Deriving or justifying fundamental constants

Is there a fundamental way to look at the universal constants ? can their orders of magnitude be explained from a general points of view like stability, causality, information theory, uncertainty?

for example, what sets the relative magnitudes of Planck's constant compared to say charge of electron or is it just a matter of choice of units.

Does the physics become more or less cumbersome, insightful if we set all fundamental constants to 1 in appropriate units.

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If a constant can be derived, it isn't fundamental any more. If one of the former fundamentals will be derived, You will know about! Even ordinary daily papers would have that as a page one headline. –  Georg Jun 2 '11 at 18:32
Physics become no more or less insightful for setting important constants to one, but the formulas become rather less cluttered and it takes less time to talk about them. –  dmckee Jun 2 '11 at 19:56

There are a number of fundamental dimensionless constants in physics. Some are ratios of similar things, such as $m_\mu/m_e$. Others are not so obviously expressed in that form, such as the "fine-structure constant" $\alpha=e^2/(4\pi\epsilon_0\hbar c)$. It makes sense to wonder why the dimensionless constants have the values they do -- one could imagine that a future theory would explain these values. (As Georg says, there is no such theory right now -- by definition the "fundamental" constants are those that don't have a deeper explanation.) On the other hand, one would not expect any fundamental theory to explain why a dimensionful constant, such as the speed of light, had the value that it did: the fact that $c=2.9979\times 10^8$ m/s is an artifact of our definitions of the meter and second. (Actually just the meter in that particular case.)
boy, i dunno why anthropic reasoning would be considered either "logically suspect" or even more so, "morally reprehensible". why would anyone consider it to be that? BTW, hi Ted. i still like that paper about Einstein's Eq that you and John did. it supports my contention that in the most natural units, $4 \pi G = 1$, as it should be. (just like $\epsilon_0 = 1$.) BTW, i would say that $\alpha$ is a ratio of like-dimensioned quantities (as is $m_\mu/m_e$). $$\alpha = \left( \frac{e}{q_P} \right)^2$$ where $q_P = \sqrt{4 \pi \epsilon_0 \hbar c}$ is the Planck charge. –  robert bristow-johnson Aug 1 '14 at 0:40