Maths, science, culture and religion

Sunday, November 07, 2004

The objective and subjective in maths and religion

If you can accept the existence of an independent mathematical world (as many mathematicians, the so-called Platonists, do), which nevertheless somehow interacts with both the physical and the mental world, then it is easier for you to accept the existence of an independent Transcendent (spiritual) world of (Christian) religion which somehow interacts with both our physical and mental worlds.

The question is not whether a mathematician invents or discovers mathematics; the question is in what relation are these two complementary aspects of his/her activity. The question is not whether what a Christian believes in has an objective existence or is purely a product of his/her mind; the question is in what relation are these two complementary aspects of his/her faith.

posted by George Virsik at 9:46 AM

6 Comments:

  • Hi George,

    I think before I can move to the second part of you post I might need a little convincing about the first. An independent mathematical world? Isn't this just another type of anthromorphising? I thought quantum physics put paid to a rational, mathematical, view of everything.

    By Anonymous Anonymous, at 11:20 PM  

  • Hi Anonymous,

    I am new to blog so I have to apologise for its form and for the length of my reply. The parallels between mathematics and religion are my hobby, I have written elsewhere about it (see e.g. my “Can religion handle cultural changes as mathematics did it for physics?” on my homepage http://www.gvirsik.privat.t-online.de/ under “Society”) and in order to get some feedback I presented here five concise theses in more or less random order. My problem: On one hand people whom I would expect to have informed knowledge on philosophy, anthropology, religion, will concentrate on the parts dealing with mathematics, how they consider all mathematics irrelevant — “Mathematicians do not know anything about real world, I could never understand mathematics”. On the other hand, mathematicians or other people whom I would expect to have no problems with understanding the mathematical point of view, will be irritated by my reference to religion which they consider a taboo or at least inappropriate in a ‘scientific’ context — “I do not think religion reflects reality outside the personal realm”. The person who does not understand mathematics thinks I want to expose his/her ignorance of something he/she should have learned at high school. The atheist or agnostic thinks I want to convert him/her.

    Coming to your question of whether religion refers to only internal experience (anthromorphising) or whether it has also some objective, external reality (‘objects’) of reference, is not unlike the problem whether new mathematical results are inventions or discoveries, i.e. whether they reflect more or less arbitrary constructions of the human mind, guided only by the rules of logic, or whether they refer to something pre-existing in the outside world, i.e. that complex numbers, the Cantor or Mandelbrot sets, or what you like, have an existence of their own like electrons, cells etc, as much as these are abstractions themselves. This dilemma was recently pointed to by Alan Connes, the founding father of non-commutative geometry (that has applications in contemporary post-Einsteinian physics) in “Triangle of Thoughts” (American Mathematical Society 2001, French original 2000), p. 2

    "... I would like to present ... two diametrically opposed points of view on mathematical activity: the viewpoints of the “Platonists”, who see themselves as the explorers of a “mathematical world” about whose existence they have absolutely no doubt, and whose structure they uncover; and the “formalists,” who take refuge behind a skeptical attitude, considering mathematics as no more than a series of logical deductions in a formal system or, in a sense, as a sort of purified language."

    I was surprised to find how many famous mathematicians were “Platonists” (for instance Cantor, Hardy, Gödel, Penrose, and Connes himself). They see themselves as “explorers of a mathematical world” perhaps not unlike contemporary (Christian) theologians who see themselves as explorers of another world, where they also encounter “truth as an absolute” the same as “Platonists” encounter it in their mathematical world. Both of them, the “Platonists” and the theologians, see their world as reflecting, modelling ‘Something out there’, they cannot grasp, cannot understand, directly.

    I think the answer in both cases — religion (its rational form, i.e. theology) and mathematics — is that it is both: an internal human construction as well as reflecting something pre-existent in the external world. Perhaps this complementarity is just an epistemological vehicle for an understanding of reality that cannot be grasped directly because the subject, the observer, is often part of the object, the observed. Today even in physics, the distinction inside/outside, subject/object is becoming more and more blurred.

    For some people reality, physical as well as human, is incomprehensible without the acceptance of a personal God; for others the physical reality is incomprehensible without reference to rather abstract pure mathematical models. Some people accept the existence of God as common sense, but often have a rather naïve view of Him; other people are aware of the need of abstract mathematics to explain physical reality but often have a rather naïve, or merely manipulative, view of it. Those who can identify with both points of view cannot afford to be naïve or simply dismissive — either in their ideas about God or in their philosophy of science, especially physics.

    Your reference to quantum physics is, I think, ambivalent: The physicists can handle mathematical models that describe the quantum world but they cannot explain why it agrees with experiments despite its internal contradictions (the Schrödinger cat). The Copenhagen interpretation is one of a number of attempts, but there are newer ones (e.g. the “many worlds” assumption). The strange properties of matter described by quantum physics are used also by the mathematician Roger Penrose to explain self-consciousness, and by the quantum physicist and theologian John Polkinghorne to explain the possiblity of divine interference with nature on the “quantum level”. You see, you cannot use quantum physics — or any other science for that matter — to prove the non-existence of a God (whatever you understand by that) as, of course, you cannot use science to prove His existence. In spite of the fact that there are still many people who believe the one or the other. It is a matter of (religious) faith, positive or negative.

    By Blogger George Virsik, at 10:50 AM  

  • Hi George,

    I certainly don’t regard mathematics as irrelevant. I think the beauty and clarity it provides is something I can only dimly perceive but do have a basic sense of. That being said I failed fifth form maths and never returned to it in a formal way so you will have to bear with me. Still at the back of the 'cave'.

    I recall that population studies in nature helped propel the development of chaos theory and of being amazed and intrigued by Mandelbrot sets emerging from simple algebraic formulas. I remember also dwelling on the idea that DNA might, in some miraculous manner, contain such a formula when I was examining the structure of fern leaves and cauliflower.

    So is the question we are asking is whether mathematics describes nature or does nature proscribe mathematics? I had proposed the former in my comment in OLO, but like you I probably subscribe to both.

    Where we differ is the sense of ‘Something out there’. Humans through the ages have filled their gaps in their understanding of the universe with Gods of all descriptions. It is understandable as those voids are not pleasant to live with. Before Darwinian evolution the existence of life and of mankind appeared to be a deity constructed miracle, why can’t we expect the “mathematical world” of the “Platonists” might receive the same treatment.

    I found it interesting that although Paul Erdos referred to a God like entity that he called the SF (Supreme Fascist) he stated “You don’t have to believe in God, but you should believe in the book”. The book was transinfinite and contained “the best proofs of all mathematical theorems, proofs that are elegant and perfect”. He doubted that God exists but when the perfect proof revealed itself he would say it was “straight from the book”.

    On quantum physics I was thinking about Einstein’s phrase “God doesn’t play dice”. If mathematics is like game of chess, simple rules facilitating the use of pure logic to produce an almost infinite numbers of combinations, then quantum physics appeared to be randomly removing the pieces.

    Cheers

    Cameron

    By Anonymous Anonymous, at 5:46 AM  

  • Hi Cameron,

    Thank you for your reply. I am sorry for not expressing myself clearly enough: people, who gave me the impression they found mathematics irrelevant, were usually rooted in humanities, not in (non-mathematical) sciences. And even then, it was not so much mathematics as such (even those who do not like it must admit its usefulness) but rather my way of thinking, influenced by working with mathematics where the distinction between inventing and discovering facts and results is far from clear. More generally, mathematics makes me see not as strictly opposing positions and views that could be explained as merely complementing each other. And, on the other hand, not to confuse aims which are essentially different: for instance, not to mix adherence to fair-play rules with the wish for one’s own team to win (e.g. in the cultural and political symbiosis of many religions including the non-religion). Or not to confuse science and religion with their possible interpretations (see my entry for 4/11/04 on this blog). Of course, I cannot claim that all mathematicians feel the same way about these, rather abstract, distinctions.

    Mathematically, chaos theory was known under the name of unstable differential equations: as a student I found the (Ljapunov) theory of stable equations rather boring but to specialists they were the interesting ones, non-stable equations were just pathological cases not worth considering. But somebody did, and they found applications in meteorology, population genetics, etc. So chaos theory became a household term used even by philosophers. A couple of decades ago the situation was similar with catastrophe theory. I myself was convinced, for a long time, that my PhD thesis was just my invention (or rather a modest twig on the tree of somebody else’s great invention), good for nothing but to prove myself. Well, in the last decade or so, it turned out that much of what our applied mathematicians back then regarded as useless creations are indispensable for the new physics (quantum gravity, string theory etc.).

    I met Paul Erdös only once, as a young tutor during his visit in Prague, where I acted as his interpreter in the early sixties. He was, and remained, an eccentric, a genius but in a very narrow field (combinatorics and graph theory). We all envied him for the fact that he, in spite of being a Hungarian citizen, could freely commute between communist Eastern Europe and what we saw as the free world. So his remarks about God you quoted are not exactly surprising to me.

    I found Roger Penrose — an atheist, or at least an agnostic, who is not only a mathematician but also involved in applications and philosophy of science — more inspiring. He considers the triangle of worlds, Physical, Mental and Platonic (see e.g. his book “The Large, the Small and the Human Mind”, CUP 1997) that he mutually interconnects through arrows. He defines the Platonic world as the “world of absolutes, in its particular role as the world of mathematical truth”. And he adds “One can well take the view that the ‘Platonic world’ contains other absolutes, such as the Good and the Beautiful, but I shall be concerned here only with the Platonic concepts of mathematics.” This leaves the door open to many non-mathematical extensions, completing his picture. Of course, one of them is the classical idealist philosophy of Plato.

    I shall not go into further details of what Penrose is saying, neither shall I try to complete the picture to suit my own world view. Also, I admit I was attracted to Penrose as a mathematician before I knew of his philosophy, so I am biased also in this respect. Suffice to say that in my original posting I was referring to the triangle of other three worlds, taken from Penrose just by analogy: Physical, Human/Mental and Supernatural (where mathematical models are irrelevant). The first one is identical to Penrose’s, the second is an extension of his; of course, the third world is unrelated to Penrose. This is the ‘Something out there’ world that the two of us sense differently, as you rightly state. But it is a world whose existence science can neither prove nor disprove. A particular person can be inclined to accept it for reasons that cannot be grasped by impersonal arguments that natural science works with. Belief in God can only be supported through science (which is not the same as proving or justifying it) given the right psychological disposition, but that is a one-legged support. The other ‘leg’ comes from culture, which is closer related to the Human/Mental than to the Physical world. This, in my opinion, could explain why there is such a variety of religions and denominations.

    You will recall Laplace’s answer to Napoleon’s question about where was God mentioned in his Mécanique Céleste: "Sire, I had no need of that hypothesis". Well, Laplace was an atheist, but this answer is often erroneously quoted as being a proof of that. No scientist (or mathematician), religious or not, needs the hypothesis of God’s existence for his/her research! There are many such examples where a position held by all educated people is dressed as if it characterised only atheists or agnostics. For instance, Penrose calls ‘prejudice’ his conviction that “there are no mental objects floating around out there which are not based on physicality.” (p. 97) That is namely also a conviction of mine, since the standard contemporary understanding of the Christian concept of soul (this is apparently what he calls mental object) is that it is the software, or rather a kind of ‘super-software’, ‘running’ on a sophisticated enough living organism.

    You refer to what is commonly called the ‘the God of the gaps’ which fulfilled a psychological need to answer questions that science could not answer. When, as a small child, I asked where did babies come from, I have been told that God brought them. I still believe this, though now I know a lot more about the ‘technology’ of how He does it, and have also a less naïve idea of who He is (or rather is not). The same about gaps in human understanding of physical phenomena through history. There can be naïve ideas about mathematics, physics, biology or religion (and, from what we know now, most of such ideas in the past were naïve) but it does not follow that we should therefore dismiss the very object of these naïve ideas. Which, of course, neither confirms nor negates the Platonist view of mathematics or the Christian view of reality. My guess is that these ideas will survive at even more sophisticated, abstract levels, though not everybody will subscribe to them or comprehend them.

    The conflict between Darwinists and Creationists is not a conflict between science and religion — though those on both sides of the silly argument still want to see it that way — but between a certain (naïve) interpretation of science and a naïve interpretation of Christian beliefs. One could perhaps understand the conflict in a historical context but in contemporary US it is absurd. Why can’t they teach children Darwinian evolution the same as they teach them about, say, the solar system, and leave it to parents to send the child to religion classes where they will be told who is behind all that, if they want to?

    Einstein’s views of quantum physics are rather obsolete. I keep away from arguments involving quantum physics, it is full of paradoxes that clever people try to resolve in very unusual ways, and even the mathematics underlying these attempts is beyond my comprehension. Where I quote, it is only from people who are authorities in the field.
    Finally, I would like to thank you for reading my pieces and giving me this opportunity to formulate more carefully my own position. I have a hierarchy of other people’s opinions, in this ascending order of preferences:

    1) trivial (sometimes even offensive) ones that I disagree with;
    2) trivial confirmations of views I hold myself;
    3) non-trivial confirmations of views I hold myself;
    4) non-trivial views, opinions, theories etc that disagree with my point of view but help me to better understand/defend my own position;
    5) non-trivial views, opinions, theories etc (that might or might not agree with my own point of view) which help me to improve, extend, amend my own position and views.

    It will be a sure sign of me getting senile when I shall avoid or ignore opinions on levels 4 and 5, and only look for those corresponding to level 3.

    With Christmas/Season’s wishes,
    George

    By Blogger George Virsik, at 5:14 AM  

  • Hi George,

    Thank you for your perseverance in replying to my posts, especially to such an obvious layman. You have certainly given me much to go on with.

    I also tend to grade the university lecturers (and professors :)) whom I know via a five point scale, but mine is based on ‘siftablity’, i.e. how much sifting I need to do to get to the kernel of what they are saying. If they come in at 4 I need to have a good sense that it might be worth it and I certainly don’t bother with anyone at 5. You are no where near that high.

    When you say “The question is not whether what a Christian believes in has an objective existence or is purely a product of his/her mind; the question is in what relation are these two complementary aspects of his/her faith.” I sense you have arrived as I have at the realisation that the existence of a ’Christian’ god has a certain irrelevance to the idea and execution of a personal Christian faith. I also believe that it takes a warm and benevolent view of humanity to find and maintain this position, irrespective of your own thoughts about the objective reality of a God.

    Although you must watch out George because with all that warmth and benevolence it is only a short step to secular humanism.

    I recall battling creationists when I was about 19 (which can be fun if they are good looking, I ended up marrying one). It is quite stunning how much ‘science’ goes into proving their case and how hard they fight to maintain the belief. If you step back you can see that this is not about evolution vs. creationism but about time. Most creationists will accept DNA changes can happen within populations for adaptive purposes but since they believe the world was created 10,000 years ago evolution can not have occurred.

    So I learnt very early never to dwell on evolution but rather on geology, geography, physics and chemistry. After one long session, where I was pushing the fact that I didn’t think God was that much of a joker that he would, at the moment of creation, extend the light from stars a million light years from us to be striking us today, I was issued with a challenge: find one example on earth of something that proved the age of the earth extended past 10,000 years. It was actually harder that one might think, especially if you can’t use carbon-dating (too unreliable) or erosion such as the Grand Canyon (the flood did it), or even the fossil record. My non-religious friends scoffed at the idea but I felt if one was to be true to science one needed to leave preconceived ideas behind, especially since then I would have some legitimacy in requesting the same.

    It took me months before I found my holy grail in some caves in NSW. A guide had remarked that a particular stalactite was 60,000 years old. When I queried the age I was told there is a finite rate at which they can grow, if the flow of calcium laden water increases past a certain point it actually erodes the structure rather than adding to it. They grow at one cubic foot every 1000 years and the edifice before us was at least 60 cubic metres in volume. It was a ‘Eureka’ moment for me, a simple incontrovertible proof, disturbed only momentarily by picture from a creationist friend of 7cm long stalactites formed under the limestone blocks at Melbourne’s war memorial (once we extrapolated out the volume it returned the 1000 year rate). However I found little desire to ram this down creationist’s throats and have rarely used it since.

    The debate is really about the thin edges of two wedges. The fundamentalists can never give up creationism because it brings into question the infallibility of the Bible, the rock on which their faith sits enabling them to navigate through the accelerating changes in their world. This also is an overt badge of faith, believing in something the rest of society sees as irrational, inviting a type of soft persecution conducive to the fundamentalist mindset.

    The other thin edge of the wedge is allowing creationism to be taught in schools, or even the dilution of evolution to placate them. Once that wall is breached it with threaten all the other sciences including I would have thought, mathematics. Therefore, with the emergence of Family First in Australia I unfortunately see U.S. style battlelines being drawn.

    Can I offer a different explanation for “why there is such a variety of religions and denominations”? Might it instead be that we either adopt faiths that mirror our attitudes to our societies, or that we attempt to mould our faiths to better fit the same. If the denomination is of a particularly large size this can be difficult, for instance birth control within the Catholic Church or the ordination of women within the Anglican Church.

    The dramatic rise in the evangelical, charismatic, fundamentalist churches can in part be attributed to the variety. ’Consumers’ are spoilt for choice. They are usually small and not homogeneous. However, spawned from an American of the thirties, they are all about personal deliverance and growth. The industry supporting them with the paraphernalia of the movement is worth billions in Australia. Thus we have a highly adaptive, well nurtured, ‘product’, reconstructed for a capitalist society, a far cry from the non-hierarchical, virtually kibbutz stye of the early church.

    These people would rightly see a huge gap of between the grand designer you feel is revealed in mathematical discoveries and an interfering, personal, responsive God answering prayers for parking spots.

    I will have a read of your ‘Can religion handle cultural changes, as mathematics did it for physics?’ over the break. I also want to pursue Paul Davies fascination with the number 137 describing it as lying at the heart of nature.

    Finally on senility, I think Erdos said there were three stages for a mathematician, the first is forgetting his theorems, the second is forgetting to do up his fly, and the third is forgetting to undo it.

    Thanks once again and Merry Christmas to you and your loved ones.

    Cheers

    Cameron

    By Anonymous Anonymous, at 11:47 PM  

  • Dear Cameron,

    Let me illustrate how I appreciate the time and effort you are spending on reading my expositions with the following example. A research student of mine, in the final stages of his PhD thesis, came to ask me to explain something to him. He spoke for about twenty minutes and then said, “Thank you, now I understand” without me having had to open my mouth throughout that time. Nevertheless, I think, I was of help to him: by doing his best to formulate the problem for me to understand, he clarified it to himself. I acted as a sort of a catalyst: he could not have used, for instance, his grandmother for that purpose because he could not have believed that she would follow, and, of course, he would not see a need to explain something carefully to himself! Well, you are certainly more than a catalyst.

    Now to your input. When you write “with all that warmth and benevolence it is only a short step to secular humanism” you remind me of the ill-fated concept of “anonymous Christians” (Since only Christians can be nice, all those other nice people are in fact Christians without being aware of it.) That was offensive to non-Christians, and is not being used any more. Nevertheless, I accept it from you as a compliment since you apparently count yourself as being a secular humanist.

    More to the point, I certainly do not think that the existence of a personal God (apparently that is what you mean by ‘Christian’) is irrelevant to … personal faith. The same as the existence of the TV transmitter is not irrelevant to the person who views a TV programme. For an outsider who never before watched TV (say, a visitor from the Middle Ages) that would be irrelevant, he would probably think that there are some small people, or rather devils, living inside the box. However, contemporary users of TV all know that there is something being transmitted from a distance, from somewhere outside, though an understanding of what it is, and how this something is being transmitted, will be different for the old lady next door, and for an electronic engineer or physicist. And the latter will also know that there is still a lot we do not understand about matter, radiation etc. So for an outside observer, Christian faith is a mental phenomenon, “God resides in the believer’s mind” and the actual existence of the referent of this faith is irrelevant. But not for the insider, be he/she a simple person or a scientifically and/or philosophically sophisticated one.

    However, what I was trying to say is more complicated than that. God both resides in the believer’s mind and has an objective existence relevant to the physical world in somewhat the same sense in which mathematical concepts both reside in the mathematician’s mind and have an objective existence (Penrose’s Platonic world) relevant to the physical “real” world. This, of course, is an unusual, untraditional (for the believer as well as for the non-believer) way of looking at the cognitive component of religious faith, or rather a new reformulation of the traditional Christian world view. Perhaps something like the Hindu doctrine of atman-brahman, but that might be far-fetched. My inspiration came from mathematics (the complementarity invention-discovery), from Penrose’s triangle of realities mentioned in my last communication, and from the famous cosmologist Martin Rees’s recent paper “In the Matrix” (http://www.edge.org/3rd_culture/rees03/rees_p2.html). I am not sure to what extent are my ideas original, but I am sure they need a more careful reformulation. I shall not go into that now.

    I did not understand your purpose in fighting those who claim the world was created 10,000 years ago (in seven days from Monday to Sunday?) whatever they call themselves. However, there is a malicious intention to confuse simple non-religious people by calling ‘creationist’ not only a fundamentalist described above, but any person whose world-view includes a God/Creator and who agrees with everything respectable scientists (atheist or not) say about how He did — or rather is doing — it. (I do not have a quote on hand, but I suspect Philip Adams might be a typical example). That is something like calling any social democrat a communist.

    Believe me, today you do not have serious educated Christians who think you could scientifically prove the existence of (the Christian) God (you had them in the past). But you can find serious people (Carl Sagan, Richard Dawkins are just two examples) arguing that science can prove the non-existence of such a God transcending that very science, by any standard definition. What serious Christians look for in science are arguments that can support their a priori faith, which also Dawkins and co. should admit they can merely do. On the other hand, the advancement of human knowledge was helped also by many futile attempts. Not only those trying to find “scientific proofs” for the existence or non-existence of God, but also by attempts to construct a perpetuum mobile, or make gold out of plumb in an alchemist’s kitchen.

    Your two wedges reflect the fact which might be irrelevant in an academic debate but is politically important, namely the large number of Christian fundamentalists in the US. This is something perplexing to Europeans — non-religious, as well as Christians, including those considered conservative. In Europe conservatism refers to moral values only, not to fighting the teaching at school of established scientific findings. You could call the Pope conservative in matters of sexual morality but certainly not in his acceptance of the results of physics or biology. I thought Australia was in this respect more European than American. You mention something called First Family. The very name would suggest that they have strong feelings about matters moral, not cognitive. Mixing these two functions of religion — you are not the only one — can lead to all sorts of misunderstandings.

    As I mentioned in my last communication, you can teach Darwinian evolution, or whatever, if you keep religion — belief in God, or unbelief in God — out of it. Darwinian evolution as a biological theory has nothing to say about a God (though, I think, Darwin himself was a believer) as for instance the Archimedes’ principle says nothing about religion. The difference is only that in the first case people were tempted to make religious conclusions — positive or negative — from scientific findings, whereas in the second case it would be more absurd. The Laplace quote from my last communication can be completed into “Science does not need that hypothesis (about God), neither can it make any conclusion about whether He exists or not.” Something like that would be a fair statement by a teacher though I am afraid not only Christian fundamentalists but first of all secular fundamentalists (secularists), might find this even-handed attitude unacceptable. Nevertheless, I cannot see any other solution.

    What you are offering as an explanation for the variety of religions is not that much different from mine, only more concretised. I principally agree, however you again mix cognitive aspects of religion, that this blog is originally about, with other aspects of Christian religion like, ethical norms (birth control), tradition (ordination of women). Mathematics, of course, is irrelevant to those other aspects. Where we differ is that I see culture, human mind and mentality etc. only as one part of religious reality, one side of the coin. The other object of reference is independent of individual minds or the mindscape. That is the complementarity, the two legs, I spoke of before, where I found helpful insights from mathematics, Penrose and Rees.

    I do not see how “the dramatic rise in the evangelical, charismatic, fundamentalist churches” has anything to do with consumer society: Bush was reelected on “values” not on economy. I would see all this rather as a backlash, a reaction to the destructive seventies that lead to political correctness in the eighties and beyond, which removed established securities and taboos and replaced them with new ones. But this again diverts from the original topic, and would certainly require more elaboration. (My comment on the US election “Evangelical zealots and whingeing secularists: Is the West facing opposite cultural dangers in USA and in Europe?” can be downloaded from my homepage.)

    You ridicule the two complementary aspects of what I claim constitutes Christian faith, but you are right in one thing: the fundamentalists — of the religious or non-religious breed — will see a huge gap between these two approaches to the same thing because it is beyond their comprehension. I have had only indirect experience with American Christian fundamentalists, but I grew up in a fundamentalist secular (Communist) society, where at the end ridicule (beside political control) remained their only argument. That was one of the reasons I chose that Goethe quote on the front of my homepage. So I am rather more surprised by the stubbornness of Christian fundamentalists than by that of their non-religious counterparts.

    You finished with a joke so let me offer one of my own making I often repeat: “I can understand everything Bertrand Russsel says (about religion) but I do not agree with him. And I agree with everything Alfred Whitehead says (about religion) but I do not understand him”.

    Repeating the Christmas wishes and adding New Year’s ones as well,
    George

    By Blogger George Virsik, at 10:57 PM  

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