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perspective [2016/07/05 20:33] nikolaj |
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| ===== Perspective ===== | ===== Perspective ===== | ||
| - | | Perspective $\blacktriangleright$ [[On reading]] | | + | | [[About]] $\blacktriangleright$ Perspective $\blacktriangleright$ [[On reading]] | [[notes on physical theories . note]] | [[On physical units . note]] | |
| - | | $\blacktriangleright$ [[On physical units . note]] | | + | |
| ==== Note ==== | ==== Note ==== | ||
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| Knowledge of and experience with existing mathematical structures, other models and computational tools, as well as the courage to come up with new ones are important here. That's true, even when the process "merely" consists of coming up with good approximations of existing models. | Knowledge of and experience with existing mathematical structures, other models and computational tools, as well as the courage to come up with new ones are important here. That's true, even when the process "merely" consists of coming up with good approximations of existing models. | ||
| - | |||
| - | == maps == | ||
| - | The notions of *time* and *probability* are philosophically difficult. When I ask myself the question "what's the most fundamental physical unit", I think my answer would be "quantity per time", i.e. e.g. Hertz. This is because the dynamics $F$ of a theory (Newton equations, Schrödinger equation, some rate equation,..) is determining just such a quantity. Granted, statistical physics doesn't quite fit this, but then again, or maybe because of that, I view statistical physics more to be combinatorics applied to physical models than a theory of physics itself. It produces physical results, yes, but so does combinatorics applied to anything in the world. | ||
| - | |||
| - | >Regarding indexing problems (in reference to the subsection "Classifying definitions" above) | ||
| - | >The situation | ||
| - | |||
| - | $$ | ||
| - | \require{AMScd} | ||
| - | |||
| - | \begin{CD} | ||
| - | E | ||
| - | \\ | ||
| - | @V{p}VV | ||
| - | \\ | ||
| - | B | ||
| - | \end{CD} | ||
| - | $$ | ||
| - | |||
| - | >often presents the task to compute an inverse for the sake of $B$-indexing subsets ($\in{\mathcal P}(E)$) of $E$. | ||
| - | >This is the case in physics, specifically kinetics in statistical physics, with | ||
| - | $$ | ||
| - | \begin{CD} | ||
| - | X | ||
| - | \\ | ||
| - | @V{\Psi\,\mapsto\,\langle H\rangle_\Psi}VV | ||
| - | \\ | ||
| - | {\mathbb R} | ||
| - | \end{CD} | ||
| - | $$ | ||
| - | |||
| - | >If $E_{\Psi_0}\in{\mathbb R}$ for ${\Psi_0}\in X$ is in the Image and conserved for dynamics $F$ in $X$, then the inverse Image of $\Psi_0$ are accessible points. | ||
| ----- | ----- | ||
| === Related === | === Related === | ||
| [[About]] | [[About]] | ||
