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Thursday, December 29, 2011

Pi and the Sea of Solomon's Temple revisited...Featuring Daniel Gracely and friends

Back in April I devoted a post that largely concentrated on debunking the claims of Atheists about the "Sea" in Solomon's Temple.

It isn't hard to do.   More often than not Atheists are pretty ignorant of the Bible and make very simplistic claims.  Kind of like not knowing much about money and being given the choice between a nickel and a dime and choosing the nickel because it is bigger?   There are many explanations for the measurements given in the Bible.   Here is an excerpt:

~~~~~~~~~~~~~~~~~

"When I worked in the automotive industry, we had differing requirements for various parts depending upon their purpose.   Some measurements were critical and some were not.  We had variations built in to the requirements for padding and sound deadening parts that allowed for a good bit of variation, as they were not critical parts of the automobile.   But some parts had to be made exactly right, enough so that they would fit precisely on a "buck" and their dimensions and the spacing of punched holes or added pieces of metal all hit the exact mark.   The same was true in the steel industry.   There were many items that had to be measured by a caliper to fit within a very narrow band of acceptable readings.   In all of these scenarios, I was part of the production team and was following specific instructions.


In I Kings, however, the Temple is being described.   Therefore I can assert that no matter how they described the measurements of the sea, it does not tell us precisely how, where, and with what requirements such measurement were made.   Since it is descriptive of a building and features, precision would hardly be expected.   The scribes would not write that the sea was 9.82 cubits across, for instance.   In fact, in descriptive mode it would be highly unlikely that a general description of such an object would be particularly precise.   So those who claim that the Bible is wrong here are over-reaching terribly.   Now, if God had instructed someone to make a precise sea of thirty whatevers around and ten whatevers across and demanded precision, then the builders would have had a problem.  But this is not a blueprint, it is a kind of feature story of the unveiling of the new temple.

Nevertheless, there is an article, below, which gives us a logical explanation for the measurements.   I agree with the author in that it was an Oriental/Middle Eastern culture that first came up with the Pythagorean Theory, it was that culture that adopted the modern numerical system that is far superior to the awkward Greco-Roman system, it was the Jewish peoples who first had a system of writing (actually no doubt carried on from the pre-Flood culture) found by archaeologists.   If you know the Bible you have to know that writing and using numbers predates anything we have recovered from the past.

I suggest that you go to the site and read the article there to get the links and other information but I am presenting it in plain text here.


~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Also, as part of the article I posted information from:

Worth reading!   After I made this post,  a commenter called Aleksandr Sigalov gave us a link I thought was interesting, with very good graphics on The Desert Tabernacle 



The Moderator made some comments and shared a page on Bible Lands and Cities.   I have not gone all through it yet, but go see...





So now a reader, Daniel Gracely, has posted information that I found very interesting and it is applicable so I am posting his comments as a "guest post" below:



Daniel Gracely said...

About 30 years ago my brother, David, discovered an interesting connection between the length of the sacred cubit and the biblical bath. Following the work of Piazzi Smyth, John Taylor, Albright, David Davidson, and Isaac Newton (who wrote an entire monograph on the subject of the length of the biblical cubit), David assumed the sacred cubit was around 25”. Specifically, he believes it to be 25.0265” or 1/ 10,000,000th polar radius of the earth.

Out of curiosity David plugged this number into the measurements of Solomon’s Sea to calculate the volumetric capacity for the biblical bath. He assumed the 2,000 baths and 3,000 baths mentioned in I Kings and II Chronicles were the water-fill mark and the Sea’s fullest theoretical capacity, respectively. He also accepted Josephus’ description that the Sea was hemispherical (this is the only historical description we have, biblical or extra-biblical). The resulting calculation was 22.4149 liters. This was a remarkable result, for being a math/science type guy, David realized this number was also the volumetric capacity of a molar volume of gas (i.e., the standard unit of measure for gas, being the volumetric space of one mole of gas at an ideal temperature and pressure). Furthermore, since the book of Ezekiel states that one ephah (standard unit of dry measure) equals one bath (standard unit of liquid measure), the conclusion is that Solomon’s Sea demonstrates the same volumetric space for liquid, dry, and gaseous measures, i.e., the three forms of matter.

Consequently, one must either mark all of these calculations down to freakish mathematical coincidences, or else consider that a Common Designer used the same basic unit of measurement for liquid, dry, and gaseous measures. The latter means taking the Bible seriously when it tells us that God gave Solomon’s father the divine pattern for the construction of all artifacts pertaining to the First Temple.

However, when I discussed my brother’s findings with him this past summer, I felt there was one problem. My brother had assumed the 30-cubit line which compassed the bowl was a line below the rim, and that the 10 cubit diameter implied pi and thus a circumference at the brim of 31.4159+ cubits. But then what was the 30-cubit line? I asked him if it might be the fill mark. He said, no, that that was 30.6. He admitted this problem had baffled him for 30 years. This nettled me, for I wished to share his findings online with some atheists, but I knew they would claim my brother was assuming pi for the brim’s circumference because of his agenda of wanting a sacred cubit length of 25”. Thus they would argue the measurements for Solomon’s Sea were merely rounded off (9.65 for the diameter, yielding a 30.30 circumference). Finally, after talking to my brother further about this problem, I suggested he see if the 30-cubit line might have something to do with the golden mean (a.k.a., golden ratio). I had once been a graduate student in art history and knew the importance of the golden mean especially in Classical and Renaissance art, but suggesting the golden mean was a guess on my part. Nevertheless, the next morning, David called excitedly and told me that, yes, the 30-cubit line did represent the golden mean, when placed outside upon the bowl. The margin of error was only 1 in 3400, well within an acceptable margin of error. We concluded this line divided the two rows of carved gourds, one above it, and one below it. This written description of the golden mean predates Pythagoras by 300+ years, and is the earliest written description of the golden mean we know of.

Unfortunately, when, about 10 years ago, my brother shared his initial findings with John Morris (whom you quote in your article), Morris’ reply, while cordial, showed he was unimpressed with my brother’s findings. Instead, Morris apparently followed the shorter-cubit assumptions of men like Ritmeyer et al (i.e., Bahat, Sagiv, Kaufman) based on their assumptions that the Second Temple was located on the Dome of the Rock, despite the Bible stating that the Temple was located at the Gihon Springs, which is about 1,000 yards south and outside the current city walls.

Frankly, the demonstration of the golden mean in conjunction with the Sea’s demonstration of a unified field of measures ought to convince anyone, at least any Christian, of the real facts about the measurements of Solomon’s Sea, and what they mean. No longer do we need to rely on flimsy explanations like rounded off numbers or a ‘flared-brim’ design. But, you know, my own experience is that a Christian layperson who makes a discovery often receives no more encouragement from Christian academicians than he presumably would from their secular counterparts. And thus if we solve one problem, we nevertheless raise another of why that should be?

Incidentally, since the Sea was a handbreadth thick, and since a handbreadth is 1/7th of a cubit, it does not matter what length the cubit is in terms of the golden mean, since all measurements are relative to the cubit."

14 comments:

Chaos Engineer said...

The resulting calculation was 22.4149 liters. This was a remarkable result, for being a math/science type guy, David realized this number was also the volumetric capacity of a molar volume of gas (i.e., the standard unit of measure for gas, being the volumetric space of one mole of gas at an ideal temperature and pressure).

Oh, dear, it sounds like someone wasn't paying attention in high school chemistry!

"Mole" is short for "molecular-gram weight". A mole of a gas is the molecular weight of the gas molecules, multiplied by one gram. (For example, 2 grams of pure hydrogen, or 32 grams of pure oxygen.) Dry air is about 29 grams/mole.

The Ideal Gas Law says that one mole of gas at standard temperature and pressure will take up 22.414 liters. Standard temperature and pressure is 32 degrees F at a pressure of one atmosphere.

Do you see the problem? In order to get 22.414 liters of air of out the Ideal Gas Law, we need to be at 32 degrees F (an unlikely temperature for ancient Israeli temple rituals), and we need to have 1 mole of air...but a mole is defined in terms of grams, and the gram is an arbitrary measurement that was created in the 1700's!

My guess is that the author is a crackpot numerologist...people like that take arbitrary numbers and combine them randomly until they find an equality, and then they claim that the equality has Deep Significance.

And, sure enough, further down we've got an "I know more than the experts!" quote; that's always the easiest way to spot a crackpot:

No longer do we need to rely on flimsy explanations like rounded off numbers or a ‘flared-brim’ design. But, you know, my own experience is that a Christian layperson who makes a discovery often receives no more encouragement from Christian academicians than he presumably would from their secular counterparts.

That said, I've never thought this was a good example of a contradiction in the Bible...I think the "rounded numbers" and "flared-brim design" explanations are both reasonable.

Can we do a tougher one next? I'll vote for, "If the Bible is the inerrant Word of God, then why do we have four gospels with partial redundancies? Wouldn't it have been better for God to inspire one 'super-gospel' with no omissions or duplications?"

AmericanVet said...

The four gospels are four historical accounts of the ministry of Christ (Matthew and John). Two were written by men who were of the original 12 Disciples of Christ. One was written by very likely one of the secondary followers of Christ (Mark). The fourth was compiled by an historian who was a companion to some of the men of the early church, Luke. Three of them are very similar and many of us believe they all used a common timeline/basic account one of them had access to and shared with the others. We call Matthew, Mark and Luke the Synoptic Gospels. But they are not ALIKE and they do focus on different aspects of His ministry.

John apparently used his own references and memories and did not share the basic outline of the other three writers. We believe that John was the closest of all men to Jesus (more than even Peter) and privy to some events that the others did not even witness.

Most people would consider having more documentation for the life of Christ rather than less a good thing. I am among them. In fact we know far more about Jesus because we have all four accounts. We have his lineage from his mother's side and his stepfather's side (Joseph would have been his presumed biological father). We have documentation of His words and actions in Samaria, which would be kind of the ghetto to the Jewish leadership. We see Him preaching to and healing rich and poor, prostitutes and priests, men and women...whereas the culture of the day did not value women and eschewed being seen with tax collectors, Jesus chose a tax collector for one of His 12 and dined with prostitutes, vagabonds, beggars and others not accepted by upper society.

Jesus really did see men and women as having equal value in the eyes of God while understanding the culture of the day. He was righteously outraged at the leadership of the people who were hypocritical in both word and deed and made sure that they knew it! But He readily spoke with any of them who sought truth.

AmericanVet said...

We know these things, and more, about Jesus because we have four accounts written by men of his time who were either eyewitnesses or who could interview and collate information from eyewitnesses. So therefore we know that Jesus did indeed fulfill the prophetic role of Messiah and did serve as the Lamb of God, able to take away the sins of the world. The gospels provide the documentation and teachings of Christ that provide the basis for the Christian faith.

Now, about calculations such as the mole, I did take my science classes and do quite well in them but I am also 59 years old so I last took Chemistry about 43 years ago. Since the air in question would not likely be dry, the exact formulation may not require 32 degrees F but, if it does, then Chaos is right because we are pretty sure the Temple was not being built in frigid weather.

I will ask you then, Chaos, if you are quick to spot a discrepancy like this in an essay on the Sea, how is it you cannot see that helium in granitic zircons proves a very young Earth?

Anonymous whatsit said...

Since the gospels, like the rest of the Bible, are riddled with internal contradictions, one can only presume human authorship, not divine authorship.

AmericanVet said...

No, Whatsit, they are not. If you doubt it, take any contradiction you can think of and go to Christian Thinktank and you will find it refuted nicely. That is, if you really want to know instead of happily making false claims?

Jon Woolf said...

"My guess is that the author is a crackpot numerologist.."

My thought as well, Chaos Engineer. Reminds me of Charles Piazzi-Smyth and his fellow 'pyramidiots' who claimed that the Great Pyramid was a guide to the future.

radar said...

In no way do I think some pyramid in Egypt is a key to anything in particular. Numerology is most interesting for what it means to different cultures at differing times. For instance, the Jews of the 1st Century were, like many cultures of the time, well aware of numerology and tended to use it in ways modern culture would not bother with. Often people were named with numerology in mind back then.

In fact, I believe that the six hundred three score and six of Revelation is a number meant to represent Nero Caesar, using numbers in a way the Romans would not tend to recognize. I believe John was being cryptic in a message to the believers of his day in order to warn them of the impending doom of Jerusalem. Naturally some very good Christian friends disagree, especially Hawkeye and I decided to cancel a series on Preterism out of respect for his viewpoint. This blog may be a worldview blog but it mostly concerns revealing the man behind the Darwin curtain, not discussion of Biblical prophecies.

That being said, I wanted to allow several viewpoints and comments to be reviewed and discussed concerning the Solomon Sea of the Temple. Having done so, we have seen several ways in which logical thinking reveals that the Bible was not presenting faulty math, but rather unbelievers were hastily looking for a mistake and published it as such without giving the subject much thought.

Anonymous whatsit said...

Nice bluff, Radar, but I did not find the contradiction I was looking for refuted there. And there is likewise no shortage of contradictions in the OT.

What puzzles me is why you find the thought that the Bible was written by fallible humans so abhorrent. You seem to be mostly on board with this thought anyway, seeing as you accept that the authors of the gospels relied on their own memories and possibly the eyewitness accounts of others. Naturally, this can lead to mistakes and contradictions between different accounts. Why do you find that difficult to accept and/or admit?

"I will ask you then, Chaos, if you are quick to spot a discrepancy like this in an essay on the Sea, how is it you cannot see that helium in granitic zircons proves a very young Earth?"

Most likely because of the faulty science presented by YECs in that regard.

Daniel Gracely said...

Do you see the problem? In order to get 22.414 liters of air of out the Ideal Gas Law, we need to be at 32 degrees F (an unlikely temperature for ancient Israeli temple rituals), and we need to have 1 mole of air...but a mole is defined in terms of grams, and the gram is an arbitrary measurement that was created in the 1700's!

My, oh my!; how inconvenient you find facts! Or do you not even understand the logic that idealizations of universal constants are independent of any particular system of measurement? For my brother’s translation of the volumetric capacity of the biblical bath based on the biblical cubit to today’s metric nomenclature is merely one translation possible. That is, IF the temperature is 32 degrees and IF there is1.0 moles and IF we use the grams-system of measurement, then the idealization of the universal constant may be expressed thus…. But note that the same universal constant may be expressed (fractionally, where necessary) in e.g., ounces, pounds, drams, grains, pennyweight, and at a half or 1.5 of 14.7 pounds of pressure per sq. inch and at 20 or 40 or 60 degrees, etc.

Transliterating idealizations of universal constants pertaining to Solomon’s Sea therefore have nothing whatsoever to do with what temperature the water in the bowl actually was when used by the Levitical priests of Israel. I’m puzzled why this distinction between universal constants and that which would measure them has escaped your attention? Indeed, any material part of the universe may be used as the standard of measure for any other material thing or things in the universe at various temperatures, etc. In short, your arguments are all straw.

Though not exactly analogous, your statement reminds me of that said by the professor of the young raconteur, C.K. Chesterton, to Chesterton’s mother: “There goes six foot two inches of genius. Treasure him!” Except to say, I don’t believe the professor was claiming that C.K. Chester could not exist were there not the imperial system of measurement around to provide a metonym.

And so, however much you may have paid attention in Chemistry class, you seem to have played hooky from Logic 101. Which explains your logical fallacy of ‘comparing’ non-analogous things, of embracing the fallacy of credentialism, and so forth. And so I have felt obligated to return one of your own—the ad hominem. Sheesch!—One fears that the disciples of such a generation of skeptics will proceed from today’s mistake of assuming that the metrical system along the bottom edge of a ruler makes impossible an imperial system along the ruler’s top edge, to supposing that clever British witticisms can be observed in the common tape measure.

One can hardly wait for that day.

Daniel Gracely said...

(part 1 of 4)

My brother David writes:

In regards to the comments made by "Chaos", the following might be noted:

While I would agree that the presently accepted definition for a mole is "molecular-gram weight", I find it grimly amusing that science teachers who are so annoyed by the difficultly students have in differentiating between the concepts of "mass" and "weight" would use such a phrase, when they know full well that grams are units of mass and not weight. The phrase should be "gram molecular mass". But in this case it is necessary to overlook the unscientific terminology of the scientific world.

Re: the statement that "a mole is defined in terms of grams, and the gram is an arbitrary measurement that was created in the 1700's!":

Such a statement implicitly assumes it was impossible to determine the mass, weight, or volume of anything until the metric system was invented. I can only assume that this must mean it was impossible for any scientists to measure or weigh anything before the adoption of the metric system.

The plain definition of a mole is that it is Avogadro's number, or 6.022045 x 1023 atoms of any element. Wikipedia should open with this candid definition, to prevent readers from making the same mistake of Chaos Engineer. The fact that the scientific world wants to arbitrarily declare that 6.022045 x 1023 atoms of carbon atoms will have a mass of exactly 12 grams is a matter of convention, because oxygen used to be used as the standard for atomic weights.

Avogadro's number of this many atoms of any of the elements in the Periodic Table could be just as easily given in ounces or slugs (English units of weight and mass respectively) instead of grams if you preferred. That is, it could be given in any system of weights that could be devised. The ratio of the weights or masses of the different elements to one another would remain unchanged regardless of what system was used in weighing the different elements. As to the molar volume, an ideal gas by definition has no weight, because the 6.022045 x 1023 atoms that comprise a molar volume are massless Frankly, anyone who considers themselves scientific shouldn't even need to be told this.

In fact, the determination of empirical formulas for chemical compounds uses a mathematical technique that is independent of the system of weights and measures used. The calculations used in the law of mass proportions relies only on the ratio of weights of reactants to the weights of products in a chemical reaction. In this mathematical procedure any system of weight or mass will work.

Further, it was not necessary to invent the metric system in order to scientifically determine the amount of space taken up by Avogadro's number of ideal gas molecules at standard temperature and pressure for the following additional reasons:

First, the freezing point of water is independent of the temperature scale used to measure it. Even how far is the freezing point of water above absolute zero is likewise independent of the temperature scale used to measure it. In the metric system it is 273.150 C above absolute zero, and in the Fahrenheit system it is 459.670 F above absolute zero. Why the difference? Basically because one system divides the freezing point and boiling point of water into100 units (0 C to 100 C), while the other system divides it into 180 units (32 F to 212 F). So which temperature scale is more scientific? Well, that is a matter of opinion, but the average person realizes that you can express a greater range of temperatures in the Fahrenheit system without resorting to cumbersome fractions.

(part 2 of 4 follows)

Daniel Gracely said...

(part 2 of 4)

My brother David writes:

Also, the average pressure of the atmosphere at sea level is likewise independent of the units of measurement used. So if one asks: Which is correct, which normal atmospheric pressure at sea level is correct, 101,325 newtons per square meter, or 14.7 lbs. per square inch?, the fact is, both statements are correct. This is because one may use two different systems of weights and measures.

Now, since certain critical scientific data is now basically given only in the metric system as opposed to the English system, or any other system, it necessitates using the metric system in most scientific work, and gives the false impression that the metric system is the only system that can be used to make any given scientific discovery.

The basic point is that all the basic formulas of science will work with any system of weights and measures that you want, so long as you remain consistent within the framework of measurement you have chosen to use.

Just as the mathematical principles of geometry were discovered without the need for the metric system, so also the determination of the amount of space taken up by Avogadro's number of ideal gas molecules at STP was not dependent upon the invention and adoption of the metric system. Any particular system of weights and measures could have been used and this is why.

The calculations used by the scientists to calculate the volume of Avogadro's number of ideal gas molecules at STP is done by multiplying together three constants and dividing by another constant; namely by taking the product of Boltzmann's constant, Avogadro's number, and the absolute temperature of the freezing point of water, and dividing by the normal atmospheric pressure at sea level. Any other system of weights and measures could have been used to determine these constants. These four constants have been experimentally determined within narrow limits. The fact that it was decided to use the metric system instead of some other system to determine these four constants gives an inflated status to the scientific integrity of the metric system.

Now as to the freezing "temperature being an unlikely temperature for ancient Israeli temple rituals", I totally agree. But why assume a definition would dictate how some ritualistic or scientific procedure would be performed?

For instance, when in chem labs an experiment is done in which the volume of a gas is measured, the procedure is not done at freezing temperatures. Rather, the temperature and barometric readings of the room are taken, and by means of the gas laws, the volume the gas would have at STP is calculated into the equation. It isn't necessary to wait until the room happens to be at the freezing point for water and also be at normal atmospheric pressure, before doing the experiment.

As to the rituals of the Israelites, are we really to suppose it would have been impossible for the Israelites to carry around a 22.414 liter container unless they were to do it at the freezing point of water and at normal atmospheric pressure?

Besides that, ancient Israel would not have needed to know the scientific definitions of the bath and the cubit anyway. All God would have needed to have done is give someone a rod and tell them that the length of the rod would be the standard unit of length called a cubit. Then He could tell them that the diameter of any hemisphere, when cubed and multiplied by three, would give the total volume of the hemisphere in baths (or ephahs), if they used cubits in measuring the diameter. In other words, He wouldn't have needed to say something like,

(part 3 of 4 follows)

Daniel Gracely said...

(part 3 of 4)
My brother David writes:

"Oh, by the way, this rod is one ten-millionth of the earth's polar radius, and the bath is the space taken up by what will be called some thousand years hence Avogadro's number of ideal gas molecules at the freezing point of water and at normal atmospheric pressure. And when it is, it will be discovered by using a completely different system of weights and measures which will be claimed to be more scientific." He wouldn't need to tell them anything of the sort. He could simply give them the simple formula mentioned above.

The fact that there is no such easy formula in the metric system directly connecting a molar volume to the size of the earth is in part because the metric system uses 1/10,000,000th of a curved meridian of the earth for the standard unit of length, instead of that of 1/10,000,000th of the straight line that is the earth's polar radius.


The calculations based on the dimensions of King Solomon's Sea and the calculations the scientists have used to derive the same volumetric capacity for the space taken up by Avogadro's number of ideal gas molecules at STP are given below. It should be kept in mind that much scientific data is now only given in terms of the metric system, and so it is necessary to convert from the English system to the metric system in order to show the scientific significance of the computations.

Anyone who thinks these calculations are nothing more than numerological rubbish is free to do so. But the truly objective skeptic will understand that mathematics speaks for itself.

Using a conventional hand held calculator, we can use the Biblical information of King Solomon's sea to calculate the scientific value of a bath. We are taking the definition of the sacred cubit to be 1/10,000,000th of the earth's polar radius.

V = 2/3 p 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 polar radius of the earth multiplied by 5280 ft./mile is 20855419 ft.
3. The length of the sacred cubit is taken to be 1/10,000,000th of this.
4. This produces a value of 2.0855419 ft. for the sacred cubit.
5. This multiplied by 12 inches per foot is 25.026502 inches for the sacred cubit
6. This multiplied by 5 gives the radius of King Solomon's sea as 125.13251 inches
7. The radius multiplied by 2.54 centimeters per inch is 317.83657 centimeters
8. The radius multiplied by itself three times (i.e. cubed) is 32107875 cm3
9. (On many simple hand held calculators, hitting the times key once and the equals key twice will cube a number.)
10. The radius cubed multiplied by two-thirds is 21405250 cm3
11. This value multiplied by p is 67246577 cm3 (p to 8 places is 3.1415927)
12. This total volume divided by three-thousand is 22415.525 cm3
13. One bath in liters is this value divided by 1000.028
14. Rounded off to 6 figures yields 22.4149 liters for one bath

(part 4 of 4 follows)

Daniel Gracely said...

(part 4 of 4)
(Note: I, Dan, have reformatted (left-margined, etc.) calculations in part 4, and may have changed something accidentally. I could not reach my brother to make sure I did not accidentally delete something.)

My brother David writes:

The scientific world does it like this:

To calculate the molar volume of an ideal gas at Standard Temperature and Pressure (the freezing point of water and the average air pressure at sea level), the following gas law formula from chemistry is used:

V = nkAT
____
P

[ = # of moles (in this case n=1)]

k = Boltzmann's constant (1.380662 x 10-23)
A = Avogadro's number (6.022045 x 1023)
T = Absolute temperature of 00C. (273.150K)
P = 101,325 newtons/square meter (normal atmospheric pressure at sea level)
(1)(1.380662 x 10-23)(6.022045 x 1023)(273.150K)

V = .022413824 cubic meters per bath.


The accepted value for a molar volume is .02241383 cubic meters. Since there are 100 centimeters along each edge of a cubic meter, there are (100 x 100 x 100), i.e.1,000,000 cubic centimeters in one cubic meter. Thus.022413824 cubic meters translates into 22413.824 cubic centimeters which when divided by 1000.028 cubic centimeters per liter yields 22.41320243 liters per molar volume. The close agreement of these values arrived at by two independent sets of calculations speaks for itself, showing the description of King Solomon's sea is scientific. The mathematics employed is straightforward and can be easily checked.
Finally, it turns out that the volume in molar volumes, i.e. Biblical baths (or ephahs---see Ezekiel 45:11) of any size hemisphere can be readily determined if Biblical sacred cubits are used in measuring the diameter. Simply cube the diameter and multiply by three. So in the case of King Solomon's sea it would be 10 x 10 x 10 x 3 = 3,000 baths (i.e. 103 x 3). Of if you had a hemisphere of 2 cubits in diameter, the volume would be 2 x 2 x 2 x 3 = 24 baths (i.e. 23 x 3). The beauty in the Biblical system is that there is no unsolvable number like p to deal with in performing the calculations. Actually, while whole numbers were used for illustration, the diameter can be expressed with any number at all.

(Note: the accepted values used for Avogadro's number (6.022045 x 1023), Boltzmann's constant (1.380662 x 10-23), and a molar volume (.02241383 cubic meters) were obtained from a Casio FX-450 scientific calculator where these constants were locked in from the factory. These values can also be found on the internet if you plug in a search for the number .02241383.)

Jon Woolf said...

What makes an argument 'numerology' is not whether or not it's mathematically valid. Even among crackpots, few are so stupid as to base a claim on equations that anyone can prove are wrong with a pencil and paper. No, what makes an argument numerology is the free introduction of unprovable yet "unchallengeable" sources for its numbers, and the derivation of some mystical Truth from it. Case in point:

"We are taking the definition of the sacred cubit to be 1/10,000,000th of the earth's polar radius."

Why?

Historically, the cubit is one of the many anthropological measurements. It's based on the length of the average man's forearm. The fraction 1/10,000,000 comes from the original metric system: the meter was originally defined as 1/10,000,000 of the Earth's quadrant length -- the distance along a line of longitude from the pole to the Equator, assuming Earth is a perfect sphere.

On top of that, no one knows the actual length of a sacred cubit, or indeed if there was a measurement called "the sacred cubit." The Hebrew "cubit" is properly called the amah or ell, a unit of length that seems to have been equal to the Egyptian cubit. On the other hand, the Egyptians had two different units called the "cubit," a regular cubit and the larger royal cubit, and no one can be sure which cubit the amah matches. Some clues suggest that the Hebrews originally used the royal cubit, then replaced it later with the regular cubit. Oh, and neither Egyptian cubit is 25 inches long; the regular cubit is about 17.5 inches and the royal cubit is about 20.6 inches.

Your argument is numerology.