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Cavin and Colombetti, miracle-debunkers, or: Can a Transcendent Designer manipulate the cosmos?

A slide presentation by Professor Robert Greg Cavin and Dr. Carlos A. Colombetti on the subject of miracles, which was used by Professor Cavin in a debate with Christian apologist Mike Licona on the Resurrection earlier this year, raises points of vital importance for Intelligent Design proponents.

As readers will be well aware, Intelligent Design theory says nothing about the identity or modus operandi of the Designer of life and/or the cosmos. Nevertheless, Cavin and Colombetti’s presentation is philosophically interesting, chiefly because the authors put forward three arguments to support their claim that Divine intervention in the history of the cosmos is astronomically unlikely:

(i) a religious argument that supernatural intervention is antecedently unlikely, which appeals to the Via Negativa and cites the authority of St. Augustine of Hippo and the Jewish philosopher and rabbi, Moses Maimonides;

(ii) a scientific argument that a Transcendent Designer, having created the laws of thermodynamics and statistical mechanics, would no longer be capable of manipulating the cosmos; and

(iii) a mathematical argument, which appeals to Bayesian logic, purporting to show that there could never be good evidence for such an act of Divine intervention.

The religious argument against supernatural intervention

(a) How Cavin and Colombetti misread Augustine and Maimonides

Let’s begin with the religious argument. Cavin and Colombetti argue that supernatural intervention by God is antecedently improbable, by appealing to natural theology (the investigation of God’s nature based on reason and ordinary experience) and the Via Negativa (which says that we cannot know what God is, but only what He is not).

To bolster their case, Cavin and Colombetti cite the authority of St. St. Augustine of Hippo (354-430 A.D.), who wrote that “Nature is the Will of God!” (De Civitate XXI, 8). But here’s what he actually said:

…[I]t is possible for a thing to become different from what it was formerly known characteristically to be…

For how is that contrary to nature which happens by the will of God, since the will of so mighty a Creator is certainly the nature of each created thing? A portent, therefore, happens not contrary to nature, but contrary to what we know as nature…

What is there so arranged by the Author of the nature of heaven and earth as the exactly ordered course of the stars? What is there established by laws so sure and inflexible? And yet, when it pleased Him who with sovereignty and supreme power regulates all He has created, a star conspicuous among the rest by its size and splendor changed its color, size, form, and, most wonderful of all, the order and law of its course!

In other words, what St. Augustine is maintaining here is that the nature of a thing is simply whatever God wants it to be. Augustine is most emphatically not saying that things have a fixed nature of their own, and that this fixed nature reflects the unchanging will of God. Rather, he affirms that God can change the course of even the stars at will – as well as their color, size and form – but that this change is not “unnatural,” not because the laws of Nature are fixed, but that the nature of a thing is to be whatever God wants it to be. Thus in this passage, St. Augustine is emphatically denying Cavin and Colombetti’s claim that supernatural intervention by God is antecedently improbable.

Additionally, Cavin and Colombetti adduce the authority of the Jewish philosophical scholar Moses Maimonides (1135-1204), also known as Rambam, to support their contention that it is extremely unlikely that God would supernaturally intervene in the course of events. Maimonides is associated with the Via Negativa (or the Way of Negation), which is built on the premise that since we cannot understand what God is, we have to learn about God by seeing what He is not. Although Cavin and Colombetti never bother to tell us why this premise makes miracles unlikely, it is true that as a young man, Maimonides upheld the view that what we call miracles are actually events which have been pre-programmed by God into the laws of nature. Rabbi Gil Student, the founder, publisher and editor-in-chief of the Orthodox Jewish Website and journal Torah Musings,describes the evolution of Maimonides’ thought in an online article titled, Rambam on Miracles (April 14, 2010):

In his earliest work, the Commentary on the Mishnah, the Rambam asserts that miracles are a part of nature. The Mishnah (Avos 5:5 in the Rambam’s edition) lists items that were created during the last moments of the six days of Creation, each of them miraculous (e.g. the “mouth” of the earth that swallowed Korach). Rambam, in his commentary to that Mishnah, explains this to mean that miracles were part of Creation. When setting the laws of nature in motion, unique exceptions to those laws were included; miracles were pre-programmed into the laws of nature. Therefore, technically, they do not violate nature but are part of it…

This was, by no means, a non-controversial explanation. Later commentators, such as Meiri and Rashbatz, disputed this interpretation and explained the Mishnah in accordance with the view that miracles are deviations from the laws of nature…

At this point, the Rambam was a Naturalist when it comes to miracles while the Meiri and Rashbatz were Interventionists, believers that God intervenes in nature…

However, there is evidence that later in life, the Rambam softened on this issue and became more of an Interventionist. In Moreh Nevukhim 3:32, the Rambam writes that God actively metes out reward and punishment in order to encourage people to observe the commandments. In Moreh Nevukhim 2:29, Rambam even calls the idea that miracles are pre-programmed into Creation “very strange” (Kafach edition, end of p. 290)… And in his Medical Aphorisms (vol. 2 p. 216), he states that the idea of an eternal universe is objectionable because it excludes the possibility of miracles.

This has led some scholars, such as Tzvi Langermann (Cambridge Companion to Medieval Jewish Philosophy, pp. 172-174) and Charles Manekin (On Maimonides, pp. 68-71), to suggest that the Rambam changed his view.

Readers will recognize Maimonides’ earlier views correspond to the view known as front-loading among Intelligent Design thinkers. Later on, however, Maimonides reverted to the traditional view that God can and does intervene in Nature.

It thus appears that the very authorities cited by Cavin and Colombetti in order to support their claim that God is very unlikely to supernaturally intervene in Nature actually refute it.

I’d like to wrap up my discussion of the Via Negativa by quoting from another thinker who belongs in this intellectual tradition: the theologian and philosopher St. Thomas Aquinas (1225-1274), who wrote in his Summa Theologica: “Now, because we cannot know what God is, but rather what He is not, we have no means for considering how God is, but rather how He is not” (S.T. I, q. 3, introduction; Benziger Bros. edition, 1947). Thomist scholar Brian Davies interprets Aquinas’ teaching about God as an exercise in negative theology:

We cannot, he [Aquinas] argues, know what God is. We must content ourselves with considering “the ways in which God does not exist, rather than the ways in which he does.” And it is here that his talk of God as Ipsum Esse Subsistens [Subsistent Being Itself - VJT] comes in. It is part of an account of ways in which God does not exist. Its chief purpose is to deny that God is a creature. As some authors would say, it is an exercise in negative theology.
(Thomas Aquinas: Contemporary Philosophical Perspectives, Oxford University Press, 2002, p. 11.)

Given that Aquinas was an exponent of the Via Negativa, what did he think about miracles? Here is what he had to say in his Summa Contra Gentiles Book III, chapter 99, paragraph 9 (That God Can Work Apart From The Order Implanted In Things, By Producing Effects Without Proximate Causes):

[D]ivine power can sometimes produce an effect, without prejudice to its providence, apart from the order implanted in natural things by God. In fact, He does this at times to manifest His power. For it can be manifested in no better way, that the whole of nature is subject to the divine will, than by the fact that sometimes He does something outside the order of nature. Indeed, this makes it evident that the order of things has proceeded from Him, not by natural necessity, but by free will.

We can see that Aquinas explicitly affirms in the passage above that God can and does act outside the order of Nature. For Aquinas, God is an interventionist.

(b) Possibility, probability and cucumbers

But Cavin and Colombetti are not finished yet. In their slideshow, they point out that possibility is not probability (p. 78), and give a humorous example to illustrate their point: “If God wills that I turn into a gigantic green cucumber then I’ll turn into a gigantic green cucumber. But it’s hardly probable that God would will this!” (pp. 80-82). The authors conclude: “The fact that God can supernaturally intervene doesn’t make it in the least bit likely that He does” (p. 83).

Cavin and Colombetti go on to argue that God’s self-revelation in Nature shows an exceptionally strong tendency not to supernaturally intervene in natural affairs – for instance, they say, He possesses an exceptionally strong tendency not to raise the dead! The authors then attempt to construct a statistical syllogism, which they describe as a standard argument pattern of inductive logic, showing that on the basis of the fact that 99.999…999% of the dead are not supernaturally interfered with by God, and, thus, not raised by Him, it follows that the antecedent probability that God would cause someone to rise from the dead is astronomically low. As I wrote above, although the authors are attempting to undermine the case for the Resurrection, the point they make has obvious relevance for Intelligent Design as well. Someone could argue in a similar fashion that since 99.999…999% of molecules are not supernaturally manipulated by God, the antecedent probability that God would manipulate some molecules on the primordial Earth to create life over 3.5 billion years ago, or to create an array of 30 animal body types 530 million years ago, is also “astronomically low.”

How should Intelligent Design proponents respond to Cavin and Colombetti’s anti-interventionist argument, which is based on the regularity of Nature? In my opinion, we have nothing whatsoever to fear from it. The reason for my optimism is that the number of discrete events that have occurred in the observable universe is finite: Seth Lloyd, in his paper, Computational capacity of the universe (Physics Review Letters 88:237901, 2002, DOI: 10.1103/PhysRevLett.88.237901), calculates it to be no more than 10^120. That’s his estimate of “the number of elementary operations that it [the universe] can have performed over its history.” All we need to show, then, in order to make the “interventionist” hypothesis a viable option, is that there is at least one system or structure existing in Nature whose antecedent probability of arising as a result of unguided evolution is less than 1 in 10^120.

In view of the fact that the world-renowned evolutionary biologist, Dr. Eugene Koonin, has estimated in his peer-reviewed paper, The Cosmological Model of Eternal Inflation and the Transition from Chance to Biological Evolution in the History of Life, (Biology Direct 2 (2007): 15, doi:10.1186/1745-6150-2-15) that the probability of even a simple life-form evolving in a region the size of the observable universe, within the time available, is less than 10^(-1,018), or 1 in 1 followed by 1,018 zeroes, I would say that Intelligent Design passes Cavin and Colombetti’s probability test in flying colors. Their statistical syllogism is rendered invalid by an even stronger syllogism going the other way. If the antecedent probability of a supernatural act of intervention is astronomically low, the antecedent probability of a living thing coming into existence without an intelligent designer is infinitesimal. Koonin himself does not infer that an Intelligent Designer made the first living thing; instead, he invokes the multiverse as an explanation for the unlikely appearance of life on Earth. However, in my recent post, Is God a good theory? A response to Sean Carroll (Part Two), I explained why this response was an inadequate one, and I argued that even a multiverse would still need to be designed.

This does not mean that we can infer that life was produced by an act of intervention by the Intelligent Designer. Front-loading is another possibility, although I should point out that physicist Robert Sheldon has written a thought-provoking article entitled, The Front-Loading Fiction (July 1, 2009), in which he critiques the assumptions underlying “front-loading.” What it does mean, however, is that intervention by an Intelligent Designer is a “live option” that is on the table for discussion.

Scientific arguments against supernatural intervention

Later on in their slideshow, Cavin and Colombetti adduce two scientific arguments purporting to show that supernatural intervention is extremely unlikely.

(a) The argument from the Second Law of Thermodynamics

Referring to the miracle of the Resurrection, the authors state that “scientific considerations show that the Resurrection has a non-zero, albeit astronomically small, prior probability” (p. 277), as “the entropy of the Universe markedly decreases in a supernatural resurrection from the dead,” and “the Second Law of Thermodynamics tells us that: the entropy of a physically isolated system is always increasing” (p. 283). It follows that “The supernatural Resurrection of Jesus by God violates the Second Law of Thermodynamics and thus has an astronomically low prior probability!” (p. 282). Again, a skeptic could mount a similar argument aiming to show that the creation of life on Earth by an act of supernatural intervention would result in a decrease in entropy and thus violate the Second Law of Thermodynamics, making it an astronomically unlikely occurrence. Let’s have a look at their argument:

The Second Law of Thermodynamics tells us that: the entropy of a physically isolated system is always increasing. (p. 283 )

…[But] since the supernatural realm, e.g., God, is non-physical, it lacks mass-energy, thus making the Universe a physically isolated system! (p. 284).

Even if God exists, He is not physical, and thus lacks energy, and so cannot exchange energy in any form with the Universe! The Universe is thus physically isolated: there is nothing with which it can exchange energy in any form! (p. 294).

The first thing I want to say here is that Cavin and Colombetti radically misconceive the way in which God interacts with the cosmos. It’s as if they think God moves things by pushing them. But that’s not how it works at all. Instead, God causes events to happen in the world in much the same way as the author of a book narrates the events that happen in it. As Thomist philosophy Professor Edward Feser put it in a post titled, Are you for real? (May 8, 2011):

The idea is that God’s causality is not like that of one character, object, or event in a story among others; it is more like that of the author of the story. Hence to say that God is the ultimate source of all causality is not like saying that He is comparable to a hypnotist in a story who brainwashes people to do his bidding, or a mad scientist who controls them via some electronic device implanted in their brains. He is more like the writer who decides that the characters will interact in such-and-such a way. And so His being the ultimate source of all causality is no more incompatible with human freedom than the fact that an author decides that, as part of a mystery story, a character will freely choose to commit a murder, is incompatible with the claim that the character in question really committed the murder freely.

The second point I’d like to make is that Cavin and Colombetti falsely assume that when God intervenes supernaturally, He is interacting with an isolated system, where neither matter nor energy can enter or exit – which is why they repeatedly point out in their slideshow that “the Universe a physically isolated system.” But it is far more reasonable to suppose that if God intervenes supernaturally, He acts by redistributing energy within an open system, such as the primordial Earth (which continually received matter from space and energy from the Sun). This kind of intervention would not violate the Second Law of Thermodynamics. By contrast, believers in unguided evolution suppose that the Sun’s energy was sufficient to drive a series of chemical reactions leading to the generation of life on Earth. This is an idle speculation on their part, as they supply no mechanism explaining how the process happened, and no calculations demonstrating that the eventual emergence of life, even within a chemical system exposed to sunlight, would be a reasonably likely occurrence (i.e. one with a probability of at least 1 in 10^120).

My third criticism of Cavin and Colombetti’s argument is that it ignores the possibility of creation (and destruction) of energy. The authors write: “Even if God exists, He is not physical, and thus lacks energy, and so cannot exchange energy in any form with the Universe!” Notice the assumption here: that a Supernatural Being interacting with the cosmos would have to do so by exchanging energy with the cosmos. However, an alternative possibility is that God creates extra energy and inputs it into the cosmos. He may also destroy an equivalent amount of energy shortly afterwards, in order to restore the total energy of the cosmos to its previous value.

The fourth reply I’d like to make to Cavin and Colombetti’s argument is that at best, it merely shows that the universe is a physically isolated system (i.e. one in which neither matter nor energy can enter or exit); what it fails to show, however, is that the universe is causally isolated. Cavin and Colombetti acknowledge this criticism, and make two ineffective replies. First, they assert that the Second Law of Thermodynamics has been shown to hold for physically isolated systems — even if they are not causally isolated from God. This assertion misses the point for two reasons: (a) it fails to rule out supernatural interventions which don’t violate the Second Law of thermodynamics; and (b) the Second Law of Thermodynamics has only been shown to hold for physically isolated systems under human-controlled laboratory conditions, whereas the possibility we are considering is that God interacts with the universe-as-a-whole, in circumstances which are entirely under His control (which may mean that the Second Law itself is temporarily suspended).

Second, Cavin and Colombetti argue that “The Second Law as part of the Via Negativa thus shows that God chooses not to supernaturally interfere with physically isolated systems!” (p. 307). We have already disposed of anti-supernaturalist appeals to the Second Law. And as we’ve seen, arguments based on the Via Negativa have a rather hollow ring, given two of the leading proponents of the Via Negativa in the Middle Ages were themselves ardent believers in miracles, in their mature years.

(b) The argument from statistical mechanics

But Cavin and Colombetti have one more ace up their sleeves: the argument from statistical mechanics. Once again the authors take aim at the Resurrection, but their point about microstates can easily be generalized to any miracle in which life is supernaturally generated from dead or inanimate matter:

Statistical Mechanics tells us that all microstates having the same energy have the same equal prior probability. (p. 309)

Statistical Mechanics thus tells us that, even if God has a chosen people, He has no chosen microstates – that is, all microstates having the same energy have the same prior probability! (p. 313)

…the equally probable microstates in which the corpse of Jesus is dead vastly outnumber those in which his body is alive! (p. 316)

Because all the microstates have equal energy, the Postulate of Equal “A Priori” Probabilities applies, and thus all the microstates have equal prior probability. (p. 320)

Because the number of microstates instantiating death and decomposition is vastly greater than those instantiating life, the prior probability that the corpse will not resurrect is virtually 100%. (p. 321)

Since the number of microstates (“ways”) in which the constituents of a body can form a corpse astronomically exceeds the number of microstates (“ways”) in which they form a living body, Cavin and Colombetti conclude that the prior probability of a specifically supernatural Resurrection is astronomically low (pp. 322-323). And I am sure that they would draw the same conclusion regarding the creation of the first life on the primordial Earth: it’s an astronomically unlikely event.

To see why the argument doesn’t work, consider a set of 1,000 dice lined up in a row. All the dice are tossed at the same time. The dice are all fair dice: thus each side of a die has the same prior probability of coming up, when the die is tossed. The number of possible sequences of the numbers 1-6 which come up on the 1,000 tossed dice and which contain no pattern that can be specified briefly (e.g. “1 to 6 repeating”) is astronomically larger than the number of sequences that do contain such a briefly specifiable pattern. And since we know that all sides of a die have the same equal prior probability of coming up, we may conclude that God has no “chosen sides” for any of the dice. Hence, by Cavin and Colombetti’s logic, we would have to infer that there’s no way even for God to manipulate the dice to form a pattern of numbers. But we would be wrong if we made that inference, for three reasons.

In the first place, even in a specified pattern of numbers, there may well be an equal number of 1′s, 2′s, 3′s, 4′s, 5′s and 6′s. (Consider for instance the sequence, “1 to 6 repeating.”) In such a sequence, God has no “chosen sides”: all values are equally represented.

In the second place, it is fundamentally wrong-headed of Cavin and Colombetti to equate the prior probability of a supernatural intervention with the prior probability of its microstates being in the arrangement specified by the Supernatural Being producing that outcome. What they appear not to realize is that miracles, if they occur, are planned and wrought from the top down, rather than from the bottom up. That is, although the microstates must eventually be specified, this is done so only because of, and logically subsequent to, the initial decision to generate a particular pattern in a system.

In the third place, the argument relating to prior probabilities of the various microstates of a system refers only to natural probabilities. Just as a die retains its natural tendency to land with equal probability on any of its sides even while some card cheat is rolling the die in a way that reliably lands on a six (which apparently can be done with practice, so I’ve read), so too, all the microstates of a system retain their equal prior probability in the natural state, even while they are being manipulated by God. (Is that “cheating” on God’s part? Of course not – he made the cosmos, after all!)

UPDATE: In a highly perceptive comment below. Sal Cordova points out that Cavin and Colombetti rely on a questionable assumption in their argument: they assume that if God made the laws of Nature, then those laws are immutable. Cordova offers a simple counter-example: “For example, I could write a computer program that spits out the number 3 every second, and then once a year it spits out 7.” In a similar vein, the mathematician Charles Babbage, in his Ninth Bridgewater Treatise (2nd ed., London, 1838; digitized for the Victorian Web by Dr. John van Wyhe and proof-read by George P. Landow), With his own Analytical Engine undoubtedly fresh on his mind, Babbage asked the reader to imagine a calculating engine that displays very predictable regularity for billions of iterations, such as a machine that counts integers. Then it suddenly jumps to another natural law, which again repeats itself with predictable regularity. If the designer of the engine had made it that way on purpose, argued Babbage, it would show even more intelligent design than a machine that merely continued counting integers forever. He concluded that miracles do not truly contravene the laws of Nature at a higher level – a conclusion he reiterated in his later autobiographical work Passages from the Life of a Philosopher (London: Longman, Green, Longman, Roberts and Green, 1864), where he wrote that miracles are not “the breach of established laws, but… indicate the existence of far higher laws.” (p. 391)

The mathematical argument against supernatural intervention

Cavin and Colombetti also formulate a mathematical argument, which appeals to Bayesian logic, purporting to show that there could never be good evidence for such an act of Divine intervention.

In response to critics of Bayesian logic who contend that arguments based on “prior probability” are unreliable and that we should try to assess the plausibility of a claim rather than its “prior probability,” the authors argue that “plausibility” is in fact the same thing as prior probability; and they cite the work of Professor Brian Skyrms as demonstrating that “any so-called “plausibility” that is not actually probability is wacky and leads to irrational beliefs and decisions!” (p. 384). Skyrms, they say, has shown that plausibility, in order to be well-behaved rationally, i.e. not wacky, must be a probability. That is, it must conform to the axioms of Probability Calculus, and hence it must satisfy Bayes’ Theorem. Besides, they add, recent studies indicate that the human brain is “hard-wired” for Bayesian reasoning (p. 389). Thus, they conclude, the Bayesian Approach shows that, in order to be well-defined, plausibility must be equal to Bayesian prior probability!

For my part, I have absolutely no objection to the use of Bayesian logic when making Intelligent Design inferences. However, I would object strongly to Cavin and Colombetti’s equation of the prior probability of a Supernatural Designer making a living thing from dead matter with the probability of the matter in question spontaneously forming itself into a living organism. That is precisely what it is not. I would, however, be quite happy for argument’s sake to assume a starting prior probability of 10^-120 as a default value that has to be cleared by a highly specified complex pattern, which would have to be shown to be 10^120 times more likely to be the product of a Designer than of an unguided process.

What do readers think?

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12 Responses to Cavin and Colombetti, miracle-debunkers, or: Can a Transcendent Designer manipulate the cosmos?

  1. Perhaps we should look from the other direction, the quantum effects of prayer on the cosmos. Catholic teaching is clear that God sustains the universe, is a personal God and can/will answer prayers. Could more prayer by more people effect the earth, calm the storms, effect discord, or change the outcome of a war? Conversely, when we turn away from Him is the universe more disorderly?

    Perhaps God will act when we ask, or has granted us some power to affect our condition.

    From the ID perspective, this would support design.

  2. VJT, you’re merciless!

  3. VJTorley,

    Cavin and Columbetti are wrong. The first assumption is that if God made laws, the laws are immutable, that is not true.

    When I studied Statistical Mechanics and Thermodynamics, in my graduate textbook by Pathria and Beale, a certain FJ Belinfante in the opening pages was mentioned as one of the pioneers of the discipline.

    There is a book by FJ Belinfante I mentioned at Uncommon Descent which shows Cavin and Columbetti can not be absolutely right:

    http://www.uncommondescent.com.....iple-1987/

    Barrow and Tipler’s ideas were actually forseen 12 years before their book by Physicist FJ Belinfante in his book Measurements and time reversal in objective quantum theory

    We thus see how quantum theory requires the existence of God. Of course, it does not ascribe to God defined in this way any of the specific additional qualities that the various existing religious doctrines ascribed to God. Acceptance of such doctrines is a matter of faith and belief.
    If elementary systems do not “possess” quantitatively determinate properties, apparently God determines these properties as we measure them. We also observe the fact, unexplainable but experimentally well established, that God in His decisions about the outcomes of our experiments shows habits so regular that we can express them in the form of statistical laws of nature. This apparent determinism in macroscopic nature has hidden God and His personal influence on the universe from the eyes of many outstanding scientists.
    F.J. Belinfante

    If there is a God who designed the “laws”, we have laws because he is choosing to do things with a certain amount of regularity, but Belinfante rightly observes God at any time can choose to stop the universe from behaving in such regular manners. It would appear God had reasons for behaving in regular manners.

    ID sympathizers believe the reason he makes the universe behave in somewhat predictable ways is to make the universe comprehensible to humans. But there is nothing stopping God from changing his convention.

    Something Cavin and Comlumbetti forget. The scientific enterprise has only an infinitesimal sample of observations from which they are extrapolating to astronomical scale. In statistics, this is highly suspect if outliers exist.

    For example, I could write a computer program that spits out the number 3 every second, and then once a year it spits out 7. Not hard for a designer to do, but using the scientific method on small samples, say a day of samples, someone could argue

    the program obeys the following ‘law’, it spits out the number 3 every second, to violate this law would be a miracle, therefore a miracles of 7 popping up is impossible

    Such an argument would be absolutely silly, but that is exactly what Cavin and Columbetti are doing, just on larger scale!

    Famous IBM physicist Rolf Landauer said the laws of physics are algorithms, and the universe is the computer. Well if the laws of physics are algorithms are, we are only describing them like the chap who is sampling a small behavior of the program to make conclusions about what “laws” govern the algorithms, except that proportionally, our sample size for all known science is even smaller than my illustration, probably by several orders!

  4. Very nicely stated, Sal.

    Here’s an experiment that I once challenged my kids with. I removed all the playing pieces off a chessboard except for a pawn in the middle. I told them, “guess the rule” and moved it one square diagonally. Then another in a different direction, and so on. Then, I began moving it two squares horizontally or vertically. The guesses kept coming. Finally, I moved it four squares forward. Eventually, they demanded to know what crazy rule I had in mind, and I confessed that the rule was “two legal knight moves in succession.”

    Rules are models (or algorithms). Each model they proposed was correct, useful for a while, but incomplete. They are also hard to guess.

    -Q

  5. Dr.Greg Cavin and Dr. Carlos should realize that when God is brought into the equation, there can be no arguments. As I have been saying in various threads God in equation leads to infinite path. There can be no finite solution at all. In fact, there is no way to check whether we are following the right path to solution. God can make His own rules, God can change probability distribution, God can gain mass and appear (when Quantum particles can gain mass, why can’t He?), so there can hardly be an argument when there is no constrain. For all we know, there can even be a solution for Squareroot[-1]

  6. Hi Sal,

    Thank you very much for your highly insightful comment. I was so impressed that I updated my post and added a link to it, for the benefit of readers. Thank you once again.

  7. Hi selvaRajan,

    I completely agree with your point regarding God’s freedom to make His own rules and change them at will. It is, after all, His universe.

  8. If no one minds I would like to bring into the picture another view of God as related to this subject of the relationship between transcendence and immanence.

    In Samkhya and Vedanta theology God creates multiple universes (all full of life) in order to accommodate the desires of a minority of souls living with Him in the transcendental world to explore what it’s like to NOT be in the presence of God and also to imitate God. God’s unique position is that He loves himself by way of his power/energy (designated in Vedanta as shakti-the female principle). I know how it sounds, but God, in the Vedantic understanding, is a simultaneously one and at the same time a dual being: Himself and His energy, who is also a free conscious agent equal to Himself. It is this divine play between God and his energy (which can take many forms) that is all of existence.

    A small part of that female principle energy emanates further conscious individual souls, who are infinitesimal but nevertheless of the same nature of God, in the idea that these souls would be also free to enjoy a relationship with God.

    At the same time, another part of God’s energy/shakti (which is conscious substance) freely and consciously but temporarily becomes unconscious and thus manipulable, exploitable, usable without consent. It is the way God defines how He is NOT, what He does not like.

    Of course this also has another purpose because in this way God gives the souls (who are infinitesimal and thus vulnerable to being covered by illussion) a choice between choosing to be in His direct presence or choosing to enter the (temporarily) unconscious energy and lose sight of Him and try to enjoy the energy without God. Much like a person at a court of the king wants to enjoy the king’s palace without the king, taking the position of the king. Since this is impossible in the absolute sense, because only God can be God, the souls are injected into the material universes made of unconscious energy to both give them an (illusory) experience that they are the masters of their fate and to provide opportunity for reform so that, ultimately, the soul would be able to freely choose to appreciate God and be received back in the spiritual world.

    Sorry for the big introduction, but it is at this point that God’s relationship with the material universe can be explored in the Samkhya-Vedanta school: The laws of the universe (including the law of karma and the laws governing the repartition of souls in various bodies) are acting impersonally so that the souls wanting to enjoy matter and exploit it can do it in a way that would keep the balance. The coherence and stability of universal laws are actually an expression of God paying continuous attention to the universe and empowering, activating his unconscious energy to act according to his orderly will for the universe, much like, say, a prison system is working seemingly automatically and in repetitive patterns because it is the will of the State for it to be so, for certain purposes: the reformation of the inmates. Of course while in prison the prison guards and the warden are visible, in the Vedanta paradigm the bars, guards and the warden are invisible, because this place is not only a place of reformation but also one in which the souls want to enjoy the world.

    So God, being always in control of his material energy is keeping the laws constant because his conscious will is, like I said, energetic, factual.

    Now, this is not as simple as it sounds, because God can also change the effect of the laws or allow a soul to change the effect of the laws under certain conditions, which, in a way are another form of the law (imagine a parallel system of exceptions). The rule in Samkhya-Vedanta is that the more one practices austerity and detachment from matter the more freedom God can give that person to act within matter and even above the “normal” laws. There are multiple practices that achieve these things, but the best ones, the ones that, according to Vedanta, God recommends is for the soul to concentrate on understanding God and devoting themselves to His will and not worry about detaching from matter, because it will happen automatically, whereas if one just concentrates on detaching from matter without an interest in God it is much more difficult. The release from the laws of matter for the souls happen at the moment when they are fully but freely devoted to God and are ready to be received back into the spiritual world.

    In conclusion, according to the Vedantic view on God’s relationship with the world, it is His will that the world works much like a machine, governed by laws that He maintains constant, while it is also His will that there are exceptions to the laws when the soul behaves in a certain way, like detaching from matter or attaching themselves to God.

    I think this view seems similar to Augustine’s.

  9. Tarmaras, beautifully explicative, even in a non-temporal sense which I believe is the essence of god’s existence, atemporality. His existence outside (or away yet part of) space-time accounts for, I think, the non-neuronal aspects, viz., A. Suarez, of quantum entanglement.

  10. Quantumman glad to find interest from you for these ideas. In terms of time, in the vedic understanding there are three conceptions of time:

    1. time as a formal sequence of events of consciousness (which is actually living in an eternal NOW)
    2. time as the structured and programmed decay of the arrangement of matter until the annihilation of order in the universe
    3. time as in terms of universal cycles and seasons, having to do with the manifestation of destiny

    According to the Vedas, the soul experiences 1., 2. and 3. as laws of the material universe, while 1. is present even beyond this world. So, even in the spiritual realm, where there is substance and form there is only 1. time . Actually the substance and form existing in the absolute world is the ideal of which our world is but a pale simulation –kind of like Plato’s ideas– but the substance is actually fully conscious all over and the form is freely chosen and subject to change at will. Like I said before, in the ultimate understanding there is nothing but consciousness and even matter is just conscious energy subjecting itself to temporary unconsciousness for a purpose: to give is some raw material to play our silly games away from the parents :) (prodigal son fable comes to mind).

  11. Thanks, Tarmaras. I like your comments about “1 time as a formal sequence of events” which implies cause and effect in other realms (non physical) I think. Your comment in “2.” implies the concept of God not being bound by the Second Law of Thermodynamics, which is anathema to all physicists in this realm – me being one but I am of this realm currently so I have no choice.

    You are correct in that I also think we are unconscious in our material form (becoming more conscious in dreams and sleep) and are waiting with hope (as prodigals) to return to the God head (or is it Atman or Brahmin – I get the two confused).

  12. Quantumman, good to hear from a physicist. Whatever goes past Calculus is transcendental to me.

    I just wanted to correct myself in case I have misrepresented or partially presented the “unconscious energy” concept; according to Vedanta, the unconscious energy (the mahamaya-shakti) is not us, it is our covering, our virtual reality suit into which we are put in order to disconnect us from the transcendental realm. But we remain conscious; even in dreamless sleep we are conscious, but because our souls rests in a state in which there is no form to perceive we don’t have anything to remember (this is a complicated concept and I think I’m already abusing this space). In short, according to this view, the soul is conscious but conditioned/incastrated/covered by the unconscious energy, maya (literally “that which is not what it seems”), and because this energy is manipulated by God according to his will it takes any form He likes, and he likes it to take the form that is suitable for us to play with. We never really control matter we just express our desires as souls and the rest is being taken care of by a sophisticated arrangement by God’s active will, His immanent aspect (again, very complicated).

    The Godhead is called Krishna (‘the all attractive’) or Rama (‘the source of bliss’) or Vishnu (‘the all pervading’) and its binary counterpart is Radha, Sita or Lakshmi, respectively (His energies). Another name for the Godhead is also Paramatman(‘the supreme self’), Parabrahman (‘the supreme Absolute/Unconditioned’) or Purushottama (‘the supreme person’). As for us, we are atman, with small a, infinitesimal emanations, of the same quality but not quantity as the Godhead. We are atman (meaning conscious self) and we are also brahman (meaning of the unconditioned/free nature). So our goal, according to Vedanta is to reconnect with the Paramatman, the supreme self, and start where we left off. At least, that’s what Vedanta says.

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