(i) stimuli signal are within the permissible limits of amplitude & chronometric-resolution (frequency);
(ii) within the complexity & sensitivity range perceivable by the recipient entity; &
(iii) maintenance of the elasticity of the state of responsiveness.
Stimuli-response is a recurring process of sensory parts & is akin to propagation of waves in water.
Stimuli is like the stone thrown in water, generating a splash & waves.
The splash is akin to noise. It is that part of the awareness that causes chaotic dissipation of energy, because the amplitude owing to strike energy is so high that the splash dissociates from the main body of water, with no generation of any identifiable periodic (recurring) pattern & hence is useless for awareness, analogously.
Hence, the phrase - ‘permissible limits’ in the definition of awareness. Because beyond the permissible limits the ‘state of responsiveness’ is no more good to produce an orderly wave-like response, and instead produces a splash.
The splash consists of those stimuli-responses, which are beyond the permissible amplitude.
Waves beautifully maintain the elasticity of the water’s position, displacing it temporarily from a mean position without dissociating it from the main body of water.
To understand the second condition of complexity, imagine hundreds of stones thrown, simultaneously.
Multiple wave interference patterns would form. Consequently, the shape of water in any locality is too complicated to even index what part of the pattern occurred from which wave, generated by which stone.
Excessive waves & their thousands of interaction points generate excessive complexity, which too fails to generate a coherent perceptible response, but for some serendipitous cases which are an exclusion from principle and not a subject matter of import for our context.
Like in music, there is a flow, a coherence in every type of communicating stimuli-response signal.
Consequently, there is a limit of amplitude (AMax), up to which the stimuli generate a response wave.
Beyond this limit, the elasticity (capability to return back to the mean position) is violated, as in the splash.
Sensory part consumes some part of the stimuli signal (permissible, in amplitude & frequency) corresponding to the minimum energy as also has a requisitioned minimum power that is needed to knock off the sensory system from its inertial state to produce a response.
Gushes of air molecules generated by a fan keep hitting a person sleeping under it and being cooled by it constantly. A large amount of energy is spent overnight, but the striking air molecules never wake him up because their power is below the needed threshold.
On the contrary, a gentle tap on the shoulder wakes one up immediately, as it has above-threshold power, though total energy delivered is very little when compared to that done by a fan through a night.
Conversely, very high power, high amplitude sound alarm for a picosecond will also not wake one up. Because though the power of the signal is very high, the time for which it is delivered is so small that negligible amount of energy is delivered, generating no response.
That is why one can quickly sweep one's hand through a flame of fire without discomfort, if the hand is moved fast enough.
Therefore, mathematically, Awareness ‘W’, is equal to the cumulative signal power divided by the Minimum energy required to trigger a response. The signal power is directly proportional to the amplitude of the signal, subject to it not exceeding AMax.
TAwareness is the latency of response,
EMin is the min. energy required to trigger a response
Signal-Powermin is the minimum power that is required to knock the sensory system off its inertial state to produce a response.
(i) Percept of signal (signified by the phrase of ‘sensible stimuli’ in the definition) is established by the capability of the recipient to react to the received stimuli signals within a predefined frequency (in case of recurring wave-like signals of light & sound). This is defined by frequency ‘f’, such that fmin≥f≤fmax, where fmin & fmax are the minimum & maximum frequencies of the sensitivity range of the recipient. Percept of signal is detailed ahead in the book.
(ii) Signal power is directly proportional to the square of both - amplitude & frequency both of which have to be within the sensitivity range of the sensory part. This leads to subjectivity of the sensory part for maintenance of the elasticity of the state of responsiveness - such that Amin ≥ A ≤ Amax. Amin. and fmin determine the minimum power that is required to knock the sensory system off, to a major deviation from its inertial state. The sensory system will not respond if either the power, or the energy delivered are not enough to knock off the sensory part from its inertial state. In the mathematical representation min signifies the minimum power required to knock the sensory system off its inertial state. Concomitantly, Amax is the maximum amplitude, beyond which the elasticity of the state is endangered. Constraints on frequency have been already mentioned in (ii) above.
(iii) Stimuli is within permissible complexity (i
This was the essential mathematical representation, but going ahead, any mathematical representation of facts has been avoided in favor of simple logical explanations.
Interested experts can derive mathematical conclusions without much effort for the various logical ones discussed ahead.
Attributes of Awareness - rate of response to stimulus; - the number of senses (sensing parameters) possessed by the aware entity; - sensitivity of each of the senses; - elasticity of the state of responsiveness of the aware entity - complexity – multiplicity of sensory signal levels per stimuli. =