Square circles and married bachelors

Married bachelors in human society

• In the minute portion of the universe that is populated by humans, the concept of marriage, and the concept of a bachelor is understood.
• Both concepts have probably changed over the years of civilisation, until they have their current meaning.
• The meanings are unknown to a baby, but as it grows, the meanings become clear to it, via school, parents, books, etc. and the child understands the terms to mean roughly what the rest of its society understands them to mean.
• The meanings are consistent, and it is easy for anyone in such a society to agree that it is impossible for there to exist a married bachelor

Married bachelors outside human society
• Anywhere else, there may be no concept of marriage, no concept of two sexes, and thus no concept of bachelors
• Given that there is no reason to think this is a universal concept, there is even less reason to think of it as having an objective reality

Physical universe
· No such thing as a square
· No such thing as a circle
· Get down to the Planck length – a circle and square would be indistinguishable
· Any bigger, and they don’t exist perfectly

Concept of square and circle
· A bright person conceptualised a perfect plane (Cartesian, Euclidean)
· Conceptualised the definition of a point, a length
· Defined a circle to be the locus of all points equidistant from a point
· Produced the concept of the perfect circle as a continuous, smooth line.
· Conceptualised a straight line, angles, right angles
· Defined a square as a set of 4 straight line segments at right angles, forming a non-smooth, disjointed, 4-sided figure.
· All these concepts were passed on and refined from mathematician to mathematician, and to generations of school children.
· They became part of many human cultures
· Within these cultures, the ideas are commonplace to the point of seeming objective.
· They are part of an agreed set of concepts that form their own consistent framework, and within which it is not possible for a square to be a circle

The separation of physical reality and human concepts
· The concepts exist within the minds of humans who have absorbed them.
· They could as easily exist within the minds of beings from civilizations apart from those on Earth
· This does not alter the fact that they are concepts only, not existing, except as approximations, in the physical universe
· There is no justification in assuming that they are objectively real.
· Within this agreed construct, there is no problem in saying that it is impossible to have a square circle.  This is a natural consequence of  the mathematical construct, but is an irrelevance in terms of physical reality.


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