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many greek mathematicians ascribed to the philosphical idea of "the world of forms" Essentially, they believe that there is a abstract dimension where perfect idealised shapes of things exist, and reality attempts to conform to these perfections. Imagine an apple, the perfect apple. perfectly smooth, perfectly shaped, perfectly colored. there are no perfect apples, but they all try their best to be this imaginary apple. The truest form of it in its idealized state. Geometric shapes also presumably live in this dimension, as well as all abstract truths and objects. Whether or not you believe this is *really* the case depends on your outlook as to whether we "invent" ideas or "discover" them.
The principle of conservation of energy states that nothing appear from nowhere. so where do thoughts and ideas and dreams come from? How can imagination create new concepts where none existed before? One idea might be that we are able to subconciously tap into this "dimension of abstraction". On the other hand, a neuroscientist would tell you that thoughts and emotions and dreams and hopes are nothing more than electrical patterns of neurons firing in a continuous way constructively interfering to produce conciousness. 'merely' a quantum wave-function constructed from those electrical signals. Where do the patterns come from? Why and how do they corralate exactly with particular thoughts? My point is, ... well i dunno. There is no point really, Just wanted to put out some food for thought.
Scientist are only really concerned with the physical world that can be experimentally tested through the scientific method. Mathematicians are slightly more open to the world of abstraction, but they must limit themselves to logic born from riggorous proofs, theorems, and agreed upon conventions which are useful for education yet limit thought along a set path. However, reality need not abide by our sense of reason nor our ability to prove. for all we know there very well could be an abstract dimension beyond space-time. But because you could never experementally test such an outlandish philosphically based claim, it might as well be discarded along with the rest of questions with no answers and statements without proof. as Godels incompletness theorem shows, some things which are true can never be proven.
If there is a take away to this tangent, its that physical reality is merely an aspect, not the whole. A piece of the puzzle, a way of looking at things. Arrogance is believing that your piece of the puzzle is the 'true' one and all other pieces invalid, as if our little brains could really comprehend the whole of it all. Be open to new perspectives even if they contradict the very 'truth' you hold dear. Our ideas of proof, of truth, and of belief are *nothing* but guesses and hopes in the face of the real infinite complexity of reality, so pick your poison and dont worry about it too much. Human beings are contradictory in nature, equal parts logic and emotion. Perhaps the universe is similar. A reality of form and meaning.