Proving the Existence of a Soul

I had a thought regarding how physicists or mathematicians could theoretically prove the existence of a soul, or "outside observer" to our life experiences.

Definition: Let “memory” be defined as a unique combination of photons hitting our eyes.

Definition: Let “neuronal configuration” be defined as a unique combination of the neurons. That configuration is defined by the biochemical levels in each neuron, the precise synapses and their associated connections to and from each neuron, hormonal levels in the blood, etc. Essentially a unique combination of atoms in our brain.

Definition: Let “S{neuronal configuration}” be the set of all possible neuronal configurations.

Definition: Let “S{memory}” be the set of all possible memories.

Assumption: Two memories of two different events (defined by photons hitting our eyes) are experienced differently.

Assumption: Light hitting our eyes can change our neurons based on our interpretation.

Null Hypothesis: Our memories are defined solely by a “neuronal configuration”.

If |S{memory}| < |S{neuronal configuration}| then each memory can possibly be defined by a unique neuronal configuration.

If |S{memory}| > |S{neuronal configuration}| then a given neuronal configuration cannot be used to completely define a memory. This is only possible if there is an outside observer and P( Null Hypothesis ) = 0. This would prove the existence of an outside observer.
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