Could the Tower of Babel Actually Stand
This excellent question on Worldbuilding Stack Exchange asks if the tower of Babel, as it is described could actually stand.
I guess there are several questions to consider when trying to answer this.
Could Ancient People Have Drawn Straight Lines Tens of Kilometers in Length?
The Nazca lines were up to 370 meters long, and could achieve surprisingly complex patterns. One of the hypotheses for how they did this was by drawing in a valley and having construction managers spotting from higher elevation.
Could a Multi-Kilometer Structure be Kept Level?
Egyptians (almost a contemporary) had sight levels consisting of a plumb line and a triangle on a table. Look here for an example.
Wooden sticks, marked at a common desired height, with string run between them was the technique used to level the pyramid. The sticks were initially sighted with the sight level, and reviewed periodically by construction site managers.
Between the two base lengths given (2.6 km and 52.5 km), the curvature of the Earth would be between 2 and 53 meters. This curvature would foil the plumb lines, as gravity is curving with the Earth. However, the alignment and design of the pyramid also indicates that the curvature of the Earth was not unknown, and near contemporaries had calculated the circumference, and thus radius, of the Earth accurately, so it would be possible for building site managers to pre-calculate the curvature and account for this 2 to 53 meter curvature that would happen at these very large dimensions.
Are There Physical Limitations to Such a Large Height and Width?
There would be some side force, due to the curvature at the very largest dimensions. To calculate angle, get the arctan of the drop (53 meters) and half the base (26 km ~ 26,000 m) = 0.11 degrees. To find the percentage of all force that is transmitted as a side force, use the sine of this angle.
At the largest dimension (52.5 km) you mentioned, this side force would be about 0.19% of the weight is being transmitted as a moment trying to crack the structure apart.
Tensile strength of mud bricks (which is the type of strength that applies here) 1.5 MPa for mud bricks and 15 MPa for fired clay bricks (same as it's compressive strength). The density of mud brick is 1520 kg/m-cubed; for fired clay brick 2000 kg/m-cubed.
Geometery (whether this tower tapers as it gets higher or is straight up) plays a very important part in total load. For a straight up tower, the total pressure on the bottom tier is the density of your brick multiplied by the structure's height (in meters). P = rho * g * height * 0.2% (the amount of load being transferred)
So, at what height would this set-up fail? 390 kilometers for fired clay brick; 52 kilometers for mud brick.
Also, since brick is not a solid piece, some of this pressure would be absorbed by the bricks shifting in the mortar. And the case mentioned was for a vertical tower - the load could be greatly reduced by tapering the structure as it rose to the top.
How About Maximum Height?
The crushing strength of modern bricks are between 3.5 to 50 MPa. Mud bricks are 1.5 MPa and fired clay bricks are about 15 MPa. The equation, for a straight tower is still that the pressure on the bottom tier P = rho * g * h
For mud brick, the highest altitude before mud bricks start crumbling is 100 meters; for fired clay bricks 750 meters; for modern bricks 2.5 kilometers. This does not include a factor of safety - normally you'd cut these values by 4x to 5x for safety. Again, you could taper the structure to reach greater heights.
For comparsion, the ziggurat of Ur stands at 45 meters and the great pyramid stands at 139 meters.
How High is High Enough?
Per here, altitude sickness begins to set in at 2,500 meters height. Also, per the same site, the highest altitude a human can reach without a compressed air supply is only 8,000 meters.
How Much Height Can We Squeeze Out of Tapering?
The advantage of such an impossibly large base is that you can do a LOT of tapering. With the largest base of 52 km, reaching altitude sickness @ 2.5 km an extremely gentle 5 degree slope (an 85 degree taper). To reach the highest possible altitude for humans @ 8km is a not-terrible 17 degree slope (73 degree taper).
At such a shallow angle, you're not really building a structure (I guess you still are), but merely piling up a mountain. If you could effectively keep the pressure distributed, only 9% to 30% of the total force is being communicated down to the bottom layer. That would allow a height of 1,000 meters for mud brick; 4,400 meters for fired brick at a 10 degree incline; and 8 km for modern brick. You would still want a factor of safety for the structure. Then again, maybe not, because this thing is so shallow.
Effects of Wind
Wind adds a small amount of pressure to the stack. The density of wind is 1.225 kg/cubic meter. A 60 mile per hour wind would add 440 Pascals, and this is without including the effects of the shallow slope.
At these very shallow slopes, the tower wouldn't fall down when it breaks. The failure mode would be more like erosion. Failure can be controlled the same way we control erosion with retention walls made of piled-up dirt, wood, or bronze.
So, I'm really surprised by this, but it's possible.