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Math, Infinity, and Beautiful Design

In his book The Blind Watchmaker, Dawkins discusses the appearance of design.

Biology is the study of complicated things that give the appearance of having been designed for a purpose.

In the context of evolution, the appearance of design makes sense. But I want to explore an area of geometry and mathematics that relates simple algorithms to beautiful appearances of design.

Welcome to the world of fractals. This is a world where I can draw a bounded snowflake that has a boundary of infinite length. It’s a world of paradox, a world where it doesn’t matter how big you are, because you won’t notice the difference when you zoom in. It’s a world of infinity, a world of endless iteration. More importantly, it’s a world of simplicity in terms of beginnings, and stunning beauty and complexity in terms of ends.

The Koch snowflake shows how simple the rules are for fractals to be constructed. One starts with an equilateral triangle. The next iteration involves the union with another triangle, which forms triangles on the periphery. Now we union the smaller triangles with rotated versions of themselves, which forms even smaller triangles on the periphery, and so on…

The resulting snowflake is not only aestheticallly pleasing, but it can also be shown to have infinite length.


The most iconic figure of fractal geometry, however, is the Mandelbrot Set.

Few people know or understand how simple the rules are that define this set. Formally, the M-set consists of all the elements C in the complex plane such that the iteration Z_n+1 = (Z_n)^2 + C is bounded, starting with Z_o = (0,0).

Computers can calculate by repeating the iteration over and over for different values of C to see if the norm of Z_n goes toward infinity.

The resulting graph of the M-set is mesmerizing. It’s a set that features very complicated arrangements of symmetry and self-similarity.

The more beautiful renditions of the M-set are created by assigning colors to values that allow Z_n to diverge, depending on the speed of divergence. As we can see below, there are all kinds of intricate “designs” in these renditions. There are seahorses and islands, shells and spirals, peninsulas and antennas.

So what can computer generated graphics show about nature, evolution, and biology life? Do fractals have any useful function besides being “beautiful”?

1) Fractals allow things that work on a large scale to be reproduced on a smaller scale (or maybe vice versa). The heart pumps blood to larger blood vessels, which branch out to smaller vessels, to smaller capillaries, and so on, and each branching pattern mimics the level above it. No designer had to use his intelligence to think about each step along the way. No God had to draw a blueprint of the location of every tiny blood vessel. Fractals allow simple patterns that work to be expanded and repeated into smaller, more intricate settings without any need to think about them, without any design.

2) Fractals are nearly ubiquitous in nature; they are found in places ranging from snowflakes and seashells to leaves and mountains.

3) Fractals are optimal for many purposes. For example, it was proven mathematically that the self-similarity of fractals allowed them to serve as the one and only optimal solution for antenna design. The fact that so many living things have fractal qualities also suggests that natural selection favored the advantages that fractals gave to certain species.

Of course, the creationists are really looking for trouble here. They look at the word “infinity” and not only do they think “intelligent design”, they think Yahweh, Jesus, and one version of one book in particular.

And they trip all over their watchmaker-design argument. After all, everything that is complex and specified must have a clear designer, right? And what do they say when we can’t find a designer for such things as fractals?

Their conjectured unknowable and untouchable god was, in fact, the very knowable Judeo-Christian God of Creation. And His methods actually express themselves as geometry. But it is a geometry that the Greeks could scarcely have imagined.

Just assert and assert and assert the superiority of your God and your One True Religion over and over again.

Let’s give them a round of applause.


Why The Religious Should Give Up

If there’s fifteen minutes of conversation that captures the common religious desperation to reconcile man-made fairy tales with objective scientific truths, it is the conversation PZ Myers had last week with Muslims in Dublin.

These are people who approached PZ at first with a vomiting of philosophical bullshit, using fuzzy First Cause arguments and nonsense like “occam’s razor must be uncaused, therefore it must be eternal.” And then, after being pressed for any kind of evidence for their theistic god, the Muslims turned to pseudoscientific embryology and a very odd understanding of why mountains exist, as detailed in the video above. After the event, the same group also talked to Richard Dawkins, and explained to him that evolution can’t be true because it is a “noncomplementary paradigm” with physics.

It is quite sad to see people so hopelessly devoted to their beliefs that they’ll twist and turn meaningless garble in religious books and claim that these words are in fact scientific truths that could have only come from revelation (like from some illiterate dude in a desert, for example). PZ is right that these same tricks are used by Christian and Jewish scholars. And PZ is even more right when he notes that comparing the Qur’an or other holy books to actual science is equating crude understandings of the universe with detailed and verifiable scientific evidence.

For example, how many times have Christians come up to you and said that the Genesis account is amazing because it predicted that the Universe had a beginning? It’s quite insulting to science, really. They purposely leave out one inconvenient truth: pretty much everything else in Genesis is completely wrong. Not just troubling or hard-to-read. Just dead wrong. It’s quite sad, therefore, that there’s another manufactured scientific controversy on Christianity Today. Apparently in Christian fairy-land, they still aren’t sure whether Adam or Eve actually existed, and that’s why there’s a scientific “search” for the historical Adam and Eve.

Give us a break, Christians. Just like there is no controversy about the fact that living things evolved or that the earth revolves around the sun, there is no controversy about this question of human origins either. It’s just another religious attempt to confuse people and to make it appear like their beliefs have a possibility of being true. UChicago’s Jerry Coyne delivers the point.

Genetic data show no evidence of any human bottleneck as small as two people: there are simply too many different kinds of genes around for that to be true.  There may have been a couple of “bottlenecks” (reduced population sizes) in the history of our species, but the smallest one not involving recent colonization is a bottleneck of roughly 10,000-15,000 individuals that occurred between 50,000 and 100,000 years ago.  That’s as small a population as our ancestors had, and—note—it’s not two individuals.

There’s a real parallel between these manufactured Christian controversies and the “embryological” Muslims. All are so convinced that their beliefs must be true and must be rooted in reality that they’ll go to any length, however intellectually dishonest, to gain temporary credibility. And when science actually does reach its limits and says, “there’s more to be discovered,” religion steps in and tries to fill in the gaps.

But notice the pattern. Religion, after initially attacking science by flinging false controversies and pseudoscience all over the place, then hijacks the later discoveries of science and claim them as its own. They’ll never win, of course, because they’ll always be followers and pirates and copycats, not leaders. As Isaac Asimov brilliantly said, science stands alone.

Don’t tell me, then, that those clever Eastern (Celtic, African, Greek, or even Biblical) sages have spoken of something that sounds like the big bang or like endless expansion. That’s idle speculation.

Show me where those sages worked out the isotropic radio wave background, or the red-shifts in galactic spectra, which alone support those conclusions on anything more than mere assertion.

You can’t. Science stands alone!

And so this post ends with the inspirational quote above, as well as the following advice: If I were a person of faith, I would just call it “faith” and not bother with science or evidence.

Creationist Bingo

There are some wacky things in life that are just so amazingly fun. Snowball fights, Nerf gun wars, Apples to Apples, and now, thanks to the UChicago SSA, Creationist Bingo.

My favorite video:

The square for this was “Life can’t come from non-life,” but I was about to put it on “Simple Stupidity/Ignorance.”

Anyways, I was very inspired to find a video more awesome than Ray Comfort’s intelligently designed banana.

Not Very Inspiring

Yes, there’s a lot of debate about “bad teachers” and “competency” in an increasingly large discussion about school reform. How much professional training do we owe teachers, and at what point do we choose to let teachers go?

Whatever your view is on these topics, I hope you agree that there’s at least one thing we cannot tolerate from science teachers: the deliberate attempt to teach creationism in the public schools.

It’s not only illegal, it’s insulting to the millions of people around this country who don’t want more religious nonsense to be subsidized by taxpayer money.

So when a Libertyville High School science teacher taught creationism, the school board decided to intervene. How? By doing nothing, apparently.

The teacher in question is a long standing D128 educator, cooperated fully with administrators looking into this concern, and we will not be recommending his termination as this is remediable behavior.

Remediable? Okay, if this was a science teacher whose students didn’t quite make the expected improvements on their standardized tests, perhaps we can “remediate” this teacher.

But this is someone who deliberately sought to violate law, undermine Illinois science standards, and mislead students about science. This is not a teacher wanting to improve his teaching; this is someone who think he has a God-given, Biblical right to teach his set of superstitious beliefs.

As posted before, an estimate 13% of public school teachers in America teach creationism. This is setting a very very bad standard. For students who want to learn real science–for secular students who feel out of place with their religious surroundings especially–this is not very inspiring.

Silly Rabbis, Tricks are For Kids

The library of idiotic and meaningless statements uttered by self-professed holy men keeps endlessly growing. When will we stop being preached to and treated like mindless children?

The Huffington Post featured a so-called A Reasonable Argument for God’s Existence by Rabbi Jacobs. One might expect another round of toned-down religious mush similar to the arguments from what I now call the New-Age Christians. Instead, we get a pseudo-argument bordering on lunacy.

One might suppose that in the six or so decades since the discovery of the DNA molecule by Watson and Crick during which researchers have been investigating the origin of life they might have come up with some pretty solid leads to explain it. The truth of the matter is that we see scientists coming up surprisingly empty-handed and that even within scientific circles, the few hypotheses they do have are shredded to ribbons by their colleagues within the scientific community.

Rabbi Jacobs wants us to think that the discovery of something means that a complete explanation for it should come from science in about sixty years. How long did it take to fully understand the atom after we first discovered it? The truth is that we STILL don’t understand everything about atoms or their origins (although we are getting closer), and that’s okay. Science does not work on a schedule; it doesn’t promise answers to really difficult questions because some man from the Huffington Post demands it. But the hardworking men and women in the field do try very very hard nonetheless.

And that’s the point. We have made so much progress on the understanding of DNA that it’s simply amazing. Just 20 years ago, many people wouldn’t have imagined how far we’ve come in sequencing not only our DNA but those of many other species, and how much closer we are getting to understanding how early life could have developed and evolved. Rabbi Jacobs, on the other hand, makes a living out of giving answers on things that he couldn’t possibly know or understand, and he attacks others for being as ignorant as he is.

There just is no evidence for it. Not one of them has the foggiest notion about how to answer life’s most fundamental question: How did life arise on our planet? The non-believer is thus faced with two choices: to accept as an article of faith that science will eventually arrive at a reasonable, naturalistic conclusion to this intellectual black box or to choose to believe in the vanishingly small odds that the astonishing complexity, intelligence and mystery of life came about as a result of chance, which of course presents its own problems:

It is not an article of faith to be open to the strong possibility that science will answer questions about life’s origins. It may entirely possible that a good explanation is far away, but the evidence is that science, again and again and again, has always pushed the frontiers of our knowledge. Not only has it done that, it has pushed back the claims of the religious and put a well-deserved check on nonsense claims and superstitions.

One of those claims is intelligent design, which Rabbi Jacobs is essentially making. When Jacobs says that the “astonishing complexity, intelligence and mystery of life came about as a result of chance,” I have no choice but to think that either he doesn’t believe in evolution (which I find unlikely) or that he has a typical but serious misconception of it (one that presupposes the driving forces of evolution are random). That’s because if we was talking about abiogenesis, he wouldn’t be referring to “intelligence” or even “complexity,” characteristics more descriptive of modern forms of life.

In short, his O’Reillian argument is this: God exists because I don’t know how shit came about.

The second trickster is Rabbi Artson, who participated in a 4-person debate with Christopher Hitchens, Sam Harris, and Rabbi Wolpe.

When asked by Sam Harris about his explanation for why innocent people encounter so much random suffering in this world, Rabbi Artson gives the following response (at 35:20).

It is a Medieval mistake based on Aristotelian thought that God has to be an unmoved mover, and thereby eternal, omniscient, omnipotent, and omnibenevolent. … I apologize for the way that philosophers kidnapped the tradition, but it is not in the Torah, and the concept is a nonsense concept.

[Sam Harris]: So you’re saying that God doesn’t have the power to change these things?

Yes, of course that’s what I’m saying. What God has is a different kind of power than that of the dictator. What I look to God to be is a persuasive power more comparable to a teacher, or a lover, or a parent who teaches and inspires you to be the best by seeing your potential and by giving you the potential to rise to it. But I don’t believe in a God that breaks the rules, who can intervene, and do magic.

God is a weak, powerless entity who just inspires people and can’t perform any miracles? That’s the God of Judaism and Christianity?

Of course, Christopher Hitchens wasn’t going to let this one slide (40:00)

One of the reasons why I like debating with the religious is that you never know what they are going to say next. Sam and I don’t mind being called predictable. We know what we think. We say straight up where we think we know, where we think it is not possible to know, why we don’t think there’s the supernatural, and so on. But this evening already we’ve had your suggestion that God is only really a guru, a friend when you’re in need. I mean he wouldn’t do anything like bugger around with Job to prove a point…


If I now tell you that must mean the book wasn’t really the word of God, you would say, “who ever believed that that ever was the word of God?” Let me just tell you something. For hundreds and thousands of years, this kind of discussion would have been in most places impossible to have, or Sam and I would have been having it at the risk of our lives. Religion now comes to us in this smiling face ingratiating way because it has had to give so much ground and because we know so much more. Don’t forget the way it behaved when it was strong and when it really believed that it had God on its side.

Afterwards, Rabbi Artson remarked that he really didn’t like participating in this debate. I don’t know what that is supposed to mean, but the audience really deserved a good debate, and I don’t think they got it. Hitchens and Harris clearly laid out their claims and arguments, while the other side served mush and kept talking about what they didn’t believe, all while changing the story to avoid difficult questions.

The last trickster is Rabbi Schmuley, whose debating style is as bad as his lack of substance. After all, if you don’t have anything worthwhile to say, why not just yell?

Inspiration of the Day: Watch the whole Hitchens, Harris, Rabbi debate. Hitchens makes a Star Wars reference somewhere in there.

Real Education Reform

Skip to 8:20. People who think that science denial is limited only to Protestant Christianity are fooling themselves.

In America, fewer than 30% of high school science teachers really teach the theory of evolution. The majority science teachers avoid the topic.

13% of high school science teachers teach creationism.

Indeed, the religious have a lot of catching up to do. So what’s the solution? How are we going to change this?

Reflections on the Supernatural

“If we can observe it, it is by definition natural.”

On a pragmatic level, there is nothing wrong with the above statement. Let’s say you see an apple fly up into the air and out of your sight. This very observation seems to fly against (literally and figuratively) what we know about gravity and how fruits normally behave, for the simple reason that under normal circumstances, there is usually not a force that propels an apple into the air. Thus, in keeping with the theory of gravity, we start to find plausible reasons for why the apple flew into the air.

Was it shot out of a cannon that we didn’t see? Was there a thin string attached to the apple and pulled on the other side by an airplane? Or perhaps more importantly, could our observation be a figment of the imagination? If so, were there other people who saw this apple?

My answer to this question of whether the mysterious flying apple is always natural phenomenon is complicated on two levels. The actual motion of the apple flying into the air (if proven beyond a doubt that I was not imagining it) is undoubtedly a natural event, for the simple reason that it happened in our universe.

Yet, I believe there is something more when we say a phenomenon is natural; a natural phenomenon not only occurs in the natural, observable world, but is wholly contained by it—in all causes and relations. To understand my point, let me point you to another hypothetical situation.

Let’s pretend we all hear a voice. I’m not talking about the kind of mysterious, unverifiable voice that is supposed to be interpreted metaphorically through vague, general signs—the kind that religious people claim is “God answering prayers.” No, I mean an audible voice (preferably in English, but Cantonese is fine too) that we can all hear with our ears.

By all means, the mysterious audible sound—constituted physically by the molecules that vibrate along with the undulating sound waves in the air—is entirely a natural phenomenon. Yet, to call the voice natural by definition is to avoid the possibility that the cause (and the event’s relations to other things) of this voice is natural, for which I point out that it could possibly not be. Scientists may try to understand the presence of this voice by hypothesizing that it comes from natural causes like alien technology or the KGB, but one could also say that the spirits of the Underworld are talking to us. The ability to observe an event does not automatically exclude the possibility of supernaturalism in that event’s causes and relations.

Don’t get me wrong. To acknowledge the possibility of supernaturalism as a part of the theoretical/paradigmatic framework for events is not to suggest that supernatural explanations are equally valid. As it stands, there is absolutely no evidence for the supernatural, or for any need to think that supernatural explanations are needed to explain anything. So much for the Intelligent Design proponents, who have been thoroughly and completely discredited in the court room and in the scientific community. And how unfortunate it is for religious people in general, whose prophets and gods happen to only talk to them in private, making revelations only by whispering to select people in illiterate and backwards places thousands of years ago, and performing great miracles only to cease whenever science starts to flourish.

No, I don’t think I’m detracting from science at all. In fact, by acknowledging the possibility of supernaturalism, I believe we can better appreciate and understand the natural explanations that we have already, thanks to the immense progress of science. I suggest therefore, that instead of laughing at the person who claims to know for sure that the mysterious flying apple was caused by Yoda harnessing the power of the Force, perhaps we could do our own investigation and work to find a natural explanation that is supported by the evidence, strong in predictive power, and logically consistent. The same goes for any similarly disputed events.

I’ll close with words from PZ Myers: “If you’ve got a religious belief that withers in the face of observations of the natural world, you ought to rethink your beliefs — rethinking the world isn’t an option.”

Maybe somebody smarter than I…

Neil deGrasse Tyson gives a vivid explanation of the “God of the Gaps” phenomenon. It is nice to be reminded of how even one of the smartest people in the world, Isaac Newton, mixed his scientific findings with all kinds of superstition.

The State of the Nation

4 in 10 Americans still hold creationist views

If you’re in a room of 100 people, odds are likely about 40 think God created humans about 10,000 years ago, part of a philosophy called creationism, according to a Gallup poll reported Friday (Dec. 17). That number is slightly lower than in years past and down from a high of 47 percent in both 1993 and 1999.

The optimists will say that this is progress, but I just want to point out how long the road really is.

Note that in addition to this group of creationists, another 38 percent of Americans believe that God directed evolution over millions of years. How this supposed process actually worked and what evidence there is of such divine interventions is never really described in detail by these people, which is not at all surprising. I, holding the radical “opinion” that extraordinary claims require extraordinary evidence, think a theory of evolution that involves supernatural guidance is an affront to the actual theory of evolution. Supernatural evolutionists maintain that all of these happenings in the past — the slow and indifferent processes that have led to the extinction of 99% of all species including multiple human species — were designed and coordinated so that we are sitting here today. This is an attack on science, not only because it speculates about the supernatural, but also, by inserting God’s hand into the picture, it destroys the role that an indifferent environment plays in determining “fitness” (a term that is too often misunderstood to be equivalent to traits like strength and intelligence). Supernatural evolution is not only bad science, nonscience, and pseudoscience, but it is based on the lie that we evolved as a specially designed creature.

For the 40 percent who think that the Earth is 10,000 years old, Richard Dawkins points that that these people aren’t just wrong, but so incredibly wrong that it is “proportional” to saying that the distance from New York to San Francisco is about ten yards.

Americans’ views on human origins varied significantly by level of education and religion, the poll found. Those with less education were more likely to hold a creationist view that God created life thousands of years ago, while college graduates were more likely to hold one of the two viewpoints involving evolution.

I know I repeat this point over and over, but there is and always has been a solution to this problem: education. Virtually every poll, every study finds that as you give people the opportunity to receive a good education (e.g., when you increase the percentage of people going to college), the baseline statistics all rise, leading to not only a decline in religiosity, but also declines in crime, poverty, along with gains in health and social harmony. This is especially why it is so important, at a time when we are beginning to realize that America is not leading the world anymore in basic science education, that we resist the attempts by creationists to pressure our public schools and universities to teach their packaged ideas. If creationists really want their ideas in textbooks, they should not take the political shortcut, but try to first get their ideas peer reviewed and published in journals, just like how every other scientist in the world operates.