- Author
- Terence Tao
- Published
- 29 December 2012
- Kind
- Expository blog post in mathematics, with no experiments
- Original
- terrytao.wordpress.com/2012/12/29/a-mathematical-formalisation-of-dimensional-analysis/
- Subject
- Mathematics and optimization
- Themes
- Saying it exactly, Checking the work
What it is
Terence Tao is a mathematician who writes the What's new blog. The post asks whether dimensional analysis has a properly grounded mathematical foundation. It is tagged expository and uses group and vector space language.
What it says
- The post says dimensional consistency helps catch errors and reveals the form of laws.
- It models quantities as depending on unit parameters, as representations of a group.
- It says a dimensionally consistent identity need only be checked for one choice of units.
- It says varying units and using inconsistent equations cannot both be kept.
- It says dimensional analysis gives necessary conditions on Sobolev inequality exponents.
- It says position and displacement vectors transform differently.
- In the abstract model, quantities live in one-dimensional vector spaces.
What evidence it gives
The post offers definitions and worked examples. It shows how the Sobolev inequality constrains its exponents. It gives no experiments or data. Claims rest on mathematical argument, and some facts are referred to other notes.
Interests and limits
The post is an exposition, not a new theorem. The equations did not come through in the downloaded text. The reach is mathematical modelling, not a physics test.
Connections
These links are this wiki's own reading, not claims the sources make.
- Everyone Says Assembly Is Untyped—Everyone Is Wrong. Tao says dimensional consistency catches errors and reveals the form of laws. gingerBill says assembly already has types: operand forms and widths. In both, the structure existed before anyone checked it. A checker only shows what the domain already enforced.