This line of reasoning is even more interesting than the original hypothesis that biological clocks drive amplification.
What you are proposing is a reversal of the causal relationship.
Instead of:
[
\text{Biological Clock}
\rightarrow
W^*
\rightarrow
\text{Amplification},
]
you propose:
[
\text{Amplification Optimum}
\rightarrow
W^*
\rightarrow
\text{Biological Clock}.
]
In this view, biological clocks emerge as a consequence of an optimal dynamical state rather than serving as the original cause.
⸻
What Is Optimal Amplification in an Embryo?
According to modern developmental biology, an embryo faces two opposing risks.
Excessive Stability
[
\tau_{\rm dwell}
\rightarrow \infty
]
The system becomes trapped in its current attractor.
The consequences are:
cells fail to differentiate,
new tissues do not emerge,
development stalls.
⸻
Excessive Instability
[
D_\Phi
\uparrow
]
[
\tau_{\rm dwell}
\downarrow
]
States appear and disappear too rapidly.
The consequences are:
developmental patterns are not reinforced,
body axes become unstable,
malformations or degeneration become more likely.
⸻
Therefore, Optimal Amplification Must Lie Between the Two
The embryo must simultaneously satisfy two requirements.
Preserve Information
[
\tau_{\rm dwell}
]
must be sufficiently large to allow:
morphogen gradients to be stabilized,
bioelectric networks to form,
tissue identities to be maintained.
⸻
Permit Reconfiguration
[
\tau_{\rm relax}
]
must remain finite so that:
cells can change fate,
new tissues can emerge,
development can continue.
⸻
Expressed in TOP-C language, optimal amplification may correspond to:
[
A_W
W\tau_{\rm dwell}
\approx
A_W^*,
]
where the value is neither too small nor too large.
⸻
How Does This Relate to Developmental Windows?
A developmental window may be interpreted as a period during which
[
A_W
]
is tuned close to
[
A_W^*.
]
At that point, a very small signal
[
\delta
]
can be amplified into a large developmental outcome
[
\Delta M.
]
⸻
For example, a tiny difference in:
membrane potential,
morphogen concentration,
mechanical signaling,
may determine:
left–right asymmetry,
anterior–posterior axis formation,
organ development.
⸻
Why Does the Embryo Not Degenerate?
This is a crucial question.
If amplification becomes excessively strong,
[
\delta
\rightarrow
\infty,
]
then every small fluctuation is amplified.
The embryo would lose stability.
⸻
Therefore, the embryo cannot operate exactly at an absolute critical point.
Instead, it must function within a regime such as:
[
\text{subcritical}
<
A_W
<
\text{critical},
]
or, in your terminology,
a resonant-but-controlled regime.
⸻
An Intuitive Picture
Imagine an attractor landscape.
Too Deep
(a very deep attractor)
highly stable,
little developmental progress.
⸻
Too Shallow
(a very flat attractor)
every perturbation disrupts organization.
⸻
Intermediate Depth
stable enough to preserve form,
flexible enough to reorganize.
This is where amplification becomes optimal.
⸻
The Most Interesting Consequence
If this perspective is correct, developmental windows are not periods during which the embryo becomes more chaotic.
Quite the opposite.
They are periods during which
[
\text{Stability}
]
and
[
\text{Plasticity}
]
are optimally balanced.
Or, equivalently,
[
\text{Memory}
\leftrightarrow
\text{Exploration}
]
is optimally balanced.
⸻
From this viewpoint, developmental clocks may not be the original cause of development.
Instead, developmental cycles, bioelectric waves, and morphogenetic rhythms may be emergent signatures of a system maintaining an optimal amplification state long enough to construct an organism without collapsing into either chaos or rigidity.
This interpretation is much closer to theories of self-organization than to the classical genetic-blueprint model of development.