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on_reading [2016/05/24 20:11] nikolaj |
on_reading [2016/07/19 23:41] nikolaj |
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| ===== On reading ===== | ===== On reading ===== | ||
| - | | [[Perspective]] $\blacktriangleright$ On reading $\blacktriangleright$ | | + | | [[On mathematical theories]] $\blacktriangleright$ On reading $\blacktriangleright$ [[On syntax]] | |
| ==== Note ==== | ==== Note ==== | ||
| One strategy in reading and taking apart the content of a physics or math text is to try and classify the parts of it into the above three points and sub-points. For each piece of text one is currently presented with, one can try and classify: | One strategy in reading and taking apart the content of a physics or math text is to try and classify the parts of it into the above three points and sub-points. For each piece of text one is currently presented with, one can try and classify: | ||
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| >I'll try to think more about how to read. I think there could and maybe should be some sort of "literature critique theory of science/math books" | >I'll try to think more about how to read. I think there could and maybe should be some sort of "literature critique theory of science/math books" | ||
| >What I can recommend (at least for papers) is the strategy of reading an intro, the end, the intro again and then the whole thing. | >What I can recommend (at least for papers) is the strategy of reading an intro, the end, the intro again and then the whole thing. | ||
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| - | 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. | ||
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| - | >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. | ||
| === Scheme === | === Scheme === | ||
