Breathtaking discovery – Jews knew the slide rule with logarithmized scale (1. Kings 7: 23-26) yet during the reign of King Solomon

1. Kings 7: 23-26

23 And he (Hiram out of Tyre, a worker in brass who worked on behalf of king Solomon; R. B.) made a molten sea (a big, round vessel; R. B.), 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. 24 And under the brim of it round about there were knops compassing it, ten in a cubit, compassing the sea round about: the knops were cast in two rows, when it was cast. 25 It stood upon twelve oxen, three looking toward the north, and three looking toward the west, and three looking toward the south, and three looking toward the east: and the sea was set above upon them, and all their hinder parts were inward. 26 And it was an hand breadth thick, and the brim thereof was wrought like the brim of a cup, with flowers of lilies: it contained two thousand baths.

Interpretation

The above section from 1. Kings includes several mysteries or provides some puzzles. At first glance, one could conclude that the old Jews had not used the formula C = π * d(circumference is equal to π times diameter) for the calculation of the circumference of a circle but the formula C = 3 * d. Had the Jews back then really used the formula C = 3 * d instead of the formula C = π * d then they had been extreme philistines yet for the conditions at that time and had provided a reason for defamation to the enemies of God how brainless his servants would be.

In and through Jesus Christ, his glorious name be praised for ever and ever, I have solved this problem, and hence, the Jews of those days are cleared from the accusation of philistinism.

Concerning that, see the following:

God and the number π – solution for the puzzle in connection with the ratio between the circumference of the molten sea (1. Kings 7: 23-26) and its diameter

A further mystery is (or was) what the two rows of knops mean which were compassing the sea round about.

“24 And under the brim of it round about there were knops compassing it, ten in a cubit, compassing the sea round about: the knops were cast in two rows, when it was cast.”

Well, to put it briefly, the two rows of knops were equal to the two fixed logarithmized scales of a slide rule.

(what you have just read, is an outright sensation because it was published in English language first time in history today at February 19, 2018 – at February 12, 2018, I have published it in German  language the very first time – please note that King Solomon ruled in the 10th century BC; that means that meanwhile, believe it or not, about 3000 years have elapsed since then, and nobody has solved the puzzle; and now in the year 2018 AD, after such a long time, it finally happened; and I give the glory to God.)

What justifies my claim that the two rows of knops represented a slide rule?

Well, when you, dear reader, would read the above section of the Bible exactly, you would notice that the number 10 (ten) appears twice there. Once, it is the diameter which is valid in the interior of the sea (the vessel wall belongs to the interior of the sea; see note, below), and the other time it is the number of knops per cubit outside on the vessel (see verse 24, above).

Do you notice something?

1 (one) is the common logarithm of 10 (ten). The diameter of the sea (when someone measured it inside the sea) of ten (10) cubits was displayed on one (1) cubit (ca. 45 cm)including ten knops. Most probably, the knops had got the function of the tick marks of a measuring rod. However, the knops were not arranged like the tick marks on a normal measuring rod which one can buy in a hardware store, but the distances between the knops were logarithmic.

log10(10) = 1

(for log10(x), the abbreviation lg(x) can be used)

When we count 10 knops beginning with a certain start-knop on the sea, we reach the end of stretch of way 1 (one cubit, lg10) – this is according to verse 24, above. According to the principle of the slide rule I assign the number 10 to the stretch of way one (one cubit, lg 10). I assign the number 100 to the stretch of way 2 (two cubits, lg100). When one adds up the logarithms of the both factors of a product a = b * c, he gets the logarithm of the product: lga = lgb + lgc. On the slide rule, the multiplication of two numbers is depicted through the addition of their logarithms. The trick is that to the stretches of way which represent the logarithms of the various numbers, the numbers themselves are assigned and not the log-value – of course, one has to be aware that these are numbers to multiply and not numbers to add (only the logarithms of the numbers are added but not the numbers themselves).

Example:

Calculation of the product 100 * 10

That means to add the stretch of way 2 (two cubits, lg100) to the stretch of way 1 (one cubit, lg10) – gives as a result stretch of way 3 (three cubits). This must be equal to the value 1000 (lg1000 = 3). We had to assign 1000 to the stretch of way 3 then we could directly read off the value of the product.

Basic principle of the slide rule; watch video, below:

 

How you can start a YouTube-Video despite error message: “An error occured, please try again later”, you can find here.

The moveable part of the “slide rule” of the molten sea was simply the string which was possibly used to measure the diameter of the sea. It was also possible to calculate without a string by counting the knops.

Something interesting:

The two rows of knops were not only a slide rule but also a simple ruler where the logarithmic scale played no role. Certainly, pilgrims from all over the world came to Jerusalem in order to convince themselves that concerning the molten sea the formula C = π * d was not valid but the formula C = 3 * d (on the condition that the diameter was measured inside the sea) which was an exceptional miracle, something really extraordinary. When the diameter of the sea had been picked up with a string then this stretch of way could be compared with the rule of knops. The result was always the same: ten cubits (ten cubits was equal to the 91th knop including the start-knop; hence, with the stretch of way on the string which was 10 cubits one reached exactly the 91th knop). Here, the logarithmic scale played no role save the fact that one had to count 9 knops per cubit instead of 10. Certainly, sometimes a high officer of a neighbouring country of Israel came by with a cubit-measuring rod and checked the two rows of knops and found confirmed that always 9 knops gave exactly one cubit (maybe 45 cm); every 9th  knop meant the addition of one cubit (in the above section of the Bible, every 9th knop is counted double because the end-knop of one section – when the knops were counted – was also the beginning-knop of the next section so that one got 10 knops per cubit as a result). This calibration was important because in this way any imputation was avoided that the priests of the Temple would have manipulated the scales. Any fraud after calibration would have been extremely difficult because the knops were cast together with the whole sea and therefore fixed, indeed – nobody could easily move them (see verse 24, above).

When the sea had not been supernatural, the result of a measurement of the diameter (given 30 cubits circumference) had had to be about 9.5493 cubits (C/π = 30/3,1415…). However, it was really supernatural and by assistance of the knops all people on earth could convince themselves that a measurement of the diameter of the sea gave the exceptional value of 10 cubits (the real diameter of the sea was 9,5493 . . . cubits, but was determined only if somebody had measured the diameter from outside in the natural, not curved space of our world using a giant calliper which would have meant an enormous technical expense because the sea was giant). For the sake of simplicity, the diameter was always measured with a string stretched over the sea whereby it was important to stretch it over the center of sea to get correct results; here, the knop scales delivered additional help because by the scale the half circumference was easily to find (knop 136). When the string was stretched from knop 1 to knop 136 it ran exactly through the center of the sea and thus the “correct” (correct regarding the inner space of the sea) diameter was measured. This measurement always gave 10 cubits because the inner space of the sea was curved (this curvature of space was supernatural, of course).

In order to convince oneself from the ongoing miracle of the molten sea, a ridiculous small string of a length of a little more than 4,5 meters (10 cubits) was a sufficient tool; one could easily carry such a string with one. Certainly, yet at that time, even poor people could afford a simple string so that everybody could convince himself of the supernaturality of the sea.

When one had convinced oneself that the pickup of the diameter was indeed 10 cubits at one of the scales, he only had to continue counting  9 knops after knop 3 (stretch of way ca. 0.477 or lg3 cubits) and reached knop 12; the start-knop of the whole scale for counting was knop number 1 because when you have a multiplication-scale the first point lg1 (factor = 1; stretch = 0) corresponds to the point zero (summand = 0; stretch = 0) of an addition-scale. The stretch of way to knop 12 was lg10 + lg3 = lg 30; the value of the product was 30.

Interestingly, the lg(π) is pretty exactly 0.5 (0.4971 . . .); that means that lgπ has always halved one section of the scale pretty exactly. This measure was easily to find. The measure for lg3 was only ca. 0.477. The knop at the point with value 30 (stretch lg30) came thus ca. 0.9 cm (see hint below) before the point with the value 31,415 . . . (stretch ca. lg31.416) which was perfectly marked through its approximate center position. Briefly: Through the fact that the 12. knop came ca. 0.9 cm before the approximate center of the second scale-section it was to realize at the first glance that the sea was supernatural because if it had not been supernatural, it circumference had to be about 31.415 . . . (stretch lg 31.416) which pretty exactly corresponded to the center of the second scale-section.

Hint: 0.9 cm = (lg31.416 – lg30) * 45 cm (I assume 45 cm for one cubit).

Do you have headaches know, dear reader?

Just take your time, maybe some days, in order to understand the issue – you could end up in getting eternal salvation; this expenditure of time could be really worthwhile.

Note:

When the diameter of the sea was measured inside the sea (including the wall), the result was about 10 cubits because the measuring-mean was crooked in the space (that was a miracle and the spectacular thing of the sea); that means it was shortened by the factor 3/π so that the diameter of the sea appeared π/3 greater than it really was. When the diameter had been measured from outside, the result had been 9.5493 meters because as long as the measuring-mean stood outside the sea, it was not crooked and displayed the value which was valid in the natural space of our world. However, in order to measure the diameter from outside, a giant calliper had been needed because the sea was giant itself and had a diameter of ca. 4.3 meters (9.5493 times 0.45 meters; measured from outside!).

“Everything is clear now?”

 

The above section of the Bible you can find here: Holy Bible

 

Use of the slide rule

 

 

How you can start a YouTube-Video despite error message: “An error occured, please try again later”, you can find here.

 

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