As a chemical engineer, one of the signs of maturity was myself and each of my classmates individually coming to accept and embrace the inevitable “magic coefficient”.

The curious always wanted to know why some magic coefficient was there. Where did it come from? How is it measured / calculated? How to derive the magic coefficient?

Eventually you learn that it’s turtles all the down. You can pick apart the magic coefficient and dive into the nuanced physics that its derived from…but then you still end up with a new magic coefficient.

So eventually, the curious students learn that the mysteries are out there for when you want to go out and explore them. But otherwise, we pick our level of abstraction for the problem we’re currently working on and accept the magic coefficients that apply to that level of abstraction.

The real trick is knowing the conditional boundaries when those magic coefficients no longed apply and you either need different ones or “here be dragons”.

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andsoitis 5 hours ago | parent | next [-]

That’s a wonderful way express that idea. Thanks for that!

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compass_copium 6 hours ago | parent | prev [-]

Are "magic coefficients" not just a result of the units you are using? Like how h-bar is 1 if you are using natural units

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nine_k 4 hours ago | parent [-]

It's a different kind. Say, some reaction should run 1.23x faster theoretically. But the theory is approximate (in order to be tractable at all), and so are its predictions. This particular element is special in its own way, diverging from the theory a bit, even though its neighbors fit well. That particular bond requires a bit less energy to break than the theory predicts, due to a complex interplay of bonds nearby, understood only qualitatively. Etc, etc.

A general theory of everything might describe all of it from first principles, without magic coefficients. But likely computing it would take a decade with current methods.

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compass_copium 3 hours ago | parent [-]

Oh alright fair enough, measured vs. expected basically?

	▲	nerdsniper 2 hours ago \| parent [-]
		More like, “the unmeasurable” or “unmodelable”. Examples could be the “A” in the Arrhenius equation or the “k” in Fourier’s law of conduction. “A” is described as being derived from the collision frequency of molecules in that specific reaction but really it’s just an arbitrary magic number you look up in a book for the specific reaction that you’re working with. It’s often relatively temperature invariant across some range of temperatures but go outside that range and it becomes a function of temperature too. Pulling up the wikipedia for “Collision theory” will show you that there has been some work to derive values of A rather than just find them all experimentally for every reaction. But it’s still very unsatisfying to the curious mind. “k” is the thermal conductivity of a particular material. Curious minds might wonder what’s hidden behind this constant. How would someone predict “k” for a novel theoretical material? Like, say, tetrahedrane? It’s been awhile, otherwise I’d walk you through a graph containing a couple hierarchical nodes where one constant leads to another equation. But it’s a bit too late to pour through Perry’s Handbook right now to jog my memory.