Tuesday, January 10, 2006

Hitchens on Dover

Here's Christopher Hitchens commenting on the most significant cultural event of 2005:


At the opening of Brideshead Revisited, Evelyn Waugh wrote of hearing one sweet and civilized word, and of the effect it had—as if a fatuous, bawling voice on a loudspeaker had been suddenly switched off. The judge's highly literate and elegant ruling in the Dover, Pa., intelligent-design case has had precisely that effect upon me. Just for once—for once—the raucous, boring, bullying noise of the religious morons is turned off, and one can hear the lucid tones of reason, detachment, culture, and irony. That the voters of the same town should have firmly retired the demagogues and dolts of their school board, and that both they and the judge should have been of a Republican tendency, only adds to my sense that the resources of civilization are not yet exhausted, and that we have wells of real intelligence upon which to draw. Please don't wake me up.


Well said.

Monday, January 09, 2006

The Bible Implies that Pi is Three. Deal With It.

Update: January 9, 6:33 pm I have slightly revised the third paragraph of this essay.




I realize I'm on blog vacation right now, but I couldn't resist responding to this little math lecture from David Heddle.

Answers in Genesis front man Ken Ham has a standard stock speech on the age of the Earth; I've heard him deliver it more than once. In one of his best lines he ridicules poeple who try to interpret the days of chapter one of Genesis as anything other than literal twenty-four hour days. He says something like: Some people say that day means a general period of time or that day refers to a long age of time or that there was a gap between the first and second day. Maybe. But sometimes day means day.

I don't say this very often, but I think Ham has a point. The clear and simple meaning of the text is that “day” refers to a standard twenty-four hour day. To interpret it any other way is to suggest that God laid out a creation story riddled with obfuscation and ambiguity.

I was thinking of that as I read Heddle's heroic and imaginative attempt to deny the obvious: that certain Bible verses unambiguously imply that pi equals 3. In particular, we look at 1 Kings, 7:23. The King James Bible presents it this way:


And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about.


The New American Bible is even clearer:


The sea was then cast; it was made with a circular rim, and measured ten cubits across, five in height, and thirty in circumference.


The term “sea” here refers to a large circular tank, but that is not the interesting part. Rather, it is the part about the tank being ten cubits across and thirty in circuferemce. Every high school geometry student knows that the circumference of a circle divided by its diameter gives you pi. In this case, we have a cricumference of 30 and a diameter of 10. That implies that pi equals three. But, actually, pi doesn't equal three.

Thus, what is being described here is a logical impossibility. Even God can't construct a circle with a diameter of ten and a circumference of thirty, just like He can't build a rock so heavy even He can't lift it. Especially in the New American version the text is so clear that you wouldn't think there'd be anything to argue about.

But Heddle is determined to convince us that the plain meaning of the text is not the correct one. So he offers up a variety of reasons for why, in this case, day doesn't mean day.

Heddle writes:


The underlying assumption is that the ancients were morons. (This assumption is usually reserved for ancient Hebrews alone. The Aztecs, for example, are assumed to be cultural and scientific geniuses who knew the secrets of the Super String landscape, which they enjoyed discussing over high protein meals derived from their own species.)

Any civilization building anything circular would have known that the ratio of the circumference to the diameter is slightly greater than 3. The Mesopotamians of a much earlier era used the approximate value of 25/8 = 3.125. The Egyptians may have had a much better value long before Solomon’s Temple. Here we see the assumption of stupidity: The Hebrews either didn’t know what their neighbors knew or they did know but didn’t bother to put accurate information into their sacred writings, in spite of its potential effect of weakening claims regarding the veracity of the holy words.


Of course, the Hebrews were not some Borg-like monolith in which things known to one were suddenly known to all. To believe that the Biblical writers erred here is simply to assume that one or a few particular Hebrews were unaware of a fairly obscure mathematical point. It is true that many ancient civilizations made impressive strides in mathematics. But it is equally true that most of the people alive at those times would have been unable to tell you about them.

The fact is, if basic geometry and the nature of pi really were common knowledge, the writers would surely have known that it is redundant to provide both the diameter and the circumference of a circle. The mere fact that they provided both suggests that either they didn't know about this redundancy, or did not assume their readers would know about it.

After all, the situation is hardly different today. Do a man on the street interview and I suspect you'd find a depressingly small percentage of people who could tell you pi to two decimal places. And it's only a tiny percentage of those who could tell you that pi represents the ratio of the circumference to the diameter.

So Heddle's snideness about the relative intellectual achievments of the Hebrews and the Aztecs is simply uncalled for.

But back to business. Heddle writes:


Not that any of that matters, because what is provided in the Bible is a description (“He made”), not a blueprint (“Makest Thou”).

There are several possible explanations—each one could stand alone but all may contribute to a certain extent.

The simplest explanation is technological. It was not possible to cast a brass object of such size in the shape of a perfect circle. So if one intended, roughly, to give its size using the (redundant) parameters of a circle—circumference and diameter, there would already be built into the description an error—given that the object was only approximately circular.

So the simplest explanation is that we are being given a rough description in terms of approximate dimensions of an imperfect shape. (Emphasis in original.)


For some reason this argument reminds me of a scene from the television show Newhart (the one in the Vermont inn, not the one where he played a psychologist). In the show Bob Newhart played an author of do-it-yourself books. He wanted his handyman George (played by Tom Poston) to build a bookcase of the right dimensions to fill a particular space along a wall. As it happened, Newhart had written a book discussing how to build such bookcases, and he wanted George to use it.

George was insulted. He gestured to the wall and said, “You want a bookcase yay tall and yay wide. I don't need a book to tell me how to do that.” Newhart replied, “Yay tall? Yay wide? My book gives you exact measurements.” George rolls his eyes and says, “Oh, I'm sorry. You want a bookcase exactly yay tall and exactly yay wide.

Heddle tells us that despite the plain statement of the text, the writers were only giving us approximate values. But the fact remains that they didn't say they were providing rough estimates. They could have. Would have been the easiest thing in the world for them to throw in a “roughly.” But they didn't.

Heddle also finds it significant that this is a description and not a blueprint. Indeed it is. So what? Rather than being told to do something impossible (build a circular structure with circumference thirty and diameter ten), we read simply that the impossible has already been done. Big improvement.

Now, as it happens I don't think it is unreasonable to conclude that the writers were simply giving round, ballpark numbers. But I'm not the one claiming that every word in the Bible is divinely inspired and infallible. Please don't tell me that on the one hand the Bible is reliable in everything it says, but on the other I have to first learn math and science from some independent source before I can know how to interpret it properly. There is no reason, outside independent knowledge that pi, in fact, is not three, to interpret those measurements as approximations. And even if you do interpret them as approximations, you're still left with the fact that the plain meaning of the Biblical text can lead you astray on matters of math and science.

But Heddle isn't done:


However, even if we assume that the sea was a perfect circle, there is no problem. For even if it was perfectly circular, it was not infinitely thin.

The figure on the left shows a scale drawing, assuming the precise measurements as provided. To put things in everyday perspective, we have converted from cubits to feet using the relationship that 1 cubit is about 18 inches. The problem is that the given diameter of 10 cubits (or a radius L of 5 cubits) extends beyond a circle with circumference 30 cubits, which has a radius of R = 4.77 cubits, by, as shown, an amount ?. A simple calculation shows that ? ? 4.1 inches.

But what if the sea had some thickness? And what if, as in the artist’s conception shown below, it was even flared at the rim? Then the 10 cubits could refer to the “outside” distance across, giving us information on its total size, while the circumference could be the inner circumference, telling us about the sea’s capacity. (See the original for diagrams)


Ingenious! But sadly ridiculous.

Under this interpretation we are supposed to view the rim of the tank not as a circle, but rather as a pair of concentric circles. A circle with a diameter of ten (leaving aside the units) would have a circumference a little larger than thirty, different from what is described. Heddle suggests that the ten refers to the diameter of the larger, outside circle, while the thirty refers to the circumference of the smaller, inside circle.

So now we are asked to believe that the circle being referred to at the end of the sentence is different from the circle being described at the beginning of the sentence. No writer in the history of the universe has ever written in such a way, and that goes double for the writers inspired by God. Again, no one would dream of interpreting the verse that way unless he was desperate to rescue the Bible form this obvious contradiction.

Heddle also suggests that the reference to the circumference of the inner circle is intended to tell us about its capacity. But had that been the intention, surely it makes more sense simply to tell us the volume of the tank.

Heddle has one more line of defense:


Finally, although it need not be invoked in this case, it is also known that eastern writing of the time was numerically imprecise—we often see this in biblical writings through the use of rounded numbers—for example in discussing Job’s possessions. This potential mitigating factor, that the writers of that era (biblical or not) treated numbers differently than we do, along with the fact that they also treated quotes differently (as faithful to the content of someone’s statement but not necessarily the precise wording) are two inconvenient (for our critics) established truths that they label as copouts. As I mentioned in the previous post, other off-limits methods to counter their claims include arguing on the basis of figure of speech, hyperbole, translation error, or proper context. For their claims regarding biblical inconsistency with science to hold water they cannot relax their unspoken assumption that the ancient Hebrews were idiots and their demand that all contested passages be evaluated, not just hyper-literally, but also as if they were written using modern style and practices.


Of course, using round numbers is standard practice today as well. But something more than round-off error is going on here. The verse describes two quantities which are related as a matter of logic. The relationship described in the verse is wrong. You can't just sweep that under the rug. No convention of ancient writing can change the fact that what is described here is plainly wrong.

A commenter to Heddle's post offered this link to an even more comical attempt to circumvent this point. Here's a taste:


The key to an alternative reading of the verse 1 Kings 7:23 is to be found in the very ancient Hebrew tradition (see, e.g., [Britannica 1985], [Banon 1987, pp. 52, 53]) to differently write (spell) and read some words of the Bible; the reading version is usually regarded as a correct one (in particular, it is always correct from the point of view of the Hebrew grammar, and this is why it could be easily either remembered or reconstructed from the written version), whereas the written version slightly deviates from the correct spelling. (Another approach, involving the comparison between written forms of the same words in 1 Kings 7:23 and Chronicles 4:2 is cited in [Posamentiern, Gordan 1984]; see more about this version of the exegesis in 4).

Such a disparity is a common feature for all Books of the Hebrew Bible; and in any such case there exists (or existed: some of this knowledge was definitely lost) a Rabbinical folklore (in fact, strict Rabbinical hermeneutical rules [Steinsaltz 1976, part three: Method], [Britannica 1985], [Banon 1987]) of interpretation of the difference in question. (Emphasis omitted)


They go on to point out that Hebrew letters have standard numerical equivalents. If you then look at the difference between the written, and reading version of the Hebrew word for “line” you get that the written version comes to 111 and the reading version comes to 106.

In light of this, they argue that the correct value of pi should be obtained by taking the three implied by the text, and multiplying it by the fraction 111/106. The result comes to 3.1415094...! A very respectable approximation (though still, I would note, not the correct value).

Do I really need to point out why this is silly? This procedure where you take the implied value of pi and multiply it by the fraction you get from dividing the written version by the reading version (I'm assuming, incidentally, that the authors of this essay are correct in making this distinction), where did that come from? I'll tell you where. It came from the realization that this is what you have to do to transform those numbers into a decent approximation for pi.

It is straight numerology. The essay talks about the strict Rabbinic rules for interpreting such situations, but that is hogwash. The answer came first. The arithmetical manipulations came later. They have no justification for their procedure beyond a desire to make everything work out the way we know it is supposed to.

So is this important? No. I address the point only because Heddle thought it was important enough not only to write about it at length, but also to heap snideness and stereotypes on people who might disagree with him on this point.

Verses like this are a useful antidote to people who would tell you that the Bible is infallible on any issue it addresses. But there are far better reasons for rejecting the idea that the Bible is divine in origin.

For example, there is the fact that the Bible describes things that are patently absurd. After reading the Gospel accounts you can conclude either that roughly two thousand years ago one dead body behaved in ways that no dead body before or since has ever behaved, or you can conclude that the Gospel accounts are inaccurate. Which do you really think is more likely?

There are also the contradictory creation stories in Genesis one and two. There is no way to reconcile the two different sequences of events with each other (and no way to reconcile either one with the fossil record).

And what about Genesis 1: 6-9 (NAB):


Then God said, &ldquol;Let there be a dome in the middle of the waters, to separate one body of water from the other.” And so it happened:

God made the dome, and it separated the water above the dome from the water below it.

God called the dome “the sky.” Evening came, and morning followed--the second day.

Then God said, “Let the water under the sky be gathered into a single basin, so that the dry land may appear.” And so it happened: the water under the sky was gathered into its basin, and the dry land appeared.


Now tell me, can you point to any familiar context in which something other than a flat surface is described as residing under a dome? If someone were describing a spherical Earth floating in an ocean of mostly empty space, would it have occurred to them talk about domes (or firmaments, if you prefer the KJB)? Of course not. And this is only one of many verses that plainly imply the Earth is flat. The question isn't whether you can contrive some meaning of the text to make it fit with modern science. It is whether anyone reading the text without a scientific background would come to the correct conclusions on the scientific questions the Bible addresses.

And there is also the fact that the Bible is completely unreliable on questions of morality. Everyone agrees on this, whether they admit it or not. After all, everyone is embarrassed by the Bible's numerous, non-condemnatory references to slavery. Likewise for its advocation of sadistic methods of execution for minor offenses. Not to mention its strange antipathy towards homosexuals.

When Heddle can find a remotely plausible way to explain these points I'll start taking him seriously again.