epiphanesque

Closing shop

2009-06-26T17:15:00.006-10:00

This blog is officially dead, no new material will be posted here. My thanks to those who stopped by.

Me ke aloha, a hui hou!

The Mechanics of Freedom

2009-06-14T20:17:00.005-10:00

After being prompted by some philosophy-oriented discussions, I realized that my older writeup on the problem of free will (A Quantum of Freedom) was not a very satisfactory work. Whether this new one is any better I dare not speculate, but in any event, here it is.

Because of its length (15 pages) I will not copy the whole thing into this blog post. Here is a link to the PDF document called "The Mechanics of Freedom" (freemech.pdf):

on my iDisk (freemech.pdf)
download page at MediaFire

Enjoy!

Algorhythm

2009-05-08T17:39:00.005-10:00

Got rhythm? Got algorithms? Then if you're like me you've got a corny new name for your latest piece of fractal beat-syncing script. Algorhythm is the latest (and probably last) incarnation of a Lua script for Oxidizer, for designing animation sequences of IFS fractal genomes, that I have been developing for the past year or so (released as seq7/seq9 previously). This version comes with a couple of built-in beat-syncing algorithms to make the job even easier.

Not much to show for it yet though, only a brief experimental clip up on the web site for now. I'll have to compose something new in order to showcase the abilities of the script. That may be a while though..

The Questionable Ethics of The Pirate Bay

2009-04-18T16:59:00.012-10:00

As a Swede-in-exile in the US, I suppose I should have an opinion on the Swedish court verdict (guilty) in the trial against The Pirate Pay (TPB) for facilitating copyright infringement.

I'll grant that The Pirate Bay are right about one thing: the solution to the copyright infringement problem isn't to outlaw file sharing, but to find a new business model adapted to the new technology. On everything else, however, I think they are dead wrong, and for all their cries of revolution, The Pirate Bay are not the ones pioneering any new solutions.

(click to continue reading)

Let me declare my own criminal record first, so that there is no mistake where I am coming from. I have file-shared a great deal in the past, chiefly music initially, and more recently mostly in the form of unlicensed anime shows from Japan. When I first discovered the peer-to-peer file sharing technology around 2001 (after the Napster shutdown, but before TPB existed), I downloaded a lot of music, and I even tried to get my mom to appreciate the wonders of file sharing, as she could now get that classical music that she had always wanted.

Today, I can offer no justification for this, except to recognize that I had not considered the ethical implications of what I was doing. It took me about 3-4 years to gradually realize that there were ethical implications, and still today many, including TPB, have either not yet made this discovery, or else have chosen to ignore it out of convenience.

Ethics isn't just for philosophers; it is deeply embedded into every culture and every society on Earth. In the modern industrialized world, normative ethics exists on every level, from the individual to the national (but still lacking a global ethic). We have developed specialized ethical codes for many sectors of society, including medicine, education, science, business, social and economic policy etc. But when more than 80% of the people, in a country that prohibits theft and protects intellectual property by copyright laws, considers theft to be permissible when it is done by a particular method (known as file sharing) - then I see a problem with the ethical system adopted by 80% of the people in that country.

For the community that uses file sharing networks to illegally obtain copyright protected material, the ethical problem, whether they acknowledge it or not, exists on two levels:

The copyright holders' rights are being violated
Illegal downloaders are sponging off the good will of paying customers

The first point is really not debatable, this is simply how it is, and it is up to each and every one to decide for themselves how they feel about this. The comparison is often made with earlier precedents, like audio tape technology and CD-burning. These were also technologies that made it possible to share copyrighted material between peers, and the argument is now made that file sharing via the Internet is no different. In reality, of course, there is a whole world of difference.

While some record labels were initially worried about this same problem many years ago, when audio cassettes were being used to copy vinyl LPs in the 70s and 80s, later replaced by CD-burning in the 90s, it was gradually discovered that the bandwidth of this method of sharing was low enough that it posed no real threat to the music industry, or to the community of artists. Blank media tax or other types of government levies were also introduced in many countries, partially in order to compensate authors for some loss of revenue due to copying.

With the Internet, however, file sharing of digital media simply isn't a comparable phenomenon - it's a complete game changer. It only takes one purchased album to be uploaded to a torrent site like The Pirate Bay, and within minutes thousands of copies may have been distributed worldwide to anyone with Internet access, and within hours, millions. The bandwidth of this sharing technology is several orders of magnitude beyond what was previously possible. There really is no precedent for this phenomenon, and the potential risk for an individual author or composer to be completely stripped of revenue is multiplied indefinitely.

The second ethical issue is that the artistic community that provides us with this digital entertainment is currently able to do so because, alongside the illegal downloaders, there is still a community of paying customers, financing the industry. One common argument that defenders of TPB often invoke is that illegal downloading evidently doesn't hurt the industry all that much because it still thrives. Hence, they conclude, it is perfectly all right for most people to file share as much as they like, because some people are still paying for the goods, thanks to which the artists and the producers are not getting ripped off.

But even the staunchest Pirate Bay supporter must realize that if everybody were to download the digital goods without paying, then, under the current economic system, the industry would collapse and cease to exist. We would be left with only pro bono artistic productions and voluntary creations, driven by personal zest, good-will and voluntary public donations.

Do not get me wrong: there already is a wealth of free music, books, videos and other artistic material already out there, and I think this is a great thing, and I help myself to much of it. And voluntary donations could certainly be sufficient to enable some lucky organizations or individuals to make ends meet. But do I think that every artist and producer could follow this model? No. While some might be able to, many are critically dependent on revenue for creating their products in the first place, as well as for livelihood. Without an assured revenue, professional studios would be too costly to operate, and the quality of artistic productions would plummet to amateurish levels.

So if the artistic industry is to survive under the current economic system and retain the quality of professional productions, then logic dictates that some customer base must be obliged to pay for the goods and rendered services.

Which brings us back to the second ethical dilemma: how is it decided who is obliged to pay and who is not? And what happens when you put these two communities face to face? How does the file-sharing freeloader justify his claim that the other person is obliged to pay, while he himself is not? This is the ethical question that TPB can not answer, and actively seeks to avoid addressing altogether.

Finally, for The Pirate Pay itself, there is also a third charge of moral bankruptcy to lay against them, and that is that they are not even trying to provide a solution to these first two ethical problems, and instead persist in defending the current file sharing paradigm as the way the system should remain.

Resuming the story of my own history with file sharing, shortly after discovering this convenient albeit illegal technology, a few of the first legal alternatives started appearing on the scene. As a Mac user, I was quick to explore and later adopt the iTunes Music Store (iTMS - opened in April 2003) for my music needs. Initially the content was weak, and the service troubled by teething problems associated with the establishment of a new infrastructure for digital delivery.

Over the space of a couple of years, however, the iTMS steadily improved on all fronts: expanded catalogs and categories, faster and more reliable downloads, higher quality digital formats, a friendly and powerful interface, fast and professional support service. Over those few years I completely abandoned file sharing for music, and have since 2006 bought nearly all my music from iTunes. Today I find their service so good that I don't even need to invoke the moral argument for why I use them: they simply offer a vastly better service than file sharing or The Pirate Bay. Plus I get to feel good about myself in a world of freeloaders. While I chose the iTunes Store for my example, they were of course far from the only ones going down this path: Amazon, Rhapsody, Napster, CDbaby and many more developed legal download services along similar lines.

The moral of this story? Establishing a new infrastructure is hard, costly and takes time. It requires investment, a business model and expertise, something which The Pirate Bay completely lacks. The Pirate Bay also claim that they are providing infrastructure, although I do not see where they are providing anything novel or particularly sophisticated: a server and an indexing and search engine. This is not very impressive by today's standards in digital delivery infrastructure, and falls far short of what is provided by the above named venues.

My other vice, that of file sharing Japanese anime, lasted for somewhat longer, since the availability in the West of unlicensed anime is limited, and the legal online services here have been slower to develop (for licensed anime available on DVD I stopped file sharing completely and bought the DVDs instead). But now there exist some really good venues for this as well, where my personal choice is Crunchyroll. These guys started out as a semi-illegal fansub outlet, but took the brave step in 2009 to go completely legal by negotiating contracts directly with anime studios for offering their shows online. There is now a large and steadily growing catalog of movies and TV shows for online streaming and download, and Crunchyroll are also pioneering simulcasts for currently running shows. This service, at a measly $15 per quarter, already outperforms any similar service offered by illegal online streaming or file sharing.

The moral of this story? By talking to the production houses and negotiating contracts, you can accomplish a lot more than fighting them tooth and nail, as The Pirate Bay have chosen to do. Not to mention sending out mocking letters, littered with insults and obscenities, in reply to the studios' cease and desist demands. If the TPB guys end up spending some time in jail, I somehow think they have themselves to blame for that, for picking a fight rather than seeking a dialogue.

To conclude, it seems to me that the artistic and entertainment industry together with their online digital delivery partners are moving in the right direction, by expanding their online services and adapting to the new Internet-based culture that has sprung into existence so quickly. While calling for new business models and a rewrite of copyright laws, The Pirate Bay in contrast appears to be doing nothing constructive toward those goals. Instead they are digging in their heels and fighting for a "business" model that dates back to the Napster of the previous century; an ethically unjustifiable model of unilateral theft. There is much irony and falsehood in TPB's claims that, between the two, the music industry are the Luddite ones. That might have been true five years ago, but in the last five years the music industry has changed; The Pirate Bay has not.

The steadily growing success of legal download services undeniably demonstrates that people want to use legal methods if they can, and if the services are good enough to be worth paying for. In my opinion the online music services are now so good that the rationale for file sharing music has completely disappeared. Books, movies and games companies have been lagging behind, but are quickly catching up and increasingly adopting new digital delivery services. These are the genuine innovators and pioneers, opening up new markets and bringing you new services that do not require you to compromise your moral principles, and they deserve your support.

The Road to Reality

2009-03-11T13:42:00.102-10:00

I finally got around to reading The Road to Reality: A Complete Guide to the Laws of the Universe (2004; 2007 rev. ed.) by Roger Penrose, and decided to write a little summary of my reading experience. It's a mixed bag, with many fascinating topics in mathematics and fundamental physics expounded expertly, complicated somewhat by a number of rather difficult mathematical concepts that I think are hopelessly inaccessible to most layman readers.

(click to continue reading)

Sir Roger Penrose (knighted in 1994) is without doubt one of our time's most original mathematicians, with a flair for the unconventional. His many contributions to mathematics and physics include Penrose tiles, spin networks (later incorporated into loop quantum gravity), the Penrose interpretation of quantum mechanics (gravitational objective reduction), and twistor theory. Having spent eight years composing his magnum opus, Penrose was in his seventies by the time The Road to Reality was released in 2004, yet he writes with a keenness of mind, alacrity and wit that belies his age.

It is beyond my abilities to give a blow-by-blow dissection of the chapters of this 1000-page tome. For the technical soundness of the material I will happily submit to Penrose's expertise, and will here merely offer some general comments on the scope and philosophy of the book.

Accessibility (or: Who might read this book?)
This book takes a deep look into the mathematical foundations of the physical universe. This means that it is, by and large, about mathematics. This alone probably places the book out of reach for a substantial portion of the layman audience, although Penrose optimistically would beg to differ. This is not really a failing of the author; it is simply the inescapable nature of the subject that no other language exists other than mathematics to communicate the beauty and power of modern physics properly. But in any case, I must consider his optimism about the book's accessibility somewhat naive, when he writes in the Preface:

"...I am an optimist and I believe that there are many out there, even among those who could never master the manipulation of fractions, who have the capacity to catch some glimpse of a wonderful world that I believe must be, to a significant degree, accessible even to them." (p. xvi)

After which he goes on to write a thousand pages of mathematical physics, most of it of a fairly advanced scope. A closer look, however, reveals that the text might be accessible at different levels, depending on whether the subject is mathematics, physics or philosophy. Although the book starts out deeply entrenched in pure mathematics, what emerges as you read on is an increasingly prosaic discussion around the relevant physics, interleaved with philosophical questions about the relationship between the mathematics and physics. The latter is undoubtedly much more accessible to a broader audience than the mathematics tutorial of the first half, so if the maths is giving you headaches initially, take heart and read on.

Nevertheless, my old physics degree notwithstanding, The Road to Reality was not an entirely easy read for me, despite my having a general understanding of differential geometry, classical and quantum mechanics, general relativity etc. going in. On the other hand, if it had been a very easy read, that would have been an insult to the eight years that Penrose spent writing this incredibly ambitious text on such a profound topic.

In the final analysis, I will have come down on the side of Penrose (although for different reasons) and suggest that this book could be recommended for anybody with a curiosity about the efforts of modern science to uncover the underlying nature of the universe. There is no doubt that many readers will be left behind by the complexity of the mathematics at some point in the book, but even so you may still be able to catch a glimpse of the wonderful and fascinating world of modern mathematical physics.

Scope
Related to the issue of accessibility is the matter of the scope of the book, in the sense, what's it really about? The clue is in the title, but it can potentially be misunderstood and invoke false expectations in the reader, so let's clarify this a bit.

First one must note that The Road to Reality is not so much a road as a roadmap, in the sense that it provides only a set of instructions for how to (potentially) get to the destination without actually going there. To actually travel down any given road that might tickle your fancy, you will have to pick up a more comprehensive textbook on the subject.

Secondly, we need to be clear about what flavor of "Reality" and "Laws" Penrose is thinking about here. We find that, in keeping with the "roadmap" philosophy, almost all of applied physics have been left out, in favor of the strictly foundational branches (e.g. Maxwell's electromagnetism, Lagrangian mechanics, etc.), from which all the other disciplines can be derived. It becomes clear that the author's goal and main interest is the underlying, ultimate reality that is the key to everything else that we observe—as opposed to the proximate realities of our current, incomplete theories and the whole of applied physics based on these, which most of us mortals would probably perceive as quite real already.

We can now say both what The Road to Reality is and what it is not: it is not a complete guide to the trove of physics that we all perceive as real; rather it is a guide to the quest for the underlying laws that we suppose form the basis for an ultimate reality, but which we do not actually perceive. If we combine these two observations and, with some poetic license, rewrite the title of the book as "A Roadmap toward Ultimate Reality" - then all of a sudden the entire book makes perfect sense, as its true scope is made clear.

Just one example: Although there's a wealth of modern classical mechanics and electrodynamics that could be expounded on at length, for the purpose of leapfrogging towards the ultimate reality, all we really need to see are the foundational Lagrangian and Hamiltonian formulations that will eventually lead us into quantum mechanics and field theory - and this is essentially what we get.

Synopsis
Although the book is not divided into any major "Parts," there is a natural division of the contents to this effect. Here follows my very brief synopsis of the book, wherein I have grouped chapters into what I perceive as the principal topics:

Mathematics (ch. 1-16, 376 pages). Extensive introduction to the mathematical tools that are to be employed, covering the basics of calculus, differential geometry (calculus on manifolds), set and group theory. Probably the most difficult part for non-experts, but the geometrical concepts introduced are foundational for the formulation of quantum gravity theories later on.
Classical physics (ch. 17-20, 110 pages). Crash course in classical theory, covering Newton's laws, spacetime concepts and special relativity, Maxwell's electrodynamics, Einstein's general relativity, and the Lagrangian and Hamiltonian formulations of Newtonian mechanics. Although formally physics, the focus is still on its underlying mathematical principles.
Quantum physics (ch. 21-26, 193 pages). Midpoint of the book moves into non-classical territory with the standard formulations of quantum mechanics, the "standard model" of particle physics, and basic quantum field theory. From here on, the physics aspect grows in importance, and the discussion becomes more concerned with empirical support and reality-checking than in previous parts.
Cosmology (ch. 27-28, 96 pages). The Big Bang chapter kicks off with a primer on the Second Law of thermodynamics and black holes, followed by an introduction to various cosmological models. The inflation hypothesis and the Hartle-Hawking no-boundary proposal are given special attention, and found to be wanting.
Quantum ontology (ch. 29-30, 87 pages). The discussion on quantum ontology picks up where the previous section on quantum physics left off, and leads into the quantum gravity section. The various standard interpretations of quantum mechanics are analyzed (e.g. Copenhagen, many worlds, decoherence, etc.) and found to be wanting. The "Penrose interpretation" of gravitational objective reduction is introduced. The problem of state reduction is identified as the major problem of current quantum theory, and the source of much trouble in QFTs.
Quantum gravity (ch. 31-34, 179 pages). The final part is a mix-and-match of various approaches to a new theory of quantum gravity, starting with supersymmetry, string theory and M-theory, followed by loop quantum gravity and twistor theory. The final chapter closes with a comparative assessment of the current state of affairs, both theoretically and experimentally, and a bit of philosophical afterthought.

Some comments on all this is in order. In starting the book with 400 pages of pure mathematics, Penrose sets the bar. The following 100 pages is supposedly about classical physics, but you can barely tell the difference, so mathematical is the presentation still. Penrose's presentation of classical physics does not much resemble any standard physics syllabus, but perhaps that of a mathematics course. This has some interesting consequences, for instance: Aristotelian "spacetime" is described as a 4-manifold, and Newtonian spacetime as a fiber bundle, although Aristotle had of course never heard of either spacetime nor manifolds, and Newton had never heard of fiber bundles.

As another example of this minimalism and modernization, the chapter on spacetime and metrics comes before classical electromagnetic theory, although most physics students will most likely have been taught about Maxwell's equations long before learning about metrics, geodesics or manifolds in math class. Given this ordering of things, Penrose now gives Maxwell's equations directly on tensor form, omitting entirely the traditional vector calculus formulation that most students will have become acquainted with in physics class. While this is a very compact and unified notation, this formula completely obscures the relationship between the electric and magnetic fields that are made explicit in the standard differential equation formulation. What do you "understand" about the reality of electric and magnetic fields by looking at an equation that merely says: dF=0 ? For a road to reality, the scenery is sometimes pretty barren.

Fortunately, after being subjected to 500 pages of mostly disembodied mathematics, something remarkable happens, which we may well call a quantum leap. The real onset of physics and reality-checking happens in chapter 21 on quantum particles, where all of a sudden we get a generous dose of it all at once. Here we also get the first hints of what Penrose sees as the fundamental roadblock in quantum mechanics, the state reduction problem and the lack of a realistic ontology, to be developed in detail in chapters 29-30. I was unfamiliar with Penrose's work in this area, and found this chapter (30) and his "gravitational Objective Reduction" to be one of the most interesting parts of the book.

Related to this, one very good thing about the presentation is that Penrose is very diligent with prefacing statements with "My own position on this is that..." or "This notation may be somewhat unconventional..." whenever he is expressing a personal opinion or using a non-standard formulation. This is fairly important, since Penrose does indeed hold some non-traditional views, especially on inflation and string theory. But he has taken great care throughout the book to make sure that there can be no confusion on the part of the reader in this regard.

When it comes to theories of quantum gravity, Penrose is not interested in just giving an overview of the current work in various directions, like a dictionary or a Wikipedia entry might. Instead he takes an active, critical look at the competing theories, evaluates their strengths and weaknesses, and estimates their prospect of success. In his assessment of string theory (ch. 31, 34), Penrose somewhat foreshadows Lee Smolin's 2006 book The Trouble with Physics, which delivered a scathing criticism of string theory and the dangers of fashion-driven research in science. Sypersymmetry and M-theory does not fare much better (these things are all amalgamated now anyway...), while loop quantum gravity is given a tentative pass to further development, although it too has its problems.

For his own brainchild, twistor theory, Penrose expresses some optimism for future development, but admits that at the moment it is no more a physical theory than string theory is. I had not understood twistor theory, nor appreciated its beauty and finesse, before reading this book, so it came as a bit of a disappointment to learn that very little research goes into this topic. If no one researches it, for sure it will never progress!

Philosophy
It is hard to classify Penrose philosophically. He's clearly a Platonic realist with regards to mathematics, but claims to be a realist with regards to the mapping from mathematics to physics. Despite talking about the subject at length (chapter 1, 34), it is not clear to me whether he really believes that the universe is ultimately governed by precise mathematical laws from this Platonic realm, or what he thinks the relation otherwise is between nature's laws and our mathematics. I'll declare my own view here: I do not think it impossible that mathematics might be so general and flexible as to be able to describe the laws of nature perfectly, without for that matter having any deeper relation to those laws.

The Road to Reality is replete with examples of Penrose criticizing others (e.g. inflation cosmologists and string theorists) for being led by mathematical "miracles" and aesthetics rather than physical considerations. Yet at the same time, he exudes a distinctly Platonic mysticism when it comes to certain mathematical topics that are close to his heart, where he perceives that there is really something "going on behind the scenes" (e.g. the "magic" of complex numbers), that there is some deep physics residing in the mathematics that we plucked from some Platonic tree. Here is just one example of many:

"It should also be remarked that just the existence of such a mathematically elegant unifying picture appears to be telling us something deep about the mathematical underpinnings of our physical universe, even at the level of the laws that were revealed in 17th century Newtonian mechanics." (p. 471)

At the end of the day, I can't reconcile all of his contradictory statements on this subject, so either I haven't understood what he's really proposing, or he's not sure himself. Leaving that aside, I'll close this review with a couple of random quotes from the book.

Regarding electroweak symmetry breaking:

"I am in no way suggesting that we should abandon the essential beautiful insights of electroweak theory, but I prefer a slightly different attitude to the breaking of its U(2) symmetry from that which is usually put forward. As I see it, Nature's true scheme for particle physics has not yet come to light. Such a scheme should be mathematically consistent and will not have the nasty habit that our present-day QFTs have, of spitting out the answer '∞' to so many reasonably-phrased physical questions." (p. 745)

Regarding cosmic inflation:

"I believe that particular caution is to be recommended in matters of cosmology, as opposed to most other sciences, especially in relation to the origin of the universe. People often have strong emotional responses to questions of the origin of the universe—and sometimes these are either implicitly or explicitly related to religious preferences." (p. 753)

Regarding quantum ontology:

"My own position, on the other hand, is that the issue of ontology is crucial to quantum mechanics, though it raises some matters that are far from being resolved at the present time." (p. 785)

A Quantum of Freedom

2008-12-18T18:41:00.096-10:00

Well here is my end-of-the-year rant for 2008, on the non-problem of free will. Raise your glass with me, and let's drink to the confusion of philosophers :-)

Cheers! (skål! sante! kanpai! prost! nazdorovia! kippis! yiamas!)

(PDF version of this article, minus the hyperlinks)

--
Introduction
Much as I laud and espouse philosopher Daniel Dennett's compatibilism theory of free will (Freedom Evolves, Dennett, 2003), I often feel that something basic is missing from the picture, and what's missing are the basics. By this I mean physics: events involving atoms and quanta, obeying the laws of quantum mechanics, which are so radically different from the laws that we experience on the level of people and human decisions. In particular, compatibilism theories leave quantum indeterminacy entirely out of the picture. In Dennett-speak, his theory explains free will on the "design level" and on the "intentional level," skipping the "physical level." To a physicist, this feels like a story starting in the middle, claiming that the details of the beginning were unimportant anyway. Well, as with Doctor Who and Gilligan's Island, this actually turns out to be perfectly true, and of course biologists, engineers, psychologists, sociologists etc. have known this for a long time (or perhaps more likely never given it a thought). But to philosophers and physicists it may not be immediately obvious why it is true, and it might leave some people (like myself) wondering, whatever happened in the chapters that we skipped?

In the following, I will try to formulate some ideas around how to philosophically bridge the explanatory gap between the quantum and the phylum, by first connecting the two, then severing the connection, and finally suggesting inverting the connection.

(click to continue reading)

Free Will and the Quantum
To start off lightly with the concept of determinism, this is the philosophical and scientific idea that all events that take place are causally connected to earlier events in an absolute and objective way. Historically, this idea has made some philosophers nervous, culminating in the so-called problem of free will: if all physical events are causally connected and determined by objective laws, how can there be any freedom to choose our actions? Wouldn't our actions then be determined by the mindless motions of atoms? The moralistic religions have capitalized on the apparent conundrum, asking: "If no free will, whence morality?" (and answering: God).

It is curious how few in the past have asked themselves the opposite question, admittedly bold, in light of the success of reductionism, whether it might not be we who are determining the motions of our atoms instead of the other way around. Not, as must be assumed, by directly channeling the wave-functions of these particles and somehow controlling them this way; but by possessing causal influence over the boundary conditions that constrain and in many cases all but determine the evolution of quantum microstates. This notion may require some Necker-cube-like inversions for some, in order to be even contemplated as a sane possibility. There is an idea that holds that all the informational content in the universe is encoded in its boundary conditions. I forget who said this (possibly Lloyd 2006; I'm too lazy to reread the book to check - my apologies if I'm mistaken). At any rate, boundary conditions are not to be sneezed at.

Well, the times they are a-changing. Today, scientists have discovered the indeterminacy that underlie quantum physics, leading some intellectuals to lazily take this as a basis for libertarianism, although nothing is really explained by this move. Some philosophers have instead pursued and constructed entirely viable compatibilism theories of free will (i.e., theories that make free will and determinism compatible realities). And yet other philosophers are exploring newfangled avenues in the intersection of mathematics and neuroscience, and are nosily asking meddlesome questions like "Who or what is really shoving what or whom around, here?" (Sperry, 1965; Hofstadter, 2007) We will touch on most of these issues, starting at the end of the quantum.

Modern quantum theory has found that nature on the level of fundamental physics is not deterministic, but probabilistic, and that this is not just an apparent feature or a practical limitation, but a fundamental property of nature (Conway & Kochen, 2008; see also hidden variable theories, Bell's theorem and experimental verifications). This has the consequence, which we need to explore in more detail, that events above the physical level are extremely unlikely to be influenced, let alone determined, by single-particle quantum events.

The disturbing notion that even a single particle could (and would) determine some (however subtle) aspect of our behavior, and deprive us of ultimate choice, is a logical consequence of Democritean atomism and Newtonian mechanics. These describe, respectively, matter as an aggregate of indivisible particles, and the motion of matter (including such particles) by a set of deterministic rules with, in principle, completely predictable outcomes. A simple thought experiment imagines that the mindless motions of atoms, via an unbroken chain of causal events connecting successively larger structures, eventually end up having causal power over people, who now appear to be completely determined by the goings-on at the atomic level. But if this were the case, why do we feel like we have free will? Either determinism must be false, or free will is an illusion, or something magic happens - or any combination of the three.

Now just for fun, let's turn things around as before and ask: since we seem to have free will, how can our atoms be free to bounce around however they please? The answer is, of course: they aren't. Keep this thought for future reference, when we shall discover that the atoms are chiefly passengers, not the drivers (then who's driving?).

"But hang on now," you should protest, "human beings consist of a huge number of particles, so even by the principles of determinism of course our actions would not determined by just any single particle, but billions and billions of them. Aren't you setting up a straw man here?"

You are partly correct in your objection, but if the upwards causality of determinism held true, then even the minute whims of a single particle might ultimately propagate into an effect on your behavior and decision-making. So we need to look at this elementary problem first, before expanding the investigation and adding more realism.

The preceding conundrum at the heart of the problem of free will is ancient history. But as we reexamine this thought experiment with quantum mechanics in place of Newtonian mechanics, something curious emerges. In quantum theory, what any given particle is doing is no longer completely determined by its internal state and the local environment (consisting of other particles and boundary conditions). To begin with, the particle is no longer localized, but spread out (or "blurred" out) according to some probability wave. Secondly, the evolution from one state to a future state is also probabilistic, rendering invalid the notion of being able to predict with absolute certainty, even in principle, a future state by having access to perfect information of the state and boundary conditions at one specific time. So what does all this mean?

Well for one thing it just means that no future state is completely determined by any prior state, and there goes the notion that quantum events of single particles could deterministically control the future of the people they populate. There are happenings going on at the physical level all right, but they do not have the direct causal power that determinism would allot them. Quantum events then, in most situations, are not by themselves able to causally affect macroscopic events. I shall state now, to be investigated in the following sections, that in everyday life, quantum events on the physical level are for all practical purposes (including causal effects) subsumed by the next higher level of description, which is that of statistical physics.

I must emphasize the qualifiers "everyday life" and "for all practical purposes" above, because modern technology allows us to build instruments that are in fact sensitive to and capable of generating single-particle events. One could imagine pathological scenarios where, say, the fate of a cat in a box was in fact at the mercy of a single quantum event on the physical level. Another example could be high-energy cosmic rays, where in an extremely unlikely scenario a single proton traveling at near the speed of light could collide with an atomic nucleus in an astronaut's brain and possibly cause some serious damage. For most of human existence and experience, however, such singular quantum events simply do not play any part in your everyday life. (Even when you take an MRI scan and billions of protons in the hydrogen nuclei of the water molecules of your body are pumped to excited spin states by radio frequency electromagnetic pulses, this has no effect on your bodily actions). And in any case, these are quantum events of origins external to your body, and not even in the same category that we were considering with regards to the issue of your atoms controlling your Self.

"All right," you might be thinking now, "so the particles of my body can not have any determined causal power over me, because their interactions are all subject to quantum indeterminacy, I get all that. But isn't there still an unbroken chain of causal events from the physical level to the intentional level, so that one could still trace a human action following a choice all the way back to a quantum event? Isn't this still just the same old determinism?"

Not at all - there are two things to note here. First of all, it only looks deterministic after the fact. We already established above that the exact evolution of a microstate is not strictly determined by any given prior microstate. This leads us to ask the more interesting question: what did in fact determine the evolution of states, and the final macrostate? Secondly, there are further and even stronger reasons for why the poor particles become causally disenfranchised as they become part of the macroscopic entity that our bodies are, and one reason is this: our bodies are not simply made of particles in a heap, but of highly specific structures of particles.

Structures and Patterns
Now let's try a different track. I have been painting a picture of the evolution of quantum microstates as a blurry and probabilistic process on the physical level, in order to hammer home the point that determinism breaks down there. This exercise might have left the mistaken impression that there is no telling (or controlling) what the particles of my body (and yours) might do; why don't our particles just take a random hike and go all their own ways? I now have to undo this intellectual damage by adding a few more layers of reality to the story, and I will broach it through a more mundane example.

What happens when, for instance, I put my hand on the steering wheel of my car to make it turn? (I had decided, out of my own free will, that I meant to do that.) At one level of description, one could say that a clump of particles (my hand) interacts with another clump of particles (the steering wheel), resulting in the turning of the wheel, and my will be done. The macroscopic phenomenon causing the wheel to turn in response to the intruding clump of particles is called friction. Friction on the physical level is a combination of electromagnetic forces between charged particles, in this case the electron clouds of atoms and molecules and the protons of atomic nuclei. The exact details of frictional force are nontrivial but also not important here; the interesting question here is, when external electric forces act on the molecules in my hand, why don't the molecules yield to the force? Even in Newtonian mechanics, the third law states that to every action there is an equal and opposite reaction. When the molecules of my hand encounter the electron clouds of the steering wheel, why don't they just scatter; what holds them all in place? Whence friction, rather than particle soup?

Although friction is a complicated effect in quantum physics terms, for the purpose of this discussion it is enough to note here that "clumps of particles" is an inadequate description in order to continue this explanation. We can see that the structure of the particles within the clumps are going to matter critically for how this plays out, and that this structure is what "holds it together."

I am initially thinking of atomic structures of the type, in order of growing complexity, simple molecules, metallic, crystalline, complex molecules (e.g. polymers, proteins, amino acids, etc.). These compound structures enable a whole new ontology of entities and possibilities - along with new causal relationships between entities on different levels. If we take one more step upwards, the next structural level is that of simple autonomous agents and cellular building blocks (see e.g. Kauffman, 1993; Nowak, 2008), and now we have entered Dennett's design level where his compatibilism theory can do the rest of the explaining. But even so, let's carry this on just a little bit further.

The key point to take home here is that if the building blocks of matter on the fundamental level has certain causal properties, the particular arrangement of matter and aggregation into structures modifies how those properties can (or more interestingly to us, can not) propagate across increasing levels of complexity. As we progress upward in structural complexity, quantum indeterminacy becomes more and more irrelevant as the classical laws of physics gradually reemerge in the shape of statistical physics, where ensembles and compound entities enjoy macroscopic determinism once again.

In retrospect we may allow ourselves to be somewhat flabbergasted now, at the oft regurgitated religious canard against materialism that "if materialism is true, then we are nothing but the motions of atoms!" But why atoms? Why not quarks and gluons that the atomic nuclei are made of? Perhaps the materialism skeptics are dimly aware that the particulars of the strong nuclear force prevents quarks and gluons from having any significant effects outside of the nucleus, except in extremely-high-energy particle physics experiments. So maybe they are happy to consider quarks and gluons as passengers and not drivers. But they still want to believe that atoms would be the ones in the driver's seat if materialism was true? Well - we have to concede that the physics are different for atoms and for quarks, and that atomic elements do in fact play various roles in the human biochemistry, which could potentially provide the opening for total control of the human body and mind. But to suppose that possessing the mere capability of chemical affinity would automatically put atoms in the driver's seat of our bodies and rob us of free will - that is simply absurd. Most atoms of our bodies are part of larger structures that effectively prevent their constituents from even attempting such a coup; they just go where they're told.

Anyway. To reiterate: to the extent that the atoms that constitute our bodies are themselves part of larger structures, the causal effects of single atoms are formidably reduced and constrained by their parent structures. Because those atoms are constrained by their parent structure, they are for all practical purposes controlled by it, turning the tables on causality. There is also nothing stopping us from carrying on this successive structural expansion and causal inversion upward, finding more instances of sub-structures being controlled by their parent structures rather than the other way around. Now who is pushing whom around?

Naturally there are shades of gray here, not everything can be categorized as easily into "causes up" and "causes down." As we look to the details, we find a very mixed picture of causal arrows pointing both ways, sometimes from the microscopic to the macroscopic, and sometimes the other way around. I am not at all suggesting that microscopic events have no effect on our macroscopic state of affairs. The energy that power us and the chemicals that mediate the control signals around our body are only two examples of many, where happenings on the physical level are vital to our functioning properly. But the question we were trying to address with regards to the problem of free will was whether, in a naturalistic and materialistic explanatory framework such as the one picture presented here, these microscopic happenings have any direct causal power over the concrete and abstract decisions that we make in everyday life. If you agree with me, then the answer to this should now be a clear No.

If this has all been too confusing and florid, let me try to sum up the key points so far:

Determinism breaks down at the physical level where quantum mechanics renders reality probabilistic.
The atoms that make up your body are to a large degree formidably constrained in their possible states and evolutions, by the boundary conditions imposed on them by the parent structures of which the atoms are an integral part.
Atoms constrained by the boundary conditions of their parent structures can have very little upward causal effect; the structure itself becomes the unit and mediator of causality.
The same reasoning can be applied recursively to many (though not all) structures that make up the human body, finding at the structural level-crossings that the causal arrows point downward, and that in these cases, the large is pushing the small around.
Biochemical processes close to the physical level of course also play a vital role in many physiological functions, so the final state of affairs is a mixed picture with causal arrows pointing both ways across most structural gaps. Macroscopic actions thus involve level-crossing causal feed-back loops.
Who, or what, is ultimately in the driver's seat then?

In all that matters to the high-level control of your Self and you body, You are the highest level structure of yourself, and you are normally the one causally pushing all the constituent structures around (occasionally though, your body will seem to be doing things that are beyond your conscious control, like yawning and sneezing - such quirks are often reflexes and fixed action patterns). When you move your right hand from the stick to the steering wheel, you do not exert direct control over entities like atoms, molecules or cells in your arm. The level-crossing instructions that caused your arm to move originated in the abstract "You" that is in control. The abstraction became encoded into electrochemical signals and propagated around your body, regulating the biochemical processes in the muscles of your arm, causing it move according to the instructions of the symbolic pattern in your brain that had issued the command.

And now we have to take just a brief peek into Pandora's box and ask: what, then, is this "you" or "I", or our "Self" that is doing the ultimate pushing around, and whose freedom is the locus of our concern? The best answer that I know to this question is given by Douglas Hofstadter in his 2007 book I am A Strange Loop. I won't quote it in full (I have a meeting), but I'll urge you to read the book, and leave you with a teaser.

If what constitutes "me" or the "I" in me are not to be found in the substrates that we are made of but in their organization, their representational patterns - then we will discover that the patterns that are You are exactly what is pushing your Self around, along with your body. When you make an abstract choice, you are both the cause and the effect; the beginning and the end of the loop. I hope that no one will think that this is still not "real" free will, but some sort of illusion; I can't see how one could possibly be any freer than this!

Epilogue
To those of you wondering what would happen to this rosy picture of free will in the case that quantum indeterminacy was discovered to be false after all, I say: not to worry. Dennett's compatibilism theory covers this case already. Dropping quantum indeterminacy from the above description will not change the fact that ontological entities at lower levels will always be physically and therefore causally constrained by the larger structures that they are part of. Quite regardless of whether the squiggles on the atomic level are fundamentally deterministic or indeterministic, their squiggles remain controlled by the boundary conditions of the structures that they inhabit, and a revision of quantum physics will not change that in the least. The effective downward causation from large to small will still hold. So, you may ask then, why even bother dragging quantum indeterminacy into the picture in the first place?? Well, because I wanted to. It is the reality as we know it today, so simply for closure, and perhaps exactly because quantum theory is so counter-intuitive, I feel that it needs to be part of the overall picture even if, ultimately, it has no explanatory power within a theory of mind and free will.

As a final word, because of the breakdown of determinism at the bottom of this explanatory ladder that I have presented, I expect that this description of free will should qualify as "real" or "genuine" free will even by religious standards. Dennett's compatibilism theory will probably be forever regarded by theists as a "fake" kind of free will or an illusion; but, as I hope to have shown here, his theory has a natural extension all the way down to the quantum level, making it perfectly harmonious also with quantum indeterminacy, and rendering this flavor of free will just as real as anything else that is real.

Merry Christmas!

Baraka (16 years later)

2008-11-02T19:36:00.047-10:00

Remastered in high definition and given new lease of life, the new Baraka DVD release shines like never before. And if you don't know what Baraka is, now is the time to find out. Just compare the old (left) and the new (right) DVD version and you'll see right away what I'm talking about (you need to compare the full-resolution images by clicking on the thumbnails, in order to see the magnitude of the difference):

I have seen this film so many times since its release in 1992, at various venues, big screen and small, home theater system and HD projector, you name it. I own the standard DVD version since before, but as I popped this new version into the Oppo DV-981HD and sat back to watch the remastered Baraka on my 720p projector I was simply blown away (again).

I can only quote Andrew Oran at FotoKem, the company that did the restoration, when he says that they have created "...what is arguably the highest quality DVD that's ever been made." I do not doubt him for a second - the new Baraka is absolutely stunning (and no, I have not been paid to endorse this product). Imagine if all DVDs could be mastered with such a quality, who then needs Blue-ray..

(click for more pictures)

Here are some more old-new comparisons:

(I hope I'm not violating any copyrights by putting up these pictures in full resolution, someone please alert me if I am.)

So Long, and Mahalo!

2008-11-01T18:42:00.015-10:00

This post is about myself: me, me, me. Today, Saturday, 1 November 2008, is my first day of unemployment with no new job waiting for me since my professional career started, about ten years ago. No more adaptive optics for me, and I never want to hear the words "PSF reconstruction" ever again.

(click to continue reading)

Well – actually there's nothing sinister about it, I feel very good now that I finally managed to escape a profession with which I have been disillusioned for maybe as long as the last five years, without even realizing this fact until very recently. Although I am embarrassed to confess that even in this endeavor I am five months behind schedule, as I actually blogged about my personal epiphany in May ("A Drive to Kona") which became the reason that I created this blog in the first place. But I am writing this post sitting at the exact same table as that time, out on the terrace at Borders in Kona, exactly where I wrote the very first post, so at least there's symmetry.

I will not write about adaptive optics or the project that finally broke me, or the sad state of affairs during the intervening period while I was procrastinating. The project has a Twiki, and if anyone is curious, the final report is here. I blame my inability to follow through last May on my much-too-generous supervisor, who no doubt used his Jedi mind powers on me in order to talk me out of it that time... This isn't the solution you're looking for. Go see a doctor. You'll come back to work.

So where do I go from here? It feels strange to say, but now that I'm no longer bound by a career that was choking me, it feels like the sky's the limit. I took the red pill, and I'm seeing the world again with completely new eyes. With the current economic crunch and a looming energy crisis, I might be easily motivated to work on renewable energy technologies, or perhaps do some science writing, or perhaps even connect with politics for the sake of lobbying for these things that are going to be extremely important for a flourishing future society. Or maybe I'll do something completely different, who knows; at any rate, I will take my time, this time, to think about things. But first I will spend a few weeks on the beach, work on my tan, and sample the good life of Hawai'i.

Aloha a hui hou kakou

Beyond Belief '08

2008-10-21T11:41:00.010-10:00

"Science as a Candle in the Dark" was the subtitle of Carl Sagan's seminal 1996 book "The Demon-Haunted World," and "Candle in the Dark" is also the subtitle of the 2008 Beyond Belief conference. Participants include Anthony Grayling, Sam Harris, Paul Davies, Jonathan Haidt, Lawrence Krauss, V. S. Ramachandran, Michael Shermer, and many more. The videos were temporarily taken down due to high demand (should eventually be available on Google video), but you can download (and please seed) a torrent of the first 24 lectures released (I don't know if there are more to be released). Also drop by RDF to discuss the material :-)

Feynman on Science

2008-10-16T15:41:00.090-10:00

Richard Feynman (1918-1988) disliked philosophy most of the time almost as much as he liked wooing women and figuring out the mysteries of the world all of the time (which were often one and the same). Yet he was occasionally struck by the "disease to philosophize" and produced many works, in the form of public talks and short essays, which are rich in scientific philosophy and deep insight. I have taken the liberty to selectively quote here from four of my favorite Feynman essays that speak on the nature and philosophy of science.

This distilled commentary is no substitute for reading the original works, which can be found in the volumes "The Pleasure of Finding Things Out," "The Meaning of it All" and "Surely You're Joking, Mr. Feynman!". Some material are available online, for instance at Feynman Online, and the 1981 BBC interview "The Pleasure of Finding Things Out".

What is science? To Feynman, it was the liberty to explore freely and to question the expertise of experts; to embrace doubt and uncertainty as the seeds of new discovery; to peer unafraid into the unknown and possibly unknowable, and to be fascinated by it all; and to pass on our knowledge to coming generations with the provisio that we may have been wrong. These are sentiments that surely resonate within many scientist's hearts and minds, and which, quite apart from their practical value in teaching us about science, possess an aesthetic allure all by themselves.

(click to continue reading)

Sources:

The Value of Science (1955)
The Uncertainty of Science (1963)
What is Science? (1966)
The Pleasure of Finding Things Out (1981)

"The Value of Science" (public address, NAS, 1955)

On the intellectual enjoyment and the fascination that the scientific worldview offers, he writes:

I would like not to underestimate the value of the world view which is the results of scientific effort. We have been led to imagine all sorts of things infinitely more marvelous than the imaginings of poets and dreamers of the past. It shows that the imagination of nature is far, far greater than the imagination of man.

He mentions, casually, one very important thing that admirers of classical philosophers sometimes forget or ignore, namely that the latter had very insufficient information available to them:

I hope you will excuse me if I remind you of this type of thought that I am sure many of you have had, which no one could ever have had in the past because people then didn't have the information we have about the world today.

On "The Grand Adventure" of science, still unsung by poets, he writes:

It is true that few unscientific people have this particular type of religious experience. Our poets do not write about it; our artists do not try to portray this remarkable thing. I don't know why. Is no one inspired by our present picture of the universe? This value of science remains unsung by singers: you are reduced to hearing not a song or poem, but an evening lecture about it. This is not yet a scientific age.

On doubt and uncertainty, the largest lesson of them all, which we are always returning to, needing to be reminded of:

I would now like to turn to a third value that science has. It is a little less direct, but not much. The scientist has a lot of experience with ignorance and doubt and uncertainty, and this experience is of very great importance, I think. When a scientist doesn't know the answer to a problem, he is ignorant. When he has a hunch as to what the result is, he is uncertain. And when he is pretty darn sure of what the result is going to be, he is still in some doubt. We have found it of paramount importance that in order to progress we must recognize our ignorance and leave room for doubt. Scientific knowledge is a body of statements of varying degrees of certainty - some most unsure, some nearly sure, but none absolutely certain.

These cornerstones of science did not come for free, they were fought for at great length and cost:

Now, we scientists are used to this, and we take it for granted that it is perfectly consistent to be unsure, that it is possible to live and not know. But I don't know whether everyone realizes this is true. Our freedom to doubt was born out of a struggle against authority in the early days of science. It was a very deep and strong struggle: permit us to question - to doubt - to not be sure.

What, then, is the meaning of it all?

What, then, is the meaning of it all? What can we say to dispel the mystery of existence? If we take everything into account - not only what the ancients knew, but all of what we know today that they didn't know - then I think we must frankly admit that we do not know.

On our responsibility as scientists, in passing on our knowledge without stunting the development of future science, Feynman has this to say:

It is our responsibility to leave the people of the future a free hand. In the impetuous youth of humanity, we can make grave errors that can stunt our growth for a long time. This we will do if we say we have the answers now, so young and ignorant as we are. If we suppress all discussion, all criticism, proclaiming "This is the answer, my friends; man is saved!" we will doom humanity for a long time to the chains of authority, confined to the limits of our present imagination. It has been done so many times before.

And concluding, it is our responsibility as scientists to:

...to teach how doubt is not to be feared but welcomed and discussed; and to demand this freedom as our duty to all coming generations

"The Uncertainty of Science" (Danz Lectures, 1963)

(Some topics from "The Value of Science" that are repeated in these lectures have been left out here, as they were quote above already)

We have three definitions of science:

Science means, sometimes, a special method of finding things out. Sometimes it means the body of knowledge arising from the things found out. It may also mean the new things you can do when you have found something out, or the actual doing of new things.

Of the three, the last is usually referred to as technology, and it in particular confers upon mankind the power to do new and unexpected, and sometimes harmful, things:

Now this power to do things carries with it no instructions on how to use it, whether to use it for good or for evil. The product of this power is either good or evil, depending on how it is used. [...] Is science of any value? I think a power to do something is of value. Whether the result is a good thing or a bad thing depends on how it is used, but the power is a value.

The Heaven and Hell of science is within our reach:

Once in Hawai'i I was taken to see a Buddhist temple. In the temple a man said, "I am going to tell you something that you will never forget." And then he said, "To every man is given the key to the gates of heaven. The same key opens the gates of hell." And so it is with science. In a way it is a key to the gates of heaven, and the same key opens the gates of hell, and we do not have any instructions as to which is which gate. Shall we throw away the key and never have a way to enter the gates of heaven? Or shall we struggle with which is the best way to use the key?

Science is the great adventure of our times:

You can not understand science and its relation to anything else unless you understand and appreciate the great adventure of our time. You do not live in your time unless you understand that this is a tremendous adventure and a wild and exciting thing.

Theologians take note. (That's just my personal remark.)

Confronting a most terrible test of human reasoning abilities:

Trying to understand the way nature works involves a most terrible test of human reasoning ability. It involves subtle trickery, beautiful tightropes of logic on which one has to walk in order not to make a mistake in predicting what will happen. The quantum mechanical and the relativity ideas are examples of this.

Science as a method of finding things out:

This method is based on the principle that observation is the judge of whether something is so or not. All other aspects and characteristics of science can be understood directly when we understand that observation is the ultimate and final judge of truth of an idea.

The exception proves that the rule is wrong:

Or, put another way, "The exception proves that the rule is wrong." That is the principle of science. If there is an exception to any rule, and if it can be proved by observation, that rule is wrong.

Limitations of observational science:

The principle that observation is the judge imposes a severe limitation to the kind of questions that can be answered. They are limited to questions that you can put this way: "If I do this, what will happen?"

Words, words, words...

Words can be meaningless. If they are used in such a way that no sharp conclusion can be drawn, as in my example of "oomph," then the proposition they state is almost meaningless, because you can explain almost anything by the assertion that things have a tendency to motility.

Where ideas come from makes no difference:

We have a way of checking whether an idea is correct or not that has nothing to do with where it came from. We simply test it against observation. So in science we are not interested in where ideas come from. There is no authority who decides what is a good idea.

There's always a finer-mesh sieve:

The old laws may be wrong. How can an observation be incorrect? If it has been carefully checked, how can it be wrong? Why are physicists always having to change the laws? The answer is, first, that the laws are not the observations and, second, that experiments are always inaccurate. The laws are guessed laws, extrapolations, not something that the observations insist upon. They are just good guesses that have gone through the sieve so far. And it turns out later that the sieve now has smaller holes than the sieves that were used before, and this time the law is caught.

On doubt and uncertainty, again:

Scientists, therefore, are used to dealing with doubt and uncertainty. All scientific knowledge is uncertain. This experience with doubt and uncertainty is important. I believe that it is of great value, and one that extends beyond the sciences. I believe that to solve any problem that has never been solved before, you have to leave the door to the unknown ajar.

"What is Science?" (Address to NSTA, 1966)

Feynman begins his talk on "What is Science?" by a reference to Francis Bacon, that highlights a problem with defining science:

There is some kind of distorted distillation and watered-down and mixed-up words of Francis Bacon from some centuries ago, words which then were supposed to be the deep philosophy of science. But one of the greatest experimental scientists of the time who was really doing something, William Harvey, said that what Bacon said science was, was the science that a lord-chancellor would do. He [Bacon] spoke of making observations, but omitted the vital factor of judgment about what to observe and what to pay attention to. And so what science is, is not what the philosophers have said it is, and certainly not what the teacher editions say it is.

This is a fairly common confusion, that what philosophers of science say that science is, is often far removed from what any given scientist might say that it is for him or her personally. In discussions on the philosophy of science, it is common to hear it stated with (over-)confidence that science is, among other things: empirical inductive, hypothetico-deductive, Popperian, or Bayesian, to mention the most common. Naturally, science is all of that and more besides, to a varying degree depending on the nature of the problem.

In the next paragraph Feynman relates his view on the scientific enterprise, from the roots of intelligence by the evolution of animals that could learn from experience (this part omitted for brevity). He comes to the key feature of non-genetic learning; the passing on of acquired information between generations, enabling exponential learning, but also the danger that comes with this:

This phenomenon of having a memory for the race, of having an accumulated knowledge passable from one generation to another, was new in the world--but it had a disease in it: it was possible to pass on ideas which were not profitable for the race. The race has ideas, but they are not necessarily profitable.

So there came a time in which the ideas, although accumulated very slowly, were all accumulations not only of practical and useful things, but great accumulations of all types of prejudices, and strange and odd beliefs.

Then a way of avoiding the disease was discovered. This is to doubt that what is being passed from the past is in fact true, and to try to find out ab initio again from experience what the situation is, rather than trusting the experience of the past in the form in which it is passed down. And that is what science is: the result of the discovery that it is worthwhile rechecking by new direct experience, and not necessarily trusting the [human] race['s] experience from the past. I see it that way. That is my best definition.

He remarks on how following form and calling it science can become pseudoscience:

Another of the qualities of science is that it teaches the value of rational thought as well as the importance of freedom of thought; the positive results that come from doubting that the lessons are all true. You must here distinguish--especially in teaching--the science from the forms or procedures that are sometimes used in developing science. It is easy to say, "We write, experiment, and observe, and do this or that." You can copy that form exactly. But great religions are dissipated by following form without remembering the direct content of the teaching of the great leaders. In the same way, it is possible to follow form and call it science, but that is pseudo-science. In this way, we all suffer from the kind of tyranny we have today in the many institutions that have come under the influence of pseudoscientific advisers.

After discussing the pseudoscience of cargo-cults, he offers another poignant definition of science:

As a matter of fact, I can also define science another way: Science is the belief in the ignorance of experts.

This is another way of expressing the foundational mindset of a good scientist, that to question the expertise of experts and take the trouble to investigate independently.

In closing he has this to say on how we pass our wisdom on to the future generation:

Finally, with regard to this time-binding, a man cannot live beyond the grave. Each generation that discovers something from its experience must pass that on, but it must pass that on with a delicate balance of respect and disrespect, so that the [human] race--now that it is aware of the disease to which it is liable--does not inflict its errors too rigidly on its youth, but it does pass on the accumulated wisdom, plus the wisdom that it may not be wisdom.

It is necessary to teach both to accept and to reject the past with a kind of balance that takes considerable skill. Science alone of all the subjects contains within itself the lesson of the danger of belief in the infallibility of the greatest teachers of the preceding generation.

"The Pleasure of Finding Things Out" (BBC interview, 1981)

Regarding anomalies in science:

The thing that doesn't fit is the thing that's the most interesting, the part that doesn't go according to what you expected.

The physics that describes nature on various levels often become dauntingly mathematical, regrettably preventing much of the public from attaining that fullest understanding of the phenomena:

If you are interested in the ultimate character of the physical world, or the complete world, and at the present time our only way to understand that is through a mathematical type of reasoning, then I don't think a person can fully appreciate, or in fact can appreciate much of, these particular aspects of the world, the great depth of character of the universality of the laws, the relationships of things, without an understanding of mathematics. I don't know any other way to do it, we don't know any other way to describe it accurately . . . or to see the interrelationships without it.

On the vagaries of quasi-science, and some insights from physics:

You see, I have the advantage of having found out how hard it is to get to really know something, how careful you have to be about checking the experiments, how easy it is to make mistakes and fool yourself. I know what it means to know something, and therefore I see how they get their information and I can't believe they "know" it; they haven't done the work necessary, haven't done the checks necessary, haven't done the care necessary.

We are explorers into the unknown:

...the way I think of what we're doing is, we're exploring, we're trying to find out as much as we can about the world. People say to me: "Are you looking for the ultimate laws of physics?" No, I'm not, I'm just looking to find out more about the world, and if it turns out that there is a simple ultimate law which explains everything, so be it, that would be very nice to discover. If it turns out it's like an onion with millions of layers and we're just sick and tired of looking at the layers, then that's the way it is, but whatever way it comes out it's, nature is there, and she's going to come out the way she is. And therefore, when we go to investigate it we shouldn't predecide what it is we're trying to do, except to try to find out more about it.

Finally, to live with doubt, uncertainty and approximate answers, forward into the unknown future unafraid:

You see, one thing is, I can live with doubt and uncertainty and not knowing. I think it's much more interesting to live not knowing than to have answers which might be wrong. I have approximate answers and possible beliefs and different degrees of certainty about different things, but I'm not absolutely sure of anything and there are many things I don't know anything about, such as whether it means anything to ask why we're here, and what the question might mean.
I might think about it a little bit and if I can't figure it out, then I go on to something else, but I don't have to know an answer, I don't feel frightened by not knowing things, by being lost in a mysterious Universe without having any purpose, which is the way it really is so far as I can tell. It doesn't frighten me.

---
And that's Feynman on science. If you know of additional Feynman quotes that deserve to be mentioned in this context, send them right in!

Random walk beat-syncing

2008-10-13T21:00:00.032-10:00

Here's a little fractal teaser: a few frames extracted from a fractal animation based a new scripting technique that I'm experimenting with (Lua/Oxidizer/flam3). The thing is still rendering frames (will link it when it is done), but in the meantime you can check out some preview clips: random walk beat-syncing. The video quality when uploading to blogger was rather poor, so follow the link and view them on my site instead.

Update 2008-10-15: rendering finished!
(stream from site, or download 83MB)

(click to continue reading)

I should write about this properly at some later time, but for now, suffice it to say that it's a method of synchronizing fractal flame animations to music by rhythmic randomized modulations of flame parameters (in particular, Xform rotation and scaling). In prototyping this stuff I had initially assembled a scripting methodology for Oxidizer/Lua (kudos to John Miller for many tips and ideas) that allowed the user to manually author control points and interpolation characteristics on a simple but generalized format. Such a control script was then parsed into an animation sequence by Lua and rendered by Oxidizer or flam3. Although this provides a flexible interface for scripting animations, it is still rather laborious to author all those control points manually.

Now, if like me you can't be bothered with this kind of tedious stuff, it would be nice if the computer would just automatically generate some nice movements and transitions synchronized to the designated beats. And so I automated the control script to have it do a one-dimensional random walk on each control channel, each transition synchronized to the beat, but randomized in direction and amplitude. With a sufficiently forgiving flame design that doesn't immediately turn into a point or a cloud of noise when moving off the initial design point, this random walk modulation was seen to produce some pretty interesting patterns.

So the first "real" product of this experiment is still in the rendering queue, a few frames of which is shown at the top. Even at as low resolution as 384x288 it will take about two days to render on my current computer (would take 10 days at 640x480 with retained quality...). In the meantime check out the previews.

On Moral Grounds

2008-09-04T01:36:00.078-10:00

Abstract
The question of whether morality needs to be grounded in an objective basis is given an answer in the negative. It is argued that meta-ethical propositions for the affirmative whose veracity can not be foreseeably established or justifiably preferred, must not be relied upon for defining an ethic.

1. Introduction
Among the more sophisticated accusations of moral inadequacy (putting it nicely) that I as an atheist living in the US have been on the receiving end of, recently there has been the issue of "moral grounding." Basically the claim is that even if I do behave morally, my morality would have no grounding without God, and in that case be an inferior kind of morality. In addressing this idea, I do not wish to give offense to Christians who do not share this sentiment or make the accusation, but it does appear to be a commonly held view among Christian apologists.

(click to continue reading)

The key issue is that Christian apologists believe in absolutes that are grounded in and given an objective basis by God (henceforth, this will serve as my definition of "objective" in the context of religious ethics). Objective morality, absolute right and wrong, absolute values, a higher purpose and meaning, and so on. As a belief, this can look like an attractive prospect, and an interesting hypothesis to philosophers. At any rate this belief, whether true or false, would be innocuous if not for the unsettling corollary that without precisely this grounding (in God), everything becomes worthless, meaningless and amoral. The more fervent Christian apologists do not hesitate to inform people at large of these supposed consequences. To me this is a concern, and perhaps even an ethical one, as most people do not possess the philosophical armor to evaluate the veracity of these claims for themselves, and may become coerced into unquestioningly believing something questionable merely out of apprehension.

Morality, value and meaning, if existing only as relative concepts, according to mainstream Christian apologia is not genuine/real/true morality, value and meaning when not grounded in some objective basis. When pressed on the point of why, exactly, morality etc. must have an objective basis, we tend to get circular arguments or little argument at all in return, which has made a proper assessment of the Christian theory difficult for me. This bears some resemblance, perhaps not coincidentally, to Plato's deeply entrenched moral realism, which was never so much argued for as implicitly assumed in his Dialogues. Two blogs that have recently brought this question to attention exemplify the Christian standpoint here, here and here. Leaving aside the more practical aspects of morality as it advices behavior and thinking, they introduce the ostensibly more important issue of grounding as follows:

"The discussion here is not about moral behavior. ... The discussion is about the grounding for moral duties and values," (source)

"The important question is not whether or not an athiest can be moral, but is there any grounding for that morality." (source)

"Christian ethics are better because they reflect the revealed character of the wholly good Person who is at the very foundation of all reality." (source)

"...even if the Atheist and the Theist are both doing something with some selfish motivation in mind, that the Theist is still being more moral because they are appealing to something higher, whereas an Atheist appeals to nothing but a meaningless system of instincts." (source)

I use these recent examples from the blogosphere with the disclaimer that they may not be representing any sort of general consensus, but they will serve as an anchor for the current discourse. But we do not take these claims at face value, and as we start to investigate their validity the question is two-fold:

#1. Is morality de facto grounded in some objective basis?
#2. Does it need to be?

The first question regarding the objective versus relative nature of morality is subject to empirical study as a starting point: what do we actually observe about the nature of morality in people? Depending on what we find, we will be instructed in what question to ask next. The second question of whether an absolute grounding of morality is necessary is a meta-ethical one, i.e., a question about the nature of ethics. Obtaining something like clear knowledge in this field is difficult, and historically rare. While there are interesting questions raised by meta-ethics, we must be cautious that we do not end up putting the cart before the horse and forget that it is ultimately ethics that speaks to how we should live the good life. This is a key point that I will return to: if meta-ethics fails to provide us with insight, we must put it aside for the moment and focus on ethics itself. If physics had depended on our first grasping the metaphysics, it would have progressed nowhere.

2. Common Ground
Throughout this analysis, together with the theistic proposition of objective grounding we must also keep in mind that there exist numerous theories of moral relativism (e.g. emotivism, contractualism, consequentualism) as well as alternative theories (e.g. evolutionary psychology) of what morality is really grounded in, which do not rely on the meta-ethical issue that is central to the Christian theory. In the final balance we must compare the salient points of them all, as we do not choose to endorse one ethic or meta-ethic by its own principles, but by how it stands in comparison to alternatives. This, at the very least, is one point of relativism on which I will not yield an inch.

While investigating question #1, it would be useful if we had a theory of what morality would look like if grounded in divine absolutes, so that we would know what to look for. Since I do not know of such a theory, we shall just have to look at first. UCSB professor of anthropology Donald Brown has compiled a list of a few hundred Human Universals (Brown, 1991) of behavior and overt language, as noted by ethnographers. Some time after 1989 "moral sentiments" was added to the list. We also find childcare, cooperation, distinguishing right/wrong, good/bad and true/false; empathy, envy, generosity admired, laws (rights and obligations), murder proscribed, rape and rape proscribed, reciprocal exchanges, revenge, retaliation, sanctions for crimes, sexual regulation, taboos, concern for what others think, and shame. To mention just a few. I included some universals unrelated to morality to remind us that it is not only the presence of some mode of morality that appears to be globally shared, but also other important human traits, as well as many less pleasant behaviors. In light of how different some of our cultures can seem superficially, it is an interesting question to ask why we see so many deep commonalities, and to speculate whether there is any mechanism that could explain them all, including the moral sense.

Commonalities notwithstanding, we can not fail to note the many differences also, within our current area of interest. If we all have some form of laws of rights and obligations, it is immediately obvious that we do not all have the same laws, as seen by comparing for instance modern western common law, Islamic religious law, and the Bible. Social taboos and views on sex are likewise observed to vary greatly between cultures, with for instance homosexuality being regarded by most secular communities as OK, by Christianity and Islam as a sin, and by some Islamic countries as a crime subject to capital punishment. Moral sentiments appear to be no exception; while some moral precepts appear to be shared universally (e.g. a sense of fairness, murder and rape proscribed), others are not. Prostitution and drunkenness considered merely tasteless or a minor criminal offense in many western countries are highly immoral acts in some Islamic countries. Autocratic governing by nepotism is nowadays considered immoral by the democratic west, which does not do that anymore. The temporal aspect is also obvious: there is an ongoing process of moralization where new subjects gradually acquire moral dimensions while others lose them. What is regarded as immoral or merely tasteless or shameful can change over time, and sometimes switch places; torture, keeping slaves, public smoking and unprotected sex are some examples. Environmental and biological issues are also becoming more and more moralized. Not only are these examples not regarded as moral issues by everyone, in some cultures they have also become moralized over time where they previously were not.

All this suggests that there is a spectrum of moral sentiments where some are mostly shared, but many are not. Thus while the presence of some set of moral sentiments have been observed around the globe, a question for theories of objective morality is how to explain the diversity of differences and changes over time in what is considered immoral. If moral laws are absolute, they must have a rather peculiar underlying formulation in order to explain all this observed flexibility.

One possibility could be that only a few of these moral principles are objectively grounded and that the rest is something different. As we shall see shortly, something like this is proposed by an alternative theory of the origins of morality, but the "grounding" in that case is of a very different sort than in the Christian theory. From the viewpoint of the Christian ethical doctrine, this diversity appears to be unexplained, or at least, we appear to have no independent (empirical) way of establishing which are the objectively grounded ones and which are not, and even if we could, there arises the ethical question of what are we to do with our current moral norms that would be thus discovered not to be grounded in God? We should require strong and convincing motivations for revising ethical practice in a system possibly working just fine, and even more for pressing it upon others.

A preliminary answer to question #1 at this point must be that if moral laws are indeed grounded in some objective basis of a divine nature, we are currently not able to infer what those laws might be from observations of moral expressions alone. This is not evidence that moral laws can not have an objective basis, but any simple theory of moral realism is in this analysis not supported by direct observations. We may expect Christian apologists to argue that evidence of the absolute nature of morality and value lies within the doctrine of Christianity itself, and the Bible. If we accept an argument like this, however, we have completely given up any hope of understanding morality by our own intellects, as we then surrender all proper understanding to a supernatural entity whose mind we have no means of truly knowing. It is in my opinion much too early to give up the investigation of how morality works, where it came from and what it should be, and it is premature to conclude that we can not understand or run these things without invoking God as an explanation.

How do other theories fare in light of these observations? Without going into too much detail, one theory that tries to unify the multifaceted expression of morality suggests that all moral sentiments fall into five distinct categories that we all possess (harm, fairness, community, authority, purity), but that different cultures rank the importance of the spheres differently (Shweder & Fiske, mentioned in Pinker, January 2008). It is proposed that the moral sense may be a human instinct rooted in the design of the brain, and that the common emergence of the five spheres as components of the moral sense is a result of our common biological ancestry and the process of evolution. To first order, these suggestions appear to be supported by neuroscience and evolutionary biology, and also the new research offered by evolutionary psychology (selected references: Sociobiology: The New Synthesis, Wilson 1975; The Selfish Gene, Dawkins 1976; The Moral Animal, Wright 1994; The Origins of Virtue, Ridley 1999; The Blank Slate, Pinker 2002). This theory explains cultural differences in the ranking of the spheres by the diverging effects of cultural evolution setting in long after the common elements of morality had been established by a much longer period of common biological evolution. That a common foundation for basic morality may have been established long ago by biological evolution is also suggested by ethologists studying primate behavior, observing in them aspects of behavior that appear to indicate basic moral sentiments in common with human morality (see e.g. Primates and Philosophers, De Waal 2006).

It is important to note that evolutionary psychology, in its effort to understand the origins and basic nature of our morality, is in itself not a theory of ethics, and does not by itself purport to prescribe moral precepts. It is regrettably a very common error among theists to succumb to some version of the naturalistic fallacy and suppose that evolutionary psychology's investigation into "is" automatically translates into a moral "ought."

The tentative conclusion of this section is that the Christian idea of an objective grounding of moral truths can not presently be confirmed by observation of people's actual moral sentiments. The evolutionary theory of the origins of morality appears to offer an explanation of both the global similarities and the cultural differences in human morality that is, at least in a preliminary way, supported by the data.

3. Grounding for What?
If moral objectivity had been clearly evidenced by observations by now, question #2 would be obviated, and the debate over moral realism would have been settled long ago. Finding no such support in the data, however, the question of whether grounding of moral values and truths in an objective basis is logically or ethically necessary acquires a different degree of importance depending on which ethical camp you are already in.

If you are already a moral relativist by whatever rationale (we noted that there are many ethical theories of this kind), you have already decided based on something that moral absolutes either do not exist, or that we can not know and therefore must not rely on them. Alternatively, if you take the view of evolutionary psychology, then even if you don't yet know what ethical system to subscribe to, you may have drawn the preliminary conclusion from the data that objective morality, in the sense of being grounded in the goodness of God, does not exist, and question #2 becomes irrelevant. However, moral relativists drawing on evolutionary psychology will still suggest that there is a foundational core of human morality that remains grounded in something that is independent of human opinion, and in this weaker sense also "objective", and that is the biological origin of a moral instinct that we all possess. In this sense, aspects of moral realism can be thought of as partially implemented by evolutionary biology, but it is of course not the same kind of objectivity as that argued for in religious ethics.

If instead you are a Christian apologist of a mind with those cited in the introduction, you are already convinced by the philosophy of your religion that moral truths are grounded in the goodness of God, and will consider an affirmative answer to question #2 to be the most important one. In order to address this question, does morality need to have an objective basis, we need a further qualifier: what is the object for which this requirement, or need, is to be evaluated? That is, if morality is to be found (somehow) to require this type of grounding, what is it that requires it? Is is human morality or de facto behavior, or an ethical theory that is going to require moral facts to be grounded in God? I believe I can rule out the first two possibilities by adopting the Christian assumption that morality is already grounded in the goodness of God, and that this in no way is observed to bring moral behavior or an absolute morality to everybody. If this is correct, then we can deduce that it is the definition and creation of an ethical theory in itself that would require moral truths to be grounded in an objective basis, that is God. If this is correct, then I have to leave it there, as we have still not seen any independent motivation for why this requirement of objective grounding should be, in fact, a requirement. The implication appears to be that the ethical system without such grounding could not work, or not be proper in some way, but exactly in what way or by what rationale is not clear. I have read comments on the implicated blogs suggesting that without this kind of objective grounding of right and wrong, justice could not exist. It's hard to take such claims seriously, when we have many theories of moral relativism and social theories indicating that justice could work just fine in the absence of absolute values or morality, and for all we know, this may be exactly the situation at the present. There is no inconsistency in moral relativism that requires the invocation of absolute moral grounding, the invocation has to be motivated from within meta-ethics.

Again, the rationale for the requirement of a morality grounded in God appears to be the doctrine of Christian ethics itself, and the Bible. But this only defers the question to asking, what is the rationale for Christian ethics and an objective moral basis, again the answer to which appears to lie within Christianity itself, making the argument circular. Of course, if you believe in the Bible, you have no problem with this, but many of the Bible's laws are clearly antiquated and no longer relevant for our age, so it is hard to view these in any absolute light. It would appear that the rationale for accepting the Christian doctrine of absolute moral grounding ultimately boils down to a matter of faith.

A different albeit more cynical possibility may lie outside of meta-ethics, namely that the object of this requirement is not Christian ethics, but Christianity itself. If it turns out that we do not seem to need absolute morality, values and meaning for living the good life, then there appears to be no need for God to provide for these things either. Arguing for the necessity of absolute grounding of morals and values in God may be one of the few remaining ways of keeping God relevant to people in a modern society, and as such an important stronghold for the Christian belief system. It is not impossible that this in itself is a contributing factor to Christian apologists defending otherwise rationally untenable positions.

Lastly there is a third ethical camp to consider, of those that are neither moral relativists nor moral objectivists a priori, and are only now trying to decide on an ethical system and arrive at a meta-ethic based on what has been inferred empirically so far. This is perhaps the most interesting situation. From this vantage point we would conclude that we do not have much evidence or support for the hypothesis that moral values are grounded in something transcendent like God, although no direct evidence against it either. The theory does not make detailed enough predictions to be either confirmed or refuted by mere observation of moral dynamics. The case made by evolutionary psychology for a biological origin of morality followed by divergent cultural evolution appears to be consistent in many details with what is observed. While we do not have absolute proof that it is correct, it lends some credibility to moral relativism and the meta-ethical proposition that moral grounding in a transcendental objective basis is not necessary. It still does not provide an ethical system, however. As it stands, we must conclude that it can not be concluded either that moral values are grounded in God or that they would need to be; the proposition remains not proven and not refuted. This seems a hopeless affair, what are we to do on the occasion? Here is my view.

4. Conclusions
In analyzing the question of grounding of moral values we have, temporarily, left the arena of ethics to explore the nature of ethics itself. If meta-ethics can help us construct a better ethic, then fine. We might think about it for a while, but if we can't figure it out, we have to put it aside for the moment and do something else. If we are stumped by conundrums in meta-ethics, we can not let that stop the development of a practical ethic, which ultimately is what society needs for helping its citizens attain the good life, regardless of whether or not we have the final answer to some deep, philosophical question about moral grounding.

Why is this question of meta-ethics and moral grounding held up as so important by Christians? I alluded to some mundane possibilities. Their insistence on this is why we find ourselves in a philosophical stalemate where, on the one hand, a meta-ethical claim is made that can not be foreseeably verified or refuted, but on the other hand is held up as a central tenet to ethics itself. It is a justified question why something that can not be practically verified should be a central tenet to anything that deals with the practical, but this is a common aspect of religious faith.

If you can't have certainty regarding absolute values and objective morality, would you settle for the relative kind if it works just as well, or at least well enough to enable the ethically good life in modern society? My hope is that everybody would answer "yes" to this question. It may sound like a sibling of Pascal's Wager, such that, in the absence of certainty, do what you're certain will be the least harmful. Except that here we're considering harm not to an individual failing to believe, but to an entire society at the mercy of unsubstantiated ideas of absolute moral grounding.

See the similarity

2008-08-11T01:26:00.034-10:00

Anyone who has visited my home page at www.twelfthnight.se will know that I sometimes like to tinker in my spare time with computer generated fractal graphics. Since last weekend, there is bound to be seen an abrupt change in style, which is already obvious at a glance: the recent fractals look somehow different.

(click to continue reading)

Following the introduction of Lua scripting into Oxidizer about a year ago, I have been using extensively a randomizing script to batch generate lots of candidate genomes (this is my preferred terminology; others call them "flames"). The script (current version is randomiz3.lua) simply randomized each element in the transformation matrix, i.e. the P1 and P2 vectors and the origin O, independently, which tends to produce mostly junk—but occasionally some would come out with an interesting pattern that could be further improved and eventually result in a rendering for the galleries. Galleries 2-6 (here) were based entirely on this method, and it probably shows.

Although some interesting patterns can be discovered this way, the efficiency is low, and there is a certain class of fractals which will almost certainly never emerge from this unconstrained randomization process (time being finite for all of us). Those are fractals that achieve their "sharp" definition by adhering to precisely defined mathematical mappings such as, for instance, similarity transforms.

Similarity transforms involve only scaling, rotation, translation and reflection. In other words, when applied to the triangle defined by (P1, P2, O) the triangle will always retain its self-similarity. For instance, the Sierpinski Gasket consists of three similarity transforms all involving a scaling by a factor 0.5 and a translation by 0.5 units. While an unbiased randomizer script explores the parameter space equally, it will almost certainly never arrive at anything like a similarity transform just by chance; close, perhaps, but never exactly. But for fractal image definition and quality, exactness can sometimes make a huge difference.

I must give credit to Pharmagician (his page at deviantart) for bringing this point to my attention, when he pointed out that Apophysis appeared to be making much sharper and better defined fractals than Oxidizer. Of course "Apo" has a long history and many expert users, who apparently well appreciate the virtues of similarity transforms (they're built right into Apo's triangle editor). Only with the relatively recent release of Oxidizer version 0.5 did it become practical to manipulate triangles in this fashion in Oxidizer, by the introduction of a new triangle editor.

Long story short, in order to obtain fractals observing similarity transforms one must explicitly apply nothing but similarity transforms from the get-go. So I set about to revamp the randomizer script to this effect. As is evidenced by the appearance of a radically new style of fractals on my home page, the new script (simil3.lua) is a very different beast. While it still produces a fair amount of junk, the success rate is much higher, and the chances of getting a sharp looking fractal with an interesting feature set is vastly improved. This comes at the expense of severely restricting the parameter space, but this is probably a penalty that many would be willing to take; there is still a vast (although finite) richness in the combinatorial composition of variations and similarity transforms.

Ultimately, I have of course done nothing but rediscover the wheel here, but perhaps this particular wheel can be of some use or entertainment to that particular community of Oxidizer users.

Both Apophysis and Oxidizer utilize the flam3 library created by Scott Draves.

An Evolutionary Argument Against the EAAN

2008-07-23T19:32:00.135-10:00

I wanted to write down some thoughts regarding the Evolutionary Argument Against Naturalism (EAAN), due to Alvin Plantinga (1993-2002, various publications). This is not a detailed dissection or a scholarly critique of the argument, just a few considerations that I came upon while distilling my own thinking on the subject. Part 1 examines some problems with the argument and proposes a counter-argument from evolution, which is further detailed in Part 2 of this article.

(click to continue reading)

1. Introduction

I recently encountered the EAAN for the first time (a summary can be read here, and a recent discussion here), and was told that it posed a serious problem for naturalism, and therefore atheism. Upon a quick inspection (i.e. Wikipedia), I was left with the impression that the argument has been picked apart with numerous flaws exposed by competent thinkers and scientists, and that this ought to be the end of the story. But apparently many proponents of the EAAN still consider it to be a powerful argument, so my interest was piqued to have a closer look.

Much of the criticism referenced above centers on philosophical minutiae, such as the requirements on and implications of defeaters, or what constitutes beliefs and mental representations—but conspicuously absent from the criticism is a thorough counter-argument from Evolution. It is this aspect of the argument that I would find the most interesting, because unlike the tireless philosophical innuendo between Plantinga and his critics, a deep dive into the evolutionary history that enabled our powerful cognitive faculties can actually be conductive to making new discoveries and learning something useful. Here is where I started forming my own response to the EAAN.

I must offer the disclaimer that I am not a philosopher nor a biologist; I am but an ex-physicist/astronomer with a keen interest in science of (almost) all flavors. Also, I can not present a full investigation such as I think ought to be the proper answer to the EAAN, as this could easily be a book-length treatise far beyond my level of expertise on the subject. I will be content for now to sketch an outline of the argument, and offer my suggestions to what some of the answers are or how they may be found or investigated (the details of which will be the subject of Part 2 of this article).

2. The Evolutionary Argument Against Naturalism

If I wanted to be provocative, I might summarize the conclusion of the EAAN as: "Because we are smart, God exists." Now that I have miffed most of my readership, here's what the hypothesis actually says:

The probability that our cognitive faculties should be mostly Reliable (the condition R), given the currently understood mechanisms of Evolution (E) under the assumption of Naturalism (N), is low.

In a brutally compressed summary, R is the proposition that our cognitive faculties (memory, perception, reason) are mostly reliable and produce mostly true beliefs, and E is our current understanding of the laws of phylogenetic development by the mechanisms of evolution (common descent, variation, natural selection). N is the assumption from naturalism that the laws which govern all things in the universe are non-teleological. I will not torment the reader with an account of how Plantinga proceeds to evaluate the hypothesis; it is not crucial for the rest of this text anyway, and the reader may consult the links and other sources for more detail.

The hypothesis is formulated in terms of the conditional probability P(R|N&E), read as "the probability of R given that N and E are true." Strictly speaking, the implication of this probability being close to zero is that either E or N (or both) must be false, which is seen by expanding P(R|N&E) (henceforth abbreviated P*) using Bayes' theorem. The preferred interpretation, however, appears to be that the trouble is with N, leading to the conclusion that naturalism must be false. Hence God. One of the reasons for this automatic preference might be that if the contradiction arose from E, it might still be possible to rescue evolution by doing more research; N, if similarly afflicted, would appear to be beyond rescue.

Before we enter into the evolutionary counter-argument, it is illuminating to inspect how mathematically troubled this probabilistic formulation of the EAAN is. It is important to realize that, notwithstanding the suggestion of logical rigor by the use of mathematical concepts, the probabilistic formulation in the EAAN ultimately boils down to subjective opinion. For some, this in itself might be enough to discard the argument as pointless.

First of all, when we consider the underlying quantity of contention P(N), we of course agree that naturalism is either true or false, not something in between, and hence that P(N) in reality is exactly equal to 0 or 1. This binary outcome propagates down to P* which similarly must be either 0 or 1. When we talk about P* having a value between 0 and 1, this is just an informal way of expressing our degree of confidence in the hypothesis given the evidence; there is no connection from P* (or P(R), or P(E) or any other function) to an actual probability density function or relative frequency function, in any mathematical sense. This means that we are supposed to be speculating about P* from an a posteriori perspective with none of the variables involved being related to empirical quantities. This premise in itself need not necessarily become a flaw of the argument, so long as we are aware of it and argue consistently.

However, the lack of mathematical definition also propagates down to the statement that P* is "low," which is left without a yardstick to calibrate what is actually meant by "low." If a different person analyzes the same argument and concludes that P* is "high"—how are they to distinguish "low" from "high" when neither is calibrated to a scale? The loosely defined qualitative properties of R, E and N that lead to an estimate of P* make quantitative statements untenable, and renders any conclusion from the argument inevitably subjective. This has not discouraged EAAN proponents from issuing the qualitative-cum-quantitative verdict that P* is "low enough" to warrant the happy interpretation that N must be false.

Yet this nebulous character of P* need not have been inevitable. A different argument might have been formulated wherein at least some of the probabilities invoked could be empirically estimated, producing an actual number to insert into the formula. For instance, if we take R to be not just our reliable cognition, but the degree of reliable cognition in any species, then we could construct the function P(R) with the current biosphere as a statistical sample. Likewise P(E) could be constructed as a function over all species available for study, describing the degree of ability of E to explain the phylogeny of each species. Challenging though this might be, we can at least conceive of some probability density functions that could be estimated numerically.

But no such considerations are invoked by the philosophers advocating the EAAN, and the moral of the story is this: Plantinga chose to formulate his argument in such terms as to defy mathematical and empirical rigor.

3. An Evolutionary Argument Against the EAAN

My initial impression of the EAAN was that it employs a straw man version of evolution (E), and that it is only by this cheap trick and a little philosophical sleight of hand that one can possibly arrive at the conclusion that P* must be sufficiently low for N to be false. One way to refute the EAAN would then be to address its shortcomings in E, but this too does not appear to convince many of its (chiefly theist or philosopher) proponents. They tend to require that a defeater is presented, which can be somewhat hard to produce given the subjective value-judgment that lies at the heart of the conclusion.

There are other ways to show that the EAAN is false, or at least veridically worthless. An alternative way to state the hypothesis is to say that R is incompatible with E&N—call this the belief B1. My proposition is here that in order to obviate the EAAN, one need only demonstrate two things: that R can exist given N (and E), and that R can develop given E (and N). If both conditions are met, then there is no contradiction between R, E and N that would require the rejection or modification of either. That is, the belief thus justified that R is compatible with E&N is the defeater to B1 that, if demonstrated, obviates the EAAN. What this implies is not that E&N guarantees a R of human qualities to arise—E makes no such claim—but that it allows it.

To show this, we must examine the conditions for R to exist and for it to develop, by investigating the following topics:

(1) Condition for existence #1: physiology
(2) Condition for existence #2: stability
(3) Mechanism of development: evolvability

To summarize the strategy of the investigation, condition (1) is to show that R does not violate N, which we can attempt to establish by consulting the topics of cognitive science such as neuroscience, psychology and computational theory. Condition (2) is to show that R is compatible with E in the sense that it must be able to coexist with all the other phenotypes also assumed to have been produced by E; this we can explore by way of population dynamics and evolutionary game theory. Finally (3) is to show that E&N allows the gradual development of R from much humbler beginnings, which entails telling the story of phylogenetic development of the brain and its mental faculties. This is the story of genes, DNA promoters, neutral drift and pre-adaptations—topics on which numerous books have been written, and on which much modern research is currently focused on.

This might start sounding like a tall order for someone who is not even trained in genetics or biology, and it probably is. Barring a complete mental breakdown (which is a realistic possibility), however, there will eventually be a Part 2 expounding on the details of (1)-(3). Until the next time!

Update 2008-07-27

Since writing the above, I have perused some literature and came across two excellent books that eminently address both items (1) and (3): "The Agile Gene: How Nature Turns on Nurture" (Ridley, 2003), and "Big Brain: The Origin and Future of Human Intelligence" (Lynch & Granger, 2008). The latter establishes the link from the brain to cognition and intelligence (R), in terms of the basic function of neurons and the properties of computational systems. This demonstrates the viability of condition (1) by delivering an unbroken chain of explanatory systems from fundamental physics to intelligence via chemistry, signal processing and cognition. An evolutionary account of the development of the human brain is given in both books, with a more detailed genetic account by Ridley and a more detailed physiological account in Big Brain. Together they provide all the information required to affirm the condition (3) also being met by contemporary evolutionary theory, as evidenced by the fossil record and the physiology of brains in currently living species.

This leaves only condition (2) to be demonstrated in order to establish the defeater that obviates the EAAN. The stability of R is actually implicitly demonstrated by condition (3): by empirically discovering the evolvability of R we have established that evolutionarily stable strategies (ESS) must exist. However, condition (2) requires us to do this from evolutionary theory alone, in order to demonstrate that the theory allows it, so I guess the work still needs to be done.

Evolutionary Dynamics

2008-06-14T15:48:00.037-10:00

This is not so much a book review per se as just a bit of commentary on a really nice book that I came across recently. Evolutionary Dynamics: Exploring the Equations of Life (Belknap & Harvard, 2006) by Martin A. Nowak is a textbook on the subject of evolutionary game theory. Nowak's claim with this book is that, through game theory, the theory of evolution has acquired a mathematical framework.

The main reason I bought this book was that, as a novice to this subject, I wanted to write some simple codes and try out a little bit of evolutionary game theory myself. To this end the book excels in its clarity and conciseness, and it provides us beginners with all the basic tools of the trade that will allow us to start exploring the dynamics of the equations of life.

(click to continue reading)

The text starts out with the basic mathematical formulations of reproduction, mutation and selection (ch. 2), and then goes into frequency-dependent selection expressed by the quasispecies equation (ch. 3). One of the main tools of evolutionary game theory is the replicator equation (ch. 4), which is a nonlinear differential equation mathematically equivalent to the Lotka-Volterra equations of population dynamics, demonstrating the equivalence between evolutionary game theory and theoretical ecology.

There is a rigorous discussion on evolutionarily stable strategies (ESS) and Nash equilibrium (ch. 4), and then we arrive at one of the prime suspects of the drama: the Prisoner's Dilemma (PD). The PD game and iterated PD has been studied intensely for the potential insights the game offers into predator-prey dynamics and the evolution of cooperation within a species. By tweaking the payoff matrix in the PD we obtain a host of familiar variants, such as the Hawk-Dove game, paper-rock-scissors, chicken and snow drift.

Then follows an extremely interesting section of the book discussing reactive strategies (sections 5.3-5.5) in the iterated PD game. It was established after Axelrod's tournament in 1978 that Tit-for-Tat (TFT) was the ruling champion of the iterated PD, when averaged over all competing strategies. But these tournaments were conducted in ideal conditions with no noise, mutations (random drift, Kimura's neutral theory), or other types of mistakes entering the game. It turns out that in the presence of noise and mistakes, TFT will lose out to other strategies, including Generous Tit-for-Tat (GTFT) and Win-Stay/Lose-Shift (WSLS).

Starting from an initial chaos of random strategies, we first observe the rise of always-defect strategies, which are then replaced by TFT. But TFT is vulnerable to invasion by GTFT, and once GTFT takes over, random drift can establish a population of always-cooperate strategies. This mixture sets the stage for WSLS to dominate the field, and once it becomes introduced it can resist invasion from all the other strategies. Interestingly, Nowak finds that there are upper and lower bounds to the size of the population within which TFT can rule, basically "not too small but not too big," which fits well with our historical perspective of how our cooperative communities evolved from smaller hunter-gather clans in the past.

These results are interesting because they have a sense of realism, and observing the competition of strategies can give us better clues as to how our own condition of cooperation and morality might have evolved. Nowak also notes that WSLS is consistent with human psychology in several ways that TFT is not: occasional defections can be forgiven, but unconditional cooperators tend to be exploited instead. How true.

The next topics of the book are games within finite-sized populations (ch. 7), evolutionary graph theory (ch. 8) and spatial games (ch. 9), and this is where I started writing my own codes to see if I could get the same results. The iterated PD can be played on a 2-dimensional grid, whereby it somewhat takes on the character of Conway's game of life implemented with a particular set of rules corresponding to the PD. Pages 150-151 and 156-157 show a set of color images of the PD played on a 100x100 grid, for different initial conditions and payoff matrices. I was happy to find that my own simple code was able to reproduce those results without too much trouble, and below are shown some sample results on a 256x256 grid.

Starting from a random seed of 10% defectors:

b=1.1

b=1.33

b=1.4

And here's starting with a single defector in the middle of the grid:

b=1.34

b=1.55

b=1.65

The "kaleidoscope" pattern emerges from the x/y symmetric rules when starting from a single point. In the case of very large b-values, the game really produces entities looking and acting like cellular automata.

If I have one gripe with the book, it would be that it does not present nearly enough numerical examples (often none at all) in the form of plots and images, in the first part of the book that goes through the basic equations. Without numerical examples, the first 120 pages read almost like a dictionary of equations and algebraic limits. This may be fine if you know all these phenomena already and just forgot the actual formula, but for someone learning the physics it is usually very instructive to have plots to look at.

Fortunately, online resources more than make up for the lack of numerical examples in Nowak's book, and the ultimate companion to Evolutionary Dynamics in hardcover has to be: Virtual Labs in Evlutionary Game Theory. This site hosts an impressive collection of online resources and Java applets for further exploring evolutionary game theory and population dynamics - go there!

Another slight peeve is that the book contains no primer on chaos, attractors or limit cycles in dynamical systems, even though these concepts are mentioned several times and often turn up in the results of an evolutionary game. Of course, a rigorous treatment of this would have doubled the size of the book, and the interested reader can always find that information somewhere else, as in for instance the excellent (if somewhat dated) Chaos and Fractals: New Frontiers of Science (2nd ed., Springer Verlag, 1992) by Petigen, Jürgens and Saupe.

Anyway. If this had been a book review (which it isn't), these two grievances, albeit very minor, would be the reason that I withheld the full score and gave the book a 4 out of 5. But in most respects this is an impressive book well worth reading and owning. For some real reviews, go here: Programs for Evolutionary Dynamics.

A drive to Kona

2008-05-28T15:35:00.005-10:00

I hated my job.

Amazingly, even after laboring under a major depression for more than three years, stubbornly refusing treatment but gradually succumbing to entropy, this thought had never occurred to me. I thought I needed to fix myself in order to be able to keep doing my job, not the other way around. Only after finally deciding to quit my job did this astonishing fact begin to materialize in my scrambled mind.

(click to continue reading)

The day after I mentally committed myself to resigning from my job, having sent an email to my supervisor announcing this intention, I went for a drive to Kona on an errand to fix my cell phone, which had been busted for several months. After two dark weeks at the bottom of the abyss of depression and yet another sleepless night of insomnia, fretting over how my supervisor was going to punish me, on my way to Kona that day I realized in sudden shock that I was driving along in a state of unmitigated elation: I felt great!

Now WTF is this? After having recently described my condition to a psychiatrist as "being unable to snap out of it because there's nowhere else to go from here" – that was exactly what happened during that drive, I had snapped out of it. Somewhere a light came on in a Freudian closet. Maybe I had gotten it all backwards.

After investing 14 years of my life in educating myself, getting those science degrees, working away as a measly postdoc and gradually building up a career – suddenly realizing that you hate your job – well it's not something you actually want to discover. But as I was driving along, it all became clear to me that my job had been the cause of my depression in the first place. I needed no other confirmation than the elation I felt as this load was lifted off my shoulders.

Such was my amazing discovery, on that day of the drive to Kona. The same evening I created this blog to celebrate this little epiphany, which, although I am soon to be unemployed after throwing away a 10-year career, I think is going to make life a lot more interesting.

I have no idea what I will be posting here in the future!