Value of pi in the Bible

[Jerusalem Blade]

I noted in a discussion earlier this year the matter of the value of pi in the Bible was brought up, and these are some thoughts on that.

Contrary to some who say the Bible erroneously gives the value of pi as 3.0, using 1 Kings 7:23 (Cf. 2 Chronicles 4:2) as alleged proof, as it says that the large basin for the ceremonial washing of the priests was 10 cubits across (180 inches), 30 cubits in circumference (540 inches), and was round. Upon first glance it does appear as though the ratio between the diameter and the circumference is said to be 3.0 instead of pi. The circumference of a circle is pi x D (3.14159 times the diameter), so it would be impossible for a round vessel to have a diameter of ten and a circumference of thirty.

However, the Scripture a few lines down, in verse 26, adds an important detail: “and it [the wall of the basin] was an hand breadth thick” (4 inches). Evidently the circumference was measured around the inside of the basin, while the diameter was measured from the outside perimeter, for if one subtracts the extra 8 inches for the thickness of the walls and measures the diameter from inside wall to inside wall the distance would be 172 inches, which multiplied by pi (3.14) would equal 540.08, which is quite accurate.

I got this solution from Harold Lindsell in his book, The Battle for the Bible, pp. 165-166. There are a number of apparent discrepancies in the Book of God, but upon close examination they can be solved, for God’s Scripture is without error throughout, and can be defended as the truth.

 

[Vladimir]

Praise the Lord. Speaking of factual support, I have recently read Did Adam Have A Bellybutton?: Ken Ham: Amazon.com: Kindle Store looking for research like this, but was very disappointed.

 

[Phil D.]

Alright, I'll stir the pot a little....

I believe that the Bible can relate various technical numbers like this in somewhat approximate terms. Another example would be in 2 Chronicles 9:25, where Solomon is said to have had 12,000 horses. Is this meant to give the exact (and constant?) number of horses he had, or is it possible that the number fluctuated with births and deaths among the herd, and so there would have been times when the exact number was, say, 12,153 horses, while at another moment in time it may have been 11,802...?

Nor do I think considering such a possibility makes one a liberal, or is necessarily a dangerous reckoning. Speaking in approximate terms, especially in technical contexts, is a completely legitimate, truthful, and in some instances like the example above, most useful method of communicating. God's Word is utterly truthful, yet God still condescended in accommodating normal human perceptions and intellectual limitations in the way He communicated that truth.

Having said all this, this is certainly not an issue that I would choose to argue in a divisive way with believers who may disagree with me.

 

[Marrow Man]

As a former math teacher, this was of special interest to me in the past. Steve's solution is a perfectly reasonable one, of course. A couple of things to note as well:

1) To say something like "the Bible says the value of pi = 3" is an erroneous statement from the beginning. The text merely gives the measurements of the basin, which is not the same thing (pi, in this case, would need to be derived from a calculation based upon the ratio of circumference to diameter).
2) I would have to go back and look to be sure, but I believe the estimation we use for the value of pi (which is an irrational number) was not calculated until the Middle Ages or early Renaissance period. Several ancient civilizations had approximations of pi (generally expressed as fractions), but all were different from our modern approximation. To insist on modern notions of precision in a passage which isn't really discussing the value of pi is a bit anachronistic.
3) The typical skeptic response in say the Bible is "wrong" here overlooks one very crucial piece of evidence -- there was an actual basin that had those actual measurements. To insist that those measurements someone violate a mathematical constant is to ignore the fact that someone could have pointed you to the actual object being discussed. A "but here it is" approach would seem to be a rather effective one in silencing such skepticism.

 

[Backwoods Presbyterian]

Math is akin to sorcery.

 

[ooguyx]

Just as in FYI, the value of Pi was calculated well before the renaissance period. For example: The first known calculations were from the Egyptians and they were pretty close. Archimedes proved the value to be between 3 and 22/7. And the Chinese had the best approximation of 355/113, which they derived in the first century (I think) and it stood as the best until 1000AD. (I love reading in the history and philosophy of math ).

I think that the answers given above are fine, but in a discussion with a skeptic, atheist, etc., I would press them for their irrational use of math in their own life. For instance, why is it that they can calculate the value of a circles circumference to its diameter on a piece of paper and them immediately go into the physical world and find that all circles will match the calculations on their paper? Even when the do something inflammatory as to deny the Bible based on its "miscalculation" of pi, they must ultimately be relying on the very God of the Bible to prove the "right" calculation.

 

[Jack K]

Steve's solution is interesting and may represent the way the measurements were taken, but I don't think there was a serious problem with the text to begin with. It's perfectly reasonable, given the genre of the text, for it to provide a rough approximation rather than mathematical precision. Rough estimates using pi=3 are common in everyday life.

 

[Andres]

In addition to what Phil and Jack have stated, I'd also consider the purpose of the Bible as a whole. Yes, it has historical elements, but it's not intended to be a history book. Yes, it contains poetry, but it's not intended to be a poetry book. I ultimately believe that in the end all science, history, math, etc will confirm/hold up to the Scriptures, but I'm also okay if on the surface I can't immediately reconcile everything because I don't see this as God's intention in giving us the Scriptures. Instead, I think as WCF 1.6 states the reason God has given us His Word is so we can know "The whole counsel of God concerning all things necessary for his own glory, man's salvation, faith and life, is either expressly set down in Scripture, or by good and necessary consequence may be deduced from Scripture..."

 

[Marrow Man]

ust as in FYI, the value of Pi was calculated well before the renaissance period. For example: The first known calculations were from the Egyptians and they were pretty close. Archimedes proved the value to be between 3 and 22/7. And the Chinese had the best approximation of 355/113, which they derived in the first century (I think) and it stood as the best until 1000AD.

Perhaps I wasn't clear in my comment, but this was my basic point -- not that no civilization had calculated pi before the Middle Ages, but that the approximations (while close) were different from our modern one (what I wrote was: "I believe the estimation we use for the value of pi (which is an irrational number) was not calculated until the Middle Ages or early Renaissance period. Several ancient civilizations had approximations of pi (generally expressed as fractions), but all were different from our modern approximation.").

 

[Semper Fidelis]

The only place where approximations don't exist is in pure math. Any time you're dealing with physical objects or even in the engineering realm in particular, you're dealing with approximations. I have two engineering degrees and its not uncommon to deal with approximations that can vary as much as 10%. In fact, many engineers effectively treat 10% as effectively zero in many applications.

The fellow who first came up with the ludicrous notion that the Bible cant be trusted for lack of precision reveals an ignorance of real life where he would not even understand that the computer he used to type his folly is engineered by even less stringent tolerances in some key components.

Sorry if I seem annoyed but sometimes the objections to the Scriptures are so silly that it's difficult not to be exasperated as by objections so facile.

 

[Bill The Baptist]

Sorry if I seem annoyed but sometimes the objections to the Scriptures are so silly that it's difficult not to be exasperated as by objections so facile

You are absolutely right. The same is true when it comes to the history of the Bible. If we held all historical figures to the level of scrutiny that biblical characters receive, we could not be certain that anyone actually existed at all prior to 100 or so years ago.

 

[Bill The Baptist]

Here is a Bible that might help clear things up

 

[Jack K]

I've only ever heard the "biblical value of pi" brought up in the context of criticism of Christian home schoolers who, it is claimed, not only teach creation rather than evolution but teach the biblical value of pi rather than the mathmatically calculated one. Of course, no Christian home schooler I know actually does that. It's a made-up criticism devised to make believers and the Bible look foolish.

 

[Jerusalem Blade]

I first wrote on this in 1998, having just left Woodstock, NY for NYC, when a science-oriented newspaper columnist in Woodstock Times published an article deriding Christians and their Bible over the issue of the "3.0 pi". I took it seriously enough to refute it, as I have above.

The leeway we posit of approximations and different standards of precision may suit some, but I prefer a more exacting precision.

 

[Afterthought]

With these kinds of things one can always know: A solution exists!

Edit: Thanks, Mr. Rafalsky, for the clearest explanation of that solution I've seen yet.

 

[Manuel]

The passage in 2 Chronicles suggest that the sea was not a perfect cylinder but it was shaped like a cup (for wine) in the shape of the flower of the lily

2Chr 4:5 Its thickness was a handbreadth. And its brim was made like the brim of a cup, like the flower of a lily. It held 3,000 baths.

So it is very possible that the sea was wider at the top with engraved ornaments all around the rim like the picture below and the diameter was measured from the top and the circumference from the middle.

 

[The Conductor]

It always seemed to me, (or at least since I took physics in high school) that the Bible was using significant digits here.

 

[Wayne]

Vladimir:

Another resource that might be helpful on this sort of thing:

http://archive.org/details/examinationof00hale

Norman Geisler wrote a more recent book on the same topic.

 

[Somerset]

Did the technology exist to measure the circumference to tiny fractions of an inch: I thought they used pieces of string with knots at intervals as regular as they could make them?

 

[Jerusalem Blade]

We tend to think of the ancients as dummies, although their architecture displays brilliant mathematical and geometrical precision. Consider the building of the tabernacle, and the later temples (and this just the Jews; the heathen also built great structures).

 

[Semper Fidelis]

The leeway we posit of approximations and different standards of precision may suit some, but I prefer a more exacting precision.

So long as you can establish, exegeticallly, that the purpose of mentioning a measurement in a particular passage was to note that precision. I know the ancients knew math but one doesn't have to even use math to measure the length and circumference of an object. The silliness of the objection is that if I measure the diameter and circumference of a round basin from a tape measure and come up with values where the ratio of the two is three to one, it says nothing about my belief about the ratio of the circumference of a round basin to its diameter but more about how precisely I cared to measure either. The objection can continue to be pushed to the absurd. Why should 2 significant digits be sufficient for God? He's omniscient. Surely he could come up with instructions for the Israelites that are even more precise than that. It doesn't stop the mouths of fools who want to be foolish.

I'm not dismissing the idea that, after all, a solution exists but simply that the ancients knew the value of pi a long time ago and I think they'd be shocked that someone would be so obnoxious as to read the instructions as if they intended it to be a report of their mathematician's understanding of pi and then accusing them of being a collective bunch of morons. In fact, it wouldn't even take someone who understood math to figure out that if they took an exact line of 30 cubits and tried to surround the basin with it that it would end up coming up short. A child with no understanding of math could say: "Daddy, this line isn't long enough."

My point is that we can sometimes spend a lot of time searching for answers to objections but some objections are absurd. One cannot simply assert that the only explanation must be one that satisfies precision if exact precision was never the intent of the author.

In fact, let me just say that the objection you cited comes from a man who lives in a city where the weatherman reports the time for sunrise and sunset every day. Surely we can't respect the opinions of a man who lives in a society that still believes that the sun revolves around the earth.

 

[JohnGill]

Alright, I'll stir the pot a little....

I believe that the Bible can relate various technical numbers like this in somewhat approximate terms. Another example would be in 2 Chronicles 9:25, where Solomon is said to have had 12,000 horses. Is this meant to give the exact (and constant?) number of horses he had, or is it possible that the number fluctuated with births and deaths among the herd, and so there would have been times when the exact number was, say, 12,153 horses, while at another moment in time it may have been 11,802...?

Nor do I think considering such a possibility makes one a liberal, or is necessarily a dangerous reckoning. Speaking in approximate terms, especially in technical contexts, is a completely legitimate, truthful, and in some instances like the example above, most useful method of communicating. God's Word is utterly truthful, yet God still condescended in accommodating normal human perceptions and intellectual limitations in the way He communicated that truth.

Having said all this, this is certainly not an issue that I would choose to argue in a divisive way with believers who may disagree with me.

It was 4000 stalls for horses and chariots and 12000 horsemen. The number of horsemen was determined by the number of stalls for horses and chariots, so the number would stay constant. It's equivalent to a modern Army saying they have 4000 tanks and 12000 tank soldiers. The total is given even if some are down for repair, on vacation, etc.

 

[Phil D.]

It was 4000 stalls for horses and chariots and 12000 horsemen.

Some translations use "horsemen" some "horses." Either way the ultimate point being made by the author seems obvious enough. Also consider that a parallel account in 1 Kings 4:26 states that Solomon had "40,000 stalls of horses". So trying to derive exact distributions or ratios in this case based on either real or imagined military criterion still remains elusive.

The total is given even if some are down for repair, on vacation, etc.

I agree, but in essence isn't this again saying that using approximations is a common (normal), wholly legitimate, and often the most useful way of relating such things?

Returning to the issue of the Sea...

With all due respect (and I say that sincerely), unless such could be shown to have been a common method of indicating these kinds of measurements in similar technical and historical situations, the idea that the circumference and diameter of the same object would be given in relation to different aspects of it (in the same immediate context) seems to me more contrived, and even a bit rationalistic, rather than persuasive. In my humble opinion, the idea that the author was simply employing the universally common and accepted method of stating things in approximate terms is the most satisfactory understanding.

Another factor here that raises some interesting issues, and potential problems for the solution proposed in the OP, is that we don't even know what the exact equivalent of an ancient cubit was - and certainly not in every situation. Most historians agree that a "common" cubit was "approximately" the same as 18 modern English inches. Yet at the time Solomon’s Temple (and thus the Sea) was constructed (10th century BC) an Egyptian "royal" cubit (as well as cubits used in some other ancient societies' regal applications) is documented (via measuring still existing artifacts against surviving descriptions of them) to have equaled about 20.6 inches. (See, Roland de Vaux, Ancient Israel: Its Life and Institutions, 196f.) Based on the volume given for the Sea in the same text (3000 "baths" = approx. 15,000 to 18,000 US gallons - and if one accepts the historical indications that the bottom of the Sea was more spherical rather than purely cylindrical or perhaps even bulbous in shape [e.g. Josephus, Antiquities, 8.3.5]), then it indeed requires using the larger cubit in order to arrive in the vicinity of the stated volume of 3000 baths.

Given the various mathematical uncertainties involved, I would again argue that simply accepting the idea that the author was employing the universally common and accepted method of close approximation (as too many other places in Scripture, I would argue), is the only way any supposed discrepancies can be fully acquitted. Nor is the reasonable point being made by an author thrown into any sort of question or disarray by their so doing.

Which brings us to what I would consider the most important issue in all this... The fact that various unbelievers will seize upon some imagined and overly technical "discrepancy" like the one being addressed here is NOT indicative that it is a rational REASON to disbelieve the accuracy, and thus the overall trustworthiness of the Bible. Rather, doing so is more an indication that one is merely looking for an EXCUSE for their current state of unbelief.

 

[Semper Fidelis]

Which brings us to what I would consider the most important issue in all this... The fact that various unbelievers will seize upon some imagined and overly technical "discrepancy" like the one being addressed here is NOT indicative that there is a rational REASON to disbelieve the accuracy, and thus the overall trustworthiness of the Bible. Rather, doing so is more an indication that one is merely looking for an EXCUSE for their current state of unbelief.

Precisely my point that they accept approximations all the time in their daily life but then comfort themselves that the Scriptures can be shown to be false on the basis of something everyone does.

 

[Jerusalem Blade]

The objections noted above to the criticism of the Bible’s rendering of the value of pi are substantial. I really have no problem with them. Though I must say that we ought not to attribute guile (as in looking for an excuse) to all unbelievers in this matter, for some may have heard said critique and are merely repeating it, it being stuck in their minds.

My purpose in posting the OP is for the benefit of those who – whatever the reason or motive – say the Bible errs at this point, that they may be shown there is a good and honest answer.

 

[Semper Fidelis]

The objections noted above to the criticism of the Bible’s rendering of the value of pi are substantial.

How so? Perhaps you can show me how they are substantial because I can't see it. There are substantial objections to some problems in the Bible but this one doesn't strike me as substantial if I can explain to a kid how approximations work. A craftsman or a lay-person would not be working with precise figures but with the tools they have to measure things

I really have no problem with them. Though I must say that we ought not to attribute guile (as in looking for an excuse) to all unbelievers in this matter, for some may have heard said critique and are merely repeating it, it being stuck in their minds.

One does not have to attribute guile to demonstrate that an objection is absurd. People unthinkingly repeat things they hear all the time. Someone comes up to me and says: "Did you know that the Bible teaches that pi is 3?" I can ask them a few questions and get them to question whether or not their objection had any merit to begin with. I also don't want the reader to go away thinking: "The entire point of this passage is that we can demonstrate that the Jews know the value of pi to four significant digits. In this manner, the Scriptures have made this knowledge profitable that we may be thoroughly equipped for every good work."

It's much like the "Jesus thought the mustard seed was the smallest seed in the world" objection. Let's say that Jesus was given knowledge that there was a seed smaller than the mustard seed that He could not have known from His human capacity.

Now suppose Christ says: "Now, as far as you know, the mustard seed is the smallest seed and yet...."

Everything after He said after that would be completely ignored.

Why? Because they'd be thinking in their heads: "What does he mean by 'As far as we know?', I thought it was the smallest seed."

Is that the point of the parable? No, and focusing on minutia distracts from the point the author is trying to make.

So, I return again to my point: As long as it can be demonstrated that the purpose of the author was to give a mathematically precise ratio of the circumference to the diameter then this defense is important. I have not been convinced that it is the author's point and, quite frankly if it is, I'm not all that impressed with only 4 significant digits.

My purpose in posting the OP is for the benefit of those who – whatever the reason or motive – say the Bible errs at this point, that they may be shown there is a good and honest answer.

And my point is that we need to determine whether the author was fine with the approximation as most of us are in everyday life. If so, then demonstrating that point removes the objection altogether without appealing to another approximate (but a little more precise) solution to pi to attempt to prove to the objector that ancient Israelites knew the value of pi. If the author's intention was to approximate then you are in fact not solving the problem because there was no problem to begin with.

 

[Jerusalem Blade]

Hi Rich,

Perhaps what I wrote was a little dense and unclear, but I think you understood exactly opposite of what I meant!

When I said, “The objections noted above to the criticism of the Bible’s rendering of the value of pi are substantial”, I was referring to your (among other) objections to the criticism of skeptics re pi etc, meaning what you and others have said on the matter was indeed substantial!

 

[Semper Fidelis]

Hi Rich,

Perhaps what I wrote was a little dense and unclear, but I think you understood exactly opposite of what I meant!

When I said, “The objections noted above to the criticism of the Bible’s rendering of the value of pi are substantial”, I was referring to your (among other) objections to the criticism of skeptics re pi etc, meaning what you and others have said on the matter was indeed substantial!

Oh...OK, gotcha. Sorry about the misunderstanding.

 

[nick]

I think that the answers given above are fine, but in a discussion with a skeptic, atheist, etc., I would press them for their irrational use of math in their own life. For instance, why is it that they can calculate the value of a circles circumference to its diameter on a piece of paper and them immediately go into the physical world and find that all circles will match the calculations on their paper? Even when the do something inflammatory as to deny the Bible based on its "miscalculation" of pi, they must ultimately be relying on the very God of the Bible to prove the "right" calculation.

Exactly. When I'm sidetracked with "Well what about the value of Pi?!?!" I say there are answers for that, but first...