weight volume surface relationships

"In a country with baby bonuses, paid parental leave schemes and a high immigration intake, to argue that rapid growth can't be avoided is like claiming that speeding is inevitable while your foot is on the accelerator." (Melvin Bolton)

We so often hear about Melbourne's 'livability' according to the specious and self-fulfilling criteria of the 'Economist group' that it is nice to hear about "Another major liveability index for cities is produced by the American consulting firm, Mercer. "The Mercer Quality of Living Survey for cities is continually being updated and it ranks more than 220 cities on scores under dozens of different criteria of liveability. In this list Vienna has come top for three years in a row and Sydney has come in at number ten, also for the past three years. Melbourne doesn't make it to the top ten and the other nine have populations smaller than Sydney's." (Melvin Bolton)

Transcript from "Finding the Right Size"
Ockham's Razor, Sunday, 14 December 2014.

Robyn Williams interviews science writer, Melvin Bolton, who talks about the work of Professor John Burden Sanderson Haldane

Robyn Williams: J.B.S. Haldane has always been a hero of mine, mainly because he was bonkers, but also because he was seriously clever. I ran a poem of his in the Science Show a couple of weeks back: ‘I wish I had the voice of Homer, to sing of rectal carcinoma…’ or something like that. Yes, Haldane wrote a poem about his tumour. He also used to blow himself up during the war to test explosive atmospheres in ships and submarines because he wanted to make them safe for soldiers and sailors. Haldane was a sort of aristo, Eton and Oxford, but also, weirdly, the communist party and he wrote magnificent pieces on sciences. He was a great science communicator, writing classics, like the once you’re going to hear about from Melvin Bolton in Yeppoon in Queensland.

Melvin Bolton: Many years ago, in England, I was trying to find my way in the dark round the back of a building, when I tumbled into a pit that led to a coal cellar. I came out in nasty bruises and had to walk with a stick for fortnight, but it occurred to me that if I'd been a much heavier person I would not have got off so lightly. It really is true that the bigger they are, the harder they fall.

I had this in mind at the time because I'd been reading an essay On Being the Right Size by J.B.S. Haldane. Haldane was a mathematician but he was so brilliant he could turn to whatever he liked in science and in 1933, after teaching biochemistry at Cambridge, he became professor of genetics at University College London. Haldane was one of the pioneers of genetics. It was he who came up with the word 'clone' in the sense that we know it today, and some of his predictions were taken up by his friend, Aldous Huxley, and worked into the novel Brave New World.

In that essay on being the right size, Haldane pointed out that if a beetle fell into a mineshaft, a kilometre deep, it would be none the worse for it. Even a mouse might get over the shock if the ground wasn't too hard, but a rat would be killed, a human would break up, and a horse would splash.

This is because the resistance to falling through air is proportional to the surface that meets the air to cause friction. And as volume and weight are scaled up, the surface area gets relatively less. A horse might be a thousand times heavier than a rat but would have only about a hundred times the surface to slow its fall.

The relationship between weight, or volume, and surface, largely accounts for all the sizes and shapes that we see in nature because things can't just get bigger and keep the same shape. It would be impossible, for instance, to have a rhinocerus shaped like a gazelle. A rhino might be four times the length of a gazelle but if the gazelle were scaled up to be four times as long, it would be 64 times heavier—its weight would increase from 30 kilos to nearly two tonnes. On the same-shaped legs it would lie in a heap, unable to stand up.

Nature can never break the laws of maths and physics so has come up with ways of working around them, just as engineers and planners do, but I'll come to that in a minute. I first want to make the point that big animals and plants are more complicated than small ones because they have to be; it's a consequence of being bigger. Single cells, like bacteria, were the only form of life on Earth for more than a billion years, and they are still highly successful but they must stay small. All exchange with the outside world has to take place through the surface, and the centre of the cell has to be close enough to the outside for gases and liquids to move adequately, just by diffusion.

When cells join together to form bigger forms of life, the surface gets proportionally smaller, the centre gets further from the outside, and there needs to be some sort of transport system such as blood or sap that can deliver the necessities of life a lot faster and more efficiently than can happen by simple diffusion.

In nature, there is often a need for bigger surfaces in places that can't be expanded any further—such as inside heads or intestines. In a bird's head the brain is quite smooth on the outside but a chimpanzee has to pack many more neurones around its brain so the surface has a lot of folds or convolutions—which increase the area without making the head any bigger. This is a process that's gone furthest of all in humans.

A small Intestine needs a huge surface to deal with digestion so the lining has projections, like the pile on a carpet. This increases the surface enormously. It varies between individuals, but an adult small intestine has a surface area of thirty to forty square metres—which is close to half a badminton court.

In a final example, let's take a simple shape like an egg, no projections of any sort. Inside a bird's egg the developing chick has the equivalent of a placenta close to the inside of the shell. The chick gets all its oxygen and gets rid of carbon dioxide through tiny holes, or pores, in the shell. and that presents a problem with bigger eggs. An emu's egg is about six times longer and wider than a sparrow's egg but it weighs about 250 times as much. The shell has to be twelve times as thick and a thick shell is a huge barrier to the passage of gases. The problem has been solved in birds by having the pores closer together, and with a much bigger diameter in thicker shells.

Evolution is essentially a numbers game and nature is made up of compromises that have evolved, step-by-step, minute by minute, through mutations and the filtering effects of natural selection over millions of years. The best compromise emerges because everything that's exposed to natural selection is weighed in the balance for such long periods of time.

Engineers, and others who build things and create new materials, are working with exactly the same constraints set by the laws of physics and maths, and they sometimes get their ideas from nature.

Professor Haldane, in his essay on size, did not get into the topic of deliberately trying to copy nature, but he did make the point that just as there is a best size for every animal, so there must be for every human institution. He pointed out that in ancient greece all the citizens could listen to a series of orators and then vote directly on matters of legislation. So philosophers at that time had reason to believe that a small city was the largest possible democratic state.

New methods of communication had changed things a lot by Haldane's time and they've changed a lot more since then. Although when you look at all the duplications of our old federal system you might think that the tyranny of distance is still a major problem in Australia.

So is it still true today that there is an optimum size for human institutions, for nations, for cities? We hear political leaders on all sides of politics declaring that they believe in a big Australia. They don't say how big, though they can't possibly think we can keep making things bigger and bigger indefinitely. They just say they believe in a big Australia as if it is a matter of belief; an article of faith.

Why do they believe it? Usually they say it's because it will produce a better quality of life for all Australians. Is that likely? How many Melbournians think that life will be better in a Melbourne that's twice the size it is now, with twice the number needing housing, services and transport?

Is there any evidence for thinking either way? Well, we can start by looking at the Human Development Index. This is published each year by the United Nations Development Programme and it ranks the UN member countries according to how well their people are doing in terms of health, education, lifespan and general standard of living.

For the past few years, Australia has come second after Norway, with Denmark third. Another index, that goes further than the United Nations one, is put out each year by the Economist Intelligence Unit, based in London. Originally called the Quality of Life Index, it's now known as the Where to be Born Index, which I suppose makes it sound more foward-looking for prospective parents as well as investors. In addition to all the basic welfare issues of health, education, security and so on, it factors in people's feelings of satisfaction with life, based on scores derived from Gallup polls. It even takes climate into consideration.

And with all that, the interesting thing is that it places exactly the same countries in the top ten that the United Nations comes up with. They are in a slightly different order; Australia comes second, with Switzerland first and Norway in third place, but the same ten countries top the list. Six of those top ten countries have smaller populations than Australia.

We can look at cities in the same way. Every year, the Economist Intelligence Unit produces liveability rankings for cities around the world. These are based on scores reached under headings that include stability, healthcare, culture and environment, education and infrastructure. In the most recent report, released in 2013, Melbourne came top of the list of 140 cities, followed by Vienna and Vancouver. Of the top ten cities, seven were smaller than Melbourne.

Another major liveability index for cities is produced by the American consulting firm, Mercer. The Mercer Quality of Living Survey for cities is continually being updated and it ranks more than 220 cities on scores under dozens of different criteria of liveability. In this list Vienna has come top for three years in a row and Sydney has come in at number ten, also for the past three years. Melbourne doesn't make it to the top ten and the other nine have populations smaller than Sydney's.

Now, these league tables may not prove anything but they certainly don't offer any support for the belief that getting bigger and bigger will do anything to improve the quality of life for all Australians. They suggest, if anything, that Melbourne and Sydney are doing well despite their size, not because of it.

And such evidence as there is from surveys here in Australia indicates that most Australians are putting up with high population growth rather than wanting it. Why we are putting up with it is another question entirely, and your guess is as good as mine.

When Big Australia believers are quizzed about their reasoning, some of them back off and say simply that our growth rate is unavoidable so we just have to keep on accommodating it—building upwards, over farmland, making more flyovers, freeways, by-passes, tunnels, whatever it takes to cope with centres getting further and further from peripheries and all the other complications of increasing size.

But in a country with baby bonuses, paid parental leave schemes and a high immigration intake, to argue that rapid growth can't be avoided is like claiming that speeding is inevitable while your foot is on the accelerator.

Professor Haldane, in case you are wondering, died in 1964 at the age of 72. His full name, incidentally, was John Burden Sanderson Haldane and he died in India, having emigrated there eight years earlier. He had also taken to wearing Indian dress, remarking that "sixty years in socks is enough." I doubt that he really did have a problem with socks, although, if there was a lot of stretching and shrinking ... no, surely not.

Robyn Williams: Maybe not Melvin, but I’ll tell you one thing that happened when Haldane went to India: Everyone expected him to turn up with tons of shiny apparatus. Instead he gave the Indian scientists pencils and paper and asked them to count the leaves on trees. As a result they found that there were two crop species instead of one. Selecting the best enabled them to double the yield. Yes, Haldane was a genius, if nuts. Melvin Bolton comes from Yeppoon in Queensland.

Next week Ockham’s Razor comes from Western Australia where Dr Peter Underwood tries to corrupt his grandson. That’ll be in Science Extra.