A blogger at a blog by the name of Gospel of Reason has written a quite popular post (judging by the comments) asserting that the Bible is not inerrant because I Kings 7:23-26 gives the dimensions of a large ceremonial bath for the temple as being 30 cubits in circumference and 10 cubits in diameter. He claims that since the requisite calculation for Pi with those dimensions results in 3 and Pi is really 3.141592654, the Bible contains error.
However, he makes a very simple mistake that underlies his entire diatribe against the Bible’s accuracy and is fatal to its thesis.
3
Also known as 3.00 or 3.0.
There you made a very fundamental, simple, high-school mathematical mistake that forms the basis of your erroneous conclusion.
There is a basic mathematical principle of precision. The precision of the calculation’s result cannot exceed the precision of the calculation’s least precise starting variables. This equation’s variables have a precision of only a single decimal place because decimal places are calculated going left to right and ending with the first zero which is followed by nothing but zeros (unless zeros are explicitly enumerated past the decimal point). For example:
30 = 1 significant decimal place
3001 = 4 significant decimal places
38700 = 3 significant decimal places
329.23 = 5 significant decimal places
30.000 = 5 significant decimal places
The calculation in question is 30/10. 3 is the correct answer. Since the equation has a precision of only one significant decimal place, the correct answer is indeed 3. 3 is not the same as 3.0 or 3.00. 3.141592654 (with a precision of 10 significant decimal places) is the same as 3.14 (with a precision of 3 significant decimal places) which is the same as 3 (with a precision of 1 significant decimal place).
Without precise measurements (such as 30.49582934 cubits/10.02348238 cubits) you cannot assert that the Bible is saying anything about digits on the right side of the decimal point because it makes no assertion to that level of precision.
My ruler asserts to be 12 inches long not 12.00 inches long. In fact, if it was measured by a highly accurate instrument, it would probably be found to measure 12.01 or 11.99 inches long. However, it is still entirely mathematically accurate to say that it measures 12 inches long because such a statement does not assert a precision beyond two decimal places.
In fact, it is quite a simple matter to see that given the asserted precision of numbers in this passage of Scripture, one is forced, if one wants to perform calculations on those numbers while being mathematically accurate, to round to the proper number of significant decimal places:
30/3.141592654 = 9.549[...] cubits. If one follows standard mathematical principles of precision (The result of a mathematical equation cannot have a greater precision than its least precise variable.), one is forced to round 9.549[...] cubits to 10 cubits. So even if the object had an exact circumference of 30 cubits (not a given since a cubit is a relative/approximate measurement depending on a person’s arm), we see that the diameter is indeed properly rounded up to 10 cubits, the asserted precision in Scripture.
In conclusion, if one uses your fallacious mathematical methodology, one can say that your blog has error in its assertion of Pi being 3.141592654 because actually Pi (to a precision of 4 million significant decimal places) is 3.141592653589793238462643383279502884197169399375105820974944592307[...] (non-truncated version found here). However, if one uses correct mathematical methodology, one sees that you are correct in saying Pi is 3.141592654 because you are not asserting a precision greater than 10 significant decimal places. In the same way, if one is careful to use standard mathematical methodology, the Bible’s figures are not shown to be in error because the figures given are accurate given the stated precision.
PS
Another person left a comment on the post giving the calculation that shows that even if one takes the measurements given as being more precise than their stated precision, one comes out with a correct and very precise result if one takes into account the handbreadth thickness of the bath. (Edited to add: Another commenter remarks that only a theoretical, perfect circle has a pi ratio of 3.141592654. It is very hard to find a physical object in the shape of a circle with that exact pi ratio. He also notes that the passage says, “circular in shape” which does not denote an exact circle.)
2 Responses
June 30th, 2007 at 4:47 pm
Tools. The question is simply a matter of tools, guys.
As an engineer I have at my disposal any number of measuring instruments, or tools. Some are highly accurate, some are much less so. I have even been known to measure an item with a piece of string when a speedy method of measuring was more important than precision.
I (and every other engineer in the world) also use various degrees of precision when referring to numbers. Hans is absolutely correct when he says 3 is equal to 3.0 or 3.00. He’s also correct when he says that out here in the real world 3.14 may as well be 3.
Only in a lab or machine shop is precise measurement crucial. Assume we’re talking in inches. 0.14 inch is just a shade over an eighth of an inch. OK, it’s 9/64 if you really want precision. But is it really? No. 9/64ths of an inch is actually 0.140625.
As to pi, I myself use 3, (just 3, not 3.14) when I’m describing the diameter-to-circumference ratio of a circle when precision is not required and a quick calculation is desired.
June 27th, 2009 at 3:27 am
Wow! The photo of Turkey on this page is absolutely Gorgeous!
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