googlef87758e9b6df9bec.html A Sure Word: Does the Bible say that Pi = 3?

Friday, March 6, 2015

Does the Bible say that Pi = 3?

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. (1 Kings 7:23)

One of the very first criticisms I remember ever hearing about the Bible is that the Bible teaches that the value of pi is three. Critics who make this claim are referring to this passage from 1 Kings where the Bible is describing a large basin made for the Temple. I wasn't even a Christian when I first heard this claim but even then I thought it sounded a little weak. It wasn't until years later, though, that I began to look at the claim seriously.

The first thing you'll notice is that the passage doesn't really say, “Pi equals three.” In fact, the passages doesn't mention pi at all. I'm pretty sure that at the time this was written, pi had not even been discovered yet. What the passage does do is give the dimensions of a round object and it is from those measurements that people extrapolate backward to calculate pi.

If you remember high school geometry, the circumference of a circle is equal to its diameter times pi (c=dp). In this case, the circumference of the molten sea is 30 and its diameter is 10. So, 30/10 would be exactly 3 – a geometric impossibility. So does it mean the Bible is wrong? Of course it doesn't. There are at least two factors we must consider that aren't included in the text.

First, we do not know exactly what is being measured. For example, exactly what is meant by the word “brim”? I assume the walls of the vessel had a certain width. Is the diameter of the “brim” measured on the inside where the liquid is held or is it measured to the outside? If the diameter is measured on the inside and the circumference on the outside (which is entirely plausible) then we can actually use the measurements of each to determine how thick the walls were.

Knowing what is being measured is not as simple as you might think. Is the altitude of a plane a measure of its height from the ground? Or is it a measure of its height above sea level? Does a plane lose altitude every time it flies over a mountain? If a plane is about to land in Denver, is its altitude only a few feet or is still a mile up? In a drawn circle, the line around the circumference is assumed to have no width. But in reality, the sides of a real world vessel – like a drinking glass – have width. Was the diameter of the brazen sea measured on the inside of the walls or to the outside? It makes a difference.

But besides not knowing exactly where the “brim” was measured, we also cannot forget the very common and acceptable practice of approximating. For example, as I write this, I'm 49 years old. However, I'm not exactly 49 years old – I'm 49 years plus some months, days, hours, etc. My exact age changes by the minute but it's acceptable to only give the year.

We approximate many things. We only ever express our height in feet and inches but our exact height could fall somewhere between the inches. We express our weight in pounds when it is usually pounds plus some ounces. Our driving speed is given in miles per hour. We talk about our income in even thousands.

Even pi is an approximation. When I was in geometry class, we only expressed pi as 3.14. When I was in machine shop, we were always told to use pi to 5 places, 3.14159. But pi is infinitely long so it can never be exactly expressed. No matter how many decimal places you wrote, you are only approximating pi. It would even be correct to say pi is 3 because that's accurate to zero decimal places.

Given the fact that the Bible doesn't use decimal places, it's very likely that the dimensions given for the brazen sea were only approximates. If the diameter of the vessel was 9.68 cubits and the circumference were 30.4 cubits, it would be acceptable to round those to 10 and 30 cubits respectively. There would be no error. Claiming the Bible is wrong for using approximations is akin to calling everyone who expresses his age in years a liar.

For this criticism of the Bible to be valid, the critic must claim to have special knowledge of 2 things: First, he must know with certainty that the dimensions given for the diameter and circumference were both measured on the outside walls of the brazen vessel. He also must know with certainty that the measurements are intended to be exact and not approximations. He cannot possibly know that either is true. In fact, the opposite is more likely the truth in both cases. Which means that people who stubbornly cling to this criticism are liars.


Steven J. said...

I apologize for not responding earlier. For what it's worth, I agree with you; the passage doesn't actually assert that "pi equals three," and that the biblical statement appears adequate to one significant figure, which is doubtless enough for the author's purpose. I think the whole argument over the inner vs. the outer edge of the basin are a bit far-fetched, though; it seems unlikely that the author would measure the diameter one way and the circumference another.

Just to be difficult, I note that at least one author has argued that this passage shows that the Hebrews didn't even have the concept of "pi," since the author feels a need to give both the diameter and the circumference, as though the latter cannot be calculated from the former. That also seems to me a stretch, though it's quite possible, I think, that the author assumed that most of his audience wouldn't know that such a ratio existed. After all, the law of Moses prescribed that the law be read aloud to the assembled people each year -- there was no provision that it be copied and placed where people could read it, probably because the vast majority of people were illiterate (even the prophet Jeremiah seems to have been unable to read and write, depending on his scribe Baruch for such things). Presumably, very few ancient Hebrews studied geometry.

Though speaking of geometry, has anyone ever considered that the bronze sea may have been hexagonal rather than circular? Then its perimeter would indeed have been exactly three times the largest distance across it.

RKBentley said...

Steven J,

No need to apologize. You're under no obligation to respond to my posts though I do appreciate your comments.

I'm absolutely convinced that the dimensions given are approximations. That fact alone is enough to render this entire criticism moot. However, I still think there is ambiguity about where the vessel was being measured. It is far easier to run a string around the outside of pool than around the inside so the circumference is almost certainly measured around the outside. However, if the brim is rounded, it might make sense to measure it from peak to peak.

Concerning the shape of the vessel, the KJV describes the sea as “round all about.” I don't think that would be an accurate description of a hexagonal perimeter but it is entirely possible that the sea wasn't perfectly round. Even a slightly out of round circle would skew the ratio between diameter and circumference depending on where it was being measured.

It wouldn't surprise me if the author of this passage was unaware of pi. I think the source you cite makes a valid point which doesn't seem to me to be much of a stretch. Something compelled him to include both measurements, though it could be as you've suggested – for the benefit of readers who don't know about pi.

One thing that I didn't mention in my post is the fact that the passage is describing a real object which was a part of the Temple, the center of Jewish culture. Do people who use this criticism believe the object was just invented like they also claim the persons of Adam or Noah are invented? That would hardly work. How funny would it be if the Law were being read to these people, describing their place of worship, and the people just looked at each other wondering, “What molten sea?” It just seems a little desperate of the critics to expect us to reject the historicity of the Bible based on some ambiguous dimensions given for an object we're certain really existed.

Thanks again for your comments. God bless!!