  Creating a quantitative theory for the cortex poses several challenges and
raises numerous questions. For instance, what are the significant scales of the
system? Are they micro, meso or macroscopic? What are the relevant
interactions? Are they pairwise, higher order or mean-field? And what are the
control parameters? Are they noisy, dissipative or emergent?
  To tackle these issues, we suggest using an approach akin to what has
transformed our understanding of the state of matter. This includes identifying
invariances in the ensemble dynamics of various neuron functional classes,
searching for order parameters that connect important degrees of freedom and
distinguish macroscopic system states, and identifying broken symmetries in the
order parameter space to comprehend the emerging laws when many neurons
interact and coordinate their activation.
  By utilizing multielectrode and multiscale neural recordings, we measure the
scale-invariant balance between excitatory and inhibitory neurons at a
population level, referred to as ensemble E/I balance. This differs from the
input E/I balance typically studied at the single-neuron level, focusing
instead on the collective behavior of large neural populations. We investigate
a set of parameters that can assist us in differentiating between various
functional system states (such as the wake/sleep cycle) and pinpointing broken
symmetries that serve different information processing and memory functions.
Furthermore, we identify broken symmetries that result in pathological states
like seizures.
  This study provides new insights into the multiscale dynamics of excitation
and inhibition in cortical networks, advancing our understanding of the
underlying principles governing neural computation and dysfunction.
