Computational Irreducibility Begins to Bite

One way to think about prime numbers is as follows:

Take a one dimensional binary pattern with all the bits set to zero. Now take the number a and starting at bit 2a set the binary bits at 3a,4a,5a etc, thus effectively describing a periodic pattern of set bits with an interval of a. This simple selection scheme for setting bits can be represented by the elementary mathematical function y = an + a where n =1,2,3,4..etc and where values of y gives us the locations of the bits that must be set.

Now, let us carry out this process of setting bits for all values of a = 2,3,4,5,6,7…. until limited by the length of the binary pattern. When this procedure has been completed all the bits that have not been set are placed at bit locations whose position value is a prime number. Basically a prime number is a number that doesn’t get selected by any of the periodic selection schemes defined by the equation with form y=an+a.

Now consider the mathematical object called “The Ulam Spiral of primes”, a concept that I got from this very interesting blog post by Mark Chu-Carroll. In the diagram below the natural numbers are arranged in spiral pattern and the primes are plotted in red.

If this process is continued and viewed from a distance this is what you get:

As MarkCC puts it:

Look at how many diagonal line segments you get! And look how many diagonal line segments occur along the same lines! Why do the prime numbers tend to occur in clusters along the diagonals of this spiral? I don't have a clue. Nor, to my knowledge, does anyone else!

Intuitions about it are almost certainly wrong. For example, when I first thought about it, I tried to find a numerical pattern around the diagonals. There are lots of patterns. For example, one of the simplest ones is that an awful lot of primes occur along the set of lines f(n) = 4n²+bn+c, for a variety of values of b and c. But what does that tell you? Alas, not much. Why do so many primes occur along those families of lines?

Interpreting this spiral diagram in terms of the 1-D binary pattern model, these 2-D spiral models are another way of generating a “bit set” selection scheme, except that these schemes are not periodic but instead the space between selections is increasing in proportion to value of n – this leads to the n² term in MarkCC’s expression. What MarkCC is telling us is that some of these selection schemes pick up a high frequency of primes. He then asks the pertinent question:

Why do so many primes occur along those families of lines?

When I heard that question the first useful thought I had was to think of Stephen Wolfram’s work on computation and in particular of his concept of computational irreducibility. Taking our cue from Wolfram the answer may be that there is no answer to this question of “why?” other than to carry out the computation itself. Let me explain:

The time required to arrive at certain computed patterns cannot be shortened beyond a minimum computation length. Wolfram brings this concept out into sharp focus: He tells us that this irreducibility means what it says: Once we have the minimum length computation in our hands there is, by definition, no other computation available to demonstrate the result any quicker.

If computational irreducibility applies to the case in point then it would mean that the only way to show up those diagonals with a high incidence of primes is to do the long calculation of generating the spiral and the primes. When we ask the question “why” in this context we are, I suggest, looking for a succinct analytical answer to the question in the form of some relatively simple algorithm demonstrating the pattern in a relatively short execution time; in other words an analytical short cut. But according to Wolfram there may be no simpler way of demonstrating the pattern than to do it the long way. Or rather, the long way is in fact the short way because there is no shorter way to do it!

Of course, we don’t know for a fact that this particular problem is computationally/analytically irreducible. But even if it is reducible we may still find that the solution to the meta-problem of determining whether or not a task is reducible is a computation that itself is plagued by the limits of computational irreducibility.

I believe the generality of Wolfram’s views on this subject are valid. I also believe that it is possible to get an intuitive feel for why they are valid. As I have already said, when human beings ask “why?” they are asking for an answer in the form of some “short” algorithm that succeeds in arriving at an answer in a “short” execution time. We are human after all and we have limited space and limited time. Unsurprisingly, then, we want answers to be reached using as little space and time as possible. But if we are going to limit space and time the computations that are open to algorithmic demonstration are going to be accordingly limited; the reason for this is fairly obvious: As soon as we make stipulations limiting computational resources those stipulations automatically exclude the overwhelming number of computations that utilize either large algorithms or large execution times (or both). The number of short algorithms executing in short time is a limited resource and their allocation to problem solution runs out long, long before they have covered the whole domain of solutions. Thus the absence of a simple analytical solution to the question of the spiral and primes may be evidence of the demand pressure on the relatively short supply of succinctly performing algorithms: The demand for fast succinct algorithms outstrips their supply and thus most problems will have irreducibly long winded solutions.

The Myth of God Incarnate

Who needs a liberal theologian to interpret the Bible’s message when we’ve got Saint Paul here to do the work for us? See here for the story (The above picture of PZ Myers was taken while he was playing on the rides at the local creationist doctrinal bargain basement) .

Problems in Young Earth Creationism Part 3: Egocentricity Geocentricity.

The incorrigible Doctor Bouw: Answers in Genesis don’t like the look of him

As a natural follow on from my two blogs on Young Earth Creationism (here and here) I must make mention of this guy, Gerardus Bouw a fundagelical geocentrist. That’s right, you didn’t mishear me, I said geocentrist; that is, somebody who believes the Earth to be stationary and at, or near, the centre of the universe.

In my last blog in this series I looked at the theory of YEC Russell Humphreys who, as he tried to solve the YEC starlight problem, took a lurch toward geocentricity. However, in spite of that Bouw is not exactly flavor of the month with mainstream YECs. One of the Answers in Genesis writers, Danny Faulkner, had a very sharp exchange with the incorrigible Doctor Bouw . But more about that later.

So, just how can someone seriously maintain an eccentric a geocentric view in the light of today’s knowledge? Well, you’d be surprised. Here’s how it can be done in two stages:

Stage 1: Coordinate system change.

The first stage involves a mathematical trick, a trick that is valid even under established astrophysics: One simply selects a coordinate system where Earth is at the origin, stationary and does not rotate. But if you do this don’t be surprised if one’s equations of motion turn out to be a noncovariant, complicated, and inconvenient. Coordinate systems are often selected for their mathematical convenience in the sense that one selects the system that makes the equations of the problem one is interested in as simple and convenient as possible. For example, if one is studying the proper motions of stars it is unlikely that one would choose a coordinate system that set the Earth’s rotation to zero because the stars would then possess huge rotational velocities that would increase in proportion to their distance from earth.

However, if one is so minded there is nothing to stop one using the Earth as a stationary non-rotating frame even though it may return rather perverse equations of motion. In fact going a step further, one can be completely non-committal about the interactions between heavenly bodies and proceed purely kinematically – that is, one proceeds only on the basis of the observed motions in the sky without regard to any dynamical theory of motion that posits the use of fields. This kinematic approach was, by necessity, the approaches of Ptolemy (2nd C) and Tycho Brahe (16th C) because these astronomers predated mechanics and gravitation. By creating models that superimposed a variety of circular motions Ptolemy and Tycho returned schemes that gave reasonable fits to what was observed in the heavens. In fact I suspect that if one tries hard enough using the Ptolemaic and Tychonian methods of using "wheels within wheels" to build the periodic motions in the heavens even better fits could eventually be achieved. The reason for this is that what is being carried out is a form of Fourier analysis of the motions. By the introduction of more and more harmonics in the form of circular motions one is effectively introducing more free variables that can be adjusted to improve fit. In fact Bouw himself seems to use the trick of multiplying variables (or “entities” as Occam would have it) in his desire to make a better fit: He does this by carefully distinguishing between what he calls geocentrism and geocentricity. According to Bouw:

In geocentricity, the earth is static, but not necessarily at the center if the universe. In geocentricity the earth is actually offset from the geometric center of the universe.

Thus, offsetting the Earth adds another free variable that can be adjusted to improve the fit of a geocentric frame of observation.

Stage 2: Positing an Ontologically Static or Preferred Frame.

Stage 2 is really the stage that sorts out the heathen from the cranks true believers. If one is going to insist on using a coordinate system that makes the linear and rotational motion of the Earth zero then there must be a good physical reason why this preferred frame of reference is used. Just to claim that the Earth is stationary on the basis of sheer strength of assertion is not enough – one has to make clear that it is stationary with respect to something, presumably something significant and important enough to warrant one’s claim. At a quick reading of Bouw’s views it seems that he posits something he calls the plenum (to be identified with the Biblical firmament in his estimation). The plenum is an ether like substance that provides the stationary absolute frame of the cosmos. With respect to that frame, according to Bouw, Earth is stationary and near the centre. And with respect to that frame the stars on the edge of the universe are rotating at unbelievable speeds as they circumnavigate the cosmos all in one day! In Bouw’s view the cosmos has some kind of holistic property that holds it all together as it rotates round the Earth.

Let Sleeping Dogs Lie.

I’ve no idea how Bouw explains such things as the dynamics of the weather which are affected by the centripetal accelerations that effectively define what "a rotating Earth" means. It looks to me as if Bouw is engaged in a one man rewrite of physics. But frankly the details of Bouw’s theories are not at the top of my hit list. In any case I suggest we leave him to his own devices and not mix with him for reasons that will perhaps become clear as I move onto to the next section. Like many other fundagelicals (such as we see at Answers in Genesis) Bouw believes he speaks with the authority of the Word of God and thus his righteous wrath is terrible to behold, as the man from Answers in Genesis, poor Danny Falkner, found out!

Geocentricity and the Bible

Let me say from the outset that the Bible is certainly geocentric in its point of view and for good reason: Suffice to say here that the Bible was written by arcadians whose natural perspective was that of an Earth rotationally and linearly static, with all motions being referenced with respect to this frame. A coordinate system where the Earth is stationary and not rotating is far more useful to the man in the street or the man working the furrow than a system where the Earth is considered to rotate. The arcadian's “coordinate system” which posited a static Earth as a preferred frame is perfectly valid for their purposes (But it is unlikely that they had in mind anything like Bouw's “plenum”.) In fact even today at the level of street and furrow a static Earth is a more useful frame than the frames used by astronomers who have other purposes.

However, let me now give you a sample of Bouw’s use of the Bible. His use of scripture is certainly worth comparing with that of YEC Russell Humprhreys. In my last blog entry on this subject I indicated how Humphreys was anxious to show that the Bible proved the Earth to be in a gravitational well. The following quote contains the “proof text” he pulled out of the hat:

But in a creationist cosmos having a center of gravity, if you were to travel outward from the center you would, on the average, go steadily "upward" in a gravitational sense. On a large scale, the heavens would be at a higher gravitational "altitude" than the earth. As Isaiah 55:9 says: "For as the heavens are higher than the earth . . ."

Now, compare that merciless violation of a Biblical metaphor with the way Bouw uses scripture in the samples provided below: (See here for the source of the quotes below)

Bouw: The earth is immobile as seen from outside the universe, that is, as seen from the third heaven, the location of the throne of God. (Note: a footstool is not a footstool if it is moving – Isa. 66:1.) And why heliocentrism instead of a-centricity or acentrism? Because the modern acentric model still divides the universe into unrelated sections; and because it was founded on the worship of the sun.

My Comment: Notice how the footstool metaphor has been interpreted to convey a literal message about motion! Are we then to interpret this to mean that the Earth is literally a footstool? Does it mean that God has feet and legs? Is it intelligible to talk of God as if He is an out-sized humunculus with a stationary frame of reference? Whether or not the Earth is moving when viewed outside the universe depends on entirely on the frame of reference – we could quite easily use a frame of reference which puts the Earth back into motion. What I think Bouw really means here is that the Earth is static with respect to his conjectured “plenum”. Notice the innuendo linking the heliocentric solar system with Sun worship. I bet the fundagelical Faulkner loved the hint that he is a crypto sun worshiper! Bouw is looking for some deep spiritual crime to hang his righteous wrath on: To this end he can satisfy himself that there is an idolatrous slant in current science, a sin punishable by death in the Old Testament.

Bouw: One of the arguments that creationists use against geocentrists is that geocentricity destroys the credibility of the creationist in the eyes of unbelievers like these two men. What makes them hard to win to the creationist cause is that they clearly see the hypocrisy. They have more insight into the nature of the argument than Faulkner has, for they cannot be “snowed” by illogical arguments. Geocentrists find that most atheists will acknowledge, as de Morgan, that geocentricity is science, whereas they will never admit that of creationism. Indeed, on a personal note, it was people like Danny Faulkner and Hugh Ross who converted me to atheism in my teen years. How? Because according to them, science led the way to the truths of heliocentrism and evolution while the Christian scholars needed thirty years or more to “come around.”

My Comment: According to Bouw AiG have not gone far enough: They must embrace geocentrism in order to help spread the Gospel rather than compromising with the heliocentric scientific conspiracy. However, I haven’t noticed ex-atheists queuing up to become geocentrists

Bouw: Here are the three strongest geocentric scriptures.

Joshua 10:13 says:

And the sun stood still, and the moon stayed, until the people had avenged themselves upon their enemies. Isnot this written in the book of Jasher? So the sun stood still in the midst of heaven, and hasted not to go down about a whole day.

Ecclesiastes 1:5 says:

The sun also ariseth, and the sun goeth down, and hasteth to his place where he arose.

And Malachi 4:2 says:

But unto you that fear my name shall the Sun of righteousness arise with healing in his wings; and ye shall go forth, and grow up as calves of the stall.

In Joshua 10:13 it is the sun that is said to stand still. God could have said “And the earth stopped turning so that the sun appeared to stand still,” but he didn’t. In effect, Faulkner claims that since it was inconvenient for God to tell the truth, he promoted the commonly accepted story, although the Holy Ghost knew it not to be true. How then can God say that he is the God of Truth and the Spirit of truth? Indeed, God’s creative power is such that his very speaking “the sun stood still” would instantly have transformed the acentric cosmos unto geocentric. It has been noted by scholars that God cannot lie because if he ever did, then the “lie” would immediately come to pass and it would instantly no longer be a lie. This they believe because God spoke the universe into being when it was not. So in a very real sense, to be consistent, those that reject the geocentric model must also reject the creationist model.

In Ecclesiastes 1:5 it is the sun that ariseth, goeth down, and hasteth. Again, God could just as well have spoken the “geokinetic truth” by simply adding the sense “seemeth to” before each of the three actions. That is, to say instead “The sun also seemeth to arise, and the sun seemeth to go down, and seemeth to haste to his place where he arose. Why did God persist in his geocentric “error”?

My Comment: Those scriptures are explained as the natural and perfectly acceptable geocentric frame and perspective of the arcadian (and moreover of any modern man in the street). But for Bouw anxious to accuse of heinous error it’s an all or nothing dichotomy: The concept of “perspective” isn’t in his book, and he doesn’t allow different perspectives to be right at the same time. Witch hunters have never been very sensitive to the notion of perspective and for Bouw the choice is between his version of geocentrism or apostasy. Notice also Bouw’s view that God “spoke the universe into being” in the manner of the magician who says “hey presto!”. In this respect his views are very similar to AiG’s concept of a God of Magic.

Bouw: In the light of this, his (that is Danny Falkner) charge that geocentrists “offer a very easy target of criticism for our critics” is revealed as sheer nonsense. Evolutionists, atheists, and agnostics in the know can easily shame creationists on the issue of geocentricity by simply pointing out the hypocrisy of their insistence that the days in Genesis 1 are literal while the rising and setting of the sun is not. Likewise, to insist that the rising of the sun is figurative while the rising of the Son is literal is also hypocrisy. Given that the geocentric model is pure physics, mathematically tractable, and realistic, and consistent with Scripture, we conclude that the creationist’s desire to reject it can only be for the sole purpose of appearing intellectual and acceptable to the world, which desire is enmity with God (James 4:4). The creationist movement is fortunate that evolutionists don’t understand these simple issues, for if they did, creationists would be shamed and held contemptible even more than they are now.

My Comment: It seems that Faulkner doesn’t want to look as though he is “with” Bouw! The self righteous indignation of Bouw (always the prerogative of those who know they are right) boils over and he shouts “hypocrite!” What Bouw is unlikely to appreciate is that Faulkner is probably right; AiG would be held in even more contempt if they became geocentrists.

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Bouw has given the YECs at AiG a taste of their own medicine; namely, a dose of crass Biblical literalism. This literalism is used as a pretext for a self righteous tirade toward those who don’t share their interpretations and who are then accused of compromise. This whole incident is a fine example of how fundagelicalism often works against itself when two opposing sides who claim to have the very “Words of God” meet and slug it out in the name of the Lord. The irresistible force meets the immoveable object! Bouw’s approach to the Bible is like that of Humphreys, only more so, thus inadvertently caricaturing and satirising AiG. Indeed, if we are to accept AiG’s approach to scripture then why not go the whole hog and, as one fundagelical preacher once put it, believe “the Bible tells it like it is” and accept Bouw’s geocentrism? No, the Bible tells it like arcadians saw the universe and that must be borne in mind. But for Bouw and AiG religion is all about their elaborate trappings of piety; namely, their concepts of right practice and right belief. And if one doesn’t accept these elaborations one may come in line for some heavy shepherding: For Bouw gives dark hints about the association of heliocentrism and idolatry and AiG writers refer to Christians who disagree with them as merely “professing” Christianity. Religionists such as AiG and Bouw pay lip service to God’s Grace: For them salvation is intimately bound up with assent to their doctrinal articles about cosmology and a move away from these beliefs is treated as a potentially grave sin. Such is the authoritarianism of those who identify their interpretations with the very Words of God.

The Anti Gravity Road Show.

John Hutchinson's House: Style over content?

I was interested to see that the web site American Antigravity (headed up by Tim Ventura*, I think) has come back on line again. It’s a fascinating mix of off-beat techno-wizardry spiced up with rumour of the impending riches of a paradigm shifting science just round the corner. I was interested to see the pictures of the Hutchinson road trip showing John Hutchinson’s laboratory-cum-house.

Inside: Wall to wall electronics

The great, legendary and eccentric Hutchinson himself appears in the pics. This guy doesn’t use wall paper but instead decorates his house with heavy duty electronic appliances salvaged from defunct naval ships that have been teleported into the Arizona desert. However, just how much is style and how much is real content I’ll never know!

Ground breaking pioneers or just lads at play?: Tim Ventura far left, John Hutchinson third from left.

What a bunch of lads. They make me laugh. The academic establishment just can’t derail their show and quash the rumour of ground breaking science. In fact any attempt to do so just adds fuel to their fire! How utterly annoying for all those serious academics! At one time everyone, apart from the odd Galileo or Luther, believed in the establishment. Now that the “rationalists” are at the helm, however, no one believes the establishment! “Unstable self-defeating philosophies” is the phrase that comes to mind. The seeds of antithesis are buried deeply in the “rationalist” mindset.

* I did a post on Tim Ventura here

Idiot Proofing Thermodynamics

Many thanks to Graciel Ilar for commenting on my post here and kindly providing the “open system” argument (with actual numbers plugged in - see below) showing that evolution doesn’t violate the second law of thermodynamics.

Although this argument is, in my opinion, valid it is not sufficiently idiot proof to convince those who are too intuitively compelled by the apparent antithesis between the rubric “increasing disorder” and evolution. For example, Granville Sewell of Uncommon Descent affiliation is not convinced by the open system argument.

For non-technical readers, the gist of the open system argument is actually easy to understand: It observes that the reduction in entropy required by life is extremely large. But the Earth is an open system that receives useable heat from the Sun implying a concomitant increase in entropy as the Sun uses up its store of free energy. Thus the increase in entropy of the Sun-Earth system as the Sun transfers heat to the Earth by far and away overwhelms the relatively small decrease in entropy required by life, thus restoring an overall increase in entropy. The weakness of 2LoT as a measure of what is going on is that it only tells us what is happening in the total “bank account” and not the sub accounts: There may be an overall loss in cash, any yet some accounts could still be increasing, but not fast enough to compensate for the general downturn in fortune.

Anti-evolutionists do not understand this argument because they just cannot see where the information is coming from to configure those ordered yet complex life forms. For them there is a strongly sensed intuitive contradiction between the compelling rubric “increasing disorder” and the localized increases in complex order we see with evolution. They have no trouble with crystal formation because they can see that the information here is coming from the laws of physics in a fairly straight forward and accountable way, but they just can’t see how the laws of physics do this for the “crystallization” of living structures.

The reason why anti-evolutionists often stumble on the entropy argument is that they don’t really understand what entropy measures. Entropy is given by S = k Log Z where k is Boltzmann’s constant and Z is the number of microstates consistent with a macro state. In the word “consistent” is embodied all that the laws of physics allow, or rather don’t allow: For the laws of physics themselves are not subject to entropy increases and they eliminate huge numbers of possible universes; thus, with respect to all that is possible our universe is highly ordered even at its most disordered. Therefore a system can move toward maximum disorder and yet remain highly ordered in an absolute sense.

However, what I would concede is that even though 2LoT is too loose a mathematical statement to contradict evolution in and of itself this doesn’t mean that evolution has actually occurred; it is conceivable that the laws of physics simply don’t eliminate enough paths through phase space to make evolution even remotely probable. Hence a measure of open mindedness is required. But I’m not open minded because people like Granville Sewell fail to understand thermodynamics and present superficial arguments against evolution; he’s going to have to think a lot harder if he is going to bring down evolution. Sewell often asks the rhetorical question “Can anything happen in an Open System?” expecting the answer “no” to be the answer unfavourable to evolution. But the irony is that if evolution has occurred it would be precisely because physics prevents anything happening in an open system that evolution is favoured!

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Mr T Reeves thank you for an insightful article. It has been proven beyond reasonable doubt that Evolution does *not* violate the 2LOT. Excerpt from the article:

When heat is transferred from one object to another, there is a change in entropy associated with that transfer:

dS = Q/T

where dS is the change in entropy, Q is the quantity of heat transferred, and T is the temperature of the object.

The earth is being bathed in radiation by the sun: the sun is giving off energy, some of which is received by the earth.

The rate of energy transfer is known:

P = dQ/dt = 1.2 x 10^17 W

when you sum over the whole surface of the earth; this is how much energy the earth receives from the sun per second (i.e. a lot).

Thus we can calculate the rate of entropy production of the earth/sun system:

dS/dt = P/Te - P/Ts

where Ts is the temperature of the sun, and Te is the temperature of the earth.

Since the sun is ~20x hotter than the earth, the P/Te term is ~20x larger than the P/Ts term.

Thus

dS/dt ~ P/Te

and plugging in numerical values, P ~ 1.2 x 10^17 W and Te = 300K,

dS/dt ~ 4 x 10^14 J/K/second

The gist: dS/dt is positive, and it's HUGE - the entropy of the sun-earth system is extremely rapidly increasing with time!

(Note that this does not include the eventuality that this radiation will (though on extremely long timescales) thermalize in deep space with the 3K CMB, which results in a further increase in entropy about 100 times larger!)

Now, how much of an entropy *decrease* is associated with the evolution of life? If it's greater than the above, there is a problem. But if it's less than the above, then the second law is satisfied, in that

deltaS_total = deltaS_sun + deltaS_life > 0

This can't be done as rigorously, but estimates can be made.

However, from thermodynamics we have the result

mu/T = -dS/dN

which, rearranged, gives us

deltaS = -N*mu/T

where mu is the chemical potential for a molecule and N is the number of molecules on the earth's surface.

The reduction in entropy due to the formation of life on earth (which we may consider as an ordering of all the molecules forming the earth's biomass), relative to that of a barren earth, is thus:

deltaS_life = S_earth_with_life - S_dead_earth ~ -Nb*mu/T

where Nb is the total number of molecules in the earth's biomass.

For a typical ideal gas, mu ~ 10*kb*T where kb is Boltzmann's constant.

The total biomass of earth is Nb ~ 10^41 (about 10^15 kg). Even multiplying by a factor of 100 to account for nonliving matter that might nevertheless be crucial to the evolution of life, Nb ~ 10^43.

Plugging the numbers in (including the factor of 100), we find that

|deltaS_life| ~ 10^44 * kb

This is a HUGE value, which leads to the mistaken impression that evolution violates the second law of thermodynamics.

However, let's compare that to the earlier value we found for the rate of increase in entropy due to the sun's radiation:

dS/dt_sun = 4 x 10^14 J/K/s = 3 x 10^37 kb/s

Dividing the two by each other

deltaS_life / dS/dt_sun = 3 x 10^6 seconds = minimum time allowable for evolution of life

3 x 10^6 seconds is about a month.

Conclusion: As long as the evolution of life on earth took more than about a month, it does not violate the second law of thermodynamics.

Even YECs agree that the earth is more than one month old.

Note that this does *not* imply that the evolution of life took a month; this is a highly idealized situation and only derives a lower limit on the time using basic physics.

The actual evolution of life took much longer, by a factor of billions.

But just one month of insolation adds enough entropy to the earth to offset the entropy decrease required to form all of the biomass on earth.

Even if this were an underestimate by a factor of a thousand, then only one hundred years would have been required to offset the reduction in entropy caused by the evolution of life.

Problems in Young Earth Creationism Part 2: Star light travel time.

In part 1 of this series I introduced the Star light travel time problem; that is, how can the YEC community maintain the Earth to be only 6000 years old given that light from the stars appears to have traversed distances of millions and even billions of light years? In this post I will be looking at the ideas of YEC theorist Ross Humphreys who attempts to solve this problem.

In my last post on this subject I mentioned the book “The Genesis Flood” published in 1961 by Whitcomb and Morris, a book which seriously put forward the suggestion that photons were created in mid flight. This is the “mature creation” theory; the view that God creates “as seen” even if it means building in the appearance of some kind of bogus history; for example, in the case of star light the Creator has to contrive pulses of light from supernovae that never happened, amongst other shows of faux history. What YECs euphemistically call “mature creation” is an adhoc philosophical bodge that quickly turns into an intellectual quagmire. As many critics have pointed out, “mature creation” so easily succumbs to a reduction to the absurd: It conjures up a picture of a deity who creates in such an arbitrary fashion that science and knowledge are undermined. It introduces the concept of artifice into creation and ultimately subverts even the assumptions needed to interpret the Bible.

Not surprisingly, then, in order to restore the concept of a Creator who creates with integrity thus restoring the concomitant integrity of science some YECs have tried to move away from the highly concocted and contrived notions of mature creation. Some YECs at least want to be seen attempting to do some real science; after all if they want to convince us that evidence of a young 6000 year old Earth is all around us, they will have to concede that the Earth really does provide signs of its true history and not merely a faux facade of its age. Likewise, if they want to be taken seriously on the star light problem YECs have to advance a scientifically tractable solution that does justice to such phenomenon as super novae.

A reviewer of Humphries at Answers in Genesis admits the problems YECs have:

Creationists who believe in short timescales of Earth history have had a few problems with cosmology. Criticisms of the standard Big Bang model have often been made, often drawing on voices of dissent coming from the academic community. However, the positive statements of a creationist cosmology have yet to emerge. ...Light from distant galaxies...... The distances are immense, with some of the estimated times of light travel measured in billions of years.

It's news to hear a YEC admitting that they have “a few problems with cosmology”, but it’s hardly news to hear that a positive YEC cosmology has yet to emerge; as many have remarked YEC “science” tends to be a science of negation – that is, no propounding of theories that join the dots of observation, but rather a seeking to undermine established theories; theirs is the strategy of tearing down rather than of building up. This negative approach is, in fact, very much in keeping the fidiest anti-science strain one often finds in “fundagelical” Christianity. This fideism is apt to label science as “man’s wisdom”, a wisdom which must be scorned and eschewed in favour of the divine gnosis that comes with a gnostic conversion that transcends reason. That is, up until now!

OK, so Humphreys has at last provided a positive statement of YEC cosmology - so what is it?

Let me start by emphasizing how basic and elementary this problem is. It involves one of the first formula I learnt in science and maths: Velocity = Distance/Time! Or in this particular connection we can express it as:

Speed of light = Distance to galaxy/ Light travel time.

This simple formula involves no appeal to some highfalutin and complex big bang theory involving multiple speculative hypotheses, but an elementary mathematical relationship between fairly well established quantities such as the speed of light and the distances to galaxies. When these values are plugged into this equation they return light travel times running into millions if not billions of years. Unlike some other YEC attempts to deal with this problem Humphreys appears to want to preserve the speed of light. (and for good reason since it is such a fundamental constant in the equations of physics). So, given that Humphreys also accepts that the distances to the galaxies may be measured in billions of light years how does he accomplish the impossible of returning a light travel time of around 6000 years? Well, the short answer is that he doesn’t….

And now for the long answer….

Neogeocentrism

In this web article Humphreys says the following about his theory (A theory he published in his book “Starlight and Time”):

In contrast to the big bang story, the Scriptural record appears to imply that the universe is in fact, an island universe. Appendix B of Starlight and Time shows Biblical evidence that (a) the cosmos has a unique center and a boundary for its matter, beyond which there is at least some empty space; and (b) on a cosmic scale of distances, the earth is near the center.

In other words Humphreys starts by assuming a finite creation with a centre of gravity; in fact according to this reviewer on AiG Humphreys assumes that all we see in the heavens today was initially concentrated in a radius of 1 light year or more. Humphreys proposes that the Earth is somewhere near the centre of this island universe and this is crucial because of what happens next: Some kind of inflation then occurs expanding the island universe and so…

…. it turns out that when the expanding universe was at a critical size (about fifty times smaller than it is now), gravitational time dilation would have been very important. My theory proposes that the cosmos was at that critical size during the fourth day of Creation Week. While one ordinary day was elapsing on earth, billions of years worth of physical processes were taking place in distant parts of the universe. This allows starlight from even the most distant star to arrive during or soon after the fourth day, the same day God created all the stars. During that day, most of the expansion of the cosmos would have taken place.

In short Humphreys is proposing some kind of asymmetrical big bang – yes, he’s actually proposing a big bang – but because the distribution of matter is asymmetrical, (that is, concentrated in a finite volume in this case) this leads to clocks running at different rates in different parts of the universe. In particular, near the centre of the big bang where the high concentration of matter implies that space is highly compressed, clocks will run more slowly than those that those less centrally placed during the inflationary period. This is the trick that allows Humphreys to deduce that time on Earth passes much more slowly than elsewhere in the universe; and it is this trick that allows light to creep at a snail’s pace across the universe for billions of years to reach the Earth where an initially high space compression slows clocks down to the point where only a day or two has elapsed!

The asymmetry or non Copernican nature of Humphreys’ cosmology is very clear from this quote:

But in a creationist cosmos having a center of gravity, if you were to travel outward from the center you would, on the average, go steadily "upward" in a gravitational sense. On a large scale, the heavens would be at a higher gravitational "altitude" than the earth. As Isaiah 55:9 says: "For as the heavens are higher than the earth . . ."

I’m always amused by the way YECs manage pull out of their hats very novel and unexpected literal readings of poetic Biblical metaphors that somehow fulfill their theories! But quite apart from that, when I read about Humphreys’ theory I was gob smacked. My first reaction was: Is that really it? Humphreys has actually made some big concessions to current cosmology. Firstly Humphreys is positing a form of big bang, although with an asymmetrical boundary condition that produces the time dilation differential which leads to a considerable slowing of clocks on Earth. Secondly, he has actually conceded the existence of an old universe – in parts. In fact since the greater part of the universe is well beyond the 6000 light year limit it follows that most of the universe, in terms of its local clocks, is a lot older than 6000 years! However, Humphreys declares that it is the gravitationally slowed clocks on Earth that really matter:

The bottom line is that relativity forces us to say by whose clocks we specify the age of the cosmos or the timing of events within that cosmos. My book points out that the Bible gives us time in terms of the "earth's frame of reference, not some other frame." Scripture says, and my theory agrees, that the universe is young as measured by clocks on Earth.

Relativistically speaking clocks in other parts of the universe are just as valid as clocks on Earth, whatever Humphreys thinks scripture tells us which clocks measure the real age of the universe. In fact in a reply to a critic (which can be found here) Humphries admits to the symmetry of clocks in relativity:

Duff claims in his second-to-last paragraph that even if my theory were true, the cosmos would still be billions of years old. But he is simply expressing a personal preference in clocks, regarding the distant clocks as more important than the ones on earth. How unrelativistic of him!

And conversely, if by personal preference we should find the distant clocks more useful a coordinate system when measuring the age of the universe we could thus equally validly declare the universe to be billions of years old! In fact given that the overwhelming volume of the universe is going to have clocks which run for millions if not billions of years we might prefer this coordinate system when doing cosmology! Moreover, the majority of planets out there in the depths of space would have existed for millions of years and thus have an old planet geology! It does seem a bit of a coincidence that Earth geologists have come to the conclusion that our own planet also displays an old planet geology..…oh, I forgot they are all part of anti-God conspiracy.

In one sense Humphreys is admitting that the cosmos at large is very old; measured in terms of the huge number of events that have actually happened out there – which only becomes apparent if we use local clocks – that cosmos returns great age. But in order to keep the YECs happy he tells us that the cosmos is not old with respect to the time dilated Earth clocks. He resolves the ambiguity in the age of the cosmos by suggesting that the Biblical convention is that of using Earth Clocks to measure time. So perhaps we should rescale our coordinate system and start measuring cosmic light travel times using Earth time – using dilated Earth time means that star light has been travelling for only for a few thousand years as measured from the moving goal posts of Earths changing rate of (with respect to the cosmos) clock ticking.

All this seems very far removed from the meaning that copper/bronze age arcadians would have invested in the text as they wrote the passages that eventually got incorporated into Genesis 1. Also, I suspect that some of today's "arcadians" - that is, the fundagelical fideist ultras - won’t like this scientific tinkering one little bit as it really introduces an ambiguity in the age of the cosmos which for those who like to be “biblical, accurate and certain” could go down like a feather sandwich.

The big question, however, is whether, Humphreys’ scheme works observationally. Conservapedia, the right wing web encyclopedia which is sympathetic to young earth creationism is not so sure:

However, this theory is not without problems. The evidence contradicts Humphrey's assumption that the earth is in a large gravity well. If the earth were in such a gravity well, light from distant galaxies should be blue-shifted. Instead, it is red-shifted. Also, gravitational time dilation, if it existed on such a large scale, should be easily observable. On the contrary, we observe (from the periods of Cepheid variable stars, from orbital rates of binary stars, from supernova extinction rates, from light frequencies, etc.) that such time dilation is minor. It is thought that here is some time dilation corresponding with Hubble's law (i.e., further objects have greater red shifts), but this is due to the well-understood expansion of the universe, and it is not nearly extreme enough to fit more than ten billion years into less than 10,000.

And yet Conservapedia claims:

This model receives cautious but wide support among creationists.

…well I suppose there is not much else out there on the ideas market to receive YEC support.

I’m not sure whether Conservapedia is right about the blue shifted light; the actual shift is the result of two competing effects – firstly expansion which red shifts light and secondly the gravitational well which blue shifts light – without wading through the calculations it is difficult to determine the net result. However, I would expect some vestige of Humphrey’s asymmetrical universe to be apparent in the distribution of cosmic matter; as Conservapedia points out we might expect to find vestigial differences between the rate at which clocks tick in distant parts of the universe and those on Earth, which as far as I am aware has not been detected as I am sure we would have heard about …oh, I am forgetting again; astronomers are all part of a sinful anti-God conspiracy.

The moral of this story is that it is not enough for YECs to bask in the detailed problems of Big Bang theory when it is clear that they have quite elementary problems of their own - the problem with star light is far more basic than Big Bang theory. Whatever the exact history of creation, the light from those distant galaxies is fairly compelling evidence of one thing; namely that those photons have made a very long and historic journey. In fact the problems for YECs increase for every light year beyond a paltry radius of less than 6000 light years. This is not a question of how the universe got started but just how long those photons have been travelling – and it is here that Humphreys actually concedes the point – yes they did travel for billions of years, whilst the Earth, Rip Van Winkle style, was stuck in a time dilation pocket. What is remarkable is that Humphreys does not deny the plain meaning of the fact that photons reach us from distant parts, implying that the universe, when measured locally, is a very old place. As an aside Humphreys’ theory also begs questions about those YEC theories which claim that galactic dynamics implies young galaxies. So who is right: Is it Humphreys who is claiming the cosmos to be very old in terms of its local clocks or is it those YECs who claim the galaxies are young?

In some ways YECs have the advantage of being able to face both ways; if their foray into positive science fails they can always retreat into mature creation theory with its great flexibility of ad hoc explanation. But in order to implement a scientific creationism they have to some extent work against mature creation theory because they are then forced to maintain that the Earth really does contain at least some evidential pointers to their claims of a 6000 year old history (like for example the concentration of salt in the seas – which they claim is evidence of a young Earth). In other words some evidences they treat as pointers to a genuine “maturity” and some evidences as a faux maturity.

But in all their difficulties YECs seldom, if ever, turn the critical spot light on what is the source of their problems, namely their interpretation of scripture; the writers of scripture were an arcadian people who thought in arcadian ways and this consideration must be factored into Biblical interpretation; God's Word comes through this interface. But modern YECs claim their interpretations of the Bible to be the very words God; God means what they say He is says. But I think it has less to do with “The Word of God” than it has with community inertia, investment and face saving. On the age of the Earth there is no chance of YECs reviewing their views without them (and their multi-million dollar creation museum investment) becoming a laughing stock – no make that, "an even bigger laughing stock". The YEC community has passed the point of no return.

The YECs have a PR problem: Any thing goes in creationism?

God and Bayes, Part 2

In my last post I mentioned an argument I once saw for the existence of God based on Bayes’ theorem. In fact I’m talking as far back as 20 years when in 1990 I read a book called “Reason and Faith” published in 1989 by Roger Forster and Paul Marston. Their argument can be found on the penultimate page of the book, page 427.

Expressed in terms of the Venn diagram notation I introduced in my last post Forster and Marston set P(A) = P(God exists) and P(B) = P(the universe is inhabitable). Let’s represent that as P(G) and P(H) respectively (“G” for “God” and “H” for “habitable”). Rendering this in Venn diagram form we have:

…where the domain labeled G represents the cases favourable to God’s existence and the domain labeled H represents the cases favourable to an inhabitable cosmos.

As they say, a picture is worth a thousand words (or a thousand calculations!): In configuring this diagram in the way that I have I’ve actually given away Forster's and Marston’s game: Notice that the area for an inhabitable universe is rather small and that very little of it overlaps onto the “No God” area. We can immediately see, then, that in this application of Bayes’ theorem most cases of H cluster with cases for G. It is therefore almost trivially obvious from the above diagram that given H, G is very probable! That is, given we live in an inhabitable universe we deduce that the existence of God is very likely! However, I must concede that giving H and G such a close relationship is a moot point and I'll come back to it below.

The first query that should be raised here is the philosophical one: Viz: Is this really a valid application of probability? In particular, in the context of an interpretation of probability based on the simple enumeration of cases is it really coherent to talk of “T items” some of which may have the property of God existing? Just what are these T items? Are they possible cosmoses? Are we saying that it is possible to imagine cosmoses where there is no God? Now, if we were drawing items from a jumbled bag of objects it is fairly obvious that this Venn interpretation works: Here talk of “T items” is intelligible and these items may have equally as intelligible properties such as colour and shape; for example, A could stand for “orange” and B could stand for “square”. However, it is far from obvious that such a banal model scales up to whole cosmoses and beyond. The upshot is that when people use probability to argue for God they tend to employ a much more philosophically diffuse concept of probability than the somewhat prosaic (and coherent) model involving shuffled objects and the enumeration of cases; usually the rather enigmatic Bayesian “degree of belief” view of probability is adopted, which I think is the view adopted by Forster and Marston. My own guess is that the human mind is built to deal with those prosaic junctures that can be treated with case enumerations; if so then the mind’s probability intuitions, when applied to the outermost cosmic frame, may not be an intelligible application.

Anyway, in spite of the foregoing philosophical disquiet, let me proceed with the actual argument used by Forster and Marsden. Firstly they actually employ a modified form of Bayes’ equation. They don’t present a proof of this modified form so I have provided it below: (I use notation like !G to mean the negation of G; that is “G false”)

Forster and Marsden present the latter equation (equation 5) with their guesstimated values already plugged in. The values they use I explain below:

P(G) = 0.000001. Here F&M are trying to take the point of view of the atheist who, although he might claim that he doesn’t believe there is a God, nevertheless may admit in his heart of hearts that his “degree of disbelief” is not absolute. He may express this level of uncertainty as, say, a “1 in a million of chance of God existing”.

P(H|G) = 0.00001 Again, F&M plug in a very conservative value for the chance of God creating an inhabitable universe if He exists.

P(!G) = 1 – P(G) = 0.99999

P(H|!G) = 0.000….0001 where “…” represents billions of zeros! It is the value of this quantity that is crucial (and contentious) to F&M’s argument. It is this value which determines, as I have noted above, that the Venn circle of inhabitable cosmoses largely resides in the circle for God.

When the above values are plugged into the equation it is fairly obvious why we arrive at a probability very close to 1 even for very small values of P(G): It is consequence of the following inequality:

P(H|G) P(G) >> P(H|!G) P(!G)

The huge difference between these two terms, which are summed in the dominator of equation 5, ensures that the denominator is all but equal to the numerator thus returning P(G|H) ~ 1. The strategy of F&M is fairly clear here: Because P(H|!G) is so small the required conclusion, P(G|H) ~ 1, even works for atheists! For one might expect even the most hardened atheist to have just a tiny, tiny little bit of doubt about his position – conceivably he might acknowledge that he feels there is a one in a billion, billion chance that God might exist. Thus according to F&M even with these small odds we still get P(G|H) ~1 because P(H|!G) is far, far smaller than even a billion billionth, having as it does billions of zeroes after the decimal point. Therefore, since it is clear that the universe is inhabitable it follows that G must exist!

But even leaving aside the philosophical contention over whether or not it is right to interpret probability in a vague Bayesian “degree of belief” sort of way, F&M’s analysis still begs questions: Viz: Where do they get the extremely low value of P(H|!G)? This seems to be based on a quote by Paul Davies where he remarks that random choices are extremely unlikely to arrive at the selection of factors required by a universe capable of evolving life. In fact the odds against such a configuration of factors coming together, if selected at random, is, according to Davies, “…one followed by a thousand billion, billion, billion zeros at least”. I believe the basic perception of Davies here is correct: The configurations we see around us are taken from an extremely rare class of possibility; therefore left to random selection alone we are looking at some absolutely minute probabilities of formation. Evolution makes no dent on this improbability: it merely trades configurational improbabilities for the improbability of selecting the right physical regime that favours evolution. Thus whilst P(Life|Evolution) and P(Evolution|Laws of Physics) may return realistic probabilities, the space of possible physical regimes seems to be so large that on the basis of random selection alone P(Laws of Physics) is vanishingly small!

Given this irreducible improbability it is no surprise that the atheist is tempted to make recourse to (very speculative) infinite universes and/or multiverses in an attempt to balance these miniscule values with huge numbers of trails. Although I am myself not impressed with such resorts (on the basis of them being effectively a kind of “turtles all the way down” type explanation), we see that Forster’s and Marston’s assumption that P(H|!G) is extremely small is not unassailable if one starts to postulate huge numbers of trials.

Whatever the weaknesses in Forster’s and Marston’s argument it is significant, however, that it was submitted in 1989, just before William Dembski and friends made their “ID” splash. At the top of the section of F&M’s book where they use Bayes’ Theorem we find the title “The Improbable Us”. By way of introduction they ask: “How apart from design, can we explain the mind boggling improbability of the inhabitable universe?” In short F&M are using a design argument here and yet they are at least sympathetic toward evolution if not evolutionists themselves. Clearly these were the days before anti-evolutionism had become so strongly identified with ID. But F&M’s basic idea is essentially the same as William Dembski’s argument; the apparent presence of highly improbable classes of outcome are assumed to point to intelligent contrivance. But, and this is something you don’t hear enough from William Dembski and friends, this improbability exists whether or not evolution has occurred.

ID arguments based on the probabilities of likely causes flow out of, I submit, a subliminal deistic theology containing a built in weakness that actually helps to undermine ID. This class of argument taps into an ulterior understanding that there is a distinction between patterns that are intelligently designed and those that are not. This can be seen in my “intelligent design” Venn diagram where it is assumed that there are possible cases which are not sourced in the intelligent contrivance of God. William Dembski’s so called “explanatory filter” also brings out this dichotomy: The filter presupposes a distinction between patterns sourced in the “natural forces” of law and chance and those that have been intelligently designed. By promoting this apparently polarized view of the artificial vs. the natural this form of ID actually suggests the way in which it can be challenged; for if it can be shown that a pattern (such as life) is a product of law and chance, then to all appearances it would seem the ID theorists have lost the argument. These theorists have inadvertently adopted a kind of dualism that gives natural forces a quasi autonomous status and in so doing they have made a rod for their own backs. As I have remarked before, this dualist philosophy very naturally leads to a premium being placed on very explicit divine interventions in the natural order: The implication is that these natural processes, in the absence of Divine intervention, are able to at least caretaker the cosmic show themselves, thus implicitly raising their status to a quasi autonomous level; thus the proof of God's presence is only manifest when He explicitly intervenes in the day to day running of the cosmos. In short this form of ID philosophy has a very close subliminal relationship with deism and atheism; for if a case can be made that natural forces are sufficient to explain, say, the configurations of living things, then it is a very short step to conclude that either God is an absentee landlord or does not exist. It is no surprise, then, that contemporary dualist ID theorists have effectively equated ID theory with anti-evilutionism, and therefore by default, are very vociferous in their attacks on evolution. Moreover, on the flip side of these attacks we find that for atheists evolution is the proof of a “blind watchmaker”. Both parties conceive natural forces in all but deistical terms, terms that ultimately subvert the belief in a part-time interventionist God.