# A Hemispherical Problem

Half of the world, or nearly so, is always in the light of the sun: as the world turns round, this hemisphere of light shifts round too, and passes over each part of it in succession.
Supposing on Tuesday, it is morning at London; in another hour it would be Tuesday morning at the west of England; if the whole world were land we might go on tracing1 Tuesday morning, Tuesday morning all the way round, till in twenty-four hours we get to London again. But we know that at London twenty-four hours after Tuesday morning it is Wednesday morning. Where, then, in its passage round the earth, does the day change its name? Where does it lose its identity?
Practically there is no difficulty in it, because a great part of the journey is over water, and what it does out at sea no one can tell: and besides there are so many different languages that it would be hoeless to attempt to trace the naem of any one day all the year round. But is the case inconceivable that the same land and the same language should continue all round the world? I cannot see that it is: in that case either2 there would be no distinction at all between each successive day, and so week, month, etc., so that we should have to say, "the Battle of Waterloo happened to-day, about two million hours ago," or some line would have to be fixed where the change should take palce, so that the inhabitants of one house would wake and say, "Heigh-ho3, Tuesday morning!" and the inhabitants of the next (over the line), a few miles to the west would wake a few minutes afterwards and say, "Heigh-ho! Wednesday morning!" What hopeless confusion the people who happened to live on the line would be in, is not for me to say. There would be a quarrel every morning as to what the name of the day should be. I can imagine no third case, unless everybody was allowed to choose for themselves, which state of things would be rather worse than either of the other two.
I am aware that this idea has been started before-- namely, by the unknown author of that beautiful poem beginning, "If all the world were apple pie," etc.4 The particular result here discussed, however, does not appear to have occurred to him, as he confines himself to the difficulties in obtaining drink which would certainly ensue.

Lewis Carroll, 1849

1. The best way is to imagine yourself walking round with the sun and asking the inhabitatns as you go, "What morning is this?" If you suppose them living all the way around, and all speaking one language, the difficulty is obvious.
2. This is clearly an impossible case, and is only put as an hypothesis
3. The usual exclamation at waking, generally said with a yawn.
4. "If all the world were apple pie,
And all the sea were ink,
And all the trees were bread and cheese,
What should we have to drink?"

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