How big is a cubit?

[Aranfan]

Hmmm... having re checked my numerical solving in excel, i now get T=0.5234. (stupid maxima)

That actually corresponds to a circle of radius 3340km, and so

1 cubit = 670km = 415 miles.

Thank you. I now have a number I can throw in the face of the Biblical inerrantists who have been bugging me.

[Steel]

Hmmm... having re checked my numerical solving in excel, i now get T=0.5234. (stupid maxima)

That actually corresponds to a circle of radius 3340km, and so

1 cubit = 670km = 415 miles.

Thank you. I now have a number I can throw in the face of the Biblical inerrantists who have been bugging me.

Yes I hope this helps. Its a bit of a double edged sword. On the one hand its totally impossible for someone to have created a pool twice the size of the atlantic, but the fact that there is a rationalisation might fuel their idiocy in some way.

On another note, it makes the ark a much more reasonable size, at 300x50x30 cubits^3, using the definition of cubit above we have that the ark was in fact 1.4x10^23 cubic metres, or about 100x the volume of earth. This should be sufficient to contain 2 of every animal, and explains what became of the ark after the flood: Jupiter.

[Aranfan]

It will. Oh, a thought occurred to me the thing was also 5 cubits tall, if that was taken into account would that change the measurement?

[Steel]

It will. Oh, a thought occurred to me the thing was also 5 cubits tall, if that was taken into account would that change the measurement?

Eeer, yes. I could run the calculation for a sphere radius r+(5 cubits) and it would be a bit more complicated and the answer would change, but there would still be a solution and it would still be of the same order. I'm not inclined to do it though.

In order to get the right length for a cubit (~45cm) you would need to have the earth radius as about 3 feet, which is even more ludicrous.

[The Duchess of Zeon]

Oh, please people - remember that way back then NO measuring was as accurate as ours is today. Back then, no one had the correct value for pi although some were closer than others. "3" was a rough approximation used by a lot of people, on a more practical level probably expressed as "three and a bit more". Lack of a definite value for pi might also explain why ancient peoples had some difficulty building things like domes, or it might not, but for sure squares and rectangles are easier to compute in some respects.

The cubit actually varied in length, with one definition being the length of an adult man's arm from elbow to fingertip. My usual reference on measurements lists the Egyptian cubit as 45 cm, a royal Egyptian cubit as 52.35 centimeters (I guess the king was supposed to be a giant among men or something), a Roman cubit as 44.4 centimeters, and an English cubit as 45.72 cubits. So... roughly 45 cm for most cubit measurements, just remember that nothing was as standardized back then as things are now.

As a matter of fact, the Babylonians had calculated Pi as 3 and 1/8, which was not atrociously bad, and were using something similar to the pythagorean theorem as well. No surprise that the rural bumfuckistan hicks in the Levant didn't pick up on it, though. Judea was sort of the equivalent of Kentucky insomuch as Near East Civilization went.

[Stark]

Wow. Primitive cultures couldn't build domes because they couldn't calculate pi, and never sat down and calculated pi, even though we know they did? LOL.

The Babylonian mathematics was even hideously arcane due to their primitive numbering system, but they could still do relatively complex maths (certainly by 21st century average mathematical 'literacy'). They could and did still use maths in science and engineering. There's a big difference between having stupid ideas and crazy legacy systems and being so stupid you can't work out a simple ratio. From a certain perspective, the complex workarounds they created to enable them to perform useful mathematics with such a broken numbering system demonstrates they were anything but stupid, even if they were arguably uncreative.

Judging the level of mathematical knowledge of the ancient world by the Bible = utterly retarded.

[Ender]

Ok, it may be the fact I'm tird and have been drinking whine all evening, but I'm at a complete loss as to what is going on in this thread. How does the fact that the earth's surface not being Euclidean have an impact on pi, which is an Euclidean constant? Pi is pi. And from there, how do we go from "pi changes with the location on the earth" to "a cubit is defined by the earth's radius, not the length of a man's arm"?

[darthdavid]

Ok, it may be the fact I'm tird and have been drinking whine all evening, but I'm at a complete loss as to what is going on in this thread. How does the fact that the earth's surface not being Euclidean have an impact on pi, which is an Euclidean constant? Pi is pi. And from there, how do we go from "pi changes with the location on the earth" to "a cubit is defined by the earth's radius, not the length of a man's arm"?

The idea is that if you draw a circle on the surface of a sphere rather than on a flat plane when the ratio between the size of the sphere and the size of the circle changes the value of π for the circle being drawn will change, and, with the right ratio, you can make the value of π exactly 3, which some biblical literalists are trotting out as an explanation for why 3 is given as the value of π in the bible. They conveniently leave out that to make the vessel being described work in this situation though is for it to be the size of an ocean, which rather puts a damper on it being the object of tribute placed in a regular temple that it's described as...

[Steel]

On a flat plane then the ratio of a circle's radius to its circumference is 2*3.14... = 2*pi

If we extend the definition of a circle to non flat places by defining it as all points the same distance from one given point which we define as the centre (this is a good definition), then it turns out that that it is not always true that the ratio of circumference to diameter is 2*3.14...

As an example, consider on a sphere you are standing at the north pole, which we will take as the centre. If you were to walk to the equator, you would walk 1/4 of the circumference of the sphere. This gives us a "spherical circle" with centre the north pole and the circumference as the equator.

Here we have that the circumference = C and the radius r = 0.25*C

Hence C = 2*2*r

and in fact here the quantity we would call pi is 2.

Now if you are very close to a sphere, then it looks flat, so drawing a very small circle you will get the normal value of pi. As the size of your circle increases "pi" will decrease, and as it starts above 3 and gets below 3, at some point it is 3. Earlier i calcualted exactly when that occurs.

Then using that we illustrated how stupid it would be to assume biblical inerrancy about the passage and say pi was 3, as that passage defined a radius, and then equating that radius with the size of the circle necessary on earth showed that a cubit had to be massive in order for the gentle curvature of the earth to result in that difference in the value of pi.

pi wont actually change depending on where the circle is located on earth, just with how big it is.

Aside: A spherical circle is actually a euclidean circle, but with a different centre and radius. In hyperbolic geometry, a hyperbolic circle is also a euclidean circle, but the again centre is not in the same place (skewed towards the middle of the plane).

[Broomstick]

Wow. Primitive cultures couldn't build domes because they couldn't calculate pi, and never sat down and calculated pi, even though we know they did? LOL.

I am getting fucking sick of people on this board turning a general statement into some goddamn axiomic pronouncement. What I said was

Lack of a definite value for pi might also explain why ancient peoples had some difficulty building things like domes, or it might not, but for sure squares and rectangles are easier to compute in some respects.

Please note the repeated use of "might". Nor did I ever say they absolutely could NOT build domes, just that there was difficulty in doing so. Just because the Babylonians in one particular era had a working value for pi doesn't mean the Egyptians had it then or thousand years earlier. It's not like folks were eager to share such knowledge with other peoples. There really aren't many, if any, examples of domes prior to Roman times, and even the Romans has some issues with constucting them.

Also note I said "ancient", not "primative" - some of the ancient civilizations were quite advanced in some aspects and calling them primative displays ignorance and a certain arrogance I find distasteful.

If you must get picky a LOT of truely technologically primative folks build simple domes like wigwams and wickiups and similar structures based on bent sticks and the like, but that's not what we're talking about because that doesn't require mathematics, just springy wood and some patience. Scaling it up and putting it into stone or other enduring materials is where things get difficult.

[Darth Wong]

It's irrelevant whether they could accurately determine pi. We're talking about the belief that the Bible is inerrant, which means that they don't need to rely on their primitive level of scientific knowledge and mathematical development in order to arrive at the "facts" in the Bible. They're all supposedly fact-checked by God, who is supposed to have ensured the accuracy of the Bible. Seriously, that's what inerrantists believe.

If we agree that the Bible is limited by the primitive mathematics and scientific knowledge of the era, then the inerrantists lose, because it means that their precious source of wisdom is nothing more than the ignorant ravings of Bronze Age goat herders.

[erik_t]

It will. Oh, a thought occurred to me the thing was also 5 cubits tall, if that was taken into account would that change the measurement?

Eeer, yes. I could run the calculation for a sphere radius r+(5 cubits) and it would be a bit more complicated and the answer would change, but there would still be a solution and it would still be of the same order. I'm not inclined to do it though.

It ought to make a substantial difference, since in that case your bowl would be on the order of 3350km deep. There would also be the issue of where depth is measured, and whether the measurement is relative to the local or global normal. Still I'd bet you'll end up within something like a factor of two. As you say, re-running the calculation is not the greatest use of anyone's time, since the Biblical passage didn't say at what depth the measurements were made anyway.

[Gil Hamilton]

As a matter of fact, the Babylonians had calculated Pi as 3 and 1/8, which was not atrociously bad, and were using something similar to the pythagorean theorem as well. No surprise that the rural bumfuckistan hicks in the Levant didn't pick up on it, though. Judea was sort of the equivalent of Kentucky insomuch as Near East Civilization went.

The Babylons used 3 and 1/8, the Egyptians used several over the course of their existence (the one that pops out at me is 3 and 1/6).

I know Archimedes came damn close to pi by using inscribed polygons in a circle to get an approximation. I believe he actually started with a hexagon and doubled the number of sides until he arrived at a 96 sided polygon that he used as an approximate for pi and then, being the great engineer that he was, gave a range between two methods they he knew fenced in the true value. What's cool is Archimedes' Method of Exhaustion was the best algorithm for finding pi for over 2000 years.

Of course, the people who would have originally talked about the dimensions of the vessel described in the Bible wouldn't be armed with even enough mathematical tools even to do Archimedes' method of exhaustion, because it requires the Pythagorean theorem and being able to do square roots. Of course, it's not necessarily fair to compare Archimedes' or any Greek mathematician with the ancient Israelites, since the Greeks by Archimedes' time had forgotten more about math than the ancient Hebrews ever knew (even the best engineers in the region in the ancient Hebrew's time were Greeks who settled that coastline, like the ones from Tyre). What may have originated in the areas idea that pi = 3 was they probably stopped at inscribing a hexagon in a circle and went with that, since any other polygon requires a bit more effort to get a ratio of circumference to diameter.

[erik_t]

Certainly if you wanted to do it on paper (papyrus, cuneiform), yes. However it ought to be pretty straightforward to make a circular object (the potting wheel existed at the time, I think) and then measure the diameter and circumference with some random string, either eyeballing the ratio or folding in half iteratively until you got a reasonable answer. 3.0 just seems lazy to me.

[Darth Wong]

Certainly if you wanted to do it on paper (papyrus, cuneiform), yes. However it ought to be pretty straightforward to make a circular object (the potting wheel existed at the time, I think) and then measure the diameter and circumference with some random string, either eyeballing the ratio or folding in half iteratively until you got a reasonable answer. 3.0 just seems lazy to me.

It seems lazy because you put value on accuracy. They didn't. It was routine practice back then to say that whenever the enemy had a really big army, it was a million men. None of those armies ever had a million men, or even close. They were so far off it wasn't funny, but as far as they were concerned, it didn't matter. If it looked like a lot of men, then it was a million. The Bible does this, and so did Greek "historians" of the era.

They just didn't give a shit about being factually accurate back then. Something modern religious people need to keep in mind when reading their literature.

[Twoyboy]

In order to get the right length for a cubit (~45cm) you would need to have the earth radius as about 3 feet, which is even more ludicrous.

Dear god, don't tell the expanding earth crowd this... they'll join forces with the bible inerrantists and we'll never hear the end of it...