A theology of the infinite

A theology of the infinite The idea o f the infinity o f God has recently come under pressure due to the modern world-view, and due to the difficulty o f proving the doctrine. How­ ever, the idea o f the infinite, as qualitatively different from the merely very large, has properties which may be applied to some traditional difficulties in Christian theology, such as the ideas o f the Trinity and the Incarnation, particularly in regard to the limitation and subordination o f the Son. Predication o f infinity to God may then make the doctrine o f God more comprehensible and rational At the same time, however, this has implica­ tions fo r the nature o f God, particularly in his relation to the material and to time. Not to be overlooked is the value o f the idea from a pastoral per­ spective.


Introduction
In traditional theologies regarding the nature o f God is found a statement o f the infinity o f God.This will usually be associated with positive statements about him, such as the ideas o f his omnipotence, omniscience and omnipresence.In deed, the idea o f G od's infinity is sometimes simply seen as a negative statement o f w hat can be referred to in positive ways.G od has all pow er, he is almighty; therefore his pow er is infinite.There is nowhere that it is possible to go to escape from G od; therefore his presence is infinite.

T he basis o f an idea o f infinity
Until recently, the idea o f G od's infinity w as accepted w ithout real question.W here the existence o f God w as accepted, it w as not questioned but that he is infinite (Bolzano, 1950:84;Rucker, 1982:9 quoting Cantor).It w as a common place throughout the M iddle Ages, due no doubt to the strong influence o f G reek philosophy on the ideas o f that period.Interestingly, A ristotle rejected the as cription o f infinity to G od on the basis that this would mean that G od w as unin Koers 60 (1) 1995:103-120 telligible (Sontag, 1962: 24).H ow ever Aquinas, despite following A ristotle in many ways, rejected this, and held that God is in fact infinite (Sontag, 1962:44).In more recent times, however, with a re-examination o f so much that had been accepted almost without question, the idea o f G od's infinity has also been doubted.In particular, the strong influence o f evolutionary ideas in every branch o f thought, notably o f course in the theory o f natural selection in the development o f diverse biological species, has contributed to a suggestion that G od, like every thing else, is in a state o f change (Gruenler, 1983: 11).Thus in distinction to the G reek and medieval ideas o f a static fixed universe and a stable society, with the obvious changes in the world being superficial com pared to the essential stability o f the universe, came the idea that all is developing, including G od himself.God is therefore not infinite, but developing in relation to a universe that is also devel oping.God is in 'process', and although he is greater than humanity, he is not absolutely so.Likewise, the ontological argument is meaningless; there is no such thing as absolute perfection.Some things are only better, bigger, stronger or w hatever, than others.All is relative.
In the light o f this suggestion, it is necessary to re-examine the basis on which G od is stated as infinite.

Philosophical basis
This root o f the idea o f infinity has already been alluded to in the reference to G reek philosophy.Augustine, "who adopted the Platonic philosophy to the Christian religion" (Rucker, 1982:3), thus believed that G od is infinite.God is apart from the world, and different from it.Being very conscious o f the limita tions o f humanity, people very naturally deny such limitations to deity.Thus B erkhof (1958:52) w rites, " ... we remove from our idea o f G od all the imperfec tions seen in His creatures, as inconsistent with the idea o f a Perfect Being, and ascribe to Him the opposite perfection" .Although B erkhof (1958:53) rejects a philosophical basis for the know ledge o f G od as " ... on human conclusions rather than on the self-revelation o f G od in His divine W ord", he does assum e the per fection o f God.Then if perfection is predicated o f God, it would seem to follow that G od is infinite (Sontag, 1962: 68).

Psychological basis
R elated to this category is the deep desire within the human personality for the existence o f an infinite being, for such a being provides a basis for security.If G od is not o f infinite pow er, there may always be the feeling that the particular problem o f the moment is actually too great for him.In the A thens o f P aul's day (Acts 17:23), the erection o f an altar to the 'unknown god' w as to ensure that every area o f life w as adequately protected by deity.
O f course, the desire for protection leads to the accusation that G od is simply a reflection o f human need, and even that he does not exist at all.B elief in a god is simply a result o f a desire for someone able to meet human problems, as Feuer bach suggested.This is essentially D escartes' view; for him the appreciation o f his finitude could only be explained in relation to the existence o f the infinite (cf.Farrer, 1959:14).An interesting variation on this is to attempt to predicate infi nite potential to human beings (as in the N ew Age movement), but then it be com es problem atic to differentiate them from a possible God (cf.Bohler, 1991:39), who is then effectively 'infinitely infinite'.

Biblical basis
Several texts may be suggested which support the idea o f the omnipresence o f God, such as in the prayer o f Solomon at the consecration o f the Jerusalem Tem ple: Behold, heaven and the highest heaven cannot contain thee; how much less this house which I have built.(1 Ki. 8:27 cf also Is. 66:1, Ac. 7:49.)Similar to this is the claim o f omniscience, such that G od know s everything (Jer. 23: 24;cf. also Ps. 139:If).
Such claims may indeed be valid, but unless the universe is looked upon as infi nite, this is not in fact a claim to infinity, but rather to being everywhere, which is not at all the same thing.
Perhaps more relevant are texts such as M ark 14:36, "Father, all things are pos sible to you" or Genesis 18:14, "Is anything too hard for the Lord?" Again how ever, these do not actually demand omnipotence.

Causal basis
A similar objection can be made against the idea that creation dem ands infinite pow er, so that God must be infinite.This is true if the universe is infinite, giving rise to a problem felt by both Augustine and Aquinas, w ho believed it to be im possible for an infinite to create an infinite (Kennedy, 1991:46).However, the infinity o f the actual universe is doubtful; in this case, w hereas it is clear that creation requires a very large amount o f pow er indeed, this is not the same as in finite pow er, but could, at least in theory, be calculated.
Further to this is the suggestion that the world may well not be created, but could be eternal, or perhaps that spontaneous creation could be a normal feature o f the universe (Davies, 1983:26, 215).

T he idea o f the infinite
To a greater or lesser degree, such thinking is based upon an idea o f G od as very large.Such size or ability or even perfection is beyond human com prehension, but really only because o f the limited ability o f the human mind to understand such ideas.
H ow ever, the term infinite does not simply mean a size greater than can be con ceived of, but means, as is the literal rendering o f the word, something without a limit.This does not mean that the limit is so far beyond human reckoning that it may be understood as limitless, but that there really are no limits at all (Bolzano, 1950:81 f.).N either o f course does the infinite simply mean something without an end.There are several non-infinites which have this property, such as the cir cumference o f a circle (Bolzano, 1950:83) or perhaps more interestingly, o f a M óbius strip (M aor, 1987:139).'O ther things are bounded and yet infinite, such as the space between two parallel lines (Bolzano, 1950:83).This understanding o f infinite is o f a qualitative difference from that o f the merely very large and so has unique properties, well known in mathematics.M aor (1987:16) refers to a " googol", ten to the pow er o f hundred, and a "googolplex," ten to the pow er o f a googol, numbers that are com pletely beyond com prehension, bigger even than the number o f atoms in the universe.He then remarks, "Big as these numbers are, they have nothing to do with infinity.In fact infinity is as remote from a googol as from 1" .Then he adds, significantly, "it follows that infinity is not a num ber at all, but a concept."This m eans that the properties o f the infinite will not be the same as those o f the finite that w e are used to.Our experience is only o f the finite, "they never tran scend to the infinite" (M aor, 1987:58).There is a qualitative difference.
An example o f this is described in Sondheimer and Rogerson (1981:149).They use the example o f the infinite set o f positive integers.H ere every num ber can be paired with members o f a set o f even numbers; thus 1 is paired with 2, 2 with 4, 3 with 6, and so on.As the series are both infinite, no numbers are left in either set.They contain the same number o f elements.However, the set o f all integers must contain odd numbers, so it should have double the number as in the set o f ju st the even numbers.Thus the paradox, which only applies as both sets are infinite, is that a set with tw ice the number o f elements has exactly the same number.Twice infinity equals infinity (Kline, 1954:396).In the w ords o f Sondheim er and Rogerson (1981:149): A continuous loop with a half twist.This then has only one side and one edge.
An infinite set can be 'put into one-to-one correspondence' with a proper sub-set of itself.This is a general property of infinite sets which is not pos sessed by any finite s e t... .It is a property such as this which can only belong to the idea o f infinity.2It is not a property o f the simply very large, even o f things larger than can actually be conceived of.

T he existence o f the infinite
It is relatively easy to conceive o f an infinite and to describe its properties.This does not, however, mean that such a thing actually exists.Particularly in mathe matics it is quite in order to describe, and to w ork with concepts which do not in fact exist in the physical world.An example o f this is space with more dimen sions than the three that we experience.It must be noted, however, that mathe matical concepts are developed in general because they have use; even if they do not have actual existence, they do have actual application.
An example o f this, related to the idea o f the infinite, occurs in the theory o f the infinitesimal calculus.This theory depends on the idea o f infinitesimally small quantities, which approach non-existence, or zero.Now, if one o f these is di vided by another, the answer is not zero (as when a zero is divided by a number) or infinity (as when a number is divided by zero), but in the limit, w here each ap proaches zero, the answ er is indeterminate.The theory o f calculus has proved to be an indispensible tool in mathematics, with enormous application in engineer ing.It is a concept which can be used, but it does not in fact depend on the actual existence on any o f its infinitesimals.Rucker (1982:9) has helpfully discussed the idea o f infinity and divided the pos sibilities into three: a fully independent absolute other-worldly being, real occur rences in the physical world, and conceptions as in mathematics.
As regards the second, the possibilities are that physical quantities are infinite in extent, or that they are infinitely divisible.Although it would seem at first sight that space and time are infinite, this would seem to be unlikely.In the case o f space, Einstein's understanding would lead to a finite but unbounded universe because o f the essentially curved nature o f space (M aor, 1987:220).He also stressed the limiting param eter o f the speed o f light in the known universe (Gruenler, 1983:75).
Incidentally, this answers the problem of God's ability to create an infinite universe, as an infinite can encompass another infinite This is not to say that the universe is infinite, but the idea of creation docs not preclude the possibility.
The concept o f entropy3 indicates that time cannot be infinite, even if it can be very long.Eventually the interaction o f m atter results in a uniform chaos in which there is no meaningful change and therefore no time.The reality o f unidi rectional change in the world leads to the necessity o f a real origin and real con clusion for this world, so a 'big bang' (Rucker, 1982:12) as origin, and either an indefinite expansion in total chaos or a 'big stop' when everything contracts again after expansion to a limit.In the second case there is a possibility o f an infinite repetition o f the expansion-contraction cycle.4However, this universe is limited in time.
The infinite divisibility o f space and time seems more practicable.It w as in this sense only that A ristotle accepted the possibility o f the infinite (Sontag, 1962:44).H owever, the atomic view o f matter and the quantum understanding o f energy would indicate the lack o f infinite divisibility.Even if m odem atom ic physics has succeeded in going beyond the atom, there is no indication o f absolute divisibil ity.From another perspective, when tw o things becom e infinitesimally close, they actually becom e one.They are no longer different (Rucker, 1982:31, refer ring also to H um e's insights).
It would seem probable that any form o f infinity is impossible in the real world.Rucker (1982:51)

how ever concludes:
There are, however, no conclusive proofs that everything is finite, and the question of whether or not anything infinite exists remains as an open, al most empirical problem ...There are various sorts o f physical infinites that could actually exist ... Each of these infinites is, in principle, avoidable; whether or not our Cosmos does actually avoid infinities remains to be seen.
However, whether or not infinites do exist, they can certainly be conceived of, and then their properties can be described.For this w e are indebted particularly to G eorge Cantor (1845Cantor ( -1918)), who put the mathem atics o f the infinite on a sound footing and described several o f the properties o f the infinite (M aor, All real events in the universe are essentially irreversible; it is impossible to restore the universe to exactly the same state as before.The second law of thermodynamics indicates that overall, any process results in a measure of order being lost, so of an increase in chaos; entropy quantifies this process, so is constantly increasing. The concept of entropy does not demand the existence of a creator, although that is perhaps the simplest explanation.It is possible, in theory, to explain even the observed increase in entropy in terms of initial natural events which produce a low entropy system, or perhaps in terms of continual creation or destruction of entropy (Davies, 1983:212).
1987:53f).Although Cantor believed that the existence o f irrational numbers5 shows that the infinite actually exists, he admitted that it is largely a thought process, actual existence being irrelevant to the values o f the concepts (M aor, 1987:54,62).
Thus, although it is impossible to divide a real thing into an infinite number of parts, there is no objection to conceiving o f such, and neither is there a fundamen tal reason why these infinitesimals could not be perceived.The Heisenberg un certainty principle6 reflects on human inability (at least witli current technology), or perhaps more exactly, on human finitude.Neither is an infinite distance or time fundamentally impossible; it is real physical infinites which are questioned.Aristotle, in Physics w rote, "the infinite has a potential existence ... there will not be an actual infinite" (M aor, 1987:54).
M y concern is with the nature o f God.Rucker (1982:51) w rites, "... once one has an infinite Absolute, one must also have many conceivable infinites as well" .It is interesting that here, as also in the case o f Bolzano (1950:101) and else w here, it is the acceptance o f God as infinite which adds weight to the argument for the existence o f other infinites.The existence o f God, and his nature o f infin ity is, however, simply accepted dogmatically as a presupposition.It cannot be proved, simply because o f its own nature.7 If G od is infinite, this immediately means that God is different from the world and from humanity (Sontag, 1962:48).He is distinct, and although He may relate to the world and to humanity, there must always be a qualitative difference; God must be beyond time and space (Gruenler, 1983:76).It is for this reason that Aquinas rejected the possibility o f the infinite in the physical world.He accepted that God is infinite, and w anted to preserve a distinction betw een the world and G od (Rucker, 1982:49).
It is well known that numbers can not all be expressed exactly.Naturally some are, such as the integers (I, 2, 3 etc.), but some are not, but are expressed in repeating decimals (such as 0,333 ...).This latter case is not real indeterminability but is because we use a number system based on 10.In other systems exactness is possible, so that 0,333 is exactly one third Nevertheless other numbers arc 'irrational', such as the square root of 2, n (the ratio of a circumference of a circle to its diameter), and e (the base of natural logarithms), and cannot be expressed exactly in any number system.
In our normal decimal system they are expressed only as infinite scries.
It is impossible to determine everything about very small particles The very act of attempting to do so changes their situation.This aspect has implications for the Ontological Argument, which depends on the definition of God as pcrfect.This aspect requires a measure of comparability, whereas an infinity cannot be compared bccausc it is indeterminate.

A pplication to C hristian theology
Although it is impossible to prove that God is infinite by any o f the ways that have been suggested, predicating infinity of God enables an explanation o f a number of features in Christian theology which are otherwise difficult to under stand.Its ability to do this would thus strongly indicate that God is infinite.The idea of Aristotle is turned around; whereas he denied infinity to God so that he could be known, God is actually better understood just because he is infinite.Whereas the concept of very large (such as a googol) is incomprehensible, an in finity is in fact better defined.It is fully compatible with rationality (Sontag, 1962:77).Whereas some o f the statements o f Christian theology have led to a rejection of Christianity because they are perceived as incomprehensible and even contradictory, their explanation in terms of the understanding of the nature of the infinite should lead to a greater acceptance of the faith (Kennedy, 1991:38).
This seeming paradox can be illustrated by the repeated tossing o f coins.Each toss gives an unpredictable result, but overall, if a large number o f tosses is per formed, the result is effectively predictable.The use o f an effective infinite en ables accurate determination.This is o f course the basis of the insurance indus try, where although individual accidents are unpredictable, overall their occur rences can be predicted with great accuracy, enabling the risks and consequent premiums to be known.This is not an absolute infinite, but a very large.The infinite is indeterminate, but the large is sufficiently close as to be usable, just as irrational numbers can only be given a practicable numerical value by approximation.8The point is that a limitation is essential because the infinite is unmanageable.Similarly o f course, if God is to relate to us, He must limit himself; a full expression cannot be appreci ated by a limited humanity.Then it follows that the degree of self-limitation de pends in the particular context.As infinite, God cannot be fully described in hu man terms; He is different, but it is possible to relate to him.
Real infinities can, however, be conceived of, described and used.Various quantities in mathematics, such as the irrational numbers (Maor, 1987:45), can be described in terms o f infinite series, some of which can be summed.In these cases the determination is exact, but the definition involves infinity (Bolzano, 1950:93).It is impossible to write down the entire series, even if it can be con ceptualized.
Thus the Biblical value of n (1 Ki 7:23) given as three, is not an error; in fact all given values are approximate to some degree, the only difference being the degree of approximation.
A further example of this is the Koch curve (Maor, 1987:78)9 which has the inter esting property o f an infinite perimeter, and in fact an infinite distance between any two points when following the perimeter, no matter how close they are.Yet the area enclosed by it is finite (Davies, 1983:15).In all these cases we have finitude and infinity in one figure.There is a combination of the incomprehensible with the comprehensible.Theologically, a parallel to this is that God is immanent, relat ing to the world and humanity, but at the same time differently transcendent.(See Maor, 1987:83 f. for some further examples combining the finite and infinite.) In these cases, the use of the infinite renders understandable an otherwise incom prehensible.This would be true of God.We can say what He must be like, but can never exactly comprehend what we mean!By means o f the infinite, his na ture can be defined, but never exactly explained.

God as Trinity
The dogmatic assertion that God is not an undifferentiated monad but is one God in three persons, however that is then understood, is distinctive to Christianity.Obviously the basic idea comes from the realization o f the divinity o f Christ, based on his own assertions and observation of his life and deeds, and then sub sequently on a realization of the divinity of the Holy Spirit.It is highly significant that this assertion took place in a religious culture that was emphatically mono theistic.The experience of Israel, particularly in exile, had led to a fear o f any thing approaching plurality in deity.This does not mean that simple monotheism is all that is to be found in the Old Testament; there are indications of plurality, such as the expression "let us make ..." of Genesis 1:26, but these are minor, and without a reading back of Trinitarianism, would not be seen as leading to it.Ba sically, the message o f the Old Testament is that of monotheism.This contrasts strongly to a Greek culture which was very ready to ascribe deity due to the ex perience of anything surprising or miraculous, as Paul and Bamabas found at Lystra (Acts 11:12).These experiences were of course recorded in the Bible, and it was the attempts to reconcile the various assertions in the Bible which eventu ally led, by means of the Trinitarian controversies, especially that associated with the name of Arius, to the developed doctrine as understood today.
With the growth of Biblical criticism, the doctrine of the Trinity has come under attack as a dogmatic invention which cannot really be deduced Biblically.If the Bible is viewed as containing much later material, especially as influenced by This is generated by starting with an equilateral triangle.At the centre of each face is placcd an equilateral triangle with each side a third of the original length.(This gives a 'star of David' .)The process is repeated on each face of the new figure, and then again on the figure then generated, and so ad infinitum.

Koers 60(1) 1995:103-120
Greek ideas, if it only contains a collection of disparate theologies, and especially if it is not to be seen as a valid revelation in its own right but a witness to religion, the doctrine o f the Trinity rests on a very flimsy foundation.Attempts of such as Barth and Augustine to suggest a second root for the Trinity, the so-called Ves tigia Trinitatis, are readily conceded to be weak.
The attack on the Trinity is of course strengthened by the difficulty o f the doc trine, and by its irrelevance to practical Christian life and devotion.It can be suggested that Christianity can be a lot more credible, and so acceptable to mod em humanity without it, and that Christianity would lose little.
It must, however, be observed that the doctrine not only explains the Biblical data, but does explain a number of other theological problems which do then oc cur in non-Trinitarian monotheism such as Islam and Judaism.For example, if God is love, how could this be possible before the creation of the world?Trinitarianism sees a solution in the inter-Trinitarian love between the Persons.Nev ertheless, these are not great advantages compared to the difficulty of under standing how God can be at the same time singular and plural.Yet, if this can be explained satisfactorily, the Trinitarian solutions to other problems become meaningful.In this respect a perception of God's infinity is helpful.
If each person is infinite, the persons together are not three times the individual but exactly the same.Each person alone is no smaller than the group but is equal.Equally, they are really distinct, and not identical.10This is not the same as Tertullian's suggestion of the unity that exists in a committee comprised of individu als, and is also more than that of Hodgson's social Trinity, which will both see the group as really more than the individuals.Here the very nature of the infinite means that the sum is exactly that o f each individual person, and that each person alone is totally God, equal to the sum of the persons.

God as incarnate
A problem that immediately arises on ascription o f deity to Jesus Christ, is how it is possible that God can be contained in a human frame.God is immense, and a human frame is so small.Thus, as already cited, when Solomon built the temple, in his dedicatory prayer he said that it was impossible for it to contain God, see ing that heaven itself could not contain him (1 Ki. 8:27).Jesus himself, in the later temple, referred to his own body as the temple (Jn.2:21).The same thing is true; if a built temple could not adequately house God, then neither could a hu man body.
Infinite sets can be easily defined to be mutually exclusive, such as the sets of all even numbers, and of all odd numbers.They arc absolutely equal, yet different.
Therefore in references to the presence o f God in the Old Testament temple, the language has a connotation of the "glory" o f the Lord (e.g.Ez. 11:23), or of a symbol such as a cloud.And yet the implication is always of a real presence of God, such as when Ezekiel spoke to the Lord in that same temple, and certainly the implication of the New Testament is that Jesus did not simply represent God, but really was God.
Such is again possible if God is infinite.A very large being could not possibly be incarnated, yet a being without limits can be.There is no question o f compress ing, or taking a part to represent a whole, but the entire person o f God was in Christ.He is limitless, and so the limits of a human body are simply irrelevant.Although Aristotle could not reconcile infinity witli form, later thought had no difficulty in so doing (Sontag, 1962:101).This is not a matter o f reconciling two 'natures', one finite and one infinite, but of recognizing that a single being may be both.
Incidentally, the acceptance of humanity in incarnation is not the same as an in herent identification with the material.Pantheism, which identifies God with the material, is impossible if God is infinite, for the simple reason that the material is inherently limited, even if it is immense."There are suggestions that the universe is infinite, but this must be impossible due to the nature of the material.Rather modem suggestions are that there is some form o f continuous creation, or that the universe is expanding from some primeval 'big bang'.Both o f these imply a very definite limitation to the material.
Naturally a rejection of an identification of God with the material universe does not mean that God is not involved in the universe both as creator and as sustainer.He can be seen as in everything, even as its 'ground of being', but is infinitely greater than the sum of everything.

God as limited
Philippians 2:7 has occasioned an enormous amount of attention in relation to the incarnation, especially with the suggestion that in order to be incarnate, the Son of God emptied himself in order to be less than divine.Such could be seen as an explanation of the incarnation and of such features o f the ignorance o f Jesus as to the date o f the second coming (Mk.13:32).It is, however, obvious that there was a limitation in the incarnation; the infinite is incomprehensible.When con fronted with the glory of God by the river Chebar, Ezekiel sat overwhelmed for God could incamatc as a universe, but not identify with it.
Yet the discussion on the kenotic theory of the incarnation led to a reaffirmation o f a full incarnation.The Son of God incarnate was not less in nature than as not incarnate.The incarnation was real.Nevertheless, there was a self-limitation, a self-restriction in order to relate to humanity.
Such a self-limitation should not in fact be surprising, as God limited himself in the creation, and especially in the creation of humanity.In order to give real free will, and in order to give real authority to the created, as the idea o f the image of God (Gen.1:26) should most likely be taken to mean, God limited himself, even if temporarily.When something is given to another, even if it is o f an intangible nature such as power, the giver is naturally diminished by the amount given.
Although a self-limitation is not an inherent limitation o f the power and authority of God, it may still be seen as unacceptable, both as involving change in God and as reflecting upon his absolute nature.However, if God is seen as infinite, with infinite power and authority, humanity can still be given real free will, power and authority, but God is in no way diminished by the gift.He still has infinite power; his authority over humanity is not at all lessened but is infinitely more than that of humanity.What is restricted is God's freedom, which is only absolute due to his infinity (Sontag, 1962:137); but to voluntarily restrict freedom is not an inherent limitation.
Traditional theologies have had difficulty with reconciling an essential unchange ability in God with Biblical references to his repentance, as well as to the facts of creation and incarnation.Whereas one solution is to see the essential idea of im mutability not ir.a Platonic immobility where any change was rejected as it would involve a move away from perfection, but in consistency, reliability or faithful ness.However, insofar as an infinity can change and still remain infinite, God may be immutable just because he is infinite (Sontag, 1962:46).
To put it another way, limitation can be seen as consistent with infinity.To give a mathematical example, a series o f even numbers by definition is limited; it does not include any odd numbers, yet it is still infinite (Bohler, 1991:38).

T he su bord ination o f the Son
A similar problem is that of the clear subordination o f Jesus, focused in the statement o f John 14:28 "the Father is greater than I".This is a key text for the argument o f the ancient Arians, and in the modem world the Jehovah's Wit nesses, with their understanding o f the Son as inherently less than God the Father, so implying a polytheism, a loss o f the unity o f God.
It is possible to explain this text in terms of the fact that at the time of speaking, Jesus was self-limiting his nature.He was less than the Father, but only then, as the context may suggest, and was anticipating a restoration of his glory after his death.Such reasoning would, however, be unlikely in the case o f John 10:29-30 where the greatness o f the Father is again referred to, but with the immediate claim of Jesus -"I and the Father are one".
Alternatively, it can be explained in terms of relation, a view that as the Son, Je sus must be less than the source of his being, the Father, even if they are essen tially equal.A human father and son are equal as regards humanity, but there is still a relational difference.
A more satisfactory way is to recognize that both Father and Son are infinite.Therefore o f course they are absolutely equal, but also each is less than the other, even infinitely so.Any infinite is greater, even infinitely greater, than any other infinite.Thus the Son can say that the Father is greater than He, but at the same time He remains equal.As Rucker (1982:6) says, "the attributes 'equal', 'greater' and Mess', are not applicable to infinite, but only to finite quantities" .

The death o f God
One other peculiarity of the infinite is that infinity minus infinity is not zero as might be expected, but is indeterminate (Maor, 1987:8).This of course follows from the fact that adding anything to infinity, even another infinity, does not in crease it.This can be suggested to have an application to the cross of Christ where God died.The absolute outrageousness o f this has caused some in the past to reject it by suggesting that only the human nature in Christ died or that he only appeared to die.Nevertheless, the real death is essential if it is to be an adequate sacrifice for sin.
The objections have been largely based in the Greek idea o f the impassibility of God who cannot suffer or change in any way.This view naturally led to a dual ism both in God and in humanity.More to the point is the idea that death dimin ished God, with implications for his ability to care for the world.However, as God is infinite, a real diminishing in his death does not in fact diminish him.

The perception o f God
If God is limited, he can never, or very rarely, have a single experience of the whole o f reality.The alternative is a fragmented God.Gruenler (1983:130) therefore has suggested that infinity is the only way of safeguarding the unity of God (cf.also Sontag, 1962:138).It can also provide a solution to the question of the perception and involvement o f God in time.12In any process of change, it is possible to conceive of an infinite number o f states: there are an infinite number o f instants in any period.This must be so to avoid the paradoxes which will otherwise occur.Kline (1954:403) refers to the prob lem of the flight o f an arrow to illustrate this.At any instant its position can be identified, but at the next instant it is in a different position.Unless the next in stant is infinitesimally close to the previous one, the arrow must be simultane ously at rest and in motion.
Mathematically the paradox is that speed is distance divided by time.In an in stantaneous change, the distance moved is zero, and as zero divided by anything is zero, the speed is zero.However, the time between instants is also zero, and anything divided by zero is infinite; thus the speed between two positions is in finite.The paradox is resolved in that zero divided by zero (or zero multiplied by infinity) is any quantity whatsoever.Thus the speed is neither infinite nor zero.Clearly this is only valid where the gap between two positions is infinitesimal, where there is an infinite number of states between the original and final posi tions.Now where there are an infinite number of instants in a finite period, or of posi tions in a finite distance, it follows that it does not matter how big that finite pe riod or distance is, there is still a one-to-one correspondence between the instants or positions in that period or distance with those o f any other period or distance, no matter how big or small that period or distance is (Kline, 1954:402).Putting it crudely, no matter how big or small a period of time, or a length o f space, it will contain the same number of instants or positions; that number is o f course infinite.
What has this to do with the nature o f God as infinite?The point is one o f per ception, for a finite mind or ability to perceive can obviously not observe every instant of time or position in space.Indeed it does not need to; Kline (1954:404) points out that the illusion of motion in a film is satisfied by the projection o f a number o f still pictures, or instants, on to a screen in succession.This number does not in fact need to be very high.Kline mentions a figure o f sixteen per sec ond, but any number of that order will be adequate, as long as it is not too low, when the illusion o f motion is lost to be replaced by that o f a series o f still pic tures, which is in fact the truth.
It is notoriously difficult to understand what time is.Perhaps the best is to see it as a description of the changes which take place compared to the changes in something else (Bolzano, 1950:131).Such a proccss of change can be seen as a succession of states following one another.Now this will be true o f the human perception of anything at all.It will be of a rapidly changing sequence of impressions, a definitely finite, and quite a low number, in any period of time.Thus a human being does not perceive everything, but only what occurs in those instants.Anything else, such as when the person blinks, is just not observed; that perception is lost because the person is in time.This is not true for God, who will observe everything.In any case, God is eternal and is effectively outside of time.13To put it in another way, a human being ob serves by means of a finite number of impressions in any period, God by an infi nite number.Unlike human perception, that o f God is total; he is omniscient.14There is a couple o f results which follow from this observation.The first is, to me, a matter of speculation.It is frequently remarked by people who are getting older that the days seem shorter than in their youth and that they cannot get so much done.Time seems to be speeding up.Surely the problem would be that the number of perceptions is decreasing with age, there are less per unit of time.(This point is not relevant to this article, but is perhaps of further interest.) The second, more importantly for theology, follows from the fact that God per ceives an infinite number of instants in any period of real time.Because of the one to one correspondence of these instants with those o f any other period, the length of time becomes irrelevant.In any period, God's perceptions are of an equal (infinite) number.Thus it is possible that with the Lord one day is as a thousand years, and a thousand years as one day (2 Pet.3:8).This is not simply a dogmatic assertion to explain the delay in the parousia, the second coming of Christ, the 'day of the Lord', but is firmly based on the nature of the infinite.(It may perhaps be suggested here that such a time difference between God's perception and that of the world can be explained by the relativity To say that God is everlasting is not adequate as it predicates the idea of time onto God; thus implying that time is infinite.If time is a measure of change, it is only meaningful where the material changes, which is not the case when entropy maximizes in the chaos of the end of the universe, and is questionable before the initial event of the universe.
To say that God is eternal is then to put him outside of time but that just as God is involved with the material, he is then able to interact with time.Not that He alters it, as that would limit the free will of people and affect the consequences of that free will, but it means that God's action has eternal effects.
An example of this is the efficacy of the atonement for the whole of time.Since it is an eternal act, it is effective for sins committed before the historical event, and also after the event.O f course as it is the infinite Christ who died, it is also effective for any amount of sin; there is no limitation.This docs not demand determinism.God's perception is of all events, both actual and possible.
theory in terms o f the change in time experienced by a moving body (Gruenler, 1983:104), so that if God were moving at close to the speed o f light, one day for him would be as a thousand years, but this would not explain the other half, one thousand years as a day, and certainly not at the same time.)

T he im plication o f infinity
Any investigation o f 'real' theology, the nature of God, must face the accusation of irrelevance to practical issues o f Christian life and experience.Yet the appli cation o f religion must be based on an understanding of what deity is like.While theology is rooted in experience o f what God has said and done, at the same time an appreciation of theology clarifies and enables experience.Here a realization o f God's infinity has several consequences.Very obviously God of infinite power is more trustworthy than one of limited power, even if that power is large beyond actual comprehension.
Less obviously, but a point repeatedly stressed by Gruenler (1983:16) is that a non-infinite God cannot have a full, simultaneous perception of the whole o f real ity, especially due to the inherent limitation of the speed o f light.Such a God cannot know everything at once, and so cannot respond to need.
While process theology is reacting against the 'immobility' of classical theism (Gruenler, 1983:14) by stressing the involvement of God in the world, such a God cannot be totally involved.In ordinary life, the greater an official, the harder it is to gain access.Such a person is too important to be concerned with every indi vidual.Yet the glory o f God's infinity is that he is so great that he can be con cerned with everything.Technically this does not need infinity, but taken in conjunction with the previous point it does.
Perhaps the most significant implication of God's infinity concerns the relation ship o f believers to God.If deity is by nature infinite, then it is impossible for a limited human being to become divine, whether in the sense o f the primeval temptation (Gen. 3:5) or in the modem versions as expressed in prosperity teaching or the New Age movement.While the infinite may accept limitation, the finite cannot become infinite.This stands in contrast to the Christian teaching of the adoption of believers as children of God (Rom. 8:15,Gal. 4:5).A Christian is not divinized, but benefits by a relationship to God. 'In Christ' is not absorption, but relation.It must be pointed out here that a view of God as personal, that is being able to relate, by no means reflects on his infinity, but actually the contrary.
In addition, human life can in no way be eternal by nature, as humanity is finite.Only God is inherently eternal (1 Tim.6:16).Thus the only way of receiving eternal life is by relation to God, through adoption.