of these neighbourhoods. Yet conservation areas cannot be locked into the past like museums where the buildings are simply preserved ‘in aspic’. They are usually places where people live, and people need the freedom to make their lives and homes as they want – not according to the diktat of a government heritage expert. Moreover, these areas have already long been lived in and altered piecemeal. So do you preserve them as they are now? Or do you restore them to what you think they were like when they were built or at a certain time in their history? And
when things need replacing, as they often do, how far do you go in replacing them with their ‘historic’ equivalents? When the leaks in a 150-year-old slate roof finally become irreparable, for instance, do you replace it with expensive hand-crafted slate, or cheaper, more leak-proof modern equivalents?

There is no easy answer to these questions and they lead to constant disputes between owners of homes in conservation areas and the heritage authorities. For most conservation areas, local authorities publish clear guidelines about what they will allow in order to preserve the neighbourhood’s special character. They may, for instance, forbid modern roof extensions, or the replacement of historic wooden sash windows with aluminium casements. It varies from area to area. Quite often, they will specify that the walls of a house in an area where all the houses are of natural stone or mellow brick may not be painted, or at least not in garish colours. This makes sense. Painting the house this way would not only destroy some of that particular house’s special historic character but would affect the unified look of the entire street which is part of its appeal.

Does the same apply to something as ‘small’ as a purple door? Well, yes it could. If the special historic character of the street or neighbourhood depends on subtle, pastel colours or even natural wood in the doors and window frames, a bright purple door could well stand out like a gap tooth and mar the overall effect. And the ‘overall effect’ is important. The idea is to preserve these areas for the benefit of
all, not just those living there. Of course, painting a door is not necessarily a permanent change that destroys any of the historic fabric, and the owner might argue that it’s her choice entirely what colour she paints the door of her own house. But the whole concept of conservation areas means that property owners within those areas give up some of their own individual rights to change their property in order to preserve the areas’ historic nature for the good of the community at large.
^*

It could be argued that everyone has an absolute right to do with their own property as they will. However, most would agree that a society in which there are absolutely no mutually agreed rules on planning could not only be ugly and chaotic and unpleasant to live in – but would be in constant battle as neighbours got into dispute when someone built a strip club next to a children’s nursery, or a steel furnace towering over someone’s quiet cottage garden. Building controls are agreed by consent, and in theory, at least, democratic local and national elections give people the chance to challenge controls they don’t agree with.

The same is true of conservation rules. It’s the individual’s choice to live in the conservation area. If the woman really has to have a purple door, yet it’s not allowed in a conservation area, then she must probably live elsewhere.

That said, it may be that some of the rules in a conservation area are unreasonable – and restrict individual freedom just too much. After all, a historic area might lose its life and much of its character if it was robbed of all individuality and change. So a careful balance has to be struck, and perhaps with the woman and her purple door the conservers might have been a little too restrictive, presenting a blank bureaucratic face rather than responding with careful consideration.

There is, of course, no definitive line about what should be preserved and what updated, so the system must not just allow continual debate but actively encourage it. Maybe if purple-door woman felt that she was listened to and that her paint choice was denied to her not by faceless bureaucrats but people who actually cared about the place she lived in, just maybe she might actually
want
to paint her door in a more subtle colour rather than feeling aggrieved because she was forced to. Or maybe the authorities would change their minds …