On 22 fév, 16:21, Sergiu Ivanov <[email protected]> wrote: > Hello, > > > > > > > > > > On Mon, Feb 20, 2012 at 9:54 PM, Harold E. <[email protected]> wrote: > > On 20 fév, 12:44, Sergiu Ivanov <[email protected]> wrote: > > >> I'm far from being an expert in this field, so my questions arise > >> rather from curiosity than from some serious background > >> considerations: what uses do you envision for this feature of > >> recovering the right constant? > > > The use of constants as units is in the heart of theoretical physics, > > since in some way it emphases the unification of several concepts. I > > will use the example of special relativity: Einstein found the formula > > E = mc², which means that the mass and the energy are exactly the same > > thing and that we do not need to distinguish between these two > > concepts, because if in some formula you use one concept, you can > > immediately replace it with the other with the help of this formula. > > The same happen for space and time (one can see this with the > > Lorentz's transformation formula). > > Aha, I think I've read about this approach to introducing units > before; your explanation brings up some vague memories in my head. > > > Then, even if we do all the computations without writing explicitly > > these constants, it's useful to write them at the end for several > > reason: > > 1. We are not accustomed to these units, because the value of > > quantities are very different than the one of our daily experiences (v > > = 0.3 c = 100000 km/s, v = 100 km/h ~ 10⁻¹⁰), and a formula will > > generally "speak" us better if we can see these fundamental constants. > > 2. Because of (1), our usual unit systems are very different, and so > > it is easier for experiences and many other things to be able to > > convert. > > 3. Again because of (1) when you learn special relativity and so on, > > you prefer to keep these factors. > > I see, this is clear. > > >> On the other hand, recovering the constant requires quite a bit of > >> analysis of the environment. For example, in a certain environment, I > >> may use E to denote something different from the total energy. > > > Yes of course, here this formula was only an example. The idea to > > recover the right factors are for example to say that in the left > > side, the unit is J.c⁻², and in the right side it's kg. So we can > > extract the good factors. If we don't have this possibility, we can > > also say that "I want that this formula has the dimension X", which is > > useful if people don't want to take in account the constants at the > > beginning. > > Going back to your original idea of manipulating units as vectors, > finding the necessary factors is equivalent to solving vector > equations with cross-products and to solving matrix equations (to some > extent), right? >
It's exactly this, but I will not do these computations since sympy has already a linear algebra module. > To me, it looks like implementing units with a sufficiently generic > approach may give you support for constants as units almost for free. > If the user can define their own base and derived units, then they may > just choose another basis and specify how units are derived. If you > can fully have custom units, you can surely have constants as units. > > Another impression of mine is that having custom units is actually the > right way to go towards the goal of having constants as units. > > I guess you have thought of these things yourself already, so I'm just > dumping my reasoning for the sake of providing a point of view. > It's a good summary of what I plan to do. Some points are still not clear for me, but they are small details. > > No problem, I posted this message with this goal! I hope that my > > explanations help you. There is a very good article of Jean-Marc Lévy- > > Leblond on this topic (www.springerlink.com/content/ > > kh1n15r56q0682v8/), but more on the philosophical point of view. > > Yes, your explanations made the whole thing much clearer to me, thank > you for your effort! :-) (and sorry for my slow response) > > Sergiu Harold -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
