And last of all we have the secondary forms of crystals…
“And last of all we have the secondary forms of crystals bursting in upon us, and sparkling in the rigidity of mathematical necessity and telling us, neither of harmony of design, usefulness or moral significance, nothing but spherical trigonometry and Napier's analogies. It is because we have blindly excluded the lessons of these angular bodies from the domain of human knowledge that we are still in doubt about the great doctrine that the only laws of matter are those which our minds must fabricate, and the only laws of mind are fabricated for it by matter.”
About This Quote
This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation.
Mathematical forms can seem beautiful yet detached from moral or practical meaning, highlighting limits of purely abstract reasoning.
In simple terms: Math can be beautiful but may lack moral relevance.
Key Takeaway
Balance abstract theory with real‑world relevance.
Themes
beauty
abstraction
limitations
Mood
contemplative
critical
Type
philosophical
scientific
When to use this quote
- education curriculum
- scientific research
- philosophical debate
Key Concepts
mathematics
philosophy of science
Questions to Reflect On
- How can we embed ethics in abstract work?
- What value does beauty bring to science?
A Different Perspective
Pure abstraction can ignore ethical implications.