Showing posts with label Teleology. Show all posts
Showing posts with label Teleology. Show all posts

Tuesday, January 31, 2017

Natural law and contraception

Catholic philosophers and theologians who support Rome's position on "artificial" birth control attempt to construct natural law arguments in defense of that position. And pop Catholic apologists recycle those arguments.

Natural law arguments can be valuable, but they need to be formulated with great finesse. Teleology, per se, isn't sacrosanct. There's nothing wrong with impeding gravity so that we can fly airplanes. Likewise, water pumps contravene gravity to make water flow uphill.

The natural goal of a chicken egg is to hatch into a chicken, but it's not immoral to violate its tells by consuming scrambled eggs. Eating veal parmesan disrupts the natural order. After all, calves were designed to grow into cows or bulls. But eating veal parmesan is not immoral–the protestations of vegans notwithstanding. 

The nose and ears weren't designed to be a platform for glasses, but it's okay to co-opt them for that purpose. 

If letting nature take its course was a general (much less universal) imperative, that would pretty much abolish the medical profession.

The point of counterexamples is to test whether you consistently apply the principle you appeal to, or whether you make ad hoc exceptions. 

The standard Catholic argument against "artificial" contraception treats procreation as a special case of a general principle: natural teleology. The question, then, is whether the general principle is sufficiently discriminating to justify that particular application–while compartmentalizing that application from other permissible examples that run counter to the ordinary course of nature.

(When I say "special", I'm not using "special" as a synonym for "exceptional"; rather, I'm using "special" as a synonym for "specific"–in contrast to generic. For instance, brain cancer is a special case of cancer. Cancer is the general category, of which brain cancer is one example.)

The question is why the other examples, which interfere with the ordinary course of nature are permissible, but "artificial" contraception is not. 

The Catholic argument begins with the general principle of natural teleology, then treats procreation as a special case of that principle. And it regards the natural teleology as normative with respect to human procreation. 

Problem is, Catholics are forced to admit that natural teleology is not a reliable indicator of normative ethics. There are ever so many cases where it's permissible to disrupt the natural order. Take pesticides. Or selective breeding. 

Or, to consider some examples involving human pregnancy, viz. epidural anesthesia during labor and delivery. A caesarian section? Those artificially circumvent or contravene the ordinary course of nature. 

What criteria can Catholics use to refine their appeal to natural teleology while preserving their appeal to natural teleology. They can't begin with that principle, then admit that it may properly be superseded in any number of cases. In that case they have no consistent operating principle. 

Sunday, February 27, 2011

Objections to the design argument


Here are two popular objections to the teleological argument:

He concedes that we often do make inferences to design (or, more appropriately, intention) in the sciences. For example, archaeologists do it when they discover artifacts. But the reason they can do this is that they already know something about the beliefs, desires and intentions of human beings. Using this background knowledge, they can specify how human beings might be expected to act and makes guesses about the artifacts they might be inclined to create. There is no analogous background knowledge when it comes to God.


Evolutionary opportunism also results in suboptimal functions and structures. As stated before, in gradually evolving a new function, organisms must make do with what they already have. Thus, functions are likely to be performed by structures that would have been arranged differently (e.g. more efficiently) if the final function were known from the outset. "Suboptimality" does not mean that a structure functions poorly. It simply means that a structure with a more efficient design (usually with less superfluous complexity), could perform the same final function equally well.


The problem with these two objections is the way they cancel each other out. If you can’t detect divine design because you can’t infer divine intent, then you can’t say an organism suffers from a design defect. You’d only be in a position to know the design was defective if you know what God intended to achieve. You can’t say an agent missed the target unless you know what he was aiming for.  

The principle of plenitude


It’s common for unbelievers to attack Christian theism by pointing out design flaws in nature. What’s ironic about this tactic is that while unbelievers pride themselves on their respect for science, their appeal to design flaws is so unscientific.

1. The unit of optimality

What’s the fundamental unit of optimality? Is the fundamental unit an individual organism?

Suppose we ask, which is better designed: the snow leopard or the African leopard?

The question is meaningless because you can’t judge design efficiency in isolation to the specific environment in which the organism must operate. A snow leopard is better designed for a frigid, mountainous habitat whereas an African leopard is better designed for the tropics. So optimal design is correlative. The African leopard would be suboptimally designed for the natural habitat of the snow leopard.

2. The balance of nature

Apropos (1), suppose we could optimize the design of prey such that prey uniformly evaded capture by predators. Would that be a better design?

The deleterious result would be twofold: (i) predators would become extinct due to starvation; (ii) prey species would become extinct due to overpopulation, overgrazing, and subsequent starvation.

Conversely, suppose we could optimize the design of predators. Would that be a better design?

The deleterious result would be twofold: (i) prey species would become extinct due to overpredation; (ii) predators would become extinct due to exhaustion of the food supply.

To maintain the natural balance, prey must elude capture often enough to maintain a replacement rate while predators must capture prey often enough to main a replacement rate.

If you improve one without improving the other, you destroy both. So what constitutes optimal design in predator and prey species is correlative.

3. Tradeoffs

Which is better designed: a lion, leopard, or cheetah?

A cheetah is built for speed. In one respect that confers a competitive survival advantage. It can take down prey that outrun slower predators.

But its superior speed comes at a cost. It has a weaker bite than leopards and lions. It lacks the razor-sharp retractable claws. Unlike a male lion, it can’t break the neck of prey with one swipe of the paw.

What about a lion? That has advantages. Because they live in groups, a lioness or two can stay behind to baby-sit cubs while the rest of the pride is out hunting. It’s easier to corner prey when you hunt in a pack. And having more hunters raises the odds of a successful kill.

But there are corresponding disadvantages. More mouths to feed. So one must hunt more often. Also, bigger animals need to eat more, although they can also take down larger prey.

There’s a pecking order in terms of who gets first dibs of the kill. The alpha males get the “lion’s share.”

If another lion dethrones the alpha male, it will kill the cubs. So one advantage offsets another advantage.

What about the leopard? It represents an engineering compromise or mean between the powerful lion and the fleet-footed cheetah. It enjoys the upsides and downsides of a solitary predator.

Is an anteater better designed than a leopard? In one respect, the specialized design of the anteater confers a competitive survival advantage. It can corner the market on a particular food source.

But the attendant downside is that it’s totally dependent on that narrow food source. If, due to natural disaster, ants, termites, and grubs are in short supply, it will starve.

By contrast, the leopard, with its flexible design, is far more adaptable. It has many food sources. In one respect, that’s a competitive survival advantage.

But by the same token it must compete with other predators (e.g. lions, cheetahs, hyenas, cape hunting dogs) for the same prey.

Man is a limiting case of engineering tradeoffs. On the one hand, man is one of the most naturally defenseless creatures on earth. But the compensation is his superior intelligence–aided by good eyesight and the opposable thumb.

4. Intentionality

Optimality is correlative with intentionality. To assess design, you have to know what the engineer intended to achieve. For instance, there are more accurate ways to tell time than a cuckoo clock. But that doesn’t mean a cuckoo clock is poorly designed. It wasn’t made to maximize accuracy.

On the face of it, the animal kingdom seems to be designed to exhibit the sheer diversity of possible strategies, solutions, combinations, and permutations.

The principle of plenitude trumps the law of parsimony.

5. Dysteleology

Since unbelievers reject natural teleology, they forfeit the right to say anything in nature is ill-designed. Something can only be poorly designed in case it was meant to perform a certain function. But if the watchmaker is blind, then the watch wasn’t ever meant to tell time. That’s adventitious. Whether it’s fast or slow is not a design defect.

Tuesday, September 14, 2010

Roger Penrose on cosmic purpose

[Roger Penrose] I’m not sure that the word “purpose” one might use in connection with the universe or the laws of physics is quite the same as the way we use the word in a personal sense: when we intend to do something. But there is a certain sense in which I would say that the universe has a purpose. It’s not just there by chance.

Some people take the view that the universe is simply there and it runs along–it’s a bit as though it just sort of computes, and we happen by accident to find ourselves in this thing. I don’t think that’s a very fruitful or helpful way of looking at the universe. I think there is something much deeper about it, about its existence, which we have very little inkling of at the moment.


S. Hawking & G. Stone, eds. Stephen Hawking’s A Brief History of Time: A Reader’s Companion (Bantam Books 1992), 142.

Friday, May 02, 2008

A Glimpse Into Teleology

One of the best offenses against Darwinism is the teleological argument. In fact, that is what Intelligent Design is (teleology = the study of design). This is most damaging to the Darwinist position because on the one hand Darwinists will repudiate teleology, but on the other hand they will employ it at every corner. To give examples of both in the same book, Ernst Mayr wrote:

Another widespread erroneous view of natural selection must also be refuted: Selection is not teleological (goal-directed). Indeed, how could an elimination process be teleological? Selection does not have a long-term goal. It is a process repeated anew in every generation.

Mayr, E. (2001). What Evolution Is. New York: Basic Books. p. 121


Yet Mayr also writes:

When the selective advantage of a skeleton developed among the ancestors of the vertebrates and of the arthropods, the arthropod ancestors had the prerequisites for developing an external skeleton, and the vertebrate ancestors for developing an internal skeleton. The entire evolution of these two large groups of organisms has since been affected by this choice among their remote ancestors.

(ibid, p. 141, emphasis added).

Evolution is an opportunistic process. Whenever there is an opportunity to outcompete a competitor or to enter a new niche, selection will make use of any property of the phenotype to succeed in this endeavor.

(ibid, p. 221, emphasis added).


Likewise, we read:

The legitimate use of the term adaptation is for a property of an organism, whether a structure, a physiological trait, a behavior, or anything else that the organism possesses, that is favored by selection over alternate traits. But the term also has been used quite incorrectly for the process ("adaptation") by which the favored trait was actively acquired. This view can be traced back to the ancient belief that organisms had an innate capacity for improvement, for steadily becoming "more perfect." Also, if one accepts an inheritance of acquired characters, activities such as the straining of the neck by giraffes "adapts" the neck to an improved construction. In this view, adaptation is an active process with a teleological basis. Some recent authors still seem to look at adaptation as such a process and therefore reject the whole concept of adaptation. But this is not defensible.

(ibid, p. 150).


Yet of adaptations, we read:

The shift from the quadropedal locomotion of a lizardlike reptile to bipedalism and flight in birds initiated a considerable restructuring of the body plan: a compacting of the whole body to have a better center of gravity, the development of a more efficient four-chambered heart, restructuring of the respiratory tract (lungs and air sacs), endothermy, improved vision, and an enlarged central nervous system. The acquisition of all of these adaptations was a matter of necessity.

(ibid, p. 219, emphasis added).


But Mayr is not the only one who falls prey to this. Indeed, when trying to describe their theories Darwinists are forced to use teleological representations. For instance, Gould wrote:

The model of the grabbag is a taxonomist's nightmare and an evolutionist's delight. Imagine an organism built of a hundred basic features, with twenty possible forms per feature. The grabbag contains a hundred compartments, with twenty different tokens in each. To make a new Burgess creature, the Great Token-Stringer takes one token at random from each compartment and strings them all together. Voilà, the creature works--and you have nearly as many successful experiments as a musical scale can build catchy tunes. The world has not operated this way since Burgess times. Today, the Great Token-Stringer uses a variety of separate bags--labeled "vertebrate body plan," "angiosperm body plan," "molluscan body plan," and so forth. The tokens in each compartment are far less numerous, and few if any from bag 1 can also be found in bag 2. The Great Token-Stringer now makes a much more orderly set of new creatures, but the playfulness and surprise of his early work have disappeared. He is no longer the enfant terrible of a brave new multicellular world, fashioning Anomalocaris with a hint of arthropod, Wiwaxia with a whiff of mollusk, Nectocaris with an amalgam of arthropod and vertebrate.

Gould, S. J. (1989). Wonderful Life. New York: W. W. Norton & Company, Inc. p. 217-218


Naturally, Gould was trying to be poetic; but one wonders if it is even possible for him to explain his “grabbag” idea without resorting to the teleology of a designer (in the above case, the “Great Token-Stringer”). One suspects not. And those outside the field of biology are oblivious to the fact that evolution is supposed to be non-teleological. In fact, they see quite the opposite. For example, James Gleick in his book on the Chaos Theory wrote:

In science, on the whole, physical cause dominates. Indeed, as astronomy and physics emerged from the shadow of religion, no small part of the pain came from discarding arguments by design, forward-looking teleology--the earth is what it is so that humanity can do what it does. In biology, however, Darwin firmly established teleology as the central mode of thinking about cause. The biological world may not fulfill God's design, but it fulfills a design shaped by natural selection. Natural selection operates not on genes or embryos, but on the final product. So an adaptationist explanation for the shape of an organism or the function of an organ always looks to its cause, not its physical cause but its final cause. Final cause survives in science wherever Darwinian thinking has become habitual. A modern anthropologist speculating about cannibalism or ritual sacrifice tends, rightly or wrongly, to ask only what purpose it serves. D'Arcy Thompson saw this coming. He begged that biology remember physical cause as well, mechanism and teleology together. He devoted himself to explaining the mathematical and physical forces that work on life. As adaptations took hold, such explanations came to seem irrelevant. It became a rich and fruitful problem to explain a leaf in terms of how natural selection shaped such an effective solar panel. Only much later did some scientists start to puzzle again over the side of nature left unexplained. Leaves come in just a few shapes, of all the shapes imaginable; and the shape of a leaf is not dictated by its function.

Gleick, J. (1987). Chaos: Making a New Science. New York: Penguin Books. p. 201-202


Because of this cognitive dissonance, teleology works well against Darwinists. If something looks designed, the simplest and straightforward reason is that it’s because it was designed. It is because of how much design is apparent in the living world that Dawkins had to take the time to pen The Blind Watchmaker in the first place. If nature didn’t have the designed appearance of a watch, Dawkins wouldn’t have needed to try to come up with an alternate explanation for it.

So teleology has found a niche in anti-Darwinian circles. I, however, would like to expand it out a bit further than that. Most recently, I’ve been studying cryptology as part of my endeavors to better understand such things as information theory, etc. Cryptology is also important since I enjoy dissecting Darwinist arguments and DNA happens to be very prominent in many of them. Since DNA is a “living code” understanding certain principals of cryptology can be beneficial.

Surprisingly, however, my thoughts have strayed from their original course in biology. The living order is teleological, and it is difficult for anyone to honestly look at it and yet still deny the inherent design. But so too is the non-living universe. Teleology surrounds us everywhere we look. It is not just in living systems, but anywhere that there is a system. And because of that, my original focus and my original purpose for reading up on cryptology (besides the fact that I’m weird and actually enjoy the subject) has expanded somewhat.

All reality is teleological.

Since my thinking has come about as the result of reading on cryptology, it perhaps wouldn’t hurt if I gave the specific example that got me thinking on this issue. William Friedman, who was instrumental in the US breaking of the Japanese cipher PURPLE in World War II, wrote The Index of Coincidence and Its Applications in Cryptography in 1920 when he was 28 years old. It was later updated somewhat after Friedman found the solution for a cipher machine using cryptographic rotors. David Khan, in The Code-Breakers, illustrates the theory in this manner:

Imagine an urn containing one each of the 26 letters of the alphabet. The chance of drawing any specified letter, say r, is one in 26, or 1/26. Now imagine another, identical urn. The chance of drawing an r is equally one in 26, or 1/26. What are the odds of drawing a pair of r’s, one after another, in a two-draw situation? The likelihood of drawing the second r is 1/26 of the chance of drawing the first, which is 1/26. So the chance of drawing two r’s in a single event, or “simultaneously,” one from each urn, is 1/26 x 1/26. Similarly, the probability of drawing two a’s is 1/26 x 1/26, of two b’s 1/26 x 1/26, and so on. Consequently, the chance of drawing a pair of letters—any pair of letters, no matter which pair may come up—is the sum of all these probabilities. It is (1/26 x 1/26) + (1/26 x 1/26) + … + (1/26 x 1/26), repeated 26 times, or 26 x (1/26 x 1/26), or 1/26. This quantity may be written as the decimal 0.0385.

Assume now an ideal cryptosystem whose ciphertexts yield a perfectly flat frequency count—one with as many a’s as b’s as c’s…as z’s. Polyalphabetics approach this in varying degrees and may, for practical purposes, be regarded as generating such ciphertexts. These texts are called “random” because they are what would be obtained if letters were drawn at random from the urn (each letter being replaced after being noted and the urn shaken to mix the lot, chance alone dictating their identities). If two such random texts are superimposed, the chance that the letter above will be the same as the letter below is the same as the chance of drawing a pair of identical letters from the two urns. This is 0.0385, or, to put it another way, there will be 3.85 such coincidences in every 100 vertical pairs. Experiment will confirm this.

Now imagine an urn filled with 100 letters of English in the proportion in which they are used in normal text—8 a’s, 1 b, 3 c’s, 13 e’s, and so on. The chance of drawing a specified letter is now proportional to its frequency. The probability that an a will emerge is 8/100ths, that a e will is 13/100ths. With two such urns, the chance of drawing two a’s is, as before, the product of the individual probabilities, or 8/100 x 8/100; the chance of drawing two e’s is consequently 13/100 x 13/100. And the probability of drawing a pair—any pair—of identical letters is the sum of all these pair-probabilities: (8/100 x 8/100) + (1/100 x 1/100) + (3/100 x 3/100) …, and so on through all 26 letters. This calculation has been made (with a slightly different frequency table). The result is 0.0667.

These two plaintext urns may likewise be replaced by two strings of plaintext. If they are superimposed, there will be as much likelihood that two letters will coincide vertically as there was that two identical letters will be drawn from the two urns. This probability is 0.0667, or 6.67 coincidences per 100 paris. For example:



text A wheninthecourseofhumaneventsitbecomesnecessaryforo
text B fourscoreandsevenyearsagoourfathersbroughtforthupo


text A (cont.) nenationtodissolvethepoliticalbandsthathaveconnect
text B (cont.) nthiscontinentanewnationconceivedinlibertyanddedic


There are just seven coincidences in the 100 pairs—precisely what theory predicts.

…[O]ne must recognize first that the superimposition of two monalphabetically enciphered texts will result in the…figure of about 6.67 coincidences per 100 vertical pairs, or 6.67 per cent of coincidences. This is because the coincidences will occur whether the letters are clothed in ciphertext disguises or not. The calculation does not ask the letters for their identities. It merely notes their coincidence. By the same token—and this is important—two polyalphabetic cryptograms enciphered in the same key and superimposed so that the two occurrences of that key are in synchronization with one another will also show 6.67 per cent of coincidences. The reason is this: In a correct (in-phase) superimposition, the two letters of each vertical pair have the same keyletter. Thus whenever a coincidence occurs in the plaintext, the letters of the pair will be identically enciphered. This results in an identical pair—a coincidence—in the ciphertext. It does not matter that a pair of e’s may be enciphered into V’s at one point and into Q’s at another, or that a coincidence of a’s becomes a coincidence of L’s here and a coincidence of F’s there. The toal number of coincidences will remain the same as the number in the plaintext.

On the other hand, if the two cryptograms are improperly superimposed, so that the keys are not in step, any coincidences will result from different keyletters operating on different plaintext letters to accidentally produce the same ciphertext letter. The coincidences will be caused, in other words, by chance. Chance alone will produce 3.85 coincidences per 100 vertical pairs in random text, and polyalphabetic ciphertext is equivalent to random text. Hence an incorrect superimposition should yield about 3.85 per cent of coincidences. But 3.85 per cent is substantially less than 6.67 per cent, and so a comparison of the percentages of coincidences at various test superimpositions should show which superimposition is correct.

An example should make things clear. A cryptosystem with the Vigenère running key THE BARD OF AVON IS THE AUTHOR OF THESE LINES…starts the key for the first message with the first keyletter, but starts the key for successive messages with the third, fifth, and so on, keyletters. If plaintext 1 is If music be the food of love, play on, and plaintext 2 is Now is the winter of our discontent, the encipherment will be these:


key THEBARDOFAVONISTHEAUTHOROFTH
plaintext 1 ifmusicbethefoodofloveplayon
ciphertext 1 BMQVSZFPJTCSSWGWVJLIOLDCODHU

key (TH)EBARDOFAVONISTHEAUTHOROFTHESE
plaintext 2 nowisthewinterofourdiscontent
ciphertext 2 RPWZVHMERWABWKVJOOKKWJQTGAIFX


A cryptanalyst, receiving these two cryptograms, will superimpose them so that they start at the same point:


ciphertext 1 BMQVSZFPJTCSSWGWVJLIOLDCODHU
ciphertext 2 RPWZVHMERWABWKVJOOKKWJQTGAIFX

Since there are 28 vertical pairs, the cryptanalyst would expect 28 x 0.0667 coincidences or 1.8676, or about 2, for a proper superimposition. But in fact he finds none, so he shifts the second cryptogram one space to the right and tries again. There will now be 27 vertical pairs. The cryptanalyst again calculates the theoretical expected number of coincidences for random and for correctly superimposed texts of this length so that he may compare the values with what he actually observes. Thus, a wrongly superimposed text would yield 27 x 0.0385 = 0.9695, or about 1 coincidence that would produced by chance alone, while a correct superimposition would yield 27 x 0.0667 = 1.2369. (These fractional differences become more pronounced with longer texts.) One coincidence appears….

Since the differences between the chance and the caused values are so slight with so few letters, the cryptanalyst might wonder whether this is not in fact a random result (which in fact it is…) and try the next superimposition. Here the number of coincidences immediately jumps. This superimposition is obviously correct.


ciphertext 1 BMQVSZFPJTCSSWGWVJLIOLDCODHU
ciphertext 2 RPWZVHMERWABWKVJOOKKWJQTGAIFX


If the cryptanalyst wishes to continue, he will find that at the next superimposition the number of coincidences falls again, to 2, and will return to begin his attack with the third superimposition…

Kahn, D. (1967, 1996). The Codebreakers. New York: Scribner. p. 377-380.


With this as the immediate background, I’ll simply note how my train of thought has progressed. When dealing with language, we are dealing with something that we know is designed. Language requires intelligence, and this is even more evident when it comes to written text. Because text is a product of intelligence, it will always display the hallmark of intelligence. One will be able to differentiate between that which is designed and that which is random.

The above examples demonstrate it beautifully. Take the illustration of putting the opening line of the Declaration of Independence above the opening of the Gettysburg address. Because both texts were written in English, and because English is designed rather than random, English traits will carry through. There will be vertical alignment of almost 7%. Random texts only have 3%. Because this is the case, even hiding English within a cipher does not destroy these traits, although it obscures it at first glance.

Design, therefore, is something that would permeate everything. It might not be immediately apparent at first glance, but there will be traits that can be sought mathematically that will yield results nowhere near what random results would give us.

Now obviously when one thinks about living systems, one can see that there are processes at work that are not random. Even the relatively simple actions of an ion pump inside a cell demonstrate values that are not what one would find in a random environment. A cell becomes charged due to the existence of these ion pumps (which is how the electrical pulse can travel the nerve), but under random circumstances the charge would dissipate.

Indeed, when thinking of what is truly random one immediately must think of entropy. The less entropy there is in a system, the less random it is. If a room has low entropy, it is because everything is ordered. If it has high entropy, it is randomized. The more ordered something is, the less random it must be.

This brings us immediately to questions of the universe as a whole. And not just in terms of entropy amongst galaxies and such. Instead, I want to ask more foundational questions.

Suppose we see iron filings arrayed on a table next to a magnet. The filings will lay in a particular pattern and won’t lay randomly. Why is this the case? Of course the immediate answer is because magnetic forces have arranged the iron filings in that manner. But why is it that magnetic forces would act in that manner? We can dig into the quantum levels, perhaps. But that merely begs the question: why is it that those quantum particals act the way they do? What is it that causes electrons to be repulsed from one another? What is it that causes protons to attract electrons? Why is it that these things always happen this way, that there is no variance…no randomness to it?

Even things that are apparently random turn out to hide hidden order. Take radioactivity for instance. Radioactive elements are used to produce random cipher keys even, because no one can predict when an alpha particle will decay. But despite how “random” the decay is, radioactive elements always decay at a specific rate. Despite the random nature, there is an over-riding law that stipulates what the half-life of that radioactive element will be. We may not be able to predict when the next alpha particle will decay, but we know that after a set amount of time exactly half of the element will have decayed.

Is that not an instance of the non-random showing itself? Like the cipher text that cannot help but display the design of the English language, if one but knew where to look, don’t the underlying laws that govern all the universe scream out that there is underlying order to even what we think is chaos?

Earlier I quoted Gleick’s comment about the shape of leaves, which are governed not by forces of Natural Selection but instead by fractal designs. The key there is “designs.” All of reality is based on these deep, inherent designs. And these designs cannot be random because they are, in fact, distinct from what we would see in a purely random field.

Naturally I know that some chaoticians say that order springs from chaos, and they will use mathematical representations of chaos to illustrate this…all the while ignoring the fact that the mathematical system that they are using to generate those fractals is itself non-chaotic. Indeed, as some may already know I’ve spent lots of time playing with what I call the “Factor Field.” It’s an Excel program that I made (you can e-mail me if you want a copy using my yahoo account. Simply put “petedawg34” and follow it with “@” and finish with “yahoo.com”, and yes defeating spambots is always fun). The Factor Field is simply a graphical representation of integers. The left-most column counts by 1. The second column by 2s. Etc. Because I used Excel, it only shows 256 wide, but it goes 65,536 deep. Here is but one example of what you can see at cell number 60,480:



This shows what I call a “starburst” pattern. You can also see the skeletons of parabolas in there, as well as many different lines of various slopes. All this was created by putting integers in patterns next to each other.

If you were to isolate some of the pixels on the right side of the graphic, the dots would look very chaotic. There would not appear to be any particular rhyme or reason for any of them to be where they are. Yet they came about due to a specific rule. There is an underlying order that created the seeming randomness that is seen. And stepping back, viewing it from the distance where one can see the whole starburst, the order is obvious.

Likewise, the factor field can make it easy to find if a number is a prime number, but it doesn’t make it any easier to predict prime numbers that aren’t shown on the graph (although via observation, I hypothesize that all prime numbers greater than 3 are numbers that end in either 1 or 5 in base-6, but that’s another blog post for another time). One can tell that previous portions of the graph affect later portions, but it is so complex that it is difficult for humans to predict how the effects will play out “off screen.”

This interplay of chaos and order is only possible because the structure of the factor field is built on order. It’s an order that displays chaotic behavior later on, but it remains order. Likewise, all the representation of chaos theory are built on mathematical models that are, themselves, strict. Math doesn’t randomly make 1 + 1 = 7. It cannot happen. And the rules of chaos mean that doing the same math formula over with the exact same data will yield the exact same result. That there are wild differences if the data is even minorly tweaked doesn’t change the fact that not tweaking it yields identical results.

In other words, even in the most random systems we can think of, because they are real, have order underlying them. Reality is not random. Reality is, at heart, the opposite of random. And what is the opposite of randomness?

Design.

Thursday, June 28, 2007

Teleological Explanation

Posted on behalf of Steve Hays...

Human curiosity leads people to ask what things are for. Teleological explanations answer “What for?” questions by appealing to forward-looking reasons.

Children learn that certain things—a snapped twig, a pattern of pebbles washed up by the tide—are not thought to be explainable in this way. But there is a vast range of phenomena which adults do try to explain teleologically. Children accept these explanations and learn rules for constructing them. Folk acceptability is no guarantee of scientific acceptability, however. Many thinkers have held that the study of purposes is no business of science.

Goal explanations are widely employed in psychology, ethology, and Artificial Intelligence; natural function explanations figure in biology; social function explanations occur in anthropology, sociology, and sociobiology.

Yet there are some whose idealized conception of good science challenges the legitimacy of goal talk, and others who believe that natural function attributions are not wholly objective.

Typically, a functional explanation in biology says that an organ x is present in an animal because x has a function F. What does this mean?

Some philosophers maintain that an activity of an organ counts as a function only if the ancestors of the organ’s owner were naturally selected partly because they had similar organs that performed the same activity.

However, this construal is not satisfying intuitively. To say that x is present because it has a function is normally taken to mean, roughly, that x is present because it is supposed to do something useful. This looks like the right sort of answer to a “What for?” question. Unfortunately, this normal interpretation immediately makes the explanation scientifically problematic, because the claim that x is supposed to do something useful appears to be normative and non-objective.

One possible ground for such a claim is that a designer meant x to do F…If the designer is held to be Nature, the claim involves a metaphorical personification. Dennett (1987) argued that discerning natural functions always involves tacitly conceiving Nature as a designer.[1]


[1] “Teleological Explanation,” W. H. Newton-Smith, ed. A Companion to the Philosophy of Science (Blackwell 2001), 492-93.