When Einstein Walked with Gödel | Robert Wright & Jim Holt [The Wright Show] 

Try Mathologer channel for the best explanation & clearly stated and demonstrated.

@Oners82 what feynman describes is the transformation of an image along an axis, precisely mathematical. Mathematics is just the formalization of exactly what you describe. We have said the very same thing in a slightly different way. Maths is entirely geometry and spacial reasoning. It is the exact same thing as how you have expressed it, except that i understand what language you speak -- you don't understand me (maths). I'm surprised you would use Feynman as an example when this is precisely his stance as well (analogous to our differing comprehensions).... To paraphrase Feynman: They say science takes away from the beauty; but do i see less... or more...?

..."in order to achieve the position seen in the reflection we must rotate on the vertical axis 180 degrees. ...front/back reflection for a 180 degree rotation..." Shit, you are absolutely right and i am completely wrong. This doesn't sound like a mathematical geometrical and spatial description at all. What was i thinking?..

you captured what I had in mind so well

So, a leftie sheep thinker, thinks about math, a method to describe reality in a abstract form, a heavy task fore some, but worth trying;)

Mathematics is reality and exists independent of the universe, it's the universe that doesn't really exist. The universe is merely a transient shadow of this underlying reality, one of infinitely many mathematical structures, not at all special except to us who happen to be derived from this particular mathematical structure. The universe is not real, there is no physical reality, those things we call particles or energy or forces are merely mathematical structures and we ourselves are merely slightly more complex mathematical structures; they are transient manifestations of the underlying mathematical reality, but do not exist in any meaningful sense beyond the mathematics reality they mirror. Our senses are flawed and limited, we can gain no meaningful knowledge from them, we can only gain the facade of knowledge by comparing our crude observations to the underlying reality of the universe, mathematics, but in the end it is just a subsection of a priori mathematical knowledge. Of course, that's only a hypothesis, just like your statement. But I'd argue it's a better hypothesis, it assumes only a priori knowledge, only reason and number, and does not add the unnecessary complexity of observation. The reliance on observation is the fundamental flaw of empiricism. Observation is so flawed and fraught with problems, from finite limitations to lack of resolution to a level of uncertainty that makes proof impossible due to only being able to ever see part of the picture, that it can never give knowledge and can only allow for conjecture.