How big is a cubit?

[Aranfan]

As we all know, in Euclidean Geometry pi is a constant and most definitely not equal to 3. However the Earth's surface is not Euclidean. And a circle drawn on the surface of the Earth will not necessarily have the same value of pi as a different circle drawn on the surface of the Earth. Knowing this, we can calculate how big a Cubit would have to be for the biblical value of 3 to be correct for the vessel.


Unfortunately I am not familiar enough with the necessary math/geometry to do this, so I'm setting the problem to SDN. How big is a cubit?


(Lets assume the Earth is a perfect sphere for simplicity. Also, if this belongs somewhere else please move it.)

[Kanastrous]

1 cubit = 45.72 centimeters.

[LadyTevar]

1 cubit = 45.72 centimeters.

Or, as the old folks did it, the length of a grown man's arm from elbow to tip of the middle finger.

[Aranfan]

Did you even read my post? I want to know how big a cubit would have to be for the biblical pi=3 to be correct on the surface of a sphere.

[Kodiak]

Did you even read my post? I want to know how big a cubit would have to be for the biblical pi=3 to be correct on the surface of a sphere.

Do you have a reference which suggests that there is any biblical calculation showing PI = 3? I know some states have put this forward as a means of simplifying math, but I never heard there were religious arguments suggesting that if you use a cubit as a measurement PI magically becomes equal to 3.

[Aranfan]

I Kings 7:23

"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."


Which by Circumference/diameter gives pi=3.

[Steel]

Balls, just did some calculations. I'll post the results in a second.

[Kodiak]

I Kings 7:23

"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."


Which by Circumference/diameter gives pi=3.

Seems like the only value worth using here is the "line of thirty cubits" which would give it a circumference of 13.716 meters. Your reasoning seems faulty to me, because this isn't a sphere, it's a round (not necessarily spherical) font. Imagine a sort of above-ground swimming pool. Here's some better scholarship on the subject:

The bronze for the molten sea was supplied by the spoils from David's campaigns (1 Chronicles 18:8). The basin was over fourteen feet in diameter, over seven feet high, and over forty-three feet in circumference. It was about three inches thick. The estimated weight is about 30 tons, and the estimated volume is about 12,000 gallons (U.S.). The brim was turned outward resembling a lily, and below the brim were two rows of gourds (but compare 1 Kings 7:24; 2 Chronicles 4:3). The sea rested on the backs of twelve oxen. The oxen were arranged in groups of three, each group facing toward one of the four compass directions (1 Kings 7:25; 2 Chronicles 4:4).

link

and here's an artist's interpretation



Calculating pi from such dimensions using cubits or any unit so that they equal 3 (again, not sure where you get that pi=3 is a religious thing rather than an ignorant thing) is problematic to say the least.

[Darth Wong]

alculating pi from such dimensions using cubits or any unit so that they equal 3 (again, not sure where you get that pi=3 is a religious thing rather than an ignorant thing) is problematic to say the least.

It's a religious thing if you are a Biblical inerrantist, because they believe that the Bible has as much factual accuracy and precision as a science textbook. So while you can just shrug off that passage as something that was not meant to be taken as a precise measurement, they can't (at least, not without being dishonest and ignoring their own premises).

[Khaat]

I Kings 7:23

"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."

Which by Circumference/diameter gives pi=3.

Actually, you can do the same thing with a compass on a circle, but you aren't measuring circumference: you get six arcs around a circle with each arc equal to the radius, inscribing a hexagon within the circle. Simplified math for simple people.

"And he made a molten sea, ten cubits from one brim to the other: it was round all about, and his height was five cubits: and a line of thirty one and four thousand one hundred and fifty nine ten thousandth parts did encompass it round about."

Somehow I don't see that making the final edit.

[Kodiak]

alculating pi from such dimensions using cubits or any unit so that they equal 3 (again, not sure where you get that pi=3 is a religious thing rather than an ignorant thing) is problematic to say the least.

It's a religious thing if you are a Biblical inerrantist, because they believe that the Bible has as much factual accuracy and precision as a science textbook. So while you can just shrug off that passage as something that was not meant to be taken as a precise measurement, they can't (at least, not without being dishonest and ignoring their own premises).

I don't see anything in the passage which is irreconcilable, unless you take 30 cubits to be its circumference AND you take the 5 cubit measurement to be a diameter. The first assumption seems logical, the 2nd doesn't.

[Steel]

Ok, so for a sphere of radius a, suppose we have a circle on the surface, which has a spherical radius rs (that is the distance you have to walk from the centre of the circle on the surface of the sphere to a distance of rs from that point along a great circle) and it also has a euclidean radius re, (with the euclidean centre somewhere inside the planet). The spherical radius is an arc length along the surface of the sphere, which corresponds to an angle T (in radians) at the centre of the sphere. So rs=a*T

In euclidean space, C=2*pi*re

And in spherical geometry, define "spi" (the spherical value of pi), by the equation

Cs=2*spi*rs

From some simple geometry, we can determine that there is a relation between re and rs, namely:

re/rs = Sin(T)/T (1)

and therefore by equating C and Cs we have:

2*pi*re=2*spi*rs

and then

re/rs = spi/pi

and by (1)

Sin(T)/T = spi/pi

Now, if we demand that spi, the value of pi in our spherical geometry is 3, we have the equation:

Sin(T)=3*T/pi

and if get T, then we get the value of rs via rs=a*T

Now, via numerical solving (eeeew... applied maths), I get that you need T=0.955 (plus some more decimal places)

which corresponds to needing rs=0.955*radius of earth

and thus we need rs=6090km

From the radius given as 5 cubits, we need 5 cubits=6090km

and now for the punchline:

1 cubit = 1220km = 760 miles


Now I laboured that calculation a bit as you said you werent familiar with the maths, so hopefully you can follow it, and i havent made a horrific error somewhere in there. And the numerical solution is correct. Just dont go thinking the bible has anything other than crap in it now ok?

[Darth Wong]

alculating pi from such dimensions using cubits or any unit so that they equal 3 (again, not sure where you get that pi=3 is a religious thing rather than an ignorant thing) is problematic to say the least.

It's a religious thing if you are a Biblical inerrantist, because they believe that the Bible has as much factual accuracy and precision as a science textbook. So while you can just shrug off that passage as something that was not meant to be taken as a precise measurement, they can't (at least, not without being dishonest and ignoring their own premises).

I don't see anything in the passage which is irreconcilable, unless you take 30 cubits to be its circumference AND you take the 5 cubit measurement to be a diameter. The first assumption seems logical, the 2nd doesn't.

Have you got some kind of reading problem?

"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."

[Kodiak]

Have you got some kind of reading problem?

"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."

oh, so we're looking at 30cubits/10cubits = 3 = pi? I guess the engineer in me finds it ridiculous to assume that bronze-age shepherds were precise to the cubit. That's a hugely flawed assumption IMHO, which I guess is what the fundies are making. There are actually people who take this as an accurate way to calculate pi? Simple engineering practice says you can only assume accuracy to within one-half of the smallest unit you can measure, so in this case I would think the error is plus-or-minus one cubit. I don't think you could ever make 30x/10x= pi.

[Darth Wong]

Well of course it's a hugely flawed assumption; one could go blue in the face listing reasons why Biblical inerrantism is stupid.

[Kodiak]

Well of course it's a hugely flawed assumption; one could go blue in the face listing reasons why Biblical inerrantism is stupid.

Trying to apply the bible to science makes as much sense as using the Silmarilion to do the same.

[Darth Wong]

What's fascinating is that people back then may not have even had a strong grasp on the modern meaning of Truth itself. In the age of empiricism, western society adopted an empirical notion of truth or falsehood. That notion was adopted even by the religious, who then tried to take that square peg and shove it into the round hole of religion. But when those Bronze-age mythologies were created, the whole idea of empiricism as the ultimate arbiter of "truth" would have been completely foreign to them. To them, the greatest truths were completely divorced from empirical fact, rather than being tied to them.

[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.

[Stark]

What's fascinating is that people back then may not have even had a strong grasp on the modern meaning of Truth itself. In the age of empiricism, western society adopted an empirical notion of truth or falsehood. That notion was adopted even by the religious, who then tried to take that square peg and shove it into the round hole of religion. But when those Bronze-age mythologies were created, the whole idea of empiricism as the ultimate arbiter of "truth" would have been completely foreign to them. To them, the greatest truths were completely divorced from empirical fact, rather than being tied to them.

On the other hand, just because they had retarded ideas doesn't mean they were inaccurate mathematically - even ancient cultures had mathematics, but they did follow absurd rules and crazy workarounds. It's amusing to me to think that even the primitive Hebrews would have been laughed at or had to gloss over passages like this around more educated or sophisticated cultures.

[Broomstick]

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.

[Aranfan]

What's fascinating is that people back then may not have even had a strong grasp on the modern meaning of Truth itself. In the age of empiricism, western society adopted an empirical notion of truth or falsehood. That notion was adopted even by the religious, who then tried to take that square peg and shove it into the round hole of religion. But when those Bronze-age mythologies were created, the whole idea of empiricism as the ultimate arbiter of "truth" would have been completely foreign to them. To them, the greatest truths were completely divorced from empirical fact, rather than being tied to them.

I have a hard time conceiving how the Truth could be divorced from empirical fact. Maybe in pure mathematics Truth can be divorced from the physical world, but even there you have evidence (checking work). How can you claim to know the Truth, any truth, without evidence to back you up?

[andrewgpaul]

That was the position of at least one Greek school of philosophy. All truths can be determined by logical thought alone. Any evidence to the contrary can (and should) be discarded, since human senses are imperfect.

[Kanastrous]

How can you claim to know the Truth, any truth, without evidence to back you up?

Start a religion. You haven't noticed?

[andrewgpaul]

Did you even read my post? I want to know how big a cubit would have to be for the biblical pi=3 to be correct on the surface of a sphere.

I noticed no-one addressed this; Pi is a dimensionless number/ No matter the definition of a cubit, pi will never be equal to three.

You can, of course, simply take all measurements and ratios to one significant figure, and that way Pi=3 is valid, but that's also independent of the size of the units.

[Steel]

Did you even read my post? I want to know how big a cubit would have to be for the biblical pi=3 to be correct on the surface of a sphere.

I noticed no-one addressed this; Pi is a dimensionless number/ No matter the definition of a cubit, pi will never be equal to three.

You can, of course, simply take all measurements and ratios to one significant figure, and that way Pi=3 is valid, but that's also independent of the size of the units.

Fucking hell! Am I completely invisible?

Theres a page long post that shows how to calculate the value of the equivalent of pi in spherical geometry.

On the surface of a sphere with a radius that of earth, if a cubit was about 700km long, then for a circle 10cubits in diameter we have pi=3.

Another example would be if the centre of a circle is at the north pole, and the circumference is round the equator, then pi=2 (as the diameter is half the circumference and hence C=2*2(='pi')*r.