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Comment by tiglionabbit | Hacker News Reader

Is it not possible to create the other "fundamental" components using combinations of other components? I know with logic gates one might think of AND/OR/NOT as fundamental but yet one can make anything out of NANDs or NORs, so they could be considered fundamental instead. It's a thing in mathematics as well that you can often define essentially the same system using different sets of prepositions.

I saw a comment later on in here that explained that memristors, resistors, capacitors, and inductors round out all four combinations of relating charge or the derivative of charge over time with flux or the derivative of flux over time.

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I'm not sure the logic gate metaphor works here, because the domain is so different, the questions relate to the charge-voltage relationship and its first and second derivatives.

Maybe a different metaphor would be better: a bank statement involves stored money (like a capacitor), and a profit/loss sheet involves effects of money moving over time (like a resistor), and you can see how they're related through integration/differentiation, but they're fundamental because you can't create a bank account by nailing a bunch of P&Ls together.

Ok, so maybe that's not a great metaphor either? ;)

The paper does discuss equivalence categories (along the lines of nth derivatives of charge and voltage) so it's probably best to refer directly to that!

> Is it not possible to create the other "fundamental" components using combinations of other components?

Unlike with logic gates it's just not possible.

Resistors have real impedance and capacitors and inductors have purely imaginary impedance so you can't bridge those two domains (it's like saying can you make a complex number by adding/subtracting real numbers).

For capacitors and inductors one have an impedance that increases with frequency and the other has an impedance that decreases with frequency. So for a given frequency they are interchangable, but as soon as the frequency changes that breaks down.

The article says that the two diagonal elements in the table of those four combinations, U = RI (or dPhi/dt = R dQ/dt, the classical resistor) and Phi = RQ (the purported memristor) describe the same fundamental element, the resistor. Which is sort of obvious, as one is just the time derivative of the other.

[Edit: got the direction of which is the derivative of the other wrong on the first try]

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