Friday, November 06, 2020

5: Axioms



Two sides of a triangle are longer than the third. 
You say that because you are a man. (Irrelevant.)

A + B > C is a geometrical truth. It can’t be disproved; it can’t be doubted; and we can’t even imagine a world where it wasn’t true. The only way Mrs Bulver could have contradicted Mr Bulver’s assertion would have been to say “You only think that because you are working on a Euclidean plane: triangles work differently on spheres”. 

However, consider the following: 

a: 2.4 + 2.4 = 4.8. If we are allowed to round to the nearest whole number, then 2.4 can be expressed as “2” and “4.8” can be expressed as “5”. So we could say “2+2=5”. 

b: Two apples plus two oranges do not make four apples or four oranges. 

c: Two plus two makes four, but two rabbits plus two rabbits may very well make several hundred rabbits. 

d: The correct answer to the question “What is the difference between 1 and 6?” is "5". But "One is even and one is odd" and "One can be drawn with only straight lines and the other can be joined with only curved lines" are also correct answers. 

e: Can you think of a five letter word which becomes shorter if you add two letters to it? 

The Right Wing Internet becomes enraged by this kind of thing. “The liberals want to teach our kids that 2+2=5 like Orwell warned us!” they cry. “Cultural Marxists say that the answers to sums are whatever they want them to be!” Mrs Margaret Thatcher, of blessed memory, affected to be outraged that some schools taught “non-racist mathematics”. 

But maths is a learned language; and one’s reaction to these edge-cases, ambiguities and double meanings might be affected by your culture or background. Boys might solve riddles better than girls; older children might see the answers quicker than younger ones. The claim that a man and a woman might perceive geometry differently is not inherently ludicrous: there might conceivably be a circumstance under which “You think that because you are a man” was a reasonable thing to say.




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