Signal Theory of Intelligence

10 The dynamics of the transformation between elementary and complex forms

10.1 Cyclical mapping as a fundamental mechanism

In each processing step, the system executes a fixed sequence of operations:

1.     Direct system:

Generation of a complex form from an elementary signal vector.

2.     Inverse system:

Reconstruction of an elementary signal vector from the complex form.

3.     Non-linearity:

Generation of a categorical state.

4.     Recursion:

This results in a cyclical alternation between two forms of representation of the same signal:

">

This alternation is a system-theoretical necessity of the architecture.

10.2 Oscillation as an emergent property

Since the sequence of operations is identical in every time step, an oscillation arises between the two forms. This oscillation is:

• stable,
• rhythmic,
• recursive,
• and independent of learning.

It is the temporal signature of the shape change and forms the basis for:

• pattern stabilisation,
• internal modelling,
• hypothesis formation,
• and thinking.

10.3 Binding as a change of form, not as synchrony

The oscillation between elementary and complex forms leads to the distributed features of a stimulus being consolidated into a unified representation. This process corresponds to the classical binding problem.

In this theory, however, binding does not arise through temporal synchrony, but through:

• composition in the direct system,
• decomposition in the inverse system,
• categorical stabilisation through non-linearity,
• and recursive repetition.

Synchrony is merely the visible epiphenomenon of this change of form.

10.4 Significance of the change of form for intelligence

The cyclical alternation between elementary and complex forms enables:

• Signal completion Missing or noisy elementary signals are supplemented.
• Coherence formation Distributed features are combined into a stable complex form.
• Prediction The system not only supplements missing signals but also anticipates future ones.
• Fabrication: When input is weak, the internal model dominates.
• Thinking The recursive cycle generates internal models that exist independently of the current input.

Thus, form change is the dynamic core mechanism from which intelligence arises.

10.5 Summary

The transition between elementary and complex forms is:

• a direct consequence of the architecture,
• an arithmetic necessity,
• the basis of signal completion,
• the origin of connection,
• and the dynamic mechanism of thought.