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How Ancients Used String to Lay Out Hezekiah's Tunnel
By Robert Kerson
4/20/2009 rkerson@snet.net
Why was Hezekiah's Tunnel dug with such a long and sinuous path? I can demonstrate that the design was, in fact, very deliberately laid out in brilliant geometric design of precise dimensions. Then the diggers succeeded in laying out the tunnel exactly as designed. This paper will detail these facts [Please refer to the figures as I discuss the text. Fig. (10) is the actual diagram of Hezekiah’s Tunnel taken from Jerusalem- An Archaeological Biography, Hershel Shanks, Random House, 1995, p. 91. All other figures are relevant tracings taken off this page. All letters refer to locations added to the Shanks diagram]. Hezekiah's Tunnel was worked out by a mathematically minded genius laying three measuring cords (strings) on the surface of the ground over a number of key spots over the soon to be dug corresponding locations of the tunnel. Nothing like this outside of Jerusalem had ever been attempted before. They discovered key locations were 300 and 600 Cubits apart. They then decided to make the third and actual tunnel full string length double 600 Cubits (also 4 times 300 Cubits, or 1200 Cubits. These cord lengths and locations possessed special sacred mathematical and geometric properties. The length of the actual tunnel's long third cord was divided into two segments. A number of special locations could be found from this pattern. The designer seems to have made mathematical and geometrical patterns within the constraints of the design. The two string lengths were snaked along the ground connecting all locations. The finished string design was the pattern of the tunnel above ground, which had to be duplicated underground as the dug tunnel, probably using the acoustic sound technique described by Ayreh Shimron [Journal of Archeological Science, Tunnel Engineering in the Iron Age: Geomorphology of the Siloam Tunnel, Jerusalem, Amos Romkin, Ayreh Shimron, Vol. 33, Issue 2, Feb. 2006, PP. 227-237.]Each of the two string lengths were dug by two teams on diggers, each following their own segment. One team actually wrote a description on their astonishment that they succeeded! The placement of three niche like bays at three bends of the tunnel were all directly under three important string locations on the surface of the ground, as was the location of the inscription placed on the wall. (One niche (8) and the small connecting tunnel segment was laid out along the first line, another niche (9) marks a point on the second, and the third niche (7) the one mentioned in the inscription near the meeting point, was the niche ('zdh') common to both Major Lines 1 and 2. ) Now that we have the basic ideas, we can go into the details. (Fig.1)- The genesis of the pattern was found in the distance from the source of the Gahon Spring, a natural feature, labeled (c ) or (2), to a natural sinkhole (10). [The fact this hole was not dug for a well, helps my supposition this was a feature of the design. This distance was found to be 600 (Hezekiah Tunnel) Cubits. [Measuring distances of natural features also was used on the Temple Mount, and also I can show, (but beyond the scope of this paper) that the mind who conceived this design also worked on the Temple Mount located nearby. I can show that a similar hand worked on the inner temple sacred square and inner temple courts which must date from the same time as Hezekiah's Tunnel.] First they laid out a line - Major Line 1- From the point marking the northern start of the tunnel (4) about 11 Cubits south of a natural sinkhole room (d) part of Warren's Shift (5), to the previously mentioned natural sinkhole (10) again measures 600 Cubits (or exactly half the length of the completed tunnel). The exact midpoint of this line measuring 300 Cubits (exactly 1/4 the length of the completed tunnel), from (10) and (4) respectively became (8), an underground niche location [Remember the point (c) at Gahon Spring? The distance from (c) to (8) is also 300 Cubits. Thus, (8) is 300 Cubits from either end of the line at (10) and (4), and also from the spring at (c), all distances being exactly 1/4 the total length of the tunnel (1200 Cubits)]. A short 11 Cubit section of tunnel running along this line brings us to another bend in the tunnel point (7), another underground niche location. Here the distance from (7) to Warren's shaft room is 300 Cubits.
Fig. 1. Major line 1.
(Fig. 2)- The second line -Major Line 2- runs from (7) to the natural designated southern end of the tunnel (g). The ratio of the distance of Major Line 2, to that portion of Major Line 1 which is the exact halfway point in the short interval between (8) and (7) to (10)the point labeled (i), is the sacred number called the Golden Mean, (1.618033989...). Also, the 11 cubit interval from (8) to (7) along Major Line 1, if extended north from (4),will reach a point in the ancient Warren's Shaft complex, (5). Then the distance from this Shaft to (7), to be marked with a niche, is also 300 Cubits. (11 Cubits was a very important distance used in the construction of the Temple built to the north.)
Fig. 2. Major Line 2.
(Fig. 3)- There existed a point on the above ground Siloam Channel, which must have been utilized- the point labeled (h). (A wall or columbarium may also have been built here.) Starting from this point, they laid out the same length as Major Line 2, to the point where a line drawn westward from (4) intersected this location is labeled (F). The half way point is marked (J) on line (h) to (f).
Fig. 3.
(Fig.4)- The sum of the cord lengths from (J) to (f) and from (f) to (4) equals the length along Major Line 1, from (4) to a point labeled (b).
Fig. 4
Fig. (5)- The distance from (7) to (b) on Major Line 1 is the same distance from (g) to a point labeled (a) on Major Line 2.
Fig. 5.
(Fig. 6)- Point (9) has the following consideration: If Major Line 2 was divided starting at (g) by the distance from (g) to (a), it could measure out three times. The remainder distance divided in half marks out exactly the distance (9) to (7). Location (9) marks the third niche.
Fig. 6.
Now the entire 1200 Cubits string length could be laid out on the surface of the ground, which had to utilize two rules: 1. The string must pass over points (g), (a), (10), (h), (b), (8) and (7) on the southern part of the hill, and points (4), and (f) on the northern. 2. The string had to be subdivided into two parts: 675 Cubits on the southern end (see Fig. 7), and 525 Cubits on the northern (see Fig. 8). Thus, the cord would have snaked across the surface in an undulating fashion. (Fig. 7) At the southern end (g), the cord would have been laid over a portion of a natural cave, and would have curved off the natural tunnel at some location heading to point (a). This explains why and where the tunnel deviates from the natural cave. Point (10), a point on or very close to the Siloam Channel, explains why the tunnel passes under the natural sinkhole, obviously because the cord snakes over this hole. We have seen in Fig. (3) how points (h) and (f) were opposites related along a line, but they were also related in being opposite eastern and western bends of the tunnel respectively. Point (h) is the other Siloam Channel marker. As the cord approached the 675 Cubits end (6), they snaked the cord Parallel to the eastern end of Major line 2, for a short distance to reach (8). They had to put a bend in the cord along this line, and it had to be exactly at point (9) to allow the total cord to be exactly 675 Cubits. They had some play but not much for if they tried to change the curvature of the cord, they would violate the rules listed above. This point (9) was also to be marked by a 'niche' which I will explain in detail later. When they had finished laying down the various cords, the exact shape of the completed underground tunnel would have been seen in the shape and size of the cord laid directly above the soon to be excavated tunnel.
Fig. 7.
(Fig. 8) Starting at the northern end (4), the cord had to be snaked along the ground to also fully use its 525 Cubits length. A slight swing to (f) was needed because a straight line from (4) to (f) would make the core to long. Just below point (j), a small jug to the west was made. The westernmost end of this jog (e), was along the line from (9) to (f). A cistern was dug here or very near this point. A fourth very small niche may have been placed here, but the point is not as significant as the other three and thus may not be marked. At the southern end, the cord may have to be tweaked to get exactly 525 Cubits, so the cord (or finished tunnel) would have to zigzag just before the terminus of the cord at (6). Why were these lengths determined? 1. The lengths have a specific mathematical relationship: the southern segment is 100+ 500+ 3/4 of 100 (i.e. 75), and the northern segment is 500 + 1/4 of 100 (i.e. 25). If we add the two fractions we get another100. 2. All significant numbers are divisible by 75 (675, 525, 300, 600, 1200), the consequence of this is that the entire tunnel could be measured by using inside the tunnel a single measuring cord, 75 Cubits long (300 is 4X, 600 is 8X, 525 is 7X, 675 is 9X,1200 is 16X). 3. Most significantly-- If the 1200 Cubits cord were to be divided into two 675 and 525 sections, these sections would be 75 C from (k) the exact center of the 1200 Cubits cord (1200/2= 600). The number '75' is significant in all three of the above measures, but it is prominent in the additions of the southern segment, where the southern team placed the inscription. That point which marked the two intersections labeled (6), was to be the intended meeting point of the two tunneling teams. Then the meeting point would to be exactly 75 Cubits from the exact center of the tunnel (k), which falls within the southern section, and appears to be where the tunnel's ceiling is at its lowest height, and the tunnel is closest to the ground surface. Notice the point labeled (7) in the figures. This point is exactly 3 Cubits from the intended meeting point (6). This means the southern tunnelers would have to dig 675-3 Cubits or 672 Cubits, and the northern tunnelers would have to dig 525 +3 C or 528 C to reach point (7). If we take the ratio of these two numbers, and square the results we get a close approximation of the golden ratio [(672/528)(672/528) = 1.6180]. The tiny interval between (7) and (6) would allow the tunnel to be divided into exactly two parts of exactly 675 and 525 Cubits. Now it was time to dig the actual tunnel. The diggers had to follow the following two rules: 1. Two teams had to be utilized digging under their cords from their respective starting points from (g) the southern end, and from (4) the northern end. 2. They had to stop digging when they both reached the 675 and 525 Cubits point of the cord at the spot labeled (6)- the intended meeting point. They utilized sound by hammering next to the undulating cord on the surface, and could use two cords inside the tunnel to know exactly how far they were progressing. They would have known exactly how many Cubits of rock to excavate to reach the meeting point, whither it was 30 C or 3C or whatever. (If women could spin another thread to make the huge veil of the temple, they most assuredly could spin any length of corded material.) When the southern tunnel team reached the bend at (9) they must have put their first 'zdh' on the wall. They put another on the bend at (8) and their final 'zdh' on the wall at bend (7). This 'zdh' was exactly 3 Cubits from the end of their tunneling operation at (6). (A 'zdh' appears to have been the ancient Hebrew miner's technical term for a crude shallow hacked crack like mark made on a tunnel wall with an axe to mark a particular spot.) Two of them would, be enlarged into a fine niche like feature seen today. The final "zdh'was finished slightly different, because of its special mathematical and geometric properties, and is the site of the only 'zdh' described in the tunnel inscription. I need not repeat why these three locations were so marked, as you can read about these properties in the text above and see them in the various figures. Suffice it to say, if you were to stand in these niches, you would be standing directly under the original cords, and would be standing in the various mathematical and geometric relationships previously discussed. The smooth finish on these niches were necessary not because of appearances (although they do represent sacred geometric locations), but must have also been used in the fine tuning of distances within the tunnel. (The depths of flat walled niches add fingerbreadth's etc. to a measuring cord) These were to be exactly 3 Cubits from the 'zdh' or finished niche at (7), and the meeting point at (6). When each team, using measuring cords as they progressed though the tunnel, found that they were 3 Cubits from the other team, they actually heard the sound of the other team behind the remaining wall! They did not randomly reach this spot. If so, then everything is do to pure chance but with all the mathematical and geometrical evidence presented, this is hard to refute. One team must have arrived before the other, but when 3 Cubits apart, they could hear the sound and the southern team recorded their astonishment that they actually succeeded!!
Fig. 8.
Another relationship in Fig. 7 is that the distance (b) to (k) equals the distance (k) to (I), and also this same distance is half (b) to (7), (not shown). Figure 9 illustrates the 3 Cubits rock wall between the two teams in relationship to the 'zdh' on the wall. Notice a very subtle point: the 'zdh' is on the left hand side of all team members working the northern side of the tunnel, and this same 'zdh' is on the right hand side of all team members working the southern side. Why is this important? This is a viable interpretation of the meaning in the third line of the inscription. "While there was still three Cubits to be hewn, there was heard a man's voice calling to his fellow, there was a 'zdh' in the rock on the right and on the left.... The waters from the spring towards the reservoir for two hundred and one thousand Cubits." [Jerusalem Revealed- Archaeology in the Holy City, 1968-1975, Ed. Yigael Yadin, New Haven Yale University Press and the Israel Exploration Society, 1976 ] The inscription holds another proof, the tunnel was laid out using the techniques described. It was located the exact same distance from the southern end of tunnel (g), as the two niches (9) and (8) were located from each other. They reused the same distance and the same general orientation of the tunnel segment (9) to (8). You can see this in fig.7, where the inscription is labeled (11). This explains why the inscription was set in the wall near the exit, but deep within the dark interior of the tunnel. A third proof the tunnel was worked out in the manner described, is the fact the southern end follows a natural cave, but at one spot the tunnel curves off into solid bedrock. The point where this occurs is exactly where the tunnel curves off into solid bedrock. The point where this occurs is exactly where the tunnel should veer off the cave's natural course as is expected if the diggers were following the presumed 1200 Cubits surface string. A fourth proof is the fact the tunnel is fairly curved at either end, but only zigzags near the meeting point, which is expected if the cords were laid out from (g) and (4) and the distances tweaked at the meeting point end (6). Two niches (9) and (7) hold a relationship as the distance from (a) to (9) equals the distance from (10) to (7). A fifth proof is the fact the inscription was curved by and from the southern team's perspective. Notice the wording of the inscription lists 'right' before 'left'. In the figure below it is apparent that the southern team's perspective sees the 'zdh' first on their right side, and the northern team's perspective is mentioned secondarily.
Fig. 9.
Fig. 10. The Full pattern
Why would such a difficult destructive, and time consuming feat be undertaken, considering the needed haste to complete the project before an impending enemy invasion? (See Chronicles 32:30 and 2-4, also 2 Kings 20:20.) They may have had to level preexisting structures on the surface. This water was very sacred as it was here that kings were anointed, and its waters were used in a number of temple purification rituals. Just as the Great pyramid of Kufu in Egypt was built holding sacred numbers such as phi, so also the tunnel of Hezekiah.