Filled Quote by Hans Reichenbach
“We must... maintain that mathematical geometry is not a science of space insofar as we understand by space a visual structure that can be filled with objects - it is a pure theory of manifolds.”
About This Quote
He argues that geometry describes abstract manifolds, not physical space, separating pure math from visual representation.
In simple terms: Geometry is about abstract shapes, not visual space.
Key Takeaway
Recognize the abstract nature of geometry.
Themes
philosophy
mathematics
epistemology
Mood
thoughtful
analytical
Type
philosophical
technical
When to use this quote
- academic lectures
- research
- teaching
Key Concepts
manifolds
abstract theory
Questions to Reflect On
- Is geometry purely abstract?
- Can visual intuition aid understanding?
![“I am much occupied with the investigation of the physical causes [of motions in the Solar System]. My aim in this is to show that the celestial machine is to be likened not to a divine organism but rather to a clockwork ... insofar as nearly all the manifold movements are carried out by means of a…” quote by Johannes Kepler](https://sms4smile.com/quotes/img-quotes/452/johannes-kepler-4278_aim_i-am-much-occupied-with-the-investigatio_1011205.jpg)
