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vol 8:
How universal?

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1: About
2: Synopsis
3: Development

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4: Glossary
5: Questions

6: Essays
7: Notes
8: History

9: Persons

10: Supplementary
11: Policy



a personal journey to natural theology

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How universal is the universe? (1967)

... things no eye has seen and no ear heard, things beyond the mind of man, all that God has prepared for those who love him.

I Corinthians 2:9


1 In 1948 Dr Claude E Shannon of Bell Telephone Laboratories published a paper titled A Mathematical Theory of Communication [Bell System Technical Journal 27 379-423, 623-656 (1948)] which helped lay the foundations for a discipline called Information Theory. Information is defined as whatever resolves uncertainty. Shannon developed a means for measuring information by the amount of uncertainty it resolved. The simplest possible uncertainty is represented by the choice between two things. This he chose as his unit. As a measure, it is the 'distance' between yes and no. Such a choice can be symbolised, in its outcome, by 1 for yes and 0 for no.

2 These two digits can form the basis for a binary number system, analogous to the decimal system in everyday use. By shortening the name of these BInary digiT another scientist at Bell named this measure of information bit. This term is the name for the measure defined by the choice between yes and no, and also of the 1 and 0, or other symbols, used to represent the outcome of such a choice.

3 The resolution of more complex uncertainties requires a number of yes-no choices. Two choices will find any member of a foursome: @ # $ %: 'is it in the left hand pair?' 'Yes'; Is it the left hand member of that pair?' 'No'. By a similar series of five questions one could pick any letter of the alphabet, with fifteen such questions any entry in a small dictionary and so on. The answers to these questions can be set down symbolically in a series ,- 100011101010110, and if the questions are asked systematically, each series will represent one determination of the uncertainty in question.

4 The number of bits in an item of information is not directly proportional to the number of uncertainties it resolves: 2 possibilities require 1 bit, 32 require 5 bits, 32 768 require 15 bits. If the number of choices is represented by C, and the number of bits by x we can write the relation between x and C as

equation 1

Turning it round, this can be written

equation 2

where log2 (which means the logarithm to base 2) is analogous to the ordinary logarithms of school days which have 10 as a base, and can be written log10 . This equation (2) is an important one in information theory.

5 In ordinary language the words 'yes' and 'no' take their meaning from the context. 'Yes, I will have sugar' is very different from 'Yes, we'll drop an atom bomb on Hanoi' which differs even more from 'Yes, God exists' . Further, there is no limit whatever to their context, so they can be called transcendental. This means that the bit is a transcendental measure. Yes and no have this property because they are meaningless in themselves. The context gives them meaning -'Yes, What?'.

6 In information theory the bit is a measure of information. We can also, as we did with the 'yes' above, designate a particular bit and ascertain its meaning. The fifteen bit word, say 100011101010110 which specifies a word in a dictionary has a certain meaning which comes from the system by which it was derived from the dictionary, and the nature of the dictionary. The bit as a measure ('fifteen bit') gives us no inkling of the meaning of this word - just as saying the Summa contains two million words tells us nothing but that it is a big book. But in its context (the dictionary and the coding system) it as meaning. Each particular bit in it also has meaning, defined not only by the context of the word as a whole, but by its relation to the other bits in the word.

7 This discussion gives us a basis for distinguishing between a bit taken quantitatively and a bit taken qualitatively. Quantitatively, it is simply a measure of information, and as such is meaningless. Qualitatively, it is the equivalent to a 'yes' in context. The change from meaninglessness to meaning is made by uniting the bit to a context.

8 The full context of any bit of information can be very wide and varied. In the example given above, the immediate context of any bit is the other bits in the binary word. Outside that are the system of derivation and then the dictionary. The definition of each of these would take us further and further afield. Here, only a small portion of the context is binary, and the rest in more conventional form - perhaps ordinary english. But there is no reason intrinsic to the binary system to prevent us from translating the whole context into binary, so that the binary system would become a language in itself.

9 Just as in an english dictionary we can define all the words satisfactorily by using other english words, so in our binary language we could define every 'word' by relating it to other words. We might note that such a language would be an ideal one, since the transcendental nature of its elements would give them the flexibility to express any concept without distortion either of the language or of the concept.

10 If we can accept and understand the possibility of using the binary system (in its essence, forgetting about notation) as a language to express all our meaning, we can take a further step. It seems quite possible that the binary language could be the 'language of reality'. This is a metaphorical sort of statement, but I will try to explain it as well as I can.

The physical representation of information

11 What follows first occurred to me while tinkering with the relation between the energy and frequency of photons. Symbolically, this relation is

equation 3

12 E stands for energy, which is 'the capacity to do work'. The water in a dam has energy because it can be made to do work on the blades of a turbine. Moving things have kinetic energy, because they can be made to do work by slowing them down. h is Planck's constant. It is a product of quantum theory. In our macroscopic world most things are continuous in one way or another. If we wish to push something, it can be done with a large and continuous range of different pressures. Physicists working with microscopic phenomena found that this was not so there, and that all things took place in steps - one could push with one pound pressure or two, but not one and a half; or one could face north or northwest, but not northnorthwest and so on. Planck's constant is a measure of the size of the steps in these phenomena. It is extremely small, which means that the discrete structure of the universe is very fine. f stands for frequency, which simply means the rate of recurrence of some particular state.

13 Now it is usually assumed (as far as I know) that a wave can carry one bit of information per second, per cycle per second of frequency. (This is relevant, for instance, to the transmission of information by radio waves - a photon is simply a 'particle' of radiation - light, radio waves, x-rays etc.) Thus a thousand cycle per second wave can transmit in the order of 1000 bits of information per second. This is, it appears, something intrinsic to photons, and not just an artefact of their use by men to transmit information. Hence we have found a quantitative relationship between information transmission rates and energy.

14 It is possible to pursue this a little further. As a result of the special theory of relativity, Einstein discovered the relation

equation 4

between energy E , mass m and the velocity of light c . By substituting for E in 3 we get

equation 5

which is equivalent to

equation 6

15 We can substitute I (bits per second), meaning information, for f to make the relationship between information flow and mass clearer:

equation 7

16 What does this mean? We have connected information transmission rates through frequency to energy and through energy to mass. Since to a physicist everything can be treated in terms of waves, this seems valid enough. So we have found a quantitative equivalence between information, measures by transcendental bits, and mass, measured in pounds or tons or grams. This may seem a little bit far fetched, but the hint is there. Mass is a primary thing, and we cannot defines it in something really prior (to a physicist it is one of the basic 'dimensions' - the other two are length and time) so we cannot easily reject anything we may discover about it. Since the bit is in a way the measure of all things, we can say that mass and energy are simply quantitative measures of the amount of information in the universe. It is prior also to frequency, so that we should say that a cycle per second is a characteristic of something that can transmit one bit per second and not the other way around.


17 Given this hint, we can approach it in a more radical way. I think it could be taken as proved that our universe is evolutionary. Evolution is a sort of motion from less perfect to more perfect. The extreme terms of such a relation would be least perfect and most perfect.

18 The most perfect is clearly God. It is obvious that the universe cannot evolve into God, but we know from our faith that it is destined to come very close to him - for each of us in the beatific vision and for creation as a whole in the New Jerusalem. Its ultimate perfection will be participation in the divine nature in a very full way.

19 The least perfect is the bit.

20 Assuming that the universe is actually evolving between these terms, what would it have been like at the time of creation. A few ideas might make the position clearer.

21 God could create a bit simply by making something exist apart from himself whose only attribute was to exist. 'Exist' here is a relative word, meaning the affirmation of something related to god and distinct from him. Such a thing would be simple, neither abstract nor concrete, and there would be no real distinction in it between relation and term.

22 It might be suspected that such an 'existent' would be pure being and another god. This is not so. As we said before, yes and no by themselves are meaningless. This existing bit is meaningless in itself. The only thing it can claim is the relationship of existence to god. It is transcendent and simple, but its transcendence and simplicity are those of 'common' or 'empty' being.

23 God is transcendent and simple, but his transcendence and simplicity are those of pure, perfect or 'full' being. Even if this idea is a bit difficult, I do not think it involves any contradictions and so is possible. It is hard to imagine such a 'thing' - neither abstract nor concrete, formless and shapeless - but this is no hindrance.

24 We can conceive a very large number of such existents all having the relation of existence to God (or being this relation) but, in the beginning, having absolutely no relation to one another. This again seems quite possible. This means that they have no context apart from god. From this it follows that in itself this new universe has no meaning, since meaning can only come to an empty affirmation through its context. So, at the pole of least perfection we have a large number of meaningless individuals. (They are just many. We cannot say that they are distinct, because that would imply relation. Their multiplicity would be a matter of divine will, not intrinsic principle).

The origin of meaning

25 We can now suppose that these existents begin to unite. As soon as two of them join, each become the context of the other and gives it some sort of meaning or definition: it is now not just an affirmation, but an affirmation connected to another. The formation of larger unions would give bigger context and sharper definition to the participants. Starting with empty existents we are moving toward complex beings with some sort of definition or essence. The elements of the language of the universe are beginning to acquire meaning.

26 Why and how do they unite? The answer to this seems to revolve about the notion of communication, which is the sharing of information.

27 The union is not that of identity, since this would defeat its purpose - if 1000 bits became identified, we would be left with one, and would have made no progress. To put one another in context and generate meaning, they must remain distinct though united. We are familiar with this possibility from the study of relation in the Trinity (mutatis mutandis).

28 This union seems to involve time. Mass is a static thing, yet in the equation (7) derived above it is related to information expressed as bits per second. The introduction of time brings with it motion. There are two kinds of motion: imperfect motion that is going somewhere, and will not be complete until it has reached its goal; and perfect motion which is not going anywhere and is complete in itself. Examples of the latter are the motions of a planet revolving around the sun, the swinging of a pendulum or the rotation of the earth. Time is related to both of these, but more perfectly to the second, since we use 'circular' or'cyclic' motion to measure time. The appearance of time in the relation between mass and information gives the impression that communication within things is a dynamic thing. Aritotle's word energeia which means 'inward activity' seems to be very appropriate to this.

29 Perhaps this is a bit too reminiscent of Heracleitus' panta rhei (everything flows). It makes time a bit too radical to the universe. It was probably Heracleitus' doctrine that drove Plato to posit eternal separate forms to account for the stability of things and knowledge. Aristotle moved back toward Heracleitus by putting a dualism in things: matter which allows them to change; form which gives them stability. While he defined transitional motion as an imperfect thing, he allowed that motion and time did not derogate from the perfection of the heavens because theirs was perfect or circular motion. Here we are saying that there is no contrariety between communication which is an activity, and form. In fact the communication of information leads to the differentiation of the participants which puts meaning into the universe.

30 This might be seen as an exemplification of Chardin's principle 'union differentiates'. This can be seen easily in higher evolution - the union of cells into multicellular creatures leads automatically to a differentiation of the cells into different organs. They do not remain a homogeneous mass. In human society the same happens. When [people] get together there is a division of labour so that each contributes a special part to the society. If this were not so the society would soon break up.

31 Our own experience of the all pervasive nature of time, and even more the experience of science should make it easier to accept as something essential. A more careful analysis of information and conmmunication would probably show that if this picture is correct, there must be time if there is to be union and evolution.

32 Why do they unite? On the one hand it sees natural for them to do so, since they are somehow ordered to communication. On the other it might seem impossible, since their union leads to the formation of more perfect beings. This would seem to be against the principle of causality. I think the difficulty comes from making the distinction between formal and efficient causality too absolute.

33 Formally, there seems to be no difficulty in having things inform one another in a sort of 'mutual definition' so that both are perfected. We might ascribe the fact of their union to a general desire or drive for perfection in the universe. This needs detailed explanation, but I think the fact of evolution, in at least some areas proven, should suffice for the present. I think a fuller treatment would be along the lines of Bernard Lonergan's concept of emergence.


34 If time is essential to the universe, what about space? At the beginning of the De Caelo Aristotle says that the universe is perfect because it has three dimensions. One of the indications of the perfection of the number three is its use in the worship of the gods. St Thomas uses this statement (Summa Theologiae I.32.1, arg 1) as an indication that it is possible to prove the existence of the trinity of persons in God. I think that one can almost show that the connection between the Trinity and the three dimensionality of space is more than fortuitous, even though, if proved, it would be simply a 'vestigium' , and not a knowledge of the Trinity 'per propria' .

35 Traditional Aristotelian logic is 'two valued' or binary, since it is based on the principle of contradiction. With the invention of symbolic logic it became possible to handle this logic much more easily and find new properties in it and make improvements. In about 1928 Jan Lukasiewicz and others developed a three valued logic. I think this is based rather on the formalism of symbolic logic rather than the interpolation of a 'tertium' in the principle of contradiction.

36 In 1962 a paper was published by Gotthard Gunther on four valued logic, which he considers to be the complete and perfect system. I am far from understanding this, and have seen nothing of his work since, but a little seems clear. Two valued logic is based on the principle of contradiction = yes-no and no medium. By the same scheme, we could say yes-no-no-no and no media. The important point is that the noes are all different. The relation of this to two valued logic need not concern us here.

37 What relation does this have to three dimensional space? When we say that space has three dimensions, we mean that it is possible to have three rods mutually at right angles in this space.

38 Four dimensional space would allow us to have four mutually right-angled or orthogonal rods. Orthogonality means that each of the dimensions is not the other and in no way participates in the others.

39 Let us call the three dimensions a, b and c to keep track of them. To separate them we need three noes - a is not b, a is not c, c is not b, and we can only affirm the same thing about one of them at a time - it is not possible to go in two directions at once, for instance.


40 The notion of participation gives us the next clue. Each person of the Trinity might be called 'orthogonal' to the others - the Father is not the Son, the Father is not the Spirit, the Spirit is not the Son, but they are all one god. This means that the trinity of persons in god is natural to being as such. Since what is natural to being as such must be participated by all beings, we can expect to find some sort of trinity in al things, even the simplest. It seems almost obvious to suppose that the three dimensional orthogonality of space is a result of the participation of the trinity in these existence.

41 In other words, all being falls into four-valued logic, which is the perfect one, and the consequence of this four-valued logic in the universe s its three dimensionality. It seems a bit far fetched to connect logic with space, which is something very imperfect, but I think the possibility is there given that the structure of the universe is in fact based on'one bit' existents. I am very unsure of the ground here (as all the way), mainly because I know so little about the logic involved.


42 This exposition is very brief and sketchy. I would like very much to go into detail, but have no room. It may be summed up, nevertheless, by giving some of the reasons which make it appear true and by comparing it with the traditional cosmology developed by Aristotle.

43 First, the most basic measure seems to be the bit. It is both the simplest possible, and transcendental. It seems natural that what can be used as the first measure of our knowledge and communication should also be a measure in things.

44 Second, our universe seems to be fundamentally evolutionary, from fundamental particles to animals to the kingdom of God. Evolution is a motion from imperfect to perfect. The extreme terms of such motion would fittingly be the most perfect and the least perfect. The bit is the least perfect and, because it is transcendental, able to participate in the divine nature.

45 Third, there is a quantitative correlation between the rate of information transmission and mass and energy; which also establishes, through the physics that we know, that time enters into the basic structure of the universe.

46 Fourth, it happens that 'information-time' is an invariant in the universe, which indicates that it is something basic. According to the special and general theories of relativity, as the energy of a thing is increased, time on it goes more slowly. Thus neither energy or time are absolute. But their product is. This means that the rate of interior communication in something of given rest mass is invariant.

47 Fifth, the quantisation of action in the universe, which is basic to quantum theory, suggests that there is some sort of discrete measure in the universe.

49 It might be interesting to note how small a bit per second is in the universe, quantitatively, compared to things of 'handleable' size. If we put m equal to one ounce in 7 above, we find that I is about 1049 bits per second. It might help to appreciate this number if we realise that were the sun, per impossibile made of talcum powder (it is nearly a million miles across) the number of particles would be getting on for 1049. This quantitative fineness can give us an idea of the structural complexity of something even of moderate size.

Comparison with Aristotelean cosmology

50 What is its relation to Aristotelian cosmology? This, especially his doctrine of matter and form, is true, and so unless the present speculation agrees with it it cannot be true. As far as I can see, it fits quite well.

51 Our primordial bits have all the attributes of prime matter - nec quid - they are meaningless: nec quale - for the same reason; nec quantum - they are the simplest and so indivisible; nec aliquid eorum quibus ens determinatur. They are the primum subiectum ex quo aliquid fit, et insunt rei iam factae .

52 In their original state they are deprived of form. They can exist independently of form, which prime matter cannot; not of themselves, because nothing apart from god exists of itself, but by the creative activity of god.

53 Similarly, our theory embraces the notions of form and act. Their union produces structures with meaning or essence. It would be instructive and interesting to follow this process of evolution through from beginning to end, but there is not space here. I think that if the nature of information is remembered the possibility of their determining form will be clear. I do not think there is any real difficulty in explaining the stability and mutability of things. If the speculation I have outlined were true, what would we gain?

54 First: as far as I can see it agrees very closely with the most basic things in modern science and fits in well with modern research in information theory, cybernetics and logic. It makes it possible to embrace the science as an integral part of theology, which in turn gives theology new information for the understanding of god and new relevance to an increasingly scientific world.

55 Second, it removes the necessity for an absolute dichotomy between matter and spirit. Prime matter has a limited potency, Material things conceived through prime matter cannot, almost by definition, be intelligent or rational. The nature of information, on the other hand, is in no way contrary to intellect. The transcendence of information means that it can be a principle of intelligent creature just as easily as of mud. Similarly it removes the sharp dichotomy between material being and immaterial knowing. I think anything which enables us to understand the universe as a unity is better, since presumably god originally designed it as something one, not divided by irreducible opposites.

56 Third, it shows how the universe is open to the future. Modern eschatology, as well as that of old, predicts an optimistic future for the universe. Given the present theory there is the possibility of almost anything without changing the nature of the universe, whereas our concept of matter requires that things be radically changed to achieve their glorification. It seems more fitting to god's wisdom that he should have created a universe capable of evolving naturally (under his guidance of course) to its perfection, rather than one needing radical remodelling on the last day.

57 Fourth, it opens the whole universe toward the supernatural. It is the task of the church to preach the gospel to every creature, not just the rational ones. We might see modern technology as the beginning of this.

58 Fifth,. a theory of knowledge developed along these lines seems to agree very well with traditional theory, and also to be capable of embracing modern developments of this theory - those made by Lonergan, who seems to be regarded as one of the most enlightened of modern scholastics, and the more'existentialist' emphases of men like Rahner. I think it can say something to physicists who are bothered by the objectivity of quantum mechanics and the computer people, who seem to be meeting serious problems in'cybernetic epistemology'. Without moving into materialism or idealism it allows being and knowledge to be seen in one perspective.

59 Sixth, in an age when technology is coming to the fore it might enable men to see the real goodness of the universe we call material and see that it is part of the plan of salvation, not a mereutile to be abstracted from and escaped as much as possible.


60 How universal is the universe? My dear people, we are already the children on God but what we are to be in the future has not yet been revealed; all that we know is that when it is revealed we shall be like him because we shall see him as he really is (I Jn 3:2).

61 The future is beyond our comprehension, but we can get an idea of it and speed its coming by studying what we already have. Contemplating the size and wonder of the universe as it stands in the light of its openness to the future must surely be a powerful incentive to men to love God. We have come a long way since the little world of St Thomas. Ours is open to all things, even participating in god. This is what I mean by universal.

62 This is rather a lot of advertisement for a very minimal exposition, but I feel that the idea merits a bit of investigation, even though I fear that its beauty and simplicity might hide some very fundamental misunderstandings on my part - fallax gratia et vana pulchritudo. It is based on remote principles and I always feel safer working with small details that are more my size. It would benefit immensely from discussion, and the man who pulls out the loose keystone, if it is there, will save a lot of work.

Brother Anthony OP (Jeffrey) [1967]


Brillouin, Leon, Science and Information Theory, Academic 1962 Introduction: 'A new territory was conquered for the sciences when the theory of information was recently developed. ... Physics enters the picture when we discover a remarkable likeness between information and entropy. ... The efficiency of an experiment can be defined as the ratio of information obtained to the associated increase in entropy. This efficiency is always smaller than unity, according to the generalised Carnot principle. ... '  Amazon  back
Chaitin, Gregory J, Information, Randomness & Incompleteness: Papers on Algorithmic Information Theory, World Scientific 1987 Jacket: 'Algorithmic information theory is a branch of computational complexity theory concerned with the size of computer programs rather than with their running time. ... The theory combines features of probability theory, information theory, statistical mechanics and thermodynamics, and recursive function or computability theory. ... [A] major application of algorithmic information theory has been the dramatic new light it throws on Goedel's famous incompleteness theorem and on the limitations of the axiomatic method. ...'  Amazon  back
Chaitin, Gregory J, Algorithmic Information Theory, Cambridge UP 1987 Foreword: 'The crucial fact here is that there exist symbolic objects (i.e., texts) which are "algorithmically inexplicable", i.e., cannot be specified by any text shorter than themselves. Since texts of this sort have the properties associated with random sequences of classical probability theory, the theory of describability developed ... in the present work yields a very interesting new view of the notion of randomness.' J T Schwartz  Amazon  back
Khinchin, A I, Mathematical Foundations of Information Theory (translated by P A Silvermann and M D Friedman), Dover 1957 Jacket: 'The first comprehensive introduction to information theory, this book places the work begun by Shannon and continued by McMillan, Feinstein and Khinchin on a rigorous mathematical basis. For the first time, mathematicians, statisticians, physicists, cyberneticists and communications engineers are offered a lucid, comprehensive introduction to this rapidly growing field.'  Amazon  back
Klir, Jiri, Cybernetic Modelling, Iliffe, SNTL 1965, 1967 Preface: 'The principal purpose of this book is to show the part played by cybernetic modelling in the solution of problems common to the animate and inanimate world. The system, its behaviour and structure are used here as fundamental concepts forming the basis of a wide approach that utilizes the model as a methodological instrument. ...' J Klir and M Valach, Prague, 1965.back
Pierce, John Robinson, An Introduction to Information Theory: Symbols Signals and Noise, Dover 1980 Jacket: 'Behind the familiar surfaces of thhe telephone, radio and television lies a sophisticated and intriguing body of knowledge known as information theory. This is the theory that has permitted the rapid development of all forms of communication ... Even more revolutionary progress is expected in the future.'   Amazon  back
Wiener, Norbert, Cybernetics or control and communication in the animal and the machine, MIT Press 1996 The classic founding text of cybernetics.  Amazon  back


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