Many of Easy FM’s listeners may be thinking that the world is coming to an end, now that James West, Mr Business Reporter, is leaving the station. So I thought that today on Mr Science we would have a chat about what actually might to our universe when its time is up.

The universe is old and massive. NASA scientists estimate that it is 13.7 billion years old. We don’t know yet how big it is, whether it is infinite in size – that is goes on for ever – or actually has a boundary of some kind, but we do know that at the moment, the universe is expanding – observations show that stars around us are getting further and further apart and are moving away from us.

But will the universe continue to expand for ever? We can see about 7 × 10^{22} stars in the universe – that is a 7 with 22 zeros after it, or about the number of grains of sand on all the Earth. Will the gravity from all these stars eventually force the universe to collapse in on itself into something like an anti-bigbang?

This theory is called the “Big Crunch”. What it predicts is that there is enough matter in the universe – the density of the universe is high enough – that gravity will eventually pull everything back into a single spot – the exact reverse of what is thought to have happened in the big bang that started the universe. This theory also allows for another big bang to arise out of the big crunch, making an universe that keeps alternating between big bangs and big crunches – like a balloon you blow up, then let the air out of, then blow up again and so on.

Another theory, and the one that is the most popular among scientists at the moment, is that the universe will not collapse in a big crunch, but will expand forever. If so, everything will get further and further apart, and colder and colder. Eventually, stars will no longer burn and black holes will sweep up stars. After this, everything will decay into elemental particles – not just the atoms that make things up, and not just the protons, neutrons and electrons that make atoms up, but down to the elementary particles that make these tiny things up.

There are other such theories of the end of the universe, but perhaps, in the end, we’ll be able to escape the death of the universe completely. Some scientists believe in multi-universes and the idea that perhaps when humans get smarter in the very distant future and have the ability to not only manipulate the Earth’s resourses, but all the energy in galaxy or the universe, then maybe we’ll be able to somehow slip into another of these multi-universes. Perhaps these other universes have different physical laws to ours and so could look rather different to ours. Some theorists even believe that we will be able to engineer universes to live in. Others even think that a big crunch might be a good thing as it would allow humans to harness massive amounts of energy – energy which could be used to process information quicker and quicker as the crunch came. As information is processed an increasingly rapid rate, it may seem to the human doing to processing that time was slowing down, thus making it seem like he is living forever! This is highly speculative, and I don’t even really understand it!

But what I do understand is that all this highly speculative science is not going solve the problem of James West leaving China Radio International, nor will the universe end when he does. So thanks to James for allowing me the chance to bring science to you every Friday, and I hope to continue doing it in the weeks to come, but without my little brother helping me along.

The mp3 can be heard here

## Wednesday 29 March 2006

### The end of the universe

### The mathematics of looking beautiful

Looking good is important to a lot of people. Gyms, cosmetic companies, clothes stores and fashion magazines all exist because of our preoccupation with looking good. So what makes someone attractive?

Greek philosopher Plato believed he found the answer in the fourth century BC, and discovered it candidate in the most unlikely place of all: mathematics.

Plato was interested in designing beautiful shapes. As strange a hobby as this may seem, his results were even stranger. When measuring the dimensions of rectangles that he considered beautiful, he found their ratio was always the same ‑ 1.618.

Although this number is nothing special to look at, it has intrigued Plato and generations of mathematicians for centuries. The ratio 1.618 can be found in many examples of objects that we consider to be beautiful ‑ from the human body to music, architecture, nature and art. This number is so special that it has been called ‘the golden ratio’.**What exactly is the golden ratio?**

The golden ratio can’t be written exactly as a decimal number, because it is irrational. It is a decimal that continues on and on, without any apparent repetition.

The best definition of the golden ratio is it is the only number that when squared is equal to the sum of itself and one. In 1996, a mathematician called Greg Fee programmed his computer to compute the golden ratio to ten million places. It took Greg’s computer approximately 30 minutes to complete.

There is an easier way to estimate the golden ratio using the Fibonacci sequence. This is a sequence of numbers where the next term is the sum of the two previous:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 … and so on.

If you divide each number in the sequence by the one before, you may notice that the quotient approaches the golden ratio:

1/1 = 1, 2/1 = 2, 3/2 = 1.5, 5/3 = 1.666…, 8/5 = 1.6, 13/8 = 1.625, 21/13 = 1.615…**Fibonacci in nature**

The Fibonacci sequence is often found in nature. The number of petals on a flower is often a Fibonacci number. Buttercups have five petals, lilies and irises have three petals and daisies often have 34, 55 or 89 petals. You might find some Fibonacci numbers in other places in your garden as well. Seeds on flower heads, such as on sunflowers, are often Fibonacci numbers. Patterns on pinecones are also based on Fibonacci numbers.

Sometimes these numbers are not exactly Fibonacci. In the case of pinecones, this can be due to deformities produced by disease or pests. In this case, the absence of the Fibonacci sequence indicates that the pine tree is not well.

Animals also display the Fibonacci sequence. The most spectacular of these are seashells. You can recreate a spiral sea shell pattern using a compass and a ruler.

Start by drawing two unit squares side by side. Together these squares form a rectangle. On the bottom of this rectangle, add a 2x2 square to make a new bigger rectangle. Beneath this new rectangle draw a 3x3 square. This creates a larger rectangle. Each rectangle is known as a Fibonacci rectangle, because the dimensions of each new square follow the Fibonacci sequence.

To complete the spiral, use the compass and to draw a quarter circle in each square to form a spiral. This shape is called a Fibonacci spiral. Similar spirals are found on snail shells and seashells.**The golden ratio in the human body**

It may be surprising to know that the golden ratio can be found in the human body. Your hands contain three bones in each finger (you may notice this more by bending them). The ratio of the longest bone compared to the middle bone and the ratio of the middle bone compared to the smaller bone are both close to 1.618.

Another place you will find the golden ratio is your height. Measure how tall you are and compare this to the distance between your feet and navel. Their ratio is close to 1.618. Your face may also contain the golden ratio. What is the ratio of the width of your mouth compared to the width of the bottom of your nose?

Some people think that the closer certain ratios in your body are to the golden ratio, the more attractive you appear.

Can you find the golden ratio anywhere else in your body?**Art imitates life**

The golden ratio can be found in art, architecture and music. The famous Greek sculptor, Phidias, was known to use the golden ratio in his sculptures of the human body. The most famous Greek building, the Parthenon, is 1.6 times as wide as it is tall. Leonardo da Vinci also used the golden ratio. He would frequently divide his canvas in this proportion.

The golden ratio has also been used by musicians. Mike Kay, an American mathematician, has examined Mozart’s sonatas and found that most of them divide into two parts exactly in the ratio of 1.618:1. Whether this was intentional or intuitive is not known.

Another researcher, Derek Haylock, found that the famous opening motto in Beethoven’s fifth symphony is repeated at the golden ratio point from the beginning of the song (32 percent of the way). Intriguingly, it is also heard at the golden ratio point from the end of the song (68 percent of the way). Other composers that appear to have used the golden ratio in their music were Bartok, Debussy, Schubert, Bach and Satie.**Is the golden ratio the key to looking good?**

No. Everybody has his or her own opinion as to what is good looking. However, the golden ratio has been used in the design of various works of art and architecture to increase their appeal.

In living organisms, it seems the presence of special numbers and proportions has provided some sort of evolutionary advantage. In nature, plants with Fibonacci numbers may be healthier and pest-free. Animals with these ratios may also appear healthier and more desirable to mates. However, the golden ratio is not the whole story. Beauty still escapes a complete explanation.