The idea of higher dimensional space can certainly provoke discussion, at KS 23 and KS4 as well at A-level. The image in the article of the carp in the shallow pond, restricted to only two dimensions, is very powerful. As the article says, if you lived in a 2D world, but could move into 3D, you could "magically" appear and disappear from the world by moving in and out of the third dimension. There is a classic book: Flatland: a romance of many dimensions by Edwin A Abbott, which explores ideas like these. It tells the story of a square living in a 2D world and is a worthwhile addition to any school library, with ideas relevant at KS23 and above.
The idea that a "Theory of Everything", explaining all physical phenomena, might be given in an equation "no more than one inch long" really brings home the power of maths. This feature is particularly relevant to A-level maths. Modern physics is founded in mathematics. Newtonian mechanics, relativity and quantum mechanics and superstring theory are mathematical models which attempt to describe the physical world. Physicists express their ideas mathematically then test them against experimental observation and modify them to improve their match with the universe. This is exactly the mathematical modelling process that forms a key part of ASA-level Mathematics. Students making ASA-level choices need to understand just how important maths is in other fields.
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