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on_reading [2016/05/24 20:11] nikolaj |
on_reading [2016/08/07 16:21] 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: | ||
| + | * **data available to authors/processing of data/theory** | ||
| * **in's and out's of a theory** Is the text presenting a notion for modeling/is something modeled? When learning about a new theory (focusing on physical theories here), a point that it's //extremely// important is to watch out for what the observables of the theory are and what it really is that needs to be obtained. The point is that (unless we do it for the pure understanding/intuition of a natural phenomena) a theory is made to compute stuff. Many concepts which appear to be of importance on the surface are really just axillary notions that the theory sets up between input and output, and those can be substituted with other things. It's important to know what the theory is really about on the input and output level. | * **in's and out's of a theory** Is the text presenting a notion for modeling/is something modeled? When learning about a new theory (focusing on physical theories here), a point that it's //extremely// important is to watch out for what the observables of the theory are and what it really is that needs to be obtained. The point is that (unless we do it for the pure understanding/intuition of a natural phenomena) a theory is made to compute stuff. Many concepts which appear to be of importance on the surface are really just axillary notions that the theory sets up between input and output, and those can be substituted with other things. It's important to know what the theory is really about on the input and output level. | ||
| * **Elaborations and mathematical theory** The physical theory might set up the dynamics $F$, necessarily written down in mathematical terms, and much of the text is pandering on that mathematical object. | * **Elaborations and mathematical theory** The physical theory might set up the dynamics $F$, necessarily written down in mathematical terms, and much of the text is pandering on that mathematical object. | ||
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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. | ||
| - | |||
| - | 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. | ||
| === Scheme === | === Scheme === | ||
