Within the cultures of the term's provenance ( Byzantine and Hellenic ) Gnosis was a knowledge or insight into the infinite, divine and uncreated in all and above all, rather than knowledge strictly into the finite, natural or material world.

Which is to say: as much as we might try to order our world with a certain set of norms and goals ( which we consider our real world ), the paradox of a finite consciousness in an infinite universe creates a zone of irreality (" that which is beyond the real ") that offsets, opposes, or threatens the real world of the human subject.

A recent development is the mathematical universe hypothesis, the theory that only a mathematical world exists, with the finite, physical world being an illusion within it.

Much of WMCF deals with the important concepts of infinity and of limit processes, seeking to explain how finite humans living in a finite world could ultimately conceive of the actual infinite.

legitimate structures might accidentally happen not to exist, and that a finite physical world might

( See Tzimtzum ( צמצום ): the notion that God " contracted " his infinite and indescribable essence in order to allow for a " conceptual space " in which a finite, independent world could exist.

The exploitation of cultural resources can be controversial, particularly where the finite cultural heritage resources of developing countries are exported to satisfy the demand for antiquities market in the developed world.

Agencies across the world have different systems for classifying incidents, but all of them serve to help them allocate finite resource, by prioritising between different emergencies.

According to Jonathan Sacks, in Shneur Zalman's system Chochma represents " the creation in its earliest potentiality ; the idea of a finite world as was first born in the divine mind.

For contingent, limited and finite creatures, no such unified world view is possible.

Like Hamilton, Mansel maintained the purely formal character of logic, the duality of consciousness as testifying to both self and the external world, and the limitation of knowledge to the finite and " conditioned.

The dualistic contrast between God and the world, between the finite and the infinite, appears in both Platonism and in Neo-Pythagorism.

Hegel responded to Kant's philosophy by suggesting that the unsolvable contradictions given by Kant in his Antinomies of Pure Reason applied not only to the four areas Kant gave ( world as infinite vs. finite, material as composite vs. atomic, etc.

… the conditions underlying limit overshoots -- population growth and resource depletion in a finite world, for example -- remain unaddressed in the corridors of power.

The gameplay of both games is reminiscent of other RPGs but more sophisticated than its peers — while the player wandered around gaining levels and equipment, there were things like a finite number of items in the world, and items stolen could be regained.

Lurianic Kabbalah describes the process of Tzimtzum ( צמצום meaning " Contraction " or " Constriction ") in the Kabbalistic theory of creation, where God " contracted " his infinite essence in order to allow for a " conceptual space " in which a finite, independent world could exist.

The story takes place in a fictional world where mana represents an ethereal, but finite, energy source.

The Primordials brought the Unshaped Chaos that was at the time, and formed it into the Creation – a flat world of finite extent, dominated by five elemental forces organised into poles in the furthest reaches of the four cardinal directions, as well as one pole in the centre of the others.

This world is finite, therefore unlimited material growth is impossible.

First step he takes from eternity ( without beginning ) to this mortal world, second step from this finite world to hereafter and last step he takes from hereafter to manifestation of Allah ".

In this sense they are reminiscent of the oscillatory universe proposed by Richard Chace Tolman: however in Tolman's model the total age of the universe is necessarily finite, while in these models this is not necessarily so.

* State models including Turing machine, push-down automaton, finite state automaton, and PRAM

Meanwhile Wenninger ( 1983 ) found a way to represent these infinite duals, in a manner suitable for making models ( of some finite portion!

Considered as an abstract model of computation, the finite state machine is weak ; it has less computational power than some other models of computation such as the Turing machine.

In momentum space the exclusion principle is valid also for finite repulsion in a Bose gas with delta function interactions, as well as for interacting spins and Hubbard model in one dimension, and for other models solvable by Bethe ansatz.

For example, automorphism groups of certain models of finite geometries are not " symmetry groups " in the usual sense, although they preserve symmetry.

< li > A finite table ( occasionally called an action table or transition function ) of instructions ( usually quintuples: q < sub > i </ sub > a < sub > j </ sub >→ q < sub > i1 </ sub > a < sub > j1 </ sub > d < sub > k </ sub >, but sometimes 4-tuples ) that, given the state ( q < sub > i </ sub >) the machine is currently in and the symbol ( a < sub > j </ sub >) it is reading on the tape ( symbol currently under the head ) tells the machine to do the following in sequence ( for the 5-tuple models ):

Because of sensitive dependence on initial conditions, some deterministic models may appear to behave non-deterministically ; in such cases, a deterministic interpretation of the model may not be useful due to numerical instability and a finite amount of precision in measurement.

As another possibility, completeness proofs based on cut-free sequent calculi usually produce finite models directly.

In the case of solid-like granular behavior as in soil mechanics, the continuum approach usually treats the material as elastic or elasto-plastic and models it with the finite element method or a mesh free method.

A second application of the compactness theorem shows that any theory that has arbitrarily large finite models, or a single infinite model, has models of arbitrary large cardinality ( this is the Upward Löwenheim – Skolem theorem ).

Moreover if the volume does not have to be finite there are an infinite number of new geometric structures with no compact models ; for example, the geometry of almost any non-unimodular 3-dimensional Lie group.

No evidence exists to suggest that the boundary of the observable universe constitutes a boundary on the universe as a whole, nor do any of the mainstream cosmological models propose that the universe has any physical boundary in the first place, though some models propose it could be finite but unbounded, like a higher-dimensional analogue of the 2D surface of a sphere that is finite in area but has no edge.

One approach and formation is model checking, which consists of a systematically exhaustive exploration of the mathematical model ( this is possible for finite models, but also for some infinite models where infinite sets of states can be effectively represented finitely using abstraction ).

The proof of the upward part of the theorem also shows that a theory with arbitrarily large finite models must have an infinite model ; sometimes this is considered to be part of the theorem.

Finite Element programs are more flexible in design ( triangular elements vs. the block elements most finite difference models use ) and there are some programs available ( SUTRA, a 2D or 3D density-dependent flow model by the USGS ; Hydrus, a commercial unsaturated flow model ; FEFLOW, a commercial modeling environment for subsurface flow, solute and heat transport processes ; OpenGeoSys, a scientific open-source project for thermo-hydro-mechanical-chemical ( THMC ) processes in porous and fractured media ; and COMSOL Multiphysics ( FEMLAB ) a commercial general modeling environment ), but unless they are gaining in importance they are still not as popular in with practicing hydrogeologists as MODFLOW is.

For a finite number of models, we can thus think of θ as the index to this family of probability models.

# An unbounded number of labeled, discrete, unbounded registers unbounded in extent ( capacity ): a finite ( or infinite in some models ) set of registers each considered to be of infinite extent and each of which holds a single non-negative integer ( 0, 1, 2, ...).

" His most-important fourth, " the principle of causality " is based on the " finite velocity of propagation of effects and signals ; contemporary physics rejects the possibility of instantaneous action at a distance.

At the time Babbitt had switched out of classics ; he would later clarify his position on the contemporary textual and philological scholarship demanded in that area, in the Germanic tradition, as a finite task, which he was unhappy to see placed above teaching based on ' eternal ' content.

In mathematics, particularly theoretical computer science and mathematical logic, the computable numbers, also known as the recursive numbers or the computable reals, are the real numbers that can be computed to within any desired precision by a finite, terminating algorithm.

In computer science, an integer is a datum of integral data type, a data type which represents some finite subset of the mathematical integers.

In formal languages, which are used in mathematical logic and theoretical computer science, a string is a finite sequence of symbols that are chosen from a set called an alphabet.

The theory of finite semigroups has been of particular importance in theoretical computer science since the 1950s because of the natural link between finite semigroups and finite automata

Common applications of the finite difference method are in computational science and engineering disciplines, such as thermal engineering, fluid mechanics, etc.

* Abstract syntax tree, a finite, labeled, directed tree used in computer science

According to the historian of science Norwood Russell Hanson: There is no bilaterally-symmetrical, nor excentrically-periodic curve used in any branch of astrophysics or observational astronomy which could not be smoothly plotted as the resultant motion of a point turning within a constellation of epicycles, finite in number, revolving around a fixed deferent. Any path — periodic or not, closed or open — can be represented with an infinite number of epicycles.

* Alternating finite automaton, in computer science

In computer science and automata theory, a Büchi automaton is a type of ω-automaton, which extends a finite automaton to infinite inputs.

But it is impossible to conceive a limit to the extent of matter in the universe ; and therefore science points rather to an endless progress, through an endless space, of action involving the transformation of potential energy into palpable motion and hence into heat, than to a single finite mechanism, running down like a clock, and stopping for ever.

* Uncomfortable science, due to statistician John Tukey: Inference from a limited sample of data, where further samples influenced by the same causality, a finite natural phenomenon for which it is difficult to overcome the problem of using a common sample of data for both exploratory data analysis and confirmatory data analysis.

( In theoretical computer science, a problem is considered " solvable " if it can be solved in principle, namely in finite time, which is not necessarily a finite time that is of any value to humans.

It encompasses mathematics ( algebra, finite groups, rings, and fields ), computer engineering ( hardware design, ASIC, embedded systems, FPGAs ) and computer science ( algorithms, complexity theory, software design ,).

In mathematics and computer science, the Krohn – Rhodes theory ( or algebraic automata theory ) is an approach to the study of finite semigroups and automata that seeks to decompose them in terms of elementary components.

In automata theory, a branch of theoretical computer science, a deterministic finite automaton ( DFA )— also known as deterministic finite state machine — is a finite state machine that accepts / rejects finite strings of symbols and only produces a unique computation ( or run ) of the automaton for each input string.

Such applications include numerical analysis, mathematics of engineering, linear programming, optimization and operations research, continuous modelling, mathematical biology and bioinformatics, information theory, game theory, probability and statistics, financial mathematics, actuarial science, cryptography and hence combinatorics and even finite geometry to some extent, graph theory as applied to network analysis, and a great deal of what is called computer science.

Generative science shows how deterministic and finite rules and parameters in the natural phenomena interact with each other to generate seemingly unanticipated and infinite behaviour.