by Brian 30. March 2014 06:43

I finally got a chance to sit down and watch the first episode of the new Cosmos series with host astrophysicist Neil deGrasse Tyson. It began with exciting animations and music to set your mind adrift like one of Sagan’s dandelions, untethered from the weight of substantive science. My daughter and I enjoyed the cosmic micro-to-macro journey, reminiscent of the intro to the movie Contact. It opened up some interesting conversation. I found Tyson’s personal experience with his mentor Carl Sagan touching and his excitement for science encouraging. But the effort to divide faith and science was both disappointing and misleading. Even though Tyson is not an atheist (he self-identifies with agnosticism) the executive producer Seth Macfarlane is an outspoken one. It seems pretty obvious to me his bias was allowed to drive the direction of the first episode.

 I’m going to skip over the first half of the show and the pop-science introduced briefly by Tyson’s comment: “Many of us suspect” everything in our observable universe is “but one tiny bubble in an infinite ocean of other universes...worlds without end.” [i] Tyson was allowed to quickly brush over this speculative, unobservable, metaphysical conjecture as if it were a genuine scientific theory. Since I’ve already blogged about the multiverse, I’ll move on to the second half of the show where for over 20 minutes I listened to Tyson attempt to widen the gap between those who look at the world through science and those who look at it through philosophy and theology. I won’t go into how badly Cosmos mishandled the history of the church and Giordano Bruno. You can read this excellent article showing how embarrassingly inaccurate Cosmos portrayed things. I do want to briefly mention how their divisive approach was unnecessary.

The new atheists, such as Richard Dawkins, believe those on the side of science must ridicule the other side of faith. There are also those like Hawking and Krauss who seem to think philosophy is dead because of the advancement of science. On the other hand, strict literalists like Ken Ham often appear to ignore any scientific view which might require a rethinking of one’s theological interpretations. The producers of Cosmos appeared, to me at least, to be fueling the fires in all of these camps. However, there are many scientists, philosophers and theologians who reject the notion science, philosophy and faith must forever be at odds. John Polkinghorne, who won the Templeton Prize in 2002, is an example of such a scientist and theologian.  I’ve blogged about this elsewhere but Polkinghorne’s words are worth repeating.

We must take account of what science has to tell us about the pattern and history of the physical world in which we live. Of course, science itself can no more dictate to religion what it is to believe than religion can prescribe for science what the outcome of its inquiry is to be. The two disciplines are concerned with the exploration of different aspects of human experience: in the one case, our impersonal encounter with a physical world that we transcend; in the other, our personal encounter with the One who transcends us. They use different methods: in the one case, the experimental procedure of putting matters to the test; in the other, the commitment of trust which must underlie all personal encounter, whether between ourselves or with the reality of God. They ask different questions: in the one case, how things happen, by what process?; in the other, why things happen, to what purpose? Though these are two different questions, yet, the ways we answer them must bear some consonant relationship to each other.

Science, philosophy and theology are all trying to make sense of the world from different angles. They all have their primary domains of inquiry into a single world; a single reality. These domains may overlap at points (contrary to Gould’s NOMA.) For example, we cannot divorce ourselves from scientific knowledge when developing a theology of creation. Nor should we air the conjecture of materialist scientists regarding unobservable constructs beyond the event horizon of our universe – at least not without the input of philosophers and theologians. So when you have an executive producer of Cosmos saying: “There have to be people who are vocal about the advancement of knowledge over faith.”[ii] It’s no wonder why the main message of the show is one of division instead of unity.


[i] Neil Tyson, 15:00-24 Cosmos Ep1.

[ii]Esquire interview Aug, 18,2009

Metaphysics and the Teleological Argument

by Brian 11. September 2011 20:24
I can say with certainty the predominant theme in Peter van Inwagen’s Metaphysics is uncertainty. In most chapters the author enters with his refutation and exits with a tenor of inconclusiveness. The liberal use of modal logic in countering some of the arguments for God’s existence appeared to be a common tactic. I kept thinking the pea must be under the cup in possible-world three, but the author’s logical sleight-of-hand was too quick for me to discern. My conclusion: There is a set of possible worlds in which van Inwagen’s use of modal logic leaves little doubt in the reader’s mind, but unfortunately our actual world is not in that set. I probably just need to brush up on modal logic - but in the meantime I want to turn to van Inwagen’s treatment of the design (or teleological) argument from the fine-tuning of the cosmos. This variation of the classical argument for the existence of God is one I personally find compelling. Here too the author leaves things unresolved and the counter-positions at par. We are told neither a rational designer nor brute materialism has the upper hand. The universe may find its ultimate origin in God or in some material realm beyond the boundary of our observable universe – take your pick. But did the author successfully make his case?

I agree with van Inwagen the Arche is either a Chaos or a Logos. The Greek word arche or origin represents the foundation of existence in which all things rest. According to the author, it is either grounded in meaningless Matter (Chaos) or purposeful Mind (Logos). The ultimate origin or First-cause of our observable universe is either God[i] who created it ex nihilo or some unobservable hyper-reality which spawned it ex materia[ii]. I agree with van Inwagen there are no other alternatives worthy of consideration. The author does a good job dispelling the nonsense suggested by some pop-writers of an observable universe exploding into existence out of metaphysical nothingness. From nothing, nothing comes, plain and simple. All attempts to state otherwise completely miss the boat on what nothingness really is. True metaphysical nothingness is what rocks dream about – as Aristotle put it. When we talk about voids in space or the quantum vacuum, those things are emphatically something. Creation from these would be considered ex materia (from material). So we are on the same page; our observable universe began to exist, and the Arche is either a Chaos or a Logos. Now it’s easy to see how fine-tuning squares with Logos (since there is an empirical correlation between fine-tuning and a designer), but how do we square it with Chaos?  
Various astrophysical constants and parameters from the Standard Model, including their relationships, are narrowly just-so for the existence of a universe with conscious observers. Van Inwagen’s recognition of the overwhelming improbability raised by these known anthropic-coincidences is in line with what most experts say on the subject today (Penrose, Davies, Hawking et al.) Nontheistic cosmologists have been working for decades to get around the theological implication of the apparent fine-tuning of the universe by offering several hypotheses, which you can read more about here. However, van Inwagen doesn’t buy most these. The author rightly rejects the Weak Anthropic Principle using his short-straw analogy. He rejects the Strong Anthropic Principle and anything involving a life principle. He doubts there will be a theory-of-everything revealing how conscious life obtains necessarily. So where does van Inwagen put his money? How do we get from a Chaos to a fine-tuned universe? His answer is the multiverse and the observer selection effect. This is the only plausible alternative to the Logos according to van Inwagen and it does seem to be growing in popularity – see Hawking’s latest book. 
Why does van Inwagen think the multiverse hypothesis is as good as a rational designer? He tells us here: 
An explanation [e.g. the multiverse] will be at least as good as that explanation [a rational designer] if it contains no element known on independent grounds to be false or improbable-for that (together with the fact that it does explain the observed phenomenon of the fine tuning of the cosmos) is really all that can be said in favor of the hypothesis of rational design.”[iii] 
So basically, the author considers both hypotheses to be little more than logically consistent proposals lacking any known defeaters. They both provide an explanation of apparent design, but that's about it. All in all, they are on par according to van Inwagen - and this is where he and I diverge. On the one hand you have an ultramundane Designer as the source of cosmic fine-tuning, and on the other, a hypothesis with ad hoc constraints and assumptions as we will see. 
The multiverse is basically an ensemble of independent universes, each one like our very own observable region. Van Inwagen uses the term cosmos to refer to one of these. He uses the term cosmoi to refer to a plurality of cosmos-siblings in the multiverse, each with its own randomized physical parameters (Physics.) So in our universe the ratio of the mass of a proton to an electron is about 1836 to one. But in another cosmos it might be two to one, or a million to one. This would apply to all of the constants and relationships found in the Standard Model as well as other cosmological values. The multiverse is then treated as a cosmoi generator where our unlikely cosmos is just one in the ensemble. And this generator must churn out more than a few cosmoi in order to overcome the magnitude of the improbability of a fine-tuned cosmos suitable for conscious observers to obtain by chance.
The author rightly recognizes the overwhelming mount improbable in the anthropic coincidences. However, he fails to mention how the problem is compounded by the fact: a suitable abode is a necessary condition for life to exist but not a sufficient condition for life to obtain. It is no better than me saying: the conditions are right for a garden in my backyard, therefore a garden in my backyard will come into existence. The height of mount improbable is not just due to the right settings for a suitable abode on the cosmoi generator, but it is compounded by the odds of life obtaining (abiogenesis) from purely material causes. Once you factor that in, it’s no wonder why the author and cosmologists like Alexander Vilenkin posit an infinite number of cosmoi. Yet van Inwagen does not seem to have any problem with this approach: 
“It’s hard to think of a reason to suppose the number of actual cosmoi would have to be finite. If the number of cosmoi were infinite, it would certainly not be surprising that some of them were suitable abodes for life.” [iv] 

Positing a mind-boggling number of cosmoi is ad hoc enough[v]. But why not stop there? Well; because the only way to secure the multiverse hypothesis is to suggest an actual infinite set of cosmoi. However actual infinities turn the multiverse hypothesis into a bizarre concept. Under this thesis, there are not only an infinite number of identical clones of myself typing this sentence right now, but an infinite number of clones typing it backwards, yesterday, and on their head. Think about it, if we open Pandora’s Box and allow for actual infinites, we turn possible-world semantics into reality! In other words, every possible world that is actualizable [vi] has in fact been actualized in the infinite multiverse. Might this include a possible world with an omnipotent and omniscient being capable of transcending its cosmos into all sibling cosmoi? I don’t see why not. In order to deny this, one has to postulate an ad hoc constraint: Being cannot transcend its cosmos – even a maximally great being. In other words, demigods exist in some cosmoi, but they are stuck there with limited greatness. Assumptions do not get much more ad hoc than this, and if you remove it, then why wouldn't an infinite number of what we think of as God exist?

But it gets worse; the Physics in each cosmos must be based on free parameters. If there were only, say ten parameters, allowing for only ten discrete values each, then you would have a mere ten billion possible Physics regardless of how many cosmoi are generated. Therefore, a much higher degree-of-freedom in how cosmoi-physics is configured must be assumed. Here’s what van Inwagen says:
“[there is] the possibility that the cosmos might have arisen as a fluctuation in some pre-cosmic analogue of the quantum field…We suppose that the cosmoi that arise in Chaos do not resemble one another as closely as the bubbles in a pot of boiling porridge resemble one another. The differences among them-which, we must remember, are the products of chance-are, or can be, of the radical kind we should describe as differences in the laws of physics and large-scale cosmic structure. ”[vii] 

The problem with the boiling porridge analogy is it oversimplifies things and obfuscates an assumption. Boiling porridge creates lots of boring blobs of oats. They’re not very interesting. Not only must the physical parameters of the cosmoi be freely variable, as I just mentioned, but the law (or laws) of the multiverse, the Arche, must allow for the generation of randomized sets of Physics suitable for life. It would be impossible to get conscious observers from Chaos without a sufficiently creative potential in the Physics generator. Imagine trying to create a functioning computer from mere plastic Lego. Regardless of the variation of shapes, the number of pieces or the number of attempts; it’s impossible. Without conductor and semiconductor materials, plastic alone will never get you there.

A parsimonious view should reject a Chaos generating Physics with the richness and complexity necessary for life to ever obtain, even with an actual infinite number of randomized attempts. Why not an infinite number of cosmoi where each cosmos is merely empty space or contains nothing but a random number of elementary particles? It seems exceedingly convenient the kinds and number of dials on the cosmoi generator even allow for conscious observers under any configuration. Now this is where van Inwagen might introduce his observer selection effect by saying, yes, it does seem odd for conscious observers to be a random byproduct of Chaos, but that’s what it takes to recognize the oddness – we have to be here. But this would assume the very thing we are trying to prove and only makes sense once you violate a parsimonious view and include the assumption the multiverse must generate rich rather than frugal Physics. 
In conclusion, the choices for Arche are not on par. On the one hand you have actual design by the Logos and on the other, apparent design by a Chaos. The Chaos option holds only as long as we accept an unobservable actual infinite [viii] set of cosmoi in a multiverse; each with different Physics; some with demigods who cannot escape their cosmos; and others with Richard Dawkins as a television evangelist. Somehow a meaningless Chaos must have the potentiality in its cosmoi generator to create not just randomized Physics, but Physics sufficiently rich and complex such that given an infinite number of spins, conscious observers will obtain instead of nothing more interesting than a sea of quarks or globules of cooked oats. You be the judge which one takes more faith.
[i] I purposely leave out gods at this point or make any claims as to the nature of God
[ii] I leave out here all of the discussion around the Borde-Vilenkin-Guth theorem ( – theists like Dr. William Lane Craig say the BVG theorem proves an ultimate beginning for the multiverse as well. However Vilenkin himself seems to have some reluctance. Alan Guth is less reluctant and said that we do not have absolute certainty but it appears there must be an ultimate beginning for a multiverse as well. If true, warrant shifts substantially to the Logos option.
[iii] Kindle 4546 of 7762
[iv] Kindle 4522 of 7762
[v] Shots at this range from 1e500 to 1e10^150 – ridiculously large (but finite) cosmoi
[vi] Actualizable meaning: where there is neither logical contradiction, nor violation of the kinds of Physics created by the cosmoi generator, nor absurdities [like a prime minister being a prime number]
[vii] Kindle 4526-4528 of 7762
[viii] I agree with the great mathematician David Hilbert that an actual infinite set is nowhere to be found outside of a concept of the mind - "let us draw the conclusion from all our reflections on the infinite. The overall result is then: The infinite is nowhere realized. Neither is it present in nature nor is it admissible as a foundation of our rational thinking - a remarkable harmony between being and thinking. (David Hilbert)" 

The Grand Design

by Brian 15. March 2011 21:18

When we think of apologetics, case-for arguments come to mind. But sometimes the apologetic enterprise is about guiding towards what is true by steering away from what is false. As C. S. Lewis wrote: Good philosophy must exist, if for no other reason, because bad philosophy needs to be answered.[i]I can think of no better example of this in recent months than a response to the book written by Stephen Hawking and Leonard Mlodinow. Having just finished The Grand Design (TGD), the primary message of the book is still very clear in my mind: Science is the only means of discovery; philosophy is dead; God is unnecessary.

One would expect minimal impact from facile rehash sprinkled with the words quantum mechanics. But throw in the media support for Hawking and anything attempting to undermine theism these days, and I am not so sure. When the new philosophy is addressed by the greatest scientist in the world, you have mass appeal ad verecundiam. Though sales of TGD are not likely to surpass Hawking’s previous book, A Brief History of Time (which sold over nine million copies), many will read this new work and be influenced by it. And even though I’ve seen a good deal of criticism online, I am also seeing a lot of positive posts on Amazon and Goodreads. Christians might fail to recognize the potential impact here. A pastor of a large church could preach to a different congregation each week for his entire career and not convey a perspective to as many individuals as just one popular book like Hawking’s last one. Do the math!

To be fair to the authors, I should tell you parts of the book were good. I enjoyed the physics and cosmology overview as well as revisiting some of the moments from science history. I also appreciated the author’s strong affirmation of cosmic fine-tuning. But the rest of the book was downright sloppy and in this blog I intend to cover what I thought were the most egregious areas.

  • Traditional philosophy is dead. The oracle of the new philosophy is the scientist.
  • M-theory is our best hope for a unified theory
  • The Hartle-Hawking no boundary model does away with the cosmological argument
  • The multiverse does away with the teleological argument from fine tuning
  • Realism is dead. Antirealism is in.

Traditional philosophy is dead
Right at the outset the reader is hit with an astonishing paragraph:

“What is the nature of Reality? Where did all of this come from? Did the Universe need a creator? … Traditionally these are questions for philosophy, but philosophy is dead. Philosophy has not kept up with modern developments in science, particularly physics. Scientists have become the bearers of the torch of discovery in our quest for knowledge.[ii]

Hawking has a Ph.D. in natural science and Mlodinow a Ph.D. in theoretical physics. Although neither of the authors are experts in philosophy, we should expect men of their caliber to at least have a cursory understanding of the field. Two of his three opening questions are primarily philosophical! A good philosopher will draw from science in answering these questions, but it is naïve to think a good scientist could tackle them without philosophy. I was so taken aback by this opening statement my mind grasped for some kind of plausible explanation for their position. But after reading the book and wading through one bad assumptive argument after another, it does appear the authors wandered out of their league. Here is a sample of what they try to embark upon in this book relying heavily on (or falling squarely in) the domain of philosophy:

  • Model-dependent realism (which is an odd sort of scientism + antirealism)
  • Why is there something rather than nothing?
  • Are the laws of physics prescriptive or descriptive?
  • Scientific determinism, freewill and the reality of miracles
  • Ontological relativism and observer-created reality
  • Applying aesthetics in determining the superiority of theories
  • The extrapolation of Feynman’s sum over histories into an ontological model

Since there is practically no new science in TGD (it rehashes what has been known for years, and even decades), one can reasonably say the novel material in this book is almost entirely philosophical! So what audacity for the authors to start out with the claim, philosophy is dead.

They like M-theory; the no-boundary model and the multiverse
I will not attempt to argue the merits of m-theory, which has been around for about 15 years.  It is worth noting however, some of the world’s leading theorists in the field hold this work-in-progress very tentatively [iii]. The jury is still out for string theory as a whole and m-theory in particular. But then don’t take my word for it, see Hawking and Mlodinow’s own words:

“People are still trying to decipher the nature of m-theory. But that may not be possible. It could be that the physicist’s traditional expectation of a single theory of nature is untenable, and there exists no single formulation.[iv]

Yet despite the tentativeness of ten-dimensional string theory and the uncertainty of the very nature of m-theory, the authors base a large part of their metaphysical worldview on it by applying their particular physical interpretations to these models with no observational support[v] and then gratuitously extrapolating.

In TGD we also see the 1983 Hartle-Hawking no-boundary proposal reheated. Again, there is nothing novel here. It is the same quantum gravity idea proposed in Hawking’s last book[vi].  Using imaginary numbers for the time variable allows Hawking to round off the beginning point of the big bang singularity. In TGD, the authors describe this by using the South Pole as an analogy. The South Pole is much like any other point they say, and nothing is south of the South Pole[vii].  Therefore, no absolute beginning to universe is necessary – problem solved. Even though a physical interpretation of this mathematical trick using imaginary numbers is tough to swallow, we’ll see how the authors believe model-dependent realism takes care of this. For more information on the Hartle-Hawking model and how it applies to the cosmological argument, check this out.

Then we get to Hollywood’s favorite from cosmology – the multiverse. Paul Davies’ treatment of this in The Goldilocks Enigma is far better than what is presented in TGD. So I won’t go into too much detail as you can read more about it here. I was surprised though by the author’s metaphysical extrapolation of Feynman’s mathematical path integration tool into an ontological model. They write (and note the tangential defensiveness):

Some people make a great mystery of this idea, sometimes called the multiverse concept, but these are just different expressions of the Feynman sum over histories[viii]…The multiverse idea is not a notion invented to account for the miracle of fine-tuning. It is a consequence of the no-boundary condition as well as many other theories of modern cosmology.

Apart from the brash dive into metaphysics from the so-called new bearers of discovery, the physical interpretation is dubious at best. Simply because a particle could take more than one path from A to B, as described by Feynman’s path-integration, doesn’t mean a particle actually takes all possible paths.  Feynman and others might assume they do, for the purposes of applying the tool, but the paths are not observable. The idea a particle actually takes an infinite number of possible paths is just one physical interpretation of the mathematical model – and an odd one at that.

In the double–slit experiment Feynman’s ideas mean the particles take paths that go through only one slit or the other; paths that thread through the first slit, back out through the second slit, and then through the first one again; paths that visit the restaurant that serves that great curried shrimp, and then circle Jupiter a few times before heading home; even paths that go across the universe and back.[ix]  Really?!

The authors fail to mention other interpretations and leave the reader thinking Feynman’s sum over histories substantiates the multiverse. This get’s downright funny when you consider model-dependent realism which essentially says for Hawking, a particle actually does take all possible paths. But for someone else who interprets the same mathematical models differently, the particles do not – and neither interpretation can be said to be more real than the other!

So that I am not accused of argumentum ad ignorantiam let me be clear in saying that I am not claiming m-theory, Hawking’s quantum-gravity model and the multiverse are false because they haven’t been proven true. What I am saying is one cannot leap from tentative mathematical models to one’s preferred physical interpretation with no observational support and then leap again to profound metaphysical conclusions without doing so hastily and gratuitously. And you certainly cannot do it without entering the realm of philosophy!That is precisely what has been done in TGD.

Let’s get real
Hawking and Mlodinow’s model-dependent realism was by far the most bizarre part of the book for me. Here’s how they describe it:


It [model-dependent realism] is based on the idea that our brains interpret the input from our sensory organs by making a model of the world. When such a model is successful at explaining events, we tend to attribute to it, and to the elements and concepts that constitute it, the quality of reality or absolute truth. But there may be different ways in which one could model the same physical situation, with each employing different fundamental elements and concepts. If two such physical theories or models accurately predict the same events, one cannot be said to be more real than the other, rather, we are free to use whichever model is more convenient…According to model-dependent realism; it is pointless to ask whether a model is real, only whether it agrees with observation.[x]


The authors give an example by comparing the 13.7-billion-year-old-universe model versus the young-universe (literal Genesis interpretation) model and say the old-universe model is more useful, but still, neither model can be said to be more real than the other[xi]. Ha! I’d love to hear how the new-atheists like Hitchens and Dawkins feel about the idea their perspective is no more real than the creationist’s! But seriously, the authors come across disingenuous here. Are we really supposed to believe Hawking and Mlodinow do not consider their interpretation more real than the creationist’s? Furthermore, the authors appear to equivocate with their terms: model, theory, physical-theory and hypothesis. They seem to use them interchangeably. But regardless, the statement: If two such physical theories or models accurately predict the same events, one cannot be said to be more real than the other, seems to disregard other factors for weighing a proposed explanation for an observed phenomenon, like: simplicity, scope, fruitfulness, conservatism along with testability[xii]. Such evaluation would involve meta-science, which may be why it is overlooked.

The fact is, one of the two hypotheses; the 13.7-billion-year or the literal-6-day-creation, is more real than the other! A careful reading of the author’s statement “one cannot be said to be more real” might lead one to conclude they are being somewhat reasonable by suggesting the problem is merely epistemic – that is to say, one is more real, we just do not know which. But that is not what they are claiming. Hawking and Mlodinow are saying neither model is more real ontologically. The authors are antirealists and reject the notion of an observer-independent world[xiii]. There is only one reason I can think of for them to choose this route: They recognize the huge gulf between their tentative mathematical models and the profound metaphysical statements they make. The only way to bridge this gulf is to do away with realism altogether and then judge their models using a narrow scientific perspective. By disregarding the philosophy of science, they can ignore qualities like conservatism which would compare and contrast their metaphysical conclusions with other knowledge-systems to see how well they hold up.

In conclusion, Hawking and Mlodinow set out on a very ambitious journey to make their case for what they believe are the answers to some very profound metaphysical problems. Why is there something rather than nothing? The authors do not answer this and only present one possible view as to why there is something rather than something else[xiv]. Is God unnecessary? According to TGD, He should be replaced by some sort of cosmic life principle, a First-Law, Physics (with a capital ‘P’); or a Force which is more at home with Star Wars than reality. Has cosmic fine-tuning been addressed? No. Although the book does a good job in emphasizing the problem, they leave the reader with the dubious multiverse – a hypothesis Roger Penrose has said is worse than useless in explaining the anthropic fine-tuning of the universe. Finally, just when I thought postmodernism was dead, it is resurrected by scientists!

[i] C.S. Lewis, The Weight of Glory (Grand Rapids, Mich.: Eerdmans, 1949), 50


[ii] Location 42 of 2387 Kindle edition


[iii] Go to for excerpts from Roger Penrose. Also see Paul Davies in the Goldilocks Enigma.


[iv] Location 1179 of 2387 Kindle edition


[v] Roger Penrose - “M-theory enjoys no observational support whatever”



[vi] A Brief History of Time pg. 136


[vii] Location 1361 of 2387 Kindle edition (also in A Brief History of Time pg. 138)


[viii] Location 1383 and 1659 of 2387 Kindle edition


[ix] Location 731 of 2387 Kindle edition


[x] Location 61, 436 of 2387 Kindle edition


[xi] Location 483 of 2387 Kindle edition


[xii] Schick, Theodore; Vaughn, Lewis (2002)


[xiii] Location 351, 412 of 2387 Kindle edition


[xiv] They never address creation from real nothingness – a quantum vacuum is not nothing

About the author

I am a Christian, husband, father of two daughters, a partner and lead architect of EasyTerritory, armchair apologist and philosopher, writer of hand-crafted electronic music, avid kiteboarder and a kid around anything that flies (rockets, planes, copters, boomerangs)

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