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"the Prime Meridian was (arbitrarily) chosen to pass through the Royal Observatory in Greenwich"

At the International Meridian Conference in 1884 41 delegates from 25 nations met in Washington, D.C., USA and selected the meridian passing through Greenwich as the official prime meridian due to its popularity - not an arbitrary decision ;)

However, the French abstained from the vote and French maps continued to use the Paris meridian for several decades.

How is a popularity contest not a shining ideal of completely arbitrary decision-making?

In this case popularity was the best criterion. Imaginary line is just that—imaginary line, no one is intrinsically better than other, so the one already popular was the best choice.

Well, the choice of GMT certainly made picking the international date line earlier. Certainly useful that 180 degrees around the world is mostly water.

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