Significance of Diameter & Circumference

Status
Not open for further replies.

Hamalas

whippersnapper
Got this interesting question today from a parishioner. It's one part mathematical and one part theological (and the mathematical part is not so much my cup of tea). How would you answer this?

"1 Kings 7:23. Two things:

1)Why give me the diameter and circumference? Obviously, if I know one I know the other.
2)Why give me the wrong circumference given a 10 cubit diameter? It should be a line of 31.4 cubits to measure around it. Assuming the 10 cubits was the outer diameter.

Is this pointing to shoddy workmanship? Unlikely for the temple. I would assume they could make a true circle. Or is this a simple rounding issue for convenience of the author?"
 

Taylor

Puritan Board Post-Graduate
Well, if the Bible were really inerrant, it would have told us that the circumference of the circle, given a 10 cubit diameter, is actually 31.41592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481 cubits. Now we only need to write that in Hebrew. :)

Of course, I am joking, but at the same time showing the ridiculousness of the question (respectfully). There is no evidence that the Bible is interested in mathematics-textbook-level calculations. We do this in normal speech and it is not considered erroneous.
 

Jack K

Puritan Board Doctor
The numbers aren't wrong; they're just rounded off. Do we imagine the volume of the basin was meant to be exactly two thousand baths, as stated a few verses later in 1 Kings 7:26? I doubt the geometry would work out to fit that number exactly.

The point of the passage is not to give precise instructions to the engineers and builders, nor to teach us math, but to give the everyday reader/hearer a sense of the size of the temple furnishings. Round numbers do that best.
 

Phil D.

Puritan Board Senior
There have been different theories proposed by evangelical scholars.

Adam Clarke:
"It - held three thousand baths - In 1 Kings 7:26, it is said to hold only two thousand baths. As this book was written after the Babylonish captivity, it is very possible that reference is here made to the Babylonish bath which might have been less than the Jewish. We have already seen that the cubit of Moses, or of the ancient Hebrews, was longer than the Babylonish by one palm; see on 2 Chronicles 3:3; (note). It might be the same with the measures of capacity; so that two thousand of the ancient Jewish baths might have been equal to three thousand of those used after the captivity. The Targum cuts the knot by saying, "It received three thousand baths of dry measure, and held two thousand of liquid measure." Source: here

Charles Ellicott
"And it received and held three thousand baths.—Literally, holding (whole) baths: three thousand would it contain. The bath was the largest of Hebrew liquid measures. Perhaps the true reading is, “holding three thousand baths,” the last verb being a gloss borrowed from Kings. So Vulg. Syriac and Arabic omit the clause. The LXX. had the present reading. 1Kings 7:26 reads, two thousand baths would it contain. Most critics assume this to be correct. Some scribe may have read ’alāphîm, “thousands,” instead of ‘alpayim, “two thousand,” and then have added “three” (shĕlōsheth) under the influence of the last verse. But it is more likely that the numeral “three” having been inadvertently omitted from the text of Kings, the indefinite word “thousands” was made definite by turning it into the dual “two thousand” Either mistake would be possible, because in the unpointed text ‘alāphîm and ’alpayim are written alike. The Syriac has the curious addition, “And he made ten poles, and put five on the right and five on the left, and bare with them the altar of burnt offerings.” Similarly the Arabic version." Source: here

Keil and Delitzsch
"It held 2000 baths; according to the Chronicles, 3000 baths. The latter statement has arisen from the confusion of ג (3) with ב (2); since, according to the calculation of Thenius, the capacity of the vessel, from the dimensions given, could not exceed 2000 baths." Source: here
 

Eyedoc84

Puritan Board Sophomore
My thought is that it held somewhere between, but close enough to be rounded up to three as a maximum quantity, but two as the typical quantity of usage.
 

py3ak

Unshaven and anonymous
Staff member
Got this interesting question today from a parishioner. It's one part mathematical and one part theological (and the mathematical part is not so much my cup of tea). How would you answer this?

"1 Kings 7:23. Two things:

1)Why give me the diameter and circumference? Obviously, if I know one I know the other.
2)Why give me the wrong circumference given a 10 cubit diameter? It should be a line of 31.4 cubits to measure around it. Assuming the 10 cubits was the outer diameter.

Is this pointing to shoddy workmanship? Unlikely for the temple. I would assume they could make a true circle. Or is this a simple rounding issue for convenience of the author?"

1. Is that obviously known? This question seems like an opportunity to raise the important point: other people in other times are different, and what is common knowledge to you or an easy calculation might have been nothing of the kind to them. Or even more significantly, does the Holy Spirit speaking in Scripture share our presuppositions?

2. There would have been some thickness to the basin itself. Because of that, "around the edge" and "side to side" might be a little inexact and given in round numbers.
 

VictorBravo

Administrator
Staff member
If you want to entertain wooden literalism, then we can say the basin was rounded but not circular. A rounded oval can be formed to have a circumference of exactly 30 cubits and a span of 10 cubits.

But, I'm of the "it's anachronistic" view. We don't read a description like this as an engineering specification.
 

CovenantWord

Puritan Board Freshman
Two possibilities worthy of consideration:
1) 3 as an approximation of pi was common Babylonian mathematical practice of the era. https://www.exploratorium.edu/pi/history-of-pi. This would have been a close enough approximation for the purpose of water storage.
2) The measurements 10 and 30 imply a measuring error of 4 and a half percent, which seems a bit high, even given the nonuse of fractions. As VictorBravo suggests above, a more likely source is the imperfections of manufacture. The basin was massive and enormous and not cast on site, so it seems reasonably likely that the final product was elliptical rather than strictly circular. If the 10 cubits measured the major axis, then a minor axis of a bit more than 9 cubits would have presented a circumference of around 30 cubits.
If this second explanation be correct, then it also answers the question of why the diameter and the circumference are both supplied. For an ellipse, both axes, or an axis and the circumference are required to describe the figure.
 

Ed Walsh

Puritan Board Senior
Got this interesting question today from a parishioner. It's one part mathematical and one part theological (and the mathematical part is not so much my cup of tea). How would you answer this?

"1 Kings 7:23. Two things:

1)Why give me the diameter and circumference? Obviously, if I know one I know the other.
2)Why give me the wrong circumference given a 10 cubit diameter? It should be a line of 31.4 cubits to measure around it. Assuming the 10 cubits was the outer diameter.

I am a professional civil construction estimator by trade, and this occurred to me.

As someone mentioned, the text also gives us the width of the brim.

1 Kings 7:26 (KJV)
And it was a handbreadth thick, and the brim thereof was wrought like the brim of a cup, with flowers of lilies: it contained two thousand baths.

A handbreadth is approximately 4"±. If you subtract 2x4" or 8" converted to cubits as 8"/12/1.5 = 0.44 cubits from the diameter, the diameter becomes 9.55 cubits, which gives a circumference of 30.002 cubits. Close enough for inerrancy?
 

J.L. Allen

Puritan Board Sophomore
I am a professional civil construction estimator by trade, and this occurred to me.

As someone mentioned, the text also gives us the width of the brim.

1 Kings 7:26 (KJV)
And it was a handbreadth thick, and the brim thereof was wrought like the brim of a cup, with flowers of lilies: it contained two thousand baths.

A handbreadth is approximately 4"±. If you subtract 2x4" or 8" converted to cubits as 8"/12/1.5 = 0.44 cubits from the diameter, the diameter becomes 9.55 cubits, which gives a circumference of 30.002 cubits. Close enough for inerrancy?
There have been different theories proposed by evangelical scholars.

Adam Clarke:


Charles Ellicott


Keil and Delitzsch
Ed,

How would you work through what Phil has brought up about the 3k vs 2k baths? I am completely ignorant when it comes to these measurements, but the first explanation seems more likely to me. Whether any of the three explanations or a different one which is not listed, what seems likely in your estimate?
 

CovenantWord

Puritan Board Freshman
I am a professional civil construction estimator by trade, and this occurred to me.

As someone mentioned, the text also gives us the width of the brim.

1 Kings 7:26 (KJV)
And it was a handbreadth thick, and the brim thereof was wrought like the brim of a cup, with flowers of lilies: it contained two thousand baths.

A handbreadth is approximately 4"±. If you subtract 2x4" or 8" converted to cubits as 8"/12/1.5 = 0.44 cubits from the diameter, the diameter becomes 9.55 cubits, which gives a circumference of 30.002 cubits. Close enough for inerrancy?
Your calculations depend on a conversion factor of 1.5 feet per cubit. Apparently there is some doubt about that: https://trustconverter.com/en/length-conversion/cubit/cubit-to-feet.html Whence did you obtain the conversion factor? Your calculations also assume that the reported diameter is outside the brim and the reported circumference is inside the brim. It's not clear why that should be the case, particularly since outside measurements are easier and more accurate. Perhaps the circumference measurement was taken in between the two rows of "ornamental buds" (NKJ) or "gourds" (NAS) cast below the rim, as a groove to keep the measuring string from drooping. The inward sloping of the walls of the sea would thus account for much of the difference between the calculated circumference (31 cubits and change) and the reported circumference (30 cubits). If we grant your assumption of outside diameter and inside circumference, I can confirm the closeness of the result: The common cubit was two spans; each span comprised three handbreadths; the royal cubit is a common cubit and a handbreadth. http://www.eifiles.cn/ic-en.htm. Thus the conversion factor is seven handbreadths per cubit. Thus the ten cubits of diameter less one handbreadth on each side would net a 9 and 5/7ths cubits inside diameter. This number times modern pi is thirty and a half cubits of circumference, which is comfortably within the margin of error of the data presented.
 

CovenantWord

Puritan Board Freshman
On further reflection, I still hold it is most likely that both the diameter and circumference were outside measurements, that the sea was essentially circular at the top, and that the measurements were taken carefully and reported faithfully. There is, however, one factor that this thread has not yet considered specifically, namely, measurement precision. The measurements are apparently presented to the nearest cubit, not to the nearest fraction of a cubit. This means that the diameter could have been anywhere between 9 1/2 cubits and 10 1/2 cubits, and the circumference, anywhere from 29 1/2 cubits to 30 1/2 cubits. When we multiply the lower end of the diameter precision range (9.5) by modern pi, we arrive at 29.8 cubits circumference, which is within the precision range of the circumference. If we multiply a diameter as high as 9.7 by pi, we arrived at a 30.5 circumference, also within the range. Thus, the reported measurements are plausible within the precision implied.
I submit these measurement sustain the claim of biblical inerrancy, because these measurements have a direct, earthy feel to them, appropriate to the work team that installed the sea.
 

Ed Walsh

Puritan Board Senior
@CovenantWord @J.L. Allen

I do NOT claim to have found the final solution. It was just one possible solution that seemed to make sense. My assumptions interested me.
I thought some others would find it interesting too.

That's the beginning and end of my offering on the subject.
 

J.L. Allen

Puritan Board Sophomore
@CovenantWord @J.L. Allen

I do NOT claim to have found the final solution. It was just one possible solution that seemed to make sense. My assumptions interested me.
I thought some others would find it interesting too.

That's the beginning and end of my offering on the subject.
I appreciate the input! These numbers go past fingers and toes, and that is above my pay grade.

All this mentioning of pie certainly has my attention, though. Pecan sounds good with some extra whip cream on top.
 

CovenantWord

Puritan Board Freshman
King College has published a very helpful discussion of this topic: "Solomon's Sea and the Biblical Pi," by Andrew Simoson [sic] (https://pillars.taylor.edu/acms-1997/8/). He discusses a large range of possibilities that would be true to the biblical data supplied. I note two that caught my interest: 1) The "lily blossom" edge was rolled over into a lip, and the diameter was measured at the widest extension of the lip, whereas the circumference was measured below, were the lip was curved back to the wall. This would account for the diameter being a few inches wider than expected. This assumption brings the diameter and the circumference into a close approximation of pi, arriving at this conclusion by a means similar to that of @Ed Walsh above. 2) The Chronicler was aware that pi is slightly larger, but chose 3 as the comparative in honor of its simplicity and symbolism.
According to my calculations (details supplied upon request), a cylinder of diameter 10 cubits and a height of 5 cubits can hold about 2,400 baths. In my (very) amateur view, having the diameter shrink towards the bottom would offer advantages for manufacture, transportation, draining, and cleaning. If this be true, then the capacity of the sea, being somewhat less than that of a straight-walled cylinder, may very well have presented a capacity reasonably approximated as 2,000 baths. Further, the Sea may have been the part of a water supply system -- the main part, to be sure, but not the only part. The Jewish Encyclopedia offers an interesting diagram depicting how this may have looked (https://d2b4hhdj1xs9hu.cloudfront.net/IJ3J358S.jpg). This arrangement seems more plausible than the priests bathing directly in the sea, or Gideons dipping water out by buckets. If this be the case, then the 3,000 baths may approximate the capacity of the whole water system, delivery system as well as Sea.
 
Status
Not open for further replies.
Top