Connotations arbitrary and invisible are connotations that don’t really matter anyway, but let’s get some idea of the issue reading some excerpts from the Wikipedia.

The search for a symbol began in 1950 when a committee was set up in order to look into the question of a European flag. There were numerous proposals but a clear theme for stars and circles emerged.

Richard von Coudenhove-Kalergi proposed that they adopt the flag of his International Paneuropean Union, which was a blue field, with a red cross inside an orange circle at the centre, which he had himself recently adopted for the European Parliamentary Union. [See Letter to the secretary general of the Council of Europe from Richard Coudenhove-Kalergi, Council of Europe.]

Due to the cross symbolism, this was rejected by Turkey (a member of the Council of Europe since 1949). Kalergi then suggested adding a crescent to the cross design, to overcome the Muslim objections. [See Letter from Richard Coudenhove-Kalergi regarding a Muslim modification to the Pan-Europa flag design, Council of Europe.]

The Consultative Assembly narrowed their choice to two designs. One was by Salvador de Madariaga, the founder of the College of Europe, who suggested a constellation of stars on a blue background (positioned according to capital cities, with a large star for Strasbourg, the seat of the Council). He had circulated his flag round many European capitals and the concept had found favour.

The second was a variant by Arsène Heitz, who worked for the Council’s postal service and had submitted dozens of designs; the design of his that was accepted by the Assembly was similar to Salvador de Madariaga’s, but rather than a constellation, the stars were arranged in a circle. In 1987, Heitz claimed that his inspiration had been the crown of twelve stars of the Woman of the Apocalypse, often found in Marian iconography. [See “Real politics, at last”. The Economist. 2004-10-28.] …