Fundamental Theorem of Computation!.txt — Mr Aidan Danielski

Fundamental Theorem of Computation::
	(1) action = computation × cost = energy × information = statespace × spacetime, (1A) [computing output from input] and [processing between input and output] is action where [computation has a cost, energy converts information into action, and all its states occupy space and time];
	(2A) one bit is two action [of unit cost; two energy units, one unit of information, two states, one location, one moment], (2B) one transistor is twelve action [of unit compute; 3 energy, 4 info, 2 states, 3 locations, 2 time units] or two states in two moments at three locations,
	(3A) Input, Output, and Compute are the statespace, (3B) all and each of [action; computation, cost, energy, information, statespace, and spacetime] ultimately total above zero, (3C) transforms have an impel action (cost) they require and expel action (return) they yield (sum act),
	(4A) bits and transistors occur in spacetime slices where input is the first- and output the last- slice (and) processing links the slices into a time-chain, (4B) spacetime = space × time, (4C) information / statespace = energy / spacetime, (4D) compute / info = energy / cost,
	(5) all sequences of computation and processing can have varying spacetime requirements for a given statespace, (6) computation chains must have (6A) enough action budgeted to afford the impel action cost [-] to then (6B) add/enable the expel action [+], (7) branching has cost,
	(8A) lines of computation can branch and merge where the cost and yield are the respective maxima of each branch [of the branch-merge unit], (8B) memory allocation and deallocation has a sequence of action costs from the time slice it's allocated to when it's deallocated [RAM],
	(9) all computer components [CPU, ALU, REGISTERS, REG LAYER-1/-2/-3 CACHE, RAM, HDD, SSD, ROM, CROM, WIRE BUSSES, WIRELESS BUSSES] have action impel+expel [compute, cost; energy, info; statespace, space, time] requirement profiles and (9A) they stack into spacetime (9B) with shapes,
	(10) statespace ^ spacetime = (complexity_order × energy) ^ information = (data_order × information) ^ energy,
	(10A) the complexity_order is how easily energy converts to (or yields) information, (10B) the data_order is how many states information has or yields,	(10A*) the complexity_order is information's price in energy, (10B*) the data_order is information's price in statespace,
	(10C) log in [base information] of [all states = statespace ^ spacetime] = complexity_order, (10D) log in [base energy] of [all states = statespace ^ spacetime] = data_order,
	(10E) spacetime × log in [base information] of [the statespace] = complexity_order, (10F) spacetime × log in [base energy] of [the statespace] = data_order,
	.
Units:
	Single:    computation [operations per afforded energy], cost [afforded energy per required energy]; energy [action per place], information [actions per actor]; statespace [states per unique place], spacetime [actors per state].
	(1+) action units = actions = (operations / energy-afforded) × (energy-afforded / energy-required) = (operations / energy-required),
	(4C+) info [action / actor] / statespace [states / unit-place] = energy [action / unit-place] / spacetime [actors / state] = [(action × states) / (actors × unit-places)],
	(4D+) computation [operations / energy-afforded] / info [action / actor] = energy [actions / unit-places] / cost [energy-afforded / energy-required] ⇒
		  [(operations × actors) / (energy-afforded × actions)] = [(actions × energy-required) / (unit-places × energy-afforded)],
	(1A+) operations per energy-required, is actions-square par actor-places, is actors per unit-place,
	(10+) statespace [states per unique place] ^ spacetime [actors per state] = (complexity_order [] × energy [action per place]) ^ (information [actions per actor]) = (data_order [] × information [actions per actor]) ^ (energy [action per place]),
	(10E+) spacetime [actors per state] × log in [base information] of [the statespace [states per unique place]] = complexity_order [], (10F) spacetime [actors per state] × log in [base energy] of [the statespace [states per unique place]] = data_order [],
Proof:
	At all points in spacetime exist a state from the set of its statespace — the integer statespace is the order of the statespace set.    The 3A lemma expands spacetime to encapsulate input, output, and data processing.    All computation has a cost.    These are all action.
	For information to exist in a place in spacetime, energy must be present for every bit (both for zero or for one) to exist in that space at that time.    A bit is placing a unit of energy in one of two places in spacetime.    Thus information is units of energy in subsets of places.
	Information is thus energy being present (high) in one state in one place in spacetime and being absent (low) in all other states in that place in spacetime.    One state in the statespace exists at all points in spacetime.    Both data and computation costs action — data existing costs energy.
	Computation itself costs energy — action in places in spacetime.    statespace × spacetime = {statespace set} × places-in{space × time}.    A point in spacetime has zero energy if it has zero information.    A place in spacetime has zero state if it has zero energy.
	Zero state in a place in spacetime requires zero cost or computation.    A computer system can disperse an action budget in sequences of different (9+) computer components present at (9A+) different points in spacetime (9B+) have different quantities of statespaces.
	TLDR:
	    Where there is information there is energy and where there is energy there are is information.    Both data and computation cost action in form of energy and/or info.
	    All places in spacetime have a statespace if information is present therein.    All pieces of energy present in one place in spacetime and not another has information.
-

NOTE TO SELF :: A CPU IS A !CLOCK !ALU !REGISTER_BANK !MEMORY_TEMPORARY !MEMORARY_PERMINANT !IO_BUS_READ !IO_BUS_WRITE !FIRMWARE_CROM !!!