2 Putting the console to good use
There is an old joke about an attendant in a museum of palaeontology. Asked by a visitor how old a particular dinosaur skeleton was, he replied ‘100 million and 5 years’. ‘That seems very precise,’ said the visitor. ‘Well,’ the attendant replied, ‘it was 100 million years old when I started here, and that was 5 years ago.’
The large dinosaurs became extinct roughly 65 million years ago (Figure 2). The last answer in Activity 2 represents that number converted to seconds. But, of course, the number 65 million is only right to the nearest million. So, if you were asked how many seconds it is since these animals died out, a sensible answer might be 2,000,000,000,000,000.
Writing a very large number like this out in full is slow, and it is very easy to miscount the zeros at the end. The answer is to use exponential notation. Here, all of those trailing zeros can be replaced by an ‘e’ (for ‘exponential’), followed by the number of zeros that have been replaced.
So the number 2,000,000,000,000,000 can be written as 2e15. Python recognises exponential notation, which is useful when working with large numbers.
Now you can tackle the question asked in the Introduction. Could all the people in the world fit on the Isle of Wight?
Activity 3 The Isle of Wight
There are various ways to tackle this question, but the simplest is probably to take the area of the Isle of Wight and divide it by the number of people in the world. The answer will represent how much space each person would get on average if everyone was crammed on the Isle of Wight. Asking whether or not this is enough space for a person to stand on will then answer the original question. Would the average footprint be enough?
The inputs – the area of the Isle of Wight and the world population – don’t need to be known very accurately. You only need rough numbers.
a. Using Google, or WolframAlpha, find:
- the area of the Isle of Wight, in square metres
- the current world population, in billions.
From Google, the area is 380 million square metres, and the population was 7.5 billion in August 2017.
b. Use the Python console below to divide the area by the population. You can use exponential notation: 380 million can be entered as 380e6 (because a million is 1 followed by 6 zeros) and 7.5 billion as 7.5e9 (because a billion is 1 followed by 9 zeros).
380e6 divided by 7.5e9 gives 0.050666666666666665. This represents just a little over 0.05 of a square metre. Could you stand on that?
c. To relate 0.05 square metres to something familiar, find the area of a sheet of A4 paper.
A sheet of A4 paper has an area of about 0.06 square metres. So, sharing the Isle of Wight among the world population would give them less than the equivalent of an A4 sheet of paper each.
This certainly isn’t enough. In fact, the maximum safe crowd density is normally reckoned to be 5 per square metre (Keith Still, 2019), giving each person 0.2 square metres, the equivalent of about three sheets of A4 paper.
So the average space per person isn’t enough and the population of the world couldn’t fit on the Isle of Wight.
Here are more questions that can be answered using a similar approach.
Activity 4 Drive me to the Moon
The British cosmologist Fred Hoyle (1915–2001) once pointed out that if there was a road at right angles to the ground, and you could drive your car upwards along it at 100 km/h, you would touch the edge of space after only an hour.
How long would it take to get to the Moon, if the road extended to it, and assuming the same speed of travel? Give the answer in months, assuming a month is 30 days.
- a.Guess the answer. Don’t do an internet search. Just think and then guess. How far away is the Moon? Could you be there next week? Next year? In your lifetime? In a thousand years?
- b.Now calculate an answer, using the console below. You will need to find the distance to the Moon. Then you can divide by the speed, and that will give the number of hours.
- c.Once you have the number of hours, convert that to days, and then to months, assuming a month is 30 days.
- d.You aren’t looking for an exact answer. This is just a thought-experiment, intended to get a rough figure, and to see if your initial guess is in the same ballpark.
The average distance to the Moon is 384,400 km.
Dividing this by 100 gives the number of hours the trip would take.
To convert that to months, first divide by 24, then by 30.
To the nearest month, driving to the Moon would take 5 months.
Tip: you can round a number to the nearest whole number using the round function, like this.
As an interesting comparison, the circumference of the Earth is a little over 4000 km. So, at 100 km/h, it would take only about half a month to circumnavigate it.
Applying the same approach as before, answer the following question about mice and elephants.
Activity 5 Of mice and elephants
How many mice would weigh the same as an African elephant?
First, write down a guess. Then do some internet research, to find the mass of an elephant and a mouse. There are different kinds of African elephant. For the purposes of this problem, you should choose the heaviest one.
The mass of the elephant will probably be given in kg and the mass of the mouse in g. Before you can compare the two, you will need to convert the mass of the elephant to g.
Once you have the two masses, you can use the Python console to divide one number by the other, to find how many mice would weigh the same as an elephant. Give your answer to the nearest thousand mice.
The mass of an African bush elephant is about 6000 kg.
The mass of a mouse is about 19 g.
First, convert the elephant’s mass to g.
Then divide the result by 19.
To the nearest thousand, the answer is 316,000, which is over a quarter of a million mice!
Tip: you can round a number to the nearest thousand using the round function with an extra input, like this.
To round to the nearest million, you would replace the -3 with -6, reflecting the fact that a thousand is 1e3 and a million is 1e6.
The next section introduces a technique for finding reasonable estimates even when there is very little information to work from.