You are here: Mathematics > General Information > Staff List > CDC Steele > articles > svithjod
School of Mathematics

The little bird of Svithjod

High up in the north, in the land called Svithjod, there stands a rock. It is a hundred miles high and a hundred miles wide. Once every thousand years a little bird comes to this rock to sharpen its beak.

When the rock has thus been worn away, then a single day of eternity will have gone by.

From The Story of Mankind by Hendrik Willem Van Loon

So, how long is a single day of eternity ? ; how long is eternity ?

The following calculation attempts to answer how long a single day of eternity is. In doing so, it is necessary to make certain assumptions.

Assumption 1 : Dimensions of the rock. Two dimensions of the rock are given as one hundred miles. The third dimension of the rock is not given. Given that the two dimensions of the rock are equal, it will be assumed that the third dimension is also the same. So, the rock is one hundred miles long, one hundred miles wide and one hundred miles high.

Of course a rock of these dimensions on the Earth could not be supported by the Earth's crust and would force its way through the crust and interact with the Earth's mantle and core. However, this leads to the second assumption.

Assumption 2 : The wording of the statement takes priority over any physical laws. Under this assumption, the rock would not force its way into the interior of the Earth.

Assumption 3 : The little bird . Just how 'little' the bird is is something that is not stated. However, the impression given is that the rock sticks out of the sea and that the bird is some sort of sea-bird. Given that the bird is stated to be small, a small seagull is more likely than an albatross, puffin etc. The process of the sharpening of the beak involves the hard rock against the softer material of the beak. It is hard to see, in a single sharpening, more than a cubic milimetre of rock being worn away. Clearly a larger volume of the beak would be worn away in a single sharpening.

Assumption 4 : Erosion . Under the time-scales involved, erosion would be expected to play a role in wearing the rock away. However, the use of the word thus in the quote invokes the assumption that no erosion takes place.

There are also certain problems as follows

Problem 1 The rock is higher than the altitude at which birds can fly. The bird can only wear away the rock from the edges of the bottom.

Problem 2 Visits of the bird occur only once each thousand years. 'Little birds' do not live for anything like that amount of time. The fact that it may be a different little bird (a descendent ?) each time is less perplexing than the question of why only some generations of birds and not others are required to sharpen their beaks.

However, it will be assumed that these problems (under assumption two) are not insurmountable.

The calculation

The rock measures one hundred miles (i.e. 161 million millimetres) in each directions. Its volume is therefore 4.2 million million million million cubic millimetres. As each visit of the little bird, a single cubic millimetre is worn away, the rock will therefore survive for 4.2 million million million million visits i.e. 4.2 thousand million million million million years. In scientific notation, this is 4.2 x 10 27 years. Hence, a single day of eternity lasts 4.2 x 10 27 years.

This introduces a fresh problem i.e. that the age of the earth is only about 5 x 109 years. After a similar period of time, it is expected that after a siilar further period of time, the Sun will expand and swallow the Earth. However, under assumption two, the ability of the little bird to continue its visits to the rock will continue unabated.

Final Remarks

The current age of the universe at 1010 years is negligible when compared with the 'single day of eternity' at 4.2 x 1027 years.

This is one of the few cases where tradition has overestimated (as opposed to underestimated) the timescales of the universe.

It is interesting to see how a combination of several accessable figures has given a final result which is far from accessible.

to the top

Page activated January 2007

Last modified: January 07, 2007 6:48:20 PM UTC.