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#### Dottoromar

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I'm still a noob, but I yet have to find something that isn't perpendicular, even in the system theory site.

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:
x'(t)=f(x(t), t)
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), 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.
x'(t)=E(t)x(t)+I(t)u(t)+F(t)y(t)
y(t)=C(t)x(t)+D(t)u(t)
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)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)
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?

#### DavidH

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So you're just going to assume it's linear?

#### Dottoromar

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So you're just going to assume it's linear?
Not assume that's linear, but approximate it as linear.

Who wants to calculate (e*π)^-(x^sqrt(2)) or something like that?

#### DavidH

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Can you calculate yourself?

#### Dottoromar

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Can you calculate yourself?
The linear approximation is good enough to describe accurately very complicated stuff, most of the time isn't even necessary to make the system time variant, so why even bother? It also makes possible very useful tricks! And the first one is a differential equation, they're very hard to solve if not linear, if at all.

#### DavidH

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You a boy or a girl?

#### Dottoromar

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You a boy or a girl?
Does it even matter?
Also, it's off topic.

You can ask everything on linear systems if you want.

#### DavidH

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Oh it's on topic alright hahahaha

Takes two formulas to make a psyche

#### Dottoromar

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Takes two formulas to make a psyche
Those formulas describe a system, which a psyche is, a very complicated one but is still a system.

#### DavidH

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Hahahaha and which formula is the system?

#### Dottoromar

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Hahahaha and which formula is the system?

#### DavidH

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I did hahahaha then I asked why there was only one, then I asked what your formula is, then I asked which formula are you, then I said there are two formula, then I asked what formula the system is you trying to make hahahaha

#### Dottoromar

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I did hahahaha then I asked why there was only one, then I asked what your formula is, then I asked which formula are you, then I said there are two formula, then I asked what formula the system is you trying to make hahahaha
The post makes it pretty clear, this one:
x'(t)=A(t)x(t)+B(t)u(t)
y(t)=C(t)x(t)+D(t)u(t)

Do you know what "linear" means?

#### DavidH

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The post makes it pretty clear, this one:
x'(t)=A(t)x(t)+B(t)u(t)
y(t)=C(t)x(t)+D(t)u(t)
That's still one formula hahahaha you don't have the other formula

#### Dottoromar

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That's still one formula hahahaha you don't have the other formula
That's all.
You can make a proper approximation of every system with that, even if it would take 20 billion dimensions.

#### DavidH

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(x'y) * (xx) = (x'y) OR (xx)

#### DavidH

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Oops I fubar'd the apostrophe on the (x'x')s hahaha

#### Dottoromar

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(x'y) * (xx) = (x'y) OR (xx)
Ok.
Now it's beyond every doubt.
If you have nothing serious to say then go play elsewhere. There are whole sections on this forum for that.

By the way, * translates to AND and + translates to OR, not the opposite.

#### DavidH

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I am saying something serious hahahaha do y'all not have XY and XX over yonder? I was under the impression it was universal for the chromosomes

#### DavidH

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Even your edit is still x'y dude hahahaha you in denial or something that you can x'x' to make either by yourself? Why do you think they call it "artificial" intelligence hahahaha why you think typology pretends there's one formula hahahaha why you think people on these forums pretend there's one formula hahahaha why you think this all isn't entirely on topic hahahaha

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