The Generalized God Equation: The Living Frequency

To ex­press the full gen­er­a­tive power of math­e­mat­i­cal ex­is­tence, Hock­ney presents the gen­er­al­ized God Equa­tion as the most ab­stract and uni­ver­sal form of Euler’s for­mu­la:

where:

• $A$ is the am­pli­tude (max­i­mum value or strength of the wave).
• $\theta$ (the Greek letter “theta,” pro­nounced “THAY-tuh”) is a phase pa­ra­me­ter that may encode fre­quen­cy, po­si­tion, time, or any com­bi­na­tion there­of.

This gen­er­al­iza­tion em­pha­sizes the time­less, fre­quen­cy-based nature of re­al­i­ty. In the lan­guage of pure fre­quen­cy, it is some­times writ­ten as:

where:

• $f$ is the fre­quen­cy pa­ra­me­ter.

For par­tic­u­lar phys­i­cal phe­nom­e­na, $\theta$ can rep­re­sent a com­bi­na­tion of vari­ables such as:

where:

• $\omega$ (the Greek letter “omega,” pro­nounced “oh-MAY-guh”) is the an­gu­lar fre­quen­cy, de­scrib­ing how rapid­ly the phase os­cil­lates, mea­sured in ra­di­ans per unit time.
• $k$ is the wave number, re­lat­ing to the spa­tial fre­quen­cy (number of wave cycles per unit dis­tance).
• $\phi$ (the Greek letter “phi,” pro­nounced “fye” or some­times “fee”) is the phase offset, de­ter­min­ing the ini­tial angle or shift of the wave.

lead­ing to the fa­mil­iar wave form:

where all vari­ables are as ex­plained above.

How­ev­er, Hock­ney’s on­to­log­i­cal math­e­mat­ics main­tains that the core re­al­i­ty is the su­per­po­si­tion of all pos­si­ble fre­quen­cy-based terms, each of the fun­da­men­tal form $A\,e^{i\theta}$, with their cor­re­spond­ing sine and cosine com­po­nents.