Thursday, November 10, 2005

The Bible and Pi

From drdino.com in an article written by Dr. Kent Hovind:

Does the Bible contain a mathematical error?

I Kings 7:23–26 and II Chronicles 4:2–5 describe a huge brass bowl built by King Solomon. If the diameter of this bowl was 10 cubits, then the circumference should have been 31.415926...cubits, not just 30 cubits! Any math student will tell you that the circumference of a circle is found by taking the diameter times Pi (3..141592653589793...). This apparent mathematical error caused me, as a new Christian, to doubt the accuracy of the Bible.

The answer is so simple! The diameter of 10 cubits is from outer rim to outer rim, the way anyone would measure a circular object. The circumference of 30 cubits, however, was of the inner circle, after subtracting the thickness of the brass (two handbreadths—one for each side) from which the bowl was made. This would be the number needed to calculate the volume of water.



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2 comments:

David Gracely said...

January, 5, 2006
Dear Rashad,

See if you like this analysis of King Solomon's molten sea.
While there is disagreement as to the length of the Biblical sacred cubit, hopefully the following information will prove useful to you, and completely settle once and for all what the true length of the cubit used in the construction of the Tabernacle and Temple was. Probably the same length cubit was used in the construction of Noah's ark as well.
Before giving the solution to this problem, it is helpful to look at the history behind the search for the true length of the Biblical cubit by scientists of the past.
Sir Isaac Newton was the first scientist in modern times to make an estimate of the cubit. He was lead to search for the length of the sacred cubit because his initial calculations on gravity were not working out right, and he suspected that the radius of the earth he was using as estimated by
Eratosthenes was off.
Eratosthenes had also made the statement that 210,000 Egyptian cubits was equal to a degree of arc along a great circle of the earth. Newton thought that he might be able to derive a more accurate value for the radius of the earth by finding out the true length of the Egyptian cubit through studying the dimensions of the Great Pyramid. He concluded that the Great Pyramid was built on the basis of two cubits, one which he called a profane cubit, and the other which he referred to as a sacred cubit. He thought that the sacred cubit (which he estimated at somewhere from 24.8 to 25.02 inches) was the same cubit used in the building of the Biblical Tabernacle and Temple. He finally settled on a value for the sacred cubit of 24.88 inches and wrote up his analysis in a rare but important monogram.
Many years later in 1859, a Christian by the name of John Taylor, a member of the Royal Society of London, submitted a paper to his colleagues. This paper was the result of a thirty-year study. His thesis was that the Great Pyramid had been built by Divine decree, as was Noah's ark, and had been built on the basis of a cubit of 25.025 inches which he believed was the sacred Biblical cubit. One ancient name for the Great Pyramid was "The Pillar of Enoch" which would lead credence to the belief that God commanded Enoch to build it. Taylor also declared from his study of the Great Pyramid that this 25.025 inch cubit had a scientific value equal to 1/10,000,000th of the earth's polar radius. The submission of his paper was made shortly after the publication of Darwin's "Origin of Species", and the Royal Society was not interested in his findings.
There was only one member of the Royal Society, a fellow Christian, who took Taylor's study seriously---Piazzi Smyth, the Astronomer Royal of Scotland. He petitioned the Society for funds to go to Egypt and check out Taylor's ideas. The Society not only refused his request, but to add insult
to injury, sent back part of the Society's yearly financial grant to the government on the plea that there was nothing going on that needed it.
Undaunted, Piazzi and his wife went with their own funds to Egypt, where he made very careful measurements of the Great Pyramid. He came to the conclusion that Taylor was indeed right.
Upon his return he informed the Royal Society of his findings. He was treated so badly that he resigned from the Society over the matter, and the history and controversy surrounding the search for the true length of the Biblical cubit has since faded with time.
The question is, can we show that these findings are of any significance? The answer is yes, provided we have two other important pieces of information.
William Foxwell Albright estimated that the Biblical bath was around 22 liters. He derived this value by comparing the broken top of a piece of pottery found at Lachish marked with the words "one royal bath" with jars that were complete.
Josephus states that King Solomon's sea mentioned in I Kings 7:23-26 and II Chronicles 4:2-5 was hemispherical and contained 3000 baths.
The passage in I Kings says that there was 2000 baths in King Solomon's sea and in II Chronicles it says 3000. If we assume that we are being told that the vessel was filled to two-thirds of its capacity and that if filled completely it held 3000 baths, we can substitute the 25 inch cubit into the dimensions given for King Solomon's sea and see what happens.
We make the assumption that the 10 cubits is the inside diameter and that the 30 cubits is a measurement that was made at a lower level. William Winston, who was the translator of Josephus and filled the chair at Cambridge after Newton, made this assumption, but used a 21 inch cubit and gave both the 2000 and 3000 baths equal weight and thus gave two different estimates for the value of a bath. If he had used Newton's highest estimate for the length of the cubit, one of his answers would have been very nearly perfect.
Using the formula for calculating the volume of a hemisphere we can proceed as follows:

V = 2/3 pi R3 (Formula for the volume of a hemisphere)
(One inch = 2.54 centimeters)
(1000.028 cm3 = 1 liter)

1. The polar radius of the earth is 3949.89 miles (1957 International Geological Survey)
2. The length of the sacred cubit is 1/10,000,000th of this.
3. The sacred cubit is thus 25.026503 inches.
4. The radius (i.e. half the diameter) of King Solomon's sea is 125.13252 inches.
5. The radius of King Solomon's sea in centimeters is 317.83659 cm.
6. The radius cubed is 32107900 cm3
7. The radius cubed multiplied by two-thirds is 21405267 cm3
8. This value multiplied by pi is 67246629 cm3
9. This total volume divided by three-thousand is 22415.543 cm3
10. One bath in liters is this value divided by 1000.028
11. This yields 22.414915 liters for one bath.

This value for the bath is the standard unit of volume in chemistry known as a molar volume and is given in chemistry textbooks as 22.414 liters. It is derived in a completely different way from the kinetic theory of gases. This mathematically connects the cubit to the bath in a very straightforward way.
It turns out that the volume in Biblical baths (or ephahs) of any size hemisphere can be derived by cubing its diameter and multiplying by three, provided Biblical cubits are used in measuring the diameter.
The Biblical talent appears to have been the weight of two baths of water (44.828 liters) which is 98.84 pounds. One of the reasons for concluding this is based on a conversation I once had with my grandmother.
I asked her what the Jews used to represent their old Biblical money. She related that once out of curiosity she went to a Jewish confessional to see what it was like, and observed that during the confessional everyone contributed a quarter.
Now every man in Israel 20 years old and up was required to give a half-shekel of the sanctuary (also known as a bekah). So if a quarter might represent a bekah, what then should a shekel of pure silver weigh?
Before the devaluation of American silver coinage, a silver dollar was defined as containing 412.5 grains of silver nine-tenths fine. Thus if it were pure silver it should weigh 458-1/3 grains, and a fifty cent piece should be representative of a shekel of 229-1/6 grains. According to a careful reading of Ex. 38:25-26, three-thousand shekels of the sanctuary would weigh a talent. Thus 3000 x 229-1/6 grains should weigh a talent. Since there are 7000 grains per pound, this works out to 98.21 lbs. for the weight of a talent.
The Biblical scholar Scofield in the Scofield Bible gives a value of 96 pounds which is apparently derived from Archbishop Ussher's estimate of a shekel's weight at 2 shillings 5 pence.
William Winston at the back of his translation of Josephus gives information which implies a shekel's weight is 232.4 grains (2 shillings 6 pence) which upon calculation yields a talent of 99.6 pounds. Thus it would suggest that we have a scientific definition for determining the weight of a talent.
As to the general consensus that the cubit was 18", this might be because the Egyptian cubit that the Israelites used in building the cities of Pharaoh was retained by them to some degree after they left Egypt.
Appealing to theological typology, Egypt is considered to be a type of the world, and we might not be unwarranted in considering Egyptian weights and measures to be of a secular rather than of a sacred nature.
As you can see, even though King Solomon's sea was broken up into pieces by the Chaldeans and the brass taken away to Babylon, dashing the hope of ever finding it intact so as to be able to actually measure it, the Lord has given us enough information to know beyond a reasonable doubt what His system of weights and measures is.
Incidently, 6 American gallons by volume are only 1-1/3% larger than 22.414 liters, and the bath was divided into 6 parts called hins. America would only have to change the inch by one part in a thousand, define the weight of two baths of water to weigh 100 pounds, and declare 6 gallons to be equal to a molar volume to refine the English system of weights and measures to be in line with the ancient and more scientifc God-given Hebrew system of weights and measures. It is not a coincidence that the country that unknowingly uses a system of weights and measures close to those God gave Israel has been a close friend to Israel.
Has any ancient artifact been found that implies that the cubit was indeed 25 inches? You may want to check out the following internet website: (http://www.thefutureevent.com/Ark.htm)

Sincerely in the Loving Saviour,


Dave Gracely

Sources consulted:

1. Dispensational Truth - Clarence Larkin. Copyright 1918.

2. The Great Pyramid---Its Secrets and Mysteries Revealed by
Piazzi Smyth. Originally published in 1880 as Our Inheritance
in the Great Pyramid. Special material copyright MCMLXXVIII
(1978) by Crown Publishers, Inc.

3. Secrets of the Great Pyramid by Peter Tompkins. Harper Colophon
Books. Harper and Row, Publishers. copyright 1971.

4. Prophecy In Stone - Noah Hutchings - Hearthstone Publishing
copyright 1996

David Gracely said...

January 5, 2006
Dear Rashad,

While there is disagreement as to the length of the Biblical sacred cubit, hopefully the following information will prove useful to you and all other fellow believers, and completely settle once and for all what the true length of the cubit used in the construction of the Tabernacle and Temple was. Probably the same length cubit was used in the construction of Noah's ark as well.
Before giving the solution to this problem, it is helpful to look at the history behind the search for the true length of the Biblical cubit by scientists of the past.
Sir Isaac Newton was the first scientist in modern times to make an estimate of the cubit. He was lead to search for the length of the sacred cubit because his initial calculations on gravity were not working out right, and he suspected that the radius of the earth he was using as estimated by
Eratosthenes was off.
Eratosthenes had also made the statement that 210,000 Egyptian cubits was equal to a degree of arc along a great circle of the earth. Newton thought that he might be able to derive a more accurate value for the radius of the earth by finding out the true length of the Egyptian cubit through studying the dimensions of the Great Pyramid. He concluded that the Great Pyramid was built on the basis of two cubits, one which he called a profane cubit, and the other which he referred to as a sacred cubit. He thought that the sacred cubit (which he estimated at somewhere from 24.8 to 25.02 inches) was the same cubit used in the building of the Biblical Tabernacle and Temple. He finally settled on a value for the sacred cubit of 24.88 inches and wrote up his analysis in a rare but important monogram.
Many years later in 1859, a Christian by the name of John Taylor, a member of the Royal Society of London, submitted a paper to his colleagues. This paper was the result of a thirty-year study. His thesis was that the Great Pyramid had been built by Divine decree, as was Noah's ark, and had been built on the basis of a cubit of 25.025 inches which he believed was the sacred Biblical cubit. One ancient name for the Great Pyramid was "The Pillar of Enoch" which would lead credence to the belief that God commanded Enoch to build it. Taylor also declared from his study of the Great Pyramid that this 25.025 inch cubit had a scientific value equal to 1/10,000,000th of the earth's polar radius. The submission of his paper was made shortly after the publication of Darwin's "Origin of Species", and the Royal Society was not interested in his findings.
There was only one member of the Royal Society, a fellow Christian, who took Taylor's study seriously---Piazzi Smyth, the Astronomer Royal of Scotland. He petitioned the Society for funds to go to Egypt and check out Taylor's ideas. The Society not only refused his request, but to add insult
to injury, sent back part of the Society's yearly financial grant to the government on the plea that there was nothing going on that needed it.
Undaunted, Piazzi and his wife went with their own funds to Egypt, where he made very careful measurements of the Great Pyramid. He came to the conclusion that Taylor was indeed right.
Upon his return he informed the Royal Society of his findings. He was treated so badly that he resigned from the Society over the matter, and the history and controversy surrounding the search for the true length of the Biblical cubit has since faded with time.
The question is, can we show that these findings are of any significance? The answer is yes, provided we have two other important pieces of information.
William Foxwell Albright estimated that the Biblical bath was around 22 liters. He derived this value by comparing the broken top of a piece of pottery found at Lachish marked with the words "one royal bath" with jars that were complete.
Josephus states that King Solomon's sea mentioned in I Kings 7:23-26 and II Chronicles 4:2-5 was hemispherical and contained 3000 baths.
The passage in I Kings says that there was 2000 baths in King Solomon's sea and in II Chronicles it says 3000. If we assume that we are being told that the vessel was filled to two-thirds of its capacity and that if filled completely it held 3000 baths, we can substitute the 25 inch cubit into the dimensions given for King Solomon's sea and see what happens.
We make the assumption that the 10 cubits is the inside diameter and that the 30 cubits is a measurement that was made at a lower level. William Winston, who was the translator of Josephus and filled the chair at Cambridge after Newton, made this assumption, but used a 21 inch cubit and gave both the 2000 and 3000 baths equal weight and thus gave two different estimates for the value of a bath. If he had used Newton's highest estimate for the length of the cubit, one of his answers would have been very nearly perfect.
Using the formula for calculating the volume of a hemisphere we can proceed as follows:

V = 2/3 pi R3 (Formula for the volume of a hemisphere)
(One inch = 2.54 centimeters)
(1000.028 cm3 = 1 liter)

1. The polar radius of the earth is 3949.89 miles (1957 International Geological Survey)
2. The length of the sacred cubit is 1/10,000,000th of this.
3. The sacred cubit is thus 25.026503 inches.
4. The radius (i.e. half the diameter) of King Solomon's sea is 125.13252 inches.
5. The radius of King Solomon's sea in centimeters is 317.83659 cm.
6. The radius cubed is 32107900 cm3
7. The radius cubed multiplied by two-thirds is 21405267 cm3
8. This value multiplied by pi is 67246629 cm3
9. This total volume divided by three-thousand is 22415.543 cm3
10. One bath in liters is this value divided by 1000.028
11. This yields 22.414915 liters for one bath.

This value for the bath is the standard unit of volume in chemistry known as a molar volume and is given in chemistry textbooks as 22.414 liters. It is derived in a completely different way from the kinetic theory of gases. This mathematically connects the cubit to the bath in a very straightforward way.
It turns out that the volume in Biblical baths (or ephahs) of any size hemisphere can be derived by cubing its diameter and multiplying by three, provided Biblical cubits are used in measuring the diameter.
The Biblical talent appears to have been the weight of two baths of water (44.828 liters) which is 98.84 pounds. One of the reasons for concluding this is based on a conversation I once had with my grandmother.
I asked her what the Jews used to represent their old Biblical money. She related that once out of curiosity she went to a Jewish confessional to see what it was like, and observed that during the confessional everyone contributed a quarter.
Now every man in Israel 20 years old and up was required to give a half-shekel of the sanctuary (also known as a bekah). So if a quarter might represent a bekah, what then should a shekel of pure silver weigh?
Before the devaluation of American silver coinage, a silver dollar was defined as containing 412.5 grains of silver nine-tenths fine. Thus if it were pure silver it should weigh 458-1/3 grains, and a fifty cent piece should be representative of a shekel of 229-1/6 grains. According to a careful reading of Ex. 38:25-26, three-thousand shekels of the sanctuary would weigh a talent. Thus 3000 x 229-1/6 grains should weigh a talent. Since there are 7000 grains per pound, this works out to 98.21 lbs. for the weight of a talent.
The Biblical scholar Scofield in the Scofield Bible gives a value of 96 pounds which is apparently derived from Archbishop Ussher's estimate of a shekel's weight at 2 shillings 5 pence.
William Winston at the back of his translation of Josephus gives information which implies a shekel's weight is 232.4 grains (2 shillings 6 pence) which upon calculation yields a talent of 99.6 pounds. Thus it would suggest that we have a scientific definition for determining the weight of a talent.
As to the general consensus that the cubit was 18", this might be because the Egyptian cubit that the Israelites used in building the cities of Pharaoh was retained by them to some degree after they left Egypt.
Appealing to theological typology, Egypt is considered to be a type of the world, and we might not be unwarranted in considering Egyptian weights and measures to be of a secular rather than of a sacred nature.
As you can see, even though King Solomon's sea was broken up into pieces by the Chaldeans and the brass taken away to Babylon, dashing the hope of ever finding it intact so as to be able to actually measure it, the Lord has given us enough information to know beyond a reasonable doubt what His system of weights and measures is.
Incidently, 6 American gallons by volume are only 1-1/3% larger than 22.414 liters, and the bath was divided into 6 parts called hins. America would only have to change the inch by one part in a thousand, define the weight of two baths of water to weigh 100 pounds, and declare 6 gallons to be equal to a molar volume to refine the English system of weights and measures to be in line with the ancient and more scientifc God-given Hebrew system of weights and measures. It is not a coincidence that the country that unknowingly uses a system of weights and measures close to those God gave Israel has been a close friend to Israel.
Has any ancient artifact been found that implies that the cubit was indeed 25 inches? You may want to check out the following internet website: (http://www.thefutureevent.com/Ark.htm)

Sincerely in the Loving Saviour,


Dave Gracely

Sources consulted:

1. Dispensational Truth - Clarence Larkin. Copyright 1918.

2. The Great Pyramid---Its Secrets and Mysteries Revealed by
Piazzi Smyth. Originally published in 1880 as Our Inheritance
in the Great Pyramid. Special material copyright MCMLXXVIII
(1978) by Crown Publishers, Inc.

3. Secrets of the Great Pyramid by Peter Tompkins. Harper Colophon
Books. Harper and Row, Publishers. copyright 1971.

4. Prophecy In Stone - Noah Hutchings - Hearthstone Publishing
copyright 1996