A well-known experiment demonstrates the preservation of the integrity of a certain structure in the absence of visible binding forces. Such an experiment was first described in 1842 but it still has not found a scientific explanation. However, an interest in it continues unabated that is reflected in Internet publications. Based on the solution of Maxwell's equations, this theoretical work shows that the experiment is explained by the conservation of electromagnetic energy inside the structure and the appearance of a standing electromagnetic wave. Based on this solution, it is shown that the structure can be made not only on the basis of ferromagnetics (known fact) but also in the form of a capacitor. It is also shown that the keeper may have a different shape. It is shown further that such designs can save not only energy but also information. This fact provides a basis for explaining such phenomena as the mirages of the past. These phenomena are astounding and await their rigorous scientific explanation. The article notes that mirages do not change their position on the ground. It is further shown that the stability of the position of the mirage can be explained by the fact that in the mirage area there are a standing electromagnetic wave, pulsating flow of electromagnetic energy, and pulsating electromagnetic mass. The center of mass does not change position. Therefore, the volume of the keeper can be considered as the volume of the pulsating mass with a constant center of gravity. This mass is held in place by gravity and does not interact with the material mass, i.e. cannot be shifted by air flow. This ensures a stable position of the keeper on the ground.