Oct 22, 2014 12:44 AM
http://plus.maths.org/content/richard-elwes
EXCERPT: [...] Do higher dimensions exist? Mathematics provides a surprisingly emphatic answer to this question. Just as a 2-dimensional plane can be described by pairs of coordinates such as (5,6) with reference to a pair of axes, so 3-dimensional space can be described by triples of numbers such as (5,6,3). Of course we can continue this line of thought: 4-dimensional space, for a mathematician, is identified with the sets of quadruples of real numbers, such as (5,6,3,2). This procedure extends to all higher dimensions. Of course this does not answer the physicist's question, of whether such dimensions have any objective physical existence. But mathematically, at least, as long as you believe in numbers, you don't have much choice but to believe in 4-dimensional space too.
Well that is fine, but how can such spaces be imagined? What does the lair of Yog-Sothoth actually look like? This is a much harder question to answer, since our brains are not wired to see in more dimensions than three. But again, mathematical techniques can help, firstly by allowing us to generalise the phenomena that we do see in more familiar spaces....
EXCERPT: [...] Do higher dimensions exist? Mathematics provides a surprisingly emphatic answer to this question. Just as a 2-dimensional plane can be described by pairs of coordinates such as (5,6) with reference to a pair of axes, so 3-dimensional space can be described by triples of numbers such as (5,6,3). Of course we can continue this line of thought: 4-dimensional space, for a mathematician, is identified with the sets of quadruples of real numbers, such as (5,6,3,2). This procedure extends to all higher dimensions. Of course this does not answer the physicist's question, of whether such dimensions have any objective physical existence. But mathematically, at least, as long as you believe in numbers, you don't have much choice but to believe in 4-dimensional space too.
Well that is fine, but how can such spaces be imagined? What does the lair of Yog-Sothoth actually look like? This is a much harder question to answer, since our brains are not wired to see in more dimensions than three. But again, mathematical techniques can help, firstly by allowing us to generalise the phenomena that we do see in more familiar spaces....