follow discussion at http://www.physicsforums.com/showthread.php?t=353907

Thank you John.  Trouble is, it was me who posted that on physics forums.  I wonder if you were ironically referring me to myself.

Dear Steve,

Actually I would say that most dynamical systems are self referential. Take the equations of an oscillator for instance (\dot{·} means time derivative):

• \dot{x} = y
• \dot{y} = -x

here, x grows as much as y dictates, but y grows opposite to x itself.

Hope that helps.

Cheers,

Fernando

Thank you fernando.  A very useful answer. As a matter of fact, the example I was thinking of is again oscillatory.  It is the Fourier transform together with its inverse. But it's good to see you (and others) see this type of system as self-referential.  Can you tell me if self reference is a standard concept taught in engineering for such systems?  Are there other systems you know of?

Dear Steve,

I would say that in dynamical systems parlance, it is more common to speak of "coupled variables". In fact, there is a small nuance here that is time.

A discretized version of the above would be something like:

• xn+1 = xn + h * yn
• yn+1 = yn - h * xn

where 'h' is time increment. How do we handle time here, with the purpose of discussing self-reference? Clearly, xn+1 implicitly depends on its previous values, through coupling with yn. But do we consider all of the {xn+1, xn, xn-1, ...} to be "self"?

I don't think it is common practice to establish that link with logic/linguistics. Besides, this kind of self-reference, or self-dependence, is not self-referential in the sense of second-order logic, for instance. It is not a mathematical expression that asserts truths about itself. Rather, maybe we should speak of recurrence here?

Cheers,

Fernando

IS the Newtons law of cooling (as an example) self-referencing?

remember the rate of change is proportional to the temperature differences, so the system is dynamically affecting itself.

But I was never told this is self referencing.

Open to learn and to actively discuss ;-)

I would think the closest thing to self reference in physics is the Copenhagen interpretation of Quantum Mechanics and specifically the collapse of a wavefunction. It is primarily a result  of a closed system being lost. A wavefunction does not collapse into a dirac delta function unless it is measured. This is problematic because the system being measured cannot be explained without reference to the system of measurement, so the measurement system must be included in the larger coupled system. But then of course you must measure the combined measurement system and what is being measured, which itself cannot be fully explained without referring to the next level of measurement....and it goes on. Turtles all the way down.