Mistake or Question?

[shernren]

Why not say in the actual text that the circumference was 3 times the ratio of 111/106 times the diameter? Explain the fact that 111/106 was used and not 22/7 or a more accurate approximation. Explain why an infinite series was not stated explicitly. Explain the exact origin of this mysterious typo or correction or whatever it is (it doesn't sound like it was in the original text)
There is a point at which analysis of scripture becomes foolish. Both these arguments are past that point.

No, what I was saying is precisely that there is no big deal to be made about this passage. 22/7 is an inaccurate ratio; 3*111/106 is still inaccurate; any ratio of integers will be inaccurate; any solution given as a root of a rational polynomial will still be inaccurate. Perhaps I came across as agreeing with busterdog; but I don't.

The ironic thing is that when we take the text "at face value", we have a circle ten cubits wide and thirty cubits across. Ironically the TEs and the detractors are far more literal here than the numerologists. The assumption that the Bible was written to specify exact mathematics and science is an extrabiblical assumption. And it is not an assumption that makes sense with internal evidence, and it doesn't even make sense with external evidence either, since almost all texts assume contemporary science instead of predicting future science. One has to read the text with that assumption (of secret knowledge of future science) in order to treat the 111/106 thing seriously; one has to begin by assuming that the surface text as it is is insufficient for the matter at hand and that a deeper meaning is required, both unwarranted. I agree that to say that "the Bible teaches that pi is 3" is a bit farfetched and quite unfair; on the other hand, to say that the Bible is accurate about pi is also rather premature, unless one can show a Biblical explanation of an infinite series. I personally think the Bible did a fine job using the science of its day to explain and reveal God. For God never saw the need to do anything like this:

 

[OldWiseGuy]

The three dimensions make sense when considering how the laver was constructed. First a flat sheet of bronze was cast; five cubits wide by thirty cubits long. This was formed into a cylinder, reflecting those dimensions. The outward flanged brim was probably formed by beating. Because this would stretch the metal as well the height dimension was probably not affected. This accounts for the brim being ten cubits across and not nine something.

Regarding Pi. Anyone skilled in the making of such cylinders would of course be familiar with Pi, but only as a measurement after the fact. The dimensions given were important, not Pi. Also, a skilled artisan, presented with these dimensions, would immediately know that the rim of this vessel was flanged outward.

 

[artybloke]

Is it a mistake or do you just need to dig deeper.

Neither. There's no secret meaning in it, why should there be?

beyond mere poetry

"Mere" poetry? As a poet, I take that very personally; poetry is the way that the ancients understood the world around them, and a great deal better, I may hesitate to venture, than the merely factual reductionism on which you seem to base your reading of scripture.

Why should the ancient Hebrew world - which didn't even have a zero or negative numbers, never mind irrational numbers like pi - be concerned with such concepts as irrational numbers anyway? Did it help them come closer to God? That's what the ancient writers were interested in, not whether the science was accurate. They could care less for science.

 

[Brennan]

I agree that to say that "the Bible teaches that pi is 3" is a bit farfetched and quite unfair; on the other hand, to say that the Bible is accurate about pi is also rather premature, unless one can show a Biblical explanation of an infinite series.

I agree. 10*pi = 30 seems fine to me as an approximation. Saying that 'the Sea encompassed thirty one feet and four tenths of one foot and one hundredth of a foot and five times one thousanth parts of a foot, and a little bit more but five significant figures is ok by God' would kinda ruin the passage. If anyone cares to look for factual inaccuracy look elsewhere. This is just wasting peoples time.

Good cartoon btw

 

[shernren]

The three dimensions make sense when considering how the laver was constructed. First a flat sheet of bronze was cast; five cubits wide by thirty cubits long. This was formed into a cylinder, with those dimensions. The outward flanged brim was probably formed by beating. Because this would stretch the metal as well the height dimension was probably not affected. This accounts for the brim being ten cubits across and not nine something. Pi just isn't important here.

I normally disagree with oldwiseguy but he has hit the spot here. Besides, taking pi as 3 isn't all too bad. The error is -4.5%; in a modern engineering context I suppose that would be pretty bad but it's quite okay by their standards. When I do physics experiments in my college lab 5% accuracy is pretty good (except when dealing with electricity or optics). Our most notorious experiment was when we took four weeks' lab sessions to measure Planck's constant via the photoelectric effect. All of us got values significantly lower than the theoretical value, and many of us had values half or even less than the theoretical. The only thing we got right was the scale, and even that occasionally went wrong.

If obscurants want to pick nits and other obscurants want to fight back with even finer nit-pickers that's their business.

 

[busterdog]

So the ratio that appears in the text (quaveh) is what, coincidence? Or do we assume a later edit?

 

[busterdog]

As a poet, I take that very personally

Why, if twere dancing you would be, there's brisker pipes than poetry,
Say for what are hopyards meant and why was Burton built on Trent?

 

[random_guy]

So the ratio that appears in the text (quaveh) is what, coincidence? Or do we assume a later edit?

I don't think its a coincidence, but I think people are making it a larger deal than it should be. My guess is someone built something 10 cubits across, then measured the circumference and got ~ 30ish cubits. The builder may have some idea that there's a relationship between the diameter and the circumference, but I doubt they understood or knew about pi.

 

[rmwilliamsll]

I don't think its a coincidence, but I think people are making it a larger deal than it should be. My guess is someone built something 10 cubits across, then measured the circumference and got ~ 30ish cubits. The builder may have some idea that there's a relationship between the diameter and the circumference, but I doubt they understood or knew about pi.

ok, that sounds reasonable.
let's just look at the error with either of the measurements.

if the diameter is 10 cubits then the circumference is roughly 31.4 cubits. if a cubit is 18.5 inches then the circumference is 580.9 inch.
30 * 18.5 is 555.0 a difference of almost 26 inch.
this is not a rounding off error. it's too large.

if the circumference is 30 cubits = 555 inch then the diameter is 176.7 inch compared to the measured 185 a difference of more than 8 inches.
again it is a very visual error and too great for a simple rounding off error.

but i think that the real issue is how we react to the problem. because mathematics saturates our culture, because our numbers are almost completely despiritualized, we really do not understand the ANE culture's very different ideal of what numbers are and what they do. We begin immediately to think about math and accuracy, this is mathematical truth to us. Look at the discussions, look at how important it can be to people. We look at math as truth, with precision and accuracy subtopics of importance. The big problem is that the first readers of Kings never thought this way. Our way of looking at math is very different than theirs and we are, again, trying to put Scripture into a modern box.

Just like science and history, mathematics as we understand it is relatively modern. We need to look at the way ancients conceived of numbers to understand what these numbers MEANT to them, not to us.

but my big point is how natural the calculations i did are to us, yet i would be surprised if anyone reading the Bible for generations could have or would have desired to even try to do such (to us) simple arithmetic. Have you ever tried to multiple Hebrew or Roman numerals? how about divide?

see:
http://www.i18nguy.com/unicode/hebrew-numbers.html
even though it expresses a Hebrew numbering system in base 10, there is no evidence that the Ancient Hebrew used a base 10 long before the Arabs worked it out.
they probably used the Babylonian base 60.

see:
http://www-history.mcs.st-andrews.ac.uk/HistTopics/Babylonian_numerals.html
http://en.wikipedia.org/wiki/Decimal

 

[shernren]

I don't think its a coincidence, but I think people are making it a larger deal than it should be. My guess is someone built something 10 cubits across, then measured the circumference and got ~ 30ish cubits. The builder may have some idea that there's a relationship between the diameter and the circumference, but I doubt they understood or knew about pi.

oldwiseguy's suggestion - someone took a sheet of metal thirty cubits long, hammered it into a cylinder, and then measured the diameter and got roughly ten cubits - also makes sense. What doesn't make sense is to exploit some vague detail in the text via completely unwarranted feats of interpretation to make the text say something it doesn't say.

After all, look at this portion from the Lambert Dolphin site:

The

has a value of 100; the

has a value of 6; thus, the normal spelling would yield a numerical value of 106. The addition of the

with a value of 5, increases the numerical value to 111.
numerological leap of logic
This indicates an adjustment of the ratio 111/ 106, or 31.41509433962 cubits.

Whose word am I suppose to take that I am to make an adjustment of 111/106? For all I know, adding 5 means to add 5 cubits, or to add 0.05 cubits, or to add 5 inches, or to add 5 light-seconds. This is really nothing more or less than a convoluted gematriyot calculation where the letters and words of Scripture are twisted to say exactly what you want them to say.

The skeptic wants to believe that Scripture says pi is 3, and reads the text in such a way that it happens.
Dolphin wants to believe that Scripture says pi is anything closer to pi than 3, and reads the text in such a way that it happens.

As for why the Hebrew chooses to employ a masculine singular noun, that's a problem for the guy who originally wrote Kings, not me. In fact, this is really more of a discrepancy between the written and read forms of the particular word used there.

 

[shernren]

even though it expresses a Hebrew numbering system in base 10, there is no evidence that the Ancient Hebrew used a base 10 long before the Arabs worked it out.
they probably used the Babylonian base 60.

Hmmm? But the fact that they ordered their numbers in multiples of powers of 10, instead of multiples of powers of 60, pretty much shows a base ten number system. For example, in a base-60 system you wouldn't have a symbol for 100, you'd use 1 x 60 + 40 -> 1,40. 200 would be 3 x 60 + 20 -> 3,20.

 

[busterdog]

Hmmm? But the fact that they ordered their numbers in multiples of powers of 10, instead of multiples of powers of 60, pretty much shows a base ten number system. For example, in a base-60 system you wouldn't have a symbol for 100, you'd use 1 x 60 + 40 -> 1,40. 200 would be 3 x 60 + 20 -> 3,20.

Base 60 would mean we are mis-counting the ages of the patriarchs?

 

[busterdog]

Whose word am I suppose to take that I am to make an adjustment of 111/106? For all I know, adding 5 means to add 5 cubits, or to add 0.05 cubits, or to add 5 inches, or to add 5 light-seconds. This is really nothing more or less than a convoluted gematriyot calculation where the letters and words of Scripture are twisted to say exactly what you want them to say.

Except the ratio is for the unusual preservation of a "spelling" issue in the text with respect to the word for "circumference", the very measure in question. And clearly there must have been two circumferences, interior and exterior. That is one heck of a coincidence.

 

[rmwilliamsll]

Hmmm? But the fact that they ordered their numbers in multiples of powers of 10, instead of multiples of powers of 60, pretty much shows a base ten number system. For example, in a base-60 system you wouldn't have a symbol for 100, you'd use 1 x 60 + 40 -> 1,40. 200 would be 3 x 60 + 20 -> 3,20.

everything i found about Hebrew numbers implied a base 10 numbering system. but both the zero and base 10 are imports from India probably originally Chinese via Islamic Baghdad.

however:
http://130.15.161.74/techserv/cat/Sect11/Hebraica.html
looking carefully shows it not to have the advanced place holding principle but rather a specific character for 20, 30 etc. so it is not a true decimal numbering system, which has a radix of 10. it would be useful if someone can find what this type of system is called. makes googling easier *grin*

in any case, the argument remains the same, without true place holding both multiplication and division are really difficult.

 

[OldWiseGuy]

The three dimensions make sense when considering how the laver was constructed. First a flat sheet of bronze was cast; five cubits wide by thirty cubits long. This was formed into a cylinder, reflecting those dimensions. The outward flanged brim was probably formed by beating. Because this would stretch the metal as well the height dimension was probably not affected. This accounts for the brim being ten cubits across and not nine something.

Regarding Pi. Anyone skilled in the making of such cylinders would of course be familiar with Pi, but only as a measurement after the fact. The dimensions given were important, not Pi. Also, a skilled artisan, presented with these dimensions, would immediately know that the rim of this vessel was flanged outward.

I have to add this to my above comments.

The outward bend of the rim was probably necessary as it would add rigidity to the open top of the vessel. The bend need not be extreme to yield this benefit. As this rim was probably covered with decorative engraving it was treated as an important, and distinct, part of the laver. Thus the measurement, which was distinctly of it and not the diameter of the main body of the laver below it.

 

[shernren]

everything i found about Hebrew numbers implied a base 10 numbering system. but both the zero and base 10 are imports from India probably originally Chinese via Islamic Baghdad.

however:
http://130.15.161.74/techserv/cat/Sect11/Hebraica.html
looking carefully shows it not to have the advanced place holding principle but rather a specific character for 20, 30 etc. so it is not a true decimal numbering system, which has a radix of 10. it would be useful if someone can find what this type of system is called. makes googling easier *grin*

in any case, the argument remains the same, without true place holding both multiplication and division are really difficult.

It is still base-10. But instead of positional notation, or place-value notation (http://en.wikipedia.org/wiki/Positional_notation) they used sign-value notation (http://en.wikipedia.org/wiki/Sign-value_notation).

To expand on your point (which didn't seem too clear to me at first), math is generally difficult when using sign-value notation and much easier when using place-value notation. For example, if I learn 7 x 7 = 49, I can straightaway extrapolate that 70 x 7 = 490. But imagine the same thing in Roman numerals: I know that VII x VII = IL, but would it then be obvious that VII x LXX = XD?

 

[rmwilliamsll]

http://en.wikipedia.org/wiki/Sign-value_notation

note: need to remove trailing ")" to make link work.
thanks. i've seen the idea before and did know the name. i think that's twice now you've found words for me here.

interestingly signed and unsigned are computer language variable distinctions. looks like they got double duty out of this word.....