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I'm sure that most of you know what they are, but before continuing I shall introduce the linear systems and to introduce them I have to talk about the dynamic systems before.

A dynamic system, just to keep the thing simple, is a system of equation that describes the velocity of a point in a space over time.

So:

But we know that the psyche interact with the outer world, so we have to add the concept of input (let's call it u(t)) and output (let's call it y(t)), the feedback is usually supposed to be work of another system, but who cares? Humans can hear their voice, right?x'(t)=f(x(t), t)

x'(t)=f(x(t), u(t), y(t), t)

y(t)=f(x(t), u(t), t)

A linear dynamic system is just a dynamic system where x' and y's functions are linear, so we don't have any strange functions, but just a set of coefficients.

But now that's linear it's easier to notice: even if it has an internal feedback, it's indistinguishible from a different system that has none:x'(t)=E(t)x(t)+I(t)u(t)+F(t)y(t)

y(t)=C(t)x(t)+D(t)u(t)

How hard is to approximate a psyche with that equation according to Socionics? If we consider the operate of one function distinguishable from the work of any combination of the other, how many dimensions has to have that x?x'(t)=E(t)x(t)+I(t)u(t)+F(t)C(t)x(t)+F(t)D(t)u(t)

y(t)=C(t)x(t)+D(t)u(t)

x'(t)=(E(t)+F(t)C(t))x(t)+(I(t)+F(t)D(t))u(t)

y(t)=C(t)x(t)+D(t)u(t)

A(t)=E(t)+F(t)C(t))

B(t)=I(t)+F(t)D(t)

x'(t)=A(t)x(t)+B(t)u(t)

y(t)=C(t)x(t)+D(t)u(t)