The age of the Earth-3: The Earth gets old again

(My latest book God vs. Darwin: The War Between Evolution and Creationism in the Classroom has just been released and is now available through the usual outlets. You can order it from Amazon, Barnes and Noble, the publishers Rowman & Littlefield, and also through your local bookstores. For more on the book, see here. You can also listen to the podcast of the interview on WCPN 90.3 about the book.)

For previous posts in this series on the age of the Earth, see here.

The Enlightenment brought with it the separation of scholarly thinking from religious dogma and this enabled scientists to think much more freely and broadly about all matters, including the age of the Earth.

As the desire for conformity with biblical estimates weakened, scientists started devising theories of the formation of the Earth and the universe and doing calculations that were not explicitly linked to Biblical theories. Immanuel Kant (1724-1793) and Pierre Laplace (1749-1847) created a new model of the universe, the nebular hypothesis, that said that stars and planets originated as clouds of gases. They used Newton’s laws of mechanics and his theory of gravitational attraction to explain the formation and evolution of the solar system.
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The age of the Earth-2: The Earth gets its first birth day

(My latest book God vs. Darwin: The War Between Evolution and Creationism in the Classroom has just been released and is now available through the usual outlets. You can order it from Amazon, Barnes and Noble, the publishers Rowman & Littlefield, and also through your local bookstores. For more on the book, see here. You can also listen to the podcast of the interview on WCPN 90.3 about the book.)

For previous posts in this series, see here.

For a long time, people were comfortable with the idea that the Earth and the universe might have been in existence for an infinite time and is undergoing repeated cycles of creation and destruction.

Things changed with the arrival of Christianity. That particular religion could not tolerate the idea of the universe occurring in cycles because that would mean that Jesus was dying over and over again for our sins, which seemed preposterous. (The discovery of sentient life on other planets is going to create problems for fundamentalist Christians as it is not clear how they would fit into the whole ‘original sin and Jesus sacrifice’ model.) So there had to be a chronology with a definite beginning and this acted as a spur to make calculations to fix the date of creation. Theophilus of Antioch (~115-183 CE), a convert to Christianity, provided an early estimate that the Earth had existed for 5,698 years until his time (Jackson, p. 13) and Julius Africanus (~200 CE) gave the creation date as 5500 BCE (Burchfield, p. 4).

These Christians based their calculations using an interpretation of the Bible (found in Psalms 90:4 and 2 Peter 3:8) that held that the Genesis story of six ‘days’ of creation was a metaphor, where each ‘day’ represented 1,000 years. The total of six days of creation was interpreted as meaning that the universe would last a total of 6,000 years. The appearance of man on the sixth day of the Genesis story represented the arrival of Jesus sometime in the last 1000 years. These calculations, based as they were on metaphorical readings of the text, lacked a certain rigor.

It took until the 1600s for the age of the Earth to become really quantified, with scholars getting down to the nitty-gritty of calculating an actual age, with the Bible again being the main source of data, and the results obtained strongly influenced thinking in the Western world. I have written before of Bishop Ussher’s (1580-1656) calculation of October 22, 4004 BCE as the day of creation (see part 1 and part 2 ) but his was just one, and not even the first, of many precise calculations around that time that used various versions of the Bible and thus arrived at slightly different values that rarely differed by more than a thousand years.

Why there was such an explosion of so many calculations done in the early 1600s is a bit of a mystery. One suggestion is that people began to realize that if the Earth was only going to last exactly 6,000 years total, then the end of the world was quite near and hence calculating the exact age of the Earth was of practical importance. After all, if you knew for sure that the world would end in a specified year with the return of Jesus, then you could make appropriate plans, or so at least religious people think though I am at a loss as to what one might do. One finds the same kind of obsession amongst present day Rapturists. They work feverishly to look for signs of the end times because they think it is very near. People seem to be strangely drawn to the idea of an imminent apocalypse, as can be seen in the commercial success of films based on that theme.

The first Bible that had carried a chronological marginal creation date was published in 1679 but it was the insertion of the creation date of 4004 BCE and the dates of other significant biblical events next to the relevant sections of Genesis in the annotated versions of the authoritative King James Bibles in 1701 that cemented that date in the public consciousness. These marginal dates continued to be printed until the late 20th century. Ussher was not cited as the source of the dates and may not even have been the source since there were other chronologies, such as that of William Lloyd (1627-1717) who became the Bishop of Worcester in 1699, that also arrived at the date of creation as 4004 BCE. Since the latter was considered the foremost chronologer of his time, he may well have been the source of the date with which Ussher is now indelibly linked, although it is also possible that his calculations were strongly influenced by Ussher’s earlier work (Jackson, p. 30).

Whatever the original source of the date, the blame for leading present day fundamentalist Christians into an anti-science cul-de-sac from which they have never emerged surely must lie at the feet of John Fell (1625-1686), Bishop of Oxford and Dean of Christ Church College and the person who for some time controlled the operations of the Oxford University Press. It was he who in 1672 proposed putting the creation date in the King James Bible. If not for that, it is possible that the idea of a 6,000 year-old Earth may have remained a speculation, one among many, that could be interpreted away as science advanced, as has happened to so many other beliefs. But putting it in the hugely influential King James Bible raised it to the level of an infallible truth for many Christians because of their belief that if something is in the Bible, it must be literally true.

Western scientists at that time (or natural philosophers as they were then known) were mostly Christians and while they may not have been as convinced about the ideas of end of the world and Jesus coming again, they saw no reason to challenge the Bible-based calculations as to the date of creation. They took their cue from these biblical calculations and saw their purpose as trying to explain how life could have appeared and how geological forces could produce the features of the Earth, such as mountains and ravines, within that short time. This naturally led to biological theories of special creation and geological theories of catastrophism, a model in which sudden and violent upheavals produced major geological changes.

While some Christians then (and young Earth creationists now) may have seen Noah’s flood as the single major catastrophe that produced all the main features, other less Biblically-literal minded scientists such as Rene Descartes (1596-1650) and Gottfried Wilhelm Leibniz (1646-1716) were willing to consider multiple catastrophes, with fire and water as the agents of these major changes, while still sticking with the biblical chronology (Burchfield, p. 5).

But with the Enlightenment, the desire for conformity with biblical estimates weakened, and people started devising theories of the formation of the Earth and the universe and doing calculations that were not explicitly linked to Biblical stories. These developments will be examined in the next post in the series.

(Main sources for this series of posts are The Chronologers’ Quest: The Search for the Age of the Earth (2006) by Patrick Wyse Jackson and Lord Kelvin and the age of the Earth by Joe D. Burchfield (1975).)

POST SCRIPT: Book signing and reception

Tomorrow (Thursday, December 3, 2009) there will be a short talk by me on my latest book God vs. Darwin: The War Between Evolution and Creationism in the Classroom, followed by a book signing and reception. All are welcome.

Where: Flora Stone Mather room at the Kelvin Smith Library, Case Western Reserve University
Time: 3:00-4:00 pm

The age of the Earth-1: The history of the search

(My latest book God vs. Darwin: The War Between Evolution and Creationism in the Classroom has just been released and is now available through the usual outlets. You can order it from Amazon, Barnes and Noble, the publishers Rowman & Littlefield, and also through your local bookstores. For more on the book, see here. You can also listen to the podcast of the interview on WCPN 90.3 about the book.)

It has been awhile since I have made the regular readers of this blog suffer through a long multipart series exploring a particular question. But my post on the interconnectedness of scientific theories spurred me to thinking about finding a good example, and the age of the Earth popped into my head as almost perfect. This series will be interspersed with posts on other topics.

The process by which science came to be interconnected can be described as beginning with a transition from ‘early modern science’ (which I have chosen to date as beginning with Galileo around 1600 CE) to ‘modern science’, that started around 1800 as new disciplines like geology, chemistry, and biology started to become mature and independent, developing their own theories and research protocols. But starting around 1900 a new trend emerged, which I will call ‘late modern science’, in which these somewhat independently developing fields began, as they grew, to encroach on each other’s territories, and the need to seek consistency among them became apparent. After some initial crises of incompatibility, by around 1930 the theories had started to mesh reasonably well.
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Transitional forms

(My latest book God vs. Darwin: The War Between Evolution and Creationism in the Classroom has just been released and is now available through the usual outlets. You can order it from Amazon, Barnes and Noble, the publishers Rowman & Littlefield, and also through your local bookstores. For more on the book, see here. You can also listen to the podcast of the interview on WCPN 90.3 about the book.)

In the previous post, I said that one thing that keeps creationists from ‘seeing’ the truth of evolution is that their teleological viewpoint makes them think that species in their current form are the aim of creation. If that is the case, why would god bother making anything else? Hence ancestral forms of current species that are unlike anything that currently exist simply have no place in their model.

Another mental block that prevents them from seeing transitional forms for what they are also arises due to this teleological viewpoint. Here they are misled by the very word ‘transitional’, which suggests something less that perfect and on the way to perfection.

In an online debate with Eugenie Scott, the head of the National Center for Science Education, Ray Comfort makes the following jaw-dropping statement where he illustrates this misconception by pointing to what he thinks is the weakness of the theory of evolution:

Nothing we have in creation is half evolved. The cow has a working udder to make drinkable milk. The bee has working apparatus to make edible honey. We don’t find a half-evolved cow or bee. None of the 1.4 million species on the Earth has half an eye. All have the necessary functioning equipment, from the brain, to the teeth, to the eye, to limbs, to reproductive necessities. Everything that we see in creation is in full working order—from the sun, to the mixture of the air, to the seasons, to fruit trees and vegetables, to the animal kingdom—from the tiny ant right up to the massive elephant.

But not only do we see this mature completion in creation; we see it displayed in the fossil record. It reveals that each animal was complete.

I went to the Smithsonian to see the fossils galore, and they were there—millions of fossils that were evidence of special creation. The Smithsonian didn’t have any transitional fossils that proved evolution (staunch believers claim that they have them, but not on display). I also visited the evolution museum in Paris (Grande Galerie de L’Evolution). I took a camera crew, and we spent an hour looking for the evolution exhibit. It didn’t have one. All it had were millions of fossils of fully formed animals that God created (my italics).

This is a perfect example of creationists not ‘seeing’ the evidence for evolution that the rest of us see. It reveals the creationist teleological belief that everything we have now is in its final form and is functioning as designed. The very use of the phrase ‘half evolved’ reveals the deep misconceptions originating from a teleological viewpoint, because that phrase is meaningless unless one sees current species as being in their final, perfectly functioning forms.

In this view, a ‘transitional’ form must be something less than perfectly functioning. What Comfort thinks evolution predicts is that transitional forms should consist of animals malformed in weird ways, like cows with udders that do not produce milk or bees that have not figured out yet how to make honey or human beings with only one leg. This displays a staggering ignorance of the most basic elements of how evolution works. But because Comfort has a teleological view that starts from the end, he cannot see that all of us, even though we are fully functioning and adapted to our present environment, are also at the same time transitional forms even though we don’t know how we will evolve in the future.

Evolution tells us what we evolved from, not what we are evolving to. Every species that lives now or has ever lived is both ‘fully evolved’ (in that it is the result of successful adaptations to its past environments) and a transitional form (in that it will evolve in the future as a result of new environmental pressures). There is no such thing as being ‘fully evolved’ in the Comfort sense of having reached unchanging perfection.

There are only three reasons I can think of for people making the kinds of extraordinary statements that Comfort makes above.

One is, of course, outright stupidity, coupled with ignorance. One should never rule that out.

Another reason is dishonesty, in that they know they are spreading falsehoods about what evolution is but think that saving souls for Jesus compensates for lying to them. One cannot rule that out either. The ranks of religious liars and charlatans are legion.

The third and most charitable explanation, which is what I am suggesting in this series of posts, is that that they simply haven’t been able to make the Gestalt-type switch from the old teleological and Platonic worldview to the modern scientific one. While scientists can look at living organisms and fossils and see them as both fully functioning and transitional, creationists can see only a ‘fully evolved’ object. This is an almost perfect example of what happens when you cannot make the Gestalt switch to see two images while viewing a single object. While scientists can look at the image below and see both a duck and a rabbit, for creationists the duck is still only a duck, and as a consequence, the two pointy-things on the left can only be its bill.

Duck-Rabbit_illusion.jpg

It is quite sad.

POST SCRIPT: Here’s a ‘fully evolved’ ape

From the BBC comedy show Not the Nine O’Clock News.

Why creationists do not ‘see’ evolution

(My latest book God vs. Darwin: The War Between Evolution and Creationism in the Classroom has just been released and is now available through the usual outlets. You can order it from Amazon, Barnes and Noble, the publishers Rowman & Littlefield, and also through your local bookstores. For more on the book, see here. You can also listen to the podcast of the interview on WCPN 90.3 about the book.)

One specific creationist religious belief whose origins I have been curious about is the bizarre argument that is advanced by anti-evolution religious people about how the lack of transitional fossils is undermining the theory of evolution. This argument mystifies scientists because of course there are huge numbers of such fossils. The evidence is incontrovertible. In fact, every living or fossilized organism can also be considered a transitional form, since change is constant. It should also be borne in mind that Darwin arrived at his theory without having the wealth of fossils that are now available, basing his arguments largely on biogeography, the similarities in body patterns of animals, embryology, and the existence of vestigial organs. Nowadays, the fossils that keep being found and the relationships that have been discovered between the DNA molecules of species have sealed the case for evolution.
[Read more…]

The power of subconscious theories

(My latest book God vs. Darwin: The War Between Evolution and Creationism in the Classroom has just been released and is now available through the usual outlets. You can order it from Amazon, Barnes and Noble, the publishers Rowman & Littlefield, and also through your local bookstores. For more on the book, see here. You can also listen to the podcast of the interview on WCPN 90.3 about the book.)

The existence and history of religion tells us that people are willing to believe things for which there is no evidence and that they will fight to hold on to them even in the face of overwhelming evidence and arguments to the contrary. But when those beliefs collapse, as they sometimes do, the switch to disbelief can often be quite sudden. I know that in my case, I had been struggling (unsuccessfully) to reconcile my scientific ideas with that of a god for some time. The realization that everything made a lot more sense if there was no god hit me like a Gestalt switch.

One specific creationist religious belief whose origins I have been curious about is the bizarre argument that is advanced by anti-evolution religious people about how the lack of transitional fossils is undermining the theory of evolution. This argument mystifies scientists because it is so palpably wrong and the fossil evidence is so strong. So where does this weird idea come from? And why does it persist?

As much of research in science education has shown, robust misconceptions are often not simply bits of false knowledge (like thinking that Portland is the capital of the state of Maine) that can be easily corrected, but instead are the manifestations of elaborate theories that emerge from a deeply rooted but fundamentally flawed premise. As long as that flawed premise remains intact and unexamined, the misconceptions that flow from it will reappear even if countered in specific cases.

I have seen this phenomenon in my own teaching of electricity to people without a science background. One of the strong misconceptions that people have about electric current is that it emerges from a source (a battery or an electrical outlet), flows through the wire, and is then ‘used up’ by the radio or light or whatever device it is connected to. They also think that a battery always supplies the same amount of current. Based on this model of electricity, they will then make wrong predictions about how current will flow in more complicated circuits, say by connecting two or more devices to the same source of current.

In actuality, current is never used up. It just flows around in a circuit. Current flows out of one end of the battery (or other source), goes through one wire to the device, passes through the device, and then flows back through another wire into the other end of the battery. The amount of current flowing out of the battery at one end is exactly equal to the amount of current flowing into it at the other end. But it is extraordinarily hard to persuade novice learners of this model, even when they want to learn about electricity and have no reasons to resist it. After all, the Bible does not say anything about electricity. When I tell them how current really behaves, they believe me because I am an authority figure. But yet the misconceptions persist.

If you teach the right model of current to people and then ask them a direct question about how current flows, they will give back the right answer. But when they are asked something indirect, like giving them a circuit and asking them to predict how current will flow, very often they will come up with an answer that is at variance with how it really will behave. If you trace the reasoning of the wrong answer back to its source, you will find that it arises from their original misconception of current being used up and the battery producing a fixed amount of current, even though they consciously thought they had rejected that old way of thinking. When you point this out, they will think that this time they have definitely overcome the misconception. But when they are given a yet more complicated circuit, very often they will make a wrong prediction again, based on the same underlying misconception.

It is only after it has been repeatedly pointed out to them the important role that their basic deep misconception plays in their surface thinking that they switch to seeing the current flowing in a circuit. Once they make that switch in their basic misconception, there is no going back. They cannot imagine that they could have ever thought otherwise.

The reason this particular misconception about current is so deeply held is because people have constructed it on their own. Most of them are not even aware that they have this underlying theory of electricity because they have not consciously thought about it. The theory is built intuitively. Nobody taught it to them, they just ‘picked it up’ because it makes sense. After all, they know that appliances have a power cord that must be connected to an electrical supply system in order to work. They know that electrical devices ‘use up’ power because batteries eventually die. The power cord looks like a single tube, like a garden hose, and thus electricity seems like it can flow only in one direction. All these things make sense by assuming their simple model. Most people do not look more closely and wonder why the plug has two prongs and they do not break open the wires or their devices and find that there are incoming and outgoing pathways for the current.

The theories that people intuitively create for themselves are the hardest to refute because they are buried deeply in their thinking and are not consciously articulated by them. The consequences of these misconceptions are often erroneous but if we only correct the consequences without understanding and addressing the source, then we will find that same misconception rearing its head each time a novel situation is encountered.

The misconceptions about how evolution works are of the same kind. They are created deep in the minds of people at an early age, often by well meaning, science-supporting adults who tell their children that ‘we evolved from monkeys’ and by some of the visual images that we have of the process of evolution, such as the one that draws it as fish→amphibian→monkey→human (with the drawing of each showing what a current typical specimen looks like).

Once these misconceptions about evolution take root at an early age by a process of intuitive thinking, they become, just like the false electricity models, hard to dislodge in adulthood even by confronting people with the most clear reasoning.

As Jonathan Swift said, “You cannot reason a person out of a position he did not reason himself into in the first place.”

Next: The role that deep misconceptions play in evolution

POST SCRIPT: How not to stalk off an interview

It is not uncommon for guests on TV or radio to get miffed about something, throw a fit, and stalk off the set. Some may even do it deliberately as a strategy, knowing it will get them publicity. But it sometimes doesn’t work out well, with some forgetting to take off either the earpiece or the mike and getting yanked, resulting in a less-than-impressive exit.

But the award for the worst interview termination must surely go to Carrie Prejean. Remember her? Here are some keywords to jog your memory: Miss California who was stripped of her title, supporter of ‘opposite marriage’, breast implants, topless photos, Donald Trump, lawsuit against Miss USA pageant, sex video.

While on a tour promoting her book, she was irked by a question posed by Larry King of all people, who is notorious for his softball questions. So she removes her mike but instead of then walking off the set, she just sits there, talks to someone off-camera, and smiles at the camera as if she was competing in a pageant, leaving King baffled as to what is going on. Watch.

The key steps in adopting evolution

(My latest book God vs. Darwin: The War Between Evolution and Creationism in the Classroom has just been released and is now available through the usual outlets. You can order it from Amazon, Barnes and Noble, the publishers Rowman & Littlefield, and also through your local bookstores. For more on the book, see here. You can also listen to the podcast of the interview on WCPN 90.3 about the book.)

Making a Gestalt-type switch is often aided by nudges from outside sources, and in the case of evolution, two such factors came into play: the age of the Earth and concerns about the effects of human population growth.

Darwin was fortunate that he lived in a time when advances in knowledge in other areas, such as the idea of uniformitarianism in geology, were coming along at the same time that he was pondering all the things he was observing on his voyage on the Beagle. The first edition of the first volume of Charles Lyell’s highly influential book The Principles of Geology was published in 1830 and was given to Darwin to read on his voyage on the Beagle that began in 1831. Its argument that small changes (such as erosion) can accumulate over long periods of time to produce major geological features such as mountains and gorges had an impact on him.
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Gestalt switches in evolution

(My latest book God vs. Darwin: The War Between Evolution and Creationism in the Classroom has just been released and is now available through the usual outlets. You can order it from Amazon, Barnes and Noble, the publishers Rowman & Littlefield, and also through your local bookstores. For more on the book, see here. You can also listen to the podcast of the interview on WCPN 90.3 about the book.)

After Darwin published his book On the Origin of Species in 1859, large numbers of people were convinced in a very short time by his arguments, although full acceptance of the mechanism of natural selection took longer. But the idea of evolution had been in the air for some time. Why didn’t people before him see what Darwin and his co-discoverer Alfred Russell Wallace saw, since they had access to much of the same evidence that he had?

A possible reason is because the theory of evolution also required a Gestalt-type switch. People had been viewing the world through a prism of Platonic ideal forms. In the Platonic view, real objects are approximations to their ideal forms and it is only the ideal forms that matter and from which we get true information. So for example, for any triangle that we draw on paper, the angles will not add up to exactly 180 degrees because of the inevitable imperfections of our drawing and the inaccuracies of our measuring instruments. But the angles of all ideal triangles (that we can only conceive of in our minds) will always add up to 180 degrees, and it is the properties of that ideal form that is important to understand, not our real-life approximations.

While this way of looking at things is perfectly suited for mathematics, it leads people hopelessly astray when applied to biology. In the case of biological organisms, the Platonic model translates into thinking of each species as having an ideal form and of real organisms as just approximations that can and do deviate from the ideal in unimportant ways. So real chickens, with all their variety, are just imperfect manifestations of the ideal, perfect chicken that we can only conceive of in our minds. It is this perfect chicken that we need to study to understand what makes a chicken a chicken, the essence of chickenhood.

But the problem is that the ideal perfect chicken will necessarily always remains the same and cannot evolve into anything else, just like a triangle will not become a square nor will the sum of its angles slowly change with time. Platonic thinking rules out change but is perfectly consistent with the idea of a god creating every species as perfect unchangeable beings and part of a grand plan.

Darwin and Wallace both realized that it is the real forms of organisms that are important, not its idealized version, and furthermore that there are no ideal forms in biology. There is no idealized chicken. The variations found in real chickens, rather than being a nuisance detracting from our understanding of the ideal chicken, actually contain the key to understanding the nature of chickens and how they and other things can change. This shift in perception made the variations in a species central to our understanding, and not peripheral.

The likely reason that Darwin and Wallace may have been able to make the switch is because they spent some time traveling to other parts of the world and saw much more of the variety of life than those who stayed pretty much in one locality. Darwin’s voyage on the Beagle confronted him with so much new information about the diversity of life in so many new locations that it forced him into new ways of thinking. Alfred Russell Wallace also had his epiphany while travelling through Asia collecting biological specimens that were exotic and new to him.

Once Darwin and Wallace had made this switch, things started falling into place. They realized that if one adds up these small variations cumulatively over a long time, then even though each one is so small that it cannot be observed with the naked eye or even in one’s lifetime, it can add up to huge changes, resulting in the emergence of new species, something that was ruled out by Platonic thinking.

Two things stood in the way of making such an idea workable. It seemed to require an inordinate amount of time, much longer than people at that time thought the Earth had existed, and it lacked a plausible mechanism for species change. An obvious objection to their model that they needed to find an answer for was why should the variations in organisms cumulatively add up to result in large changes? Why could they not simply vary randomly leaving, on average, no net change?

This is where other factors can play a role in making a Gestalt switch in perception.

Next: The key steps in ‘seeing’ evolution

POST SCRIPT: Jon Stewart parodies Glenn Beck

This clip has been all over the political blogs but it is well worth seeing. Utterly hilarious.

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Perception changes in physics

(My latest book God vs. Darwin: The War Between Evolution and Creationism in the Classroom has just been released and is now available through the usual outlets. You can order it from Amazon, Barnes and Noble, the publishers Rowman & Littlefield, and also through your local bookstores. For more on the book, see here. You can also listen to the podcast of the interview on WCPN 90.3 about the book.)

In an earlier post, I suggested (following Thomas Kuhn) that Gestalt-type switches can play an important role in the creation and adoption of new theories in science. Today I want to look at specific examples of such changes.

Take the case of a simple pendulum, made by hanging a small weight from a fixed point by a string and setting it in motion by pulling it back and releasing it. What had been observed from time immemorial is the weight swinging back and forth with decreasing amplitude before finally coming to rest at the lowest point in its trajectory. People used to interpret this motion as the pendulum weight, when released, ‘seeking’ (to use anthropomorphic language) to get to its final resting place at the lowest point in its trajectory, but initially overshooting the mark, trying again to get to the lowest point, overshooting again by a smaller amount, and so on, until it finally reaches its destination and stays there.
[Read more…]

Gestalt switches in science

(My latest book God vs. Darwin: The War Between Evolution and Creationism in the Classroom has just been released and is now available through the usual outlets. You can order it from Amazon, Barnes and Noble, the publishers Rowman & Littlefield, and also through your local bookstores. For more on the book, see here.)

In the history of science, we have often seen a theory being accepted and used over a long period and then replaced with a new one, with the transition occurring over a relatively short time. Sometimes the new theory is fairly simple and we marvel as to why people did not think of it before. For example, the Copernican heliocentric model is not a complicated idea when compared to the previous geocentric model. Similarly Newtonian mechanics can be formulated in terms of laws that are very simple mathematically and easy to understand. The essential ideas of Darwin’s theory of evolution by natural selection can also be stated in a few simple sentences.
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