Link to current text
MATH.13:3 - Forces
| Force | Tension |
|---|
| Structure of interest | A transformation can preserve one structure while changing a criterion, condition or distinction needed by the question. |
| Whole problem and law | Symmetry of a law can relate different input problems; a conclusion about one fixed problem needs its data preserved as well. |
| Solution multiplicity | A transformation preserves the solution set, but individual solutions can move within it. |
| Computational saving | Symmetry can reduce repeated work, while the output may need information lost by the reduction. |
| Physical use | A mathematical symmetry can suggest a conserved quantity; its conservation needs the relevant dynamics or theorem. |